VDIBuch
Andreas Küchler
High Voltage Engineering Fundamentals · Technology · Applications
VDIBuch
Andreas Küchler
High Voltage Engineering Fundamentals – Technology – Applications
Andreas Küchler Schweinfurt, Germany
VDIBuch ISBN 9783642119927 DOI 10.1007/9783642119934
ISBN 9783642119934 (eBook)
Library of Congress Control Number: 2017941508 Springer Vieweg © SpringerVerlag GmbH Germany 1996, 2005, 2009, 2017, 2018 Original german edition published with title: Hochspannungstechnik This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acidfree paper This Springer Vieweg imprint is published by Springer Nature The registered company is SpringerVerlag GmbH Germany The registered company address is: Heidelberger Platz 3, 14197 Berlin, Germany
Preface The main task of high voltage engineering is to gain technological control of high electrical field strengths and voltages. Their effects can impressively be observed in nature (or in a high voltage laboratory) as “lightning and thunder phenomena” if the “insulation system consisting of air” is failing. Formerly, historical authorities such as Zeus, Jupiter or Wotan have been responsible for these natural forces and their risks. But now, the high voltage engineers guarantee for the safe and reliable function of all electrical insulation systems. Only in this way, all the other technical applications of electricity are made available. In consequence, high voltage technology is both a key technology for a wide spectrum of technical applications that are indispensable for the modern society and a crosssectional technology integrating different scientific disciplines. High voltage engineering is a fascinating, challenging, interdisciplinary and multifaceted field of activity that will always be a prerequisite and essential support for the technical progress. High voltages enable the generation, transmission and distribution of electrical energy at relatively low currents and ohmic losses. The minimization of power loss preserves resources and reduces emissions and it is therefore a prerequisite for secure, economical and ecofriendly electricity supply. Furthermore, high voltage and ultrahigh voltage AC and DC networks are prerequisites for the development of remote energy sources, for the largearea load balancing and for a transnational energy market. Additionally, high voltage technology has wideranging industrial applications, such as for example Xray devices, lasers, high efficiency light sources, lithotripters, shock wave generators, fragmentation devices, accelerators, transmitter tubes, copiers, electrostatic precipitator or coating and enameling devices. Problems of high voltage engineering must also be tackled in power electronics and for the electromobility, in the area of electromagnetic compatibility, in physical and technological research, or in the field of hightemperature superconductivity. For all applications it is common to choose high electrical field strengths on the one hand in order to ensure that the dimensions, weight, material usage, costs, losses and environmental pollution remain as low as possible. On the other hand, the electric field stress must always be lower than the dielectric strength of the insulating materials so that discharges and a destructive breakdown can definitely be excluded. Between these poles, the tasks of engineers are largely to implement economical and technically optimal system solutions. For that purpose, high voltage engineers should be primarily wide ranging and practice oriented and should have a theoretically sound overview. The concept of the book consists of a systematic, coherent and comprehensive presentation of fundamentals, technologies and applications. For this purpose, high voltage engineering is classified into six main topics: • • • • • •
Electrical stresses by fields and waves (Chapter 2) Dielectric strength of gases, liquids and solids (Chapter 3) Dielectric system characteristics of insulating materials (Chapter 4) Insulating materials and their technology (Chapter 5) Testing, measurement and diagnosis (Chapter 6) Typical insulation systems for different types of stresses (Chapter 7).
VI
Preface
Already the basic Chapters 2, 3 and 4 include practical examples, applications, notes and exercises. Also the description of technologies and applications in the Chapters 5, 6 and 7 is always related to the fundamentals. Special emphasis is laid on the presentation of scientific and practical contexts as well as on clarity in words and illustrations. A comprehensive keyword index and an extensive bibliography shall facilitate access to special issues and to further sources for the reader. The book is therefore suitable both for the initial training of high voltage engineering in classroom studies or private studies and for the deeper guidance to specific areas and to specialist technical literature. It is intended to be useful as a workbook in academia and in the professional work. This edition of “High Voltage Engineering” is equivalent to the fourth edition of the German reference book “Hochspannungstechnik”, and for the first time it is also published in English language. For more than 20 years, the previous German editions are widely used by undergraduate and postgraduate students, engineers, scientists, universities, manufacturers, service companies and utilities. In 1996 the first edition was initially developed from the author’s lectures at the University of Applied Sciences WürzburgSchweinfurt. The new editions in 2004, 2009 and 2017 were always stimulated by strong interests of the readership. In each case, comprehensive revisions, adaptions to the state of the art, stronger involvements of application subjects and inclusions of new and innovative topics were made. Therefore, the English edition includes numerous improvements in details and many extensions and new features being related to the great actual challenges in high voltage engineering. For example, ultrahigh voltage AC and DC transmission with voltages of more than 1,000 kV, DC cable runs with more than 500 kV, switchgear with alternative insulating gases and transformers with alternative insulating liquids are built. That’s why the sections about insulation systems for high voltagc DC transmission in Chapter 7 were fundamentally revised and much expanded, regarding stresses, dielectric strength and design for DC voltages and with regard to transformers, bushings, cables and fittings for HVDC. This is supplemented in Chapter 3 and 6 by sections about the generation and evaluation of partial discharges at DC voltage. Additional current topics are the introduction of socalled “alternative” climatefriendly insulating gases instead of SF6 and the use of socalled “alternative” ecofriendly insulating liquids instead of minearal oil. Revisions have also been made in the sections about the conduction behavior and the dielectric behavior of solid and liquid dielectrics (Chapter 4), about the oscillating behavior during impulse voltage tests (Chapter 6) and about transformer testing (Chapter 7). On the suggestion of renowned expert colleagues, it is finally proposed in Chapter 3 that the term “electronegativity”, which is commonly used in high voltage engineering, should be replaced by the term “electron affinity”. At various places in the text, references to new technical regulations and standards are also made. This is, however, possible only in extracts or examples, according to the current but impermanent status of standardization. The reader must finally consult the appropriate valid and updated regulations and standards directly. The limited space of the book naturally necessitates also intense abridgement of many contents and a very subjective compromise between completeness and depth. I therefore request all experts to be lenient towards the author if they find their special subject to be inadequately dealt with. I hand over this book to the reader, with a request for comments and suggestions which are always welcome. Please contact [emailprotected]. Now, my personal recommendation would be “to read with a pen”, that is, to understand the examples, exercises and field plots through own calculations and to delve into interesting topics through
Preface
VII
written side notes and extracts. Useful supplements for this could be a mathematical formulary and textbooks on experimental physics, basic electromagnetic theory or material sciences. Many expert colleagues and friends have supported me during the creation of the first three German editions. As I could already express my gratitude for their help in these preceding editions, I now want to thank all direct and indirect supporters who were the prerequisite for the fourth German edition and for the first Englisch edition of “High Voltage Engineering” in the present form. With many colleagues from universities I could conduct an intensive scientific discourse, for which I would like to give my thanks to the professors Dr. R. Bärsch, Dr. F. Berger, Dr. G. Chen, Dr. Ch. Frank, Dr. S. Grossmann, Dr. S. Gubanski, Dr. V. Hinrichsen, Dr. F. Jenau, Dr. M. Koch, Dr. J. Kindersberger, Dr. M. Liebschner, Dr. H. Okubo, Dr. R. Patsch, Dr. R. Plath, Dr. K. Rethmeier, Dr. M. Rossner, Dr. S. Tenbohlen, Dr. W. S. Zaengl (†) and Dr. M.H. Zink. Furthermore, my sincere thanks go to Dr. I. AtanasovaHöhlein, Dr. K. Backhaus, S. Bhumiwat, M. Chmielewski, Dr. W. Exner, S. Eyring, Dr. J. Fabian, Dr. R. Färber, R. Fritsche, Dr. J. Fuhr, Dr. W. Hauschild, A. Hopf, M. Hörmann, Dr. Ch. Hurm, Dr. S. Jaufer, Dr. U. Kaltenborn, Ch. Krause, Dr. M. Krüger, N. Kurda, A. Langens, Dr. C. Leu, L. Lundgaard, M. Pegelau, Dr. R. Pietsch, Dr. U. Piovan, B. Preidecker, Dr. U. Prucker, K. Rädlinger, M. Rösner, J. Roßmann, Dr. J. Schiessling, B. Schlittler, Ph. Schmitt, T. Schnitzer, J. Seiler, B. Spatta, Dr. J. Speck, Th. Steiner, J. Titze and E. Zerr for many expert discussions and suggestions. I am also grateful to the companies that contributed to the preparation of the editions by photographic material and professional exchange. The University of Applied Sciences WürzburgSchweinfurt (FHWS) and the Faculty of Electrical Engineering provided a sound scientific basis for this publication by the implementation of high voltage engineering in teaching and research. And of course, my students have been a great help owing to their questions, contributions and theses. Important scientific and professional support was also given by our current and former staff members M. Fell, S. Harrer, B. Hochbrückner, F. Hüllmandel, F. Klauer, H.P. Öftering, A. Reumann, Dr. F. Schober, S. Sturm, F. Swobodnik and I. Wirth. I am also very grateful for that. Furthermore, Omicron Electronics GmbH and B. Walker deserve very high recognition and reward for the great assistance in translating from German to English. Finally, special thanks go to Ms. S. Bromby, to Mr. Th. Lehnert and to SpringerVerlag GmbH for editing the book, for great patience and understanding and for very good cooperation. Last but not least, these thanks also include my family. My sons Florian and Sebastian could provide valuable tips from the students’ perspective. Also my parents Ursula and Johannes contributed significantly to the development of the work because of their continuous encouragement and permanent support. Nevertheless, the realization of the edition was primarily achieved due to the great understanding, the strong backing and the enormous patience of my wife Christiane. Schweinfurt and Hammelburg, March 2017 Andreas Küchler
Contents
Preface …………………………………………………………………………………… V Contents ……………………………………………………………………………….. Symbols and Abbreviations …………………………………………………………
IX XIX
1 INTRODUCTION ...............................................................................................................1 1.1 The Function of High Voltage Technology ............................................................................ 1 1.2 Applications of High Voltage Technology.............................................................................. 1 1.3 Perspectives of High Voltage Engineering ............................................................................. 2 1.4 Overview ................................................................................................................................... 3
2 ELECTRIC STRESSES .....................................................................................................5 2.1 Basic Field Theory.................................................................................................................... 5 2.1.1 Field Quantities ................................................................................................................. 6 2.1.2 Equipotential Lines, Potential, Voltage and Capacitance ................................................. 7 2.1.3 Maxwell’s Equations......................................................................................................... 9 2.1.3.1 Maxwell’s Main Field Equations 2.1.3.2 Maxwell’s Continuity Equations 2.1.3.3 Material Equations
10 10 12
2.1.4 Classification of Fields.................................................................................................... 13 2.1.4.1 Static and Stationary Fields 2.1.4.2 Quasistationary (Inductive) Fields in Conductors 2.1.4.3 Quasistationary/ Quasistatic (Capacitive) Displacement Fields in Dielectrics 2.1.4.4 Nonstationary, Timevarying Fields (Electromagnetic Waves)
14 15 17 20
2.2 Electrical Stresses in High Voltage Engineering ................................................................. 21 2.2.1 DC Voltage Stress ........................................................................................................... 22 2.2.2 AC Voltage Stress ........................................................................................................... 23 2.2.3 Switching Impulse Voltage Stress (“Internal Overvoltages”) ........................................ 25 2.2.4 Lightning Impulse Voltage Stress (“External Overvoltages”) ........................................ 25 2.2.5 Fastrising Impulse Stresses (“Fast Transients”) ............................................................ 26 2.2.6 Mixedfield Stresses ........................................................................................................ 28 2.3 Conduction and Displacement Fields in Homogeneous Dielectrics ................................... 29 2.3.1 Analytic Evaluation of the Continuity Equation (Gauss’s Law) ................................... 30 2.3.1.1 General Calculation Method
30
X
Contents 2.3.1.2 Spherically Symmetric Fields 2.3.1.3 Cylindrically Symmetric Fields 2.3.1.4 Uniform (Homogeneous) Fields 2.3.1.5 Field Distortions by Space Charges
31 33 37 38
2.3.2 Analytic Solution of Poisson’s Equation ........................................................................ 39 2.3.3 Graphical Field Mapping (for Plane Fields) .................................................................. 40 2.3.4 Conformal Mapping (for Plane Fields) ........................................................................... 44 2.3.5 Charge Simulation Method ............................................................................................. 48 2.3.5.1 Conducting Spheres (Point Charges) 2.3.5.2 Field between Two Conducting Spheres (Spheretosphere Gap) 2.3.5.3 Parallel Line Charges 2.3.5.4 Fields in the Vicinity of Cylindrical Conductors
48 54 58 60
2.3.6 Similarity Relations, Field Efficiency Factor (Schwaiger’s Utilization Factor) ............. 71 2.3.7 Measurement of Stationary Conduction Fields .............................................................. 74 2.3.7.1 Analogy between Dielectric Displacement Field and Static Conduction Field 2.3.7.2 Measurements on Semiconductive Paper (“Resistive Paper”) 2.3.7.3 Measurements in Semiconductive Liquids (“Electrolytic Tank”)
75 75 76
2.4 Conduction and Displacement Fields in Inhomogeneous Dielectrics ................................ 76 2.4.1 Conductivity and Polarization ......................................................................................... 77 2.4.1.1 Conductivity 2.4.1.2 Polarization
77 78
2.4.2 Multidielectric Arrangements ........................................................................................ 81 2.4.2.1 Boundary Conditions at Interfaces 2.4.2.2 Interface Orthogonal (Normal) to the Field („Field Displacement“) 2.4.2.3 Interface Parallel to the Field (Tangential Interface) 2.4.2.4 Interface Inclined (at an Angle) to the Field (“Refraction Law”)
81 82 84 85
2.4.3 Analytical Calculation of Multilayer Dielectric Arrangements ...................................... 86 2.4.3.1 Plane, Cylindrically Symmetric and Spherically Symmetric Multilayer Arrangements 2.4.3.2 Gaps and Cracks 2.4.3.3 Interstices (TriplePoints) 2.4.3.4 Dielectric Cavities and Spheres 2.4.3.5 Electric Forces at Interfaces
87 92 93 97 98
2.4.4 Direct Voltage and Transients......................................................................................... 99 2.4.4.1 Analogies to the Dielectric Displacement Field 2.4.4.2 Typical DC fields 2.4.4.3 Transient Processes
99 102 105
2.4.5 Field Grading at Interfaces ............................................................................................ 110 2.5 Numerical Field Calculation ............................................................................................... 113 2.5.1 Overview ....................................................................................................................... 113 2.5.2 Charge Simulation Method ........................................................................................... 115 2.5.3 Finite Difference Method .............................................................................................. 116 2.5.4 Finite Element Method.................................................................................................. 119 2.6 Rapidly Changing Fields and Traveling Waves ................................................................ 124 2.6.1 Guided TEM Wave ....................................................................................................... 125 2.6.2 Reflection Processes ..................................................................................................... 129 2.6.2.1 Basics 2.6.2.2 Equivalent transmissionline circuit 2.6.2.3 Multiple Reflections
129 131 132
2.6.3 Examples ....................................................................................................................... 135 2.6.3.1 GasInsulated Switchgear (“Fast Transients”) 2.6.3.2 Protection Zone of a Lightning Arrester 2.6.3.3 TravelingWave Generators (TransmissionLine Generators)
135 137 138
Contents
XI
3 ELECTRIC STRENGTH ...............................................................................................141 3.1 Introduction to Statistics ..................................................................................................... 141 3.1.1 Statistical Descriptions of Discharge Processes............................................................ 141 3.1.1.1 Random Variables 3.1.1.2 Cumulative Distribution Functions 3.1.1.3 Parameter Estimation 3.1.1.4 Example: Series of Measurements
141 142 144 145
3.1.2 Description of Discharge Processes by Distribution Functions .................................... 147 3.1.2.1 Comparison of Empirical and Theoretical Distribution Functions 3.1.2.2 Gaussian Normal Distribution 3.1.2.3 Weibull Distribution 3.1.2.4 Parameter Estimation
147 148 150 153
3.1.3 Statistical Size Effects ................................................................................................... 153 3.1.4 Correlation and Regression, Lifetimestress Relationship ............................................ 157 3.2 Gas Discharges...................................................................................................................... 159 3.2.1 Gas Discharge Characteristics ...................................................................................... 159 3.2.1.1 Nonselfsustained and Selfsustaining Discharge 3.2.1.2 Gas Discharge Characteristic, Operating Points 3.2.1.3 Manifestations of Gas Discharges
159 160 162
3.2.2 Spacechargefree Discharge in a Uniform Field (Townsend and Paschen) ............... 164 3.2.2.1 Townsend’s Ignition Condition (Avalanche generations, Townsend Mechanism) 3.2.2.2 Ionization and Attachment 3.2.2.3 Electron Affinity and Electronegativity 3.2.2.4 Paschen’s Law
165 169 173 174
3.2.3 Spacechargedominated Discharge, Streamer Discharge ............................................ 180 3.2.4 Impulse and Highfrequency Breakdown ..................................................................... 183 3.2.4.1 Statistical and Formative Time Lag (Discharge Delay) 3.2.4.2 Voltagetime Characteristics 3.2.4.3 Highfrequency Breakdown
183 186 187
3.2.5 Discharges in Nonuniform Fields ................................................................................ 188 3.2.5.1 Predischarges and Breakdown 3.2.5.2 Polarity Effect 3.2.5.3 Corona Inception, PreDischarges 3.2.5.4 Breakdown Voltages 3.2.5.5 Impact of Different Parameters
188 189 192 194 196
3.2.6 Surface Discharges ........................................................................................................ 199 3.2.6.1 Arrangements with Surfaces 3.2.6.2 Ignition of Surface Discharges 3.2.6.3 Development of Surface Discharges 3.2.6.4 Pollution Flashover
199 200 202 203
3.2.7 Spark, Arc and Lightning Discharges ........................................................................... 206 3.2.7.1 Spark discharge 3.2.7.2 Arc Discharge 3.2.7.3 Lightning Discharges 3.2.7.4 “Ball Lightning”
206 208 211 215
3.3 Discharges in Liquid and Solid Dielectrics ........................................................................ 215 3.4 Discharges in Liquids ........................................................................................................... 217 3.4.1 Discharge Mechanisms in Mineral Oil ......................................................................... 217 3.4.1.1 Stages of Oil Breakdown 3.4.1.2 The Liquid before Ignition 3.4.1.3 Initial Processes 3.4.1.4 Discharge Propagation
218 220 222 226
3.4.2 Important Parameters Influencing Breakdown in Mineral Oil ..................................... 231
XII
Contents 3.4.2.1 Water and Pollution 3.4.2.2 Temperature Dependence 3.4.2.3 Pressure Dependence 3.4.2.4 Barriers and Insulated Electrodes, Dependence on Gap Width 3.4.2.5 Time Dependences, Time Factors
231 233 234 234 236
3.4.3 Partial Discharges (PD) in Mineral Oil ......................................................................... 238 3.4.4 Other Insulating Liquids ............................................................................................... 239 3.5 Discharges in Solids.............................................................................................................. 240 3.5.1 Electrical Breakdown .................................................................................................... 241 3.5.2 Thermal Breakdown ...................................................................................................... 242 3.5.3 Ageing, Erosion Breakdown and Lifetime ................................................................... 246 3.6 Partial Discharges (PD) ....................................................................................................... 249 3.6.1 Causes of Partial Discharges ......................................................................................... 249 3.6.1.1 Corona Discharges 3.6.1.2 Internal Partial Discharges at AC Voltage 3.6.1.3 Internal Partial Discharges at DC Voltage 3.6.1.4 Surface Discharges
250 251 254 255
3.6.2 Sources of Partial Discharges ....................................................................................... 256 3.6.2.1 Sources of Partial Discharges in Gases 3.6.2.2 Sources of Partial Discharges in Liquids 3.6.2.3 Sources of Partial Discharges in Solids
256 256 257
3.6.3 Classical Interpretation of Partial Discharges ............................................................... 258 3.6.3.1 Classical Interpretation of Partial Discharges for AC Voltage 3.6.3.2 Interpretation of Partial Discharges for DC Voltage
258 262
3.7 Vacuum Breakdown............................................................................................................. 263 3.7.1 Physical Process ............................................................................................................ 263 3.7.2 Technical Strengths ....................................................................................................... 265 3.7.3 Applications .................................................................................................................. 266
4 DIELECTRIC SYSTEM CHARACTERISTICS ........................................................269 4.1 Polarization in the Time and Frequency Domain ............................................................. 269 4.1.1 Description in the Time Domain ................................................................................... 269 4.1.2 Description in the Frequency Domain .......................................................................... 272 4.2 Dielectric Parameters ........................................................................................................... 272 4.2.1 Permittivity Hr ................................................................................................................ 273 4.2.1.1 Polarization Mechanisms 4.2.1.2 Frequency Dependence (Dispersion) 4.2.1.3 Temperature Dependence 4.2.1.4 Field Strength Dependence 4.2.1.5 Mixed Dielectrics
273 274 275 276 276
4.2.2.1 Conductivity in Gases 4.2.2.2 Conductivity in Liquids 4.2.2.3 Conductivitiy in Solids 4.2.2.4 Influence of Field Strength and Temperature
277 277 279 281
4.2.2 ConductivityN................................................................................................................ 276
4.2.3 Loss or Dissipation Factor tan G ................................................................................... 282 4.2.4 Complex Permittivity .................................................................................................... 284 4.3 Description of Dielectrics ..................................................................................................... 287 4.3.1 Classic Parallel and Series Equivalent Circuits ............................................................ 287 4.3.2 Description of Dielectric Material Properties ............................................................... 289
Contents
XIII 4.3.2.1 Linear Polarization Equivalent Circuit for Solid Materials 4.3.2.2 Dependence on Temperature 4.3.2.3 Drift, Diffusion and Injection in Liquids
290 291 293
4.3.3 Description of Geometrical Properties .......................................................................... 296 4.3.3.1 Maxwell’s Twolayer Model 4.3.3.2 Simple Layered Arrangements 4.3.3.3 Complex Geometries
296 298 298
5 INSULATING MATERIALS ........................................................................................301 5.1 Gases ...................................................................................................................................... 301 5.1.1 Air ................................................................................................................................. 302 5.1.2 Sulfur Hexafluoride (SF6) ............................................................................................. 302 5.1.3 Alternative Insulating Gases ......................................................................................... 304 5.2 Inorganic Solid Insulating Materials .................................................................................. 306 5.2.1 Porcelain and Ceramics ................................................................................................. 306 5.2.2 Glass .............................................................................................................................. 308 5.2.3 Mica Products ............................................................................................................... 309 5.3 Highly Polymerized Plastics ................................................................................................ 309 5.3.1 Reactions of Formation and Crosslinking ................................................................... 310 5.3.2 Thermoplastic Insulating Materials .............................................................................. 311 5.3.2.1 Polyethylene (PE and XLPE) 5.3.2.2 Polyvinyl Chloride (PVC) 5.3.2.3 Polypropylene (PP) 5.3.2.4 Hightemperature Resistant Thermoplastics 5.3.2.5 Polyamides (PA) and Aramides 5.3.2.6 Polytetrafluoroethylene (PTFE) 5.3.2.7 Polymethylmethacrylate (PMMA), Acrylic Glass
311 313 314 315 315 316 316
5.3.3 Thermosetting Materials and Elastomers ...................................................................... 317 5.3.3.1 Epoxy Resins (EP) 5.3.3.2 Polyurethanes (PU) 5.3.3.3 Phenolic Resin and Resinbonded Paper (RBP) 5.3.3.4 Elastomers and Shrinkable Sleevings
317 322 323 324
5.3.4 Silicones ........................................................................................................................ 325 5.3.4.1 Properties of Silicones 5.3.4.2 Hydrophobic Insulators 5.3.4.3 Other Applications of Silicones
325 326 329
5.3.5 Nanodielectrics ............................................................................................................ 330 5.3.5.1 Introduction 5.3.5.2 Principle of Nanostructuring 5.3.5.3 Dielectric Properties 5.3.5.4 Applications
330 331 331 332
5.4 Insulating Liquids ................................................................................................................ 333 5.4.1 Technology of Insulating Liquids ................................................................................. 333 5.4.2 Mineral Oil .................................................................................................................... 334 5.4.3 Synthetic Insulating Liquids ......................................................................................... 337 5.4.3.1 Polychlorinated Biphenyls (PCB) 5.4.3.2 Silicone Liquids ("Silicone Oils") 5.4.3.3 Other Organic Liquids
337 337 338
5.4.4 Vegetable Oils and “Natural Ester Liquids” ................................................................. 339 5.4.4.1 Vegetable Oils 5.4.4.2 Natural Ester Liquids
340 340
5.4.5 Water ............................................................................................................................. 341
XIV
Contents
5.4.6 Liquefied Gases............................................................................................................. 342 5.5 Fibrous Materials ................................................................................................................. 345 5.5.1 Paper and Pressboard .................................................................................................... 345 5.5.1.1 Electric Strength 5.5.1.2 Dielectric Properties, Moisture and Ageing 5.5.1.3 Condition Assessment 5.5.1.4 Manufacture and Processing
345 346 349 349
5.5.2 Synthetic Fibrous Materials .......................................................................................... 354
6 TESTING, MEASURING AND DIAGNOSIS .............................................................355 6.1 Quality Assurance ................................................................................................................ 355 6.1.1 Quality Assurance Systems ........................................................................................... 355 6.1.2 Certification and Accreditation ..................................................................................... 356 6.1.3 Calibration ..................................................................................................................... 356 6.1.4 Insulation Coordination................................................................................................. 358 6.1.4.1 Principle of Insulation Coordination 6.1.4.2 High Voltage Tests 6.1.4.3 Surge Arresters
358 362 363
6.2 Generation of High Voltages ............................................................................................... 365 6.2.1 Generation of AC Voltages ........................................................................................... 367 6.2.1.1 Principles of Generation 6.2.1.2 Test Transformers 6.2.1.3 Cascade Arrangement 6.2.1.4 Capacitive Voltage Rise in Transformers 6.2.1.5 Series Resonance Test Systems 6.2.1.6 Requirements for Test Voltages in Laboratories and Onsite
367 368 370 371 373 376
6.2.2 Generation of DC Voltages ........................................................................................... 379 6.2.2.1 Highvoltage Rectifier 6.2.2.2 Rectifier Circuits 6.2.2.3 Switchedmode Power Supplies 6.2.2.4 Electrostatic Generators
380 380 383 384
6.2.3 Generation of Impulse Voltages ................................................................................... 386 6.2.3.1 Impulse Voltage Waveforms 6.2.3.2 Singlestage Impulse Voltage Generators 6.2.3.3 Multistage Impulse Voltage Generators 6.2.3.4 Overshoot and Back Swing 6.2.3.5 Impulsecurrent Generators 6.2.3.6 Combined Test Circuits 6.2.3.7 Special Impulse Generators
386 389 391 394 396 397 398
6.3 High Voltage Measurement Techniques ............................................................................ 401 6.3.1 Measuring Spark Gaps .................................................................................................. 401 6.3.1.1 Spheretosphere Spark Gap 6.3.1.2 Rodtorod Spark Gap
401 404
6.3.2 Electrostatic Voltmeter ................................................................................................. 405 6.3.3 Field Sensors ................................................................................................................. 406 6.3.3.1 Electrically Short Sensors 6.3.3.2 Electrically Long Sensors 6.3.3.3 Potentialfree Probes 6.3.3.4 Generatormode Sensors (“Field Mills”) 6.3.3.5 Electrooptical and Magnetooptical Field Sensors
406 407 407 407 408
6.3.4 Voltage Dividers ........................................................................................................... 412 6.3.4.1 Response Characteristic 6.3.4.2 Divider Designs
412 413
Contents
XV 6.3.4.3 Stray Capacitances 6.3.4.4 Lowvoltage Arms 6.3.4.5 Coupling Circuits
416 417 418
6.3.5 Instrument Transformers ............................................................................................... 419 6.3.5.1 Voltage Transformers 6.3.5.2 Current Transformers
419 420
6.3.6 Measurements of R.m.s. Value, Peak Value and Harmonics ....................................... 422 6.3.7 Current Measurement .................................................................................................... 424 6.3.8 Electromagnetic Compatibility (EMC) ......................................................................... 425 6.4 Diagnosis and Monitoring ................................................................................................... 426 6.4.1 Dielectric Measurements............................................................................................... 426 6.4.1.1 Dissipation Factor and Capacitance 6.4.1.2 Insulation Resistance, Conductivity 6.4.1.3 Dielectric System Response
426 429 431
6.4.2 Partial Discharge (PD) Measurement and Diagnosis .................................................... 433 6.4.2.1 Partial Discharge Measurement Circuit 6.4.2.2 Apparent Charge, Partial Discharge Energy 6.4.2.3 Sensitivity and Calibration 6.4.2.4 Signal Processing and Signal Evaluation 6.4.2.5 Interferencefree measurement 6.4.2.6 Partial Discharge Diagnosis 6.4.2.7 Synchronous Multichannel Partial Discharge Measurement 6.4.2.8 UHF Partial discharge Diagnosis 6.4.2.9 Nonelectrical Methods of Partial Discharge Diagnosis
434 435 437 438 441 443 447 452 453
6.4.3 Chemical Analyses ........................................................................................................ 454 6.4.3.1 Determination of Water Content 6.4.3.2 Gasinoil Analysis 6.4.3.3 Highpressure Liquid Chromatography (HPLC) 6.4.3.4 Determination of Degree of Polymerization of Cellulose
454 455 460 461
6.4.4 Insulating Material Tests ............................................................................................... 461 6.4.4.1 Dielectric Measurements 6.4.4.2 Breakdown measurements 6.4.4.3 Creepage Currents and Tracking Resistance 6.4.4.4 Arc Resistance 6.4.4.5 Additional Tests for Insulating Materials
461 461 464 465 466
6.4.5 Optical and Acoustic Diagnosis Methods ..................................................................... 466 6.4.5.1 Optical Waveguides 6.4.5.2 Visual Diagnostics 6.4.5.3 Acoustic Diagnostics
466 467 467
6.4.6 Determination of System Properties ............................................................................. 468 6.4.6.1 Impulsecurrent Waveshapes 6.4.6.2 Transfer Functions, Frequency Response Analysis FRA 6.4.6.3 Frequency Response Measurements 6.4.6.4 Reflectometry
468 468 470 470
6.4.7 Dielectric Diagnosis ...................................................................................................... 470 6.4.7.1 Time and Frequency Domain 6.4.7.2 Selective Measurements 6.4.7.3 Dischargevoltage Measurement 6.4.7.4 IRC Analysis 6.4.7.5 Recovery Voltage Analysis 6.4.7.6 PDC Analysis 6.4.7.7 Frequency Domain Analysis 6.4.7.8 Dielectric Diagnosis in Time Domain and Frequency Domain
471 472 474 474 475 477 485 486
6.4.8 Online monitoring ......................................................................................................... 487 6.4.8.1 Monitoring of Transformers 6.4.8.2 Monitoring of Bushings
488 490
XVI
Contents 6.4.8.3 Monitoring of Rotating Machines 6.4.8.4 Monitoring of XLPE Cables and Fittings 6.4.8.5 Monitoring Other Equipment
492 493 494
7 APPLICATIONS .............................................................................................................497 7.1 Typical Insulation Systems for AC Voltages ..................................................................... 497 7.1.1 Cables and Accessories ................................................................................................. 497 7.1.1.1 Paperinsulated Cables 7.1.1.2 Plasticinsulated Cables 7.1.1.3 Gasinsulated Lines (GIL) 7.1.1.4 Cable Accessories (Cable Fittings) 7.1.1.5 Testing Cable Systems
497 499 501 501 505
7.1.2 Bushings ........................................................................................................................ 507 7.1.2.1 Field Grading or Potential Grading 7.1.2.2 Calculation of Capacitive Grading 7.1.2.3 Designs
508 508 510
7.1.3 Transformers ................................................................................................................. 512 7.1.3.1 Oilfilled Transformers and Drytype Transformers, Reactors 7.1.3.2 Windings and Onload Tap Changer 7.1.3.3 Design of Oilboard Insulation 7.1.3.4 Manufacture 7.1.3.5 Transformer Testing 7.1.3.6 Operation, Diagnosis and Maintenance
513 514 517 524 525 533
7.1.4 Capacitors...................................................................................................................... 537 7.1.4.1 Structure of the Dielectric 7.1.4.2 Drying and Impregnation 7.1.4.3 Capacitor Designs 7.1.4.4 Measuring Capacitors
537 538 539 539
7.1.5 Circuitbreakers ............................................................................................................. 540 7.1.5.1 Development of Switching Devices 7.1.5.2 SF6 Compressedgas CircuitBreaker 7.1.5.3 Vacuum Circuitbreaker
540 541 544
7.1.6 Electrical Machines ....................................................................................................... 546 7.1.6.1 Lowvoltage Motors 7.1.6.2 Machines for High Powers 7.1.6.3 Cable Generators, Cable Machines
547 548 551
7.2 Typical Insulation Systems for DC Voltages ..................................................................... 552 7.2.1 Electrical Stess, Strength and Design for DC Voltage.................................................. 552 7.2.1.1 Dielectric Stresses at DC Voltage 7.2.1.2 Dielectric Strength at DC Voltage 7.2.1.3 Dielectric Properties of Materials 7.2.1.4 Design of Insulation Systems for DC Voltage
553 553 554 559
7.2.2 Capacitors for Direct Voltage (DC Capacitors) ............................................................ 560 7.2.3 HVDC Transformers ..................................................................................................... 561 7.2.3.1 Dielectric Stresses 7.2.3.2 AC and Steadystate DC Voltage Stresses 7.2.3.3 Stresses during Voltage Variations 7.2.3.4 Transition Processes (Transients)
561 564 567 568
7.2.4 HVDC Bushings ........................................................................................................... 571 7.2.4.1 Internal Insulation 7.2.4.2 External Insulation
571 572
7.2.5 HVDC Cables and Accessories..................................................................................... 574 7.2.5.1 DC Cables 7.2.5.2 Paperinsulated HVDC Cables 7.2.5.3 Plasticinsulated HVDC Cables
574 576 576
Contents
XVII 7.2.5.4 Emerging HVDC Cable Technologies 7.2.5.5 HVDC Cable Accessories 7.2.5.6 HVDC Cable Testing
578 578 580
7.2.6 Highfrequency Chopped DC Voltages ........................................................................ 580 7.2.6.1 Applications 7.2.6.2 Insulation Problems 7.2.6.3 Test Techniques
580 581 581
7.3 Typical Insulation Systems for Impulse Voltages ............................................................. 581 7.3.1 Electrical Stress and Strength ....................................................................................... 581 7.3.2 Energy Storage .............................................................................................................. 582 7.3.3 Impulse Capacitors (Energy Storage or Surge Capacitors) .......................................... 583 7.3.3.1 Capacitor Design 7.3.3.2 The socalled “Capacitor Inductance” 7.3.3.3 Dielectric and Service Life
583 584 584
7.3.4 Barrier Systems ............................................................................................................. 585 7.4 Other Applications ............................................................................................................... 587 7.4.1 Lightning Protection ..................................................................................................... 587 7.4.1.1 Ensuring EMC 7.4.1.2 External Lightning Protection 7.4.1.3 Internal Lightning Protection 7.4.1.4 Lightning Protection Zone Concept
587 588 590 591
7.4.2 Pulsed Power Technology ............................................................................................. 592 7.4.2.1 Impulse current circuits 7.4.2.2 Acoustic Shock Waves 7.4.2.3 Pulsed Particle Beams and Laser Beams 7.4.2.4 Electrodynamic Generation of Nanocrystalline Materials 7.4.2.5 Electrodynamic Fragmentation 7.4.2.6 Electrohydraulic Fragmentation 7.4.2.7 Electroporation in Biological Cells
592 592 593 594 594 595 595
7.4.3 Light Technology and Laser Technology ..................................................................... 596 7.4.4 Xray Technology ......................................................................................................... 597 7.4.5 Electrostatic Particle Precipitation, Ionization .............................................................. 597 7.4.6 Spark Plug ..................................................................................................................... 598 7.5 Superconducting Equipment............................................................................................... 600 7.5.1 Superconductivity ......................................................................................................... 600 7.5.2 HTSC Conductor Materials .......................................................................................... 602 7.5.3 Insulation and Cooling with LN2 .................................................................................. 603 7.5.4 Applications .................................................................................................................. 604 7.5.4.1 SMES Superconducting Magnetic Energy Storage 7.5.4.2 Fault Current Limiter, Switch 7.5.4.3 Cables 7.5.4.4 Motors, Generators 7.5.4.5 Transformers
604 605 606 607 607
8 REFERENCES ................................................................................................................611 9 INDEX ..............................................................................................................................631
Symbols and Abbreviations
Variable scalar quantities are written in italics, vectorial quantities are represented in bold and italics, e.g. v(t) and E(x,t). For timedependent currents, voltages and charges, small letters, such as i, v and q are used, for timedependent field quantities, capital letters such as E(t) are used. Peak values are characterized by umbrella hat V. or caret on the letter, for example, Ê and Û Constant quantities and r.m.s. values are symbolized by capital letters, such as E, I, V and Q. Symbols with underlining signify complex quantities, for example z, i and v. The applied units generally correspond to the International System of Units (SI units). Only for the units of pressure, temperature and time, also the traditional and descriptive units 5 of bar (1 bar = 10 Pa), degrees Celsius (°C) and the usual time units are resorted to.
Symbols In the following section, the most important symbols are explained. They are arranged according to small letters, capital letters and Greek letters. The meanings of different indices result from the text. Unfortunately, using the same symbols for totally different quantities cannot be completely avoided because of the overlapping of different science disciplines in the fields of high voltage engineering. The reader is therefore requested to infer the applicable meaning from the context of the text. a b c
Distance, width, coefficient, exponent Regression coefficient, constant Constant
d e e
Distance, flashover distance Elementary charge, unit charge e = 2.718281..., , Euler number, base of the natural logarithm f Frequency, impulse factor, shape factor f (...) Function of ... g Acceleration due to gravity g (...) Function of ... h Height, frequency or empirical distribution function (statistics), absolute air humidity i Current, counting index j Imaginary unit, counting index k Constant, counting index, lifetime exponent k Boltzmann constant l Length, counting index m Mass, counting index n Number (quantity), counting index, optical refractive index p Geometry factor, potential coefficient, pressure, power loss density, pfactor, probability q Charge r Radius, distance, divider ratio, relative air humidity s Distance, Laplace operator, steepness, empirical standard deviation s Spatial vector t Time
XX
tan G Dissipation factor u Velocity, coordinate (wplane), measurement uncertainty v Voltage, coordinate (wplane), empirical variation coefficient w Energy density, water content (relative or absolute) w Complex number x Space coordinate, length x Spatial vector x Definite value of a random variable y Space coordinate z Space coordinate, axial length z Complex number A, A A
Area (vector and magnitude) Voltagetime area, Constant (Paschen’s law), Al Aluminium (chemical symbol) Ar Argon (chemical symbol) B, B Magnetic flux density B Constant (Paschen’s law) B Boron (chemical symbol) C Capacitance C Carbon (chemical symbol) Ca Calcium (chemical symbol) Cl Chlorine (chemical symbol) Cu Copper (chemical symbol) D, D Dielectric displacement density D Complex r.m.s. phasor for the dielectric displacement density D Distance, diameter, theoretical density function (statistics) E, E Electric field strength / intensity / stress (vector and magnitude) E Complex r.m.s. phasor for the electric field strength F, F Force (vector and magnitude) F Theoretical distribution function, probability (statistics) F Fluorine (chemical symbol) Fe Iron (chemical symbol) G Conductance, shear modulus H, H Magnetic field intensity (... strength) H Hydrogen (chemical symbol) He Helium (chemical symbol)
Symbols and Abbreviations
I, I J, J J J K K L M Mg N N Ne O P, P P P Q R R S, S S Si T V V, V W X Y Y Z Z
D E J G
Current, complex r.m.s. phasor Conduction current density Complex r.m.s. phasor for the conduction current density Iodine (chemical symbol) Capacitance coefficient, constant, Kerr constant Potassium (chemical symbol) Inductance, length Mutual inductance Magnesium (chemical symbol) Number Nitrogen (chemical symbol) Neon (chemical symbol) Oxygen (chemical symbol) Electrical polarization Real power, power loss Phosphorous (chemical symbol), Charge, reactive power Resistance, radius, range (statistics) General chemical group Complex power, apparent power Sulfur (chemical symbol) Silicon (chemical symbol) Time, period, temperature Volume, variation coefficient Voltage, complex r.m.s. phasor Energy, Probability (statistics) Reactance, random variable Random variable Admittance (complex conductance) Characteristic line impedance, intrinsic impedance Impedance, complex phasor Angle, ionization coefficient Ionization coefficient Surface ionization coefficient Loss angle, relative air density,
Symbols and Abbreviations
Weibull exponent tan G Dissipation factor H Permittivity K Field efficiency factor, space charge density, attachment coefficient, capacitive voltage overshoot, voltage efficiency (impulse circuit) Temperature N Electrical conductivity O free path length, thermal conductivity P Permeability, ion mobility, expectation value Q Optical frequency, continuous index U Resistivity, reflection, refraction or transmission coefficient (traveling waves) V Surface charge density, force per area, standard deviation V(t) Step function W Time constant, propagation time (traveling waves) M Potential Z Angular frequency
XXI
CCA Charging current analysis CD Coupling device CIGRÉ Conseil International des Grands Réseaux Electriques CISPR Comité International Special Des Perturbations Radiophoniques CO Carbon monoxide CO2 Carbon dioxide CSM Charge simulation method CTI Comparative tracking index D DAC DBT DC DC
Discharge Damped AC voltage Dibenzyl toluene Direct current Prefix characterizing timeindependent electric quantities DCA Discharge current analysis DEC Dielectric equivalent circuit DFT Discrete fourier transform DIL Design insulation level DKD German calibration service DP Mean degree of polymerization DSP Digital signal processor DTE Ditolylether DVA Discharge voltage analysis EMC EN EP EPR EPS Eq. ESD
Electromagnetic compatibility European standard Epoxy resin Ethylenepropylene rubber Equipotential surface Equation Electrostatic discharge
AC
Alternating Current (amplitude current) AC Prefix characterizing alternating electric quantities ACLD AC long duration test (outdated) ACSD AC short duration test (outdated) AMF Axial magnetic field contacts ASTM American Society for Testing and Materials AV Applied voltage test
FCL FDA FDM FDS FEM FeO FFT FID FT FW
Fault current limiter Frequency domain analysis Method of finite differences Frequency domain spectroscopy Finite element method Iron oxide Fast Fourier transform Flame ionization detector Fast transients Filament winding
BEM Boundary element method BNC Benzyl neocaprate
G1, 2 Spark gap 1, 2 GC Gas chromatograph GIL Gasinsulated line
4
Contact angle
Abbreviations
XXII
Symbols and Abbreviations
GIS GasInsulated Switchgear GRP Glassfiber reinforced plastic GWP Global warming potential HDPE Highdensity polyethylene HEMP High altitude electromagnetic pulse HPLC High Pressure/Performance Liquid Chromatography HTSC Hightemperature superconductivity HTV Hightemperature vulcanization (silicone) HV High voltage HVAC High voltage alternating current HVDC High voltage direct current IEC
International Electrotechnical Commission IEEE The Institute of Electrical and Electronic Engineers IEM Integral equation methods IR Infrared light IRC Isothermal relaxation current IVPD Induced voltage test with PD measurement IVW Induced voltage withstand test KFT
Karl Fischer titration
LCC Linecommutated converter LDPE Lowdensity polyethylene LFH Lowfrequency heating LHe Liquefied helium LI Lightning impulse LIC Chopped lightning impulse LN2 Liquefied nitrogen LSI Liquid Silicone LSF6 Liquefied Sulfur hexafluoride LTS, LTSC Lowtemperature superconductivity LV Low voltage LV Arcperformance index MBT MCM MIPB MOM MP
Monobenzyl toluene Monte Carlo method Monoisopropylbiphenyl Method of moments Metallized paper
NEMP Nuclear electromagnetic pulse
OFC OIP OLI OLTC OSI
Oxygenfree copper Oilimpregnated paper Oscillating lightning impulse voltage Onload tap changer Oscillating switching impulse voltage
PA Polyamide PAI Polyamidimide PC Polycarbonate PCB Polychlorinated biphenyl PD, pd Partial discharge PDC Polarization / Depolarization current PDE Partial discharge extinction PDI Partial discharge inception PDM Partial discharge measuring device PE Polyethylene PES Polyethersulfone PF Phenolic resin (phenol formaldehyde resin) PFL Pulse forming line PI Polyimide PMMAPolymethylmethacrylate PP Polypropylene PR Polarity reversal PSU Polysulfone PTB Physikalischtechnische Bundesanstalt (Federal Institute of Metrology) PTFE Polytetrafluoroethylene PTI Proof tracking index PU Polyurethane PVC Polyvinylchloride PVDF Polyvinylidenfluoride PXE Phenylxylylethane RBP RIP RIS RIV RMF r.m.s. RTV
Resinbonded paper Resinimpregnated paper Resinimpregnated synthetics Radio interference voltage Radial magnetic field contact Rootmeansquare Roomtemperature vulcanization silicone RVA Recovery voltage analysis RVM Recovery voltage method RW Regulating winding SCSM Surface charge simulation method SF6 Sulfur hexafluoride SI Switching impulse voltage
Symbols and Abbreviations
SiC Silicon carbide SIR Silicone rubber SMES Superconductive magnetic energy storage SSB Superconductive Current Limiter T TCD TEM TF TP TP UHF
Thermal defect Thermal conductivity detector Transverse electromagnetic (wave) Transfer function Triple point Thermal fault with paper decomposition Ultra high frequency
XXIII
UHV Ultra high voltage UV Ultraviolet light VDE
VLF VPI VSC
Verband der Elektrotechnik Elektronik Informationstechnik (Association for Electrical, Electronic and Information Technology) Very low frequency Vacuumpressure impregnation Voltage source converter
XLPE Crosslinked polyethylene ZnO
Zinc oxide
1 INTRODUCTION 1.1 The Function of High Voltage Technology The main task of high voltage technology and engineering is to keep high electric field strengths under control. They do not only occur in apparatus operated or tested at high voltages, they can also be found in apparatus at comparatively low voltages and with small insulation, e.g. in thin capacitor insulations made of polymer films. The electric field strength, and not the voltage, is the relevant quantity for the electric strength (“breakdown strength”) of insulating materials. Nevertheless, our discipline is usually called “high voltage technology” and “high voltage engineering”, which is not strictly correct. Basically, high voltage engineering has to guarantee that the electric stress, given by the electric field strength E, is significantly smaller than the electric strength (breakdown strength) Ed always, i.e. under all possible circumstances: “Stress” E 300 kV) Vm = 300 362 420 525 765
kV, kV, kV kV, kV.
(common in Germany),
Note: In a very general sense, “high voltage” is any voltage level above low voltage (1 kV). The boundaries between medium and high voltage depend on local circumstances, history or common usage. Nevertheless, the band 30 kV to 100 kV frequently contains the accepted boundary. The abovementioned classification is used in German transmission and distribution systems for instance. Note: Sometimes in Germany the standardized voltage levels Vm = 12, 24, 123, 245 and 420 kV are still denominated with the old “nominal voltages” 10, 20, 110, 220 and 380 kV (400 kV).
Insulation breakdown is normally determined by the highest occurring value of the AC voltage, i.e. by the peak value. For sinusoidal voltages and under normal service conditions, the insulation between phases (linetoline, index “LL”) is stressed with the peak value
Û V LL =
2 · Vm
(2.21)
and between phase and ground (linetoground, index “LG”) with the peak value
V LG = Û
2 · Vm / 3 .
(2.22)
Electrical equipment is designed and rated to withstand this continuous voltage stress for many decades. For a short time, powerfrequency overvoltages can occur, e.g. during a sudden load reduction. In grids up to Vm = 123 kV the neutral point (star point) does not always have a solid grounding. In the case of a single phaseto
ground fault, the neutralpoint potential is therefore shifted and the insulations between the unaffected phases and ground are stressed with the phasetophase voltage according to Eq. (2.21). Resonant overvoltages at power frequency should be excluded by the grid topology, but they can occur together with harmonics. The strength of insulation against powerfrequency overvoltages has to be proven by means of a specified AC voltage withstand test with a duration of 1 minute (“rated shortduration powerfrequency withstand voltage test”). The r.m.s. value of the test voltage is always specified in relation to the highest voltage for equipment Vm [11]. This reference of test voltages to the maximum voltage stresses in service is called “insulation coordination”, Section 6.1.4. The test voltage value is nearly 3·Vm for the lower voltage levels and approx. between 2·Vm to 1.5·Vm for the higher levels. This shortduration test voltage is an important design parameter for insulation systems. For the higher voltage levels a successful AC voltage withstand test is not sufficient. Depending on the kind of equipment, insulation quality must be guaranteed by the proof of partial discharge (PD) intensity limits at different AC test voltage levels (see Section 3.6, 6.4.2 and Chapter 7). AC voltage tests on cables with high capacitances are performed with very low frequency (VLF) f = 0.1 Hz in order to reduce the capacitive reactive power. Alternatively, tests with higher frequencies can be performed with resonance test circuits instead of the less meaningful DC tests, Figure 2.24, Section 6.2.1. Transformers must be tested with increased frequencies (e.g. with f = 100 Hz for 50 Hz transformers and f = 120 Hz for 60 Hz transformers) in order to avoid saturation of the magnetic core after exceeding the design voltage and at the start of the test voltage. If the
2.2 Electrical Stresses in High Voltage Engineering
frequency is doubled, the induced voltage Vi ~ wB/wt ~ Z·B is also increased by a factor of two without any increase in magnetic flux density B, Figure 2.24. Significantly higher frequencies occur if the line voltage contains harmonics. This can result in a distortion of the voltage curve, so that peak values differ significantly from the peak values of a sinusoidal voltage with the same r.m.s. value. Furthermore, harmonics can cause enhanced capacitive currents and enhanced dielectric losses. Lossy and thick insulation systems (e.g. in old power factor correction capacitors with oilimpregnated paper insulation) are subject to higher thermal stresses.
2.2.3 Switching Impulse Voltage Stress (“Internal Overvoltages”) Pulseshaped overvoltages can be caused by switching operations in the electrical grid, e.g. by interruption of a currents during the opening of inductive circuits. As the origin is in the grid itself, the switching impulses (SI) are called “internal overvoltages”. For equipment with Vm > 300 kV the electric strength against SI overvoltages is normally proven during a type test. The peak value of the standardized “rated switching impulse withstand voltage” VrS is defined in relation to Vm as part of the insulation coordination [11], Section 6.2.3.1. Normally the peak time Tp (time to crest) is 250 μs and the time to halfvalue (tail time) is 2500 μs. During the calculation of electric fields in common insulating systems, quasistatic (quasistationary) conditions in the form of dielectric displacement fields can be assumed, which are determined by permittivities, cf. Section 2.1.4.4. The errors of a quasistationary analysis are negligible up to lengths of approx. 5 km, if Tp = 250 μs, Eq. (2.137), Figure 2.24.
25
2.2.4 Lightning Impulse Voltage Stress (“External Overvoltages”) Direct lightning strikes into power apparatus cause travelling waves in the widely distributed overhead lines and cables. These waves lead to very high shortduration overvoltages. Also lightning strikes into line towers, overhead ground wires or into other structures nearby can lead to rapidly changing fields and traveling wave processes being coupled in. As the surges are generated atmospherically, i.e. they are caused by external lightning impulses (LI), we refer to “external overvoltages”. Amplitudes and time responses of external overvoltages are subject to strong variations. Nevertheless, characteristic properties are a fast rising voltage in the μs range and a significantly slower decline of the overvoltage impulse (Section 6.2.4). For of electrical power equipment a standardized lightning impulse voltage with a socalled front time T1 = 1.2 μs and a time to halfvalue (tail time) T2 = 50 μs is defined. As part of the insulation coordination, the different service voltage levels Vm are each associated with a peak value of the “rated lightning impulse withstand voltage” VrL [11]. They are more than twice the socalled shortduration AC withstand voltage. For the calculation of electric fields, quasistatic (quasistationary) conditions and dielectric displacement fields can be assumed in relatively small systems only, i.e. for dimensions limited to approx. 25 m, Figure 2.24. In systems with distributed parameters (distributed systems), e.g. in cables and overhead lines, the wavecharacter of the fields must be considered. This is especially the case if the trailing part of the impulse voltage is chopped. Depending on the inductance of the circuit, chopping times far below 100 ns can occur. In circuits with low losses (e.g. if a nondamped capacitive voltagedivider is used), the chopping can be an excitation of significant transient traveling wave oscillations.
26
2 ELECTRIC STRESSES
Another example for pulsed electric stresses is the discharging of energy storage capacitors, which are often referred to as impulse capacitors, Figure 2.24. Typically the discharge periods or the timeconstants of the discharge processes are in the μs range. Therefore in smaller systems quasistatic fields can be assumed. (Impulse) discharge circuits of high power pulse technology (pulsed power) are used in many technical applications, Section 7.4.2:
and grinding of inhomogeneous or composite materials, e.g. for recycling applications [12].
x Electroporation can be applied for the opening and disruption of biological cells at room temperatures with low energy consumption. x High energy impulses can be used to generate very fast temperature rises for the production of nanometric particles by melting and condensing.
x In medical engineering acoustic shockwaves are generated by igniting a spark gap in water or by an electroacoustic transducer. The energy is supplied by the discharging of a high voltage capacitor. For example, in a lithotripter the resulting shock wave is focused on a kidney stone (nephrolith) or a gallstone in order to pound it to tiny pieces.
x Pulse discharge circuits are necessary for the power supply of impulse lasers and for other impulse (flash) light sources.
x In production technology focused acoustic shock waves can be used for highspeed forming of metallic materials.
There are many examples of fast rising impulses in different technical applications:
x Shock waves are used for electrodynamic fragmentation, i.e. for the fragmentation
2.2.5 Fastrising Impulse Stresses (“Fast Transients”)
1.) In gasinsulated switchgear (GIS) discharge processes are caused for example by flashovers or by switching of disconnectors.
H u E
H, E, u
Figure 2.23: Propagation of traveling waves within and on the outside of a gasinsulated switchgear (GIS) after a breakdown in gas (schematic illustration without respect to reflections).
2.2 Electrical Stresses in High Voltage Engineering
DC voltage
AC voltage
Switching Steadystate operations DC voltages Polarity reversals Days ... months
27
Hours,
VLF 0.1 Hz T = 10 s
Changes in minutes
Impulse voltage
AC
AC SwitchingLightning100/ 120 Hz 50/ 60 Hz impulse voltages impulse voltages 10 .. 500 Hz T = 20 ms T = 10 ms
250/ 2500 μs
v(t) T
t
v(t)
Pulsed discharges
Rise times in the
v(t)
nsrange t
v(t)
t
v(t)
1.2/ 50 μs
Fast rising impulses
E(t), H(t)
v(t)
2T
t
t
t
t
Electrical conduction fields stationary quasistationary J= NE
v
Equivalent circuits with resistances
E H
E = Z = P H H L
"Electrostatic" fields/ Quasistatic (quasistationary) displacement fields D= H E
Z, t
Equivalent circuits with capacitances
R
Electromagnetic waves
C
Highvoltage directcurrent
System with distributed parameters
Threephase alternating current
(HVDC) transmission
"Internal" (switching)
"External"
Chopped
overvoltages
Discharging of impulsecapacitors:
Lasers
Medical eng.
50(60) Hz
Charging devices Electrostatic percipitator Coating Electrostatic flock finishing
Cable testing
harmonics n·50/ 60 Hz
Transformer testing Resonance testing (onsite)
Switchingimpulse withstand tests
Fast transients
(lightning) lightning impulses
Monitors
Xray tubes
C
Lightningimpulse withstand tests
Biotengineering
Pulsed power Nuclear Electromagnetic Pulse (NEMP)
Production Impulse lasers Partial Discharge Recycling
(PD) impulses
Figure 2.24: Overview of important technical voltage stresses in high voltage engineering: Typical time curves (top), kinds of fields and equivalent circuits (middle) and typical applications (bottom).
Because of the high gas pressures and the low insulation distances, discharges have rise times in the ns range, therefore they can excite traveling waves. Owing to the length (frequently many meters) of the coaxial tubular conductors and shielding, traveling waves can often propagate without significant damping. At discontinuities of the line impedance reflections occur, and different waves are superimposed. Normally they propagate within the tubular shielding, but via the bushings they can also propagate outside, Figure 2.23 and 4 [13]. Therefore, highly stressed insulations (e.g. in transformers and bushings) are endangered by significant transient overvoltages. In unfavor
able situations, the excitation of selfresonances (e.g. in the transformer windings) can result in further voltage overshoots. Wave propagation on the outside of the shielding can cause unwanted electromagnetic interferences in the secondary systems of the plant. Specific measures have to be taken in order to guarantee “electromagnetic compatibility” (EMC). 2.) Testing of power equipment with respect to very fast voltage transients is normally performed together with a lightning impulse test by a fast “chopping” of the voltage by means of a chopping spark gap. The time to chopping is 4 to 6 μs (chopped lightning impulse, choppedwave lightning impulse).
28
For the calculation of fast transients, the fastchanging character of the processes must be considered. Mostly the transients can be described as guided TEMwaves on coaxial lines (traveling waves, Section 2.6). On a surface with constant phase (wavefront) the closedloop integral about E·dx is zero (the vectors H and B do not penetrate the wavefronts!), therefore voltages between the inner and the outer conductor can be defined according to Eq. (2.17). Attention: The definition of voltages with components parallel to the direction of wave propagation is no longer possible! 3.) Other examples for very fast rising highvoltage impulses can be found in pulsedpower technology for the generation of extremely short impulses with extremely high power ratings. These pulses are generated by means of travelingwave lines and they are used to feed particlebeam accelerators in science for the investigation of materials in extreme conditions and for the ignition of controled nuclear fusion processes. The rise times and the halfvalue widths of these impulses are in the range of some ns and some 10 ns resp., peak power and peak voltage reach the TW and the MV range [14], [15]. 4.) In the case of a nuclear explosion in the space outside of the Earth’s atmosphere, it is expected that the action of the resulting radiation in the atmosphere will separate positive and negative charge carriers in the vertical direction. Separation and recombination of charges will cause a pulsed electromagnetic field, the socalled nuclear electromagnetic pulse (NEMP). It is expected that high overvoltages will be induced in the widely distributed systems of telecommunications, information technology and energy transmission and distribution. 5.) If a high AC field strength is applied to an insulation defect, partialdischarge (PD) impulses occur, normally without causing an immediate breakdown. These impulses also have very short rise times in the ns range. For a single partial discharge the dissipation of energy and the charge magnitude are very small.
2 ELECTRIC STRESSES
Nevertheless, the discharge impulses are a dangerous phenomenon of AC voltage stress, owing to their erosive effects in sensitive, mainly organic insulating materials. The fast changing electromagnetic field of partial discharges is important for partial discharge measurements. 6.) The transmission characteristics of highvoltage measuring systems are determined by means of stepgenerators providing rectangular pulses with rise times in the ns range. Because of the large spatial dimensions, traveling wave oscillations on measuring cables and direct coupling of free electromagnetic waves must be considered [18], [19].
2.2.6 Mixedfield Stresses In many cases electric stresses are a combination of the cases described above. Then it is often difficult to determine the electric field strengths and the relevant electric strengths. Important examples: 1. Superposition of DC and AC voltages in the converter transformers of HVDC systems. 2. DC voltage and polarity reversal tests: A stationary conduction field and a quasistationary displacement field are superimposed, if the amplitude or the polarity of the voltage is changed. Depending on conductivity N and selfdischarge timeconstant H/N, it takes a very long time to approach a new steadystate condition. During such a transient process, significant stresses can occur on materials in a layered insulation, which are much less highly stressed initially and in the steady state. 3. Rectifier and converter circuits: Many electronic devices are stressed with a superposition of DC, AC and impulse voltages. 4. Energystorage and impulse capacitors: During the charging process, the dielectrics are stressed with an increasing voltage. Depending on the time of storage, the field after voltage application approaches a steadystate conduc
2.3 Conduction and Displacement Fields in Homogeneous Dielectrics
tion field. During the discharging process there is a pulsed stress, often in the form of a damped oscillation. 5. Fast transients: Rapidly changing traveling waves are superimposed on the actual field condition given by the quasistatic power frequency state. Thereby high overvoltages can occur, for which the equipment is not insulated sufficiently.
In field calculations for the determination of electrical stresses, the different kinds of fields are normally calculated separately and superimposed linearly into mixed stresses. In contrast to magnetic materials with nonlinear magnetization curves, solid insulating materials behave more or less linearly, as long as discharges do not occur. Liquid dielectrics can have nonlinear conductivities, however, Section 4.2.2.2. In situations with mixed stresses, it is often difficult to evaluate calculated field strengths. For the example of impulse capacitors, the steadystate DC voltage is absolutely noncritical in comparison with the fast changing stress during the discharging process, although the amplitudes are identical in both cases. For practical design purposes, breakdown and lifetime tests are necessary, with conditions close to the real service conditions.
29
If the whole field volume that is to be considered consists of a single homogeneous (uniform) insulating material (dielectric), the field distribution is not determined by material properties (permittivity H, conductivity N) and the electric field calculations are based on the same relationships. Therefore, the field calculation methods, which are described in the following, can be applied for most of the. First of all, the direct analytic evaluation of the field equations is performed (Section 2.3.1 and 2.3.2). It allows the calculation of basic field configurations with homogeneous, spherically symmetric and cylindrically symmetric fields. Some important high voltage field configurations can be approximated from this. A graphical method (Section 2.3.3) allows a qualitative or semiquantitative field sketch to be determined using some simple drafting rules. Often this is very valuable for a first qualitative estimation of field conditions. The method of conformal mapping (Section 2.3.4) allows the calculation of some special cases, e.g. the field stress enhancement at the edges of a parallelplate capacitor (edge field). By means of the fields of equivalent charges (Section 2.3.5) it is also possible to calculate important field configurations, e.g. sphere against sphere or cylinder against plane.
2.3 Conduction and Displacement Fields in Homogeneous Dielectrics
In many cases, only the maximum field strength is of interest. For many field configurations, it can be derived from already calculated cases by similarity relationships and geometry factors (Schwaiger’s field efficiency factor, Section 2.3.6).
For static, stationary and slowly changing (quasistatic, quasistationary) fields in insulating materials, the electric field can be regarded as irrotational, i.e. as an electrostatic field. An induced electric curl field does not occur or can be neglected. Therefore, the definition of potential differences and voltages is acceptable.
Before numerical field calculation methods were available, the only possibility for the determination of field strengths in systems with arbitrarily shaped electrodes was the measurement of electrical conduction fields in a semiconductive liquid (electrolytic tank) or on a semiconductive paper (field plotter), Section 2.3.7).
30
2 ELECTRIC STRESSES Example: Spherical electrode in free space
2.3.1 Analytic Evaluation of the Continuity Equation (Gauss’s Law)
The magnitude of the electric field strength E shall be calculated as function of voltage V and radius r for the spherically symmetric arrangement according to Figure 2.31. The counterelectrode with the negative countercharges is assumed to be infinitely far away.
2.3.1.1 General Calculation Method
If Eq. (2.117), i.e. the Continuity Equation for conduction and displacement current
³³ A
wD ( J + wt ) d A
=
0,
is integrated over the time, it results in “Gauss’s law”, Eq. (2.121) and (2.31). It states that the integral of the flux density D over any closed surface, i.e. the total displacement flux ³³ D·dA, equals the charge Q enclosed.
³³
D dA
= Q
(2.31)
Step 1: The surface of a sphere with the radius r is chosen as the closed surface for integration. Thereby the symmetry of the configuration is utilized, because the displacement density has a constant magnitude D(r) over the entire chosen surface. Furthermore, the vectors D and dA are parallel to each other, over the entire closed surface. The scalar product D·dA equals the product of the magnitudes D·dA. The displacement density is constant all over the surface of integration, and it can be brought out from under the integral sign in Eq. (2.31):
³³A
=
D (r)
³³A
dA
2
D(r) · A(r) = D(r) · 4Sr
With Eq. (2.31), field calculations can be performed for some basic configurations in four steps: Step 1: For configurations with symmetrical fields, Eq. (2.31) is solved for the magnitude D of displacement vector D, in order to get a relationship between fieldgenerating charge Q and the electric field strength E = D/H.
dA Closed surface A
Q
Dielectric displacement density
D E
Figure 2.31: Spherically symmetrical electrode in free space (Gauss's law).
Q
= Q
This gives 2
D(r) = Q/(4S r )
and
2
E(r) = Q/(4SH r ) .
(2.32)
The magnitude of the electric field strength decreases 2 proportionally to 1/r , i.e. quadratically with the radius.
Step 2: In high voltage engineering the electric field strength E normally has to be given as a function of the applied voltage V. This is possible, if the field strength, which is derived from Gauss’s law according to Eq. (2.31), is integrated according to Eq. (2.17): 1
r
R
=
The remaining integral over the closed surface gives the 2 surface area A(r) = 4Sr itself:
A
Electrostatic field
D dA
V 21 = 'M 21 = M 2  M 1 = ³ E d x (2.33) 2
Thereby a relationship between Q and V is determined, i.e. Q = f(V). Step 3: According to Eq. (2.110) the ratio of Q and V defines the capacitance C of the field configuration:
C = Q/V
(2.34)
2.3 Conduction and Displacement Fields in Homogeneous Dielectrics
31
field
to (2.38). Maximum field strength occurs at the electrode surface.
is derived from the first step with E = f(Q) and from the second step with Q = f(V).
Note: The field of the conducting sphere in free space with a vanishingly small radius R o 0 approaches the field of a point charge. This theoretical case is important for field calculations with the equivalentcharge simulation method, Section 2.3.5.
Step 4: The desired relationship strength E and voltage V
between
E = f(V)
Step 5: In an additional step, maximum values of field strength can be determined and optimization problems can be solved, e.g. the minimization of maximum field strength. Example: Spherical electrode (continued) Step 2: Continuing with the former example, the voltage between the electrode surface with radius r = R and the counterelectrode (carrying the negative countercharges) with the radius r o f is given by 䌲
VR䌲 =
䌿E (r ) dr =
R
f
if the integration is performed radially, i.e. in parallel with the electric field E. Therefore it gives (2.35)
Step 3: From that, the capacitance is derived:
C = Q / V = 4S H R .
(2.36)
Step 4: According to Eq. (2.32) and (2.35) from steps 1 and 2, the electric field strength is
2
E(r) = V R/r .
(2.37)
Step 5: Maximum fieldstrength is found on the electrode surface for the smallest possible radius r o R, i.e.
Emax = E(R) = V / R .
Example: Sharpedged point electrode
V = Êmax·R = 5 kV. From Eq. (2.38) we conclude that Û
Q/ (4SH R) ,
Q = 4 SH R V .
Generally, sharp edges (with small radii R) must therefore be avoided in high voltage engineering, in order to avoid electrical overstressing of the adjacent insulating material.
The field in the vicinity of a metallic point electrode shall be calculated approximately as a spherically symmetric field with R = 1 mm. What is the expected peak V for the inception of discharges in air (Êi = 5 voltage Û kV/mm)?
Q 䌲1 䌿 dr 4 ʌH R r2 Q ª 1º 4 ʌ H «¬ r »¼ R
=
The smaller the radius of curvature R of an electrode, the higher the electric edgefield strength will be, Eq. (2.38).
(2.38)
2.3.1.2 Spherically Symmetric Fields
The electric field of a “conducting sphere in free space” was calculated in the former example, see Figure 2.31 and Equations (2.36)
Note: High field strengths at sharpedged point electrodes do only occur in a small volume close to the point. The inception field strength is therefore significantly higher than the commonly used peak value Êi = 3 kV/mm = 30 kV/mm which is valid for air gaps in the centimeter range, Figure 3.215. Discharge inception cannot be described exactly by specifying a constant inception field strength, see Chapter 3.
In high voltage engineering, field stress enhancements at sharp edges are reduced by sufficient radii of curvature. In many cases, sharpedged parts have to be protected by shielding electrodes (e.g. spheres or toroids). The field strengths on the surface can be estimated by approximation from Eq. (2.38) if approximately spherically symmetric conditions are assumed with a counterelectrode very far away: Emax = V / R
(2.38)
The capacitance in air can be approximately described according to Eq. (2.36) using the rule of thumb
32
2 ELECTRIC STRESSES
C/pF  R/cm .
(2.39)
Note: If the counterelectrode (e.g. the grounded wall, ceiling or floor) is located at a finite distance, higher capacitances and field strengths occur. Numerical field calculation methods achieve a significantly better accuracy than the analytic estimation, Section 2.3.5.
dA Closed surface A
Example: Shielding electrodes
Q
R1
The diameters of shielding electrodes for use in air (Êbd = 30 kV/cm, Hr = 1) and insulating oil (Êbd = 150 kV/cm, Hr = 2.2) shall be sized for the voltage amV = 10 kV, 100 kV and 1 MV so that the field plitudes Û strengths do not exceed 2/3 of the breakdown field strength.
R2
r
E, D
The diameters are derived from Eq. (2.38):
V / (2/3 · ÊD) . D = 2 R = 2Û
V Peak voltage Û
10 kV
100 kV
1 MV
D C
1 cm 0.5 pF
10 cm 5 pF
1m 50 pF
Insulating D Oil: C
2 mm 0.2 pF
2 cm 2 pF
20 cm 22 pF
Air:
Figure 2.32a: Spherical capacitor (or cylindrical capacitor resp.).
Note: The results show that high voltage laboratories need shielding electrodes with diameters in the meter range. Much more compact high voltage equipment can be designed by means of electrically stronger insulating materials (e.g. insulating oil or sulfur hexafluoride SF6). It has to be considered that Ebd of insulating oil is not a constant value, but inter alia is dependent on the width of the oil ducts (“volume effect”, “distance effect” or “size effect”, see Chapters 3 and 5).
A socalled spherical capacitor consists of an inner sphere with the radius R1 and a counter electrode consisting of a concentric outer sphere with the finite radius R2, Figure 2.32a. The calculation of field strength is performed in five steps, analogous with the calculation steps for the spherical electrode in free space: The use of Gauss’s law (eq. (2.31), Step 1) on the spherically symmetrical configuration according to Figure 2.32a gives the same equation (2.32) again because of the similar field conditions. E decreases with the radius r pro2 portional to 1/r (step 1).
E(r) E max
~ 1/ r 2
With outer electrode Without outer electrode
E max
~ 1/ r 2 0
R1
R2
r
Figure 2.32b: Field strength curves E(r) for the spherical capacitor.
The integration of the field strength according to Eq. (2.32) (Step 2) must not be performed from radius R to infinity, because the field is limited to the space between the inner and outer electrodes, i.e. integration has to be performed between the radii R1 and R2. Inserting the new integration limits and V12 = V, we obtain
2.3 Conduction and Displacement Fields in Homogeneous Dielectrics
V
=
and Q
=
Q
(
4 SH
4 SH 1 1 R1 R2
1 1 ) R1 R2
(2.310)
(2.311)
V.
The capacitance of a spherical capacitor is given by C = Q/V (Step 3):
C
=
4 SH 1 1 R1 R2
(2.312)
=
1 1 ( R1
1 2 V )r R2
(2.313)
For the extreme value R2 >> R1 Eq. (2.312) and (2.313) approach Eq. (2.36) and (2.37). The maximum field strength at the inner sphere with r = R1 (Step 5) is higher in comparison with the sphere in free space, Figure 2.32b. The areas under the field strength curves correspond to the integral of the function E(r), i.e. to the applied voltage V. We obtain the maximum field strength from Eq. (2.313) for the radius r = R1 on the surface of the inner sphere (surface or edge field strength): E max =
E1 =
strengths E1. The optimum inner radius R1 for a minimum surface field strength E1 is between 0 and R2 therefore, and it is determined, if the derivate of E1 with respect to the variable R1 is set to zero, see Eq. (2.314): wE1 wR 1
R2 2R1 R V ( R 1R 2 R 12 )2 2
=
! =
We obtain for R1 and E1min: R1 = R2 / 2
and
E1min = 4 V / R2 (2.315)
The field strength curve between inner and outer electrodes is derived from Eq. (2.32) and (2.311) (Step 4): E(r)
33
R2 R 1R 2
V R 12
(2.314)
From the calculated field strengths optimization problems can be solved by means of extreme value determination: For a given outer radius R2 the inner radius R1 shall be chosen so that the maximum field strength (surface/edge field strength) E1 will be minimal. In the extreme cases R1 o 0 and R1 o R2, there are infinitely high surface/edge field
Another example for optimization problems is the maximization of the capacitively stored energy 2 W = ½ C V by variation of the inner radius R1 for a given outer radius R2 and an permissible field strength Ebd. This is particularly important for capacitors in which the greatest quantity of energy is to be stored for given dimensions. The capacitively stored energy is calculated according to Eq. (2.312) and (2.314)
W = ½ C V
2 1
W = ½ [4SH R1R2(R2  R1) ] [Ebd (R2  R1) R1/R2] 2
2
3
W = Ebd 2SH (R2  R1) R1 /R2 2
3
4
W = Ebd 2SH (R2R1  R1 ) /R2 In the extreme cases R1 o 0 and R1 o R2 the field energy is minimal, i.e. W o 0. The radius R1 for maximum field energy is determined, if the derivate of W with respect to the variable R1 is set to zero: wW/wR1
=
2
2
3
Ebd 2SH (R2 3R1  4R1 ) /R2
= 0
The result for R1 is
R1
=
R2 3/4.
(2.316)
For many applications in high voltage engineering the electric field can be regarded as spherically symmetric, either by approximation or in limited field regions, Figure 2.33. 2.3.1.3 Cylindrically Symmetric Fields
The so called “cylindrical capacitor” consists of concentric (coaxial) cylinders with the radii R1 and R2, Figure 2.34. To begin with, field
34
2 ELECTRIC STRESSES
R R1
R
R2 R1
R2
Connecting element with high voltage conductors
R
Rightangle busbar arrangement in a GIS (gasinsulated switchgear)
Shielding electrode in the corner of a room Shielding electrode in free space
R1
Compressed gas capacitor (standard gas capacitor)
R2
Figure 2.33: Examples for spherically and cylindrically symmetric fields in HV engineering (approximations).
distortions at the edges of the cylinders are neglected, i.e. it is assumed that there is a twodimensional field, which does not change along the axis of the cylinders.
enclosing the inner cylinder. It consists of a cylindrical lateral surface with the radius r and the cylinder length z, and two plane end areas, Figure 2.34.
Calculation of field strengths is performed in five steps, as in the case of the spherically symmetric field:
The lines of dielectric displacement density D are nearly orthogonal to the vectors of the area elements dA of the end areas. For the integration over the total closed surface, the contribution of the end areas can therefore be neglected. On the lateral surface D and dA are in
For the application of Gauss’s law, Eq. (2.31), Step 1, a closed surface is defined, completely
r R2
D, E
R1
D, E
Cylindrical inner conductor End area
E(r)
Cylindrical lateral surface (length z )
Closed surface
E max With outer cylinder ~ 1/ r
Cylindrical outer conductor
z
Without outer cylinder 0
R1
R2
r
Figure 2.34: Cylindrically symmetric electrode configuration (top) with field strength profile (bottom).
2.3 Conduction and Displacement Fields in Homogeneous Dielectrics
parallel, so the vector product can be replaced by the scalar product of the magnitudes. D(r) is nearly constant on the lateral surface and can be brought out from under the integral sign. The remaining integration of dA over the lateral surface gives the surface area value A = 2Sr z Q = D(r) ³³ dA = D(r) A = H E(r) 2Sr z The magnitude of the electric field strength decreases with the radius r proportional to 1/r: E(r) = Q / (2SH z r)
(2.317)
The integration of field strength E(r) from the inner to the outer cylinder according to Step 2 and Eq. (2.33) with V12 = V gives V
=
Q
=
i.e.
Q 2 SH z 2 SH z R ln 2 R1
ln
R2 , R1
V .
(2.318)
(2.319)
The capacitance of the cylindrical capacitor is C = Q/U (Step 3):
C
2 SH z = R ln 2 R1
(2.320)
In Step 4 the field strength profile between inner and outer cylinders is evaluated from Eq. (2.317) and (2.319): E(r) =
V r ln
(2.321)
R2 R1
The area under the field strength curve equals the voltage (potential difference) between the cylinders, which is the integral of E(r) in radial direction, Figure 2.34. In step 5 the maximum field strength is derived from Eq. (2.321) for the radius r = R1:
E max =
E1 =
V
R R 1 ln 2 R1
(2.322)
35
Also for cylindrically symmetric fields we find: the smaller the radius of curvature R1 of the inner cylinder the higher the electric field strength at the inner cylinder will be, Eq. (2.322). However, the increase of field strength is smaller than in the spherically symmetric field. Small radii are also to be avoided in cylindrically symmetric fields in order to stay below the breakdown strength of the adjacent dielectric materials. Eq. (2.322) gives the maximum field strength for the ideal cylindrically symmetric field and not the field strength at the edges of the cylinders. Significant field stress enhancements and high local fields can occur there depending on the electrode profiles at the electrode edges. Note: It is natural to look at a “cylindrical conductor in free space”, as was done for the “sphere in free space”, i.e. the extreme case with the counterelectrode with the negative countercharges is assumed to be infinitely far away, i.e. R2 o f. If the field strength is integrated according to Eq. (2.317), the result is an infinite voltage (potential difference), which can directly be seen from Eq. (2.318). For a finite potential difference and R2 o f the field strength will be zero, see Eq. (2.321). Therefore it is always necessary to consider an outer cylinder with a finite radius R2 < f in a cylindrically symmetrical field. The field between two cylinders approaches the field of an ideal “line charge” for the extreme case R1 o 0 and R2 o f. This theoretical extreme case is important for field calculations with the equivalent charge method together as with “point charges” and other equivalent charges (Section 2.3.5). Nevertheless, the countercharges are not located infinitely far away, but are also line charges at finite distances.
From the calculated field strengths optimization problems can be solved by means of extreme value determination: For a given outer radius R2 the inner radius R1 shall be chosen so that the maximum field strength (surface/edge field strength) E1 will be minimal. In the extreme cases R1 o 0 and R1 o R2, there are infinitely high surface/edge field strengths E1. The optimum inner radius R1 for
36
2 ELECTRIC STRESSES
minimum surface field strength E1 is between 0 and R2 therefore, and it is determined from Eq. (2.322), if the derivate of E1 with respect to the variable R1 is set to zero. During the differentiation, the rules for derivate of a fraction have to be applied to the whole fraction at first. Additionally, the rules for the derivate of a product have to be applied for the differentiation of the denominator [6]. R R R 2 0  [ ln 2 + R 1 1 ] R1 R 2 R 12 R 2 ( R 1 ln 2 ) R1 R2  [ ln  1] R1 ! V = 0 2 R ( R 1 ln 2 ) R1
w E max = V wR 1
w E max wR 1
=
R1 and E1min are derived from Eq. (2.322): R1 = R2/ e
and
E1min = e V/ R2 (2.323)
Note: The irrational number e = 2.71828... is the base of the natural logarithm and it is occasionally called “Euler number” or “Napier’s constant”. Another example for optimization problems is the maximization of the capacitively stored energy 2 W = ½ C V by variation of the inner radius R1 for a given outer radius R2 and a permissible field strength Ebd. This is particularly important for capacitors in which the greatest possible quantity of energy is to be stored for given dimensions. The maximum stored energy is calculated according to Eq. (2.320) and (2.322) 2
W =
½ C V
W =
½ [2SH z / ln (R2/R1)] [Ebd R1 ln (R2/R1)]
W =
Ebd SH z R1 ln (R2/R1).
2
2
2
In the extreme cases R1 o 0 and R1 o R2 the field energy is minimal, i.e. W o 0. The radius R1 for maximum field energy is determined, if the derivate of W with respect to the variable R1 is set to zero:
wW/wR1 =
2
Ebd SH z
2
2
·[2R1 ln (R2/R1) + R1 (R1/R2)(R2/R1 )] 2
= Ebd SH z R1[2 ln (R2/R1)  1] = 0 The result for R1 is
R1
=
1/2
R2 / e
.
(2.324)
For many applications in high voltage engineering the electric field can be regarded as cylindrically symmetric, either by approximation or in limited field regions. Some examples are already shown in Figure 2.33. Cylindrically symmetric fields also occur in highvoltage cables, in gas insulated switchgears, in bushings and close to cylindrical conductors. Example: Thin wire
The field in the vicinity of a thin wire shall be approximated by a cylindrically symmetric field with R1 = 1 V mm and R2 = 1 m. What is the expected peak voltage Û for the inception of electrical discharges in air (Êi = 4 kV/mm)? From Eq. (2.322) it is concluded that
V = Êmax R1 ln (R2/R1) Û
= 27.6 kV
Note: High field strengths at thin conductors with very small radii only occur in a small volume close to the conductor. Inception field strength is therefore significantly higher than the commonly used value Êi = 3 kV/mm = 30 kV/cm which is valid for air in the centimeter range, Figure 3.215. Discharge inception cannot be described exactly by a constant inception field strength, Chapter 3. Example: Tubular conductor and cable
The diameters of highvoltage conductors with coaxial outer conductors shall be sized for use in airinsulated tubular conductors (Êbd = 30 kV/cm, Hr = 1), in oilinsulated tubular conductors (Êbd = 150 kV/cm, Hr = 2.2) and in thermoplasticinsulated cables (polyethylene, Êbd = 450 kV/cm, Hr = 2.2). Peak voltages shall be V = 10 kV/ 100 kV/ 1 MV; 2/3 of the breakdown Û strength must not be exceeded and the outer diameter shall be as small as possible. The smallest outer diameters are achieved, if the ratio of the radii R2/R1 = e is chosen such that the maximum field strength E1 is minimal. With Ê1min = 0.67 Êbd we get
2.3 Conduction and Displacement Fields in Homogeneous Dielectrics D2 = 2 R2 = 2 e Û/ (0.67 Êbd)
and
D1 = 2 R1 = 2 Û/ (0.67 Êbd). Note: The same result is obtained by extreme value determination, i.e. if Eq. (2.322) is solved for R2, and if the derivate of R2 with respect to R1 is set to zero in order to determine the minimum. Voltage
V Û
Air:
D2 2.7 cm D1 1 cm C´ 56 pF/m
100 kV
1 MV
27 cm 10 cm 56 pF/m
2.7 m 1 m 56 pF/m
Insulating D2 5.4 mm Oil: D1 2 mm C´ 122 pF/m
5.4 cm 2 cm 122 pF/m
54cm 20 cm 122 pF/m
D2 1.8 mm D1 0.7 mm C´ 122 pF/m
1.8 cm 0.7 cm 122 pF/m
18 cm 7 cm 122 pF/m
Polyethylene:
10 kV
Note: The result shows that the application of electrically strong insulating materials (insulating oil, SF6, polyethylene) allows very compact designs in compari
37
son with air. The assumption of a constant value for Êbd neglects that the electric strength of insulating oil and polyethylene decreases with increasing insulation thickness (“volume effect”, “size effect”). The mentioned voltages and field strengths are shortterm strengths, as may be used for designs with respect to shortterm voltage tests. Permissible service voltages and field strengths are significantly lower, especially for oil and polyethylene (Section 2.2.2 to 2.2.4). The capacitance per unit length C’ only depends on the permittivity Hr, because the ratio of radii is the same in all cases.
2.3.1.4 Uniform (Homogeneous) Fields
Between two parallel plane electrodes at a distance d there is a uniform electric field with the constant field strength E = V/d (“parallelplate capacitor”). In the first instance, field distortions at the electrode edges shall be neglected. Even in this simple case, the calculation of field strength is performed in the five steps mentioned above, just in order to illustrate the method: For the application of Gauss’s law (eq. (2.31), Step 1) a closed surface is defined, enclosing one of the electrodes completely. It consists of a surface A between the plane parts of the electrodes and of additional faces in the outer parts of the field volume, which extend surface A to form a closed surface, Figure 2.35. The outer faces are only penetrated by a small displacement flux ³³ D dA; its contribution to the total flux over the closed surface is therefore neglected.
D, E
A
Closed surface
Between the electrodes, D and dA are in parallel, so the product of the vectors can be replaced by the scalar product of the magnitudes. D is nearly constant on the surface A and can be brought out from under the integral sign. The remaining integration of dA over the surface A gives the area of the surface A itself:
E(x)
E0
Q = D ³³ dA = D A = H E A 0
d
x
Figure 2.35: Uniform electric field in a parallelplate capacitor (approximation without consideration of field distortions at the electrode edges.
Therefore, the magnitude of the electric field strength E is constant for all values of x between the electrodes: E(x) = Q/(H A) = E0 = const.
(2.325)
38
2 ELECTRIC STRESSES
The integration of field strength E(x) according to Eq. (2.33) (Step 2) from one electrode to the other gives V = E0 d = Q d/(H A) . This means Q = H A V/d .
(2.326)
The capacitance of the parallelplate capacitor follows from C = Q/V (Step 3): C = H A /d
(2.327)
The field strength curve between the elec
E(x) = E0 = V/d = const.
(2.328)
The area under the field strength curve equals the voltage (potential difference) between the electrodes which is the integral of E(x) in the xdirection, Figure 2.35. The indication of maximum field strength (Step 5) is unnecessary for the uniform field. Nevertheless, field stress enhancements can occur at strongly curved edges of the electrodes (see also Figure 2.38 and 2.39). 2.3.1.5 Field Distortions by Space Charges
D, E
+Q
trodes is calculated from Eq. (2.325) and (2.326), Step 4:
Electric discharges in gaseous dielectrics can generate “space charge clouds” which strongly modify („distort“) the local electric field. Space charges can also be generated in liquid and solid insulating materials under the influence of electrical stresses.
Qtot
Example: Space charge in a parallelplate capacitor
The influence of space charges and the basic calculation method are explained for the example of a uniform field with constant and positive space charge density K. (volume density of charge). The countercharges are assumed to be on the negative electrode, Figure 2.36:
A
Closed surface
With space charge
E(x)
Without space charge
E0
During the application of Gauss’s law (eq. (2.31), Step 1) it has to be considered that the total enclosed charge within the closed surface is dependent on the actual position of the surface between the electrodes. The total charge consists of the sum of the charges on the enclosed electrode and the (space) charges within the enclosed insulating volume:
Q(x)
d
x
M (x)
= Q + ³³³ K dV = Q+KAx !
= D ³³ dA
U with space charge without space charge
= D A = H E A.
This means that the magnitude of the electric field strength E between the electrodes is no longer constant; it increases linearly with x and it becomes maximal at the counterelectrode at x = d, Figure 2.36:
E(x) = Q(x)/(H A) = Q/(H A) + x K/H 0
d
x
Figure 2.36: Space charges in the dielectric of a parallel plate capacitor (see fig. 2.35).
(2.329)
The further calculation can be performed in analogy to the steps described above, but it is to be considered that the total stored charge Qtot consists of the positive
2.3 Conduction and Displacement Fields in Homogeneous Dielectrics charge Q on the electrode and the positive charge ³³³ K dV = d A K stored in the dielectric. Qtot
= Q + d·A·K
Thereby the capacitance C = Qtot/V is increased. The potential no longer decreases linearly with x, but is described by a second order polynomial, which can be derived by the integration of Eq. (2.329), Figure 2.36.
In nonuniform fields, e.g. in spherically or cylindrically symmetric fields, space charges can increase or decrease the (geometric) inhomogeneity (nonuniformity) of the field, depending on polarity. Thereby the discharge behavior in nonuniform fields is strongly influenced (“polarity effect”, Section 3.2.5.2). Note: Especially in the insulation of a capacitor consisting of layers with different materials (Section 2.4), the space charges stored in the material and the surface charges at the interfaces can cause a dangerous “recharging” of the electrodes and a “recovery voltage”, even after a temporary short circuit of the electrodes (Section 2.4.4.3). Therefore, capacitors must be shortcircuited permanently.
2.3.2 Analytic Solution of Poisson’s Equation The continuity of the displacement density is described by Eq. (2.31) in integral form. The equivalent in differential form is div D = K.
(2.330)
According to Eq. (2.18) the field strength is E =  grad M and Poisson’s Equation can be derived. It can be used for electrostatic (irrotational) fields: 2
div grad M = M = ' M =  KH (2.331)
39
are expressed differently depending on the coordinate system (Cartesian, cylindrical and spherical coordinates) [2], [3], [6]. Poisson’s Equation is written in Cartesian coordinates (x, y, z) w2M w2M w2M + + w x2 w y2 w z 2
M '
KH (2.332)
in cylindrical coordinates (r, D, z) 2 2 1 w ( r wM ) + 12 wM2 + wM2 r wr w r wz r wD
M '
KH
(2.333)
and in spherical coordinates (r, D, ) ' M
1 w 2 wM (r w r ) + 2 1 ww ( sin wwM ) r2 w r r sin1 w2M + 2 2 wD 2 r sin
KH
(2.334)
Note: The derivation of Eq. (2.332) to (34) is omitted and referred to the literature [2], [3], [6].
The application of Poisson’s Equation shall be exemplified for the uniform field of a parallelplate capacitor without space charges, Figure 2.35. Nevertheless, all the other cases in Section 2.3.1 can be calculated. Example: Uniform field without space charges Step 1: At first, Poisson’s Equation is simplified to Laplace’s Equation (K = 0) which is only dependent on the variable x. Naturally, Cartesian coordinates are used here, with M(x,y,z) = M(x). Now Eq. (2.332) is 2
'M = w
Mwx
2
=  KH = 0 .
Step 2: The simplified differential equation is solved in general form, by two integrations in this case: wMwx
=
k1
und
M(x)
=
k1 x + k2 .
Step 3: The integration constants k1 and k2 are determined from the boundary conditions. From
Note: Poisson’s Equation is called Laplace’s Equation for K = 0.
M(x=0) = V
we obtain
M(x=d) = 0
The differential operators div (divergence), grad (gradient), (nabla, Hamilton’s operator, del operator) and ' (delta, Laplace’s operator)
we obtain 0 = k1d + k2 .
With the solutions k2 = V and k1 = V/d the potential is
V = 0
M(x) = V (1  x/d)
+ k2
and from
40
2 ELECTRIC STRESSES
Step 4: For a given potential distribution, the electric field is defined unequivocally. The vector of the electric field strength E can be obtained by the calculation of the gradient according to Eq. (2.18). In a uniform field with Cartesian (x, y, z)coordinates the result E = grad M = {wMwx, 0, 0} = {U/d, 0, 0} .
gives a constant magnitude of the field strength E = V/d = E0 = const.
q.e.d.
Note: If Poisson’s Equation is evaluated in cylindrical or spherical coordinates, the calculation of the gradient (the field vector resp.) must also be performed in cylindrical or spherical coordinates, Eq. (2.18), [2], [3], [6]. According to the steps described above, the symmetries of the configuration should be used for the simplification of Poisson’s Equation. The general solution of the differential equation gives a general expression for the potential distribution and the constants of integration have to be determined by means of the boundary conditions. The electrostatic field strength is derived from the potential distribution by calculation of the gradient.
2.3.3 Graphical Field Mapping (for Plane Fields) Normally, technical field configurations in high voltage engineering differ more or less from the basic configurations discussed in the former chapters. Therefore it is helpful to draw qualitative distributions of field lines and equipotential lines graphically, i.e. freehand, just by approximation and without any complicated calculations. If some drawing rules are regarded, a field map or field pattern for a plane (twodimensional) configuration can be created. It gives a qualitative impression of the electrical stress, but with appropriate care it is often also possible to roughly determine field strengths and capacitances. Graphical field mapping gives a good impression of the distribution of field lines and equipotential lines. Therefore, it can be used to support basic physical understanding and to perform plausibility checks of numerically calculated field distributions, i.e. to exclude coarse calculation mistakes.
The value of the graphical mapping lies in the rapid creation of a qualitative overview map, which cannot replace a numerical calculation, but which can prepare for and supplement it. Furthermore, graphical mapping requires a thorough analysis of the field geometry. Thereby a valuable and deep understanding of the physical character of the electrical stress is created. The drawing rules are deduced from the properties of field lines and equipotential lines. (Frequently just referred to as “potential lines”). At first, a plane, twodimensional field is discussed, which does not change in the third dimension and can be drawn in the drawing plane, Figure 2.37: 1.) Field lines and equipotential lines are orthogonal (rectangular to each other). 2.) Electrode surfaces are equipotential surfaces (normally reference and high voltage potentials are 0 % and 100 %). 3.) Field lines and electrode surfaces are orthogonal (deduced from 1. and 2.). 4.) The distance a between two equipotential lines is always related to the same potential difference 'V. The distance b between two field lines (or displacement lines) is always related to the same charge 'Q on the electrodes, i.e. to the same displacement flux. From this it follows that the element capacitance 'C = 'Q/'V, which is related to every “box” or element with a length z, is equal for all “boxes” (elements) on the field map:
'C = 'Q/'V = H z b/a = const.
(2.335)
This means that the aspect ratio b/a is equal for all elements: b/a = const. (2.336) The best way for field mapping is to draw square elements, i.e. if b/a = 1 is chosen. The aspect ratio is correct, if the four sides
2.3 Conduction and Displacement Fields in Homogeneous Dielectrics
41
of the square element touch an inscribed circle, Figure 2.37. Traditional tools of graphic field mapping are blank paper, pencil and eraser (rubber); also good choices are simple graphics programs which make it easier to improve the map iteratively. It is advisable to begin with the drawing in an area where the potential distribution is known. The electrode contours give an orientation for the distribution of the equipotential lines. As a first approximation, field lines are drawn orthogonally to the equipotential lines and the electrode contours. The aspect ratios of the resulting boxes have to be constant according to Eq. (2.336). Irregularities with respect to the drawing rules (1. to 4.) indicate how the actual map has to be improved by repositioning of field lines and equipotential lines. In practice there will often need to be a greater number of iteration steps in order to achieve a satisfactory result. The graphical method of field mapping shall be explained for the practically important example of the fields at the edges of a parallelplate capacitor, Figure 2.38 and 2.39: Example: Edge field of a parallelplate capacitor Step 1 (Figure 2.38a): At first, the known potential distribution in the uniform or known part of the field is drawn (1). The further course of the equipotential lines is approximately orientated with the given electrode contours (2).
Note: It is advisable, to start with a small number of equipotential lines only (e.g. lines for 0 %, 25 %, 50 % 75 % and 100 %). The completed map can be further refined by interpolation if necessary. Step 2 (Figure 2.38a): The map is supplemented by field lines rectangular to the equipotential lines, with the aspect ratio b/a = 1. It is advisable to proceed along an electrode contour (e.g. on the high voltage side).
The inscription of circles shows whether the aspect ratios of the boxes differ significantly from the desired value 1 in cases (3). Step 3 (Figure 2.38b): Now the initial map is improved. In this example the distance between the 25 %line and the lower electrode is increased (4). The 75 %
100 %
'V
75 % 50 %
a
b 'Q
'C
25 % 0%
z: Length of the configuration Figure 2.37: Graphic mapping of field lines and equipotential lines for twodimensional fields. line is shifted closer to the upper electrode (inner side and edge), the distance to the outer side is increased considerably (5). It must be taken in to account that the field strength in the electrode edge region must decrease from the upper electrode towards the lower electrode, i.e. the distance of the equipotential lines increases. A check of the aspect ratios and the angles shows that the field map still needs to be improved. Step 4 (Figure 2.38c): The final field pattern is obtained by iterative approximations with respect to the drawing rules.
In the given example it is advisable to start with the inscribing of circles in the region with the uniform field and to proceed towards the regions with nonuniform fields (6). Position and direction of the equipotential lines and the field lines and the diameters of the inscribed circles have to be adjusted iteratively and stepbystep.
The evaluation of a completed field pattern provides approximate information about the location and magnitude of maximum field strength, the field strength profiles along contours and the capacitance to be assigned to the electric field. The field strength for any element of the field pattern is E  'V/a .
(2.337)
'V is the potential difference and a is the distance between two equipotential lines for the considered element (“box”). E is the medium field strength in the element (“box”), its accuracy depends on the accuracy of the drawing.
42
2 ELECTRIC STRESSES
a) Rough approximation
of field lines and equipotential lines
(2)
50 %
75 %
(3)
(1)
25 %
(2)
b) Improved field lines and equipotential lines (5) 75 %
50 %
(4) 25 %
Figure 2.38: Graphical mapping of field lines and equipotential lines for the twodimensional (plane) edge field of a parallelplate capacitor in different stages of iteration:
c)
Further improved field lines and equipotential lines 75 %
50 %
a) A first rough approximation which does not match the drawing rules in many items. b) Improved map according to the mismatch in a former step. c) Further improved map generally matching the drawing rules. For qualitative conclusions, iteration c) is often sufficient.
(6) ..... ooooooo
25 %
2.3 Conduction and Displacement Fields in Homogeneous Dielectrics
Field strengths, which are taken from graphic field patterns, have to be handled with care. In general, accurate quantitative values require a numerical or an analytical analysis if possible.
The whole field volume can be regarded as a series and parallel connection of equal element capacitances 'C, Figure 2.37. The number of parallel branches np and the number of series connections ns can be counted from the field map. According to Eq. (2.335) and with b/a = 1 the total capacitance is Ctot = 'C np/ns = H z np/ns
(2.338)
Often the determination of capacitance is possible with less inaccuracy. Capacitance is an integral quantity and Graphical inaccuracies compensate each other as a result of the integral view of the entire field space. Example: Edge field of a parallelplate capacitor (continued) Step 5 (Figure 2.38c and 2.39): The point of maximum field strength is at the inner side of the electrode curvature. The magnitude of maximum field strength is
43
symmetric fields, which are twodimensional as well. For the example in Figure 2.37, it is now assumed that there is a horizontal axis of rotation at the lower line in the Figure. Thereby the rodshaped elements 'C with the length z are transformed into circular, ringshaped elements with the circumference 2Sr:
'C = H 2Sr b/a Because of 'C = 'Q/'V = const., the aspect ratio of the elements is b/a = const./r .
(2.339)
Therefore, the aspect ratio b/a has to be adjusted depending on r, proportional to 1/r. Thus, the accurate drawing of a field image is much more difficult. Graphical field mapping can also be applied to configurations with several dielectrics (Section 2.4). Additionally to the drawing rules described above, it is necessary to consider the “refraction laws” for field lines and equipotential lines at the interfaces between insulating materials, Figure 2.410 and 2.425.
Emax  'V/amin = 0.25 V /amin. The minimum distance amin between the 100 % and the 75 % equipotential line is nearly half that in the uniform region of the field. Therefore, the field stress enhancement factor is approximately 2. Indeed, the real maximum field strength will be somewhat higher because the field strength is not constant within the smallest square element, and the measurement according to Eq. (2.337) gives a medium value for the element only. A field strength profile along the 100 % electrode contour can be determined from the field pattern with Eq. (2.337), Figure 2.39. The capacitance of the ideal parallelplate capacitor C0 = H A/d has to be increased by an additional edgefield capacitance Cedge: Ctot = C0 + Cedge. Cedge is calculated with Eq. (2.338) for z = 1 m in air and for the region which is displayed in Figure 2.38c (i.e. just the region with the “circles”, but only at the curvature and at the outer side): Cedge
 'C np/nr
= H z np/nr = H z 5/4  11 pF.
The described graphical method can be used for plane twodimensional fields. Nevertheless, it can also be applied to rotationally
s
Outer side Curvature
Inner side
E max
E(s)
E0 s Inner side
Curvature
Outer side
Figure 2.39: Qualitative profile of field strength magnitude along the 100 % electrode contour (coordinate s).
44
2 ELECTRIC STRESSES
For threedimensional fields only rough qualitative drawings are possible without any quantitative information. In general threedimensional field lines do not lie in a drawing plane, they penetrate it normally. Therefore it is not possible to draw the field lines in a plane. A twodimensional field map has to be restricted to the equipotential lines, which are the intersecting lines between the equipotential surface and the drawing plane. Meaningful field patterns can only be calculated with numerical field calculations (Section 2.5). Nevertheless, rough sketches are valuable to support the engineer’s imagination and physical understanding, but they must not be overestimated.
The basic idea of conformal mapping is to transform the x,yplane (together with a given complicated electrode configuration) into a u,vplane, where the electrode configuration can be calculated easily. Afterwards the solution is transformed inversely, back into the x,yplane, Figure 2.310. For this purpose, the geometric x,yplane is regarded as a complex zplane (z = x + jy) and the geometric u,vplane as a complex wplane (w = u + jv). Thereby, the two geometric axes are replaced by a real and an imaginary axis. The so called conformal mapping is performed by a complex function w
=
f(z)
or u + jv =
2.3.4 Conformal Mapping (for Plane Fields) Conformal mapping is a method for the analytic calculation of some important twodimensional highvoltage fields. Note: Conformal mapping was of high importance before numerical field calculation methods were available. Today it is of historical interest mainly: There are only a few important field configurations still based on conformal mapping.
Inverse transform jy
w= f ( z ) Transform z = g (w) jv
z plane
x
f(x + jy).
It maps the points from the zplane onto the wplane. The complex function has two important properties [2], [3], [6], Figure 2.310: x
Figures of finite size may be subject to deformations by conformal mapping, but the angles between curves, and hence the orthogonality of field lines and equipotential lines is preserved, i.e. confomal mapping is isogonal.
x
Figures of sufficiently small size preserve their shape, and infinitesimal elements described by field lines and equipotential lines preserve their aspect ratio during the transformation.
Note: These statements are not valid for the origin, which is a singularity (pole).
w plane
u
Figure 2.310: Conformal mapping of field lines and equipotential lines from the complex zplane into the wplane.
This means that potential fields, which are calculated in the zplane, preserve their potential field character during the transformation onto the wplane and vice versa, Figure 2.310. Nevertheless, the macroscopic field pattern may be deformed. Note: Mathematically, every regular function of a complex quantity f(z) = f(x+jy) fulfills Laplace’s Equation (2.322) for the twodimensional case, i.e. if the space charge K is zero:
2.3 Conduction and Displacement Fields in Homogeneous Dielectrics 2
w fwx
2
2
=
x,yplane (D = 90°) into a plane electrode in the u,vplane (2D = 180°), Figure 2.311.
+ f ´´(z) (wzwy) =
In the u,vplane, the field above a plane electrode is a uniform field and the potential increases linearly with voltage V and with the distance v (k is a constant):
w fwy
+
f ´´(z) (wzwx) f ´´(z) 1
2
2 2
2
+ f ´´(z) j
f ´´(z)
2
=
 f ´´(z)
M = v Vk
= 0 q.e.d.
From
This is the equation for equipotential lines in the wplane. The relation between w and zplane is given by
f(x+jy) = w = u(x,y) + j v(x,y)
w
w fwx 2
2
2
2
2
2
2
2
2
2
=
2
+ w uwy + j w vwy ) =
2
+ j w vwx + w vwy ) = 0.
w uwx + w uwy )
2
2
2
2
2
2
If the curves in the wplane, which are defined by v = const. ~ M, are regarded as equipotential lines (Figure 2.310 right), the function M(x,y) ~ v(x,y) = const. defines the potential distribution in the x,yplane. The orthogonal curves with u = const. can then be regarded as field lines, Figure 2.310. Example: The function w = z jD 2
2 2
j2D
The function w = z = (z·e ) = z ·e doubles the angles D of all complex vectors z emanating from the null point. The function can therefore be used to transform an electrode consisting of two orthogonal walls in the
Inverse transform jy
= (x + j y)
2
2
2
(x  y ) + j x y .
Therefore, the equipotential lines (v = const.) are hyperbolas in the x,yplane, symmetric with respect to the bisecting line between x and yaxis.:
!
This equation can only be fulfilled, if real and imaginary parts are both zero. This means that the functions u(x,y) and v(x,y) are both solutions of Laplace’s Equation.
2
z
u+jv =
2
w fwy
+
w uwx + j w vwx )
2
=
and
it is further concluded that 2
45
M ~ v = x y = const. For the field lines (u = const.) there are hyperbolas symmetric with respect to x and yaxis.: 2
2
u = x  y
= const.
The potential distribution in the x,yplane is
M = vVk = xy Vk. In the x,yplane, the potential of the rectangular electrodes is set to zero (reference electrode). The equipotential line with the diagonal distance a from the origin is selected as a counterelectrode with the potential M = 2 V. The constant k = 2/a is determined with the bound1/2 ary condition M = V for x = y = a2 :
M = x y V 2/a
z = w 1/2
w =
w plane
z plane
2
z2
Transform jv V 0,75 V
a Figure 2.311: Conformal mapping of field lines and equipotential lines for a rectangular electrode: w = z 2
a 90°
a
1,0 V 0,75 V 0,5 V 0,25 V
x
0,5 V 0,25 V 180°
0 u
46
2 ELECTRIC STRESSES
The electric field strength E is the gradient of M: E
=  grad M
E
=  V 2/a
2
= {wMwx, wMwy, wMwz} {y, x, 0}
=
2 V ( x 2 y 2 ) /a
jy
w = c ln z
The magnitude is E
Conductor bundle with 2, 4, 6, ... subconductors [2]
2
x
R
.
r0
In the inner corner of the reference electrode (x o 0, y o 0) there is no longer any field strength, i.e. E o 0. At the surface of the hyperbolic high voltage electrode 1/2 in the axis of symmetry (x = y = a/2 ) the field strength is E = 2 V/a, i.e. twice as high as in a uniform field with the same electrode distance a. However, field strengths increase further outside the axis of symmetry.
Elliptical cylinders [2] jy w = c 1 arcosh ( z /c 2 ) x
The situation close to the axis of symmetry is comparable with a curved conductor (e.g. a tubular conductor) in the corner of a building. Generally it is difficult to find a function which transforms a given configuration into a calculable basic configuration. Therefore a different technique is used: starting from given functions w = f(z), one investigates field configurations that arise in the x, y plane. In this way a large number of technically relevant configurations could be calculated analytically. Meanwhile, any field configuration can be directly calculated numerically (Section 2.5). Therefore, it is not necessary to discuss all of the many special cases that are more or less suitable for conformal mapping; they can be found in the literature [2], [3], [4], [16], [17]. Figure 2.312 shows some calculable configurations and the related transforms. Some are discussed in the following.
Screen grid [2]
jy
x w = c 1 ln (2 sin c2 z ) Edge field of a parallelplate capacitor (Rogowski's profile) [16]
jy
v =S
v=S
a v =0
Example: Conductor bundle
In order to reduce the field strengths at the surfaces of conductors of high voltage overhead lines (for the voltage levels Vm = 245 kV and above), single conductors are normally replaced by conductor bundles.
z =
x
a (w + 1 + e w ) S
Figure 2.312: Examples for twodimensional fields, which can be calculated by conformal mapping. (see the literature).
2.3 Conduction and Displacement Fields in Homogeneous Dielectrics
A conductor bundle consists of n parallel subconductors with the radius r0. They are uniformly distributed on a circle with the radius R, and they have the same potential, Figure 2.312 top. An equivalent radius R´ for a single cylindrical conductor with the same capacitance against a distant counterelectrode is calculated by means of the function w = ln z for small subconductor radii r0 > r0)
E = 0.5·V/r0 .
2.3.5.3 Parallel Line Charges
Some important configurations in high voltage engineering can be calculated by means of line charges with a uniformly distributed charge Q along the line length L. In the following, the electric field in the vicinity of two parallel line charges with equal magnitude but opposite polarity is discussed, Figure 2.321. The potential distribution in the field volume is determined by the superposition of the two potentials assigned to the two line charges. It is a twodimensional field so that consideration of a plane orthogonal to the line charges is sufficient, Figure 2.322. The countercharges and the reference potential MB = 0 cannot be considered to be at an infinite distance as for the spherically symmetric field. Here, infinite potential difference would occur, see Section 2.3.1.3. For calculation purposes finite radii rB1 and rB2 are introduced in order to specify the distances between the charges and the coaxial countercharges. They can be eliminated later on, if counter charges at large distances are assumed, Figure 2.322. The calculation is performed with the assumption and superposition of two cylindrically symmetric fields around the two line charges. The superposition of the potentials M1 and M2, which are assigned to the charges +Q and –Q, is performed at point P. With Eq. (2.318) we find
2.3 Conduction and Displacement Fields in Homogeneous Dielectrics
59
Reference potential, very far away
y
+Q
rB2
a
rB1
L Q
P
z
r2
r1
x
+Q/L
Q/L a
Figure 2.321: Infinitely long line charges in parallel (threedimensional view).
M
M1
+
M2
Q L r B1 Q L r B2 ln ln 2ʌH r1 2ʌH r2 Q L §¨ r B1 r 2 ·¸ ln . ¨ r1 r B2 ¸ 2ʌH © ¹
Figure 2.322: Infinitely long line charges in parallel (sectional view).
It can be shown that the field lines are circles too. They all pass through the intersections of the line charge axes +Q and Q with the plotting plane [2]. This results in a graphical plotting method for a field and equipotential line plot, Figure 2.323: x
At first, a circle with the radius r = a/2 is plotted through the chargeaxis points +Q and Q. The two semicircles describe two field lines.
x
At any point P1, P2, ... the “fieldline circle” and the “equipotentialline circle” intersect orthogonally.
x
Owing to symmetry, all center points M1, M2, ... of the equipotentialline circles are located on the xaxis. Furthermore, the radii M1P1, M2P2, ... touch the fieldline circle tangentially, and the center points are determined from the intersections of the tangents at P1, P2, ... with the xaxis.
x
Additional field lines are plotted as circles with center points on the yaxis.
If the reference potential is assumed to be far away, i.e. if and
r1, r2, a ln(a 2 x) ln(a 2 x)@ 2ʌH wx
º Q L ª 1 1 « 2 ʌH ¬ ( a 2 x) (a 2 x) »¼
2
= a + 2a / (k 1)
(d/2)  r0
ln
The field strength profile E(x) = Ex(x) along the xaxis is derived from Eq. (2.371):
= a + 2b
2
61
º Q L ª 1 1 « 2 ʌH ¬ (a 2 x) (a 2 x) »¼ (2.372) The same result is obtained by direct superposition of the field strengths, Eq. (2.317). Figure 2.325 shows the profiles of potential and field strength along the xaxis between the conductors according to Eqs. (2.371), (72). Within the conductors themselves, the equations of the charge simulation method give false results. The potential within an ideal conductor is constant, the electric field strength tends towards zero. Outside of the conductors, for x > d/2 + r0 and for x < d/2  r0, potential and field strength magnitudes decrease in the outward direction. The field strengths at the outside of the conductors are significantly lower than the field strengths at the inner sides where the conductors are facing each other. For the calculation of capacitance C, the potential difference V is determined as a function of the equivalent charge Q from Eq. (2.371): V =
M(x = d/2 + r0)  M(x = d/2  r0) Q L ª a / 2 d / 2 r0 a / 2 d / 2 r0 º ln « » 2 ʌH ¬ a 2 d / 2 r0 a 2 d / 2 r0 ¼
62
2 ELECTRIC STRESSES
Q L a / 2 d / 2 r0 ln ʌH a 2 d / 2 r0 The capacitance is equal to the ratio C = Q/U: ʌH L a / 2 (d / 2 r0 ) ln a / 2 (d / 2 r0 )
C
(2.373)
With the distance a between the charges according to Eq. (2.370), the capacitance can be written as function of the geometric quantities d and r0: ʌH L
C
ª d ln « « 2r0 ¬«
§ d · ¨¨ ¸¸ © 2r0 ¹
2
º 1» » ¼»
(2.374)
For large distances d and accordingly for small radii r0, i.e. for d >> r0, Eq. (2.374) is simplified: 
ʌH L d ln r0
2.5
5
10
Capprox/C
0.757 0.973 0.996 0.9992
Error in %
24.3
2.7
20
0.4
0.08
I.e. for many electrode arrangements in high voltage engineering, the simplified Eq. (2.375) can be used, if the distance d of the conductors is much greater than the radius r0. Maximum field strength results from Eq. (2.372) at the conductor surface at x = d/2  r0. In order to get an exact solution, Q is replaced by Q = C·V with C according to Eq. (2.374): 2
Note: The deviation of Eq. (2.374) from Eq. (2373) requires some intermediate steps. Thereby it is reason1/2 out in the able to cancel the expression (d/2  r0) argument of the logarithm, and to make the denominator rational by expanding the fraction.
C
d/r0
(2.375)
Note: This approximation can also be derived directly from Eq. (2.373), if the distance a between the charges is assumed to be equal to the distance d between the conductors for large distances d, Eq. (2.370). Therefore, we find for the numerator in the argument of the logarithm a/2 + d/2  r0  d  r0  d. The denominator is
a/2  d/2 + r0 = b + r0  r0,
§ d · ¨¨ ¸¸ 1 © 2r0 ¹
V Emax
ª d 2 r0 ln «« d 2r0 ¬«
º 2 § d · ¨¨ ¸¸ 1» » © 2r0 ¹ ¼»
(2.376) For d >> r0, i.e. for large distances d or small conductor radii r0, Eq. (2.376) is simplified: V
E max 
2 r0 ln
(2.377)
d r0
For thin wires, the inception voltage for corona discharges can be derived, if the inception field strength Ei for discharges is known: Vi

Ei · 2 r0 · ln(d/r0)
(2.378)
The validity limits of Eq. (2.377) and (2.378) result from an error estimation for different ratios d/r0:
as the distance b between line charge and conductor axis is small in comparison with the conductor’s radius r0.
d/r0
5
The validity limits of the approximation Eq. (2.375) result from an error estimation for different ratios d/r0:
Eapprox/E
0.637 0.813 0.904 0.951
Error in %
36.3
10
18.7
20
9.6
40
4.9
2.3 Conduction and Displacement Fields in Homogeneous Dielectrics
63
height h above or beside a conducting plane. This case can be reduced to the former example of parallel cylinders, if the conducting plane is regarded as a plane of symmetry or an equipotential surface with the potential M = 0 and if the arrangement is complemented symmetrically with a second cylinder (image conductor), Figure 2.326. The capacitance C of the arrangement is twice the capacitance C´ of the associated parallel cylinders. With Eq.
Thus, the approximate Eqs. (2.377) and (2.378) for the maximum field strength and for the corona inception voltage are only accurate enough for large ratios d/r0. Therefore, in general the exact solution from Eq. (2.376) must be used. Example 2: CylindertoPlane
A common high voltage electrode arrangement is a cylindrical conductor, which is led at a
y
M = +V/2 M
M = V/2 +Q/L
'M = V
Q/L
M
a /2
d /2
r0
0  d /2
 a /2
M  d /2 + r0 V /2
x
d /2  r0
M (x)
x
V /2 E x (x) E max
E min x Figure 2.325: Parallel cylindric conductors: Potential and field strength profiles along the connecting line of the conductor centre points (xaxis) in the x,yplane. The profiles within the conductors can not be determined from the equivalent charges.
64
2 ELECTRIC STRESSES exceeding 2/3 of the breakdown voltages. Furthermore, the capacitance per unit length of the configuration shall be calculated. In all cases the ratio h/r0 = 10 shall be assumed to be equal.
+Q/L V
h C = 2 C´
d´
E
Solution: Because of the ratio d/r0 = 20, approximate Eq. (2.380) for the maximum field strength will provide an error of approx. 10 % (see above estimate). Therefore, the exact Eq. (2.376) is evaluated: If 2r0 is factored out in the denominator, the equation can be solved for r0. For d and V the terms 2h and V´ = 2V have to be inserted:
2 Vˆ 0.67 Ê D
C = 2 C´ r0
V´
2 (10 1) ln ª10 10 2 1º «¬ ¼» =
Q/L
10 2 1
V /ÊD 0.5540·Û
The capacitance can be estimated from Eq. (2.379) with a small error.
Figure 2.326: Cylindric conductor above a conducting plane. Field calculation by means of a symmetric image charge.
(2.375) and d´= 2h >> r0 the capacitance is C

2ʌH L 2h ln r0
.
(2.379)
The maximum field strength is obtained from Eq. (2.376) or (77), if the voltage V and distance d are replaced by V´ = 2 V and d´ = 2 h >> r0: 
V
V: Voltage Û
10 kV
100 kV
1 MV
Air:
r0 h C/L
2 mm 2 cm 18.5 pF/m
1.9 cm 18.5 cm 19 cm 1.85 m 18.5 pF/m 18.5 pF/m
Oil:
r0 h C/L
0.4 mm 3.7 mm 40.8 pF/m
3.7 mm 3.7 cm 3.7 cm 37 cm 40.8 pF/m 40.8 pF/m
Note: As shown in all the examples with the spherical electrode (Section 2.3.1.2), with the cylindrically symmetrical tubular conductor (Section 2.3.1.3) and with the cylindertoplane arrangement (in the current example) it is also shown here that airinsulated equipment for the MVrange needs insulation distances and radii of curvature of the order of meters.
(2.380)
Much more compact dimensions are possible with electrically strong materials (e.g. insulating oil or sulfur hexafluoride gas SF6).
For the corona inception voltage of a thin wire above a conducting plane we find
Attention: The electric strengths assumed to be constant in these examples for simplicity, are not constant in reality. They depend, for example, on the type and duration of the electric field stress, on the insulating material thickness, on the insulating volume, on the electrode surface, on the inhomogeneity of the field or on environmental influences (pressure, temperature, water content, .... ) for instance.
Emax
Vi

2h r0 ln r0
.
Ei · r0 · ln (2h/r0) .
(2.381)
Example 2a: CylindertoPlane (numerical example)
The diameters and distances of cylindrical conductors above conducting planes shall be dimensioned for application in air (Ê = 30 kV/cm, Hr = 1) and in insulating V = oil (Ê = 150 kV/cm, Hr = 2.2) for the peak voltages Û 10 kV, 100 kV and 1 MV without the field intensities
The capacitance per unit length does not change with the dimensions h and r0 because of the assumption of a constant ratio h/r0, which determines the capacitance, in this example.
2.3 Conduction and Displacement Fields in Homogeneous Dielectrics
65
Example 3: Overhead ground wire
(Shielding effect and field stress enhancement)
ES
Grounded wires above overhead lines are used to protect the phases against direct lightning strikes. Here, it shall be investigated, to what extent the vertical electrostatic field in the atmosphere (i.e. in the air) is influenced by a grounded wire (radius r0, height h above ground), Figure 2.327.
r1 P E0 0
The original field in the air E0 is assumed to be uniform; it is directed in the negative xdirection. The potential is
M1 =
Q 2ʌH L
ln
r2 r1
.
At the surface of the grounded wire (and in the plane of symmetry, i.e. on the ground surface), the sum of the potentials must be zero. This condition can be used to calculate the magnitude of the influenced charge Q:
M1
M
M2
= 0
M
E0 x
r2 Q ln = 0 2 ʌH L r1
For all points on the wire surface, the distances to the equivalent charges +Q and Q are r1  r0 and r2  2h approximately. Because of the large height h >> r0, the equivalent charges are close to the axes of the wire and its image. With x  h the charge is Q
r2
E0·x .
In the ground wire a charge Q is influenced whose field ES is superimposed on the original field E0. The additional field of the charges in the wire against the grounded plane can be calculated from the superposition of the fields associated with Q and with an image charge Q on the xaxis at x = h. According to Eq. (2.367), the potential is
M2
h
x
2ʌH L
E0 h 2h ln r0
.
(2.382)
Image charge Figure 2.327: Distortion of the electric field in air by a conducting overhead ground wire.
The field strength on the xaxis is the derivate of the potential with respect to x according to Eq. (2.372) or it is the superposition of the field strengths according to Eq. (2.317). Q is inserted from (2.382): E x (x)
= E0 +
E +Q
+ E Q
(17)
Q = E0 + ( 1 S H L h  x
(82)
= E0 
E 0 ·h ( h 1 x 2h ln r0
+
1 ) h+x
+
1 ) h+x (2.383)
Note: The discussion of the signs shows that the original field E0 and the additional field of the charges have opposite directions underneath the ground wire (0 < x < h). Above the ground wire (x > h), the field E0 in the air and the field contribution of the upper equivalent charge +Q are superimposed with the same sign; the field contribution of the image charge –Q is in the opposite direction, Figure 2.327.
The field strength at the ground surface (x = 0) is
66
2 ELECTRIC STRESSES
'M ii 'M ia(l)
Ma
'M aa
r0a
'M ai(r)
Ma
y
Mi
+Q
M
r0i
Mi
Q
x
0 a di
c
c
da Figure 2.328: Calculation of eccentric conductors with equivalent line charges in parallel.
E x (0)
= E 0 (1 
2 ). ln 2h r0
(2.384)
Note: For a ratio h/r0 = 1000 the field strength is Ex(0) = 0.74 E0, i.e. there is only a weak shielding of the original field at the ground surface. Improved shielding efficiency is achieved by a screen grid, e.g. by an arrangement of parallel grounded wires at small intervals. At the upper side of the wire, the contribution associated with upper equivalent charge Q predominates according to Eq. (2.382). The contribution caused by the distant image charge Q and the original field E0 can be neglected. With the conditions x = h + r0 and 2h/r0 >> 1 Eq. (2.383) provides E x (h r0 ) 
h / r0 E0 2h ln r0
.
(2.385)
Note: For a ratio h/r0 = 1000 there is a field stress enhancement of E/E0 = 132. In cases of very high field strengths E0, discharges are possible at sharp edges of grounded conductors. Especially during a lightning discharge, a discharge channel propagates from the cloud
towards the ground and causes a very high increase of the local electric field strength in a limited field region. This can be regarded as an increase of the primary field E0 which initiate upward discharges starting from overhead line wires, lightning conductors or other grounded structures. The discharges propagate upwards, meet the downward discharge within a limited range and cause a conducting path to the ground. Example 4: Eccentric tubular conductor
The electric field between eccentric tubular conductors (cylinders) can be calculated with parallel line charges, if the outer and the inner conductor are interpreted as equipotential surfaces in the field of two mirrorsymmetric line charges, Figure 2.323 and 2.328. The cylinder radii r0i and r0a and the lateral offset of the cylinder axes c (eccentricity) are given. The distance a of the equivalent charges and distances di and da of the center points are unknown. Therefore, the Equations (2.370) ff cannot be applied directly. The solution can be based on the fact that the charge distance a is equal for both the arrangement with the large cylinders (r0a, da) and for the arrangement with the small cylin
2.3 Conduction and Displacement Fields in Homogeneous Dielectrics
ders (r0i, di). With Eq. (2.370) and Figure 2.328 we get the following solution 2
a
2
2
= di  4r0i
da  di
2
2
2
= da  4r0a 2
2
2
2
= 4r0a  4r0i 2
2
(di + 2c)  di = 4r0a  4r0i 2
di
2
(2.386)
From this all unknown geometric quantities in Figure 2.328 are determined. The charge distance a is determined from Eq. (2.370), the distance da is da = di + 2c. Instead of a difficult general calculation, a numerical evaluation with specific numerical values is recommended here. Numerical example: It shall be investigated how much capacitance and maximum field strength are changed for an arrangement with eccentric tubular conductors (r0i = 5 cm, r0a = e·r0i = 13.59 cm, c = 1 cm) in comparison with coaxial configurations. From Eq. (2.386) we get di = 158.73 cm. From this da = 160.73 cm and a = 158.41 cm are derived. The maximum field strength at the surface of the inner cylinder can be determined from Eq. (2.376) with d = di and r0 = r0i, if the voltage V is interpreted as potential difference 'Mii between the two inner cylinders. =
'Mii / 32.45 cm
(*)
The potential difference 'Mii has to be related to the potential difference 'Mai(r) between the outer and inner cylinders on the right side: The xaxis intersects the inner cylinders at xi = ±(di/2  r0i) = ±74.37 cm and the outer cylinders at xa = ±(da/2  r0a) = ±66.78 cm. For points xi and xa on the negative xaxis the potentials can be calculated with Eq. (2.371):
Mi
=
'Mii
I.e.:
2
3.458·Q/(2SHL)
=
2.464·Q/(2SHL)
From this, the potential differences are given:
2
= (r0a  r0i  c )/c
Emax
Ma
67
=
(3.458 + 3.458)·Q/(2SHL)
=
6.916·Q/(2SHL)
'Mai(r) = =
( 2.464 + 3.458)·Q/(2SHL) 0.994·Q/(2SHL)
The ratio of the potential differences is 'Mii/'Mai =
6.958 .
The maximum field strength is calculated from Eq. (*): Emax
=
'Mai 6.958 / 32.45 cm
=
'Mai / 4.664 cm .
In the cylindrically symmetric case, maximum field strength according to Eq. (2.322) is E(cyl)max
=
'Mai / 5 cm .
The field stress enhancement caused by the eccentricity c = 1 cm is 7.2 %: Emax/E(cyl)max =
1.072
Note: The capacitance Cai between the inner and the outer cylinder can be calculated, if the capacitances Cii and Caa between the cylinders of the same size are calculated with Eq. (2.374). Cii can then be regarded as a series circuit consisting of Cia, Caa and Cai, Figure 2.328. From this the magnitude of the equivalent charge Q = Cai·'Mai is also determined. Eq. (2.371) and (72) then allow one to calculate potential and field strength profiles along the xaxis.
Example 5: Threephase overhead line (“Working capacitance”)
A threephase overhead line is a so called multiphase system, consisting of a number of parallel cylindrical conductors with different potentials and insulated against each other. The calculation of multiphase systems is possible by means of equivalent line charges and their image charges. For a detailed analysis the basic literature can be consulted [2], [4].
68
2 ELECTRIC STRESSES
As an example, a threephase overhead line connected to a threephase AC voltage system shall be considered (complex r.m.s. values of the phase voltages: V10, V20, V30). Perfect symmetry of the voltages, the conductor properties (line parameters per unit length) and the currents (I1, I2, I3) is assumed. During the calculation of threephase systems, lines and cables are described by line impedances determined by series resistances, series inductances, parallel capacitances and parallel conductances. The charge simulation method allows the calculation of a socalled “working capacitance” of a threephase system. This is not the capacitance between oppositely charged conductors, such an arrangement does not exist in a threephase system. The working capacitance Cb is defined by the singlephase capacitive charging current IC1 in a symmetric threephase overhead line without load. In the positivesequence network (i.e. in a transformed singlephase equivalent circuit) the following relationship is established: IC1 =
jZ Cb · V10
(2.387)
Physically, the charging current IC1 is not only fed from the displacement field that is associated with the phasetoground voltage V10. The fields between the considered phase L1 and the other phases L2 and L3 cause additional displacement currents to be coupled in, i.e. there are additional influences of the phasetophase voltages V12 and V31, Figure 2.329. In order to calculate with the simple Eq. (2.387) despite this, it is necessary to define a working capacitance Cb whose magnitude takes into account the influence of all interferences. Note: The simple assumption of a singlephase equivalent circuit, consisting solely of the socalled positivesequence network, and considering capacitive couplings by the magnitude of the working capacitance, is only valid in the case of perfect symmetry. This means that the threephase system has to be built symmetrically and that it has to be operated symmetrically too.
From the physical viewpoint, the singlephase equivalent circuit (the socalled positivesequence network) is not identical with the phase L1 alone. Capacitive and magnetic couplings to the neighboring phases are taken into account by the magnitudes of the working capacitances and working inductances. In the case of asymmetric threephase systems, the three coupled circuits L1, L2 and L3 are transformed into three decoupled circuits (positivesequence network, negativesequence network and zerosequence network) in order to allow a simpler and clearer calculation (method of symmetrical components [20]). A working capacitance can no longer be specified because the condition of symmetrical voltages and fields is no longer fulfilled. In the special case of perfect symmetry, the singlephase equivalent circuit is identical with the positivesequence network. According to Eq. (2.387) 1/(jZ Cb) = V10/IC1 is the “positivesequence impedance” of the unloaded line (resistive and inductive components are neglected).
The working capacitance Cb shall be calculated from the ratio of the charge q1 on line L1 to the phase voltage v10. The quantities q1 and v10 are the instantaneous values of the time variant quantities. The charging current iC1(t) or IC1 has to carry the charge q1 to and from the conductor. The influence of the ground is taken into account by image charges, Figure 2.329. The voltage v10 is equal to the potential M1, which is established by the superposition of the contributions from all equivalent charge pairs:
M1 = M1(q1,q1) + M1(q2,q2) + M1(q3,q3) For overhead lines, the charge distances a12, a13, D12, D13 and D11  2h are very large in comparison to the conductor radius r01. The potential at the surface of conductor L1 is determined with Eq. (2.367):
M1
q D q1 2h q D ln 1 2 ln 12 3 ln 13 2 ʌHL r01 2ʌHL a12 2ʌHL a13
The distance from any charge (with the exception of q1) to the surface of conductor L1 is approximately equal to the charge distance to the charge q1. The distance from q1 to the conductor’s surface is approximately equal to r01.
2.3 Conduction and Displacement Fields in Homogeneous Dielectrics
I C1
q 2 M2
L2
V 12 L1
69
V 23 V 31
a12 a13
M1 q 1
L3
V10
q 3 M3
h1
Threephase AC system above ground with the reference arrows for the complex r.m.s. values of the voltages and currents (top).
M
D12
D13  q3
 q1
Arrangement of equivalent line charges and image charges for the determination of the socalled "working capacitance" (right).
 q2
Figure 2.329: Calculation of the "working capacitance" for a symmetric threephase system with the charge simulation method. The influence of the ground is taken into account by image charges.
In a geometrically perfectly symmetric system, the equivalent distances are equal to each other. In practice, cyclic exchanging of the phase positions compensates for the asymmetries: h1
= h2
= h3
= h
r01
= r02 = r03 = r0
D12 = D23 = D31 = D a12
= 2h
= a23 = a31 = a
1 ª D Dº «q1 ln q2 q3 ln » 2ʌHL ¬ r0 a¼
In a symmetric threephase system the sum of the charges is zero: q1 + q2 + q3
=
This gives the condition q2 + q3
=
 q1 .
For the potential M1 it follows that
q1 ª D Dº ln » «ln 2 ʌHL ¬ r0 a¼
M1
q1 a ln r0 2 ʌHL
.
From this the working capacitance is derived:
With this the expression for the potential of conductor L1 is simplified:
M1
M1
Cb
q1
M1
2 ʌHL a ln r0
(2.388)
It is worth noting that the working capacitance, which could possibly (but misleadingly) be understood as capacitance between conductor L1 and ground, does not depend on the distance h between conductor and ground. The working capacitance is exclusively dependent on the distance a between conductors and on the conductor radius r0. For overhead lines with conductor bundles, the radius r0 is to be replaced by the much larger equivalent radius R´ according to Eq. (2.340), i.e. it gives a greater working capacitance than
70
2 ELECTRIC STRESSES
L2
L3 K 23 K 12
K 20
L1
K 31
K 10
K 30
Note: Because of the high capacitive reactive power, economic AC power transmission with cables is normally limited to lengths of a few 10s of km.
The measurement of the working capacitance Cb is performed via partial capacitances, Figure 2.330. The charging current IC1 is constituted from the superposition of all displacement currents that are coupled into L1 and which are calculated from the capacitance coefficients K1j and the associated potential differences V1j:
Figure 2.330: Coupling and ground capacitances (capacitance coefficients) of a threephase system.
for single conductors. It can be calculated from Eq. (2.388). If several threephase AC systems are operated in close proximity to each other, e.g. on the same tower, the working capacitance is influenced. The former calculation for M1 has to be complemented with further terms associated with the additional AC conductors. Owing to the relatively large distances, they are generally of minor importance. Generally, the charge simulation method also allows one to calculate the working capacitance of a threephase cable or a threephase gasinsulated line, for which the distances between the conductors are comparable with the conductor’s radii [2]. In practice, values measured and specified by manufacturers are used, but they are only valid for a specific product. High and very high voltage cables are designed as singlephase cables with cylindrically symmetric fields, so that the working capacitance corresponds to the linetoground capacitance according to Eq. (2.320). The typical magnitude of the working capacitance per unit length is approximately Cb/L  10 nF/km for overhead lines and Cb/L  120 nF/km for singlephase polymer cables (with Hr = 2.2 and Ra/Ri = e , Eq. (2.320)). For oilimpregnated paper cables and for cables with a smaller radius ratio Ra/Ri (e.g. medium voltage cables with a large conductor crosssection), significantly higher values can occur.
IC1 = jZ[K10V10 + K12V12 + K31(V31)] Because of the symmetry, K12 = K31: IC1 = jZ[K10V10 + K12(V12  V31)] By means of a vector diagram it can be shown that V12  V31 = 3 V10 in a symmetric threephase system. Thereby we get IC1 = jZ [K10 + 3·K12] V10 . The comparison with Eq. (2.387) gives the working capacitance: Cb
=
K10 + 3·K12
(2.389)
The capacitance to ground K10 and the coupling capacitance K12 are determined from two measurements: During the first measurement, L2 and L3 are grounded, i.e. K20 and K30 are shortcircuited. *
The measured capacitance C between L1 and ground is *
C = K10 + K12 + K31 = K10 + 2·K12 . During the second measurement the conductors L1, L2 and L3 are connected to each ** other. The measured capacitance C between L1L2L3 and the ground is now **
C
=
K10 + K20 + K30 = 3·K10 .
For the partial capacitances we find **
K10 = C /3 and
*
**
K12 = C /2  C /6 .
2.3 Conduction and Displacement Fields in Homogeneous Dielectrics
From this the working capacitance can be expressed as a function of the measured values * ** C and C : Cb =
*
(2.390)
For the calculation of field strengths, the magnitude of the equivalent charges can be determined with Eq. (2.388). The calculation is performed at a specific point in time that is characterized by specific instantaneous values of the potentials (or phasetoground voltages)M1, M2, M3 and by the instantaneous values of the associated equivalent charges q1, q2, q3, Figure 2.331. Nevertheless, the analytic calculation of field strengths from the gradient of the resulting potential (or from the vectorial superposition of the different field components) is very complex. Furthermore, the result is only valid for the considered instant. For other points in time, other field distributions, i.e. other locations, directions and magnitudes of the maximum field strength, are produced. Note: The maximum voltage difference between the phases L1 and L2 is given for a sinusoidal voltage v10(t) o = sin Zt at the time point Zt = 60 with magnitude 3 · 2 ·Vph. The potential of phase L3 is zero at this time. If the conductors are arranged in a triangular configuration (i.e. in an equilateral triangle) and if ground
L2
M  Vph 2
q1(60 ) = q2(60 ) = Cb·'M/2 o
o
L1 and L2 can be approximated as parallel cylindrical conductors, Figure 2.325.
2.3.6 Similarity Relations, Field Efficiency Factor (Schwaiger’s Utilization Factor) In the above sections, the common analytical methods for the calculation of electrostatic (and quasistatic) fields were described. Of course, the high voltage problems and examples discussed are not complete, they are more exemplary in character, in order to introduce the methods and the ways of thinking. It is clear that there is no standard procedure that always gives the desired result. It is often necessary to have a good deal of intuition, training and experience in order to find the best calculation methods and appropriate simplifications.
Such calculation results are given in the basic literature on electrical engineering theory, e.g. for capacitances of different electrode configurations [2].
Z t = 60°
q2=  q1
and
q3(60 ) = 0
It is a substantial improvement for a quick and practical solution if one can avoid doing one’s own complex calculation, i.e. if already available results can be used.
M q3 = 0
"Snapshot" at
influences are neglected, the maximum field strength is located at the conductor surfaces of L1 and L2 close to the connecting line between these two phases, Figure 2.331. Because of o
**
3·C /2  C /6
L3
71
q1
E
L1
M
M + Vph 2
Figure 2.331: "Snapshot" for the instant of maximum field strength at the surfaces of L1 and L2 (influence of the ground is neglected).
In high voltage engineering, the central question has also to be answered: “What is the maximum field strength in the given insulation arrangement?” The result can be specified independently of the applied voltage, if the maximum field strength Emax is given as a multiple of the mean field strength E0 between the electrodes.
72
2 ELECTRIC STRESSES
p = f (geometry) = f (s, r)
E0 is equal to the uniform field strength in a parallelplate capacitor with the same electrode distance s: 1 (2.391) E max = K E0 E0 can also be regarded as the mean field strength between the electrodes: P2
Emean =
1 ³ E dx s P1
=
V s
=
E0
The maximum field strength for a given voltage V is determined from Eq. (2.391) by inserting E0 = V/s. The factor K = E0/Emax is the field efficiency factor or utilization factor according to Schwaiger [21], it describes the “degree of uniformity” of the field. The inverse quantity 1/K is referred to as the degree of nonuniformity. In a uniform field Emax = E0 and the field efficiency factor is K = 1. In a very strongly nonuniform field Emax >> E0 and the field efficiency factor or utilization factor is K 0.6 (or Kcyl. > 0.6). For stronger nonuniform fields
74
2 ELECTRIC STRESSES
with smaller field efficiency factors, Figure 2.334 can only be used for rough approximations.
Thus
Example: Sphere gap
From Figure 2.334 the field efficiency factor for the equivalent arrangement with rotational symmetry
The maximum field strength in a sphere gap with r0 = 0.2 d shall be estimated (see Section 2.3.5.2, example “sphere gap”).
Krot
At first, the field efficiency factor of an equivalent plane configuration with the same sectional view shall be determined. It is an arrangement of two parallel cylindrical conductors with r = r0 and with the electrode distance (flashover distance) s = 0.6 d = 3 r. From the charge simulation method we obtain with Eq. (2.376)
Emax(plane)
=
1.462 V/(d  2r0)
=
1.462 E0 s/(3 r0)
=
1.462 E0 .
Kplane =
1/1.462

=
0.684 .
0.48
is taken. As expected, the arrangement is significantly less uniform. The maximum field strength
Emax(rot)

V/(s·0.48)
=
2.1·V/s ,
is in good agreement with Emax = 2.21·V/s, calculated with the charge simulation method in Section 2.3.5.2 (sphere gap example).
It can be seen from the above numerical example that Figure 2.334 and Eq. (2.395) can be useful tools for the calculation of rotationally symmetric arrangements, if the field efficiency factor of the equivalent plane arrangement can be determined easily. Nevertheless, the method is only an approximation.
Field efficiency factor (concentric spheres) 1.0
2.3.7 Measurement of Stationary Conduction Fields
0.9 0.8
Normally, the electric fields to be determined cannot be measured directly, or there are no suitable measuring methods (see Chapter 6). Therefore, we are dependent on the indirect determination of stresses by calculation.
0.7 S p h e r e
0.6 0.5 0.4 0.3 0.2 0.1
Region of a generally accepted approximation [22]
0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Field efficiency factor (concentric cylinders) Figure 2.334: Comparison of the field efficiency factors of plane and rotationally symmetric electrode arrangements for the example of f cylindrical and spherical capacitors.
In addition to the described analytic methods, procedures were established for the pointbypoint measurement of static conduction fields, in order to determine complex potential distributions. In practical applications, these methods are nowadays largely replaced by more flexible and more accurate numerical field calculation methods. Nevertheless, the analogy between steadystate conduction fields (at DC voltage) and quasistatic (slowly vaying) displacement fields (at AC voltage) is of basic importance and of great educational value.
2.3 Conduction and Displacement Fields in Homogeneous Dielectrics
because of its (residual) conductivity. A stationary conduction field will inevitably develop.
2.3.7.1 Analogy between Dielectric Displacement Field and Static Conduction Field
The determination of potential fields by the measurement of static conduction fields is based on the analogy with the slowly changing dielectric displacement fields, see also Section 2.1.4. This means that permittivity H and displacement density D have to be replaced by the conductivity N and the conduction current density J, Eq. (2.119) and (20): D = H·E
is equivalent to
75
J = N·E
Nevertheless, the electrostatic field caused by charges is a good approximation for slowly changing displacement fields in insulating materials with very low (residual) conductivity, if the conduction current density J can be neglected in comparison with the displacement current density wD/wt,see also Section 2.1.4.4.
Basically, there are two methods of interest for the measurement of conduction fields, twodimensional measurement on semiconductive paper and threedimensional measurement in semiconductive liquids.
(2.396) For both kinds of fields, the electric field strength E is determined from formally identical equations. Instead of the charge Q as the source of the field, the current I is injected into the arrangement: Q = ³³ D dA is equivalent to I = ³³ J dA (2.397) The electric field strength E and the derived quantities, potential M and voltage V, are equivalent for the two different kinds of fields. In particular, Laplace’s Equation (2.331) ff without space charges and current sources in the insulating volume
'M = 0
2.3.7.2 Measurements on Semiconductive Paper (“Resistive Paper”)
Twodimensional conduction fields can be generated with the aid of semiconductive paper by means of conductive electrodes, which are pressed onto the paper or which are painted with conductive varnish. The edge of the paper must be far away from the field region of interest in order to avoid field distortions by the artificial boundaries. After the application of a DC voltage to the electrodes, the measurement of potential magnitudes is performed for all points of interest by means of a metal probe, which is put on the paper, point after point.
(2.398)
is equally valid in both cases. This means that the described field calculations for the electrostatic fields caused by charges are also valid for static conduction fields. Conversely, potential distributions that were measured in static conduction fields are valid for quasistatic displacement fields generated by charges. Note: The fields, which are calculated with fixed (static) charges, are often referred to as “static electric fields”. However, this is an auxiliary picture only, since the static case cannot exist in a real insulating material
Normally, the measurement is performed in a bridge circuit with a null indicator in order to achieve a measurement without any reaction. During the measurement it is useful to adjust the bridge to a distinct potential value so as to enable following the associated equipotential line on the surface of the paper by means of the probe. By suitably marking the points, an equipotential plot is generated.
Measurements on semiconductive paper allow us to consider different conductivities N (and different permittivities H) by stacking papers in different numbers. However, good contact between the sheets is required.
76
2 ELECTRIC STRESSES
2.3.7.3 Measurements in Semiconductive Liquids (“Electrolytic Tank”)
Any threedimensional field arrangement can be measured (field plotter) pointbypoint by lowering the electrode arrangement into a semiconductive liquid (e.g. in a waterbased electrolyte). In principle the original electrode itself can be investigated, if an electrolytic tank of sufficient size is available.
x
The movement of charge carriers in the electric field causes a socalled conduction field. This is described by the socalled (residual) conductivity N of the insulating material.
The field limitations at the basin walls must not have any influence on the field in the region of interest. Therefore, basin dimensions have to be large in many cases.
In Section 2.3, the fields in homogeneous dielectrics were calculated with constant permittivities H and constant conductivities N, i.e. it was assumed either that there was a perfectly homogeneous dielectric in the field volume, or that there was absolutely no matter (perfect vacuum). Dependences on environmental parameters (e.g. temperature), field dependences (nonlinearities) and dependences on direction (isotropy) are not considered.
The simulation of different permittivities with liquids of different conductivities, which must be in contact at their interfaces without any mixing, is not readily achievable.
Under these conditions, there is absolutely no influence of the material parameters H and N on the potential distribution and on the magnitude and direction of the electric field E.
A threedimensional field pattern requires a large quantity of data to be measured. Therefore an automatic measurement process with positioning of the measurement probe (“field plotter”) is recommended.
Nevertheless, in reality the field quantities D and J depend on material properties. Thereby the capacitance C of the electrode arrangement
Of course, the probe that is immersed inserted in the liquid must be insulated against the liquid, with the exception of actual measurement tip.
2.4 Conduction and Displacement Fields in Inhomogeneous Dielectrics Matter in the electric field has a significant influence on the formation of the field and potential distribution:
x
Additional fields are caused by polarization, i.e. by displacement of charge carriers (ions, charged atoms, molecules and molecule groups) or by orientation of existing dipoles in the electric field. This is described by the permittivity H of the insulating material.
C =
Q U
=
³³ D d A = U
E dA H ³³ U
(2.41) is also dependent on the permittivity H. In addition, the volume resistance R and the conductance G of the electrode arrangement is a function of the conductivity N: G=
I 1 ³³ J d A = = = U U R
E dA N ³³ U
(2.42) Note: From these equations the “selfdischarging time constant” of the insulating material is derived as
Wd =
RC =
H N
(2.43)
(see also Section 2.1.4.3, example of the selfdischarging of a dielectric). I.e. for a given capacitance C the resistance R can be calculated directly, if Wd is known.
Homogeneous insulating materials can only be found in some areas in a high voltage engi
2.4 Conduction and Displacement Fields in Inhomogeneous Dielectrics
neering insulation system, e.g. as air insulation in overhead lines, as pressurized gas insulation in enclosed switchgear (GIS) or as cable insulation in coaxial cables. Insulation systems in service always need further insulation components, e.g. string insulators (overhead lines), post insulators (enclosed switchgear) or cable terminations (cables). Generally, it is not sufficient to regard the homogeneous insulation parts only, also the parts with different insulating materials must be considered. Complex insulation systems (e.g. in transformers, bushings, cable fittings) always consist of a number of components with different insulating materials (e.g. oil, impregnated paper, impregnated pressboard, polymeric films, porcelain, epoxy resin, silicone or air). Field and potential distributions in arrangements with a number of insulating materials can differ significantly from field and potential distributions in homogeneous arrangements. Especially at the interfaces, there are refractions of field vectors, refractions of equipotential lines and discontinuities of field quantities. In the following the physical reason and the mathematical description of polarization and conductivity in insulating materials is discussed (Section 2.4.1). This allows one to calculate the basic insulation structures with interfaces orthogonal, parallel and inclined to the field direction (Section 2.4.2). The use of analytical field calculation methods for insulating systems (Section 2.4.3) allows the calculation of some important special cases, e.g. for layered capacitor insulations, coated electrode surfaces, barrier systems, ruptures and slots, bubbles and voids, and for triplepoints and interstices at the electrode surfaces. At first, the discussion refers to the quasistatic dielectric displacement field (for an AC voltage) and to materials with different permittivities H. Because of the analogies described in Section 2.3.7.1 the results can be transferred to
77
the stationary conduction field (for a DC voltage) and to materials with different conductivities N (Section 2.4.4).
2.4.1 Conductivity and Polarization In most cases, the atomic structure of matter, i.e. the presence of charged protons and electrons, cannot be detected directly because of a statistically uniform distribution of the charges. They are either mobile (free) or immobile (fixed). 2.4.1.1 Conductivity
The forces of the electric field accelerate mobile charges and impacts slow them down. Statistically averaged, there is constant drift velocity v and a constant current density J, which are proportional to the electric field strength E [24], [25]. The Material Equation (2.120) describes this relation with the proportionality coefficient N (conductivity): J =
N·E
(2.44)
Note: In gases, the linear relation is no longer valid for high field strengths. At first, there are saturation effects and then, the current increases again because of the production of further charge carriers by impacts. (see Chapter 3).
In liquid and solid insulating materials, Eq. (2.44) can often be used as a good approximation. Depending on the type of the mobile charge carriers, ion conductivity and electron conductivity are distinguished. Conductivities of insulating materials strongly depend on the materials used, impurities, manufacturing processes and service conditions (e.g. on temperature, sometimes also on stress duration and field strength). For example, conductivities often increase exponentially with the temperature. The differences between different insulating materials can be many orders of magnitude. A more accurate assessment follows in Chapter 4.
78
2 ELECTRIC STRESSES
The reliability of a field calculation for a stationary conduction field (i.e. for a steadystate DC voltage) depends very strongly on the reliability of the conductivity values used. For practical applications, special attention must be given to the determination of relevant conductivity values.
E Atom
Polarization by deformation: 1. electron polarization 2. atom polarization
2.4.1.2 Polarization
The forces of the electric field can displace immobile positive and negative charge carriers against each other, and polarization of the insulating material is caused, Figure 2.41. There are a number of different polarization mechanisms [24], [25]:
x
x
x
x
x
The displacement of the negative electron shell relative to the positive nucleus deforms the atom. It is called electron polarization or polarization by deformation. The displacement of atoms carrying different charges deforms molecules. It is called atom polarization or polarization by deformation as well. The displacement of differently charged lattice elements in a crystal lattice causes the lattice polarization. The orientation of polar molecule groups, molecules or particles (socalled electric dipoles) is called molecular polarization or orientation polarization. Furthermore, the accumulation of charge carriers at macroscopic or microscopic interfaces between materials with different conductivities causes polarization of the dielectric, i.e, the socalled interfacial polarization.
The influence of different polarization processes is always the same: From the superposition of many dipole fields, an additional electric field EDip is generated, which is superimposed on the original field E0 of the same arrangement without insulating material (“vacuum field”), Figure 2.42b:
E
Crystal lattice
Lattice polarization
Polar molecules (dipoles)
E
Molecular polarization Orientation polarization
Figure 2.41: Polarization of insulating materials by the forces of an electric field (right).
E =
E0 + EDip
(2.45)
The dipole field, generated by the displaced charges, is oppositely directed to the original vacuum field. Therefore the magnitude of the resulting field is E =
E0  EDip .
(2.46)
The physical relations shall be explained by means of a thought experiment: An insulating material is inserted into a capacitor with the charge Q, Figure 2.42a and 2b. Thereby the charge Q on the electrodes is not changed, if the capacitor is not connected to an external voltage source, i.e. constant
2.4 Conduction and Displacement Fields in Inhomogeneous Dielectrics
Q
Figure 2.42b: Additional electric field caused by the polarization of a dielectric for a given constant charge Q.
Q0
E0
Figure 2.42a: Electrostatic field in vacuum.
Figure 2.43a: Electrostatic field in vacuum.
Q = const.
Figure 2.43b: Binding of additional charges on the electrodes by polarization of a dielectric at constant voltage.
EDip
Q
E0
charge Q = D·A and constant dielectric displacement density D =
H0·E0 =
const.
are assumed. With Eq. (2.46) D is D = =
H0·(E + EDip)
H0·E + P .
(2.47)
The fraction H0·E is associated with those charges on the electrode, which are not compensated by the polarized charges in the insulating material. Accordingly, they generate an electric field E which is reduced in comparison with E0, see also Eq. (2.45) and (6).
E0
V = const.
Q
E = E0
Usually, the influence of the polarization, i.e. the influence of the insulating material, is described by a factor Hr , the socalled relative permittivity (relative dielectric constant). Thus, the general Material Equation or the Constitutive Relation (2.12) and (19) is defined: D =
H0·E + P.
The term P = H0·EDip is referred to as (di)electric polarization. It has the same dimension as the electric displacement density D. The vector P =  H0·EDip can be seen as the fraction of the displacement density D, for which the electric field is compensated by the polarized charges. Generally the displacement density is D =
79
H0·Hr·E
(2.48)
The absolute permittivity of vacuum H0 (electric constant) and the relative permittivity Hr are often combined as permittivity H (dielectric coefficient/ constant):
H =
H0·Hr
(2.49)
From the equality of the Equations (2.47) and (8) the polarization P is derived: P =
H0·(Hr  1)·E
(2.410)
In vacuum there is no polarization, i.e. P = 0 and Hr = 1. In the presence of matter we always find Hr > 1. According to Eq. (2.41), the insertion of a dielectric material causes an increase of capacitance:
80
2 ELECTRIC STRESSES
C =
Hr·C0
tivities. Some values are Hr = 3.5 for polyvinyl chloride (PVC), Hr = 3.5 ... 4 for epoxy resin (EP), Hr = 5 for castor oil and up to Hr = 7 for cellulose fibers.
(2.411)
Note: Up to now it was assumed that a capacitor both without and with a dielectric material carries a defined constant charge Q. In this case, the insertion of the dielectric is associated with a polarization that reduces the field strength E = E0/Hr and the capacitor voltage V, Figure 2.42.
x
Similar reasoning can also be performed for a capacitor with a constant voltage V and a constant field strength E, both sustained by an external voltage source. In this case, the insertion of a dielectric is associated with a polarization that binds additional charges on the electrodes in addition to the existing electrode charge Q0, Figure 2.43. The additional charges must be supplied by a current from the connected source. The increase of the charge Q on the electrodes corresponds to the increase of the displacement density D =
H0·Hr·E =
Hr·D0 .
(2.412)
Then the polarization P in Eq. (2.47) can be interpreted as the displacement density, which is associated with the additional charges that are bound on the electrodes.
The values of the relative permittivities depend strongly on the relevant polarization mechanisms, Fig 2.44. In the following some typical values (for room temperature and power frequency f = 50/ 60 Hz) are discussed:
x
In a perfect vacuum, there is no polarizable matter. Therefore the permittivity is Hr = 1.
x
In gases, there is little matter in comparison with liquids and solids, and the atoms or molecules do not have a polar character. Because of electron polarization there is a small, often negligible increase of the relative permittivity. For ambient air we find Hr = 1.0006.
x
x
Materials with symmetric, nonpolar molecules have comparatively small permittivities, caused by electron, atom or lattice polarization. For mineral oil and for polyethylene (PE) the relative permittivity is approximately Hr = 2.2 to 2.3. Asymmetric and more complex molecules often have high dipole moments. Because of molecular polarization (orientation polarization) there are higher relative permit
Liquids with polar molecules of high mobility have very high permittivities because of molecular polarization (orientation polarization). We find Hr = 40 approximately for glycerin and Hr = 81 for water. Note: Both water and glycerin, have a comparatively high ionic conductivity. Therefore, they can be used as dielectrics for very short impulse stresses only.
x
Extreme relative permittivities Hr > 1000 can be observed in socalled ferroelectrics. Close to the transformation temperature of a crystal structure the binding conditions can change so as to cause a socalled “polarization catastrophe”, i.e. an extreme increase of the permittivity, under the influence of the electric field [25]. This effect is strongly dependent on temperature and field strength; it occurs only in the direction of certain crystal axes. For barium titanate Hr = 3000 ... 7000 approximately.
N N
H
O
H
H
H
C
C
H
H
H
Cl
C
C
H
H
Symmetric nitrogen molecule (electron polarization only). Strongly polar and very mobile water molecule (orientation polarization). Symmetric polyethylene chainmolecule without dipole moment (no orientation polarization). Asymmetric polyvinylcloride chainmolecule with strong dipole moment (orientation polarization).
Figure 2.44: Examples for polarization mechanisms in insulating materials.
2.4 Conduction and Displacement Fields in Inhomogeneous Dielectrics
Permittivities are not constant quantities; they vary mainly with temperature T and frequency f of the electric field, see Figure 2.45 and Section 4.2. With increasing temperature the mobility of given dipoles increases on the one hand, and on the other hand the Brownian motion and thermal agitation cause an increasing destruction of dipole orientation by collisions. Therefore, an increasing temperature can be associated with an increasing relative permittivity Hr at first, because of the increasing mobility of the dipoles formerly “frozen” at lower temperatures. This is often accompanied by a structural change of the insulating material. Further increasing temperatures then result in decreasing relative permittivities, Figure 2.45 (top) and Figure 4.213. With increasing frequency, the polarization is influenced by the mass inertia and interaction of the dipoles, which is maximal for the orientation of larger dipoles and minimal for the electron polarization. With increasing frequency, the dipoles cannot follow the field changes without delay, because of their mass inertia. Therefore, the relative permittivity is strongly dependent on frequency (dispersion): Generally Hr decreases with increasing frequency in steps, which are associated with the stepwise dropout of different polarization processes, Figure 2.45 (bottom), 4.23 and 4.213. Note: Similar to the resistive losses in a conduction field (current losses), polarization losses (dissipation, dielectric losses) occur during the polarization process. These losses are caused by collisions and energy dissipation during the repetitive reorientation of the dipoles with the frequency of the applied field. At low frequencies, the polarization losses are small, because of the low repetition rate. At high frequencies, there is no polarization any more and no dissipation consequently. Maximum losses are produced in the range of the transition frequency, Figure 2.45 bottom, see Chapter 4. For sinusoidal AC fields the dielectric displacement current and a fictitious loss current (describing the losses both by conduction current and by polarization) can be described in frequency domain by a complex relative permittivity. The real part equals Hr and the imaginary part describes the losses, see Section 4.2.4.
81
2.4.2 Multidielectric Arrangements For multidielectric arrangements, special boundary conditions for field quantities of slowly changing fields at dielectric interfaces can be derived from Maxwell’s Equations (Section 2.4.2.1). Multidielectric arrangements with interfaces orthogonal, parallel and inclined to the field direction are discussed for the dielectric displacement field, which is normally assumed for alternating fields in insulating materials (Section 2.4.2.2 to 2.4.2.4). The stationary conduction field at DC voltages is discussed analogously in Section 2.4.4. 2.4.2.1 Boundary Conditions at Interfaces
The interface between two different insulating materials is considered, Figure 2.46. From the integration of the electric field strength E along a very small closed path P1P2P3P4P1 on both sides of the interface, Faraday’s law gives according to Eq. (2.132)
Hr
Transition region with polarization losses (dissipation)
Dipoles are immobile 1 ("frozen")
Thermal agitation destoys orientation of dipoles
Dipoles become mobile (f = const.)
T
Hr
Transition region with polarization losses (dissipation)
Dipoles follow the field without any delay
1
Dipoles cannot follow the fast changing field any more
(T = const.)
f Figure 2.45: General dependence of the relative permittivity on the parameters temperature T and frequency f for a dielectric with orientation/ molecular polarization (schematic), cf. Figure 4.213.
82
2 ELECTRIC STRESSES
³ E ds = E 1t ·s + (E 2t )·s = 0.
Dielectric 1
Therefore, the tangential components of the electric field strength are equal on both sides of the interface:
E1t
=
E2t
(2.413)
If the line P1P2P3P4P1 is regarded as contour of a closed surface, it can be concluded from Gauss’s law/ continuity Eq. (2.135) that all the current entering the enclosed volume on one side of the interface has to leave it on the other side. This condition is expressed by the continuity of the normal components of current densities (both conduction and displacement current density): J1n + wD1n/wt = J2n + wD2n/wt
(2.414)
In many cases, it is possible to confine oneself to the special cases of the stationary conduction field (without displacement current) and the dielectric displacement field (without conduction current). Therefore, in the case of the stationary conduction field (at DC voltage), the normal component of the conduction current density J continuously passes through the interface:
J 1n
=
J 2n
(2.415)
For the dielectric displacement field (at AC voltage, if the conduction current can be neglected) the normal component of the displacement density D continuously passes through the interface:
P2 E1
D1 E2t
P3 E2
D2n
(2.416)
In the following, the dielectric displacement field alone is discussed. It can normally be assumed in insulating materials for alternating fields at power frequency and above. Because of the analogy of the Equations (2.415) and (16), the results can be transferred to
P4
D2 E2n
Dielectric 2 Figure 2.46: Vectors of the electric field strength at an interface between two dielectrics.
the stationary conduction field for DC fields (Section 2.4.4). For this purpose, in particular the ratio of the permittivities H1/H2 must be replaced by the ratio of the conductivities N 1/ N 2. 2.4.2.2 Interface Orthogonal (Normal) to the Field („Field Displacement“)
For “sandwiched” dielectrics, if the interface between two dielectric layers (with permittivities H1 = H0·Hr1 and H2 = H0·Hr2) is orthogonal to the electric field, the displacement density continuously passes through the interface, Figure 2.47. The magnitudes of the field quantities D and E are identical with the magnitudes of the normal components. According to Eq. (2.416) the displacement densities D1 = D2 are equal, i.e. E1
D1n =
P1
E1n
E1t
E2
=
H2 . H1
(2.417)
The magnitudes of the field strengths and the permittivities are inversely rated to each other. The dielectric with the lower permittivity is stressed with a higher field strength than the material with the higher permittivity. This effect is called “field displacement” into the dielectric with lower permittivity.
2.4 Conduction and Displacement Fields in Inhomogeneous Dielectrics
Note: The field displacement is of fundamental importance in high voltage engineering. For instance air or gasfilled insulating layers, which have a comparatively low electric strength, are stressed with strongly enhanced field strengths because of the field displacement effect. Gasfilled gaps, cracks, cavities, shrink holes and voids are some of the most frequent/common reasons for defective insulations and partial discharges, Figure 2.48. Partial discharges (PD) mostly cause a slowly progressing erosion of the insulating material, finally leading to breakdown. In nonuniform fields, the field displacement effect can be used to reduce the stress on regions with high field stresses and to displace some of the stress into regions with lower field strengths. For the partially uniform field of the parallelplate capacitor according to Figure 2.47, the voltage is V =
V1 + V2 =
E1·d1 + E2·d2 .
83
5.71 kV/mm = 1.43·Ê0 and Ê2 = 2.86 kV/mm = 0.71 Ê0, calculated with Eq. (2.418) and (19) and with d1 = 8 mm. The field strength in the oil is increased by 43 % through the insertion of the plate. Note: The highest field displacement occurs for a very thin oil gap. With d1 > r1, Figure 2.415.
1.) According to Eq. (2.38), the voltage at the metallic spherical electrode must not exceed V = ÊL · r1 = 60 kV Û
Ê1 (r0 )
ÊResin
r r1
H r2 r
r0 r1
Figure 2.415: Spherical metallic electrode (left) and coated electrode (right) with the same external radii.
r02 {
H 1 1 ( 1 1) } r0 H2 r1
and Ê2 (r1 )
ÊAir
Vˆ
H 1 H 1 ( 1 1) } r12 2 { H 1 r0 H2 r1
If the ratio of the two field strengths is calculated, the voltage and the bracket in the denominator are eliminated: ÊResin / ÊAir =
2
2
(r1 ·H2) / (r0 ·H1)
The solution for r0 is r0 = 0.42 cm. With this V can then be value, the maximum voltage Û calculated from one of the two conditions mentioned above: V = Û
H r1
Vˆ
132 kV
Thus, the admissible voltage at the coated electrode is twice as high as the admissible voltage at the metallic electrode. Nevertheless, on larger electrodes it is difficult to produce thick coatings, which are free from defects and which are able to carry the major fraction of the voltage. For practical applications, large metallic electrodes and toroids are used, if there is enough space in the ambient air.
92
2.4.3.2 Gaps and Cracks
Gaps and cracks in highly stressed insulations are defects, which must always be avoided. Gasfilled gaps remain between insulation layers for example, if the impregnation of the residual interstices is incomplete. Cracks often are caused by material ageing after long periods, and they mostly originate from mechanical and thermal stresses. Cracks can also originate from shrinkage stress during the curing of castresin insulation bodies. Gaps and cracks parallel to the electric field are particularly critical because they bridge a major part of the insulation distance (up to the whole insulation distance) with an interface of very low electric strength and with tangential stress. Normally, the macroscopic field distribution is not influenced very much, but within the gap and at the interfaces there are microscopic field stress enhancements and significantly reduced electric strengths, see Section 2.4.2.3 (Parallel/ tangential multilayer dielectric). Example: Glassfiber reinforced plastics (GRP) have an extraordinarily enhanced mechanical strength because of glass fibers, which are embedded in the polymer matrix. Rods and tubes made of reinforced epoxy resin are used as mechanically and electrically stressed parts of suspension insulators, post insulators and housing insulators. These applications require a durable chemical bonding of the resin and the glass surfaces, free of any voids and defects. The bonding can be achieved by the application of a facing (primer) on the glass surface (silane glass primer). Incomplete or defective priming results in detachment of the fibers from the resin. In the very long cracks and cavities that arise humidity can be accumulated, which results in a significant decrease of the dielectric strength.
Gaps and cracks orthogonal to the electric field can approximately be regarded as multilayer arrangements with interfaces normal to the electric field, Section 2.4.2.2. The field strength Ei in a gasfilled crack or gap (Hri = 1) is enhanced by the factor Hr/Hri = Hr in comparison with the original field strength, because of the field displacement effect according to Eq. (2.417):
2 ELECTRIC STRESSES
Ei =
Hr · E
(2.433)
Because of the low electric strength of airfilled gaps, the inception voltage of partial discharges is very low. The discharges can erode insulating materials and they can eventually cause breakdown (breakdown by erosion). Example: Detachment of a dielectric
The epoxy casting resin in a cylindrical capacitor (R2 = 5 cm, R1 = R2/e, Hr = 4) shrinks during curing onto the inner conductor, and it is partially detached from the outer conductor, leaving a circumferential gap with the width di between 0 and 1 mm, Figure 2.416. The r.m.s. value of the applied voltage Vpdi, for which inception of partial discharges is expected, shall be calculated. The electric strength of air under standard atmospheric conditions is approximately Ê = 30 kV/cm = 3 kV/mm; it decreases with increasing distances, see Figure 3.215. Thus, the strength of the air gap is lowest for the highest gap width di = 1 mm. For this distance, the strength Ê(1 mm) > 4 kV/mm. If a constant field strength is assumed in the circumferential gap, discharge inception is expected to be at di = 1 mm. The inception voltage Vpdi is calculated from Eq. (2.321) for the field strength at the outer radius r = R2 and from Eq. (2.433) for the field stress enhancement in the gap: Vpdi = E · R2 · ln (R2/R1) = (Ei/Hr) · R2 · ln (R2/R1)
di
r R1
R2
Figure 2.416: Detachment of a dielectric from the outer cylindrical conductor during the shrinking onto the inner cylindrical conductor.
2.4 Conduction and Displacement Fields in Inhomogeneous Dielectrics With the partialdischarge inception field strength Êi > 4 kV/mm, the partialdischarge inception voltage is V pdi > 5 kV (peak value) or Vpdi > 3.5 kV (r.m.s. Û value). Note: The discharge inception at V = 3.5 kV represents practically an extreme loss of electric strength. Without the formation of a gap, the highest relevant field strength would occur at r = R1. If the admissible field strength in the epoxy resin is Êmax = 40 kV/mm, the V max = 74 kV admissible maximum voltage would be Û (peak value) or Vmax = 52 kV (r.m.s. value) according to Eq. (2.322). Note: Resinbonded paper bushing
Formerly used RBP bushing cores are “solid” insulation bodies (“hard paper”) wrapped with Kraft paper and bonded or laminated with phenolic resin without being fully impregnated (RBP, resinbonded paper). The bushing cores could not be fully impregnated without residual air volumes in order to avoid high mechanical stresses and cracks during the curing process. Therefore, partial discharges could occur already at the service voltage both orthogonal and parallel to the paper layers, but the phenolic resin has a durability that is sufficient in many cases. Nevertheless, according to modern criteria, permanent partial discharges and erosion are a significant quality defect because surface discharges parallel to the paper layers, partial breakdowns and full breakdowns cannot be excluded. Nowadays, cavityfree and dischargefree RIP insulating bodies are used (RIP, resinimpregnated paper) as bushing cores. They are wrapped with crepepaper, dried, impregnated completely with liquid epoxy resin under vacuum and cured. Example: Capacitor dielectric of polymeric films
A capacitor dielectric is wound on from polypropylene film (thickness 12 μm, Hr = 2.2). Between adjacent layers, there are nonimpregnable airfilled gaps with a maximum thickness of 7 μm. The admissible voltage for fourlayer insulation shall be estimated. As the electric strength decreases with increasing gap width, discharge inception is expected for the maximum width di = 4 μm. According to Paschen’s law for air, the V i > 360 V or approximate electric strength of the gap is Û Êi > 90 V/μm, see Section 3.2.2.4. According to Eq. (2.433), the field strength in the polymeric dielectric is approximately Ê = Êi/Hr > 41 V/μm. Therefore, the whole dielectric with a thickness d = 4 · 12 μm = 48 μm can be stressed with a voltage in the V > 48 μm · 41 V/μm = 2 kV. This is a rough range of Û estimation of the partial discharge inception voltage
93
only, a more accurate calculation of the multilayer insulation according to Eq. (2.427) would not be very useful. Note 1: Higher voltages are possible, if the maximum airgap width can be reduced. Then it has to be ensured that the field strength in the polymeric films does not exceed the respective electric strength. Note 2: The partial discharge behavior in capacitor dielectrics made of films or papers is essentially determined from the edges of the metal foils, which are wrapped as electrodes together with the dielectric layers. At the edges, there are strong field distortions, field stress enhancements and interstices without films or papers. Therefore, the impregnation of highvoltage capacitors is always necessary.
2.4.3.3 Interstices (TriplePoints)
Tangentially stressed interfaces are particular weak points of an insulation arrangement, Figure 2.417 (left). Therefore, this “supporttype arrangement” is avoided where possible and the interface is arranged orthogonal to the electric field forming a “creepage surface”, Figure 2.417 (right). Thus, tangential stresses are significantly reduced, and they decrease outwards to negligible small values. Because of the proximity of three materials, the considered microscopic region is called “triple point” or interstice between electrode and dielectric plate. Unfortunately, there is an increased normal electric field stress in the interstice between insulating plate and bent electrode because of the field displacement effect. If the material in the interstice (e.g. air) has only a weak electric strength, the partial discharge inception volt
Triplepoint
Triplepoint
E
E1 E2
Figure 2.417: Insulating plate between electrodes: "Supporttype arrangement" with tangential stress of the interface (left) and "creepage surface" with normal stress of the airfilled interstice (right).
94
2 ELECTRIC STRESSES
age can be very low. At (significantly) higher voltages, the discharges can grow into creeping/ surface discharges and result in surface flashover. Therefore, the insulation arrangement is called a “creepage surface”. Note: The creepage surface is a basic problem of highvoltage engineering, which cannot be avoided in many technical arrangements. Many technological measures are taken therefore, in order to prevent discharge inception in the interstices close to triplepoints and to prevent the inception of surface discharges [26]. For a rough estimation of the partial discharge
Triplepoint
d 1(x) H r1 E 1 V 1
Hr
H r2 E 2 V 2
d2 'x
x
'x
x
Figure 2.418: "Creepage surface" with highly stressed interstice (left) and an equivalent model of a small section for an approximate calculation (right).
12 11 10 Electric strength 9 in the interstice Ê1 8 kV/mm 7 6 5 4 3 d = 10 mm d 2 = 5 mm 2 2 Field strength in the interstice 1 0 0,0 0,5 1,0 1,5 2,0 2,5 3,0
d 1 /mm Figure 2.419: Field strength in an interstice as function of airgap width at 8 kV (peak value) for insulating plates with a thickness of 5 mm and 10 mm (bottom) compared with the electric strength (top). The permittivity ratio is assumed as 1:5.
inception voltage Vpdi, it is simply assumed that there are small sections with regionally uniform field, Figure 2.418. The interface is orthogonal to the field, being uniform but different on both sides of the interface. The gap width d1 in the interstice increases with the distance x from the triplepoint. A section 'x is considered with approximately uniform field regions 1 (interstice) and 2 (insulating plate). According to Eq. (2.418), the field strength in the interstice is E1 (d1 )
V
H d1 d 2 r1 H r2
.
(2.434)
Example: Electrode edge on an insulating plate
An electrode edge on an insulating plate according to Figure 2.418, is discussed. Figure 2.419 shows the numerical analysis of Eq. V = 8 kV (V = 5.7 (2.434) for a total voltage Û kV r.m.s.), for the insulation thicknesses d2 = 5 and 10 mm and for the permittivity ratio Hr1/Hr2 = 1/5. There is a decreasing field strength in the interstice with increasing gap width d1. If the insulating thickness d2 is doubled from 5 mm to 10 mm, the field strength at d1 = 0 is reduced to half the magnitude, but a further decrease across d1 is slower. Figure 2.419 also shows a curve of the electric strength in the interstice. The increase of strength with decreasing airgap width d1 is typical for many insulating materials, e.g. for air, SF6 and insulating oil. The curve in the picture is approximately valid for air at atmospheric pressure and room temperature. For an insulating plate with thickness d2 = 5 mm, the field strength in the gap reaches the electric strength of the gap at approximately d1 = 1.2 mm, and partial discharges occur. ObviV = 8 kV (V = 5.7 kV r.m.s. ously, the voltage Û value) is the partial discharge inception volt
2.4 Conduction and Displacement Fields in Inhomogeneous Dielectrics
95
V pdi (Vpdi r.m.s.). Normally, r.m.s. values age Û are given.
account the ratio Hr1/Hr2 ~ 1/2, which is already included in these factors [22].
If the insulation thickness is doubled (i.e. d2 = V = 8 kV 10 mm), there are no discharges at Û (V = 5.7 kV). Nevertheless, Figure 2.419 shows that the curve of the electric strength is reached if the voltage (i.e. the field strength) is only increased by about 40 %.
Example: Edges of metal foil electrodes in capacitor insulations
Note: Obviously, there is no linear relation between the insulation thickness d2 and the peak value of the partial discharge inception V pdi: voltage Û
V pdi ~ Û
d2
0.5
According to Eq. (2.434), the field strength in the interstice depends on the product d2·Hr1/Hr2. In accordance with the described model, the peak value of the partial discharge inception voltage for surface discharges is Vˆpdi kV
a
2K
§ d 2 H r1 · ¨ ¸ . (2.435) ¨ cm H ¸ r2 ¹ ©
A theoretical proportionality factor K = 18 (for air) could be determined from Figure 2.419. Unfortunately, experiments show that the factor can be significantly smaller. Probably, the theoretical model (with regionally uniform fields according to Figure 2.418) is too simple. Furthermore, surface effects and different electrode shapes are not taken into account. Nevertheless, the general dependences of Eq. (2.435) are in good agreement with experiments for the exponent a = 0.44 ... 0.5 [22], [23]. At sharp electrode edges the factors are approximately K = 8 for air and K = 21 for SF6 [23]. For insulating oil a factor K = 20 can be derived from [23]. Note: For different electrode edges under oil, factors between 21.6 (paper wrapped conductor on paper insulation) and 15.6 (for sharp electrode edges on paper insulation) are reported without particularly taking into
For wound capacitors the metal foil electrodes and the insulating films or papers are wound together; remaining gaps and voids are filled completely with an impregnating medium, Figure 2.420. The electrical connection of the foils, which are displaced to left and right relative to each other, is either made at the ends with metallic tabs or made by largearea end contacts via all protruding foil edges, Figure 2.420 (top). Very high field strengths occur in the interstices between the dielectric layers at the edges of the metallic foils. The critical point is not the normal (radial) field stress in the impregnating medium at the bent electrodes (as in the former example). In this case, the tangential (axial) stress on the dielectric interfaces is mainly problematic, which arises because of extreme field stress enhancements at the strongly curved electrode edges, Figure 2.420 (bottom). An approximate calculation is performed for an equivalent cylindrically symmetric arrangement with R1 = dM/2 and R2 = dM/2 + dI. The curved electrode edge with a very small radius of curvature R1 = dM/2 is regarded as the “inner conductor”; the adjacent metallic foils are regarded as the “outer conductor” and they are replaced by an auxiliary cylinder with the radius R2 = dM/2 + dI. To a first approximation, the multilayer arrangement of the dielectrics has no influence on the maximum magnitude of the electric field strength in the impregnating medium because of the tangential direction of the field Eedge at the electrode edge, Figure 2.420 (bottom). This means that the field is parallel (tangential) to the surface of the films or papers, see Figure 2.49. With Eq. (2.322), the field strength at the edge of the foil (edge field strength) is given by
96
2 ELECTRIC STRESSES
U
ERand
R R1 ln 2 R1
E0 d I , 2d I dM ln (1 ) dM 2
and the field strength enhancement is the reciprocal of the field efficiency factor K ERand E0
2d I dM
1
K
ln (1
2d I ) dM
.
(2.436)
The numerical analysis of Eq. (2.436) shows that significant field stress enhancements can occur, even for round edges, Figure 2.421 (lower curve). If further enhancements by im
11 10 E cylinder 9 3 ·E 0 ERand 8 E0 7 E cylinder 6 5 E0 4 3 2 1 0 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0
d M /d I
Figure 2.421: Field enhancement in a rolltype capacitor element at the edges of a metallic foil electrode. Lower curve: Calculation with the assumption of a cylindrically symmetric field. Upper curve: Taking into consideration additional field enhancement by imperfections of the surface.
perfections of the surface are considered, a factor of 3 is realistic according to Eq. (2.362), and field stress enhancements are even more extreme, Figure 2.421 (upper curve).
E edge
H rI
E0 Auxiliary cylinder
H rZ
R2 R1
dI dM dI
Figure 2.420: Rolltype capacitor with largearea end contacts of the axially shifted metal foils (top) and sectional view for the righthand edge of the foils with equipotential lines (bottom).
Numerical example: A capacitor consists of paper insulated windings with an insulation thickness dI = 50 μm, which are impregnated with mineral oil. The edges of the 6 μm thick aluminum foils are folded, in order to guarantee a smooth curvature at the edges. Partial discharge inception was measured at a r.m.s. ACvoltage of 3 kV. The field stresses between the foils and at the edges of the foils shall be calculated. The field strength between the foils within the papers is E0 = 3 kV / 50 μm = 60 kV/mm for the uniform field region. Because of field displacement, there is a higher stress in the impregnating oilfilled gaps, E0oil = Hrpaper/Hroil·E0 ~ 120 kV/mm. At the edges a field stress enhancement Eedge/E0 = 3.7 is calculated from Eq. (2.436) or Figure 2.421 with dM = 2·6 μm = 12 μm (thickness is doubled at the folded edges) and dM/dI = 0.24. This gives the edge field strength as 220 kV/mm. Such an electric strength can be expected from oil gap widths in a range of a few μm [27]. However, the estimated very high field strength only occurs very close to the strongly curved edge. The field strength decreases very strongly with increasing distance ~1/r, i.e. at a distance of 6 μm (r = 12 μm) it is 110 kV/mm and at a distance of 18 μm (r = 24 μm) it is just 55 kV/mm.
2.4 Conduction and Displacement Fields in Inhomogeneous Dielectrics
Note: Normally, the calculation of edge field strengths and partial discharge (PD) inception voltages is not possible for practical applications, because of many unknown parameters. Therefore, experiments with different insulation designs are necessary, in order to determine the acceptable stress. For sharpedged cut aluminum foils, the PD inception voltage would decrease from 3 kV to 2.5 kV (E0 = 50 kV/mm) in the abovementioned example. On the other hand, a significant increase of PD inception field strength could be achieved by means of special synthetic insulating liquids. Theoretically, the volume of a capacitor can be minimized by choosing an optimal thickness dM for the metal foils: For dM o 0 the field stress enhancement factor becomes infinite, i.e. the admissible field strength and the energy density approach zero. For dM >> dI the dead volume of the foil vM is very much greater than the energy storage volume of the dielectric vI and the energy density approaches zero. Inbetween there must be a maximum of overall energy density. w =
2
0.5 H E0 vI/(vI + vM)
(2.437)
This equation can be used for the determination of the maximum energy density w, if the admissible edge field strength is given and if the equations for the volumes and Eq. (2.436) for E0 are used: The derivate of w with respect to the ratio dI/dM is set equal to zero. The resulting transcendental equation is solved iteratively with dI/dM = 0.24. This means that the metallic foil should theoretically be about four times as thick as the insulation. In practice, the optimum can be assumed for much thinner foils: The admissible edge field strength is not constant. It increases significantly with decreasing radius of curvature. The best insulation design has to be determined experimentally, as mentioned above.
97
2.4.3.4 Dielectric Cavities and Spheres
Completely closed cavities in a medium with higher permittivity are defects, they can be observed e.g. as bubbles in insulating liquids, as shrink holes in epoxy resin bodies or as voids in porcelain insulators, Figure 2.422. Dielectric spheres in a material with lower permittivity can also be defects, e.g. nonconductive particles in oil or in gas. The basic effect of field displacement was already discussed for gaps and cracks in Section 2.4.3.2. For spherical defects bounded on all sides, the field distortion is less pronounced. In solving Poisson’s/ Laplace’s Equation (2.334) for the spherically symmetric arrangement, Figure 2.422, it has to be considered as a boundary condition that there is a uniform field E0 at infinite distance. Furthermore, the boundary conditions of Eq. (2.413) and (16) have to be fulfilled at the sphere’s surface. The solution is a uniform field within the sphere [2]: E1 =
E0 · 3 H2/(H1 + 2 H2)
(2.438)
Outside of the sphere, at the sphere’s surface on the xaxis (which is determined by the field vector E0), the solution is
M const.
E 2 H2 y E 1 H1
x
E0
Figure 2.422: "Dielectric sphere" as a model of a cavity in an insulating material or as a model of a dielectric particle.
98
2 ELECTRIC STRESSES
E0 · 3 H1/(H1 + 2 H2) .
2
(2.439)
V= wFwA = ½·E1 (H2  H1) H1/H2. (2.440)
The comparison of Eq. (2.438) and (39) shows that the magnitude ratio of the field vectors normal to the interface is the reciprocal of the permittivity ratio, see Eq. (2.417), transversely layered dielectric. The continuity of the tangential components E1 = E2 applies on the yaxis at the sphere’s surface.
The force acts from the higher towards the lower permittivity parallel to the field (longitudinal tensile stress).
E2 =
In the case of a dielectric cavity with a lower permittivity H1 < H2 the field strength E1 in the cavity is enhanced in comparison with E0. The maximum value is E1 = 1.5·E0 for H1 > H2, according to Eq. (2.439). Therefore, dielectric particles can cause significant field strength enhancements in liquid and in gaseous media, and they can reduce the electric strength, especially in liquids. 2.4.3.5 Electric Forces at Interfaces
Often it is particularly troublesome that particles can follow the electric field forces and accumulate in the region of highest field strength. The mechanical tensile stress exerted by an electric field orthogonal to an interface is [2]
In a nonuniform field, the forces on opposite sides of a dielectric body are no longer equal. The resulting force pulls the body towards increasing field strength. Example:
In insulating oil, fibrous impurities are aligned parallel with the field lines, especially in the nonuniform regions of the field. This reduces the electric strength of long oil gaps significantly (fiberbridge breakdown, suspended solid particle mechanism). Also in gasinsulated switchgear, the electric strength is reduced by the presence of dielectric (and conductive) particles [28].
Also, the field component Et tangential to an interface exerts a force orthogonal to the interface and towards the lower permittivity. The socalled lateral pressure is
V
=
wFwA
=
½ · Et (H2  H1) .
2
(2.441)
The tensile stress on metallic electrode surfaces
V
=
wFwA
=
½ · En H
2
(2.442)
results from the field that is always acting orthogonally to the surface and parallel to the field. Note: Eqs. (2.440) to (42) can each be deduced from an energy balance for an imaginary displacement of the interface by an infinitesimal shift 'x by the desired force F. This results in a change of electric field energy, which is equal to the exerted mechanical work F·'x. The mechanical pressure Vor the tensile stress V is determined if the force F is divided by the area A [2].
2.4 Conduction and Displacement Fields in Inhomogeneous Dielectrics
2.4.4 Direct Voltage and Transients There is a perfect analogy between the stationary conduction field at a pure DC voltage and the formerly discussed dielectric displacement field.
99
cal of the resistance) in the conduction field. The following equations describe a parallelplate capacitor e.g.: C =
H·A/d
G = 1/R = N·A/d . (2.446)
From this analogy, the principles of the conduction field are deduced (Section 2.4.4.1). They can be used for calculation of some typical examples of insulation systems stressed with DC voltage (Section 2.4.4.2). In many cases, there are no stationary conditions: If a DC voltage is switched on, reversed in polarity or changed in magnitude, a displacement field is generated. Then, a transient process takes place, approaching a new stationary condition (Section 2.4.4.3).
The comparison shows that all relationships for the dielectric displacement field are also valid for the stationary conduction field, if the permittivity H is replaced by the conductivity N, the displacement density D by the conduction current density J and the capacitance C by the conductance G. This is also valid for the deduced Eqs. (2.417) to (2.432), which are related to interfaces orthogonal, parallel and inclined to the electric field direction.
2.4.4.1 Analogies to the Dielectric Displacement Field
For the interface orthogonal to the electric field, the continuity of the conduction current density J1 = J2 = J orthogonal to the interface is valid. By analogy with Eq. (2.417), it is concluded that
The basic Material Equations (2.119) and (2.120) contain a perfect analogy between the fields of the dielectric displacement density D and the conduction current density J. The corresponding equations and boundary conditions are compared against each other below for the displacement field (left) and the conduction field (right): D =
H· E
J =
N· E
(2.443)
The continuity of the normal components for the field quantities D and J is given with Eq. (2.415) and (2.416): D1n =
D2n
J1n =
J2n
(2.444)
According to Eq. (2.413) the tangential component of the electric field strength E is also continuous at interfaces, both for the displacement field and for the conduction field: E1t =
E2t
E1t =
E2t
(2.445)
Instead of a capacitance C in the displacement field, there is a conductance G = 1/R (recipro
E1 E2
=
N2 . N1
(2.447)
The field strength magnitudes and the conductivities are in inverse ratio to each other. Analogously with the dielectric field displacement, the material with the lower conductivity is stressed with a higher field strength than the material with the higher conductivity. Note: Conductivities often differ by several orders of magnitude. Thus, the material with the higher conductivity is almost completely without stress, but the material with the lower conductivity is stressed with nearly the whole voltage. This is an almost complete field displacement. Figure 2.423 shows field and potential distribution for the conductivity ratio N1 : N2 = 1 : 10. The normal components of the conduction current density Jn are certainly continuous at the interface, but the normal components of the displacement density Dn are not continu
100
2 ELECTRIC STRESSES
100 %
d
N1
1
E
80 %
1
60 % 40 % 20 % 9%
N2
d2
V
E2
Figure 2.423: Field and potential distribution in two dielectrics with an interface orthogonal to the electric DC field (coductivity ratio 1 : 10).
ous. The difference between the displacement densities D1n and D2n is equal to a surface charge density V at the interface. This effect is called interfacial polarization, Figure 2.423:
V
=
D2n  D1n
=
H2 E2  H1 E1
=
E1·(H2·N1/N2  H1)
E according to Eq. (2.445). The current densities are different on both sides of the interface because of the different conductivities: J1 = N1E and J2 = N2E. According to Eq. (2.446) there are different arearelated conductances and resistances on both sides of the interface. It should be noted that for DC voltage stress, the interface parallel to a DC field is especially critical: Conductive deposits and pollution layers (e.g. caused by contaminations, impurities or wetting) can cause field distortions and extreme field stress enhancements if there are only slight nonuniformities in the layer, Figure 2.424. For an interface inclined to the electric field, the different conductivities cause a refraction of the DC field lines and DC equipotential lines in the stationary conduction field (refraction law) by analogy with Eq. (2.421): tan D1 tan D2
(2.448)
In the case of a short circuit at the electrodes, the surface charge (interfacial polarization) does not disappear immediately, it decreases with the time constant R2C1, which is determined by the geometries and by the material properties N2 and H1, see also Figure 2.116. If the short circuit is opened too early, an unexpected and therefore dangerous recharging of the electrodes (a socalled “recovery voltage”), can occur (see Section 2.4.4.3). Example: Capacitor with mixed dielectric
In capacitor dielectrics, made of oilimpregnated paper layers and highresistive polymeric films, there is an almost complete field displacement into the polymeric films. A numerical example was already discussed in Section 2.1.4.2. The example shows that the polymeric films almost entirely produce the insulation. The paper layers are mainly used as impregnation wicks.
For an interface parallel to the electric field, the tangential field E is theoretically not influenced by the adjacent materials, i.e. E1 = E2 =
=
N1 N2
(2.449)
D1 and D2 are the angles between the area
vector A (orthogonal to the interface) and the field vectors E1 and E2, Figure 2.425.
N2
N1
E1
N2
N1
E2 E1
E2
Figure 2.424: Interface parallel to a DC field. Left: Ideal potential distribution. Right: Potential distribution with a nonuniform conductive pollution layer causing extreme local field enhancements.
2.4 Conduction and Displacement Fields in Inhomogeneous Dielectrics
Dielectric 1
Highly resistive
M = const.
N1
N1
D1
D2
E2
D1
E1n E1t
Dielectric 2
E2n
N2
N2 >> N1 Comparatively conductive
E1
Dielectric 1
E1
M = const.
101
In many practical applications, conductivities on both sides of the interface are very differo ent. For N2 >> N1, the angle D2 approaches 90 , even for very small angles D1. In the more conductive material 2, the field lines are almost parallel and the potential lines are nearly orthogonal to the interface, Figure 2.426 (bottom). In the more resistive material 1, the field lines are almost orthogonal and the equipotential lines are nearly parallel to the interface, Figure 2.426 (top). Note: This circumstance can clearly be explained by the fact that a current can only flow nearly parallel to the interface in the comparatively conductive material. Therefore, field lines must orient themselves almost parallel and equipotential lines almost orthogonal to the interface. In the highly resistive material, the field lines are almost orthogonal to the interface, which is similar to the situation close to a conductive electrode. Example: In oilinsulated equipment for high DC voltages, the potential distribution in oil can be controlled by forming a uniform oil duct of higher conductivity between highly resistive pressboard barriers and other highly resistive insulating components (e.g. for bushings) [7].
For inclined layererd dielectrics there is also a surface charge at the interface. It can also be calculated from the difference of the normal components of the displacement density D.
E2
D2
N2 Dielectric 2 M = const.
M = const.
Figure 2.426: Refraction of field lines and potential lines in a stationary conduction field at the interface between insulating materials with very different conductivity.
E2t
Figure 2.425: Vectors of the electric field strength and potential lines at an interface inclined to the electric field for two dielectrics with different conductivities ("Refraction" of field lines and potential lines at an inclined interface for a stationary conduction field).
The calculation of DC voltage fields is not only complicated by the possibility of large differences of the conductivities. Furthermore, it is often difficult to get reliable numerical values, since conductivity is dependent on the exact material composition, on manufacturing process technology and very strongly on the temperature. Some examples are described below:
x
Different porcelain mixtures have different conductivities.
x
The conductivity of oilimpregnated paper increases with the water content.
x
The conductivity ratio in an oilpressboard insulation may be 100 : 1 at 20 °C (test temperature). At 90° C (service temperature) the ratio is just 10 : 1.
It was already mentioned in Section 2.4.1.1 that in practice it is very important to determine reliable and applicable conductivity values. Because of the high degree of possible variations, a field calculation with wrong conductivity values can lead to completely wrong results.
102
2.4.4.2 Typical DC fields
Some examples for typical DC fields shall be discussed below. Because of high conductivity differences, strong temperature dependences and the sensitivity to pollution layers, there are field distributions which are completely different from a comparable AC field. Example 1: Capacitor with mixed dielectric
The example of a DC capacitor with a mixed dielectric, made of polymeric films and oilimpregnated paper with a hundredfold greater conductivity, has already been discussed several times (Sections 2.1.4.2 and 2.4.4.1). It was shown that nearly all the voltage has to be insulated by the electrically strong polymeric films. The paper layers are relieved of the electrical stress to a large extent because of their significantly higher conductivity. It is disadvantageous that the paper volume does not contribute to the capacitive storage volume. Therefore, it is desirable for weight reasons to design the insulation without any paper, which is only used as “impregnating wick”. Then, good impregnation has to be guaranteed by adequate surface texture of the films. Note: For AC voltage, the papers are stressed with a field strength, which is half as high as in the polymeric films because of the field displacement, see Eq. (2.417) with H2/H1 = 2. Nevertheless, the field strength in the paper can be the critical quantity that limits the voltage, because of the very high electric strength of polymeric films. Thus, the design does not make full use of the excellent electric strength of the polymeric films, and it is desirable therefore to replace the paper by polymeric films (allfilm dielectric).
2 ELECTRIC STRESSES
the current. As a result, there is a temperature gradient T(r) from the inside to the outside. Because of the strong temperature dependence of the conductivity, a conductivity gradient is also caused. This results in a continuous field displacement from inside to outside. Depending on the conductor’s temperature and the insulating material, the field profile is more or less equalized, Figure 2.427 (curves 2 and 3). Nevertheless, the designer of the cable has to take into account that the cable has to withstand the voltage not only in the warmedup service operation, but also in the cold starting condition.
N( T ) = N ( r ) E r
Conductor
T
T (r) r
E E(r) 2 3 1
Example 2: HVDC cable
In a high voltage DC cable with a homogeneous dielectric there is a cylindrically symmetric field. According to Eq. (2.321), the field strength decreases proportional to 1/r between the inner and outer conductors, Figure 2.427 (curve 1). During service operation, the inner conductor is heated by the ohmic losses due to
r R1
R2
Figure 2.427: DC cable with a conductivity gradient caused by a temperature gradient and modification of the initial field distribution (curve 1) due to the space charge accumulation (curves 2 and 3).
2.4 Conduction and Displacement Fields in Inhomogeneous Dielectrics
The continuous variation of conductivity is accompanied by the accumulation of charge in the insulating material. In contrast to multilayer dielectrics, the charge is not accumulated at the interfaces, here it is distributed as space charge over the entirety of the inhomogeneous insulating material. This leads finally to the deviation of the field stress profile from the initial profile ~1/r.
103
completely different potential distribution within the oil, Figure 2.428 (middle). The distribution is mainly determined by the electrode geometry, and the highly resistive bushing acts as a highly resistive boundary of the comparatively conductive oil volume. In this way, a very high tangential stress of the bushing surface can occur.
This field concentration can be avoided by a very large electrode diameter in very large oil The space charge is of high importance for the tanks (cylinder). However, this is not generally operation of the cable because the remaining an economic solution. charge can cause very high field stress enhancements after a polarity reversal. FurtherIn the case of the given narrow installation more, space charge can cause a dangerous reconditions, the tangential field strength can charging of the cable, if a short circuit bealso be reduced by a system of highly resistive tween inner and outer conductor is opened again. Because of the high capacitance of long cables, even relatively low “recovery Potential lines voltages” can accumulate Grounded cylinder 0% at AC voltage significant and dangerous Flange amounts of charge. 25 %
Example 3: HVDC Bushing
A high voltage electrode in oil shall be connected via a capacitively graded bushing, both for AC and DC, Figure 2.428. At AC voltage, the capacitive grading layers have approximately the intended potentials, because of their mutual capacitances. In this way the tangential stress at the bushing surface is significantly reduced, Figure 2.428 (top). Also at DC voltage, the intended potential distribution is approximately achieved within the bushing core, because of the mutual resistances of the grading layers, i.e. the grading is now resistive and no longer capacitive. Outside the bushing, there is a
Bushing
50 % 75 %
High voltage electrode (HV conductor) Potential lines at DC voltage
Comparatively conductive oil Highly resistive bushing core
Highly resistive pressboard barriers
Comparatively
conductive
Potential lines at DC voltage
oil duct
Figure 2.428: Connection of a HV electrode in oil via a capacitvely graded bushing at AC voltage (top) and DC voltage (middle and bottom). Improved potential distribution at DC voltage by highly resistive pressboard barriers (bottom) [7].
104
2 ELECTRIC STRESSES
cylindrical pressboard barriers with different lengths (pressboard barrier system), Figure 2.428 (bottom). In this way a uniform oil duct shall be formed, with a current flow between high voltage and ground and with an almost uniform potential distribution.
Note: The barriers have an important function also at AC voltage: Although the influence of thin barriers on the AC field strength in the oil gaps is small, the electric strength of these gaps is significantly improved by a subdivision into smaller gaps.
The grading capability of the barriers at DC voltage is based on the external potential grading in the oil duct, which is adjusted to the internal grading of the bushing’s grading layers. The internal bushing itself cannot influence the stationary conduction field outside the bushing [7], [10].
On the outdoor insulators of wall bushings, pollution layers develop by deposition of dust and dirt. The exposure to water by rain or by moisture condensation causes a comparatively high surface conductivity, Figure 2.429.
Example 4: HVDC wall bushing
At AC voltage, the field distortion by conduction currents on the surface (creepage currents) is normally negligible, because of the comparatively high capacitive displacement currents.
At elevated temperature, the conductivity differences between the materials and the grading capability of the barriers are reduced. A calculation with sufficient accuracy can only be achieved by numerical field calculations (see Section 2.5) with correct conductivity values.
At DC voltage, wet pollution layers, which have a significantly higher conductivity than the bushing insulator, cause very strong field distortions, especially if the pollution layer does not cover the surface completely and uniformly.
According to the refraction law Eq. (2.449), it is concluded that the potential lines in the oil duct emanate from the highly resistive materials (bushing and barriers) almost orthogonally, see Figure 2.426. Around the electrode, the interfaces are orthogonal to the field (and parallel to the equipotential lines). Here, the field is displaced from the comparatively conductive oil gaps into the highly resistive barriers. Therefore, the thickness and number of the barriers must be such that the barriers can withstand the whole DC voltage.
In HVDC installations for outdoor sites, the nonuniform rain on bushing insulators (e.g. in the lee side of a building) is especially critical at higher voltages, Figure 2.429. The high voltage potential can be shifted along the surface for long distances down to the transition zone between the dry and the wet surface. This is comparable with a sharp electrode on a
Nonuniform rain Building
0%
Potential lines at DC voltage 25 %
50 %
75 %
Bushing (outdoor side) 100 % dry
wetted
100 %
Figure 2.429: Airside of an HVDC wall bushing with the formation of a wet and conductive surface layer. Because of the nonuniform rain only a part of the surface is bridged at DC voltage, see figs. 2.41 and 2.
2.4 Conduction and Displacement Fields in Inhomogeneous Dielectrics
creepage surface (Figures 2.417, 18 and 24) with extreme tangential and radial field stress enhancements, which can cause a flashover (comparatively bestcase) or a radial breakdown of the bushing (worstcase). Therefore, it is very often necessary, to apply hydrophobic (waterrepellent) silicone paste on the insulator surface, in order to avoid the formation of conductive liquid films on the easily wettable porcelain surface. The application and regular renewal of the silicone paste can be avoided, if the porcelain insulator is replaced by a composite insulator made of a glassfiberreinforced plastic (GRP) tube (i.e. reinforced epoxy resin tube) with elastomeric silicone rubber (SIR) sheds [7], [8], [9], [10], see Section 5.3.4 with Figure 5.318.
105
variant displacement field is more like Figure 2.430 (top). Furthermore, space charges accumulate at the interfaces of the polymeric films during the preceding steadystate DC phase. During an oscillating discharge, there are multiple polarity reversals, and a timevarying displacement field is superimposed to the steadystate space charge field. Thus, the electric field stress at the edges of the foils is much higher than for a pure DC or AC stress alone, see Section 7.3.3. The lifetime of an energy storage capacitor or an impulse capacitor is therefore given by the number of possible discharges depending on the charging voltage, the frequency of the discharge oscillations and the relative magnitude of the first amplitude with reversed polarity (backswing ratio) [29].
Example 5: Energy storage capacitor
Energy storage capacitors are charged with DC voltage, and they are in general discharged by electric pulses or damped highfrequency oscillations. During the charged condition, i.e. during a steadystate DC stress, the potential distribution close to the edge of a foil is significantly different from the AC distribution shown in Figure 2.420, see Figure 2.430. The impregnating gap that ends at the interstice at the edge of the foil, is filled with oil and normally has a higher conductivity NZ than the adjacent insulating films with NI. Thereby, a comparatively uniform gap is formed, where a conduction current can flow through the oil and grade the potential, Figure 2.430 (bottom). Thereby, the stress at the edges of the foil is significantly reduced. Therefore, the DC strength of a capacitor dielectric is in practice significantly higher than the AC strength. A factor of about three can often be assumed. The critical stress in an energy storage capacitor does not arise during the steady state DC stress, but during the fast discharge impulse or the discharge oscillation. The associated time
2.4.4.3 Transient Processes
The abovementioned DC voltage stress assumes a steadystate condition, which requires very long times between hours and days for highly resistive insulating materials. According to Eq. (2.141), times should be much
Potential lines at AC voltage
E edge
H rZ H rI
E0
Potential lines at DC voltage
E edge E0
NZ NI
Figure 2.430: Electric field stress at the edges of the metallic foils in a capacitor dielectric at AC voltage (top) and reduced field stress at DC voltage (bottom) due to a comaratively high conductivity in the oilfilled interstice between the plastic films.
106
2 ELECTRIC STRESSES
longer than the selfdischarging time constants of the relevant materials: t
>>
Wd =
H N
(2.450)
For the application of a DC voltage, the following phases must be distinguished (see Figure 2.116): a) If the DC voltage is applied as a step within a very short time (in comparison with the relevant time constants of the dielectric system) a dielectric displacement field can be assumed at first. It is determined by the permittivities H. Geometrically simple configurations can be described by equivalent networks consisting of capacitances only. b) Then, a transient process takes place, which consists of charging and discharging processes among the different dielectrics. A mathematical description requires the Material (Constitutive) Equations D = H E and J = N E together with the Continuity Equation (2.135) in their general form. Both conduction current density J and displacement current density wD/wt have to be considered.
Geometrically simple arrangements can often be described by equivalent networks consisting of capacitances C (for the description of the displacement current) and resistances R (for the description of the conduction current). Voltages and currents are then calculated with the methods of network analysis. The Laplace transform is very useful for this purpose [2], [30], [31]. Note: The description of a material by a single permittivity (capacitance) and a single conductivity (resistance) neglects that the polarization process of the material takes time and can continue for comparatively long times until the steady state is reached. Polarization processes are therefore described by a more complex equivalent circuit, which contains RC elements with different time constants for describing the different polarization mechanisms, see Section 4.3.
c) After the decay of the transient process, a steady state is reached, which depends on the conductivities (or resistivities) of the insulating materials only (Section 2.4.4.1 and 2.4.4.2). Geometrically simple arrangements can be described by an equivalent network consisting of resistances only.
In DC applications it often happens that a given state is changed into another state by a transient process. Examples are the transients after a polarity reversal (e.g. during an HVDC voltage test), after an increase or decrease of the DC voltage magnitude, after a short circuit, after a discharging process or during the development of a recovery voltage. A calculation of the mentioned transitions can be performed in the following steps: a) At first, the initial state has to be calculated. In the easiest case, this is the steady state. In an equivalent network, the initial state is given by the initial charge state of the equivalent capacitances. The initial state of a complex arrangement, which cannot be described by an equivalent network any more, has normally to be described by a numerically calculated field pattern or an equipotential line plot. b) The subsequent voltage step can be described by a voltage source in an equivalent network. In more complex arrangements, which are described by field or equipotential plots, the dielectric displacement field associated with the voltage step can be superimposed on the initial field distribution in the form of a field plot. This gives the dielectric stress directly after the voltage step [7], [10]. c) The transient process can be determined by a transient network analysis in an equivalent circuit. For geometrically complex arrangements numerical field calculations have to be based on transient field theory. For practical applications it is often sufficient to calculate the steady end state.
Hereafter, some practical examples are discussed:
2.4 Conduction and Displacement Fields in Inhomogeneous Dielectrics
Example 1 deals with the application of a DC voltage to a multilayer capacitor dielectric. The recovery voltage after the short circuit of a capacitor is considered in example 2. Example 3 shows that there can be stress enhancements in some dielectric layers during a transient process. Example 4 discusses the complex field conditions in a barrier system during a polarity reversal of a DC voltage. Example 1: Application of a DC voltage
Steadystate and quasistatic capacitive fields in a twolayer capacitor dielectric were already discussed in Section 2.1.4.2 and 2.1.4.4. The twolayer dielectric is made of polymeric films and oilimpregnated papers with d1 = d2 = 30 16
μm, Hr1 = 2.2, Hr2 = 4.4, N1 = 10 14
S/m and N2
= 10 S/m, Figure 2.111, 15 and 16. The transient process shall be discussed. As the interfaces between the materials are also equipotential surfaces, the transient process can be described with an equivalent network containing capacitances C1 and C2 to
V
V
gether with the parallel resistances R1 and R2: Immediately after the application of the DC voltage the dielectric displacement field causes a “capacitive voltage distribution”, i.e. the polymeric films are stressed with 2/3 and the papers with 1/3 of the voltage. In an approximately exponential transient process, the capacitance C1 of the high resistive polymeric films is charged over the resistance R2 of the comparatively conductive oilimpregnated papers (time constant W = R2C1) until the steadystate (“ohmic”) voltage distribution is reached. This can take many hours to complete. The polymeric films always have to withstand the whole DC voltage, the papers are stressed with only 1 % of the total voltage. Example 2: Recovery voltage
For the capacitor in the abovementioned example, the steadystate voltage at the equiva
Compensation of the partial voltages during the shortcircuit
u (t)
v 1 C1
R 1 V/ 3 C1
R1
v 2 C2
R 2 V/ 3 C2
R2
V/ 3
v 1' (t) v 2 = V/ 100
W2
v '(t)
107
Selfdischarging of the partial capacitances after the opening of the short circuit
v '(t)
v 1' C1
R1
v 2' C 2
R2
Slow selfdischarging of the highly resistive dielectric (plastic films)
W1
0 Steadystate DC voltage stress
v 2' (t)
H1 N1 H2 N2
Fast selfdischarging of the comparatively high conductive dielectric (oilimpregnated paper)
t
 V/ 3 Figure 2.431: DC voltage stress and recovery voltage at a dielectric consisting of plastic films and oilimpregnated paper with a hundred times the conductivity (more explanations see in the text).
108
lent capacitance C1 (polymeric films) is nearly the whole voltage (approx. 0.99·V), whereas C2 (papers) is only charged to 0.01·V, Figure 2.431 (left). During a short circuit of the capacitor at the external terminations, the charge Q1  C1·V is distributed among the two parallel partial capacitances C1 and C2, which have the same voltage, but with opposite polarity. The voltage between the outer terminations is thus zero. Theoretically, the voltages are v1' = v2' = (1/3)·(C1·V)/C1 = V/3 for C2 = 2 C1, if Q2 = C2·0.01·V is neglected, Figure 2.431 (middle). The difference of the capacitively stored energies, before and after the short circuit, is dissipated as ohmic loss in the resistance of the short circuit. If the short circuit is not opened again, the parallel capacitances C1 and C2 are exponentially discharged via R2 2W, there are deviations because of reflections coming from the other end of line 2. At the end of line 2 (z = zb), the traveling wave does not arrive before the single propagation time t = W, and the voltage vb(t) follows the incident wave vi(tW) with a timeshift W for two further propagation times. Note: This example shows that a traveling wave propagating from a cable to an overhead transmission line can cause significant overvoltages by reflections. This also applies to fast transients in gasinsulated switchgear (GIS) at the bushings, which are connected to the overhead lines. For a transition from a high characteristic impedance (overhead line) to a low characteristic im
2·f(zut) = v + i·Z = const.
and in –zdirection
2·g(z+ut) = v  i·Z = const.. (2.621)
The propagation of the traveling wave from one end of the line to the other is equivalent to
R1 V
Z, W
va
vb
v R2 t= W
b
Z
V t = W
Resistance line for the voltage v
R2
t = W t = W
t =
R1
Resistance line for the voltage v
a
+Z
t = W Figure 2.613: Description of the traveling wave propagation with Bergeron's method.
i
2.6 Rapidly Changing Fields and Traveling Waves
the transition from one resistance line to the other along the lines according to Eq. (2.621), i.e. along the “Bergeron lines” (thin lines in Figure 2.613). The gradient of the Bergeron line is dv/di = Z or dv/di = Z. It is advisable to choose the scales for v and i in such a way that the Bergeron lines lie at an angle of 45° to the axes and are thus mutually perpendicular. We start at a time instant t = W at the line end (b) with the voltage vb = 0 and we reach the start of the line (a) at the time instant t = 0 with the starting voltage va, which is caused by the voltage step V. The voltages for multiples of the propagation time W are found on the respective resistance line. Graphical methods are often unsuitable for solving complex travelingwave problems. In particular, problems with damped lines, nonohmic terminations, frequency dependences and nonlinearities can only be solved with networkanalysis programs. Thereby, a number of electrically short equivalent lineelements can approximate long lines according to Figure 2.62. Another possibility is approximation with controlled voltage sources with delayed voltages [40].
135
2.6.3 Examples Travelingwave phenomena play a role in many high voltage applications. In the following, three examples are discussed, the disconnector circuits in gasinsulated switchgear (Section 2.6.3.1), the protection zone of a lightning arrester (Section 2.6.3.2) and impulse generation by travelingwave generators (Section 2.6.3.3). 2.6.3.1 GasInsulated Switchgear (“Fast Transients”)
If a disconnector between a deenergized overhead line and an energized busbar in a gasinsulated switchgear (GIS) is closed, there is a breakdown of the remaining clearance between the approaching contacts shortly before the contacts touch each other, Figure 2.614. Then, a very fast rising traveling wave is propagating on the coaxial line of the switchgear bay (1), and it is reflected at the bushing capacitance (4). These waves are the socalled fast transients, already mentioned in Section 2.2.5. They can propagate in the coaxial lines of a GIS with very low damping.
Gasinsulated switchgear (GIS) with singlephase housing
Overhead line
Busbar
Gasair bushing
Disconnector
(2)
Z2
Z1 (1)
Parasitic line
(4)
Z3
(3)
Figure 2.614: Generation of a traveling wave 1 by connection of a deenergized overhead line to an energized busbar. Wave 1 is reflected at the gasair bushing (wave 4) and transmitted or refracted resp. (waves 2 and 3). The transmitted (refracted) waves propagate along the overhead line (wave 2) and along the parasitic line between GIS housing and conducting grounded structures of the building (wave 3).
136
The transmitted (refracted) wave is split into two waves that propagate along the overhead line and along a parasitic line between the enclosure of the GIS and the conducting parts of the GIS building (waves 2 and 3). The amplitudes of the different traveling waves are determined by the characteristic (line) impedances Z1, Z2 and Z3. Furthermore, the capacitance C of the bushing has to be considered in the first moment, because it must first be charged from the incident wave. See Figure 2.69. According to the equivalent transmissionline circuit Figure 2.68, the voltage amplitude of the incident wave can be determined by two factors, i.e. by the voltage difference between the energized and deenergized lines at the instant of the clearance breakdown between the approaching contacts and by the characteristic (line) impedances of the adjacent lines on both sides of the disconnector. Because of the reflection at the relatively high characteristic impedance of the overhead line (Z2), a significant voltage enhancement can occur, which stresses the insulation of the bushing, the switchgear and the overhead line. The traveling wave (3) occurring between the GIS enclosure and other conducting structures is especially critical. Because of the low characteristic (line) impedance Z3, the voltage amplitude is low. Nevertheless, this wave can cause significant damage in insufficiently protected secondary equipment (measurement systems, control equipment etc.) [41]. For instance, a momentary rise of the enclosure potential above ground potential can cause back flashovers into lowvoltage circuits, e.g. into information technology circuits. Generally, rapidly changing electric and magnetic fields leaving the GIS can cause strong interference with neighboring circuits and systems. Therefore, ensuring electromagnetic compatibility (EMC) is of particular value in system design in order to avoid malfunction and damage. Note: During the closing of the disconnector, the described breakdown with the subsequent
2 ELECTRIC STRESSES
transients is not the only process. After the equalization of the potential on both sides of the disconnector, there is no longer any current and the discharge expires. Because of the sinusoidal voltage on the busbar, a voltage difference is reestablished and the insulating gap between the still moving contacts breaks down again. Furthermore, a higher number of reignitions occur until the contacts are fully closed. Very steep voltage and current gradients are generated thereby. Similar processes occur if the disconnector is opened. With increasing distance of the contacts, the breakdown voltage increases and results in increasing amplitudes of the traveling voltage waves. The voltage enhancements caused by reignitions are superimposed onto voltage enhancements caused by slow switchingtransients. Note: In largescale gasinsulated switchgear, reflection processes occur which are difficult to understand and yet still depend on the switching state of the substation. Insulation stresses caused by fast transients are often determined by measurements and by complex numerical simulations. For example, the direct connection of transformers to a gasinsulated switchgear requires a very careful analysis of the transients: Because of the high characteristic impedances of transformer windings, high voltage enhancements caused by reflections can be expected. Additionally, particularly in bigger installations, voltage enhancements can be caused by resonances and slower transients. Note: Fast transients can cause stresses in insulation regions, which are without any stress in a static or quasistatic case. An example is given by a bushing core, Figure 2.615. At first, the incident wave is split up in relation to the characteristic impedances of the coaxial lines, which are formed by the concentric grading layers. Therefore, waves can also propagate in parasitic lines between the grounded flange and the outermost gradingfoil and between the highvoltage conductor and the innermost gradingfoil.
2.6 Rapidly Changing Fields and Traveling Waves
137
2.6.3.2 Protection Zone of a Lightning Arrester
v
Lightning arresters are nonlinear components (resistors), which limit overvoltages and which carry a very small leakage current only at operating voltage. Principles and designs are discussed in Section 6.1.4.3. For a metaloxide arrester, the current increases very strongly if the voltage exceeds the rated voltage Vr, Figure 2.616. During a lightning impulse stress, the voltagecurrent characteristic of the arrester and the lightning current (which can be calculated in an equivalent transmissionline circuit according to Figure 2.68) determine the value of the socalled residual voltage Vres, which defines the lightning impulse protection level Vpl. Note: For a lightning arrester consisting of a nonlinear resistor in series with a spark gap, the protection level is defined by the sparkover voltage of the gap.
An arrester in the course of an overhead transmission line is now discussed, its location is point 1, Figure 2.617 (top). As long as the amplitude of the incident traveling wave is below the protection level Vpl, it is assumed for simplicity that the arrester remains highly resistive and that there are no reflections, Figure 2.617 (middle). If the amplitude of the traveling voltage wave exceeds the protection level, the arrester becomes lowresistive; there are reflected and transmitted wave components that reduce the voltage amplitudes before and
Vr
V res = V pl Rated voltage
Vm Leakage current (μA ... mA)
Lightning current (kA)
i
Figure 2.616: Ideal v,icharacteristic of a metaloxide lightning arrester.
after the arrester, Figure 2.617 (bottom). The resulting voltage distribution is depicted for two different time points by bold lines. The voltage drop 'v at the arrester causes two traveling waves with amplitudes 'v, which are propagating in the opposite +z and –z directions. In the propagation direction of the incident wave (+z direction), the voltage is limited to the protection level Vpl throughout the line. Furthermore, in front of the arrester there is a socalled protection zone Lp, where a given maximum voltage Vmax is not exceeded. It can be seen from the two time points depicted in Figure 2.617 that the voltage limit Vmax at point 2 is valid for any time point. This means that the increasing voltage of the incident wave is always compensated by the increasing voltage of the reflected wave within the protection zone Lp. The incident voltage wave (highlighted in grey) is drawn for a time point at which the
Gasinsulated switchgear
Transformer side Grounded enclosure
v1 v ( z,t ) v 2 v3
** **
* Highvoltage conductor
Figure 2.615: Transient field stresses in a bushing core above and beneath the grading layers at ground and highvoltage potential, i.e. in regions, which are without any field stress in a static or quasistatic case, (*) and (**).
138
2 ELECTRIC STRESSES
permitted voltage Vmax is reached at point 2. After that time point, the reflected wave limits the voltage magnitude to Vmax. The length of the protection zone Lp shall be derived from Figure 2.617. The (spatial) gradient of the wave front is
'v/Lp = wv/wz
= wv/wt)·wz/wt)
1
1
= wv/wt)·u . With 2·'v = Vmax – Vpl the protection zone is Lp
= ½·(Vmax – Vpl)·u / wv/wt).
(2.622)
Numerical example: A lightning arrester with Vpl = 150 kV shall limit a traveling wave rising on a threephase line with a front gradient wv/wt = 500 kV/μs, so that, within the protection zone Lp, only 80 % of the lightning impulse voltage for the 123 kV voltage level shall be reached (this means that Vmax = 0.8 Tranmission line
Arrester
z
1 Incident voltage wave Protection level
Vpl 2
Lp 'v Vmax
z
1 Protection zone
'v Vpl 'v
Figure 2.617: Protection zone of a lightning arrester with interference (i.e. compensation) of oppositely traveling voltage waves after the ignition of the lightning arrester (bottom).
·550 kV = 440 kV). The phase velocity is v = 300 m/μs. According to Eq. (2.622) the relevant protection zone is Lp = 87 m. Note: For the protection zone of a lightning arrester also Lp/ m  Vm/ kV
(2.623)
is given as a rough guide in [22]. Vm is the maximum voltage for equipment (Section 6.1.4). More accurate calculation methods, which consider statistical error rates and acceptable error probabilities, normally give shorter protection zones [124]. Note: The calculation of a protection zone according to Eq. (2.622) is also valid for arrangements with an opencircuit or a high impedance at the end of the line (e.g. a transformer winding) [39]. The distance between arrester and line end or termination must not exceed Lp. The lightning arrester can be at the end of the line.
2.6.3.3 TravelingWave Generators (TransmissionLine Generators)
According to the principle of a socalled cable generator, the capacitively stored energy on a charged transmission line is converted by discharging into a very fast rising impulse in a matching impedance, Figure 2.618. After the breakdown of the switching spark gap, a traveling wave with a voltage amplitude V/2 is propagated on the output line and is absorbed in a load impedance R = Z, which is matched with the characteristic impedance of the line. On the charged line (charging voltage V), a traveling wave with the voltage amplitude V/2 is traveling in the –z direction. After the reflection at the opencircuit line end, the reflected wave propagates with –V/2 in +z direction and discharges the line completely. A squarewave pulse is thereby generated in the load with a voltage V/2 and a halfvalue width tH = 2·WL, which corresponds to twice the propagation time on the charged line. Note: In practice, the (parasitic) inductance of the switching spark gap reduces the output voltage gradient wv/wt. Furthermore, mismatches and line damping cause impulse distortions.
Another principle is the discharging of two parallel lines in the socalled Blumlein gen
2.6 Rapidly Changing Fields and Traveling Waves
erator, Figure 2.619. Both lines with the characteristic impedance Z are connected to their highvoltage conductors. The load R = 2Z is connected to the two grounded conductors via an output line with the characteristic impedance 2Z.
After the charging of the lines to the voltage V, the load is without any voltage, Figure 2.619 (top). After the ignition of the switching spark gap, the upper line is discharged by a traveling wave with the amplitude –V, see no. 1 in Figure 2.619 (middle). At the output end of the line, the characteristic impedance changes from Z to 2Z+Z = 3Z. The reflection and transmission coefficients according to Eq. (2.619) and (17) are rv = 1/2 and Uv = 3/2. This means that the reflected wave travels backwards with the amplitude –V/2, see no. 2. The transmitted (refracted) wave with the amCharging device
139
plitude 3V/2 is divided in the ratio of the characteristic impedances onto the output line to the load (V) and onto the lower pulseforming line (V/2).. The counting direction for the associated voltages is shown by reference arrows in the figure. At the load R = 2Z, which is matched with the output line, there is a voltage step vR(t) = V after the wavefront arrives. The backwards traveling waves on the lines are reflected at the shortcircuited spark gap (SC) on the upper line and at the opencircuit (OC) on the lower line, with and without polarity reversal, see no. 3. The reflected waves, which are transmitted into the output line, have the same polarity and (analogously to refraction no. 2) the amplitude V/2 both, see no. 4. Therefore, the field of the first wave, which was transmitted to the load, is completely compensated with a delay of 2·WL. The voltage Charging device
Switching spark gap
Pulse forming line
Switching spark gap
Load
Pulseforming lines
Z
+V
E
Z
2Z
Z
WL
3
SC 1
Absorption of the wave in the load
3
OC
Time characteristic of the voltage at the load resistance R=Z
V /2
v R(t) 2W L
Figure 2.618: Generation of squarewave pulses by discharging of a pulseforming line (travelingwave generator).
t
4
+V /2 V /2
z
z
R = 2Z
WL
V /2 V /2
Z
E
R=Z
V
Load
V
2
V
V /2 V /2
SC: shortcircuit OC: opencircuit Time characteristic of the voltage at the load resistance R = 2Z
vR(t) 4
V
vR(t)
2W L
Figure 2.619: Generation of squarewave pulses by discharging of parallel pulseforming lines (Blumlein generator).
t
140
2 ELECTRIC STRESSES
Capacitive storage device
Travelingwave generator Particlebeam diode as a load "Target" approx. 50 ns approx. 1 μs
Minutes
typical storage times
Figure 2.620: Module of a pulsedpower generator with spatial and temporal compression of the stored energy (schematic).
at the load decreases from V to zero. Further waves, which travel backwards into the line, compensate each other. An important application of transmissionline generators is the generation of squarewave impulses for stepresponse measurements on measuring systems. Cable generators are mainly used for this purpose. Another application is the pulsed power technology for the spatial and temporal compression of electromagnetic energy in an extremely powerful impulse [42]. For the generation of extreme energy densities, a number of generators are circularly arranged around the target as modules that are triggered simultaneously [14]. The travelingwave generator arrangement can be a driver circuit for the acceleration of particles in basic research applications in physics, Figure 2.620. For example, matter could be brought into extreme conditions in order to ignite nuclear fusion reactions. The principles of the cable generator or the Blumlein generator are chosen depending on voltage and load impedance. The generators are designed as coaxial lines or as parallelplate lines [15]. Voltage enhancements can be achieved by multiple reflections at additional switching spark gaps, i.e. by socalled doublebounce switching [43]. Water is used as an insulating medium because of its very high relative permittivity Hr = 81 and because of its high dielectric breakdown strength. Thereby
high amounts of energy can be stored for short times. Furthermore, the phase velocity is reduced to u = u0/9 = 3 cm/ns and the length of a line can be reduced by a factor of 9 in comparison with air, see Eq. (2.68). Because of the comparatively high conductivity of water, the energy can only be stored for a short time in a range of microseconds (μs). Therefore, it is necessary to charge the waterinsulated line very rapidly from a conventional capacitor bank with approximately the same capacitance (see impulse generators, Section 6.2.3). The capacitor bank can store the energy for longer times, and rapid charge transfer is performed by oscillation. At the voltage maximum, the switching spark gap is ignited before significant selfdischarging of the waterinsulated capacitance can occur, Figure 2.620. The synchronous triggering of the switching spark gaps for the parallel operation of a number of modules places extreme demands on the triggering devices. Example: Waterinsulated impulse generator
A waterinsulated travelingwave generator according to Figure 2.618 shall be designed with coaxial lines for the generation of impulses with energies as high as V = 500 possible. The peakvalue of the voltage shall be Û kV and the halfvalue width tH = 50 ns. The maximum permissible field strength in water is Êmax = 100 kV/cm. According to Eq. (2.324) the maximum field energy of 0.5 a coaxial line is given for R2/R1 = e = 1.65. With the V = 1 MV the radii R1 = 20 cm charging voltage V = 2Û and R2 = 33 cm are calculated from Eq. (2.322). The length of the line is determined by the propagation time 0.5 WL = tH/2 = 25 ns with L = WL·v0/Hr = 83 cm. From the Equations in Figure 2.65, the capacitance C = 7.5 nF and the characteristic impedance Z = 3.3 : is derived. The current amplitude of the output impulse is Î = V /Z = 150 kA and the power is P = 75 GW. Û 2
The capacitively stored energy W = ½ C·V = 3,75 kJ is ideally completely transferred into impulse energy W = V ·Î·tH = 3,75 kJ. In practice, losses must of course be Û considered.
Other impulse circuits and many applications of highvoltage impulsetechnologies are described in Section 7.3.2 and 7.4.2 [482].
for discharges, of breakdown voltages and of discharge times can be observed, Figure 3.11. Therefore, it seems natural to describe these quantities as random variables and to determine the characteristics of discharges by statistical methods. In the following, basic principles of statistical methods are described. Comprehensive discussions can be found in the literature [44].
3 ELECTRIC STRENGTH It is a basic task of high voltage engineering to keep the electric stresses lower than the electric strengths of the materials under all possible circumstances. Unfortunately, the electric strength is a quantity that is subject to significant statistical variations, Figure 3.11. In the following, an introduction to statistics is given at first (Section 3.1). If the electric strength is insufficient, the insulation fails and discharges occur. They depend on the type of insulating material. Discharges in gases (Section 3.2) differ significantly from discharges in other dielectrics (Section 3.3). Special attention is paid to liquids (Section 3.4), solids (Section 3.5) and vacuum (Section 3.7). Discharges that do not lead directly to breakdown are known as partial discharges (Section 3.6). They are especially important for diagnostic measurements and for ageing processes.
3.1.1 Statistical Descriptions of Discharge Processes 3.1.1.1 Random Variables
For example, the breakdown voltage of a spark gap is determined by an applied AC voltage that is increased until the breakdown occurs. If the test is repeated several times, it can be noted that an “exact breakdown voltage” does not exist, and the breakdowns occur at different voltages, Figure 3.11a. Note: Voltage rise tests can also be performed with DC voltage. In the case of impulse voltages, the continuously increasing voltage must be replaced by consecutive impulses with stepwise increasing peak values.
3.1 Introduction to Statistics
By means of a very high (infinite) number of tests, the voltage Û V bd50 with a breakdown probability of 50 % could be determined, as well as a certain withstand voltage (breakdown probability 0 %) and a certain breakdown voltage (breakdown probability 100 %).
The failure of the electric strength, i.e. electric discharges, can no longer be described deterministically because of a high number of different physical parameters. Furthermore, a high statistical variance of inception voltages V Û
V Û
v (t)
lg (V/ V0 )
Û Vbd50 Lifetime characteristic
t
Impulse voltagetime characteristic t
n
a)
b)
Voltage rise tests
Upanddown method Breakdown No breakdown
c) Impulse voltage test, breakdown time (Gasinsulated gap)
Figure 3.11: Examples for the stochastic character of discharge processes. © SpringerVerlag GmbH Germany 2018 A. Küchler, High Voltage Engineering, VDIBuch, DOI 10.1007/9783642119934_3
lg( t/ t 0 ) d) Constantvoltage test, time to breakdown (Solid insulation)
142
In practice, the number of tests is always limited. The characteristic values of a discharge have to be estimated from a limited number of measured values. The accuracy of the estimate is increased with the number of equivalent tests. Example: Upanddown method
The upanddown method is a procedure by which to estimate the 50 % breakdown voltage, Figure 3.11b. It can be applied for the estimation of the impulse strength of gasinsulated spark gaps. The test is started with a voltage where no breakdown is expected, and the voltage is increased in steps of 'v. As soon as a breakdown occurs, the voltage is decreased by 'v. For the consecutive steps, the voltage is increased if a breakdown does not occur, and it is decreased if the breakdown happens. Thereby, the voltages swing stepwise up and down around the 50 % breakdown voltage V bd50. It can be estimated as the arithmetic mean value Û of a predefined number of voltagevalues. The counting starts with the first breakdown. The exact statistical analysis is described in the literature [44].
During a statistical analysis it is assumed that a random sample is taken from an (unknown) basic population. In the case of breakdown tests on a given insulation arrangement, a limited number of breakdowns is taken at random from the theoretically infinite number of all possible breakdown tests on such an arrangement, Figure 3.12. A statistical analysis has to estimate the distribution of the infinite basic population as accurately as possible, based on as low a finite number of tests as possible (i.e. on a sample size as small as possible). The infinite basic population is a theoretical fiction and will remain unknown forever; every statistical statement is therefore an estimate. Nevertheless, it becomes better and better as the number of tests is increased. Instead of the breakdown voltage, other quantities can also be considered as random variables. Examples are breakdown field strength, partial discharge inception voltage, inception field strength or time to breakdown, Figure 3.11c and d. Generally, a random variable is
3 ELECTRIC STRENGTH
described by capital letters X and their definite values obtained by random sampling are given by small letters x. Note: Often, these strict distinctions are not considered in practice: For example, it is often said that a “determination” of a 50 % breakdown voltage Vbd50 is performed, but in reality only an estimate vbd50 is calculated. It is not possible to determine parameters of the (always unknown) basic population, but we can only determine empirical parameters, which are used as estimates of the population parameters. Note: Here, capital and lower case letters do not describe magnitudes and timevarying functions as usual, but they represent random variables and their definite values obtained by random sampling.
3.1.1.2 Cumulative Distribution Functions
The procedure of a statistical analysis shall be explained for the example of a breakdown test with the voltage rise test according to Figure 3.11a, Figure 3.12. Ten breakdown voltages are a random sample taken from a fictitious basic population. Arranged in the order of the tests, they are a master database (master list), which must not have any trend, i.e. any systematical dependence of the values. They must be stochastically independent, which can be tested graphically or by special mathematical test algorithms [44], [396]. The distribution list with sorted values is plotted as a cumulative frequency polygon or a cumulative frequency curve (empirical distribution function) h(x) with x = vbd, Figure 3.12. For the example of ten test values, every single value represents a rate of occurrence of 'h = 10 %. The empirical distribution function is only an imperfect estimate for the cumulative distribution function of the total population. A safe insulation design requires statements about
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143
very low breakdown probabilities (e.g. 1 % breakdown voltage), which cannot be determined directly if the number of breakdown values is small. For this purpose, a mathematical or theoretical distribution function F(x) is sought, which approximates the empirical distribution function h(x) as well as possible, and which can be extrapolated down to very low probabilities, Figure 3.12. The most important cumulative distribution functions are the Gaussian normal distribution (Section 3.1.2.2) and the Weibull (extreme value) distribution (Section 3.1.2.3). Note: By analogy with the cumulative frequency polygon, the theoretical distribution function is often known as the cumulative distribution function, it is the integral of the (probability) density function, Figure 3.15. Note: By means of graphical and arithmetical tests, it can be investigated, which type of
* Unknown basic population *
Random sample (master list) e.g. 10 breakdown values, test for statistical independence
*
Sorted random sample values as cumulative frequency polygon (empirical distribution function)
of a suitable fitting function/ * Selection theoretical distribution function
100 %
h (x) F (x)
function gives the best approximation of the measured values (statistical distribution test) [44], [396]. After the selection of the distribution type, the mathematical distribution curve has to be described numerically by parameters, which are estimated from the measured values. These parameters are different depending on the type of the distribution function, Section 3.1.2.2 and 3.1.2.3. This type of parameter estimation is known as a point estimate. It gives mean values or variances, which can be used to describe a Gaussian normal distribution for instance. The point estimate is further explained in the following sections. A mathematical distribution function is only an estimate for the (always unknown) cumulative distribution function of the total population of all possible values. By means of an
90 % confidence limit
80 % 90 % confidence limit 60 %
(e.g. normal or Weibull distribution)
* Estimation of parameters *
40 %
Mathematical distribution Specification of a
* confidence level (e.g. 90 %) *
Calculation of confidence intervals (e.g. with 90 % confidence limits)
of a withstand voltage * Estimate with low breakdown probability, e.g. as 1 % breakdown voltage with a 90 % confidence interval
20 %
Cumulative distribution function (mathematical/ theoretical distribution function)
Cumulative frequency polygon (empirical distribution function)
1% 0%
x 01 v bd01
x50 vbd50
Confidence interval
Figure 3.12: Statistical analysis of breakdown values from a voltage rise test according to fig. 3.11a.
x vbd
144
interval estimation, confidence intervals are determined containing the distribution function of the total population with a specified probability (e.g. 90 %), Figure 3.12. For a small sample size, confidence intervals are broad and the estimate is very uncertain. With increasing sample size, confidence intervals decrease and the certainty of probability statements increases. Calculation of confidence intervals is described in the literature [44], [396]. The practical importance of the mathematical distribution function and the associated confidence interval is the determination of voltages with very low breakdown probabilities (socalled withstand voltages). According to Figure 3.12, the estimate x01 = vbd01 for the 1 % breakdown voltage (more generally for the 1 % quantile of a probability distribution) can be determined from the mathematical distribution curve. Furthermore, it can be said that the 1 % breakdown voltage can be found within the 90 % confidence interval (limited by the confidence limits) with a probability of 90 %, Figure 3.12. Note: Unfortunately, these confidence intervals are very broad at low breakdown probabilities for many dielectrics, especially for liquid and solid insulating materials. Therefore, statements about low breakdown probabilities are only possible with high uncertainties. In engineering design, a withstand voltage therefore needs an additional safety margin. 3.1.1.3 Parameter Estimation In the following, the point estimate of parameters is described, which are generally valid, i.e. which are not related to any special distribution function (empirical parameters). Sometimes they can also be used in mathematical distribution functions, e.g. in the Gaussian normal distribution. We distinguish measures of mean values and measures of statistical dispersion. The (fictitious) parameters of the basic population are discussed together
3 ELECTRIC STRENGTH
with these (empirical) parameters, which are calculated from a limited number of measured values. a) Measures of mean values For the basic population consisting of all possible values, the mean value or the (mathematical) expectation value is defined as the value μ or E(X), which is expected for the random variable X. Formally it is given as the (infinite) sum of all single values xi, weighted with their individual probability pi:
P
E( X )
f
¦ pi xi
(3.11)
i 1
Another measure of mean values is the median, the central value or the 50 % quantile (the 50 % value) q50 = x50, which is the central value of all single values xi. Half of the values xi is below and half of the values xi is above the median. In reality, only an empirical distribution of a limited number n of discrete measured values xi can be determined. If all values xi exist only once, i.e. if the rate of occurrence is hi = 1/n, the empirical estimate of the expectation value μ is the arithmetic mean value by analogy with Eq. (3.11): xm
x
n
¦ hi xi
i 1
1 n ¦ xi  P . ni 1
(3.12)
The empirical central value or the empirical median qˆ 50 xˆ 50 is either the value that is situated in the middle of the sorted values (for an uneven number of measured values) or the mean value of the two values in the middle (for an even number of measured values). Half of the measured values are below and half of the values are above the central value. The median is often used as an estimate for the arithmetic mean value. Note: In statistics, empirical quantiles are often characterized by a “^”. In order to avoid confusion with peak values, which are very important in high voltage engineering, this characterization is not used below.
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145
Note: The 50 % breakdown voltage vˆbd50 is the empirical median (central value) of the random variable “breakdown voltage” Vˆbd . In the latter case, the meaning is again peak values!
b) Measures of statistical dispersion The statistical dispersion of the basic popula2 tion is described by the variance V , which is the meansquare deviation of the random variable X (i.e. of all individual values xi) from the 2
expectation value μ. Formally, V is given as the square of the deviation (xi  μ), weighted with the individual probabilities pi:
V2
E( X P)2
f
¦ p i ( xi P ) 2
(3.13b)
The empirical variance according to Eq. (3.15a) with the weighting 1/(n1) would give an indeterminate expression “zero/zero” for n = 1. Form this it is clear that it is not possible to give any statements about statistical dispersions with a single measured value only.
V2
and V(X) = V/μ
are the standard deviation V and the variation coefficient V. Empirical measures of statistical dispersion for a finite number n of discrete measured values xi are the meansquare deviation 1 n ¦ ( xi x m ) 2 n i 1
s n2
(3.14)
and the empirical variance
The quantities
s
s2
and v
s / xm
Note: Another empirical measure of statistical dispersion is the range R:
xmax  xmin
(3.16)
3.1.1.4 Example: Series of Measurements Empirical distribution of breakdown voltages: In a voltage rise test 19 breakdown voltages are determined (master database, master list):
 V  V
For small random sample sizes n, enhanced values of 2 the empirical variance s and for the empirical standard deviation s result from weighting with the factor 1/(n1). For large sample sizes n, the difference between 2 weighting with 1/(n1) and 1/n disappears, and s or s 2 can be considered as good estimates for V or V.
R =
1 n ¦ ( xi x m ) 2  V 2 (3.15a) n 1 i 1
s2
2
Note: The empirical variance s and the empirical standard deviation s (r.m.s.d.) are not calculated with the relative rate of occurrence 1/n (as could be expected 2 from Eq. 3.13 for the variance V and the standard deviation V), but with the factor 1/(n1). This is necessary for reliability purposes, as in Eq. (3.14) and (5a) only the estimate xm = x can be used instead of the expectation value μ. For a theoretical case with n = 1, the meansquare deviation according to Eq. (3.14) would always give the 2 value sn = 0 as the values xi and xm = x are identical. Nevertheless, a higher dispersion could exist and could be calculated with a larger random sample. Therefore, the weighting with 1/n is too optimistic.
The quantities
V
Note: Unfortunately, v and V have to be introduced as general statistical quantities here. Nevertheless, the characters v and V are mostly used for voltages in this book. Please consider the relevant context.
(3.13a)
i 1
pirical variation coefficient v, which are used as estimates for the standard deviation V and the variation coefficient V.
(3.15b)
are the empirical standard deviation s (rootmeansquare deviation, r.m.s.d.) and the em
vbdi/kV = 102; 100; 107; 98; 95; 100; 104; 99; 92; 102; 103; 99; 97; 95; 101; 104; 98; 94; 100. In a distribution table, the values are sorted and the rates of occurrence are calculated:
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3 ELECTRIC STRENGTH
Voltage Rate of occurrence Cumulative frequency in kV absolute relative absolute relative
92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109
1 0 1 2 0 1 2 2 3 1 2 1 2 0 0 1 0 0
0.05 0 0.05 0.1 0 0.05 0.1 0.1 0.15 0.05 0.1 0.05 0.1 0 0 0.05 0 0
1 1 2 4 4 5 7 9 12 13 15 16 18 18 18 19 19 19
0.05 0.05 0.1 0.2 0.2 0.25 0.35 0.45 0.6 0.65 0.75 0.8 0.9 0.9 0.9 0.95 0.95 0.95
If the distribution list is lightly populated only, it is often advisable to sort the values into classes. In the given example a class interval d = 3 kV is chosen (start at 91.5 kV), see the horizontal lines in the distribution list: Class in kV
Rate of occurrence absolute relative related to d
Relative cumulative frequency
The curve of the relative (breakdown) density h related to the class interval d = 3 kV is a density function h/d that can be used to read off estimates for the probability density, Figure 3.13b. Note: The probability density can be approximated by a density function, which is also known as a probability density function. It is the derivative of the (cumulative) distribution function, see Figure 3.15.
1,0 0,9 0,8
Relative cumulative frequency h6
0,6 0,5 0,4 0,3
Central value (median)
Staircase function
v bd50
0,2
v bd /kV
0,1 0,0
90 92 94 96 98 100 102 104 106 108 110 s
> 91.5  94.5 > 94.5  97.5 > 97.5  100.5 >100.5  103.5 >104.5  106.5 >106.5  109.5
2 3 7 4 2 1
0.1 0.15 0.35 0.2 0.1 0.05
0.033 /kV 0.050 /kV 0.117 /kV 0.067 /kV 0.033 /kV 0.017 /kV
0.1 0.25 0.6 0.8 0.9 0.95
The curve of the relative cumulative frequency h6 describes the empirical distribution function, Figure 3.13a. The arbitrarily chosen division into classes determines the curve of the staircase function, which differs somewhat from the cumulative frequency polygon with the single values. Estimates for the probability of a breakdown at different voltages can be taken from the empirical distribution function. At 94 kV, the breakdown probability is approximately 10 % (vbd10, 10 % quantile) for example. For voltages above 104 kV, a breakdown can be expected in more than 90 % of the test cases (vbd90, 90 % quantile).
Cumulative frequency polygon
0,7
vbdm s R
Figure 3.13a: Relative cumulative frequency (rate of occurrence) of measured values as empirical distribution function with and without division into classes.
Frequency density 0,12 0,1 0,08
Class interval d = 3 kV
d
frequency/ interval ratio h/d /kV 1
0,06 0,04 0,02 0,0
90 92 94 96 98 100 102 104 106 108 110
v bd /kV Figure 3.13b: Relative (breakdown) frequency related to the different classes as estimates of the probability density (probability density function).
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147
Numerical example: The following parameters are calculated from the values of the previous example, Figure 3.13a: x
Arithmetic mean value, Eq. (3.12) xm
x
=
vbdm
=
99.47 kV
Central value (median) (from Figure 3.13a) x50
=
vbd50
= 100
kV
15
kV
x
Range, Eq. (3.16) R =
x
Empirical standard deviation, Eq. (3.15a) s = 3.82 kV
x
Variation coefficient, Gl. (3.15b) v = 3.84 %
3.1.2 Description of Discharge Processes by Distribution Functions
nonlinear division of the vertical ordinate is made for a linear division of the horizontal abscissa: The percentage values of the distribution curve F(x) in the upper figure are transferred to the straight line in the lower figure. Mathematically, this is a transformation of the linearly divided ordinate by means of the in1 verse function F (x). After a series of measurements is taken, the master database is sorted and a distribution table is built. Then, a hypothesis about the type of the distribution is established and the cumulative frequency distribution is drawn in the corresponding probability paper plot. This allows us to compare the shape of the empirical distribution function with the straight line of the theoretical distribution (test of the distribution type), fig, 3.14. In case of doubt, 100 %
For the mathematical description of an empirical distribution function, the measured values are approximated by a theoretical mathematical function, which best fits the measured values. Then, the mathematical function allows statistical parameters, probabilities and confidence intervals to be calculated. Note: The mathematical distribution function is just a formal and arbitrary approximation of measured values without direct respect to the underlying physics. In the following, the Gaussian normal distribution and the Weibull distribution are discussed. Many other distributions are described in the literature [44], [396]. 3.1.2.1 Comparison of Empirical and Theoretical Distribution Functions At first, the type of cumulative distribution function must be selected for the best fit of the measured values. A practical test procedure is the use of a socalled “probability paper plot” (probability grid) with axisdivisions that give straight lines for the tested distribution type, Figure 3.14. The figure indicates how the
80 %
F ( x)
60 % 40 % 30 % 20 % 0%
99 %
F ( x) 90 % 80 % 60 % 40 % 30 % 20 % 10 % 1%
x
Figure 3.14: Curve of a mathematical distribution function (top), which is a straight line in a corresponding "probability paper plot" (bottom), compared with the empirical distributions of two different series of measurements.
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3 ELECTRIC STRENGTH
the comparison has to be performed with different probability grids corresponding to different distribution types. Note: The comparison between empirical and theoretical distribution function can also be performed mathematically. Nevertheless, trends in the range of very low and very high probabilities can often be estimated better by the graphic method [44].
After the approximation of the empirical distribution curve as a straight line in a probability paper plot, the characteristic values of the corresponding distribution can be taken from the graph. Then, the probability for the occurrence of an incident (e.g. breakdown at a given voltage) is normally calculated from the mathematical distribution function. Especially for very low and very high probabilities (e.g. for calculating certain withstand and certain breakdown voltages), significant errors can occur if the hypothesis deviates from the real distribution. Note: The estimation of a distribution parameter (e.g. mean value or standard deviation) from a limited number of measured values is the socalled point estimation. The point estimate lies within a statistical confidence interval, which can be determined by means of an interval estimation (confidence estimation). The confi
1
Today, the statistical analysis of measured values can be performed automatically with numerical programs. Thereby, the measured values undergo a test for stochastical independence, a determination of the distribution type, point estimations for the parameters to be determined, and interval estimations for the confidence intervals. 3.1.2.2 Gaussian Normal Distribution The Gaussian normal distribution describes random variables, which can be considered as a sum of many independent and arbitrarily distributed random variables, each of which only contributes to the sum to a minor extent. Therefore, the normal distribution can be applied to many processes in nature, science and technology, e.g. to stochastic noise or statistical measuring errors. The normal distribution is symmetric to the expectation value μ, and it is of infinite width, i.e. from x =  f to x = + f.
D (x )
VS V
PV P PV 100 %
dence interval is the region where the point estimate (e.g. the mean value) lies with a given probability (e.g. of 90 % or 95 %). The larger the sample size that is chosen, the smaller the confidence interval that can be assumed. Therefore, the higher the number of measured values that is determined, the higher the accuracy of the point estimate [44], [396].
x
F (x )
84 %
Note: In contrast to this, discharge processes are characterized by a lower and an upper limit, i.e. by a definite withstand voltage and a definite breakdown voltage. Nevertheless, the normal distribution is used for approximation in many cases, but it will not always be possible to approximate a given empirical distribution by a normal distribution satisfactorily. In many cases, the Weibull distribution allows a better fit.
The probability density function 50 %
D ( x) 16 %
PV P PV
x
Figure 3.15: Gaussian normal distribution with probability density function D(x) and cumulative distribution function F(x).
1
V
2ʌ
e
( x P )2 2V 2
(3.17)
is described by the expectation value μ (approximated by the arithmetic mean value xm according to Eq. (3.12)) and the standard deviation V, which is estimated by analogy with Eq. (3.15a), Figure 3.15:
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149
1 n 2 ¦ ( xi xm ) n 1 i 1
V 2  s2
(3.18)
The cumulative distribution function F(x) is given by integration of the probability density function Eq. (3.17): x
³ D( x) d x
F ( x)
(3.19)
f
With the probability density function according to Eq. (3.17), this integral cannot be ex1,0 0,9 0,8
pressed by an analytical function. Therefore, the probability density function D(x) is expanded into a power series (Taylor’s series), which can be integrated in parts [39]. Then, the cumulative distribution function F(x) is given as a series expansion, which cannot be represented by an analytical function, but from which numerical values can be calculated. In practice, these values are taken from tables [6]. An extract is given in the following: x
D(x)
F(x)
x =
μ  4.0·V μ  3.5·V μ  3.0·V μ  2.5·V μ  2.0·V μ  1.5·V μ  1.0·V μ  0.5·V
0.0001/V 0.0009/V 0.0044/V 0.0175/V 0.0540/V 0.1295/V 0.2420/V 0.3521/V
0.00003 0.00023 0.00135 0.00621 0.0228 0.0668 0.1587 0.3085
x =
μ
0.3989/V
0.5
x =
μ + 0.5·V μ + 1.0·V μ + 1.5·V μ + 2.0·V μ + 2.5·V μ + 3.0·V μ + 3.5·V μ + 4.0·V
0.3521/V 0.2420/V 0.1295/V 0.0540/V 0.0175/V 0.0044/V 0.0009/V 0.0001/V
0.6915 0.8413 0.9332 0.9772 0.99379 0.99865 0.99977 0.99997
Cumulative frequency
h6
0,7 0,6
Distribution function of the Gaussian normal distribution
0,5 0,4 0,3 0,2
v bd /kV
0,1 0,0
90 92 94 96 98 100 102 104 106 108 110
V
v bd V
Figure 3.16: Comparison of an empirical distribution (cumulative frequency polygon) with a theoretical distribution function (Gaussian normal distribution). Frequency density 0,12 0,1 0,08
d d = 3 kV
Specific frequency h/d /kV 1
Density function of the Gaussian normal distribution
0,06 0,04 0,02 0,0
90 92 94 96 98 100 102 104 106 108 110
v bd /kV Figure 3.17: Comparison of the empirical density function (frequency density) with a theoretical density function (Gaussian normal distribution).
By means of parameter estimation for μ and V, the theoretical normal distribution is fitted to the empirical cumulative frequency polygon. Example: Series of measurements (continued from Section 3.1.1.4)
For the example treated in Section 3.1.1.4, the estimate for the expectation value is μ  xm = 99.47 kV and the estimate for the standard deviation is V  s = 3.82 kV. The corresponding distribution and density functions of the Gaussian normal distribution are compared with the empirical distribution and density functions, Figure 3.16 and 7.
If there is a sufficient correspondence (as in the case of the example) between hypothesis and measurement, i.e. between the Gaussian normal distribution and the cumulative frequency polygon, it is justified to calculate
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3 ELECTRIC STRENGTH
probabilities by means of the theoretical distribution function. In the case of x = μ  3V = 87.0 kV for example, there is only a negligible breakdown probability of 0.13 %, i.e. this value can be considered as an estimate for the withstand voltage vbd0. For x = μ + 3V = 110.9 kV, the breakdown probability is 99.87 %, therefore this value can be considered as a definite breakdown voltage vbd100. In a similar way, the question is answered, at which voltage a certain and given breakdown probability can be expected. An interpolation between given values (or percentages) of the cumulative distribution function in tables may have to be performed for this purpose. Note: Probability density functions are derivatives of cumulative distribution functions. Therefore, they are more sensitive to variations, and they are less appropriate for a comparison between empirical and theoretical functions, Figure 3.17.
3.1.2.3 Weibull Distribution
With x d x0 we obtain F(x) = 0. The probability density function D(x) is the derivative of the distribution function F(x), Figure 3.18 (top). Some special values of the cumulative distribution function F(x) are calculated from Eq. (3.110): Initial value
x = x0
F(x) = 0
63 % quantile
x = x63
F(x) = 0.63
End value
x=f
F(x) = 1
(e.g. withstand voltage)
(e.g. certain breakdown voltage)
The Weibull distribution can be described by the three parameters x0 (location parameter, initial value, lower extreme value), x63 (63 % quantile) and G (Weibull exponent, shape parameter or slope). Sometimes the difference z63 = x63  x0 is called the scale parameter. By means of the location, shape and scale parameters, the threeparameter Weibull distribution usually gives a good approximation of the cumulative frequency polygon for a se
The Weibull distribution is an extreme value distribution that is limited at the lower end. It is especially suitable for the description of breakdown processes, as it is normally assumed that there is a minimum breakdown voltage vbd0 (withstand voltage), i.e. a location parameter x0 (lower extreme value, initial value), Figure 3.18. The idea that a considered event (e.g. the breakdown of an arrangement with many parallel insulation gaps) occurs as the extreme value of all possible events (e.g. in the weakest insulation gap) gives an analytical expression for the cumulative distribution function [44]. It is valid for all values x that are higher than the initial value x0 (e.g. the withstand voltage):
F ( x)
1
e
{
x x0 G } x63 x0
(3.110)
D (x)
F( x )
x0
x 63
x
x0
x 63
x
100 % 63 %
Figure 3.18: Weibull distribution with density function D(x) and distribution function F(x).
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151
ries of measurements, see Figure 3.12 for example. Normally, the Weibull approximation is better than the approximation by the unlimited Gaussian normal distribution with two parameters. An estimate for the 63 % quantile can be taken directly from the cumulative frequency polygon. For example, from Figure 3.12 we obtain x63 = vbd63 = 100.6 kV by interpolation between the 0.6 and 0.65 values. It would be an oversimplification to take the lowest value of the cumulative frequency polygon as an estimate for the initial value x0 (e.g. x0 = 90 kV from Figure 3.12). In practice, there is a very high uncertainty regarding such an estimation, especially for small sample sizes. In order to avoid incorrect conclusions, e.g. if a withstand voltage is to be determined, a smaller value must be chosen for x0, which cannot be estimated accurately in most cases. Therefore, x0 is very often set to zero (x0 = 0). Thereby the cumulative distribution function is simplified to the twoparameter Weibull distribution, which cannot be adapted to empirical distributions as well as before. The Weibull exponent G can be estimated as the slope of a straight line in a loglog diagram. From Eq. (3.110) we obtain {
x x0 G } x 63 x 0
ln {1 F ( x)}
.
x x0 G lg { } x 63 x 0
lg { ln
1 } 1 F ( x)
. (3.112)
Eq. (3.112) is the equation of a straight line, if the common logarithm on the right hand side is the ordinate value, the logarithm on the left hand side is the abscissa value and the Weibull exponent G is the gradient. In order to establish a probability paper plot, both logarithms are evaluated numerically, and this gives a probability grid for the Weibull distribution with logarithmicallysubdivided axes, Figure 3.19: Abscissa
and
ordinate subdivision
z/z63
lg{z/z63}
F(z) lg{ln[1  F(z)]}
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 2 3 4 5 6 7 8 9 10
1  0.699  0.523  0.398  0.301  0.222  0.155  0.097  0.046 0 0.301 0.477 0.602 0.699 0.778 0.845 0.903 0.954 1
0.01 0.02 0.05 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.99
 1.998  1.695  1.290  0.977  0.651  0.448  0.292  0.159  0.038 0.081 0.207 0.362 0.663
lg { ln [ 1 F ( x) ]}
=
and z63 =
x  x0 x63  x0 ,
The cumulative frequency polygon in Figure 3.12 and 3.16 shall be approximated by a Weibull distribution function. For the 63 % value (quantile), x63 = vbd63 = 100.6 kV is directly taken from Figure 3.19. An estimate must be found for the initial value x0. For example, the withstand voltage x0 = 87.4 kV, which was estimated by means of a Gaussian normal distribution, is taken for this purpose. Thereby we obtain
With the transformations
we obtain
z z 63
Example: Series of measurements (continued)
For the graphical representation in a probability paper plot, the common logarithm is calculated on both sides:
z
G lg
(3.111)
z
=
and z63 =
x
 x0
=
x  87.4 kV
x63  x0
=
13.2 kV.
Now the abscissa in Figure 3.19 can also be subdivided into voltage magnitudes:
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3 ELECTRIC STRENGTH
x/kV 92 93 94 95 96 97 98 z/z63 0.348 0.424 0.500 0.576 0.652 0.727 0.803
With the values from Figure 3.12, a cumulative frequency polygon is established, which can be approximated by a best fit straight line, Figure 3.19.
99 100 101 102 103 104 105 0.879 0.955 1.030 1.106 1.182 1.258 1.333
The Weibull exponent G can be estimated from the straightline gradient of an empirically determined distribution curve. For that purpose, the coordinates z1 and z2 for two points
106 107 108 1.409 1.485 1.561
99 %
0.1
0.2
0,3 0.4
0.6 0.8 1
3 z z 63
90 % 80 % F( z )
2
4
=
5 6 7 8 10 x
 x0 x 63  x 0
70 % 60 % 63 % 50 % 40 % 30 % 20 %
10 %
5%
2% x 63 1% 100 104 108 92 94 96 90 xx/kV = v bd /kV The abscissa with voltages is related to the example in the text only, it has to be calculated individually for every analysis. It is determined by the individual values for x and x . 0 63 Figure 3.19: Probability paper plot for the Weibull distribution with logarithmic axes in a normalized representation (ordinate and upper abscissa). Cumulative frequency polygon for the example in fig. Bild 3.12 together with an abscissa subdivided into voltage units that are related to the example (lower abscissa). Approximation of the empirical distribution in fig. 3.12 by a best fit straight line.
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153
on the straight line are inserted into Eq. (3.112). From the difference of the two equations
G ·[ lg
z z1  lg 2 ] = z 63 z 63
lg { ln
1 } 1  F ( z 1)
 lg { ln
1 } 1  F ( z 2)
the exponent is calculated as:
lg { G
ln [1 F ( z1 ) ] } ln [1 F ( z 2 ) ] z lg 1 z2
(1) Parameters can be estimated by graphical approximation  see above for examples. (3.113)
For the series of measurements in the described example according to Figure 3.13 and 9, the function value at z1/z63 = 0.29 is F(z1) = 2 % = 0.02, and the function value at z2/z63 = 1 is F(z2) = 63 % = 0.63. With Eq. (3.113) the exponent is calculated:
G =
ples are given in Section 3.1.1.3 and in the two preceding sections. In these cases, parameters were determined by graphical approximation of straight lines for example. Furthermore, there are a number of statistical estimation techniques that will be at least briefly mentioned here:
3.15
With this, all parameters of the Weibull distribution (x0, x63 and G) are estimated for the given example.
Note: From Eq. (3.111) and (12) it can be seen that the magnitude of the exponent G is strongly dependent on the definition of the initial value x0. If x0 is changed, a new determination of G has to be performed.
(2) Parameters can be estimated by calculation of empirical moments as estimates for theoretical moments (method of moments). In this context, the measures of mean values according to Eq. (3.12) are moments of first order and the measures of statistical dispersion according to Eq. (3.14) and (5) are moments of second order. (3) Parameters can be estimated with the maximum likelihood method in such a way that the probability of the statistical sample is maximal. (4) The least square method provides parameters with the minimal rootmeansquare deviation. These methods and the methods of interval estimation require thorough analyses of the mathematical fundamentals of statistics, which cannot be given here [44], [396].
3.1.2.4 Parameter Estimation The Weibull distribution and the Gaussian normal distribution are extraordinarily important in high voltage engineering. Nevertheless, they are only discussed as examples. There are a number of other distributions which are used in high voltage engineering (e.g. lognormal distribution, doubleexponential distribution, Wohlmuth’s twolimit distribution, gamma 2 distribution, F  /chisquared distribution, F/Fisher distribution, t /Student distribution, and mixed distributions). Deeper discussions can be found in the literature [44], [396]. The parameters for the description of the different cumulative distribution functions have to be estimated from measured values. Exam
3.1.3 Statistical Size Effects It is a problem of high voltage engineering that breakdown voltages, breakdown strengths and lifetimes are normally determined with small laboratory test samples, with a small number of test objects, or during only short test durations. Then, these results have to be transferred to insulations of large size, to a large number of objects or to very long stress durations. According to experience, electric strengths (e.g. the 50 % breakdown voltage) decrease if the size of the arrangements, the number of test objects, or the stress duration is “enlarged” (law of enlargement), for example:
154
3 ELECTRIC STRENGTH
very short stress durations does the accidental presence of a free start electron influence the magnitude of the breakdown voltage (or field strength).
Critically stressed volume
m·A 1 A1
m·V 1
Statistical volume, area, distance and length effects are based on the fact that a breakdown needs a highly stressed insulation volume.
V1 Area effect
1 2 3 4 Effect of large numbers
Volume effect
m
Figure 3.110: Size effects for the examples of area effect, volume effect and largenumber effect, with greycolored critically stressed insulation volumes.
x
with increasing insulation volume, area, distance or length (volume, area, distance or length effects),
x
with increasing number of equal test objects (Largenumber effect) and
x
with increasing stress duration (time effect, lifetime characteristic).
For a statistical explanation of these strength reductions, the insulation arrangement must be subdivided into smaller parts, which can be subject to breakdowns independently from each other, and which have a known cumulative distribution function (e.g. from experiments). The condition of stochastical independence is not always fulfilled, e.g. for the time effect. Insulations that break down after different stress durations are not equal in terms of statistics. They are differently aged by timedependent chemical and physical processes. For most of the solid and liquid dielectrics, there is a functional dependence of the electric strength on the stress duration, additional to the statistical dispersion. Only in the range of
In strongly nonuniform fields, a critically stressed volume can only be found in a thin layer close to the curved electrode, Figure 3110. If the arrangement is enlarged, primarily the enlargement of the electrode surface area adjacent to the highfield volume has to be considered (area effect). Insulation defects reduce the electric strength only if they are close to the electrode surface. In uniform and weakly nonuniform fields, the whole (critically stressed) insulation volume has to be considered, if the arrangement is enlarged (volume effect), Figure 3.110. Insulation defects reduce the electric strength throughout the dielectric volume. Highly stressed areas, volumes and parallel test objects shall each be considered as “parallel connections” of m equal and independent elements (area elements, volume elements or test objects), Figure 3.111. It will be assumed
F ( v bd ) 100 %
Ff( v bd )
Pf = 0 m
Pm = P1
Fm( v bd ) F1 ( v bd )
63 % 50 %
P1
v bd 0
v bd 50 v bd 63
v bd
Figure 3.111: Statistical size effect for the parallel operation of m equal and independent elements described by a distribution function with a lower limit (e.g. Weibull distribution).
3.1 Introduction to Statistics
155
that the cumulative distribution function F1(vbd) for the breakdown voltage of a single element (index 1) is known (breakdown probability). The cumulative distribution function Fm(vbd) for the breakdown voltage of m parallel elements (index m) will be calculated. The withstand probability P1 for a single element 1 (probability that a breakdown does not occur) is considered: P1(vbd) =
1  F1(vbd)
(3.114)
If a number of equal elements are equally stressed, the withstand probability Pm decreases. It can be calculated by multiplication of the individual probabilities of the elements: Pm
Example: Capacitor bank
A capacitor bank is made of 40 capacitors with an individual breakdown probability F1(10 kV) = 0.1 % at the charging voltage V = 10 kV. For a parallel operation of the capacitors, a breakdown probability F40(10 kV)  40·0.1 % = 4 % is to be expected. This is an unacceptably high value for equipment which is destroyed during a breakdown. Therefore, the charging voltage must not be raised above a safe withstand voltage Vbd0.
Statistical size effects mainly result in a reduction of the 50 % and the 63 % breakdown voltages, fig, 3.111. This reduction can be calculated for the Weibull distribution according to Eq. (3.110). With Eq. (3.115) the withstand probability is
[e
Pm (vd )
= P1·P1·P1·P1· ...... ·P1
e
= [1  F1(vbd)]·[1  F1(vbd)]· ...... ...... ·[1  F1(vbd)] m
= [1  F1(vbd)]
(3.115)
Note: For m o f, the withstand probability Pm approaches zero, i.e. the breakdown becomes certain, but only if the voltage is above the initial value vbd0, Figure 3.111. Below this value, a breakdown cannot occur (“singlepoint distribution”). Therefore, a correct determination of the initial value vbd0 is highly desirable, especially in the range of low breakdown probabilities. In the range of low breakdown probabilities F1(vbd) K). In regions with low field strength the attachment of electrons (D < K) predominates.
DK !
fulfilled
N crit not fulfilled
x0
x d
Figure 3.218: Development of electron avalanches in a nonuniform field close to a negative electrode tip. Regions with positive and negative Top: effective ionization coefficients. Middle: Field strength curve along the xaxis. Bottom: Avalanche development with electron numbers above and below the critical number.
3.2 Gas Discharges
to exceed the value kst/ki. The value for SF6 is approximately 0.7 kV. Note: For nonuniform SF6 insulations the critical electron number Nkrit can be reached even for comparatively short path lengths x, in comparison with air for example. This is caused by a strong increase of the effective ionization coefficient De with E/p above the field strength limit (E/p)0 = 8.87 kV/(bar·mm). Therefore, very limited local field strength enhancements by surface roughness or particles can trigger a streamer mechanism, even if the field strength limit is not yet reached in the macroscopic field. The sensitivity of SF6 insulations against surface roughness and contaminations by particles requires special care during manufacturing and assembly processes of gasinsulated switchgear (GIS). Therefore, they have to be tested onsite for freedom form partial discharges after the final assembly.
The former considerations are basically valid in nonuniform fields both for negative and positive point electrodes. During the integration procedure according to Eq. (3.248) and (49) it has to be considered that the avalanche grows in the +x direction for a negative and in the –x direction for a positive point respectively.
3.2.4 Impulse and Highfrequency Breakdown 3.2.4.1 Statistical and Formative Time Lag (Discharge Delay)
Only static breakdown voltages and field strengths have been considered previously. This means that the voltage is applied over such a long period or is increased so slowly that breakdown delay effects cannot be observed at all. In the case of fast rising voltages it has to be considered that breakdown does not occur directly at t = t0 when the voltage exceeds the static sparkover voltage V0. Breakdown cannot develop before an initial electron occurs after the statistical time lag ts (ignition delay) and before a conductive streamer has developed
183
during the formative time lag tf (streamer formation delay), Figure 3.219. The formation of a high current discharge and the final voltage collapse coincide with a comparatively short time of voltage collapse tc, which is determined by the spark resistance laws and by the elements and properties of the discharge circuit. During the total time to breakdown tT =
t0 + ts + tf + tc
(3.253)
the stressing voltage v(t) with the peak value Vmax can significantly exceed the static breakdown voltage V0. This means that the impulse factor f =
Vmax/V0
(3.254)
can be much greater than one. Note: The sum of statistical and formative time lags tbd =
ts + tf
(3.255)
is also known as the discharge time lag. Very often, the time of voltage collapse tc is comparatively short and can be neglected. The statistical time lag ts is caused by the stochastic character of electron generation by ionizing radiation and thermal processes. The Initial electron is present
Voltage collapses
v(t) V max Voltagetime "area"
A
V0
t0
ts
Static breakdown voltage
tf
tc
t
Figure 3.219: Discharge delay by the statistical time lag and by the formative time lag for a transient voltage stress (impulse voltage).
184
3 ELECTRIC STRENGTH
time lag decreases with an increasing highly stressed gas volume as the probability for the generation of an initial electron increases with an increasing critically stressed gas volume (volumetime characteristic). Because of statistical size effects according to Section 3.1.3, the 50 % value of the ignition delay time (i.e. the statistical time lag ts50) decreases with increasing number of critically stressed volume elements 'V, Figure 3.220. Thereby, Wm = 1  Fm is the probability for the absence of an initial electron in m volume elements 'V, which decreases with increasing volume. For very large volumes, ts50 therefore becomes very small. In a given volume, the probability F(ts) for the presence of an initial electron (initiating an avalanche) approaches 1 with increasing ignition delay time ts. The statistical time lag for air is in the region of a few 10 ns only if the electrode distances are longer than 1 mm [39]. Longer statistical time lags can be found for SF6, because of the attachment of free electrons to gas molecules. The statistical time lag can be practically eliminated by irradiation of the cathode with ionizing ultraviolet light. Furthermore, it can be reduced by a very rough cathode surface with local field stress enhancements causing
F (t )
Wf = 0
s 100 %
m
W1
50 %
Note: Very high values of statistical time lags are measured in small voids, bubbles or cavities within dielectric materials. The probability for the presence of an initial electron is significantly reduced in small enclosed gas volumes, see Section 3.6.1.2.
The formative time lag tf from the first avalanche to the formation of a conductive channel (i.e. the spark formation time) can have very different values. If Townsend’s generation mechanism is considered, many consecutive avalanche and ion transit times are required for the formation of a conductive channel. The formative time lag is of the order of 10 μs. The Townsend mechanism can only occur for small pd values and for voltages close to the static breakdown voltage V0. At high overvoltages according to Figure 3.219, the ionization coefficient D increases significantly. Therefore, the transition to the streamer mechanism occurs even for significantly smaller pd values, and the streamer mechanism can be assumed in most of the practical cases. The propagation velocity (growth velocity) of the streamer channel u(x, t) = dx/dt
V = m· 'V
u(x,t) = K·{E(x,t) – E0(x)}.
0 s50(f)
t
s50 (m)
V = 1· 'V
t
s50(1)
t
(3.256b)
If the dependence of the field strength on the variables position x and time t is described by the functions g(x) and v(t), i.e. by E(x,t) = g(x) · u(t) ,
t
(3.256a)
increases with E(x,t) if the reference field strength for streamer inception E0(x) is exceeded [418]. Assuming a proportionality, it can be stated that
V of
Wm = W1
field emission of electrons at high overvoltages.
s
Figure 3.220: Statistical size effect for the decreasing the statistical time lag with the increasing critically stressed gas volume.
(3.256c)
it is concluded that dx/dt = u(x,t) = K · g(x) · {v(t) – V0} . After separation of the variables x and t, two corresponding integrations from one electrode
3.2 Gas Discharges
185
to the other (along x from x = 0 to d) and from the beginning of streamer formation to the beginning of voltage breakdown (over t from t = t0 + ts to t0 + ts + tf) can be performed: d
dx 䌿K ·g ( x)
circuit
t0 ts tf
䌿 {v(t )  V0 } dt .
t0 ts
(3.256d)
The voltagetime area A is also identical with the left hand side of Eq. (3.256d), which exclusively consists of geometric quantities and gas properties. Therefore, A is a constant quantity which is typical for a given arrangement (Kind’s voltagetime law or equal area criterion) [418]:
䌿{v(t )  V0}dt
R (t) C
Note: Below the reference voltage V0, the conditions for streamer formation are not fulfilled and streamers are not possible. The reference voltage is nearly identical with the static breakdown voltage.
t0 ts
L
i (t)
According to Figure 3.219, the right hand side of the equation describes a voltagetime area A below the voltage curve v(t) and above the reference voltage V0. The area is related to streamer formation only and can therefore be called a formative area.
t0 ts tf
Voltage collapses
A
const.
(3.256e)
If the formative area A is related to the static breakdown voltage V0, a characteristic time A/V0 is defined for the given arrangement. It can vary between 10 ns (for nearly uniform arrangements) and some 100 ns. A/V0 is strongly dependent on the field efficiency factor K, but not so much on the flashover distance d [418]. Note: For very nonuniform arrangements, the formative area A can also be related to the flashover distance d. For airinsulated pointtoplane arrangements, the constants A/d = 400 kV·μs/m (negative point) and 650 kV·μs/m (positive point) are given as approximate values [16].
In nonuniform fields discharge delay times are longer than in uniform fields, because of the
sp
stray
v (t)
v (t) tc
t
Figure 3.221: Ringing discharge process of a (stray) capacitance and collapse of the voltage after fomation of a conductive streamer.
comparatively small gas volume with high field strength. Thereby, they show a higher scatter and the formative time lag is prolonged, because of the decreasing streamer velocity in the lowfield region, Eq. (3.256b). The time tc that is necessary for the final collapse of the voltage corresponds to the spark formation time. It depends on the parameters of the discharge circuit and the timedependent values of the spark resistance Rsp(t). In most cases, the final breakdown causes a damped ringing during the discharging of stray and circuit capacitances via the circuit inductance and Rsp(t), Figure 3.221. A quartercycle is approximately equivalent to the time of voltage collapse tc. Note: Very fast voltage collapses in the region of a few ns can occur in gasinsulated switchgear (GIS) because of the small distances and low inductances. For example, the time constant of the current increase during discharging of a line with the characteristic line impedance ZW = 50 : is W = L/ZW = 2 ns only, if the inductance of a ten centimeter long discharge channel is approximately L = 10 cm·1 nH/mm = 100 nH, see Figure 2.68. Furthermore, the voltage collapse at enhanced pressure can be extremely fast in electronaffine gases, Section 3.2.7.1 and Eq. (3.292). Thereby, traveling waves are excited on the weakly damped lines, causing significant overvoltages (fast transients, Section 2.6.3.1). Voltage collapses in airinsulated equipment
186
3 ELECTRIC STRENGTH
are significantly slower because of longer spark formation times, longer insulating distances and higher circuit inductances.
v (t) (1)
A 3.2.4.2 Voltagetime Characteristics
If it is assumed that the statistical time lag and the time of voltage collapse are negligible in comparison with the formative time lag tf, the impulse voltagetime characteristic for the breakdown process can be determined from the equal area criterion (Kind’s voltagetime law) according to Eq. (3.256e), see Figure 3.222: For a given impulse voltage curve v(t) (e.g. lightning impulse voltage 1.2/50 μs) and for a given arrangement with static breakdown voltage V0 and voltagetime area A, an initial electron should be present immediately after exceeding V0, i.e. the statistical time lag is neglected (ts = 0). Thereby, an avalanche/ streamer starts and approaches the electrodes. Breakdown occurs as a voltage collapse when a conductive streamer is formed between the electrodes. This is assumed after the voltagetime area A is reached, see curves no (1) to (4) in Figure 3.222. If the necessary voltagetime area is not reached although V0 is exceeded, streamer growth stops before a conductive channel between the electrodes develops and the breakdown no longer occurs, (curve no. 5). The impulse voltagetime characteristic is determined from the correlation of breakdown times and voltage peak values of the considered voltage curve. The voltagetime characteristic increases towards shorter times. It is of general importance in high voltage engineering that electrical stress amplitudes can be increased if stress durations are reduced (impulse voltagetime characteristic). Example: Sparkgap lightning arrester
Sparkgap lightning arresters can be built with low static breakdown voltages V0 close to 100 V if they are filled with inert gases. Because of their voltagetime characteristic, fast rising overvoltages can overshoot signifi
A
(2)
A
(3)
A
(4)
V0
(5)
t Figure 3.222: Determination of a voltagetime characteristic according to Kind's equal area criterion A=const. for a lightning impulse voltage 1.2/50 μs. cantly up to some kV before they are chopped by a gas breakdown. Therefore, only coarse protection is realized, e.g. in order to divert high lightning currents. Sensitive components have to be protected additionally by an electronic fine protection.
The voltagetime characteristic is strongly dependent on the shape of the corresponding impulse voltage curve. This can easily be explained by the equal area criterion. Voltagetime characteristics measured with the standard lightning impulse voltage (1.2/50 μs) cannot be directly applied to other voltage curves. Measured breakdown times often show a large scatter. On one hand, the scatter results from the statistical time lag and from the variation of the formative time lag especially in nonuniform fields. On the other hand, limited variations of the area A have a significant impact on the breakdown time if the voltage curve is close to the limit case of the criterion, see Figure 3.222 curve (4). Therefore, the empirical determination of a voltagetime characteristic gives a broad band. If enough data are available, cumulative frequency polygons for breakdown times can be considered and curves for breakdown probabilities of 5 % and 95 % can be calculated enclosing 90 % of the expected breakdowns.
3.2 Gas Discharges
187
In many cases the Gaussian normal distribution is applied and the breakdown band can be delimited by the threefold empirical standard deviation on both sides of the arithmetic mean value tm. Thereby, estimates for a certain withstand time tm  3V and a certain breakdown time tm + 3V are calculated according to Section 3.1.2.2. Note: Instead of the breakdown time the breakdown voltage can also be regarded as a random variable. Example: Chopping spark gap
During testing of highvoltage equipment (transformers, bushings etc.) tests often have to be performed with “chopped lightning impulses” in order to simulate the impact of very fast voltage transients. For this purpose, a chopping spark gap is connected in parallel to the test object; the gap has to spark over within a time interval between 4 and 6 μs [52]. If it is not possible to use a triggered spark gap which can be specifically ignited at a predefined time, preliminary tests are necessary in order to determine the scatter of the breakdown times at a given test voltage amplitude. If necessary, the electrode distance has to be adjusted so that all breakdowns occur within the specified time interval. Note: During the testing of components for gasinsulated switchgear (e.g. grading capacitors) very fast voltage collapses are required in order to simulate the impact of fast transients. Very short streamer formation times cannot be achieved in a spatially extended impulse circuit with an air gap, therefore “chopping under SF6” is often required. For this purpose, the chopping spark gap is integrated into the enclosed and SF6 insulated test
(1)
(2)
In strongly nonuniform fields the streamer propagation velocity is significantly reduced in the lowfield regions, see Eq. (3.244b). Therefore, the formative time lag tA is long and the voltagetime area A is large. Voltagetime characteristics show a significant increase towards shorter times. Example: Insulation coordination
Outdoor installations and simple protective airgaps have voltagetime characteristics with comparatively high gradients because of their non uniform fields and long flashover distances, Figure 3.223. Gasinsulated switchgear (SF6 insulated GIS) with more uniform fields and with shorter flashover distances have only gently sloping voltagetime characteristics. If the reference voltage V0 is the same, a breakdown is to be expected at first in SF6, unless the stress in the GIS is reduced by traveling wave refractions.
3.2.4.3 Highfrequency Breakdown
(3)
Figure 3.223: Voltagetime characteristics for a simple airgap (1), an insulating gap in a GIS (2) and a lightning arrester (3).
In uniform and weakly nonuniform fields there are high field strengths along the entire path between the electrodes and favorable conditions to streamer propagation exist if the reference voltage V0 is exceeded. Therefore, the streamer propagation velocity according to Eq. (3.244a) is high, the formative time lag tf is short and the voltagetime area A is small, see Eq. (3.356). Voltagetime characteristics are comparatively flat down to a few 100 ns.
Valvetype/ sparkgap arresters are made of a series connection of spark gaps with a nonlinear SiC resistor. The spark gaps have a flat voltagetime characteristic in order to fulfill their protective function, including for fast rising overvoltages, according to the principles of insulation coordination. Modern metaloxide arresters no longer need spark gaps, Section 6.1.4.3.
v (t)
~ 1 μs
vessel in order to achieve a very fast voltage collapse (see Figure 3.221, comments above and Section 3.2.7.1).
t
In contrast to transient impulse stresses, highfrequency stresses are longlasting. With increasing frequency up to 1 MHz, the breakdown strength of air at standard atmospheric conditions decreases down to 80 % of the 50 Hz strength [46]. This is caused by re
188
3 ELECTRIC STRENGTH
moval of mobile electrons close to the anode and by residual positive ions which form a positive space charge cloud. After the polarity reversal, the positive space charge is in front of the cathode and increases the local field strength significantly.
Then, the ionization coefficient has to be integrated along the electron path x according to Eq. (3.29b). Unfortunately, there is no universally valid result such as Paschen’s law for the uniform field, but rather the result depends on the individual field geometry in this case.
The breakdown strength increases again above 3 MHz. Then, the electrons cannot follow the fast changing field without decelerating and the field distortion by residual positive ions no longer occurs. Additionally, the statistical discharge delay has a strengthincreasing effect. At 100 MHz the strength is 1.5 to 1.6 times higher than at 50 Hz [46].
In weakly nonuniform fields, there are favorable ionization conditions with De > 0 along the whole path between the electrodes if the field strength is sufficiently high. As soon as the ignition condition for the Townsend or the streamer mechanism is fulfilled, breakdown occurs immediately. Predischarges do not occur above a critical field efficiency factor Kc, Figure 3.224. For air under standard atmospheric conditions, the critical value is Kc  0.2.
In nonuniform fields, highfrequency predischarges (both corona and surface discharges) show higher currents and higher light intensities than lowfrequency predischarges because the lowfield regions can be bridged more easily by higher displacement currents, which are proportional to frequency. This causes a reduction of breakdown strength because of the early inception of leader discharges, see Section 3.2.5. Note: In solids (and sometimes also in liquids) there are dielectric losses (dissipation) that strongly increase with frequency. If heat transfer conditions are too unfavorable, thermal instability and the socalled thermal breakdown can occur at comparatively low voltages (in comparison with 50 Hz), see Section 3.5.2.
3.2.5 Discharges in Nonuniform Fields 3.2.5.1 Predischarges and Breakdown
Prior to the ignition of a gas discharge in a nonuniform field, spacechargefree conditions can certainly be assumed, but the field is not uniform, as was assumed for the derivation of Townsend’s ignition condition, Section 3.2.2.1. For the calculation of electron avalanche growth and for the determination of an ignition condition, it is necessary to consider the variation of the ionization coefficient D(E) with the field strength E(x) and with the location D(E(x)) respectively, see Eq. (3.210).
In strongly nonuniform fields, high field strengths and favorable ionization conditions (De > 0) only occur close to the curved electrode surface if the field efficiency factor K is below the critical value Kc. In the lowfield region, De becomes negative for electronaffine gases (SF6, oxygen and air), because of predominant electron attachment processes, Figure 3.218. If the ignition condition is fulfilled at the curved electrode, predischarges (corona discharges) occur without immediately causing breakdown. They begin as glow discharges (Townsend mechanism) at the curved electrode surface in the highfield region only. With increasing voltage, spacecharge dominated streamer discharges (bunch discharges) start, which can propagate into the lowfield region as long as the background field is strong enough. If the background field strength is too low for streamer growth, the streamer fades away. The remaining lowfield gas volume between discharge head and counterelectrode is an ohmiccapacitive impedance stabilizing the predischarge, Figure 3.23b. Note: The stabilization of glow discharges in a strongly nonuniform field can be explained by the following simplified model [2]: The predischarge at a curved electrode shall approximately be regarded as an increase of the effective electrode radius [2]. If a concentric outer
3.2 Gas Discharges
189
Vi , Vbd Breakdown voltage
Vd
Predischarge (corona) inception voltage
Vi strongly
20 %
weakly nonuniform field
100 % Field efficiency factor
K
Figure 3.224: Predischarge (corona) inception and breakdown voltage in strongly and weakly nonuniform fields at constant electrode distances.
For very long flashover distances (more than 1 m), sufficiently long stress durations and sufficiently fast voltagetime responses, the streamer growth, which is driven by collision ionization and photoionization, can be intensified by thermal ionization. Thereby, a highcurrent and bright channel is formed, which is known as a leader or leader discharge. At the head of the leader there are divergent streamer bunches supplying the leader’s channel with the current that is necessary for thermal ionization. The conditions for leader discharges in atmospheric air, at distances of some meters and voltage amplitudes of many 100 kV are fulfilled for a switching impulse voltage of 250/2500 μs (positive point electrode) or a power frequency voltage (halfcycle with positive point electrode) due to displacement currents and current durations, but not for lightning impulses or DC voltages. 3.2.5.2 Polarity Effect
conductor with the radius Ra is assumed, there is a minimum field strength for a specific radius of the inner conductor, e.g. Ri min = Ra/e for cylindrically symmetric arrangements, see Section 2.3.1.2 and 2.3.1.3. If the radius of the glow discharge is smaller than Ri min (strongly nonuniform field), an increasing glow radius would cause a decreasing field strength and a stabilization of the predischarge. For radii that are greater than Ri min (weakly nonuniform field), an increasing glow radius would cause an increasing field strength. The glow radius would no longer be stable and breakdown would occur immediately, which is in agreement with Figure 3.224.
The inception voltage Vi of predischarges (corona discharges) decreases with decreasing field efficiency factor (i.e. with increasing nonuniformity of the field), Figure 3.224. The breakdown voltage Vbd is stabilized at a higher level because of space charge clouds shielding the curved electrode (“point electrode”). Discharge processes are strongly influenced by the polarity of the point electrode (polarity effect). Breakdown occurs only at a higher voltage Vbd, if the field strength in the lowfield region is sufficiently high for streamer growth to the counterelectrode.
In a nonuniform field, there is a significant difference between the corona inception voltage and the breakdown voltage, which are both strongly dependent on polarity. For a negative point electrode, the predischarge inception voltage is comparatively low, but breakdown only occurs at comparatively high voltages. For a positive point electrode, the predischarge inception voltage is comparatively high, but the breakdown occurs at comparatively low voltages (polarity effect). The reason for this apparently inconsistent behavior is the formation of a positive space charge close to the point electrode. It will be explained for the example of a pointtoplane arrangement with a very nonuniform electric background field Eg, Figure 3.225: For a positive point electrode, avalanches have to start within the gas volume because of the very low field strength at the cathode, Figure 3.225 (left). A first avalanche can start, if external radiation generates an initial electron within the region with positive ionization coefficient (i.e. close
190
3 ELECTRIC STRENGTH
point electrode. A positive space charge cloud remains in front of the point electrode because of the comparatively immobile positive ions, Figure 3.225 (left middle). Thereby, the electric field strength is reduced in front of the point electrode, and it is enhanced in the lowfield region in front of the plane electrode, Figure 3.215 (left bottom). Simultaneously, the ionization boundary x = x0 with De = 0 (at E = E0) is shifted towards the plane electrode. The field stress enhancement in the lowfield
to the point electrode). The avalanche grows into the direction of increasing field strength towards the point electrode. If the critical number of electrons Ncrit is reached, new consecutive avalanches are permanently initiated within the gas volume by intense photoionization (streamer mechanism). Therefore, the first avalanche is followed by an abruptly increasing discharge current and a stable glow discharge. The electrons are removed via the positive
De > 0
Eg
De < 0
De > 0
x
Space charge density
x
Space charge density
x d
x0
E(x)
De > 0
Eg
De < 0
x0
E(x)
De < 0
E0
x d
De < 0
E0
E(x) Eg( x)
Attachment of electrons to gas molecules
x
De > 0
E(x) Eg( x)
Figure 3.225: Polarity effect in a nonuniform field for a positive point (left) and a negative point electrode (right). Top: Streamer propagation in highfield regions with positive effective ionization coefficient. Middle: Formation of positve space charges by remaining positive ions in the highfield region (left and right) and formation of negative space charges by attachment of electrons in the lowfield region (right). Bottom: Field strength curve E(x) along the xaxis for the spacechargefree background field (thin lines) and for the spacechargedominated resulting field (bold lines) with a shifting of the ionization boundaries.
x
3.2 Gas Discharges
191
region improves the conditions for streamer growth into the lowfield region and for breakdown.
Accordingly, the breakdown at AC voltage is to be expected at the peak of a halfcycle when the point electrode is positive.
For a negative point electrode, an initial electron has to be provided on a very small surface on the point electrode. Therefore, a long discharge delay can be caused by the statistical time lag before a free electron is available, see Section 3.2.4.1. If the inception voltage is reached, a series of sporadic corona impulses occurs, which also depend on the work function of the cathode material [25].
Example: Dielectric ion screen
The initiated streamers propagate into the lowfield region, Figure 3.225 (right top). After crossing the ionization boundary De = 0, the number of electrons in the avalanche is reduced by attachment to electronaffine gas molecules, and a negative space charge is generated in the lowfield region, Figure 3.225 (right middle). Close to the point electrode, the avalanches leave a positive space charge cloud. Thereby, the electric field strength is significantly enhanced in front of the point electrode, and the field distribution is made uniform in the lowfield region up to the plane counterelectrode Figure 3.225 (right bottom). Simultaneously, the ionization boundary x = x0 with De = 0 (at E = E0) is shifted towards the point electrode. Note: The increase of the negative space charge can reduce the field strength in front of the negative point electrode so that the predischarge is extinguished. It is ignited again after the negative ions have drifted to the anode. Thereby a continuous series of socalled Trichel impulses is generated. The repetition rate increases with increasing voltage because of the increasing ion drift velocity. If the drain of negative ions is equal to the regeneration, the intermittent impulse discharge changes over to a continuous predischarge.
For the negative point electrode, streamer propagation into the lowfield region and breakdown are postponed by the equalization of the field strength profile, Figure 3.225 (right bottom). Therefore it can always be stated that Vbd (neg. point) > Vbd (pos. point).
(3.257)
Field distortion by ions can be shown impressively by a thin insulating screen (dielectric ion screen) between point and plane electrodes in air under standard atmospheric conditions, Figure 3.226. Without a screen, DC breakdown voltages are very different for positive and negative point electrodes, as was stated above, Eq. (3.257). If the dielectric ion screen were to be replaced by a plane metallic electrode at the potential of the point electrode, the field between the two planes would be uniform with breakdown voltages according to curve (1). For medium distances the dielectric ion screens show very similar behavior for both polarities, see curves (2) and (3). For a positive or a negative pointelectrode, positive or negative ions respectively are deposited on the screen surface. They displace the pointelectrode potential onto the screen and homogenize the field distribution between the charged dielectric screen and the plane counterelectrode. The screen is most effective when close to the positive point electrode because the drift of positive space charges into the lowfield region is prevented, see Figure 3.225 (left). Close to the plane counterelectrode,
120
Vbd /kV
Uniform field with d = 40 mm
(1)
100
(2) 80 Negative point without screen 60 Neg. point
positive point without screen
40
(3)
20
x
10
Point electrode
Pos. point
40 x /mm
20 30 Dielectric ion screen Plane
Figure 3.226: Impact of a dielectric ion screen on breakdown voltage in a very nonuniform d.c. field for a positive and a negative point electrode in air under standard atmospheric conditions.
192 the ion screen has the effect of a displaced space charge region for both polarities. This is similar to the positive pointtoplane arrangement without a screen and with a positive space charge that is responsible for the low breakdown voltages.
During fast transient voltage stresses (e.g. lightning impulse voltages), space charges cannot be accumulated as discussed above. In weakly nonuniform fields, even the first avalanche causes breakdown (streamer discharge). Therefore, the negative point electrode has a lower breakdown voltage than the positive point electrode because of the better avalanche starting conditions, see Section 6.3.1.1 (polarity effect for the sphere gap). Also for rodrod spark gaps, there are other dependences because of corona discharges on both sides, see Section 6.3.1.2.
3.2.5.3 Corona Inception, PreDischarges If the voltage is increased at a very nonuniform pointtoplane arrangement and different predischarge phenomena can be observed prior to breakdown, Figure 3.227. They depend on voltage, polarity and flashover distance d. The inception of corona discharges takes place if the ignition condition for the streamer mechanism in the spacechargefree background field according to Eq. (3.249) is fulfilled. To a firstorder approximation, the direction of integration and the polarity of the point electrode play a minor role. Actually, the inception behavior is also influenced by the electrode material and by the statistical time lag for the generation of initial electrons. The ignition condition can be interpreted analytically both for concentric cylinders (E ~ 2 1/r) and for concentric spheres (E ~ 1/r ) by the application of an ionization coefficient according to Eq. (3.221), [39]. As a result, transcendental equations are deduced. They can be solved for the inception field strength Ei if the exponential functions are approximated by second order polynomials (parabo
3 ELECTRIC STRENGTH
las). The following assumptions are made: a given radius of curvature for the inner electrode RC = R1, a large radius of the concentric outer electrode R2/R1 > 5 and a relative air density G. Ei =
1/2
G K1 {1 + K2/(G RC) } .
(3.258)
For different gases, the constants K1 and K2 are listed in table 3.25, both for cylindrical and spherical symmetry. If the corona inception voltage is reached at first, an intermittent corona occurs because of the statistically scattering generation of initial electrons. At slightly higher voltages, field conditions start to change because of space charge accumulation close to the point electrode, see Section 3.2.5.2. A stable and continuously burning glow discharge is formed. In a dark room, it can be seen as a continuous weak bluish glow or a continuous corona, Figure 3.227 (right bottom). Note: In the case of a negative point electrode, the socalled Trichel impulses occur at first, Section 3.2.5.2. Table 3.25: Constants for the corona inception voltage according to Eq. (3.258). K1
——————
K2
——————
kV/cm Air N2 SF6
30.0 44.0 90.5
cm1/2 Cylinder
Sphere
0.33 0.28 0.12
0.47 0.40 0.17
Since glow discharges in air need a specific voltage per unitlength EG =
25 kV/cm
(3.259)
(for standard atmospheric conditions), the range of a glow discharge is limited. At higher voltages, isolated streamers grow out of the diffuse glow discharge and propagate into the lowfield region because of their spacecharge field. Superposition of many streamers gives bunchlike discharge phenom
3.2 Gas Discharges
193
Predischarge phenomenon
Existence ranges of discharge phenomena
Vbd , Vi MV
Vbd()
Leader d.
Leader mech. Thermal ionization
Specific voltage drop per unit length 1.5 ... 0.1 kV/cm
Vbd(+) 4,5 ... 7 kV/cm Streamer discharge
Streamer mechanism Collision ionization
10 ... 15 kV/cm
Glow discharge
Townsend mechanism Collision ionization
Vi kV
for air at standard atmospheric conditions
Flashover distance cm
d
m
25 kV/cm
Critical field efficiency factor K
crit
Figure 3.227: Existence ranges of predischarges in an airinsulated pointtoplane arrangement (schematic). Inception and breakdown voltages as a function of flashover distance d for positive and negative points (left). Predischarge phenomena and the corresponding specific voltage drop along the discharge channel (right), [22].
ena for both polarities (streamer/ bunch discharge), Figure 3.227 (middle). A negative streamer discharge (coming from a negative point electrode) has to propagate through a volume with a field strength that is reduced by space charges, Figure 3.225 (right bottom). Therefore, the negative streamer needs a comparatively high specific voltage drop, which has to be provided by the background field (values for air at standard atmospheric conditions):
bottom). Nevertheless, such a discharge activity stretches out in the opposite direction with time, and it is therefore commonly known as a “positive streamer”. It propagates through a volume with a field strength that is enhanced by space charges. Therefore, the positive streamer only needs a comparatively low voltage drop, which has to be provided by the background field): ES(+) =
4.5 ... 7 kV/cm
(3.261)
Negative streamers start directly at the point electrode and propagate for comparatively constant lengths depending on field geometry, Figure 3.227 (right middle).
Values are valid for air at atmospheric standard conditions; the lower value applies to longer distances above 20 cm. Thus, the range of a positive streamer is much longer than the range of an equivalent negative streamer. This is in accordance with the lower breakdown voltage.
A socalled “positive streamer discharge” (coming from a positive point electrode) consists of electron avalanches propagating towards the point electrode, Figure 3.225 (left
Positive streamers start randomly distributed within the critically stressed volume. Therefore, the individual streamers have different lengths. They can combine in front of the point
ES() =
10 ... 15 kV/cm
(3.260)
194
3 ELECTRIC STRENGTH
electrode forming channels with higher currents, Figure 3.227 (right middle). Consequently, positive streamers have a more irregular and erratic appearance than negative ones. At high current densities, a bright channel of a socalled leader discharge exists, in which thermal ionization generates a large number of additional charge carriers. Since conductivity increases dramatically, the leader only needs a very low specific voltage drop, which has to be provided by the background field): EL =
0.1 ... 1.5 kV/cm
(3.262)
Values are valid for air at standard atmospheric conditions. The higher applies to shorter distances above approximately 1 m. Thus, the range of a leader is very large. After the inception of a leader discharge, very long distances will be bridged if the voltage is slightly increased.
Leader discharge inception voltages are only slightly below breakdown voltages and must therefore be avoided. At the head of the leader, there is an intense leader corona supplying the current to the leader channel. A leader always consists of a thermally ionized highcurrent channel and a bunchlike streamer corona at its head, Figure 3.227 (right top). The conditions for the formation of a thermally ionized leader channel are
x
a sufficiently extended corona,
x
a sufficiently long stress duration and
x
a sufficiently fast voltagetime response with high displacement currents.
These conditions are normally fulfilled for long flashover distances of more than 1 m in air and for both switching impulse voltages (250/2500 μs positive point electrode) and for power frequency voltages (point electrode at positive halfcycle), but not for lightning impulses or DC voltages.
Note: Leader discharges can also develop on the surfaces of thin insulating materials (surface discharges) at significantly lower voltages because there is a comparatively high capacitance between the discharge corona and the counterelectrode. Therefore, a high displacement current can be supplied to the thermally ionized discharge channel.
3.2.5.4 Breakdown Voltages Breakdown voltages in atmospheric air can be described as follows: Fields with a very weak nonuniformity (field efficiency factors between K = 1 and K  0.8) can approximately be described by equations for uniform fields, Eqs. (3.235), (42) and (43). The calculated voltage values are valid for DC, AC, switching impulse and lightning impulse voltages because the ignition delay in the uniform field is short owing to the high streamer propagation velocity in a semiuniform field. In weakly nonuniform fields (field efficiency factors between K  0.8 and Kcrit  0.2), Eq. (3.258) can be used to calculate inception voltages, which are identical with the breakdown voltages in this case: Vbd =
Vi =
Ei·K·d
(3.263)
In strongly nonuniform fields (field efficient factors K < 0.2), stable predischarges occur before the breakdown. Very roughly, breakdown voltages can be estimated if the range of a predischarge 'a is compared with the flashover distance d. According to Figure 3.228, the discharge range of a streamer 'aS can be calculated from the potential curve of the background field Mg(x) and from the specific voltage drop along the discharge channel ES·'aS, Eqs. (3.259) to (62). The discharge grows as long as the voltage drop in the discharge can be provided by a potential difference in the background field. The breakdown voltage is
3.2 Gas Discharges
195
reached if the discharge range reaches the counterelectrode, i.e. if 'a = d.
ters and decimeters, lower values for longer distances in decimeters and meters.
For flashover distances of a few mm, glow discharges with EG = 25 kV/cm can be assumed and the breakdown voltage can be estimated by
For very long flashover distances above 1 m and AC or positive switching impulse voltages, a leader discharge with currentgathering streamers develops, Figure 3.227. In this case, the breakdown voltage is the sum of the voltage drops VS and VL in the streamer and in the leader
Vbd G 
EG·d .
(3.264)
For longer flashover distances, streamer discharges can be assumed: Vbd S 
ES·d
(3.265)
Specific voltage drops per unitlength ES are given by Eqs. (3.260) and (61). Higher values are valid for shorter distances in centime
S
(3.266)
at the moment at which the whole flashover distance is bridged: d
=
'aL + 'aS
(3.267)
Note: For this reason, there are technological and economical limits for maximum AC transmission voltage levels.
E(x)
The literature contains calculation and estimation methods for leader breakdown [16], [22].
E(x) Spacecharge dominated field
ES ' VS
Example: Rodtoplane arrangement
Eg (x)
x
Background field
'a
M (x)
VL + VS
For very long flashover distances, the specific voltage drop per unitlength is very low and the breakdown voltage now increases only slightly with distance, Figure 3.229.
' VS 'a
Vbd L =
d
S
'a
1.) The field efficiency factor of the arrangement will be estimated for the model of a sphere in free space according to Eq. (2.38):
S Discharge
ES
' VS
K = E0/Emax = (V/d) / (V/Rc) = Rc/d = 0.01. Obviously, the arrangement is very nonuniform. If the voltage is increased, stable predischarges will occur.
Background field M g (x) 'a
S
The discharge behavior of a rodtoplane arrangement with a flashover distance d = 1 m and a radius of curvature Rc = 1 cm at the end of the rod will be described for different voltage wave shapes.
x d
Figure 3.228: Estimation of a predischarge range from the specific voltage drop per unitlength within a discharge in comparison with the potential curve of the background field for a positive streamer [22].
2.) Corona inception will occur at Ei = 44 kV/cm, Eq. (3.258). According to Eq. (2.38) or (3.263), this is equivalent to an inception voltage Vi = 44 kV that is nearly independent of the (very long) flashover distance V i = 44 kV is equivalent to the U d. For AC voltages, Û r.m.s. value Vi rms = 31 kV.
196
3 ELECTRIC STRENGTH
V bd (1) A.c. power frequency voltage U Û (2) Switching impulse voltage
3 MV (2) (1)
times to breakdown, without changing the flashover distance, see Figure 3.222 and Section 3.2.4.2 on voltagetime characteristics. In a nonuniform field, these characteristics are much steeper than in a uniform field because of the slower streamer propagation velocity, Figure 3.223.
2 MV
3.2.5.5 Impact of Different Parameters
1 kV/cm Leader breakdown
1 MV
5 kV/cm Streamer breakdown 0 MV 0m
4m
8m
12 m
d 16 m
Figure 3.229: Peak values of the breakdown voltage for a.c. voltage (1) and positive switching impulse voltage (2) in a pointtoplane arrangement for very long flashover distances d in air [22]. 3.) Negative DC voltage: With Eq. (3.265) and ES() = 10 kV/cm, a streamer breakdown is expected at Vbd S() = 1 MV. A measured value is 900 kV [22]. 4.) Positive DC voltage: With ES(+) = 5 kV/cm, a streamer breakdown is expected at Vbd S(+) = 500 kV. 5.) Power frequency AC voltage: Breakdown is exV bd U pected in the positive peak with ÊS(+) = 5 kV/cm at Û = 500 kV or Vbd rms = 353 kV respectively. For longer flashover distances, breakdown voltage is no longer proportional to distance because of the incipient leader mechanism, Figure 3.229. 6.) Negative and positive switching impulse voltages: Breakdown voltages are comparable with DC values. Measured values are slightly higher for negative and slightly lower for positive polarity (1.1 MV and 450 kV) owing to the incipient leader mechanism, Figure 3.229. Note: At sufficiently long flashover distances, positive switching impulses have a lower dielectric strength than shortduration lightning impulses and slowly rising AC halfcycles because there are optimum conditions for the leader mechanism. Therefore, a minimum strength is given at a “critical time to crest” [16]. 7.) Peak values for negative and positive lightning impulse voltages (1.1 MV and 550 kV) are slightly above the corresponding DC values. This reflects the breakdown behavior while the test voltages are increasing in steps. The first breakdowns occur in the tail of the voltage curve at a voltage that is lower than the recorded peak value, Figure 3.222. Note: While the impulse voltage amplitudes are increasing, there are increasing overvoltages and shorter
The discussions on nonuniform electrode arrangements in the earlier sections mostly consider airinsulation under standard atmospheric conditions. The variation of the parameters geometry, pressure, temperature, gas humidity, type of gas and field distortions has significant influences in many cases. For details, see the specialist literature [16], [22], [46], [53], [54], [55]. Only some basic dependences will be discussed here: 1.) The geometry of the pointtoplane arrangement is the extreme case of a nonuniform field with the lowestpossible field efficiency factor. Other arrangements, even the pointtopoint arrangement, have lower field strengths at the nonuniform electrode, Figure 3.230. First, this causes higher corona inception voltages. Secondly, breakdown voltages are also enhanced, but they are determined primarily by the dominant discharge mechanism. The growth of the streamers and leaders is primarily dominated by the space charge field and not so much by the background field and the electrode geometry. Note: For an ideal pointtopoint arrangement that is completely symmetrical relative to ground, there is no polarity effect. There is always one side from which a positive streamer with its comparatively low specific voltage drop can start. In practice, a polarity effect cannot be avoided because one of the point electrodes is often connected to ground and the maximum field strength is reduced there by means of the grounded structures in the environment.
2.) The influence of pressure, temperature and air humidity can be described by an airdensity correction factor k1 and by an airhumidity correction factor k2 [133]. The real breakdown voltage Vbd is deduced from the breakdown voltage Vbd 0 under standard atmospheric conditions:
3.2 Gas Discharges
Vbd =
197
Vbd 0·k1·k2
(3.268)
Pointtoplane arrangement
The atmospheric standard conditions are temperature air pressure air humidity (absolute) and air humidity (relative)
T p h r
E
= 20 °C, = 1023 mbar, = 11 g/m³, = 60 %.
Pointtopoint arrangement
For the airdensity correction factor, based on the curved character of the Paschen curve we use the approximation m
k1 = G
(3.269a)
The relative air density contains the parameters pressure (mbar) and temperature (°C) 293 K p 1013 mbar 273 K T
G
(3.269b)
Note: If there are only small deviations from the standard atmospheric conditions in a uniform field, the Paschen curve Eq. (3.234) or (35) can be linearized in the density range 0.9 < G < 1.1, and an exponent m = 1 can then be used, see Section 6.3.1.1.
The breakdown in a strongly nonuniform field is not determined by the inception of predischarges, it is determined by the growth and propagation of the streamer discharge. Therefore, the influence of air density decreases with increasing nonuniformity of the field, and the exponent m decreases from one to zero [133]. The exponent m is tabulated as a function of a parameter g, which gives the ratio of the breakdown voltage Vbd and the specific voltage drop of a positive streamer discharge Vstreamer = 500 kV/m · d: g
Vbd kV d) G k (500 m
(3.269c)
The factors G and k contain an airdensity and an airhumidity correction respectively [133]. Under standard atmospheric conditions, both factors are equal to one. Above g = 1 the exponent is m =1. I.e. the breakdown voltage is
x
E
x
E(x) Pointtoplane
Pointtopoint
x
V
d
Figure 3.230: Field strength curves for pointtoplane and pointtopoint arrangements at the same flashover distance d and at the same voltage V.
assumed to be proportional to airdensity according to Eq. (3.269a) and (68). Note: Since the specific voltage drop in a negative streamer is approximately twice as great as in a positive streamer, positive streamers determine breakdown, Figure 3.227. Dielectric tests with impulse voltages are normally performed with positive polarity. Negative polarities are only used as an addition. Therefore, the above mentioned relationships refer to the positive streamer.
The influence of air humidity is negligible for uniform and weakly nonuniform fields and for negative streamer discharges. The breakdown voltage increases with the absolute (and not with the relative) air humidity only for positive streamer discharges. The correction for humidity is w
k2 = k .
(3.270a)
The exponent w is tabulated as a function of the parameter g. It is w = 1 close to g = 1, for g
198
3 ELECTRIC STRENGTH
Vbd , Vi
Kcrit Weakly nonuniform
Strongly nonuniform
Stable corona
Vbd
Critical field efficiency factor
0.4 Weakly nonuniform arrangement 0.3
Vbd = Vi
0.2
Vi
Strongly nonunifiorm a. stable predischarges 0.1
p max
p crit
p
1
2
3
4
5 p /bar
Figure 3.231: Effect of the variation of gas pressure on the discharge behavior of a pointtoplane arrangement [39] (schematic).
Figure 3.232: Variation of the critical field efficiency factor with pressure in sulphure hexafluoride SF6 [22], [55].
< 0.2 and g > 2 the exponent w decreases to 0, i.e. there is no longer an airhumidity correction. For AC voltages, the dependence on the absolute air humidity h is given by the factor
cantly during increasing pressure, Figure 3.231. At low pressure, a significant difference can exist between inception voltage Vi and breakdown voltage Vbd, which disappears at high pressures. Obviously, the “strongly nonuniform arrangement” has changed into a “weakly nonuniform arrangement” just by increasing the pressure above a critical value pcrit. This can also be interpreted as a decrease of the critical field efficiency factor Kcrit with increasing pressure, Figure 3.232. For a given arrangement (K = const.), an increase in pressure shifts the discharge behavior from a range with predischarges to a range without.
k
1 0.012 (
h /(g/m 3 )
G
11) . (3.270b)
The range of validity and variations for DC and impulse voltages are described in the standard [133]. If a relative air humidity of 80 % is exceeded, the dielectric strength of surfaces can be reduced significantly because creepage currents can cause field distortions and pollution flashover. Note: The empirical relationships for airhumidity correction are in good accordance with measurements for long flashover distances (d > 1 m) and correspondingly high voltages. For shorter distances (d < 0.5), i.e. mainly for medium voltages (up to approx. 200 kV), the described method is difficult to apply and can provide incorrect results [387]. In particular, surface creepage arrangements show reductions of flashover voltages in the medium voltage range even at above 50 to 60 % relative air humidity [387]. Nevertheless, this is a surface effect that is sensitive to relative air humidity and not a gasbreakdown effect that would be sensitive to absolute air humidity.
3.) For compressedgas insulations, the influence of high pressure can no longer be described by the linear approach according to Eq. (3.268) to (70). The discharge behavior in a strongly nonuniform field can change signifi
The suppression of predischarges with increasing pressure can be explained by the decreasing range of photon emission with increasing gas density, which significantly degrades the conditions for secondary avalanches and streamers. Example: Locally fixed defect in a GIS
Faulty production or mounting procedures in a compressedgas insulation system can cause locally fixed defects, e.g. tips, edges, burrs or metal chips. Such defects cause a very nonuniform local field, and they show a pressure dependence according to Figure 3.231. Breakdown voltages can be stabilized at a comparatively high level by predischarges, but they can occur for sufficiently long lasting stresses only (DC, AC and switching impulse level). Lightning impulse breakdown and predischarge inception can occur at lower voltages, significantly dependent on the degree of nonuni
3.2 Gas Discharges formity. Lightning impulse and partialdischarge AC tests can therefore be used as indicators for locally fixed defects in gasinsulated switchgear (GIS). Example: Free particles in a GIS
In a compressedgas insulation system, free particles can also occur, e.g. chips, abraded matter or welding sputter. Similar to fixed defects, they also distort the field. Additionally, they can be electrically charged, lifted by electric field forces from the less curved electrode (liftoff voltage) and migrate to the counterelectrode where the field is enhanced by the charges of the particles. These particles are discharged at the electrode, reloaded, lifted again, transported to the counterelectrode and so on repetitively. Particle movement doesn’t play a role for the shortlasting lightning impulse stress, but it causes partial discharges and a strong decrease of AC and DC breakdown voltages. Therefore, gasinsulated switchgear must also be tested with AC voltage after the final mounting, in order to test for free particles.
3.2.6 Surface Discharges 3.2.6.1 Arrangements with Surfaces Multilayer dielectrics containing a gaseous dielectric have interfaces that are known as “surfaces”. Field calculations are described in Section 2.4.2 (for AC, switching impulse and lightning impulse voltages) and in Section 2.4.4 (for DC voltage). In highvoltage engineering, surfaces are characterized by three circumstances:
x x x
First, they occur in very large numbers in string and post insulators, bushings, cable terminations and insulating housings. Secondly, they only have a very weak dielectric strength Thirdly, surface discharges are comparatively strong and have a high erosive effect.
Therefore, surface discharges are one of the main problems in highvoltage design. Surfaces occur in three different basic types. 1.) For an electric field, perpendicular to a surface, the direction of electrical gas discharges is also perpendicular to the surface.
199
This is not a surface discharge in a narrow sense. Nevertheless, significant field stress enhancements can occur owing to field displacement (Section 2.4.2.2 and 2.4.4.1). Partial discharges in cracks, gaps and voids can erode many organic insulating materials and lead to erosion breakdown. 2.) For an electric field, parallel to a surface, the macroscopic field is theoretically not influenced by the surface, Section 2.4.2.3. Nevertheless, the dielectric strength of such an arrangement is lower than the strength of a comparable gasinsulated gap because the microscopic field is distorted by the irregularity of the surface and because only weakly bound chargecarriers are released. Furthermore, significant field distortions can be caused by surface contamination, wetting and pollution layers. Since the field is tangential, the gas discharge also develops parallel to the surface. Often, the discharge is ignited at the triplepoint between electrode, insulating material and gas. The dielectric strength of a gasinsulated gap could only theoretically be achieved under ideal laboratory conditions. If arrangements with fields parallel to the surface cannot be avoided in practice, sufficiently long flashover distances and a sufficiently high field efficiency factor are necessary, e.g. in the case of insulators in GIS or overhead line insulators. Note: For post insulators in GIS, the tangential field component is reduced by inclination of the surface. For overhead line insulators, the impact of pollution layers is reduced by undulating screen profiles with long creepage lengths and sometimes by hydrophobic surface properties. The field strength at the triplepoint is often reduced by an appropriate electrode configuration.
3.) For insulation systems with tangentially stressed interfaces against solid or liquid dielectrics, the low strength of tangential surfaces would limit withstandvoltages to very low values, and the high strengths of the dielectrics would only be partially exploited. Therefore, creepage arrangements (creepage surfaces) are used with insulating materials that reach far beyond the electrode edges into the lowfield regions, Figure 3.233.
200
Unfortunately, a uniform tangential field distribution cannot be achieved thereby because a strong field stress enhancement exists at the triplepoint at the electrode edge. Therefore, predischarges occur at very low voltages, but the breakdown is prevented by the insulating material. If the voltage is increased, a guided gasdischarge will develop along the surface (surface discharge, creepage discharge), which will finally reach the counterelectrode and end up in flashover. Owing to its general importance, the basic creepage arrangement (Section 3.2.6.2 and 3.2.6.3) and the pollution flashover (Section 3.2.6.5) will be discussed in more detail in order to deduce methods for the suppression of surface discharges.
3.2.6.2 Ignition of Surface Discharges Field distributions for impulse and AC voltage stresses are normally exclusively determined by the dielectric displacement field, i.e. by the permittivities H1 and H2. Here the geometry of the electrode edge has a strong influence, Figure 3.235. The field can be described by a purely capacitive equivalent circuit, consisting of the capacitances 'C of the insulating layers and stray capacitances in air 'CS, Figure 3.234 (left). If there are sufficiently conductive pollution layers, additional surface resistances 'R are necessary for the case of AC voltage stress, Figure 3.234 (middle). In the case of DC voltages, the field distribution is determined by the conductivities of the insulating materials and the conductive layers; the gas is comparatively highresistive. The equivalent circuit consists of a purely ohmic lattice network with longitudinal and transverse resistances, Figure 3.234 (right). a) Impulse and AC voltage (Dielectric displacement field) At very sharp electrode edges, a high tangential field strength component exists and stable glow discharges can form, Figure 3.235 (left). The inception voltage can be esti
3 ELECTRIC STRENGTH
80 %
60 %
40 %
20 %
Gas
d
Solid or liquid insulating material
Figure 3.233: Creepage surface with equipotential lines (simplified, without considering refraction of the equipotential lines at the interface).
mated from the assumption of a cylindrically symmetric edge field with inner radius Rc and outer radius d Vi 
Ei·Rc·ln (d/Rc).
(3.271)
The order of magnitude for the inception field strength at cylindrical electrodes is given by Eq. (3.258). This does not take the interaction with the surface into account. At smoothly curved electrode edges, discharge inception is caused by the normal field strength component in the gasfilled interstice, Figure 3.235 (right). There, the field strength is enhanced by dielectric field displacement. A discharge is ignited, if the ignition condition is fulfilled at any location within the interstice. During ignition, the surface of the insulating material helps to supply free charge carriers. The field conditions in an interstice were already used in Section 2.4.3.3 for estimation of the partial discharge inception voltage Vi in a dielectric displacement field, Figures 2.418 and 19:
Vi
~
d
Hr
(3.272)
Note: Numerical values can be calculated with the empirical equation (2.435).
Since the dielectric strength of the gasfilled gap decreases with gap width, a breakdown is to be expected in the mm range, Figure 2.419. Therefore, the first discharge occurs perpendicularly to the surface in a comparatively uniform field. Immediately after ignition, the discharge will turn into a steamer propagating
3.2 Gas Discharges
201
'C S
'C S
'R l
'R 'C
'C 'x
'R q
'x
Figure 3.234: Simplified description of tangential field distributions on creepage sufaces by equivalent circuits with distributed parameters for different kinds of stresses: Left: Circuit for impulse and AC stresses (dielectric displacement fields only). Middle: Circuit with recognition of conductive pollution layers for AC voltages. Right: Circuit for DC voltages (conduction field only).
parallel to the surface under the influence of the tangential field component (“creepage discharge”). Glow discharges do not occur. b) Pollution layers for AC voltage A calculation of tangential field strength can be performed by means of an ohmiccapacitive equivalent circuit, Figure 3.234 (middle). Stray capacitances 'CS are neglected for this case, although this is not always justified close to the electrode edge [26]. The related surface capacitance per unit length and the related surface resistance per unit length are C' = 'C/'x = H0Hrb/d and R' = 'R/'x = R/b. The variables b and d are the width and thickness of the insulating material, R is the specific surface resistance (resistance of a square surface element). The differential equations (line equations) for current and voltage are set up for an infini
E
Triplepoint
E1 E2
Figure 3.235: Ignition of surface discharges by the tangential field component at a sharp electrode edge (left) or by a normal field component at a smoothly curved electrode edge (right).
tesimal element 'x of the lattice network. An exponentially decreasing tangential field strength is derived from the solution for the voltage distribution. If the maximum field strength value at the electrode edge is identified with the dielectric breakdown strength Ebd at the interface, the equation can be solved for the corona inception voltage Vi: Vi
E bd
E bd
Z C' R'
Z RH 0 K
d
Hr d
(3.273)
Hr
Formally, this equation is equivalent to Eqs. (3.272) and (2.435) respectively. Empirical values for K are given there; Vi is calculated as the r.m.s. value, Section 2.4.3.3. Note: Eq. (3.273) is not only valid for plane geometries. Figures 3.233 and 34 can also be interpreted with a vertical axis of rotation, without the product C'R' = H0HrR/d changing. The width b is to be replaced by the circumference 2Sr, which is also canceled out. In the case of a horizontal axis, C' is to be calculated according to Eq. (2.330).
Note: The experimentally determined constants K do not show a clear dependence on surface resistance R [26]. Therefore, it is assumed that partial discharge inception is caused by the dielectric displacement field even if there are pollution layers, as long as surface conductance is not too high.
202
3 ELECTRIC STRENGTH
Outer conductor
Solid insulation
Inner conductor
s
tion layer in a steadystate conduction field, if the surface resistance R is sufficiently low and uniform.
Glow discharge
3.2.6.3 Development of Surface Discharges After the inception of partial discharges and at the time of an increase in voltage, a surface discharge develops similar to a pure gas discharge in a strongly nonuniform field. The insulating material only acts as a barrier guiding the gas discharge and preventing direct breakdown (guided gasdischarge).
Surface streamer discharge
Surface leader discharge
Under the influence of tangential field components, (surface) streamer discharges develop. At a curved electrode edge, they start directly from the breakdown of the air gap, and at a sharp electrode edge, they emerge from the preceding glow discharge, Figure 3.236.
(Leader + Streamer)
RL
'C
Hr
d
Figure 3.236: Development of surface discharges on a cylindrical insulator surface.
c) DC voltage (Steadystate conduction field) The lattice network according to Eq. 3.234 (right) gives exponentially decreasing tangential field strength and an inception voltage according to Eq. (3.273), if the specific capacitive conductance ZH0Hr is replaced by the conductivity N of the insulating material:
Vi
Ed
d N R
(3.274)
Conclusion: For all the Eqs. (3.271) to (3.274), there is only a slight increase of inception voltage Vi with insulating material thickness d. Dielectric strength is reduced by a high relative permittivity Hr in a dielectric displacement field, and it is enhanced by a (uniform) pollu
Owing to the high lateral capacitance, the streamers carry much higher currents than streamers in a pointtoplane arrangement in air. For AC and switching impulse voltages, current densities allowing thermal ionization and inception of leader discharges are already reached for streamer ranges of a few centimeters. For a pure gasinsulated arrangement, streamer ranges of approximately one meter would be necessary for leader inception. The surface leader discharge (creeping discharge, creeping spark) consists of a leader channel with low resistance RL (similar to a trunk) and a leader head of currentgathering streamers with high lateral capacitance 'C (similar to branches or bunches). The length of the leader is determined from the equilibrium between the given voltage drop at RL and the required voltage for the leader discharge channel, Figure 3.236 (bottom). Since the required voltage per unit length for a leader discharge decreases with increasing length, the leader can easily bridge long distances with increasing voltage, and complete flashover can quickly be reached.
3.2 Gas Discharges
203
Therefore, increasing the flashover distance cannot increase the flashover voltage significantly! In practical applications, the flashover voltage Vf is less important than the inception voltage for leader discharges VL, which must be prevented in any case for technical insulations.
Example: Castresin bushing without field grading
For a cylindrical castresin bushing (Hr = 4.5) with the inner conductor diameter Di = 1 cm, the inception voltage for leader discharges VL shall be calculated as a function of the outer diameter Da = Di + 2d. Eq. (3.277) is used for the calculation of a table of values. The surfacerelated capacitance per unitarea is given by Eq. (2.320): 1
The inception of leaders at VL can be derived from a simple estimation: If the increasing voltage for AC or switching impulse stresses is approximated by a voltage step with amplitude VL, 'C will be charged via RL with constant voltage. In this case, the ohmic losses Wth in RL are equal to the capacitively stored energy
'C'A = SH z ln (Da/Di)/(SDaz) = 2H{Daln(Da/Di)}
1
Table of values: Da d 'C'A VL
2 0.5 0.574 33
4 1.5 0.143 61
8 3.5 0.048 98
16 7.5 0.018 151
cm cm 2 pF/cm kV
2
½·'C·VL . If it is also assumed that the leader inception with thermal ionization is characterized by exceeding a minimum loss energy Wth > Wmin, it follows that ½·'C·VL
2
= Wth > Wmin .
(3.275)
Thereby, a limit for the leader inception can be given:
VL = (2Wth/'C)
0.5
(d/Hr)
~
0.5
(3.276)
This proportionality is in good agreement with the empirical equation for AC voltages:
VL
25.8 kV {
pF/cm
2
'C / 'A
0.44
}
(3.277)
The specific capacitance per unitarea 'C'A can be calculated from geometry. For plane arrangements it follows that [16] VL
75 kV
{1 H
r
d 0.44 } . cm
(3.278)
Note: The factor and the exponent in Eq. (3.277) are only weakly dependent on pressure and the nature of the gas. The application of SF6 and increasing the pressure do not give the same enhancements of dielectric strength as in a uniform field.
Obviously, increasing the insulation thickness is not a very effective method for increasing the leader inception voltage VL. An analogous conclusion can be drawn for the application of materials with lower permittivity Hr; furthermore, there are only a few different materials available. At higher voltages, arrangements with geometric, capacitive (dielectric), resistive or nonlinear field grading are therefore used (Sections 2.4.5, 5.4.5, 7.1.1.4, 7.1.2.1 and 7.1.6)
3.2.6.4 Pollution Flashover Rain, precipitation from fog, dew or moisture absorption causes wetting or humidification of insulator surfaces depending on the atmospheric conditions. In combination with dirt deposits, electrolytically conductive pollution layers are formed. Coastal areas with saline fog, locations with roadsalt fog, and environments with high air pollution (e.g. by dust, soot, oily particles and dissociable contaminants) are especially at risk. The field distribution in a DC field is determined by pollution layers even at low pollution layer conductivities, Figure 2.429. In an AC displacement field, only high conduction currents in the pollution layer can influence
204
3 ELECTRIC STRENGTH
the field distribution. In the case of impulse voltages, conduction currents are normally negligible in comparison with displacement currents. Nevertheless, an impulse voltage can prolong an already burning AC prearc and cause breakdown.
J
(a)
Owing to the spatial and temporal development, pollution flashover is also called creepage flashover, Figure 3.237.
J
(b)
At first, the current density lines of the surface leakage current (creepage current) are displaced from locations with reduced conductivity (e.g. at dry zones) to areas with higher conductivity, Figure 3.227 (a). For leakage currents in the range of 10 to 100 mA local heating occurs at locations with higher surface current densities close to the edges of the dry zones. Thereby, water is evaporated and the dry zones are lengthened perpendicularly to the current density lines (b). Ultimately, the current density is high enough to ignite a prearc (d) by thermal heating. If the current path were to be interrupted (c), a high voltage 'V would be built up across the dry zone and a prearc would also be ignited (d). Note: The total voltage for prearc inception can be very low in comparison with the flashover voltage. It depends primarily on the wetting of the surface and on the pollution layer conductivity.
Stable predischarges (i.e. prearcs) can only exist, if there is a stable working point on the gas discharge characteristic, Figures 3.22 and 3a. The current is limited by the resistance of the conductive pollution layer in series with the arc. The resistance must be low enough, i.e. the inclination of the resistance line in Figure 3.23a has to be so low that it intersects the arc characteristic at working point no. 1. The drying of the pollution layer in the environment of the root point of the arc causes a lengthening of the stable burning prearc along the current density lines, Figure 3.227 (e). The series resistance of the conductive layer decreases slightly, but the arc voltage increases very significantly. This is equivalent to
'V (c)
J (d)
J (e) Figure 3.237: Phases of pollution flashover: a) Displacement of the "creepage current" by a dry zone with local heating. b) Increase of the dry zone by ohmic losses, acceleration of surface drying. c) Interruption of current flow after surface drying along the whole insulator circumference. d) Flashover of the dry zone, development of an electric arc (prearcing). e) Extension of the dry zone and the arc length by surface drying.
a shifting of the gas discharge characteristic towards higher voltages, Figure 3.23. If the sum of the arc voltage and the voltage drop along the resistive layer is higher than the source voltage, the arc will be quenched. If the voltage sum always stays below the source voltage, the prolongation of the arc will lead to flashover. This is only possible for a low pollution layer resistance (i.e. for a high pollution layer conductivity) or for a low inclination of the resistance line.
3.2 Gas Discharges
205 lk
f
a
1 ³ b dl k
(3.281)
f / N* .
(3.282)
as
R
=
Typical layer conductivities are given in [16], i.e.
t
N* = 5 μS for weak to medium pollution, N* = 10 μS for medium to heavy pollution and N* = 40 μS for extremely heavy pollution.
li
s
lk
Figure 3.238: Outdoor insulator with creepagepath lengthening by means of shed profile.
Note: If the voltage source is weak, the internal resistance of the source can cause quenching of the arc and simulate an enhanced flashover voltage. Therefore, the determination of flashover voltages requires a strong voltage source with a low internal impedance or a low relative shortcircuit voltage [56].
The magnitude of the creepage currents is determined by the resistance of the insulator surface. The resistance is given by an integration of the resistance element dR along the creepage path lk: d lk
dR
N ǻs b
(3.279)
's is the thickness of the conductive layer and b is the positiondependent circumference of the insulator. The pollution severity is characterized by the socalled layer conductivity, which is defined as product of conductivity and layer thickness:
N*
=
N·'s
(3.280)
Thus, the surface resistance R is given by the layer conductivity N* and a shape factor
The development of a pollution flashover is also influenced by the insulating material. Thermally and chemically resistant surfaces (porcelain glazes, glass) are not permanently modified by weathering or by surface discharges in most cases. Longlasting predischarges on surfaces of organic materials can cause erosion and enhancement of wettability. During diffusion of water and contaminants into the bulk material, conductive paths can be generated, which can initiate a socalled tracking flashover [22]. Even silicones can lose their waterrepellent (hydrophobic) properties under the impact of electrical discharges, but a recovery of surface properties can occur because of the diffusion of lowmolecular silanes [57]. The following methods can be used in order to avoid pollution flashover: 1. The basic method is the lengthening of the creepage path lk by means of a shed profile, Figure 3.238. The ratio of creepage path length lk to insulator length li is determined by the ratio of shed overhang a to shed spacing t. The ratio lk/li  2 is chosen under normal pollution conditions and lk/li  3 under difficult conditions. The insulator length li or flashover distance s (thread measure) is dimensioned according to the impulse voltage withstandlevel. Values between 2.5 and 5 cm/kV are common creepage path lengths for outdoor conditions; they are related to the r.m.s. value of the applied operating voltage. The lengthening of the creepage path (i.e. the increase of the surface resistance) is not the only effect of insulator sheds. They also pro
206
vide protection of the underside against rain and dirt deposition and they help dry and clean zones to remain, which are able to withstand the applied voltage. The partial voltages can be kept low by means of a higher number of sheds. For extreme requirements, there are special shed profiles, e.g. the socalled antifog sheds with additional vertical ribs on the undersides. 2. In the case of severe pollution, the natural cleaning effect of rain might not be sufficient, and regular cleaning of the insulators would be necessary. Eventually, this can be done automatically by permanently installed spraying units. If pollution is extreme, a waterrepellent (hydrophobic) silicone paste (“silicone grease”) can be applied every year. 3. Composite insulators with silicone elastomer sheds (“silicone rubber sheds”, SIR sheds) are a good alternative to the common porcelain insulators. They preserve their waterrepellent property (hydrophobicity) for decades, and they can transfer hydrophobicity to the attaching contaminants by diffusion. Thereby, the formation of coherent liquid films is impeded [9], [57]. Note: The terms “silicone rubber” or SIR are widely used. However, the material is a synthetic elastomer, not a natural rubber. Note: Composite insulators with hydrophobic SIR sheds have extraordinary surface properties. Nevertheless, it is a disadvantage that the hydrophobicity can be lost under the influence of corona discharges, Section 5.3.4. Coronas can occur on a bedewed surface if the tangential background field is above 0.3  0.5 kV/mm [471]. The electric field forces deform the water drops and form tips that cause the water drop corona affecting hydrophobicity. Close to the fittings, surface field strengths of 0.8 to 1 kV/mm can be reached. Therefore, maximum field strengths should be reduced by an appropriate design, e.g. by means of grading rings. If the corona stress is only temporary and of short duration, the hydrophobicity will recover by diffusion of lowmolecular silanes, Section 5.3.4.
The application of SIR sheds has significantly improved the flashover behavior for DC stresses, especially for HVDC bushings with rated voltages above 500 kV [7], [8], [10].
3 ELECTRIC STRENGTH
4. It was proposed to retrofit DC bushing porcelain insulators that are at flashover risk. Socalled booster sheds consisting of silicone discs with large diameters are distributed along the insulator length in order to interrupt developing prearcs [58], [8].
3.2.7 Spark, Arc and Lightning Discharges During the breakdown of a gasinsulated gap, a conductive channel is formed by electron avalanches, the current increases and the voltage collapses. Ultimately, a highcurrent discharge develops; it is the consequence of insulation failure, not the cause. However, different kinds of highcurrent discharges are of great importance in highvoltage engineering: Spark discharges (Section 3.2.7.1), arc discharges (Section 3.2.7.2) and atmospheric lightning discharges (Section 3.2.7.3) will be discussed.
3.2.7.1 Spark discharge During breakdown, the gasinsulated gap is bridged by a streamer at first. Owing to intense collision ionization the conductivity of the
i(t) C q (t)
Vbd v (t)
R sp(t) v (t)
Vbd /2 R sp(t)
i(t) tc
Deionization
t
Figure 3.239: Spark resistance, spark formation time (time of voltage collapse), voltage and current for the discharging of a capacitance (schematic), see also Figure 3.221
3.2 Gas Discharges
207
channel increases and spark resistance Rsp(t) decreases from very high initial values down to very low final values, Figures 3.221 and 39. In the case of a steadystate source voltage, the transient spark develops into a permanent electric arc with a constant final current (Section 3.2.7.2). If a source with finite energy content is discharged, only transient current and light impulses will occur. After their decay, the discharge gap deionizes by recombination processes and the spark resistance Rsp(t) increases again, Figure 3.239. Note: The time characteristic of the spark resistance is important for equivalent circuit simulations of discharge circuits. They often experience significant nonlinear damping as a result of Rsp(t). The time of voltage collapse tc from 90 % to 10 % is also known as the spark formation time.
Note: The spark formation time can play a role in the discharge delay (Section 3.2.4), but often it is short in comparison with the streamer formation delay (formative time lag) and is therefore often neglected. The short spark formation time in SF6 is jointly responsible for the short rise times of fast transients in gasinsulated switchgear GIS.
The increase in charge carrier numbers through collision ionization can be described by an increase dn of electron density n along the distance dx with the effective ionization coefficient De: dn =
De n dx .
(3.283)
The increase in the electron density with time results from the drift velocity of electrons u = dx/dt: dn/dt =
De n u .
(3.284)
If the electron current density J = n·u·e (with the elementary charge e) is approximately equal to the total current density J, the increase in the electron density is dn/dt =
De J / e .
(3.285)
The electron density n at a given time t is calculated by integration:
t
t
D e e 1 ³ J (t ) dt
n
D e e 1 A1 ³ i (t ) dt
1
1
n = De · e · A · Qsp(t)
(3.286)
In this equation, Qsp(t) is the charge that has flowed through the spark until time t. The current density J(t) = i(t)/A is assumed as constant over the cross section area A. The spark resistance Rsp(t) is calculated with the spark length lsp, the electron mobility μ and the conductivity N = μ n e:
Rsp(t) = =
lsp / (N A) =
lsp / (μ n e A)
lsp / {μ De Qsp(t)}
(3.287)
Eq. (3.287) is Toepler’s sparkresistance law, which can also be written with the empirically determined Toepler constant kT:
Rsp(t) =
kT·lsp / Qsp(t)
(3.288)
The Toepler constant is almost independent of pressure and field strength, Tables 3.26. Table 3.26: Toepler constants for different gases [16]. Air Nitrogen
kT = kT =
0.5 ... 0.6 ·10 0.4 ·10
4 4 4
Argon
kT =
0.85·10
SF6
kT =
0.4 ... 0.8 ·10
4
Vs/cm Vs/cm Vs/cm Vs/cm
Note: Toepler’s sparkresistance law is derived from the idea of collision ionization; i.e. it is only valid as long as the Toepler mechanism or the streamer mechanism can be assumed. If thermal ionization has to be assumed, an alternative approach will give a better fit: The RompeWeizel spark resistance law assumes that the resistance is inversely proportional to the dissipated energy:
Rsp (t )
kRW lF t ³0 uF (t ) iF (t ) dt
(3.289)
Both spark resistance laws describe a very fast decreasing spark resistance.
208
3 ELECTRIC STRENGTH
The spark formation time tsp shall be estimated for a capacitance C that is charged to the breakdown voltage Vbd and discharged via the spark resistance Rsp(t), Figure 3.229. With the instantaneous value of the charge in the capacitance
q(t) = C·v(t) = C·Vbd – Qsp(t), the voltagetime characteristic is calculated according to Eq. (3.288): v(t )
Rsp (t ) i (t ) kT lsp
kT lsp
dq ( ) dt Qsp (t )
dv ( C ) . dt C {Vbd v(t ) }
(3.290)
After separation of the variables v and t, the differential equation (3.290) can be integrated and solved for v(t) [46]:
Vbd
v(t ) 1
e
V bd t k T l sp
(3.291)
Integration constants are determined by the theoretical boundary conditions v(f) = Vbd, v(0) = Vbd/2 and v(f) = 0, Figure 3.239. A practical limitation of this infinitely long time is given, for example, by the time interval for the collapse of the voltage v(t) from 0.9 Vbd down to 0.1 Vbd [16]. It can be calculated from Eq. (3.291):
tsp = 4.4 kTlsp/Vbd = 4.4 kT/Ebd . (3.292) This means that the spark formation time tsp is not dependent on the value of the discharged capacitance. If a large capacitance has to be discharged, the large charge transfer will cause a low spark resistance and a high current. The spark formation time tsp is mainly dependent on the breakdown field strength Ebd = Vbd/lsp that is given prior to the breakdown incident. Therefore, tsp depends on the type of gas. With 4
kT = 0.5·10 Vs/cm, we calculate for atmospheric standard conditions
in air (Ebd = 30 kV/cm) tsp = 7.3 ns and in SF6 (Ebd = 90 kV/cm) tsp = 2.4 ns. There is only an indirect dependence on flashover distance due to the dependence of breakdown field strength on distance. The dependence on pressure is strong, and it is given by the breakdown field strength, i.e. if pressure is increased, Ebd will increase and tsp will decrease. Note: From these relationships it is clear that there are very short spark formation times (or times of voltage collapse) for compressedgas equipment, especially with SF6 gas. Traveling waves with rise times in the nsrange (fast transients) can therefore occur in the case of breakdowns or disconnector switching actions,. Note: The steepness of current increase and voltage collapse is not only determined by the spark formation time but also by the system properties of the discharge 1/2 circuit, e.g. by the natural frequency Z = (L·C) , Figure 3.221. Gasinsulated lines must be regarded as systems with distributed parameters (travelingwave transmissionlines). According to the equivalent transmissionline circuit in Figures 2.68 and 10, the time constant for the voltage collapse and the current increase is W = Z/L. With Z = 50 : and L = 100 nH (for a 100 mm long discharge channel), we calculate W = 2 ns. Even in this case, the inductive time constant is significantly longer than the spark formation time (tsp < 1 ns for p > 2 bar).
3.2.7.2 Arc Discharge During breakdown of a gasinsulated gap, a conductive spark channel is generated by collision ionization and photoionization at first. Then, a high current density causes thermal ionization within the discharge column and thermionic electron emission at the cathode. Owing to the highly conductive arc plasma in the discharge column, anode potential is displaced close to the cathode and high field strengths and field emission occur. This causes the total voltage drop along the discharge gap to decrease to very low values of approximately 10 to 100 V. Owing to the intense thermal ionization, the electric arc is characterized by an intense light emission.
3.2 Gas Discharges
209
In circuitbreakers, the arc develops during the opening of the switching contacts. Shortly before the separation of the contact pieces, the current narrows down to a very small contact area. Owing to the high current densities, the temperatures are sufficiently high for thermal ionization; and after the liftoff of the contact pieces, the current flows without any interruption through the thermally ionized channel (electric arc). For the most part, the voltage drop of the arc is a socalled cathode fall because positive ions accumulate directly in front of the cathode. Negative ions cause a significantly smaller anode fall. Owing to the high conductivity, the voltage drop within the arc column is comparatively small for shorter discharge lengths, and it increases linearly with the arc length. The arc column consists of largely ionized plasma. The low voltagedrop along an electric arc and a completely different voltagecurrent characteristic (see Figure 3.2.2) are explained by a completely different process of charge carrier generation. It was already mentioned with Eq. (3.22) that the decreasing V,I characteristic for a steadystate condition of the arc can be derived from the equilibrium between the generated Joule heat Pgen and the removed heat Ptrans that is transferred to the environment:
Pgen
=
Ptrans
(3.293)
The generated heat power is given by the product of current and voltage Pgen, = V·I, the removed (transferred) heat power is a function of arc temperature T, arc radius R and arc m length larc, i.e. Ptrans = larcR f(T) [47]. The equilibrium gives
V·I
=
m
larcR f(T) .
(3.294)
The variables on both sides of the equation are only independent of each other to a firstorder approximation. Actually, the current I is a 2 function of arc crosssectional area SR and of
temperaturedependent conductivity N(T). These conditions are better described by a modified approach [16]:
V·I
n
~
larc
(3.295)
With n = 0.5 ... 0.25, the voltage drop decreases with increasing current and increases nearly proportionally with length. The properties of the arc are strongly influenced by environmental conditions: If the arc is cooled, the generated heat power has to compensate for the cooling, and the voltage drop will be greater. Depending on the source impedance, the current can also be enhanced. The equilibrium between heat generation and heat transfer will be reached at a higher temperature. Typical values within the arc plasma are between 4000 K and 10,000 K, in some extreme cases up to 50,000 K. At 20,000 K, nearly all gas atoms are ionized [2]. The properties of the arc are strongly dependent on pressure. The cross sectional area decreases with pressure because the number of charge carriers per unit area increases with pressure. Therefore, the current density also increases. To a first approximation, a proportionality can be assumed: 2
SR ~ 1/p
and
J ~ p.
(3.296)
Also the voltage drop along the arc increases with p, and therefore the power loss density increases quadratically with pressure. An increasing current mainly causes an increasing current density; the arc crosssectional area increases only slowly. Often, the arc is subject to magnetic forces, which are intended to enlarge the currentcarrying loops. At higher currents, magnetic forces can become stronger than the buoyant forces on the hot plasma in the arc. For AC voltages, a loadindependent sinusoidal arc current is assumed, which is determined (i.e. imposed) by the series impedance
210
and the source voltage of the circuit, Figure 3.240. After the current zero crossing (1), there is still a residual ionization, and the voltage in the positive current halfwave increases with current owing to the ohmic resistance. If the ignition voltage is reached (2), the voltage and current will follow the negative V,I characteristic of the arc until the current maximum is reached (3). While the current is decreasing, the voltage increases again, but to a lesser extend because the conductivity of the arc channel has increased in the meantime. Increasing arc voltage and decreasing arc current lead to extinction of the arc (4). After the current zero crossing, the behavior is analogous in the negative current halfwave. If the discharge channel is sufficiently deionized during the current zero crossing, the positive (or negative) current cannot increase again, the arc will be extinguished permanently and the recovery voltage increases between the electrodes (5). The main problems of arc discharges in circuitbreakers are the extinction of the arc, the deionizing of the gas volume and the insulation of the fast rising recovery voltage between the electrodes (contact pieces). Switching consists of three phases: 1. The extinction of an arc is caused by a perturbation of its conditions of existence. This means that the required arc voltage is increased so much that a stable working point is no longer possible, i.e. the V,I characteristic is displaced upwards so far that it no longer touches the resistance line, Figure 3.23a. In this case, the current through the discharge channel decreases and is interrupted. This situation can be achieved by lengthening the arc, increasing the pressure, forced cooling or separation into a number of partial arcs. For AC, the interruption of current occurs during the current zero crossing and the shifting of the V,I characteristic impedes the reignition. 2. The deionization of the discharge channel by recombination of charge carriers occurs automatically when the ionized gas cools down after the interruption of the current. De
3 ELECTRIC STRENGTH
ionization can be accelerated by forced cooling. As this occurs, the dielectric strength of the insulating gap has to increase faster than the recovering voltage. Note: For AC circuitbreakers, the natural current zero crossing supports deionization and facilitates current interruption. For DC circuitbreakers, a natural current zero crossing does not exist and current interruption is heavily impeded. It can be supported by reverse currents fed from auxiliary circuits.
3. The maximum of the recovery voltage, which has to be insulated by the opened switching gap, can be significantly greater than the operating voltage stresses because of commutation processes and transients (switching overvoltages, internal overvoltages). The voltage stress during switching operations is simulated by switchingimpulse test voltages (Section 2.2.3). The compressed gasblast circuitbreaker with SF6 has established itself among the different switching principles for HV power circuitbreakers. The electronaffine sulfur hexafluoride is both an effective cooling and extinguishing medium for the arc plasma and an dielectrically strong insulating medium. During contact separation, the electric arc is exV 5 Ignition
Vi
Extinction
Ve
2
Positive current halfwave
4 3
Î 1
+Î
I
 Ve Extinction Negative current halfwave
 Vi
Ignition
Figure 3.240: Electric arc at AC voltage and loadindependent imposed AC current with current zero crossing (1), ignition (2), current maximum (3) and extinction (4). Voltage recovery after deionizing (5).
3.2 Gas Discharges
posed to high pressure and intense blowout with SF6 (Section 7.1.5.2). Note: The arc plasma contains highly reactive sulfur and fluorine ions that react to form residuefree SF6 during cooling down. The presence of water has to be excluded, in order to avoid the formation of toxic byproducts.
In a vacuum circuitbreaker, the current is interrupted in the current zero crossing by deionization of a metalvapor plasma. Note: Owing to the limited dielectric strength of the vacuuminsulated gap, vacuum circuitbreakers can only be used in the medium voltage range (Section 7.1.5.3). Moreover, the fast current chopping would cause fast transients. Nevertheless, the seriesconnection of synchronously switching vacuum switching tubes is a possible option for replacement of SF6 circuitbreakers.
3.2.7.3 Lightning Discharges Atmospheric lightning discharges can cause severe damage. In the field of electrical engineering systems malfunctions and destruction are caused by socalled external overvoltages. Important systems, e.g. energy transmission grids, communication systems and data transfer nets or important buildings need lightning protection systems. Equipment for energy transmission is additionally tested with standard lightning impulse voltages in order to guarantee sufficient dielectric strength in case of an external overvoltage. In central Europe, the probability for the progression of a lightning discharge down to ground level is ap2 proximately 2 lightning strikes per km and year, but there are significant deviations, both locally and globally. However, external overvoltages regularly occur in distributed electricity supply systems. The formation of thunderclouds is related to strong and humid air. Two kinds of thunderstorms can be observed: 1. A heat thunderstorm is caused by the summer heating of groundlevel air and by an unstable atmospheric layering of warm air close to ground and cold air above. At disturbances of the layering, e.g. at a ground surface un
211
evenness, humid and warm air starts to ascend, accelerates upwards (chimney effect) and cools down owing to the decreasing atmospheric pressure. In the process, the humidity condenses and forms convective clouds, i.e. clouds with vertical development reaching up to 10 km into the troposphere. Heat thunderstorms are typical summer thunderstorms occurring at ground temperatures above 30 °C, mostly in the afternoon and mainly (but not necessarily) on mountain sides. 2. A front thunderstorm (stormy front) is caused by a cold front moving under warm and humid air masses, triggering upward currents of air as a result. In the westwind zone of the northern hemisphere, active frontthunderstorm areas move eastwards in front of lowpressure areas. They often develop in the seasons with changeable weather conditions. Note: Sometimes dust storms, forest fires or volcanic eruptions can also cause thunderstorms, but this will not be discussed in the following.
In the strong chimneylike updrafts (5 to 30 m/s) of a thundercloud, positive and negative charges are separated, both by upwards moving water droplets and by downwards falling ice crystals, hailstones and rain. Charge separation are probably caused by many different processes, e.g. atomizing of droplets, bursting of ice crystals and electric influence of dipole charges in droplets, which are disrupted into positive and negative droplets [16], [47]. A typical charge distribution of a thundercloud consists of a highaltitude region with positively charged ice crystals, Figure 3.241 (left). The center of negative charge is located underneath, at an altitude of approximately 5 km. Downwards falling sleet and hail stones can cause a smaller region with positive charge at a lower altitude and associated with strongly positive rain at ground level. A thundercloud develops within 30 to 45 min. Finally, the updrafts come to a halt, and cold downdrafts and “thunder squalls” occur. Rain falls within the next 30 minutes. As thunder cells can develop repetitively, thunderstorm activity can last for longer periods.
212
3 ELECTRIC STRENGTH
Temperature
Charge distribution
Altitude 10 km
30 °C
+
+
+
+ + 20 As + + + + + + + + + 
0 °C


ELVE
100 km
  + 4 As   +++   24 As

Ionosphere 8 km
+
+
+
Charge transfer
+
+
6 km
+
+
Sprite
+
+
Blue jet
Leakage current
4 km
Static electric field
Cloudtocloud 2 km
+30 °C Positive rain
10 km
+
Troposphere
+ +
E
 


Cloudtoground




Groundtocloud




Figure 3.241: Charge distribution in a typical heat thundercloud (left) and upperatmosphere lightning and discharge phenomena (right).
The majority of lightning discharges or lightning flashes consist of discharges within the cloud (cloudtocloud lightning), Figure 3.241 (right). A lower percentage of lightning discharges consist of downward flashes, i.e. discharges between cloud and earth. They can be identi
fied from discharge branches growing towards the ground, Figure 3.242 (left). In most cases, negative charge is flowing to ground (negative cloudtoground lightning), but a minority consist of positive cloudtoground lightnings, depending on the charge distribution in the cloud, Figure 3.241 (left). For a very low percentage, upward flashes were observed, starting from tall structures on ground. These groundtocloud lightnings can be identified from discharge branches growing towards the cloud, Figure 3.242 (right). Note: Worldwide, there are always a few hundred active thunderstorms. On average, the downward flashes carry negative charge to ground; positive charges are accumulated in the ionosphere and distributed all over the world., A global static electric field is thus generated that is determined by the balance of lightning currents and atmospheric leakage currents, Figure 3.241 (right). Note: At the end of last century, upperatmospheric lightning above the thunderclouds was also observed from space, i.e. blue jets between thunderclouds and the lower ionosphere and socalled sprites and ELVEs (Emissions of Light and Very Low Frequency Perturbations from Electromagnetic Pulse Sources) at very high altitudes between several 10s of km and approx. 100 km, Figure 3.241 (right) [483], [484].
Figure 3.242: Downward and upward flashes.
In the following, the development of a negative cloudtoground lightning flash is dis
3.2 Gas Discharges
213
8
1 2 4 3 5
4
7 5 6
Figure 3.243: Development of a negative cloudtoground lightning flash: 1 to 5: Descending stepped leader discharges and accumulation of negative space charge (approx. 300 to 1000 μs). 6: Upward and downward (connecting) leaders, initiated by field enhancements at discharge head and ground. 7 to 8: Main discharge (return stroke) with discharge of negative space charge (approx. 10 to 100 μs). NN: Subsequent flashes following the preionized channel (approx. during 10 to a few100 ms).
cussed in more detail, Figure 3.243. There are four stages; the descending stepping leader discharge starting from the cloud (approx. 300 to 1000 μs), the upward and downward leaders connecting close to the ground, the highcurrent main discharge (return stroke, approx. 10 to 100 μs) and a number of subsequent flashes through the preionized channel (within 10 to a few 100 ms). If the breakdown field strength is exceeded, an electrodefree bipolar streamer discharge can start within the cloud and propagate in opposite directions both towards ground (negative side) and into the cloud (positive side). The ionized channel is also referred to as a descending leader. Owing to a lack of charges, the channel cannot grow steadily towards ground and the leader propagation stops. Discharges at the opposite end deliver additional charges within 15 to 100 μs, the field strength at the discharge head increases and the next partial breakdown step occurs. Thus, the leader propagates in steps, each with a length of approx. 50 m (stepped leader) and with a com
paratively low current. The direction of the individual steps is highly irregular because of local field distortions caused by space charges. Branching can also occur as a result of local field stress enhancements. At first, the descending leader discharge path is nearly independent of structures on the ground. Even tall buildings and mountains can be bypassed because they cannot influence the local electric field direction at the discharge head over longer distances. Close to ground, the descending stepped leader discharge causes very high field stress enhancements and initiates positive upward and negative downward leaders that are approximately 10 m long. The socalled connecting leaders originate from exposed grounded structures and from the discharge head, connect and cause final breakdown between the stepped leader and ground (see pointtopoint arrangement, Figure 3.230). Note: Owing to the limited range of upward and downward leaders, lightning strikes are also possible alongside higher buildings, towers and mountains. Air termi
214
3 ELECTRIC STRENGTH
nations of lightning protection systems have a limited cone of protection only.
The discharge propagates along the preionized channel from ground towards the cloud (return stroke) and discharges the negative space charge stored alongside the channel. The return stroke is the main discharge that is visible as a lightning flash and audible as thunder. Current magnitudes can reach peak values of from a few kA up to a few 100 kA within a few μs. The current decay can last for a few 100 μs. This behavior can be explained by the large amount of charge in the discharge head allowing a rapid increase of current after contact to ground, Figure 3.244. Note: The individual current curves differ significantly. Nevertheless, a standard lightning impulse voltage with a front time of 1.2 μs and a time to halfvalue on wave tail of 50 μs is defined in order to simulate the influences of lightning impulse currents on power equipment by a standardized test method, Figure 3.244, Section 6.2.3.
After replenishment of charges from the cloud, the preionized channel can be used for some subsequent strikes, generally with lower current amplitudes. Lightning strikes can cause severe harm and damage to men, animals, buildings, trees and technical systems. In the following direct and indirect influences on electrical and electronic systems shall be discussed. Traveling waves, overvoltages and electromagnetic forces are direct influences of lightning strikes, e.g. in the phase conductors of a threephase system. Additionally, heat generation can damage conductors in the impulse current path. Voltage drops across ohmic and inductive impedances are indirect influences. They cause transient potential differences between statically grounded parts and they can cause “back flashovers” from grounded conductors into active lines of electric and electronic systems [41]. The strong and timevarying magnetic field of the lightningimpulse current induces high voltages in loops. They can endanger
i
1 μs
t
q E
Figure 3.244: Currenttime characteristic of the return stroke.
electronic systems and they can cause flashovers between conductors without sufficient separation. Section 7.4.1 describes lightning protection. Lightning flashes are described by four lightning current parameters, which allow estimation of expected damage: 1. The peak value of the current allows us to determine the maximum ohmic voltage drop at grounding resistances and to calculate overvoltage amplitudes on traveling wave lines (see Section 2.6.1, example). Mostly, Î is between 5 and 100 kA; sometimes a few 100 kA can occur. 2. The rate of current rise di/dt allows the calculation of voltage drops at inductive impulse current diverters and the calculation of induced voltages in nearby conductor loops. Therefore, the rate of current rise is the most important parameter for the description of induced voltages in electrotechnical systems. Typical values of the rate of current rise di/dt are between 1 and 100 kA/μs. 3. The charge of an impulse current ³ i dt is a measure for the heat energy ³ 'v·i dt generated at the root point of the arc, if a constant voltage drop 'v is assumed at the root point. This energy is related to the fusing of metallic conductors. The range is 0.5 up to some 100 As.
3.3 Discharges in Liquid and Solid Dielectrics 2
215
4. The integral of the squared current ³ i dt is related to the ohmic losses in the conductors 2 R·³ i dt and to the mechanical impulse (momentum) ³ F dt. Typical values are between 3 7 2 10 and 10 A s.
ning strikes into wet soil. In laboratory experiments with pulsed energy transfer into water droplets, spherical plasmamagnetic entities (plasmoids) were successfully generated and kept glowing for approximately 0.3 s [440], [485].
Lightning discharges are further described in Section 7.4.1 on lightning protection. Lightning current parameters that are assumed for protection purposes are listed in Tables 7.4.11 and 2.
Note: In laboratory experiments, the discharge is ignited at a negative rod electrode within a ceramic tube that is open at the top. The tube contains a small amount of water, which is brought into a glowing plasma condition by a discharge, and which expands upwards with high velocity. The discharge plasma is extended across the edge of the ceramic tube and comes into contact with the outer water surface, and the salted water provides a contact to the anode. Owing to the buoyant forces, the expanding plasma is detached from the water surface with a velocity of approximately 1 m/s. Owing to its charge, it takes a spherical shape. The glow duration of 0.3 s is much longer than typical ionization times in gasdischarge plasmas, but it is significantly shorter than observed durations in nature. Excitation processes of molecules, which cause a longlasting chemiluminescence in flames, are the object of current research [441], [442]. There could be additional chemical contaminants in the water, on the ceramic tube surface or on the electrodes that influence the color and duration of the glow.
3.2.7.4 “Ball Lightning” For a long time, reports about socalled ball lightning have been comparatively frequent, but so far there is no commonly accepted physical explanation. Therefore, a discussion in a textbook may be too early, but interested readers should be given some information in spite of this, as it might be one of the oldest known highvoltage phenomena of all: There are historical eye witness reports from ancient scholars, mediaeval rulers, Nobel Prize winners and many other people. In modern times, chance pictures and video sequences have been taken, but a scientifically founded and reproducible observation does not yet exist. Note: There are many diverse and speculative attempts at explanation. They include optical illusions, mental delusions caused by pulsed magnetic fields, methane gas flames, plasma balls, black holes, nuclear reactions and esoteric phenomena. Furthermore, “ball lightning” might be used for different physical phenomena.
Nevertheless, some often described properties can be figured out from the various reports. “Ball lightnings” are described as luminous effects with different colors. They occur in conjunction with a thunderstorm, have a spherical shape and can exist for comparatively long times between seconds and minutes. The balls can have destructive effects and explode, or they can be harmless and fade away. The described phenomena could be related to plasma balls that might be generated by light
3.3 Discharges in Liquid and Solid Dielectrics Discharges in liquid and solid dielectrics also develop by the acceleration of electrons, collision ionization and avalanche formation. However, they cannot be described by a universal physical theory as is possible for gases with their homogeneous and well definable properties. The groups of “solids” and “liquids” consist of very many materials with very different physical and chemical properties. They are subject to variations of material compositions, production conditions, contamination, defects and ageing processes. This results in strong statistical dispersion and changes of breakdown strengths. The difference between ideal strength (under laboratory conditions) and technical strength (under application conditions) can be more than one order of magnitude.
216
3 ELECTRIC STRENGTH
1000
Ebd
HDPE (0.01 mm³) PE (40 μm, d.c. voltage)
kV/mm (0.1 mm)
100
(1 mm) SF6 (3 bar)
10
(10 cm)
Strongly purified liquids L SF6 (liquified, 5 mm) Mineral oil (degassed, 40 μm) PXE Mineral oil (dry)
SF6 (1 bar)
Mica (crystals) PE (extruded) Paper (oilimpregnated)
Paper (unimpregnated) Mineral oil (wet)
Air (1 bar) 1
Gases Vacuum
Ne (1 bar)
Strongly contaminated liquids
Liquids
Solids
0.1 Figure 3.31: Ranges for breakdown field strengths at AC voltage (50 Hz) for atmospheric pressure, ambient temperature and insulation thicknesses in the cmrange (other conditions are mentioned in brackets). LSF6 (Liquified sulfurhexafluoride), Abbreviations: SF6 (Sulfur hexafluoride), PXE (PhenylXylylEthane), PE (Polyethylene), HDPE (Highdensity polyethylene).
Basically, the inception of discharges is impeded with increasing density of the material structure (decreasing free pathlength for charge carriers) and with increasing binding forces of the electrons. Accordingly, the dielectric breakdown strength increases from gases through liquids to solids, but a large number of influences blurs this picture, Figure 3.31. Figure 3.31 gives breakdown strengths for liquid and solid dielectrics. Technically pure materials can be found in the middle of the given ranges, highly purified materials or very thin layers are at the upper ends and contaminated materials at the lower ends. For gases, the technically achievable design strengths are significantly closer to the physical limits. Gaseous, liquid, and solid insulating materials have their specific advantages and disadvantages. Without respect to their dielectric strength, they are especially suited as “construction materials” for specific purposes:
1.) Gases have the following advantages: Low weight, perfect impregnation properties, well defined properties, longterm stability, insensitivity to electrical discharges or selfhealing properties (even in case of arcs) and low cost (for air). It is disadvantageous that breakdown strengths (at atmospheric pressure) are low and that stresses because of dielectric field displacement are high. Gas (air) is the “natural” insulating material (e.g. for overhead lines and switchgears), which is only replaced by liquids or solids if necessary. 2.) Liquids have different advantages: Good impregnation properties, high breakdown strengths and high thermal conductivities by convection. On the other hand, there are the following disadvantages: Higher weight, breakdownstrength degradation by ageing and contamination, thermal expansion, the necessity for sealed housings and higher costs. Liquids are the typical impregnation materials for electrically stressed cavities (in capacitors,
3.4 Discharges in Liquids
217
instrument transformers and capacitors. Additionally, other liquids based on natural or synthetic sources are used for special applications, Section 3.4.4.
transformers, cables, etc.). They are also used for the convective transport of heat (e.g. in transformers). 3.) Solids also have specific advantages: High breakdown strengths (e.g. for thin films), reduced stresses because of field displacement and their applicability as mechanical construction materials. Lowviscosity resins can be used for impregnation; in the cured state, they allow “dry”, i.e. oilfree constructions. It is disadvantageous that heat conductivities are low, that electrical discharges can cause irreversible destruction, that weights are high and that there are high technological requirements.
3.4.1 Discharge Mechanisms in Mineral Oil Basically, the breakdown strength of mineral oil decreases significantly with voltagestress time, Figure 3.4.11. Owing to multiple unknown parameter influences (type, form and number of particles; water content, stressed volume, electrode surface, distance, oil convection, uniformity of the field …), breakdown tests show large differences and dispersions which cannot normally be adequately described by theory. Therefore, empirical parameter dependences are most important for practical dimensioning.
Solids are used in highly stressed dielectrics (capacitors, bushings, cables), for the embedding of conductors with high surface field strengths (transformers, electrodes, cable terminations) and for mechanical construction elements with insulating properties (string, post and housing insulators, switch rods, partition plates etc.).
Example: In a weakly nonuniform electrode arrangement, the 1 % breakdown values can be lower than half the 50 % breakdown values for long lasting AC voltage application [59], Figure 3.4.12. This is a dramatic increase of statistical spread, in comparison with shortduration voltage applications (impulse voltage) and in comparison with gas discharges.
3.4 Discharges in Liquids Insulating oils based on mineral oil are the most important insulating liquids, Sections 3.4.1 to 3.4.3. They are used in large quantities in transformers both as insulating and as cooling liquids (“transformer oil”). Furthermore, mineral oil is used as impregnating liquid in oilfilled equipment, e.g. in bushings,
The high number of relevant parameters has initiated many experimental investigations since the 1950s, in order to find statistically justified relations between test conditions and dielectric strength. Nevertheless, there is not yet a consistent theory of oil breakdown which is comparable with the theory of gas dis
40 Impulse breakdown (Discharge delay) 30 Figure 3.4.11: Breakdown strength of a liquid dielectric as a function of voltagestress time (transformer oil, d= 2.5 mm, V= 200 mm³) without respect to the statistical dispersion which increases with time, see fig. 3.42.
1s
1 min
kV/mm
10
1d
Fiberbridge breakdown
Ebd
20
1h
Electronic breakdown, streamer breakdown (Percolation theory)
"Intrinsisc breakdown"
1m 1a
30 a
Water, contamination, gassing
"Weaklink breakdown"
t /s 10
9
10
6
10
3
10
10
3
10
6
10
9
218
3 ELECTRIC STRENGTH
98 %
Weibull distribution
63 % 50 %
F(Vbd ) F(E bd) 2% 1% R.m.s. values
E bd V bd
4 5
180 220
9.2
10.5
410 470
14
620
kV/mm
kV
Figure 3.4.12: Breakdown frequency as a function of voltage and field strength in technically clean and dry oil at AC voltage (f = 50 Hz, voltage rise rise 8 kV/s) between excentric tubulal electrodes (Da = 600 mm, Di = 80 mm, d = 72 mm, l = 300 mm, field efficiency factor 62 %), oil flow 100 l/min [59].
charges. For very short voltagestress times, the discharge behavior seems to be similar to the discharge behavior in gases, Figure 3.4.11, but the direct formation of electron avalanches by collision ionization in an ideal liquid is not conceivable at first glance; free pathlengths are not long enough and the typical breakdown strengths are not high enough. Note: In the past, it was assumed that the liquid contains lowdensity volumes, which could be seen as oilvapor “mircobubbles” [59]. In these bubbles, free path lengths could be available, allowing collision ionization similar to gas discharges (“masked gasdischarge”). The increasing breakdown strength with decreasing stress duration would be equivalent to the voltagetime characteristics of gas discharges, Figure 3.4.11; and dependences on the static pressure could also be explained consistently, Figure 3.4.25. There are different theories for the generation of microbubbles [59]: Lowdensity volumes could occur even below the boiling temperature because of the thermal (Brownian) motion of molecules. Furthermore, it seems to be possible that density differences occur by electrohydrodynamic motion of charged volumes. Another idea assumes that space charges expand by electrostatic repulsion causing lowdensity volumes. Additionally, discharges could be ignited by charge transfer between particles and electrodes. High electric field strengths at microscopic tips at electrodes could additionally cause current injections, local overheating and density reductions.
As early as 1970, a physical theory of oil breakdown was developed on the basis of discharge current measurements and optical
imaging, [426]: High local field strengths at electrode tips cause a strong increase of conductivity, together with space charge formation and equalization of the field distribution. From such an impulsefree darkcurrent discharge or continuous discharge (1), luminescent and thermally ionized discharge channels erupt repetitively at very high field strength (2). By analogy with gas discharge physics, these channels are referred to as leaders, Hauschild [426]. The channels transfer the electrode potential into the liquid with a voltage gradient of approx. 1 kV/mm. The discharges can be stabilized in a strongly nonuniform field. At sufficiently high voltages or in a uniform (or weakly nonuniform) field, the leader channels can reach the counterelectrode and generate the main discharge, formed by a highcurrent backward leader (3). Note: In today’s terminology, the described discharge phenomena are often referred to as primary (1), secondary (2) and tertiary (3) streamers. But in terms of discharge physics, this is not correct where thermally ionized channels are concerned; these would be better referred to as leaders [426]. Today, the term “streamer” imprecisely describes the propagation of lowdensity volumes without respect to their physical origin. Please note that gasdischarge physics uses the term “streamer” only for a spacechargerelated discharge channel generated by collision ionization, Section 3.2.3.
Owing to physical investigations, the theory of oil breakdown is now much more sophisticated. Different stages from the first initial processes to the final breakdown process (the socalled streamer development) can now be described in detail, Section 3.4.1.1 to 3.4.1.4. In the following, physical theories (Section 3.4.1) and empirical parameter dependences (Section 3.4.2) are described and discussed.
3.4.1.1 Stages of Oil Breakdown By means of highspeed cameras, shadow images of different discharge stages can be taken. They show the propagation of volumes with low density and thus give a sophisticated picture of oil breakdown, Figures 3.4.13 and 7ff. In oil gaps, breakdown processes start at
3.4 Discharges in Liquids
219
the electrode surfaces and they are related to the generation of gasfilled microcavities. Gas discharge processes occur in these cavities.
(2) After the application of an electric field, electrons are injected into the liquid. Structural differences of electrode surface areas, oxides and pollution layers cause strong local differences of the work function and for the injection of electrons. Very high injection current densities of the order of kA/mm² can occur, especially at microtips [423].
Note: So far, similarities with gas discharges can be explained (voltagetime characteristic, pressure dependence), but it is not yet clear, whether microcavities are the reason for the discharges or whether discharges generate the microcavities. Different mechanisms are discussed in the literature. In all experimental investigations on mere oil gaps without barriers, discharges start at the electrodes. Therefore it is assumed that both the properties of oil and the interaction with the electrode surface play an important role.
Under the influence of a strong field, the conductivity of the liquid increases nonlinearly. Electrons are injected at the cathode and build up a negative space charge that weakens the field and restricts the emission. At the anode, electrons are stripped in the liquid and focused (concentrated) in front of the positive tips. This significantly increases local field strengths.
In the following, the different stages will be discussed in detail, but an overview is given at first, Figure 3.4.13: (1) Without a field, the liquid is in an unordered state. At the interfaces between liquid and electrodes, electrochemical double layers (Helmholtz layers) are formed; they reduce the work function for electrons [402], [404]. 1 Condition without field
In the liquid, current density lines are concentrated at preferential surface points. At these points, energy is transferred into the liquid causing local enhancements of temperature
2 Influence of increasing field strength
3 "Initial process" (microscopic)
Double layer Current flow Orderless state
Structuring of conductive, charged and lowdensity volumes
Conductivity increase
Particle drift
E
5 4 Discharge inception Propagation of discharge channel (Stepped discharge)
Radiant propagation of lowdensity volumes Primary streamer
t Stepped discharge as a sequence of ignition and extinction Secondary discharge channel, transition to a leader (also named "secondary streamer")
Figure 3.4.13: The stages of oil breakdown, see also Figure 3.4.110.
Formation of lowdenstity volumes at ~1000 kV/mm 6 Main discharge
Tertiary discharge
220
and conductivity. The conductive paths are connected to the electrode and charged accordingly. The charged current paths form semispherical and regular bunchlike structures in the liquid because of their electrostatic repulsion. As a result, preferential paths for current flow are imprinted in the liquid (percolation theory). (3) At very high local field strengths between 250 and 1000 kV/mm (i.e. far above the macroscopic technical breakdown strength of approx. 25 kV/mm), microscopic volumes with low density are generated, which can be regarded as gaseous. Their bunchlike and branching structures in the liquid can be detected by shadow images. There are three different theories describing the initial processes of discharge evolution in strong electric fields: (a) discharges caused by collision ionization within the liquid [403], [407], (b) destruction of surface tension [404] and (c) currentinduced conductivity increase [310], [423]. Note: In addition to these (intrinsic) initial processes in the liquid itself, influences of weak links (contaminants) have to be considered.
(4) Today, the bunchlike and radially expanding lowdensity regions are referred to as “streamers” in the literature. This is not quite precise, because there is no reference to the physical cause. Nevertheless, as long as the initial or primary streamers are caused by collision ignition, i.a. at high local voltage drop, this wording is in accordance with gas discharge theory, cf. Section 3.2.3. (5) A discrete branched secondary discharge channel develops from the uniformly structured branchlike primary streamers as a stepped discharge similar to the leader discharge of a cloudtoground lightning flash, Figure 3.243. As high current densities at low local voltage drops occur during the stepped growth of the channel, thermal ionization, i.e. a leader discharge is assumed [426]. Nevertheless, the phenomenological term “secondary streamer” is further used in literature without physical reason.
3 ELECTRIC STRENGTH
A positive channel propagates stepwise and with high velocity (approx. 2 mm/μs) towards the counter electrode, which is always reached. The discharge is interrupted and ignited several times during propagation. A negative channel leaves a positive space charge cloud behind which weakens the local field and limits the discharge range and velocity (approx. 0.1 mm/μs). Thus, the negative channel is less dangerous than the positive one [405], [406]. (6) For long streamer lengths or if the counter electrode is reached, the conductive channel is used for a highcurrent luminescent tertiary discharge (main discharge) with high conductivities and temperatures causing oil vaporization, gas discharges, ionization, light emission and voltage collapse. After this overview, the stages of oilbreakdown will be discussed in detail in Sections 3.4.1.2 (The liquid before ignition), 3.4.1.3 (Initial processes) and 3.4.1.4 (Discharge Propagation).
3.4.1.2 The Liquid before Ignition
a) The liquid without a field Even without a field, there are free charge carriers in the liquid, mainly in the form of positive and negative ions and a few quasifree electrons. The charge carrier density is determined by the equilibrium of recombination and ionization (dissociation). At the interface between oil and electrode, there is a thin and diffuse electrochemical double layer with a thickness of approx. 100 nm. There is a preponderance of negative charge in the liquid, whereas the positive image charges are situated on the electrode [402], Figure 3.4.13 (1). Note: The microscopic field strengths can reach 1000 kV/mm. Electrons need an energy of approximately 4 to 5 eV (work function) in order to leave the electrode against such a field. Normally, there is an oxide layer on the metal electrode surface with traps that can exchange a limited number of electrons with the liquid.
3.4 Discharges in Liquids
Double layers, energy levels and microscopic field strengths are strongly dependent on surface roughness, surface conditions and contaminants, and they are subject to strong local and temporal variations. This might be one of the reasons for the high statistical spread of oilbreakdown, which can often be observed.
b) Impact of an external field An external field changes the double layers at the electrodes. At the (negative) cathode, electrons are injected into the liquid and a negative space charge is built up. It weakens and homogenizes the field in front of the electrode, thus reducing the injection. The injection process can only start again when the space charge has been removed by charge carrier drift. A repetitive process results that is comparable to the gasdischarge Trichel impulses. In front of the (positive) anode, the microscopic field is significantly enhanced because drifting electrons, which were generated in the liquid or at the cathode, are concentrated (focused) close to surface inhomogeneities. This explanation corresponds to the observation that breakdowns are caused by positive streamers in most cases (polarity effect). In the liquid, the mean free path lengths are short. Even at high field strengths, electrons cannot get enough energy for collision ionization processes and avalanche formation. Therefore, it is hardly imaginable that the processes are comparable to gas discharges; it seems to be more reasonable to compare the processes with the energyband model of an amorphous solid dielectric.
221
uids decreases within the transit time of the ions. At higher field strengths, energyband structures and potential walls are displaced according to the potential gradient. Consequently, tunneling, hopping and generation of quasifree electrons in the conduction band are made easier. The conductivity increases significantly, Figure 3.4.13 (2) left, Section 4.2.2.2. Note: It is assumed that even “quasifree” electrons are not completely free. Owing to the high material density, they remain in a permanent interaction with the molecules and lose energy continuously. Therefore an accumulation up to the ionization energy seems to be impossible [310]. Nevertheless, there are controversial opinions regarding this, Section 3.4.1.3 (a) [402], [407].
c) Imprinting processes in the liquid (percolation) There is an interesting theory about imprinting processes in the liquid: The percolation theory [310], [423] assumes that an ideal liquid without a field is without any longrange order and remains in a condition of complete disorder, which is in contrast to a solid. In this situation, there are no energy levels within the liquid which can absorb charge carriers. Under the influence of an electric field, the molecules are arranged and a shortrange order is generated with different energy levels, which are occupied by electrons. Drifting, hopping and tunneling electrons polarize the adjacent molecules and create new energy levels that facilitate the motion of subsequent electrons. As a result, coherent regions with enhanced conductivity and enhanced current density (allowed zones) are generated. In these regions, electrons “percolate” through the oil. In a limited volume, molecules are arranged in regular (shortrange) order, Figure 3.4.14 (bottom).
Note: The energy levels of the charge carriers are described by erratic energyband structures similar to an amorphous solid (conduction and valence bands, traps), Figure 3.52. Electrons can move along chain molecules by tunneling and hopping. During the transition between molecules, electrons have to get over higher potential barriers (intermolecular transition). Quasifree electrons in the conduction band are generated by energy transfer from thermal motion, radiation or the electric field.
Note: “Percolation” refers to the imprinting of preferential directions for charge carrier movement in the oil by the incipient charge transport itself. This process is analogous to a coffee percolator, in which the water percolates through the coffee powder and impresses macroscopic propagation structures.
At low field strengths, the ions drift to the electrodes where they are neutralized or accumulated [486]. Thus, the conductivity of liq
Ordered ranges can be built by generating clusters from charge carriers and molecules, they can be extended by charge supply from
222
3 ELECTRIC STRENGTH
the electrodes and they can be connected to each other. Thereby, the liquid is structured with temporarily stable quasicrystalline clus5 ters (consisting of up to 10 molecules and with dimensions up to 0.1 μm), which are separated by disordered regions. Similarly to an amorphous solid, there are “allowed zones”, which can carry electrons and in which electronic charge transport occurs by quantummechanical processes (hopping, tunneling) [310], see also Figure 3.52. The electronic charge transport through the liquid takes place by charge transfer between the allowed zones. The higher their number and the higher their degree of order, the higher currents can flow.
3.4.1.3 Initial Processes
The conductive paths are spherically or semispherically arranged under the influence of the local field close to microscopic tips by the repulsion forces of the space charges, Figure 3.4.13 (2) right.
The inception field strength for positive streamers is lower than for negative streamers (polarity effect), Section 3.4.1.2. The physical nature of the initial processes can be explained by a number of different theories, Figure 3.4.1
E.g. cathode ()
Basically, the intrinsic breakdown of the pure liquid itself and the weaklink breakdown caused by contaminants have to be distinguished. Experiments with very sharp pointelectrodes show that the inception of streamers in pure liquids requires very high local field strengths of the order of
E = 1000 kV/mm
E
E
E
1000 kV/mm
The actual ignition of the breakdown process is called the initial process.
x = rTip
250 kV/mm
Gas discharge
Electron avalanche in the liquid
First Microbubble
3 ns, 3 pC
rB = rTip= 3 μm
High local field strength
E
A
E
Series of bubbles
E
E
E
S
S
S
A E.g. anode (+)
2  3 mm/μs
Figure 3.4.14: Different theories about initial breakdown processes in insulating oil at an electrode (E) with high local field strength. Top: Generation of microbubbles by electron avalanches in the liquid at very high local field strengths (“hot micro cavities”). Bottom: Arrangement of allowed (conductive) zones (A) around an interconnected source region (S): Interconnection with the electrode (E), structuring of the conductive zones, current increase and gas formation (G) by vaporization (percolation theory).
3.4 Discharges in Liquids
4. They describe the initial processes in different ways, (a) as avalanche formation in the oil itself, (b) as a reduction of surface tension, (c) as an imprinting, structuring and heating of the liquid or (d) as a thermal instability in wet and conductive cellulose fibers. Different technological influences have to be taken into account (e). The sections a), b), and c) describe initial processes for intrinsic breakdowns, sections d) and e) refer to weaklink phenomena.
a) Avalanches in the oil (“hot microcavity”) Tobazéon [403] assumes that collision ionization and electron avalanche formation can occur in the liquid itself for a field strength of approximately 1000 kV/mm. Note: Lewis gives the following explanation based on a reduction of the collision cross section with increasing electron energy: At 1000 kV/mm, collisions would be elastic and the electrons would keep their energy, which could be accumulated up to the ionization energy of approx. 9 eV [402]. Furthermore, electron exchange processes (Auger processes) could generate high energy electrons at the electrodes [407]. Owing to a simple estimation, Tobazéon’s theory is quite plausible, if the situation at a point electrode with a μm radius is compared with a gas discharge: The ratio of oil density (800 kg/m³) to air density (1,2 kg/m³) and the ratio of the inception field strengths of approx. 1000 kV/mm (oil) to 3 kV/mm (air) are in the same order of magnitude.
In a nonuniform field, the range of the avalanches is very limited, because free charge carriers are trapped below 250 kV/mm. As a result of energy dissipation, every avalanche causes a microcavity or a microbubble with a radius approximately equivalent to the pointelectrode radius (up to approx. 10 μm). Subsequent avalanches (approx. 3 pC every 3 ns) generate a series of bubbles which gives enough length for the ignition of gas discharges and for their development into a socalled streamer [403], Figure 3.4.14 (top). Note: For tests with sharp point electrodes, it was observed that only the positive streamer inception depends on pressure and not the negative streamer [414]. For the positive point electrode, it is concluded that there is a concentration of current, overheating and pressuredependent vaporization (see c)). The negative streamer is
223 assumed to start with an electron avalanche directly in the liquid phase as described above.
b) Destruction of surface tension (“cold microcavity”) Lewis [407] has also shown that the surface tension of the liquid is reduced at high field strengths. This means that the cohesion of the liquidmolecules could be broken up at the locations of the highest electric field strength (especially in the double layer at the anode) and a “cold” microcavity could occur. In such a cavity, collision ionization processes could occur, and initial electrons could be generated by charge transfer between incident charge carriers and the electrode (Auger process). In this case, the electric discharge would be the consequence and not the cause of the initial process.
c) Interconnecting of electrodeliquid interfaces (percolation theory) According to the percolation theory, conductive (“allowed”) zones in the liquid are arranged at points of locally focused field lines. The current flow causes an imprinting (percolation), which further increases the conductivity, Section 3.4.1.2 [423]. Note: Kist [310] assumes that the interfaces between metal, oxide and liquid block at first, switch through after a threshold is exceeded and interconnect an “allowed zone” in the liquid with the electrode, Figure 3.4.14 (bottom). This zone becomes an inception or source region which is charged from the electrode and creates a spherical microfield. The allowed (or rather conductive) zones are arranged in the spherical microfield. They are enlarged by means of charge supply from the electrodes (electrons at the cathode, “holes” at the anode.
Owing to electrostatic repulsion, the growing conductive and charged zones are arranged in treelike or threadlike spherical structures. The structuring imprints channels for increased current flow, which causes local heating and vaporization of the liquid when energy dissipation becomes high enough. The resulting radial and branched primary streamers are oriented in the direction of the microscopic field.
224
3 ELECTRIC STRENGTH
Lowdensity streamers also play an important role in percolation theory, but they aren’t the reason for the current flow. Streamers are the consequence of the current, which already exists because of fieldinduced ordered states. Electric discharges can be ignited in the gaseous streamers, which were generated by overheating. Thereby, a pressure dependence according to a) could be explained. d) Wet fibers (fiberbridge breakdown)
Owing to the electrostatic field forces, fibrous impurities can drift in the direction of the electric field lines and line up as fiber bridges, especially during long stress durations. Often, the hygroscopic cellulose fibers contain water in the percentage range and they form conductive paths which are overheated. Evaporated water generates microcavities and causes the socalled fiberbridge breakdown at comparatively low field strengths, Figure 3.4.22. These processes are relevant both for DC and for AC voltage stresses because the 1000 Pointtoplane Positive streamer inception
E i ~ A 0.17
100
Uniform field Breakdown
Lesaint and Top [413]
Trinh [412] 10
6
10
0.001
0.01
3
10
0.1
Statistical investigations show that discharge inception is subject to significant size effects. First of all, it seems contradictory that extremely high inception field strengths of 1000 kV/mm occur on highly rounded tips with rtip = 1 μm, and that inception field strengths decrease with increasing radius or electrode area down to macroscopic strength values of approx. 10 kV/mm, Figures 3.4.15 and 6. It has been discussed for a long time whether these size effects are volume, area or distance effects. [408] … [411]. Note: This ambiguity results from the experimental difficulty of distinguishing these influences: if one of the parameters is changed, the other two cannot be kept constant at the same time. It has been shown that experimental data from distribution functions for a unit volume or for a unit area can be extrapolated over 8 orders of magnitude both by a volume rule and by an area rule. [412].
The oil condition and the type of voltage stress profile are obviously strong influences. These influences can be explained by the difference between intrinsic breakdowns, which are determined by the properties of the oil itself (in the case of small “faultless” electrode surfaces), and weaklink breakdowns, which are caused by impurities such as particles, water or significant surface defects.
3
1
1
The initial process is a local thermal instability (thermal breakdown), similar to the processes according to the percolation theory c). However, breakdown occurs at significantly lower field strengths because of the weak links.
e) Technological influences
There is very good experimental evidence that wet fibers reduce AC and DC breakdown voltages and increase statistical spread [59]. Therefore, weaklink breakdown caused by contaminants and intrinsic breakdown of the liquid itself have to be distinguished.
Ei 50 % kV/mm
stresses of dielectric interfaces do not depend on polarity. In the case of impulse voltage, stress duration is not long enough for particle drift.
10 A / cm² 10
r tip / mm
Figure 3.4.15: Size effects for impulse voltage stresses at point electrodes with different tip radii rtip [413] and at plane electrodes with different electrode areas A [412].
1.) Intrinsic breakdowns occur in very clean oils, for very short stress durations (impulse voltages) and for very small electrode areas. They show very high local inception field strengths of about 1000 kV/mm and low statistical spread, Figures 3.4.15 (left) and 6 (left).
3.4 Discharges in Liquids
2.) Breakdown strength decreases with increasing size of the arrangement, including in the case of lightning impulse voltages, Figures 3.4.15 and 6. Because stress duration is not sufficient for particle drift, an electrodearearelated weaklink breakdown is observed. It is caused by faulty electrode surfaces or by adjacent particles. In this way, a certain influence of the oil quality can be explained. Note: It was shown experimentally that the assumption of an area rule gives a good fit over more than 12 orders of magnitude, Figure 3.4.15 [413], [412]. Additionally, experiments with artificial field stress enhancements show that high and constant microscopic inception field strengths occur at local tips, even for low averaged (i.e. macroscopic) inception field strengths [414]. This means that the local field strength at a field nonuniformity, and not the average field strength, is responsible for streamer inception. In order to explain the size effect according to Figure 3.4.15 as an area effect, it has to be assumed that surface defects cause the field stress enhancement factors between 10 and 100 and that the probability for the existence of such defects increases significantly with increasing stressed electrode area. First of all it doesn’t seem plausible that typical surface roughness causes such extreme field stress enhancements. Therefore, it is assumed that particles adhering to the electrode surface cause a strong tip effect [413], [415]. The extreme difference between high microscopic and low macroscopic inception field strengths, which at first appeared to be contradictory, thus seems to be quite plausible to explain. Note: The size effect for streamer inception is interpreted as an area effect here. Nevertheless, streamer propagation is of course strongly influenced by the flashover distance, Section 3.4.1.4.
225
cur, Figure 3.1.46 (left). However, there is a significant decrease in AC breakdown strength with increasing size of the insulation arrangement and with increasing particle content of the oil, Figure 3.1.46 (right). The observed size effects can be explained well both by volume and by size effects. They are consistent with the idea of initial processes, which are triggered at the electrode surfaces by drifting particles from the oil volume. Note: In particleloaded oils, the probability of a particleinduced weaklink breakdown increases with the number of available particles per unit area. In particular, oils with wet fibers show weaklink breakdowns with a large statistical spread during longlasting voltage stresses [59]. Obviously, slow particle drift through the oil reduces the longterm strength; shortterm impulse strengths are not dependent on particles. By means of the addition of conductive particles it was determined that free particles trigger the discharge at comparatively low field strengths, just at the instant of electrode contact. It is assumed that the field strength at the particle’s end is significantly increased without a protective
1000 Pointtoplane (Lesaint [445]), streamer inception (20 streamers/min.) Ê Ê
Ei 50 % kV/mm 100
Uniform field, breakdown (Trinh [412]) Ê
3.) Volumerelated weaklink breakdowns occur, if particleloaded oils and longlasting voltage stresses (AC or DC voltage) are subject to particle drift and breakdowns at comparatively low voltages with a high statistical spread [59]. Figure 3.4.16 [445] shows the strength for an impulse voltage (dashed line, see Figure 3.4.15) which is not influenced by weak links in the oil volume. For very small insulation arrangements and for AC voltages, there are discharge inception field strengths, which are even slightly higher than for impulse voltages [445]. This is explained by injected space charges homogenizing the field distribution for AC voltages and by the small size, for which volume effects do not yet oc
10 Erms
AC (25 mg cellulose / l oil) AC (filtered oil)
Erms
Impulse voltage fig. 3.4.15 (filtered oil) 6
10
0.001
0.01
3
10
0.1
3
1
1
10 A / cm² 10
r Tip / mm
Figure 3.4.16: Size effects for AC voltage stress (peak values) for tips with different radii rTip [445] and electrodes with different areas A [412]. Intrinsic breakdowns (for AC only for small areas/ volumes and for impulse voltage) as well as weaklink breakdowns (for AC for two different oil qualities).
226 spacecharge cloud that could reduce the field strength [415].
These processes are not only volume effects but also distance effects, because the free oil gap in the field direction determines how fast and how many particles can drift towards the electrode. Furthermore, distance effects play an important role in streamer propagation, Section 3.4.1.4. Conclusion: Initial processes and discharge inception depend on microscopic surface properties and oil quality (particle and water content); they are initiated at the electrode surface. The intrinsic breakdown only dominates for very pure oils, for very short impulse voltage stresses or for small electrode areas. With increasing electrode areas, an arearelated
3 ELECTRIC STRENGTH
weaklink breakdown affects breakdown strength, (area effect). For oils with a high particle content and with a sufficiently long voltage stress, a volumerelated or distancerelated weaklink breakdown dominates because of particle drift (volume or distance effects). For technically purified oils, the arearelated and the volumerelated effects can be superimposed. From this the decrease in breakdown strength with stress duration can be explained, Figure 3.4.11. The voltagetime characteristic plays an important role in the design of insulation systems, and it is characterized by the socalled impulse factor, i.e. by the ratio of impulse to AC breakdown strength.
3.4.1.4 Discharge Propagation After the discharge process is started by an initial process, the discharge develops from the source region. Often, all kinds of lowdensity structures that propagate under the influence of an electric field are often referred to as “streamers”, irrespectively of wether or not they are electrical discharges at all, streamer discharges with collision ionization (i.e. streamer discharges in a strict sense) or leader discharges with thermally ionized channels, Figure 3.4.17.
a) Polarity effect Positive discharge channels are much more dangerous than negative ones because they have a lower inception voltage (polarity effect), Figure 3.4.17, and they may result in a lower breakdown voltage. Note: Figure 3.4.17 is a sequence of eight shadow images with intervals of 500 ns. There is a positive tip at the bottom and a negative tip at the top of each picture. It can clearly be observed that the visible positive discharge phenomena (at the lower tip) start approximately two intervals earlier than the negative ones (at the upper tip). Figure 3.4.17: Negative and positive discharge channels (at the upper and lower tips). Pointtopoint electrode in insulating oil. The delayed start of the negative discharge corresponds to the polarity effect [424], Figure R. Badent, IEH Univ. Karlsruhe.
Additionally, the penetration power and the range are larger for positive channels than for negative channels. This is due to the fact that a
3.4 Discharges in Liquids
227
negative space charge cloud is formed in the region around the negative channel owing to highly mobile electrons, and this homgenizes and weakens the local field at the channel’s head. For the filamentshaped channels of the positive channel, significantly higher local field strengths at the discharge head, better propagation conditions and greater penetration power result, Figure 3.4.18. Consequently, insulation tests with positive voltage usually present tougher stress conditions and are generally explicitly stipulated in the test specifications. b) Propagation modes The propagation of discharge channels is generally determined by the arrangement (homogeneity of the field, distance) and hence there can be four different propagation modes whose propagation velocity differs respectively by approximately one order of magnitude and which exhibit partially distinctive structural differences. The methods of classification and description of different authors are not consistently the same, Table 3.4.11. Note: The first mode with very low propagation velocity occurs only under special conditions at very sharp edged points and is of no significance for many breakdown processes. The practically relevant propagation modes no. two, three and four are sometimes also referred to as primary, secondary and tertiary streamers [423], but actually, the last two aren’t streamers [426].
c) Propagation in a nonuniform background field The most important physical investigations were conducted for discharge propagation in a strong nonuniform field with impulse voltages, far above the 50% discharge voltage of the arrangement. Thus, the discharge can be sparked off in a controlled manner and synchronized with high speed recordings. 1.) Under these conditions, the discharge begins with the regularly structured primary streamers (second mode), whose filamentous and branched spherical structure is oriented towards the radial microfield in the region around the nonuniform point electrode, Figures 3.4.18 and 9. The propagation velocity is in the range of 2 to 3 mm/μs and is stabilized by the buildup of space charge associated with the streamer propagation and by the streamer’s charging current (selfregulation). Note: The increasing field strength at the head which results from the discharge growth and which has an accelerating effect is reduced again by the space charge built up in the adjacent channels and by the throttling of the supply of charge. Note: For this form of discharge, different terms such as “primary streamer” [310], “second mode”, “microcrown” [406] or “fanshaped filaments” [413] are used as descriptions, Table 3.4.11.
Table 3.4.11: Propagation modes of discharge phenomena (or socalled streamers )in mineral oil Hauschild [426]
Leader discharge Second mode Third mode Ultrasound discharge Very fast discharge
Fourth mode Extremely fast discharge
Badent [423]
Primary streamer
Secondary “streamer”
Tertiary “streamer”
Torshin [406]
First step “micro crown”
Step wise discharge propagation
0.1 to 1 mm/μs For a strongly non Only for very sharp points (r < 1 μm) and uniform field for very low voltages
2 to 3 mm/μs Normal case with selfregulation by space charges
~ 10 mm/μs Start mode at the point as well as just in front of the counter electrode
Top, Massala and Lesaint [405]
For a quasi homogeneous field
First mode Slower subsonic discharge
(only for negative streamers)
(only for very large increase in the field >50 kV/mm)
> 100 mm/μs Develops from the streamers that are greatly accelerated in the third mode and is selfluminous
228
3 ELECTRIC STRENGTH
2.) For distances greater than approx.. 50 mm, discrete discharge channels, socalled secondary streamers (third mode), with a high velocity of 10 mm/μs or more erupt from the primary structure and rapidly pass over the oil gap, since the velocity stabilization caused by space charges loses its effectiveness, Figure 3.4.110 In the case of positive polarity, wide ranging and irregular discharge channels are formed and they spark through the entire gap in a stepwise sequence of ignition and extinction (stepped discharge [406]) , Figure 3.4.13: After the (re)ignition of a formerly extinguished channel, the discharge head is connected to the pointelectrode potential via a
Figure 3.4.18: Positive discharge channels (socalled primary streamers) with umbelshaped or spherical structure [424]. Rod to plane in insulating oil, with r = 5 mm and d = 50 mm. Voltage: lightning impulse voltage 1.2/50 ȝs approx. 250 kV. Light exposure time 100 ns, image distance 500 ns.
conductive channel. By reducing the potential difference, the discharge is extinguished again, but the charged head is still further accelerated by the field so that a larger potential difference is recreated, which in turn leads to reignition of the discharge channel. Note: The discharge channel is of high impedance and low impedance in phases, and it does not give rise to any permanent collapse of voltage across the channel. That is, there is not initially a permanent thermally ionized channel but there are recurrent collision ionization processes which can finally lead to thermal ionization. In gas discharge physics, this is a transition from the streamer discharge to leader discharge [426].
3.) From this mode, the streamers can change into a faster, high current and selfluminous propagation mode, the socalled tertiary streamer (fourth mode) at more than
Figure 3.4.19: Negative discharge channels (socalled primary streamers) with branched structure [424]. For explanations see Figure 3.4.17. Figures 3.4.18 and 9, R. Badent, IEH Univ. Karlsruhe
3.4 Discharges in Liquids
229
Figure 3.4.110: Propagation of negative and positive discharge channels (top and bottom). Point to plane in insulating oil. Left to right: regular primary streamers, eruption of fast discrete channels (socalled secondary streamers) and inception of selfluminous main discharge [425], see also Figure 3.4.13. Images by R. Badent, IEH Univ. Karlsruhe.
100 mm/μs. In the terminology of gas discharge physics, this must instead be referred to as a leader discharge [426]. The main discharge that leads to this breakdown results in partially discharging of the smaller secondary branches, Figure 3.4.18 (bottom right) and to a blast wave that can also be identified in the shadow image, Figure 3.4.19 (bottom). Positive and negative channels show different structures, Figures 3.4.18 to 10. The formation of negative channels is less regular and the transition to the socalled secondary streamer is less identifiable in the structural changes. The propagation modes can better be distinguished by the different velocities. Note: Oil breakdown was also described with the help of the percolation theory as a sequence of socalled streamer discharges [423], [310], Figure 3.4.111: After creation of a source volume, imprinting of the liquid (percolation) and inception of primary streamers, higher local field strengths at the streamer head lead to a wideranging percolation structure with extended states, increased charge flow and drastically increasing current. This phenomenon, which is described as a percolation threshold, is the basis for the wideranging secondary streamer that erupts from the primary structure with higher propagation velocity in the direction of the macroscopic field. Streamer propagation in oil shows a distinct polarity effect: Umbelshaped primary streamers are formed at the positive point electrode (anode) in the permitted areas of the microfield at a comparatively
slow rate; the transition to secondary streamers requires significantly higher local field strengths, Figure 3.4.111 (left). At the negative point electrode (cathode), the space charge formed by injected electrons delays streamer inception, Figure 3.4.111 (right)
The type of appearing discharge modes depends significantly on the external conditions: In a strongly nonuniform field, predischarges (primary streamers) can occur without resulting in breakdown. The prerequisite for this is that the voltage is not too much above the partial discharge inception voltage (discharge inception voltage) or that the stress duration, for example, in the case of an impulse voltage, is so short and the flashover distance is so large that the streamer cannot reach the counter electrode. The range of positive discharges in this case is greater than that of negative ones. For impulse voltage stress, the voltage stress can significantly exceed the voltage necessary for breakdown for a brief period ("overstressing"). With adequately large flashover distances, this results in the formation of the sequence of discharge modes as explained above.
d) Discharges in a uniform background field The abovementioned d modes are generlly possible also in a uniform or weakly nonuniform background field. However, there are
230
3 ELECTRIC STRENGTH
three significant differences that influence discharge propagation:
ports the effect of the space charge which limits and regulates the discharge velocity.
1.) In a uniform field, discharges start at local defects, whose position is generally not known.
Positive discharge channels, at first, occur as socalled primary streamers with the “normal” velocity of 2 to 3 mm/μs. In the case of large flashover distances, the positive channel corresponds to a “stem with a bunch” (or a leader), whose stem is extinguished and whose bunch drifts away electrodefree until its potential is shifted so much that the stem reignites (stepped discharge). The relatively constant propagation velocities of v = 2 to 3 mm/μs have been observed both in uniform as well as
2.) The field strength is relatively high over the entire distance, so that positive discharge channels with high penetrating power practically always lead to breakdown. 3.) The largearea electrode of equal polarity present behind the discharge channel weakens the local field at the discharge head and sup
Positive point electrode (anode)
Negative point electrode (cathode)
Disordered state without field A A E
S
A A
Formation and arrangement of permitted (and more conductive) volumes (A) under the effect of an electric field, Exchange of charge between source volume (S) and electrode (E) Formation and arrangement of permitted volumes (A) under the effect of the field and the supply of charge (percolation)
2  3 mm/μs
1132 mm/μs
> 100 mm/μs
Increased current flow, heating and vaporization in the micro field: umbel shaped primary streamer 400  600 kV/mm
Sucessive linking of permitted volumes through pulsed electronsupply leads to rapid growth of the primary streamer (300  400 kV/mm) and to a rapid transition to the secondary streamer
1  16 mm/μs
3  55 mm/μs
Farreaching secondrary streamer in the macroscopic field with exponetially increasing current Selfluminoustertiary streamer
> 65 mm/μs
Attention: the socalled "streamers" above are physically leader discharges, as long as thermal ionization is domiant. Figure 3.4.111: Explanation of breakdown processes in nonuniform oil insulated electrode arrangements through the percolation theory; inception field strengths result from the values of the applied impulse voltage and from the radius of the point, streamer velocities from the temporal distances of shadow images [310], [423].
3.4 Discharges in Liquids
231
nonuniform fields. That is, the field around the positive discharge head has distinct selfregulating properties. The faster, secondary propagation modes with v >10mm/μs are only reported for very high overvoltages from approx. 50kV/mm, which can only be applied as a shortterm impulse voltage [405]. In weakly nonuniform fields, Torshin has observed fast discharges with stepwise propagation [406] even for average field strengths of 12 kV/mm.
strict the length, charge and energy consumption of a discharge channel (barrier effect). It must, therefore, be concluded that the effect of barriers is better for finer division of the oil gaps in the field direction.
Negative discharge channels are highly branched and have an almost ballshaped (spherical) charge distribution which homogenizes the field, slows down the discharge and brings it to extinction after a limited range [405]. For low voltages, the propagation can occur in a slow first subsonic mode at approx. 0.1 mm/μs. If the discharge head has passed through a field strength minimum at about half the flashover distance, the “point of no return” is reached and this leads to breakdown.
Note: It must also be noted that insulation components of cellulose are very hygroscopic in dry condition and hence the oil is kept dry over wide ranges. This is an important prerequisite for the high electric strength of insulating oil, see Section 3.4.2.1.
e) Barriers and insulated electrodes The electric strength of oil insulated gaps can be considerably increased by using insulating barriers and insulated electrodes, since both the initial processes at the electrode surfaces and discharge propagation are significantly influenced by this. Note: In practice, barriers and electrode insulations of high quality insulating pressboard or transformerboard (made of pure cellulose), which are suitable for impregnation and wetting with oil, have proven to be both technically and economically excellent [27], [82], Section 3.4.2, Section 5.5, Section. 7.1.3, Section 7.2.3 and Section 7.3.4.
Coatings can mask electrode surface defects, can hamper injection at the cathode and focussing of electrons at the anode, prevent the contact of particles with the electrode and may restrict the energy input into the discharge. Barriers obstruct the electron transport from the cathode to the anode, they prevent particle drift over larger distances (distance effect) and they reduce the weak link volume (volume effect). Finally, the barriers obstruct the imprinting of the liquid (percolation structure) that precedes the breakdown and they may re
Note: It must be noted that introducing barriers and electrode coverings into the field volume causes changes in the field distribution which can sometimes be disadvantageous, but which can also often be specifically exploited.
3.4.2 Important Parameters Influencing Breakdown in Mineral Oil The physical laws of oil breakdown described in Section 3.4.1 unfortunately do not allow the calculation of electric strengths, as is possible, for example, for gas discharges using Paschen‘s law. The relationships are too complex and too many parameters are involved. Therefore, insulation systems must be designed based on tried and tested semiempirical relationships in order to take the various influencing parameters into consideration [65].
3.4.2.1 Water and Pollution In the case of very long stress durations, a drastic reduction in the strength can occur owing to water (moisture), pollution and ageing, Figure 3.4.11. In particular, even the absorption of water in small quantities leads to a loss of strength, Figure 3.4.21. For a relative water content of 100 %, the solvent power of the oil is depleted; this leads to the formation of free water in the form of an emulsion with a drastically reduced residual strength of 15% to 20% of the strength of dry oil. This is generally equivalent to a complete loss of the insulation strength and must be avoided under all circumstances.
232
3 ELECTRIC STRENGTH
The measure for this is the solvent power of oil for the water. As long as the water content in oil remains far below the saturation limit, the electric strength also remains high. Therefore, oilinsulated highvoltage equipment must always be filled with oil that is dried and degassed under vacuum to a few ppm of residual moisture. The ingress of water during operation must be prohibited by constructive measures, for example, by air hermetic sealing or with the help of dryers filled with desiccant. Despite this, during the course of time, water content can increase owing to air contact of the oil, through diffusion via walls and sealing systems or owing to oil decomposition (oxidation) as a result of oil ageing. Therefore, the oil quality must be checked periodically. The oil strength is also greatly reduced by fibers, especially by cellulose fibers along with moisture (fiberbridge breakdown). Compact particles cannot bypass larger oil gaps, and therefore, they have a lesser influence on the strength [59]. This means that a large flashover distance and a large oil volume favor the formation of moist fiber bridges, Figures 3.4.21 and 3.4.22.
Ê bd1% kV/mm 30
(1)
Solution
Emulsion
Technically pure oil
20 10 Oil with fibers 0% 100 % Water content w rel (relative moisture content) Figure 3.4.21: AC voltage strength of technically pure and fiber containing insulating oil [59]. d = 1 mm, volume = 14 cm³, with oil flow d = 5 mm, volume = 25 cm³, without oil flow Curve (1) corresponds to about 50 % breakdown field strength determined according to VDE 0370 section 1 with d = 2.5 mm (r.m.s. value) [16].
Figure 3.4.22: Formation of fiber bridges under the effect of an electric field (right) in an oil loaded with dielectric fibers (left).
For both alternating voltage and for direct voltage, the fibers drift in the direction of electric field gradients, that is in the direction of increasing field strengths, and form linked, largely unbranched fiber bridges within seconds to minutes, which reduce both the strength and the insulation resistance. The dynamics of fiber bridge formation are greatly accelerated by increasing particle content and especially water content. The formation of a fiber bridge is associated with partial discharges [443], [444]. Note: In contrast to a solid insulation that is irreversibly destroyed by a breakdown, repeated breakdowns in oil are possible without loss of strength, if the energy is not too large, if the accumulation of soot particles is not yet too great and if the resultant free gas is removed or released. However, the regeneration capacity of oil is limited and must not be compared with that of gases.
The oil quality can be checked by determining the breakdown voltage in a standardized test arrangement, Figure 3.4.23. However, oil quality data based on different test arrangements cannot be directly compared! Note: It must be noted that despite similar test conditions and same flashover distance d=2.5mm, different breakdown voltages occur for different arrangements and this cannot be interpreted just by different field efficiency factors (degrees of homogeneity) [16]. In the case of ASTM electrodes, the comparatively large volume used between the plates and the sharp edged rims reduce the strength. The strength is increased again by the increased oil flow in the nonuniform field.
While carrying out the test according to IEC 60156 (VDE 03705) [177], a sinusoidal alter
3.4 Discharges in Liquids
233
nating voltage (50 Hz) with 2 kV/s is rised until breakdown occurs. The arithmetic mean value from 6 successive breakdown voltages is specified as the r.m.s. value. Gases and breakdown products must be removed from the stressed volume by stirring and a two minute waiting time between the single breakdown tests. Note: From curve (1) in Figure 3.4.21 it can be inferred that the breakdown voltage determined according to or IEC 60156 (VDE 03705) only decreases significantly for relatively large relative water contents. Also sensitivity towards detection of particles is low. Particles and fibers can be better detected if a cylindrical electrode arrangement with a larger test volume is used and the voltage is increased in a stepped manner with one minute waiting times [59]. Thus, the probability of the formation of a particle constellation or fiber constellation that causes a breakdown is increased.
3.4.2.2 Temperature Dependence The influence of moisture and fibers on the electric strength of oil is shown in Figure 3.4.21 as a function of relative moisture or of relative water content. Since the solvent power for water and hence also the relative humidity change with temperature, there is a distinct temperature dependence of the electric strength. The solubility of insulating oil for Spherical cap electrodes d 25 36
~3,8
According to IEC / VDE [62]
Sphere to sphere
Plate to plate
Diameters 12.5 mm
Diameters 25.4 mm Sharp edges
Electrodes according to UTE [63]
Electrodes according to ASTM [64]
Field efficiency factors for d = 2.5 mm
K = 0.97
K = 0.87
K 1
Switching 200/5000 μs impulse voltages 250/2500 μs 0.7 (0.8) AC voltage, peak value Voltage rise: 30 s 10 kVr.m.s./min Stress duration: 1 minute 3 hours
0.45 (0.59) 0.36 (0.53)
Direct voltage 1 minute
0.20 (0.26)
bare [39] 1 0.7
0.55 0.35
For [22]: Values in brackets relate to insulated electrodes. For [39]: Values from measurements for lightning impulse voltages up to 1250 kV in a cylindrically symmetric arrangement (Ra = 100 mm, Ri variable). Example: Oil gap with d =2 mm According to Figure 3.4.26, an oil gap with d = 2 mm between bare electrodes has a “discharge inception field strength” of about 13.2 kV/mm for a oneminute AC voltage stress. Therefore, the reliable withstand field strength lies below Ebd = 13.2 kV/mm for the r.m.s. value and below Ê = 18.7 kV/mm for the peak value. According to Figure 3.4.12, the 50 %breakdown voltage is larger by the factor 410 kV/220 kV = 1.85 than the 2 % breakdown voltage, which is equated in rough approximation with the values according to Figure 3.4.26. By extrapolation of Êbd50  1.85·18.7 kV/mm = 35 kV/mm to a lightning impulse voltage stress of Êbd50  2·35 kV/mm = 70 kV/mm (factor 1/0.5 = 2, see Table 3.4.21), a value that comes close to the measured 50 % impulse breakdown field strength of 74 kV/mm is obtained, Figure 3.4.25.
Also for gap widths in mm range, one can deduce from this example that the curves given in Figure 3.4.26 correspond to a low breakdown probability of a few percent and that the 50 % breakdown field strengths, in accordance with Figure 3.4.12, are about twice as high. Example: Oil gap with d =20mm An oil gap with d = 20 mm between blank electrodes, according to Figure 3.4.26 , has a “discharge inception field strength” of about 6 kV/mm for oneminute AC voltage stress. This corresponds to a breakdown probability of about only a few percent. The reliable withstand voltage, therefore, lies below V = E d = 120 kV for the r.m.s. value or below 170 kV for the peak value. If this value is extrapolated according to Table 3.4.21 to a lightning impulse voltage of 170 kV/0.5 = 340 kV, then the breakdown probability is significantly less than that for AC voltage V = 120 kV, since the statistical dispersion of breakdown voltages for lightning impulse voltage is less than that for AC voltage. This implies that this estimation is on “the safe side”. According to Figure 3.4.12, the 50 % breakdown voltage is larger by the factor 410 kV/220 kV = 1.85 than the 2 % breakdown voltage, which is equated to a rough approximation with the values according to Figure 3.4.1.26. For AC voltage, a value of about Vbd50  220 V bd50  310 kV serves as a rough indicative kV and Û V bd50  310 value. For lightning impulse voltage, Û kV/0.5  600 kV would result as the orientation value. Measured values [39] also correspond to this. If the 1 % V bd50 [66], breakdown values are set at about 70 % of Û then for the 1 %breakdown voltage, a value with a magnitude of 660 kV·0.7 = 420 kV is estimated.
In the oil channels of transformers, test stresses of 5 to 10 kV/mm for AC voltage (r.m.s. value) and about double those values for lightning impulse voltage are permitted. [23], [67]. The widths of the oil channels must be dimensioned according to Figure 3.4.26 in dependence on the local field strengths in the transformers. The permissible operating field strengths (r.m.s. values of AC voltage) are substantially lower and range from approx. 2 kV/mm for devices with air contact with the oil up to 5 kV/mm for hermetically sealed devices [16]. The graduation of test voltages is taken from Tables 6.12 and 6.13. It takes the time factors into account and shall ensure the coordination of equipment insulations for a particular voltage level (insulation coordination). The
238
3 ELECTRIC STRENGTH
large difference between test voltages and operating voltages shall also take the loss of strength owing to ageing in decadelong operation into consideration.
3.4.3 Partial Discharges (PD) in Mineral Oil In highly nonuniform fields, stationary partial discharges (PD) can occur in oil, similarly to PD in gases, during which the streamers stabilize as a result of space charges, without reaching the counter electrode and without resulting in a direct breakdown. The partial discharge inception field strength of point to plane arrangements is a more sensitive indicator of gas content, water content and contamination of oil than the breakdown voltage in an approximately uniform field [16], [22], Table 3.4.31. The comparatively high edge field strengths are responsible for the fact that in an appreciable field volume, the field strength is increased so much that primary streamers can be initiated. From this it is also understood that significantly greater field strengths are possible at the sharp edges of capacitor foils than in the uniform field volume between capacitor foils, see Figure 2.420 and example in Section 2.4.3.3 (“Edges of metallic foil electrodes in capacitor insulations”). Table 3.4.31: Partial discharge inception (PDI) field strengths at hyperbolic point electrodes in oil (r.m.s. values) [16] Insulating oil
Radius
EPDI kV/mm
Mineral oil (wrel = 10 %)
100 μm
170
Mineral oil (wrel = 100 %)
100 μm
110
Mineral oil
6 μm
785
Phenylxylylethane (PXE)
6 μm
981
Example: Edges of metallic foil electrodes in capacitor insulations (Continued from Section 2.4.3.3) For the numerical example for Eq. (2.436) and Figure 2.421, at E0 = 60 kV/mm, an edge field strength of Eedge = 220 kV/mm was estimated at an ideally round edge (Redge = 6 μm). If a further enhancement of the field is assumed owing to unevennesses of the edge surfaces, one arrives at the order of magnitude given in Table 3.4.31. Moreover, it must be noted that the rather cylindrically symmetrical field at the foil edge decreases more slowly with increasing distance from the edge than a spherically symmetrical field at the point electrode. Therefore, partial discharges must be expected at the cylindrical foil edge for lower field strengths.
Furthermore, it can be concluded that conductive particles which lead to a local field stress enhancement owing to the point electrode effect become less critical with decreasing particle size as the local partial discharge inception field strength increases to very large values. The most common cause for partial discharges in insulating oil is gas bubbles or gas layers. The field strength in gas is increased through dielectric field displacement. While increasing the voltage, the Townsend’s ignition condition is reached in the gas for relatively low voltages and this leads to partial discharges.
Free gas in oil, similar to free water, means an extreme loss of strength, very much below the strength of technically clean oil and usually below the typical values of test field strengths. Free gas in oilimpregnated devices must be avoided under all circumstances. For estimating the field strength in oil during the inception of partial discharges in gas, at first the partial discharge inception field strength in gas is determined. It is calculated from the breakdown voltage of the gas gap according to Paschen’s Law (3.225) for air and hydrogen or according to Eq. (3.243) for SF6 as well as from the flashover distance d in the gas. For spherical bubbles, the bubble diameter must be used, since the ignition condition is initially fulfilled for this longest possible path while increasing the voltage see Figure 2.422. The inception field strengths in gas can be converted to field strength values in oil with the field displacement equations (2.438)
3.4 Discharges in Liquids
239
for spherical bubbles or with Eq. (2.418) for plane gas layers. Example: Spherical gas bubble in oil The estimation described gives the effective partial discharge inception field strength according to Eq. (3.42) as a function of bubble diameter d in oil with air bubbles under atmospheric standard conditions: d:
10
100
1000
Eoil PDI
20
5
3
μm kV/mm
These values must be understood as orientation values, since in Eq. (3.225) with k = 5, no special surface value was used for the feedback factor J However, owing to the use of double logarithms, J has only a weak influence on the result.
The example shows that very small air bubbles (d Vb
High dissipation factor (loss factor) tan G of the insulating material, that is to say, high dielectric power loss PG.
x
Increased dielectric losses owing to the total harmonic distortion of the applied voltage.
x
Disproportionately high increase of dissipation factor (loss factor) and dielectric power loss with the temperature T.
2
b
In practice, the following factors favor the development of the described thermal instability: x
V < Vb
P ( T)
Psup
1
Prem Ta
Dielectric power loss Ohmic conductor losses
T1 'Tab
Tb
T
T2
Figure 3.53: Balance of supplied and removed heat for thermal breakdown with stable (1) and instable (2, b) working points for determining the socalled thermal breakover voltage.
3.5 Discharges in Solids
243
harmonic distortion factors in the network, as the power loss increases with the frequency, Eq. (3.52).
Example: Epoxy resin bushing Bushings between the hot oil of a transformer and the gas volume of an enclosed switchgear are specially thermally stressed: the heat supply through the conductor, the relatively high dielectric losses of some epoxy resins at higher temperature and the high ambient temperature lead to a situation in which a thermal equilibrium can occur only for a very high insulating material temperature. The thermal stability, therefore, must often be verified by means of a thermal stability test. Note: The socalled RIP (resinimpregnated paper) bushings are made of a crepe paper core with alumina grading layers impregnated with an epoxy resin, see Sections 5.3.3.1 and 7.1.2.3.
Example: Thermal stability test Thermal stability is verified by simultaneous stress of a test object with voltage and current. Thermal stability, which is a steadystate condition, is assumed if the observed parameters, such as dissipation factor tan G or conductor temperature, do not vary over a period of 5 hours.
Example: Thermal breakdown owing to ageing Even a successful thermal stability test offers no guarantee of thermal stability over a long period of time. In the case of mineral oilimpregnated paper, a significant increase in the dissipation factor can occur owing to thermally accelerated ageing. In insulations with unfavorable heat transmission conditions, for example in thickwalled insulated bushings, this can result in exceeding the thermal stability limit, Figure 3.57.
No breakdown strength with the meaning of a material specific quantitiy can be given for thermal breakdown. The breakdown voltage (“breakover voltage”) for a specific arrangement is derived from consideration of the balance of supplied and removed heat, taking the geometry and ambient conditions into account, Figure 3.53. The supplied thermal power Psup results from the sum of the power loss PG in the dielectric and the heating effect of the externally supplied ohmic losses in the conductor PI: Psup =
PG + PI
(3.51)
PI is independent of temperature to a first approximation. Owing to the exponential increase in conductivity, PG(T) and the dissipation factor tan G also increase exponentially with the temperature, Figure 3.53: PG =
2
V ZC·tan G(T) V 2 ZC tan G a e E (T Ta ) . (3.52)
Note: The frequency dependency included in Eq. (3.52) leads to a strong increase in losses with increasing frequency. Additionally, also the dissipation factor often increases with an increase in frequency. Thus, thermal problems can occur at high frequencies, for power electronic switching impulses and, often unexpectedly, even for AC line voltages with high harmonic contents, Section 4.2.4. Assuming linear materials, dielectric power loss results from the superposition of loss components that are associated with the individual components of the frequency spectrum, see Eq. (4.220). The removed heat Prem is proportional to the heat transmitting surface A(x), the thermal conductivity O and the gradient of insulating material temperature grad T = wT/wx in the direction of heat flow x: Prem =
O·A(x)·wT/wx
(3.53)
In Figure 3.53, it is assumed for simplification that the insulating material temperature T is locationindependent. The removed heat is then determined by the heat transfer at the surface of the insulating material and is proportional to the difference (T – Ta) between T and ambient temperature Ta. Prem can be plotted as a straight line against T. In the stationary state, supplied and removed heat are equal (thermal balance): Psup =
Prem
(3.54)
If the applied voltage is lower than the breakover voltage (V < Vb), a stable working point 1 and an unstable working point 2 are possible.
244
3 ELECTRIC STRENGTH
For temperatures T > T1, the removed heat is greater than the supplied heat. The stable working point 1 with the insulation temperature T1 is readjusted by cooling down. It does not lead to breakdown. Only when the temperature of the insulating material is pushed above T2 by a temporary additional heat supply is the arrangement no longer thermally stable, since the supplied heat is permanently greater than the dissipated heat. On increasing the voltage further, the losses in the dielectric also increase until Psup(T) and Prem(T) no longer intersect, and in any case it leads to thermal escalation: the voltage is above the breakover voltage (V > Vb). If, in the borderline case of the thermal breakover voltage (V = Vb), both the power curves touch each other at an unstable point b, this leads to thermal breakdown. Owing to the idendity in gradients, the following applies at the “breakover point”: wPsup/wT = wPrem/wT
(3.55)
Note: From Figure 3.53 it can be seen which
a)
Ta T
b)
c)
(Ohmic losses)
By using dielectrics with lower losses or by reducing the ohmic losses in the conductor, the power curves for Psup(T) for uniform voltage are shifted downwards. The breakover voltage is only attained after increasing the losses Psup(T) by increasing the voltage. A steeper increase in the power lines Prem(T) results from more effective heat removal, for example by cooling. Thus, higher losses Psup(T) and a higher voltage are necessary to attain the breakover voltage. A reduction in the ambient temperature Ta shifts the power line Prem(T) to the left. Here too, higher losses Psup(T) and a higher voltage are necessary to attain the breakover voltage.
Using equations (3.51) to (3.55), the thermal breakover voltage (breakdown voltage) can be calculated for different arrangements. This always shows that the breakdown voltage no longer increases linearly with the insulating material thickness d. Moreover, significant variations occur depending on the arrangement. Global thermal breakdown and local thermal breakdown are distinguished, Figure 3.54. In the first case, general (“global”) warming
d)
x
Ta T
e)
T
T x
x
x
Ohmic losses
Ta T
measures can be applied to shift the thermal breakdown to higher voltages:
Ta Global thermal breakdown
Local thermal breakdown
Figure 3.54: Heat flow for global and local thermal breakdown for example arrangements. The areas of highest temperature T (hot spots) are marked with white bars. a) Plane arrangement with global heating and heat transfer through the electrodes on both sides. b) Plane arrangement wiht heat transfer on one side and with additional thermal loading by ohmic losses. c) Coaxial arrangement with thermal loading by ohmic losses (for example, cables or bushings). d) Plane arrangement with local heating and axial heat transfer through the electrodes on both sides. e) Plane arrangement with local heating and radial heat transfer into the cooler dielectric.
Ta
3.5 Discharges in Solids
takes place in a homogeneous dielectric with uniform stress. In the second case of a nonuniform or nonuniformly stressed dielectric, only a locally restricted (local) warming occurs, which in the case of thermal instability leads to the formation of a breakdown channel. In the literature, for example, instances a) and e) are calculated according to Figure 3.54 [16]. For plane arrangements with heat removal on both sides through the electrodes according to Figure 3.54 a) and d) (Kreifuß approach), a thermal breakover voltage Vb that is independent of insulation thickness d results from Eq. (3.51) to (5). Note: Instead of a derivation, a plausibility consideration is presented here: by doubling the insulation thickness d, and for the same applied voltage V, the field strength is halved and the specific power loss (power loss density) is reduced to one fourth. Owing to the doubled volume, the power loss is halved, see also Eq. (3.52), with halved capacity. Owing to doubling of the insulation thickness, the thermal resistance is also doubled and the removed heat for the same temperature difference is halved. In a presentation according to Figure 3.53, therefore, only the two curves Psup(T) and Prem(T) are reduced in equal measure. Therefore, the same temperatures develop in the insulating material, and the breakover condition is attained for the same voltage.
Significantly different values for the thermal breakover voltage are obtained for different materials, Table 3.51 [47]. In the case of thin insulations, these values cannot be attained, since the breakdown is not caused thermally but electrically. The significance of the thermal breakover voltage is that the breakdown voltage strength of lossy dielectrics can not be increased further by increasing the thickness of the dielectric. The limits are a few cm for dielectrics with comparatively high losses and a few 10 cm for lowloss dielectrics. Note: Table 3.51 also shows that some materials, under unfavorable heat transfer conditions, are not suitable for highvoltage insulations. For example, PVC cables can at the most be used up to the medium voltage range. Even in the case of cast resins, an increase in losses in the region of the glass transition temperature can lead to thermal problems depending on the type of resin. Al
245 though oilimpregnated paper is suitable as a highvoltage insulating material, it can however lead to thermal instability in the case of extremely high field strengths (in capacitors) and in the case of poor heat removal (for large capacitances), Table 3.51: R.m.s. value of thermal breakover voltage for different materials in a plane arrangement according to Figure 3.54 a) and d) for f = 50 Hz and T = 20 °C.
Quartz (depending on the purity) 2....20 MV Mica (depending on the purity) 7....18 MV Steatite (depending on density) 1.5...9.8 MV Hard porcelain (dto.) 0.4...2.8 MV Glass (20 °C) 2......6 MV Glass (350 °C) 0.1...0.2 MV Polyethylene (PE) 3......5 MV Capacitor paper 3.5...4 MV Sulfate paper 0.6 MV Polyvinylchloride (PVC) 0.1...0.2 MV
According to Figure 3.54 e) (Wagner approach), for a narrow channel of increased conductivity with lateral heat dissipation, the same power loss per unit length occurs, if both the voltage V and the channel length d or the insulation thickness d are doubled. However, experience shows that the breakover voltage is not proportional to thickness d but to the root of d: Vb ~
d
1/2
(3.56)
Apparently, the radius r of the discharge channel increases with increasing insulating material thickness or channel length d. Therefore, the heatproducing volume grows more than proportional to d and the breakover voltage increases more slowly than the insulation thickness d. Generally, the thermal breakover voltage is not only dependent on the material but also on the arrangement, on the external heat sources and on different ambient conditions (temperature, heat transfer). Therefore, with simplifying analytical calculation, only simple cases can
246
3 ELECTRIC STRENGTH
be discussed and general trends are described (see above.). In many cases, the insulating material volume can be divided into thermally similar volumes for a calculation. For example, for the case of bushings, discretization into the insulation layer volumes between electrically and thermally highly conductive metallic grading layers makes sense. The solutions for all partial volumes lead to an equation system which can be solved iteratively, for example. Below the breakover voltage, an iterative solution converges on a temperature distribution. Above the breakover voltage, there is no convergence. In very complex cases, a nonlinear thermal field calculation with temperature dependent material parameters must be carried out on the basis of an electric field calculation. The method of finite elements is generally applied for this.
3.5.3 Ageing, Erosion Breakdown and Lifetime a) Ageing processes Solid insulations may not be stressed over long periods with the voltages and field strengths that are possible for short periods owing to electrical and thermal breakdown, Figure 3.51. There are many mechanisms that lead to ageing and to a reduction in the quality of solid insulations and enforce the setting of relatively low operating field strengths:
x
Mechanical, chemical and thermal stresses as well as weather influences and radiation can lead to brittleness and formation of cracks.
x
Partial discharges and creepage currents in existing or newly formed defects (cavities, conductive points, pollution layers, and cracks) particularly attack organic insulating materials. Progressive erosion ulti
mately leads to socalled erosion breakdown.
x
Under the effect of penetrating moisture, the material structure can change owing to hydrolysis (for example, depoymerization, decomposition of bondings or delamination of fiber reinforced materials).
x
Under the combined effect of moisture and electric fields, conductive tracks caused by electrochemical changes can appear, they initiate socalled electrochemical breakdown (e.g. formation of “water trees” in polyethylene cables).
x
Owing to thermal stress of insulating materials, conductivities and dissipation (loss) factors can increase. This can lead to completely changed field distributions for DC voltages and to thermal instabilities or thermal breakdown for AC voltages.
The danger of the above mentioned ageing mechanisms depends primarily on to what extent the mentioned effects on the insulating material can be foreseen and preemptively ruled out during design and production. b) Lifetime characteristics The socalled lifetime characteristic is an important dimensioning tool, which is determined with the help of constantvoltage tests according to Figure 3.113. It primarily describes the ageing of insulation under the effect of an electric field, Figure 3.55. The curves of lifetime characteristics are dependent not only on the type of material but also on various other conditions. For example, for polyethylene films, the type of impregnation (air, SF6 or oil) is decisive for its service lifetime, but in contrast short term strength is hardly influenced, Figure 3.55. The loss of service life is especially drastic in the case of partial discharge erosion owing to air impregnation. In the case of epoxy resin insulations, the high strengths of the actual resin (EP 1) are not made use of in technical insulations, since local increases of field strength enhancements
3.5 Discharges in Solids
247
caused by production only allow a reduced background field (EP 2). In bulk insulations with large volume, the probability of inhomogeneities that increase field strengths increases, so that an additional reduction in strength must be expected (EP 3) according to the statistical law of size (size effect). The service lifetime of insulation can therefore only be determined through experiments with samples that were manufactured under the actual production conditions. The lifetime stress relationship according to Eq. (3.121) is Êbd/Ê0 =
(tbd/t0)
1/k
.
(3.57)
According to Eq. (3.122) a double logarithmic representation results in a straight line with the gradient 1/k. Here the lifetime exponent k is characteristic of a specific ageing mechanism. If the ageing mechanism changes in the course of time, then the gradient of the lifetime lines also changes. With the values from Tables 3.52, and for a known short term strength Ê0 (for a stress duration t0), the lifetime tbd for a stress Êbd can be roughly estimated according to Eq. (3.57). 100
PE EP 2 EP 3
10
PE+SF6 PE + air
Êbd50 kV/mm 1 10
2
10
10
2
10
4
k Dielectric
Application
Polyethylene PE + SF6 PE + Oil Paper + Oil
Cables Films 9 Films 30 Capacitors 30...40 Cables 30...40 Transformers Porcelain Insulators Epoxy resin 12
Êbd Êop (1 min) (30 yr.) kV/mm
kV/mm
140 > 200 > 200 180 55 ...80 20 ...30 125 125
3 ... 7 < 40 < 40 < 20 3 ... 7 1 ... 3 1.5... 4
Note: Frequently, lifetime characteristics are extrapolated from experiments ranging over several months up to 30 years (2.6 105 h). Owing to the associated uncertainties, operating field strengths must be specified much below the 1 % breakdown values at the time of the nominal service life (for example, at 30 years).
The ageing effect of other environmental influences must be simulated through practice oriented experiments. Often, short term electric strength and other material properties are determined after artificial ageing under intensified conditions (accelerated ageing). The “conversion” of artificial ageing time under intensified conditions to actual ageing periods is, however not generally possible. c) Examples of ageing
PE+Si
EP 1
Table 3.52: Guide values for the short duration strengths (1 minute), lifetime exponents and operating field strengths (30 years) for some insulations for f = 50 Hz and T = 20 °C [22], [16], [23].
10
6
t /h Figure 3.55: Lifetime characteristic for different dielectrics at AC voltage [22]: PE: PE films in air, SF6 and silicone oil. EP 1: Epoxy resin in model arrangement (d =1 mm). EP 2: Insulation sample with locally increased field through corrugated metal foil layers [69]. EP 3: Like EP 2 in large volume insulations.
1.) For example, the influence of air humidity or direct exposure to water can be simulated by immersing in water at 50 °C or 100 °C. Thus, of diffusion processes and hydrolysis processes are accelerated. In this way, comparative material investigations can be carried out in an accelerated time scale. Such investigations are especially important for all types of compounds and interfaces, such as bondings, vulcanizations, fiber reinforced plastics or epoxy resins with fillers in which the chemical bonds can be weakened or broken by hydrolysis. 2.) Material compatibilities, similarly, are generally investigated at increased tempera
248
3 ELECTRIC STRENGTH
tures to attain acceleration. Thereby, the compatibility of dielectrics, casings, paints, seals and conductor materials with liquid and gaseous impregnating media must be verified. Incompatibilities can be seen inter alia in the form of swelling, dissolution, chemical decomposition, gas formation or weakening of mechanical and electric strength. 3.) Increases in temperature and moisture have a strong accelerating influence on the ageing of organic insulating materials. In particular, paper is mechanically weakened by depolymerization of cellulose molecules, that is to say through decomposition into components with shorter chain lengths. Figure 3.56 (Bouvier diagram) distinctly shows that poorly dried paper and high operating temperatures lead to an extremely accelerated decomposition of paper. That is, high operating temperatures, for example in transformers, require well dried paper (relative water content of the paper w < 0.5 %). 4.) In the case of oilpaper insulations, ageing
Relative depolymerisation rate 1000
120 °C
100 °C 80 °C
1
0,1 0,2 %
1% 2% Water content w
Nonsignificant dissipation factors at room temperature
thermal stability limit
t =1 t max Service life end
= 0.9 = 0.5 =0
Aged New
RT
Operating temperature
Tmax
T
Figure 3.57: Worsening of thermal stability of an oilpaper dielectric due to increase in dissipation factor at power frequency, caused by ageing during the lifetime (schematic).
can also lead to an increase in the dissipation (loss) factor, which can only be detected at increased operating temperatures, Figure 3.57. This is due to high thermal stress in the regions around the hot spot of the insulation. Thus, the insulating oil is decomposed and this process is accelerated by increased temperatures, oxygen and catalytically effective materials. Conductive and polar decomposition products are formed. It is especially critical that these increases in dielectric losses cannot be identified through diagnostic dissipation factor measurements at power frequency and at normal ambient temperatures, Figure 3.57 (left).
100
10
tan G
3%
Figure 3.56: Relative depolymerisation rate of paper as a function of water content for various temperatures (Bouvier diagram according to [70]) with the reference value 1 for w = 0.2 % and T = 80 °C.
4%
With increasing temperature, the losses of aged materials also increase more intensely than those of new insulations, Figures 5.52 and 3.57, so that under suitable conditions (operating temperature, insulation thickness, heat removal and ambient temperature) there is a risk of further overheating with accelerated thermal ageing leading to acute thermal instability or thermal breakdown, Figure 3.53. The thermal stability limit of insulation is only reached at high temperatures for new materials (with lower losses), Figure 3.57 (lower
3.6 Partial Discharges (PD)
curve). During the course of ageing, the losses increase and always limit the permissible temperatures to steadily decreasing values. The end of service life is reached if the thermal stability limit is reached at the maximum possible operating temperature, Figure 3.57 (upper curve). Note: For the diagnosis of this dangerous development, online monitoring that is not yet currently available would be ideal, Section 6.4.8.2. In the case of offline diagnostic measurements at room temperature, PDC analysis can be applied as greatly increased polarization currents indicate a welladvanced ageing process [236], [392], [398], Section 6.4.7.6 f), Figure 6.4.79.
5.) Another example is ageing through erosion of solid insulation by partial discharges associated with repetitive pulse stresses, such as in impulse capacitors, in motor insulations with enamelinsuated wires or in oilpressboard barrier systems, see Sections 7.3.3 and 7.3.4.
3.6 Partial Discharges (PD) Partial discharges (PD) are discharges that affect only a part of the insulation distance and that do not immediately lead to breakdown, they take place in all types of insulation systems. Often, partial discharges do not affect shortterm electric strength. However, in the case of organic insulating materials, erosion due to partial discharges, mainly in case of frequent and repetitive discharge impulses at AC voltage and repetitive impulse voltages, leads to a usually drastically reduced service life. Hence, the occurrence of partial discharges is an important criterion for the evaluation of insulation quality also for DC voltage. In the case of DC voltage, discharge frequency and erosion efficiency are enormously reduced, and the question can be raised whether PD at DC voltage is still a danger for the insulation system. The answer is: “That depends”. For example, charge displacments on interfaces or the charging of surfaces by corona discharges can lead to field distortions and flashovers. Hence, the occurrence
of partial discharges is an important criterion
249
for the evaluation of insulation quality also at DC voltage. Nevertheless, the interpretation of PD is much more difficult than the interpretation of PD at AC voltage. The intensities of partial discharges as well as a few other parameters (e.g. PD inception and PD extinction voltages) are generally measured while testing the withstand voltage of a device. Thus, the criterion for passing a highvoltage test is not only the shortterm strength but also the partialdischarge behavior (intensity limits, inception and extinction voltages) that has been recommended in the standards for specific categories of devices (e.g., highvoltage transformers, highvoltage cables etc.), or which has been individually agreed upon between the manufacturer and the customer. In the following sections, the causes of partial discharges (Section 3.6.1), important sources of partial discharge (Section 3.6.2) and characteristic properties (Section. 3.6.3) are described. Based on this, experienced highvoltage engineers can, in many instances, present an intuitive diagnosis on the cause of defect and the location of defect. The methods of modern data processing allow a multitude of extensive methods of analyses for which there are different possible approaches (Section 3.6.3). The actual measuring technique for acquisition and diagnosis of partialdischarge data is described in Section 6.4.2.
3.6.1 Causes of Partial Discharges Causes of partial discharges are local increases in field strength (for example, at conductive points or through field displacement) or local reductions in electric strength (e.g. owing to gasfilled cavities). During discharge processes, there is a large difference between DC voltage, AC voltage and impulse voltage. Partial discharges have the greatest technical significance for AC voltages due to the erosion of sensitive materials. A distinction is made between corona discharges at conductive electrode tips in air or in
250
3 ELECTRIC STRENGTH
gas insulated arrangements, internal partial discharges within insulation and surface discharges at interfaces. During partial discharge measurements, interfering signals are also recorded that belong to the socalled background noise level and which are neither associated with the external nor with the internal insulation of the tested device. A great technical effort must be made to reduce the background noise to a tolerable level, Sections 6.3.8 and 6.4.2.
age is increased. For a peak electode at earth potential, corona inception accordingly takes place at a positive maximum, Figure 3.61. For a further increase in voltage, partial discharge inception follows in the other halfcycle.
3.6.1.1 Corona Discharges
The discharges are a close sequence of current impulses, which discharge a partial capacitance of the discharge gap and appear as current impulses i(t) in the capacitively closed external electrical circuit. After an impulse, the space charges built up during the discharge must first recombine or drift away before another discharge can ignite, so that a relatively regular sequence of impulses occurs (Trichel impulses, see Section 3.2.5.2 and Figure 3.225).
According to Section 3.2.5, corona discharges occur in the strongly nonuniform field of a gas insulated electrode arrangement, if the ignition voltage is exceeded when the voltage is increased. They occur for AC voltages in an area of maximum voltage, as long as the voltage is higher than the corona inception voltage, Figure 3.61. For this, the ignition voltage at a negative point is slightly lower than one at the positive point (polarity effect). For a peak electrode at highvoltage potential, corona discharges appear at first in a negative maximum of the voltage cycle when the volt
Note: The inception voltage for the discharges must not be confused with the breakdown voltage of a point to plane arrangement which is at much higher values for strongly nonuniform arrangements. The breakdown voltage is significantly lower at a positive point than at a negative point, since the field strength at the negative plane is increased by the formation of a positive space charge (see Section 3.2.5.2 Polarity Effect).
In the case of DC voltage, a continuous corona discharge results from an uninterrupted sequence of current impulses after exceeding the ignition voltage, Figure 3.65 (top right no. 2).
i (t) v (t)
Point to high voltage, plane to earth potential. Bottom: Point to earth potential, plane to high voltage.
v (t) u> U
Top:
The discharges begin for negative polarity of the point in the respective halfcycle. For a further increases of voltage, discharges are also ignited in the other halfcycle. The discharges occur as a close sequence of current impulses (Trichel impulses).
t
i (t)
Figure 3.61: Corona discharges in a gasinsulated pointtoplane electrode arrangement for slightly exceeding the partial discharge inception voltage:
u> U
Z
Z
i (t) v (t)
t i (t) v (t)
3.6 Partial Discharges (PD)
251
Discharge current impulses occur even for impulse voltages after exceeding the ignition voltage. However, generally they cannot be filtered out from very large and rapidly changing surge currents. Therefore, the discussion of partial discharges is restricted to AC and DC voltage stresses here. Note: Corona discharges, which occur in air outside of a device, i.e. outside of a solid, liquid or encapsulated insulation, are also described as external partial discharges. Note: Corona discharges at sharp edges in a test set up can lead to an unacceptably high noise level for partial discharge measurements. Therefore, if corona discharges in the negative or positive halfcycle are detected, points and edges on the highvoltage side or on the ground side of the test set up must first be checked.
Insulating material
3.6.1.2 Internal Partial Discharges at AC Voltage
Internal partial discharges occur in defects within solid or liquid insulations. Defects are frequently formed by gasfilled cavities or bubbles. During partial breakdown in a cavity, field changes occur that are associated with charge transfers in the cavity and at the external electrodes Figure 3.62 (top left and middle). The latter can be recorded by sensitive partial discharge measurements that are decribed in Section 6.4.2. Whenever the voltage at the cavity experiences a voltage excursion corresponding to the ignition voltage, the next discharge takes place.
Insulating material
Cavity ionized
Cavity insulating
v (t)
Field theoretical description of a cylindrical cavity before and after partial breakdown (left insulating, right ionized cavity) [216]
vCav(t) without PD
Partial discharge event PD
C0
CS Ignition voltage Extinction v.
v (t) vCav(t) C Cav Insulating material with cavity
Capacitive equivalent circuit for an insulating material with a cavity (Cav)
vCav(t) with PD
Gray: Phase angle area of external voltage v(t), in which partial discharges can occur
Figure 3.62: Internal partial discharges (PD) at AC voltage in a gasfilled cavity. Top: Field theoretical model with equipotential lines before and after the partial discharge event (left and right) with measured test voltage curves and partial discharge impulses (extreme right). Bottom: Equivalent circuit model for a cavity (left). External voltage v(t) and cavity voltage without PD well as cavity voltage with PD, i.e. along with ignition and extinction of PDs.
t
252
3 ELECTRIC STRENGTH
Ignition voltage
vCav(t) without PD
Extinction voltage
t
vCav(t)
with PD
Figure 3.63: Existence of partial discharges below the partial discharge inception voltage, i.e. without the peak value of the cavity voltage attaining the value of the ignition voltage.
Therefore, internal discharges occur typically in the area of larger voltagetime gradients at regular intervals with equal voltage excursions, as the recharging of the defect is primarily performed in a capacitive way, Figure 3.62 (top right). Note: Analytical calculations are possible for spherical and ellipsoidal cavities [209]. The example according to 3.6.2 (top) was evaluated with the help of numerical field calculations and the calculated and measured charge values matched well [216]. In practice, however, geometries are almost always unknown and hence quantitative calculations are impossible. Principal considerations are therefore usually restricted to a simple capacitive equivalent circuit, Figure 3.62 (bottom). Strictly speaking, this is however not correct since the equipotential surfaces do not exactly coincide with the cavity surfaces so that the allocation of capacities is at best possible as an approximation.
In a simplified capacitive equivalent circuit, an individual partial discharge impulse can be described as the discharge of a cavity capacitance CCav. The recharging is carried out for AC voltage by the capacitive displacement current that flows via the partial capacitance CS. that is assumed in series. C0 approximately corresponds to the total capacitance of the insulation arrangement, that is, C0 >> CS. Besides, CCav >> CS and often even C0 > CCav can be assumed: C0 (>)
CCav >>
CS
(3.61)
With no ignition of partial discharges, the cavity voltage vCav(t) follows the external voltage v(t) according to the capacitive divider ratio of CS and CCav with no phase shifts, Figure 3.62 (bottom right).
If the cavity voltage exceeds the ignition voltage Vbd of the gas gap (see Paschen’s law Eq. (3.235), (42) and (43)) and if an initial electron is available, the cavity voltage collapses down to the value of an extinction voltage Vex. The cavity capacitance is recharged capacitively via CS with unchanged rate of voltage rise. That is, the individual partial discharge event acts similarly to a downward displacement of voltage curve by the voltage difference 'V = Vbd  Vex, Figure 3.62 (bottom right). Depending on the cavity voltage magnitude, multiple partial discharges can often occur up to the voltage maximum, i.e. the ignition voltage can be reached, voltage breakdown can occur and the voltage curves can be displaced by 'V several times. In the next halfcycle, the repeated displacement of the cavity voltage curve leads to a very early attainment of the ignition voltage, possibly even before the zero crossing of the externally applied voltage v(t). In Figure 3.62 (bottom right), the phase relation of the partial discharges is marked by grey shading of the voltage curve v(t). A typical discharge area begins before the zero crossing and extends along the voltage curve ascending towards the maximum. Note: When the AC voltage is increased, the first discharge might take place at an phase angle close to the maximum, since the ignition voltage Vbd is attained there for the first time, but in the next and in subsequent halfcycles discharges already occur during the increase in voltage before the negative or positive maximum is reached as a result of the voltage curve displacement.
On lowering the AC voltage, the partial discharges can continue to exist, even when the peak value of the cavity voltage no longer attains the value of the ignition voltage. As a result of the displacement of the voltage curve by 'V in each halfcycle, the ignition voltage is exceeded at least once for each halfcycle, Figure 3.63. Theoretically, the partial discharge extinction (PDE) could be around 50 % below the partial discharge inception (PDI). Actually, reductions of around 10 to
3.6 Partial Discharges (PD)
35% are inception"
observed.
253
"Partial
discharge
Generally, devices must be dimensioned in such a way that the operating voltage is always below the partialdischarge extinction voltage, so that partial discharges that are ignited by a temporary overvoltage are definitely quenched again at the operating voltage. Note: The regular discharge sequence according to Figure 3.62 is substantially disturbed in practice. For lower voltages, the lack of initial electrons in small cavities mainly leads to a statistical dispersion of partial discharge inception voltages. A regular discharge only occurs for higher voltages, since initial electrons are available owing to ionization in the cavity. Note: The simple equivalent circuit according to Figure 3.62 offers only an inaccurate description of the actual field distribution. For example, the conductivity of insulating material or conductive decomposition products at the surface of the cavity can lead to a phase shift of the cavity voltage. Even a temporary reduction of the field strength in the cavity is in fact possible through diffusion of conductive discharge products, [71]. Note: During the inception of a partial discharge, impulses occur according to the streamer mechanism, since no conductive electrodes are available for the release of new initial electrons. Thus, inception voltages occur that have values about 10% above the values expected according to Paschen’s law. The halfvalue width of the impulses is accordingly very short at a few ns [67]. In the literature, the inception field strength for streamer discharges in cavities is specified with [209]
E
V 25.2 m·Pa · p·[1
8.6 pd m·Pa
]
the statistical ignition delay. Figure 3.64 shows the example for spherical cavities in epoxy resin. The smaller the diameter d of the cavity, the lower is the probability of the presence of an initial electron and that much greater is the average ignition delay time or the statistical dispersion time tS until the emergence of an initial electron and until the start of streamer development. Thus, there is a risk that a cavity up to a specific size in the mm range remains undiscovered during a oneminute AC voltage test if the partial discharge could not be initiated early enough. However, the probability of discharge inception increases in practical tests, since cavities do not appear alone but form a part of a larger volume. Moreover, the inception probability increases if the field strength significantly increases beyond the static inception field strength of the cavity. Example: Air bubble in insulating oil For insulating oil with spherical air bubbles, it shall be specified at which field strengths in the insulating oil (background field E0) partialdischarge inception and partialdischarge extinction are to be expected. The field strength E1 in the gas bubble is increased by field displacement relative to the field strength E0 in oil (see Figure 2.422). According to Eq. (2.438) it follows that E1 = 1.222 E0 with Hr1 = 1 (air) and Hr2 = 2.2 (oil). During an increase in the voltage, the ignition condition is at first fulfilled at the longest path in the center of the
(3.62)
Depending on the material, the cavity surfaces become so conductive through ageing based on partial discharges that the discharge changes from the streamer mechanism to the Townsend mechanism within a period of few minutes to an hour. The inception voltages, then, correspond to Paschen’s law. The halfvalue width of the impulse increases to 80 to 800 ns for flashover distances of 0.1 to 1mm. Since approximately the same charge is transfered, the current amplitude is significantly lower. [67].
In the case of internal partial discharges, it must be noted that the streamer inception is delayed under certain circumstances owing to
100 k Theoretical relation 10 k
tS s
Measurements 1000
1 min
100 10 0.1
1
10
d / mm Figure 3.64: Ignition delay in spherical cavities as a function of diameter d [209].
254
3 ELECTRIC STRENGTH
bubble. Assuming Paschen’s law, according to Eq. (3.235) the following is applicable:
V bd = Û
Ê1 d =
1.222 Ê0 d =
B pd/ln (A pd/k). 1
With the constants A = 1130 (bar mm) , B = 27.4 kV/ (bar mm) and k = 5, the partialdischarge inception field strength in oil under atmospheric standard conditions (T = 293 K, p = 1 bar) is E0 PDI = 15.9 kV/mm /ln (226 d/mm),
(3.63)
after conversion to r.m.s. values. This results in the numerical values mentioned in Section 3.4.3 for the "spherical gas bubble" example. In the case of partialdischarge extinction field strength, up to 30% lower values must be adopted.
Insulating material
3.6.1.3 Internal Partial Discharges at DC Voltage
Also in case of DC voltage stresses, internal partial discharges can occur in defects within solid or liquid insulations such as in gasfilled cavities or bubbles. During partial breakdown in a cavity, field changes occur that are associated with charge transfers in the cavity and at the external electrodes Figure 3.65 (top left and middle). The latter can be recorded by the same sensitive partial discharge measurement methods as for AC voltages, cf. Section 6.4.2. Whenever the voltage at the cavity experiences a voltage excursion corresponding to the ignition voltage, the next discharge takes place.
(1) On: Transient stresses with PD
Insulating material
(4) Off
(3) Discrete single PD events at DC
Cavity insulating
(2) Superimposed corona discharges at DC
Cavity ionized
Field theoretical description of a cylindrical cavity before and after partial breakdown (left insulating, right ionized cavity) [216]
v (t)
Applied DC voltage
Partial discharge event PD
R 0 C 0 R CavC Cav v
(t) steadystate cavity voltage without PD
Cav
v (t) vCav(t)
Ignition
voltage
Extinction voltage
vCav(t)
with PD
R CavC Cav Insulating material with cavity
Resistivecapacitive equivalent circuit for an insulating material with a cavity (Cav) and residual conductivity (R)
Figure 3.65: Internal partial discharges (PD) at DC voltage in a gasfilled cavity. Field theoretical model with equipotential lines before and after the partial discharge event (left and right) with measured test voltage curves and partial discharge impulses (extreme right). Equivalent circuit model for a cavity (left). External voltage v(t) and cavity voltage without PD well as cavity voltage with PD, i.e. along with ignition and extinction of PDs.
t
3.6 Partial Discharges (PD)
For an applied constant DC voltage, the cavity must be recharged via the highlyresitive insulation material, which can take very long times in the range of minutes. Therefore, internal discharges at DC voltage typically occur after long periods of time, Figure 3.65 (top right). Note: In practice, geometric conditions of the insulation defects are almost always unknown and hence quantitative field calculations are impossible. Principal considerations are therefore usually restricted to a simple resistivecapacitive equivalent circuit, Figure 3.65 (bottom), which is an extension of the capacitive equivalent circuit according to Figure 3.62 (bottom). Strictly speaking, this is however not correct since the equipotential surfaces do never exactly coincide with the cavity surfaces so that the allocation of capacities and insulation resistance is at best possible as an approximation.
If a DC voltage is switched on, an initial capacitive displacement field and a subsequent transition process occur, in which the defects can also be recharged capacitively so that an increased but decreasing PD activity can be observed, Figure 3.65 (top right no. 1). The figure shows a practical example which includes the superposition of a permanent external DC corona (no. 2). For a steadystate DC voltage stress, the recharging of a discharged cavity capacitance CCav can only happen very slowly with the time constant RS·CCav via the high insulation resistance RS being in series with CCav, Figure 3.56 (top right no. 3 and bottom right). Whenever the ingnition voltage is reached, PD events occur comparatively regularly, but with scattering of times and amplitudes as the the ignitition voltage is scattering and cannot be well defined. The PD events at DC voltage are significantly less frequent than for AC voltage, and they are in the range of seconds, minutes or hours. This large spread is caused by the fact that conductivities of insulating materials can easily vary over several orders of magnitude. The long time constants require very long durations of DC voltage withstand tests, some
255
time in the range of several hours, in order to reach the steady states within the insulation system that must be tested. Unfortunately, also after a long test duration, “spontaneous” breakdowns are still possible without any preceding indication by partial discharges. Also the interpretation of PD measurements at DC voltage is significantly complicated, mainly as there is no relation to a phase angle or to a voltage difference [465], [512], [513], cf. Section 3.6.3.2. 3.6.1.4 Surface Discharges
Creepage discharges frequently develop from electrode edges similar to corona discharges. Therefore, their inception is often dependent on the magnitude of the currently existing AC voltage v(t). If this increases during the voltage half cycle, the length of the streamer and the intensity of the discharges become greater. Thus, creepage discharges frequently exhibit intensities increasing from the zero crossing to the peak, Figure 3.68. A polarity effect is produced with the involvement of the electrode. Note: If the discharge channel only burns normal to the surface and has not yet deviated into surface direction, the conditions can be described according to Figure 3.234 (left) by an equivalent circuit which corresponds to the equivalent circuit for internal partial discharges according to Figure 3.62. Directly after the partial discharge inception these discharges would be comparable with internal partial discharges.
In the case of increased voltage, the surface discharges can bridge long lengths with the formation of streamers. Thus, irregular impulses with large charge transfer and half value widths of several 10s of ns occur. In the case of DC voltage, surface discharges can no longer be fed by capacitive displacement currents. However, surfaces can accumulate surface charges, e.g. due to DC corona. Then, the surface charge can be partially discharged by single, highcurrent and farreaching surface discharge impulses that can possibly lead to flashover.
256
3 ELECTRIC STRENGTH
3.6.2 Sources of Partial Discharges Typical sources of partial discharges in gaseous, liquid and solid insulating materials are described in the following sections. For the estimation of partial discharge inception voltages/ field strengths, refer
x
to Section 3.2.5.3 (corona inception) with Eq. (3.258),
x
to Section 3.2.6.2 (surface discharges) with Eq. (3.271) to (74) and also (2.435), to Section 3.2.2.4 (Paschen’s law) with Eq. (3.235), (42) and (43),
x x
to Section 3.4 (oil breakdown) with Figure 3.4.26 and Table 3.4.31, as well as
x
to Section 3.6.1 (partial discharge causes) with Eq. (3.62) and (3),
3.6.2.1 Sources of Partial Discharges in Gases
Typical sources of corona discharges in gases are closely rounded point s and edges, conductors with (very) small diameters and sharpedged particles, Figure 3.65 (top). In practice, surface defects, scratches, roughness and dirt deposits on electrodes as well as conductive particles, e.g. in the form of metal chips, often lead to partial discharges. Production and assembly of gasinsulated switchgear (GIS) therefore require special care and partial discharge testing is carried out after assembly. Surface discharges in gases represent one of the basic problems of highvoltage engineering, Figure 3.65 (bottom). In practice, they are suppressed for example by capacitive potential grading (for bushings), by geometrical field grading (for cable entrance fittings) as well as by elongations of creepage paths and hydrophobic surfaces (for insulators), see Section 2.4.5.
3.6.2.2 Sources of Partial Discharges in Liquids
Small radii of curvature in conductors, points and conductive particles are less critical than in gases owing to the higher strength in liquids, Figure 3.66 (top left). In liquids, the release of gas in the form of bubbles or gas layers has a serious effect, Figure 3.66 (top right). Owing to field displacement, already electrically weak gas bubbles are yet more heavily stressed so that partial discharges are initiated in oil at very low background field strengths, see Eq. (3.63). Furthermore, water (moisture) causes a significant reduction in electric strength, especially when dropshaped water is released. Oilinsulated devices must, therefore, be well dried and filled with degassed and dried oil under vacuum. Also tangential overstresses of insulating material surfaces, such as at the metallic foil edges in capacitor dielectrics and in the pressboard barrier systems of transformers, can lead to surface discharges, Figure 3.66 (center and bottom). In the pressboard barrier system, partial discharges can even occur as a result of the breakdown of individual oil gaps, for example, by the formation of fiber bridges.
Point
Thin wire
Particle
Creepage configuration Corona discharge Streamer discharge Figure 3.65: Partial discharge sources in gases.
3.6 Partial Discharges (PD)
257
3.6.2.3 Sources of Partial Discharges in Solids
Figure 3.67 (top left and right). Extended cavities occur also in incompletely impregnated layers such as those between smooth polymeric films in capacitor dielectrics.
Owing to the high electric strength of solid insulating materials, partial discharges are practically always caused by defects in the dielectric. These defects almost always consist of cavities which are filled with lower molecular components from the surrounding media owing to diffusion processes. Therefore, lower electric strength can often result from airfilled cavities, in which the stresses are greatly increased owing to field displacement, Figure 3.67.
Extended delaminations in fiberreinforced materials are especially dangerous. These can allow large insulation gaps parallel to the electric field to be bypassed by gas or probably even by diffused water, Figure 3.67 (bottom left). Critical interfaces parallel to the electric field are also produced by pushing cable entrance fittings on to the cable dielectric, Figure 3.67 (bottom right).
Cavities closed on all sides usually occur owing to incompletely degassed cast resins or owing to secondary chemical reactions (for example, for polyurethane resins containing moisture), Figure 3.67 (top left). Also, progressive erosion, for example owing to “water trees” in polyethylene cable insulations, ultimately leads to the formation of cavities, Figure 3.67 (bottom right). Moreover, detachments between electrode and dielectric as well as cracks and gaps in the dielectric can occur owing to reaction shrinkage, mechanical stresses, brittleness and inadequate adhesion,
After a discharge, solids no longer have the ability to regenerate, as in gases and liquids. That is, partial discharges lead to a progressive erosion and therefore must definitely be prevented. This results in extreme requirements for the production quality of solid insulations. Vacuum casting of cast resins, the impregnation of interfaces, the use of bonding agents (sizing, silanization) for fiberreinforced materials or materials containing fillers and the use of semiconductive layers at the interfaces between insulating materials and electrodes shall be mentioned as key words.
2
Barrier
Point electrode
1
3
Gas bubbles
Particle
Creepage configuration in oil
Gas layers
Cavities, holes without (1) and with (2) electrode contact as well as detachments (3)
Cracks, gaps and imperfect laminations or impregnations
Capacitor dielectric with metallic foil edge 1
E Barrier arrangement with fiber bridge
2
E Tangentially stressed interfaces
Figure 3.66: Partial discharge sources in liquids.
Delamination of fiber interfaces (FW)
Cable with entrance fitting (1) Cavities from "treeing" (2) Cavities at interfaces
Figure 3.67: Partial discharge sources in solids.
258
3 ELECTRIC STRENGTH
3.6.3 Classical Interpretation of Partial Discharges 3.6.3.1 Classical Interpretation of Partial Discharges for AC Voltage
According to Section 3.6.1, different causes for partial discharges also appear in different partial discharge phenomena with characteristic properties. As a result, the type and location of the defect can be presumed in many cases. However, even modern diagnosis systems very often fail owing to the multitude of probable sources of partial discharges, to the complexity of insulation systems and to the superimposition of partial discharges from different defect sources. The measured intensity of partial discharges is not so helpful for error diagnosis since only the “apparent charge” at the connections of the test object and not the "actual charge" of a partial discharge impulse itself can be recorded, see Section 6.4.2.2. However, meaningful parameters in the discharge images that can be represented with an oscilloscope are
x
phase angle of partial discharges,
x
polarity effects,
x
impulse frequency and impulse regularity,
x
changes in intensity with the voltage, as well as
x
the ratio of inception voltage to extinction voltage (hysteresis).
Figure 3.68 shows a few characteristic partial discharge images with their reference to the applied AC voltage as a phaseresolved pattern. The amplitude of an impulse on the screen of the oscilloscope is an indicator of the impulse charge, if the current impulses are amplified and integrated in a partial discharge measuring circuit by a sensitive partial discharge measuring device. The relevant partial
discharge measuring technique is described in Section 6.4.2. Figure 3.68 reflects the respective state shortly after the inception of partial discharges, and the images change considerably for higher voltages. Moreover, the figures represent single defects whose images are not blurred owing to the overlapping of different effects. Corona discharges at points appear owing to the polarity effect both in gases (a) and liquids (b) as regular impulses of constant magnitude close to the AC voltage peaks at the negative point electrode. Thus, it can be distinguished
whether the discharges take place on the highvoltage side (left side in the figure) or on the ground side (right side in the figure). The frequency of the impulses increases with the voltage. In liquids, larger irregular discharges occur when the point is of positive polarity. In gases, this can be observed only for distinctly increased voltages. Discharges in cavities (shrink holes, bubbles, gaps, cracks, detachments ...) and on surfaces can be identified from a phase position for an increase in the voltage to the maximum.For a contact to an electrode (c), different images appear in the halfcycles owing to the polarity effect. Here the larger impulses occur at the positive electrode. Here too, discharges on the ground side and on the highvoltage side can be distinguished. Discharges without contact at an electrode (d) show a comparable image in both halfcycles. Caution: Unfortunately, the development of phaseresolved partial discharge pattern is intensely dependent on the voltage shape. That is, a voltage highly distorted by harmonics no longer gives the partial discharge images known from sinusoidal voltages. It is therefore essential to use an undistorted sinusoidal test voltage profile for the interpretation.
3.6 Partial Discharges (PD)
a) Corona discharge in gas at a point, against a plane. Regular impulses with constant amplitude, frequency increasing with the voltage.
259
t Point at high voltage
t
Point at ground
(For higher voltage, dischcharges also occur in the other halfcycle) b) Corona discharge in oil at a point, against a plane. gegen eine Platte. Smaller, regular impulses with constant amplitude, frequency increasing with the voltage. c) Cavity discharge or surface discharge with onesided contact to an electrode (Surface discharges can be identified through irregular and intensive streamer discharges at higher voltages). d) Cavity discharge or surface discharge without electrode contact, discharges between insulated conductors. e) Creepage discharge or surface discharge
t
t Point at high voltage
Point at ground
t Electrode at high voltage
t
Electrode at ground
(The amplitudes of both half cycles vary by minimum of factor of 3)
t
t
(The amplitudes of both half cycles vary by maximum of factor 3)
For creepage discharges and surface discharges, the intensities increasing from zero crossing to peak is often observed.
t
t f) Contact noise (left) and g) Discharges from electrodes on floating potential (right).
"Contact noise" between poorly connected conductors in the area of the largest (capacitive) current, that is at voltage zero crossing. The contact noise can extend over the entire period. It disappears when the conductors are welded.
Metallic part at floating potential. Regularly recurrent discharges at equal intervals. Frequency increasing with increasing voltage, however amplitude (charge) is constant. Sometimes discharges occur in pairs and wander over the image.
Figure 3.68: Characteristic partial discharge pattern for the observation with the oscilloscope. The impulse amplitude is a measure for the apparent charge [67], [72].
260
Q pC
3 ELECTRIC STRENGTH
log PD intensity
Surface discharge (streamer) Large cavity (Streamer) Small cavity Corona (Glow discharge) Contact noise
V /kV
Figure 3.69: Characteristic curve of partial discharge charge intensity Q against voltage V. PD inception (PDI) PD extinction (PDE)
At higher voltages, surface discharges show very intense and irregular streamerdischarges that can bridge across larger stretches of surface and which frequently show a growing intensity with the voltage amplitude (e). Contact noise (f) occurs for poorly connected conductors (electrodes, connecting leads, shields) in the area of maximum capacitive charging current (that is, near voltage zero), if the nonconnected metallic part is connected by a flashover and recharged by a current impulse. Metallic parts at floating potential (particles, chips, free electrodes ...) can be recharged or discharged by partial discharges (g). This causes impulses of constant amplitude to occur at constant intervals. The frequency increases with the voltage. Impulse groups that drift across the image often occur.
Another important criterion for the identification of partial discharges is the curve for partial discharge intensity (partial discharge intensity or apparent charge Q) against the
voltage, Figure 3.69. A logarithmic charge scale is recommended for this.After the inception of discharges, corona discharges do not significantly change their intensity until there is a change in the discharge mechanism (streamer inception). Inception voltage and extinction voltages are nearly identical; a small difference can only be caused by the ignition delay.
In case of cavity discharges and surface discharges, in accordance with Figure 3.63, the extinction voltage is distinctly lower than the inception voltage. For large cavities and for surface discharges, a steady increase in the intensity with the voltage is observed. Surface discharges finally develop into streamer discharges of high intensity. For the practical execution of partial discharge analysis, the evaluation and diagnosis scheme according to Figure 3.610 has proven its value. It is based on the observation partial discharge images with an oszilloscope and on the determination of partial discharge intensities (apparent charge in pC) with a classical partial discharge measuring device [73]. The partial discharge images and their phase angles are plotted on ellipses (to save space). Note: There are also partial discharge measuring devices that show the partial discharge images on an ellipse. Note: For transformers, the measured phase relation of a partial discharge to the phasetoground voltage does not necessarily correspond to the actual phase angle of the impulse at the defect point, since, according to the location of the defect, different voltages (for example, three phasetoground voltages and three phasetophase voltages) can be responsible for the partial discharges. Note: Under favorable circumstances, the location of the defect can be roughly concluded by threephased recording of partial discharges. Great progress in defect localization for different equipment was achieved by the synchronous multichannel PD measurement, Section 6.4.2.7.
In a hysteresis test, which must not be carried out too far above the partial discharge inception voltage, the ratio of partial discharge in
3.6 Partial Discharges (PD)
ception voltage to partial discharge extinction voltage is determined. In doing so, one can generally distinguish between corona discharges on the one hand and cavity discharges and surface discharges on the other hand. During a voltage increase test according to Figure 3.69, information may be gained about the size of the cavities and the existence of surface discharges. In a continuous test at constant voltage, the discharge behavior can vary significantly, so that indications on the risk of partial discharges may be given. For example, gas bubbles in insulating oil can completely dissolve or can steadily increase under the effect of partial discharges. Thus, partial discharges can die out or lead to breakdown, depending on the type of oil, see Section 3.4.3. For a contact to an electrode (c), different images appear in the halfcycles owing to the polarity effect. Here the larger impulses occur at the positive electrode. Here too, discharges on the ground side and on the highvoltage side can be distinguished. Discharges without contact at an electrode (d) show a comparable image in both halfcycles. Caution: Unfortunately, the development of phaseresolved partial discharge pattern is intensely dependent on the voltage shape. That is, a voltage highly distorted by harmonics no longer gives the partial discharge images known from sinusoidal voltages. It is therefore essential to use an undistorted sinusoidal test voltage profile for the interpretation.
At higher voltages, surface discharges show very intense and irregular streamerdischarges that can bridge across larger stretches of surface and which frequently show a growing intensity with the voltage amplitude (e). Contact noise (f) occurs for poorly connected conductors (electrodes, connecting leads, shields) in the area of maximum capacitive charging current (that is, near voltage zero), if the nonconnected metallic part is connected
261
by a flashover and recharged by a current impulse. Metallic parts at floating potential (particles, chips, free electrodes ...) can be recharged or discharged by partial discharges (g). This causes impulses of constant amplitude to occur at constant intervals. The frequency increases with the voltage. Impulse groups that drift across the image often occur.
Another important criterion for the identification of partial discharges is the curve for partial discharge intensity (partial discharge intensity or apparent charge Q) against the voltage, Figure 3.69. A logarithmic charge scale is recommended for this. For a contact to an electrode (c), different images appear in the halfcycles owing to the polarity effect. Here the larger impulses occur at the positive electrode. Here too, discharges on the ground side and on the highvoltage side can be distinPartial Discharge Evaluation and Diagnosis Scheme Date:
Asessment of the defect:
Name:
PDI:
kV
EPDI/o
Test object:
PDE:
PDI/PDE:
kV
E PDI/max
(if the field strength values are known)
Observation of phase position:
Phase resolved pattern
V = (.......%)· V PDI =
pos.
kV neg.
Phase resolved pattern
V = (.......%)· V PDI = pos.
kV
Phase resolved pattern
V = (.......%)· V PDI =
neg. pos.
regular irregular
regular irregular
regular irregular
Impulses per half cycle
Impulses per half cycle
Impulses per half cycle
kV neg.
Observation of intensity curves: Hysteresis test
Test for voltage increase
Continuous test
Q = f (V)
Q = f (V)
Q = f (t)
1000 pC
10000 pC
10000 pC
100 pC
1000 pC
1000 pC
10 pC
100 pC
100 pC
1 pC
V /kV
10 pC
V /kV
10 pC
t /min
Figure 3.610: Partial discharge diagnosis scheme for the documentation and the evaluation of partial discharge observations with the help of an oscilloscope and a classical PD measuring device [73].
262
guished. Discharges without contact at an electrode (d) show a comparable image in both halfcycles. Caution: Unfortunately, the development of phaseresolved partial discharge pattern is intensely dependent on the voltage shape. That is, a voltage highly distorted by harmonics no longer gives the partial discharge images known from sinusoidal voltages. It is therefore essential to use an undistorted sinusoidal test voltage profile for the interpretation.
At higher voltages, surface discharges show very intense and irregular streamerdischarges that can bridge across larger stretches of surface and which frequently show a growing intensity with the voltage amplitude (e). Contact noise (f) occurs for poorly connected conductors (electrodes, connecting leads, shields) in the area of maximum capacitive charging current (that is, near voltage zero), if the nonconnected metallic part is connected by a flashover and recharged by a current impulse. Metallic parts at floating potential (particles, chips, free electrodes ...) can be recharged or discharged by partial discharges (g). This causes impulses of constant amplitude to occur at constant intervals. The frequency increases with the voltage. Impulse groups that drift across the image often occur.
Another important criterion for the identification of partial discharges is the curve for partial discharge intensity (partial discharge intensity or apparent charge Q) against the voltage, Figure 3.69. A logarithmic charge scale is recommended for this. Note: The classical partial discharge interpretation is often made more difficult by the superimposition of partial discharges on several defects. The described criteria are generally only applicable to a single (dominant) defect or to the
3 ELECTRIC STRENGTH
overlapping of congeneric errors. The differentiation between similar, but different errors is often not possible. Again, great progress in differentiation between different defects was achieved by the synchronous multichannel PD measurement, Section 6.4.2.7. Despite intensive research, for a long time it has not been possible to go beyond the limits of classical partial discharge diagnosis. But modern data technology today allows advanced computer aided interpretation approaches, Section 6.4.2.6 ff. The entire topic of data acquisation and evaluation of electrical and nonelectrical partial discharge signals is dealt with in Section 6.4.2.
3.6.3.2 Interpretation of Partial Discharges for DC Voltage
The interpretation of partial discharge events for DC is not yet as developed as that for AC voltages. Since a phase relation to an AC voltage cannot be produced, the above mentioned classical visualization and interpretation procedures are largely missing. Even the definition of inception voltages and extinction voltages is not possible because of the longlasting transition processes in the insulation system and the long durations between single discharge impulses. Possible remaining parameters are the impulse shape or the frequency spectrum and the apparent charge of an individual impulse, the time difference to the preceding and to the following impulse, the apparent charge of the preceding and the following impulse, the impulse frequency (repetition rate) as well as the temporal development of the discharge process. Traditionally, for direct voltages, individual partial discharge impulses are plotted against time. Generally, DC partial discharge impulses occur regularly, but only very rarely.
3.7 Vacuum Breakdown
For internal discharges, that is for discharging a defect within an insulating material, the defect must at first be recharged, usually via very large insulation resistances and with very long timeconstants. During a DC voltage withstand test, it is often required that only a specific number of impulses of a specific magnitude may occur within a time window. Even external interference impulses can be significantly more difficult to identify than for AC voltages, since they are individual events without any phase relation. Note: Corona discharges in air behave totally different; they occur in the form of very frequent regular discharges, which are determined by space charge formation, Section 3.2.5.2.
It was therefore proposed that the M, Q, N pattern for AC voltages are to be substituted by 't, Q, N pattern for DC voltages [465]. This implies that time difference 't between successive impulses would appear instead of the phase angle M. It was shown that in this way a differentiation between different types of defect is possible. External discharges in air are represented, for example, by very small time differences and by a low statistical spread of the charge Q. For internal discharges, time differences occur that are longer by many orders of magnitude and these are slightly dispersive for strongly scattered charge values. Based on the abovementioned parameters, histograms can be calculated that differ for the basic types of defects and that enable a diagnosis of insulation systems right through to initial approaches for automated classification [512], [513]. The impulse form is another starting point for the interpretation which provides very good classification results on labscale samples and with a highfrequency and distortionfree coupling between discharge location and a broadband PD measuring system [514]. However, it is problematic that the impulse form normally
263
is greatly distorted on the path between the source and the sensor, as with AC voltages. A great step forward for partial discharge diagnosis for AC voltages and DC voltages is given by the synchronous multichannel PD measurement of impulses from the same source, Section 6.4.2.7: by developing amplitude relations or propagation time relations, all impulses can be assigned to a certain, although perhaps as yet unknown source. In this way, the separation and identification of interference sources and partial discharge sources is considerably improved.
3.7 Vacuum Breakdown In many cases, the insulation of higher voltages is even necessary in a vacuum, such as in Xray tubes, transmitting tubes, image tubes, accelerators, superconducting equipment, satellites or vacuum switches, Section 7.1.5.3.
3.7.1 Physical Process While considering the electric strength of a vacuum, it is not enough to consider only the limiting case of Paschen’s law for pd Æ 0: in vacuum and as well as in gases with very low pressures, there are practically no gas particles between the electrodes, the free path lengths are significantly larger than the electrode distances and no increase in charge carrier number can occur owing to collision ionization. Theoretically, Paschen’s law would subsequently lead to an infinitely high breakdown voltage; see Section 3.2.2.4, Figure 3.213 and Eq. (3.238). Of course, an infinitely high breakdown voltage cannot be attained even in a vacuum; it is other physical processes, primarily at the electrodes, which determine the vacuum breakdown [316]:
264
3 ELECTRIC STRENGTH
a) Breakdown between electrodes The breakdown is initiated by processes at the electrode surfaces that are not dependent on (very low) gas pressure. Thus, a metal vapor is formed in which the breakdown takes place by collision ionization [23], [67], [316]: At the cathode surface, at very high local microscopic field strengths Eμ, a field emission of electrons in the vacuum takes place. The work function or potential barrier for frequently used metals (copper, stainless steel) amounts to about I = 4.5 eV and is overcome beyond about Eμ = 1000 kV/mm by the quantummechanical tunnel effect, Figure 3.71. Owing to field stress enhancements at microtips or at conductive channels in oxide films, significantly lower macroscopic field strengths Em are sufficient for field emission: Eμ
=
E·Em
(3.71)
The field stress enhancement factor E can be considered as the reciprocal of a microscopic field efficiency factor and is of the order of magnitude of a few 100 to a few 1000. Thus,
Potential energy
Metal Work function
I
Vacuum
Emission level without field
Occupied states
Emission with field (Tunnel effect)
e e e
x
Figure 3.71: Field emission at the cathode surface during vacuum breakdown.
Electron emission can initiate breakdown by two processes:
1.) The microtips heated by the field emission current vaporize explosively and release the metal vapor responsible for the breakdown. For this cathodeinitiated breakdown, local 8 2 current densities above 10 A/cm are possible. 2.) For anodeinitiated breakdown, the electrons released at the cathode owing to field emission are accelerated as an electron beam towards the anode which is locally heated up until the anode material vaporizes. This also results in Xray bremsstrahlung. New initial electrons are generated at the cathode as a result of feedback. In the course of a generation mechanism, finally metal vapor plasma is formed [16]. Note: Adsorbed gas layers can also vaporize at the anode surface under electron bombardment and facilitate ionization processes and avalanche processes. At the cathode, adsorbed gas layers can reduce the work function.
Breakdown processes induced by field emission can be expected to have approximately constant breakdown field strength. For larger distances of 5 to 10 mm, processes gain influence under the participation of charged particles. They are accelerated in the field and create a microplasma on impact on the electrode. Critical velocities for this are approx. 100 m/s. Thus, a nonlinear relation between breakdown voltage and distance results, Figure 3.72.
Potential profile with field
Fermi level
even for field strengths of the order of magnitude of 1 to 10 kV/mm, field emission processes must be expected.
Moreover, the migration of particles takes time so that shortterm lightning impulse stresses give rise to more rapidly increasing strengths with increasing distances than longterm AC voltage stresses.
3.7 Vacuum Breakdown
265
b) Conditioning In an electrode arrangement, an improvement of the microscopic surface structure and a considerable increase in the breakdown strength can be attained by means of conditioning (partly above 300 %). It is assumed that emission centers for predischarge currents, that is microtips or gas layers, are reduced and microparticles are removed during the conditioning process. Current conditioning, thermal conditioning and spark conditioning are approved conditioning procedures. Spark conditioning consists of a larger number of breakdowns during which breakdown voltages increase. The energy of the breakdowns must be limited by protective resistors to an extent so that no new microtips can be created. An (undesired) degradation of the arrangement is described as deconditioning. A prerequisite for the relatively high electric strength in a vacuum is the high quality of the vacuum. Even low gas densities lead to a drastic loss of strength to the point of the Paschen minimum, Figure 3.213. Therefore, not only the electrodes must be conditioned. Other components (shields, insulators) can also contain adsorbed gas layers and these must be removed by annealing. The quality of the vacuum can be maintained over a long period of time with getter materials of rare earths.
Vbd
~
d
(3.72)
For larger distances, for which accelerated particles initiate the breakdown, the icrease of breakdown voltage Vbd is often approximated by the square root of the distance d, Figure 3.72. The introduction of an exponent D is more precise: Vbd
~
(d /mm)
D
(3.73)
The exponent, however, varies from D = 1 to about D = 0.3 depending on the distance [316]. The following is valid as a rough approximation for the r.m.s. value of the breakdown AC voltage [67]: Vbd rms  30 kV·(d/mm)
1/2
(3.74)
The impulse voltage strength is not very much different from the AC voltage strength. As a guide, 1/2 Vˆbd  30 ... 40 kV·(d/mm) for d < 2mm
and
(3.75)
V / kV Û
V r.m.s./ kV
500 400
3.7.2 Technical Strengths 300
a) Strength for AC and impulse voltages The previous explanations show that the strength of an electrode arrangement under vacuum depends on many parameters and can therefore vary, depending on the test set up. For very small distances (d < 2mm), field emission induced breakdowns and constant breakdown field strength are expected. This corresponds to a linear dependence of breakdown voltage on the electrode distance:
200 100
10
20
30
40
Figure 3.72: AC voltage strength and lightning impulse voltage strength in vacuum (according to [316]).
d /mm
266
3 ELECTRIC STRENGTH
Vˆbd 
60 kV·(d/mm)
1/2
for d > 2mm
are given in [67]. A more exact investigation of vacuum breakdown shows that there is a distinct dependence on the material and the condition of the electrodes.
These shields, along with electric field grading, also serve as protection against the direct depositing of metal vapor plasma on the insulator surface. Owing to this, increasingly conductive layers would be formed on unshielded insulator surfaces over a period of time, which would have a very negative effect on the electric strength of the interfaces.
3.7.3 Applications
b) Breakdown along surfaces
a) Classical applications
The strength at the surfaces of insulating material (glass, ceramics) is distinctly reduced in vacuum owing to emission processes.
The classical application areas of vacuum insulation are electron tubes, vacuum interrupters and picture tubes. Although they are increasingly losing significance owing to semiconductor technologies, xray tubes and vacuum circuitbreakers are still of high importance, they are described in detail in Sections 7.4.4 and 7.1.5.3. A few special applications are mentioned here.
The starting points are the triple points between the metal electrode, insulator and vacuum, Figure 3.73. Owing to microscopic field displacement, comparatively low macroscopic field strengths are sufficiently high for the emission of electrons. At the insulator surface, comparatively loosely bound electrons can be released owing to collission ionization (secondary electron emission) and an avalanche can be formed (“electron cascade”). Thus, the surface is charged and adsorbed gas layers are detached and ionized.
b) Magnetic insulation Impulse generators for generating high power impulses with extreme peak values in the MV, MA and TW ranges (pulsed power technol
Measures for increasing the strength at the interfaces are especially
x
a specific reduction of the field strength at the triple point to prevent electron emissions,
x
a conical design of the triple point,
x
a coating of ceramic surfaces with CuO2 and Cr2O3,
x
a polishing of the surface or
x
an annealing at 1000 °C for removing absorbed gas layers.
Example: In vacuum circuitbreakers, the tangential stress of ceramic surfaces in the area of the triple point must be completely avoided in practice by covering the surfaces largely with metallic shields, Section 7.1.5.3 and Figure 7.1.53.
Cathode () Tripel + point + + + Ceramic
Vacuum
e e e e e e e e
Field emission Collission ionization Secondary electro emission Avalache, electron cascade Charging of surface Releasing of a gas cloud
Anode (+)
Figure 3.73: Reduced surface strength in vacuum.
3.7 Vacuum Breakdown
ogy), use the socalled line generators with energy storage, traveling wave transmission lines and water insulation with higher permittivity for the temporal and spatial compression of impulse energy, see Section 2.6.3.3 and 6.2.3.2 d). Often, the impulse must be transferred to a line insulated with vacuum and to the matched load, for example to a socalled particle beam diode in which ions or electrons are highly accelerated. The impulse traveling on a vacuum insulated line (guided TEMwave, Section 2.6.1), is thus linked to a strong magnetic field. The electrons emerging from the cathode, owing to the forces of the electric field, are forced on to a curved track by the Lorentz force of the magnetic field and ideally led back to the cathode. Above a critical current value, the electron bombardment of the anode required for vacuum breakdown is inhibited (magnetic insulation) [439]. Note: At the front and rear of the impulse, current and magnetic field strength are reduced so that the magnetic insulation is no longer effective. However, if the impulse is considered as a guided TEM wave, then, according to Eq. 2.610 and 12, even a lesser stress is given through the electric field.
c) Insulations for different pressures Insulation systems, caused by external circumstances, can sometimes be exposed to different pressures down to the level of a vacuum and they must still retain their insulating properties under all circumstances. An example is the insulation of devices, which are transported from the Earth’s surface into space. Thus, the Paschen minimum with an extremely low strength of approx. 330 V is passed, if air or the subsequent space vacuum are provided as the insulation medium, Figures 3.213, 24, Table 3.2.3. The environment of superconducting installations is evacuated as thermal insulation has to be guaratueed, see Section 7.5. Large magnetic coils, such as those seen in nuclear fusion
267
technology or in particle accelerators, must be discharged quickly in special instances, for example during a quench (loss of superconductivity), so that the ohmic heat loss occurring in the expanding normal conductive area does not lead to damage [450]. For this purpose, the coil is usually connected in series with an external ohmic load resistor. The voltage thus enforced reaches the tens of kV range and effects a discharge of the coil according to wi/wt = V/L. In this situation, the conductor insulation as well as the surrounding vacuum can still work as insulation. However, if gas should enter into the vacuum space owing to leakages and the conductor insulation should exhibit weak spots (for example, small cracks), here too the Paschen curve will be traversed and the insulation fails when the Paschen minimum is approached. Therefore, in the given examples it is necessary to design the insulation systems in such a way that they include the socalled “Paschen strength”. This is, for example, possible when all voltage carrying conductors are enclosed by a solid and “electrically sealed” (that is, gap free) insulation, on whose external surface the ground potential is applied as a closed shell with the help of conductive covering, comparable with the semiconductive layers (screens) on a cable insulation. The external vacuum volume or gas volume that may have low strength, is thus maintained completely free of field. In this case, for superconducting insulation systems, there exists the difficulty that the electric strength must also be assured at low temperatures close to absolute zero. This has especially to be considered during the choice of suitable insulating material (coefficients of thermal expansion, crack formation) and suitable processing techniques. ” The Paschen strength, i.e. the strength against discharges in the Paschen minimum, can neither be tested under atmospheric pressure nor under evacuated conditions. The completely assembled insulation system must instead be tested in a vessel that can be evacuated and in the relevant gas (such as air, nitrogen, helium)
268
at different pressures. [451]. After adjusting the different pressure levels, the test voltage is applied in each case for a specific period. Thus, the Paschen curve including the minimum is passed through (Paschen test). For
3 ELECTRIC STRENGTH
this, no discharge between the conductors and ground coverings or walls of housing may occur. The Paschen test is well suited for finding production defects that cannot be identified at other pressures.
4 DIELECTRIC SYSTEM CHARACTERISTICS
mechanism needs time and energy and thus, for high frequencies, the dipoles cannot follow the field or can only follow it with a delay, as in Figure 2.45. This result in farreaching consequences dealt with below in the time and frequency domain.
In addition to the electric strength dealt with in Chapter 3, there are many other important characteristics of insulating materials:
4.1.1 Description in the Time Domain
The electric field is significantly influenced by dielectric properties, i.e. through different polarization phenomena that are usually described by parameters such as permittivity and dielectric dissipation factor and by the conductivity, cf. Section 2.4. They will be dealt with in detail in Chapter 4. Other characteristics such as surface resistance, tracking resistance, arc resistance and water repellence (hydrophobicity) are more related to the surface area and less to the material volume itself. Materialspecific data are given in Chapter 5. Further, the insulating materials, according to a common and adequate terminology of the past, are always “construction materials” for devices or installations [81]. Important characteristics are already compiled and summarized in Section 2.2. The characteristic profile of an insulating material must be compatible with the technical requirements. I.e. mechanical, thermal and chemical characteristics as well as their processing technology must always be taken into consideration and it is of utmost significance in many cases (Chapter 5).
4.1 Polarization in the Time and Frequency Domain In Section 2.4.1, the dielectric characteristics such as “conductivity” and “polarization” were explained without taking the timebased transients into consideration. The explanation was only about the fact that the orientation of dipoles according to the type of polarization © SpringerVerlag GmbH Germany 2018 A. Küchler, High Voltage Engineering, VDIBuch, DOI 10.1007/9783642119934_4
The system characteristics of a dielectric can be determined, for example, in the time domain by measuring a step function response, i.e. with the help of a step voltage or a field strength step function, Figure 4.13. E(t)
=
E · V(t)
(4.11)
V(t) is the socalled unit step function. E(t) is the dielectric system response in the time domain. The vacuum field is formed under a very large charging current impulse by the field step and, according to Eq. (2.47), the charge density H0E results at the electrodes, Figure 4.11 (left). The delayed orientation of dipoles (polarization) creates additional charges on the electrodes with a charge density increasing with time Pi(t), Figure 4.11 (center). Note: Generally there are many polarization mechanisms that are denoted by different indices i. The polarization thus results from the superposition of individual mechanisms:
¦ i Pi (t )
P(t )
(4.12)
After the dipoles are orientated, a steadystate current flows, Figure 4.11 (right): J
=
N·E
(4.13)
These procedures can be described for linear materials with the help of a network model, Figure 4.12. The formation of the vacuum field corresponds to the charging of the vacuum capacitance C0. The steadystate current flows for t Æ f through the DC resistance Rf. When describing the delayed and timevarying polarization Pi(t), it is assumed that the rate of change wPi/wt is proportional to the actual difference between Pi(t) and the steadystate end value Pi(f) (Debye approach):
270
4 DIELECTRIC SYSTEM CHARACTERISTICS
wPi wt
1
Wi
>Pi (f) Pi (t )@
(4.14)
This differential equation produces a polarization that is exponentially tending towards Pi(f):
Pi (f) [1 e
Pi (t )
t
Wi
]
(4.15)
Note: A generalization that goes beyond the exponential approach according to Eqs. (4.14) and (5), is given in the literature [269]. However, most of the practical problems can be resolved and demonstrated using the exponential approach described.
According to Eq. (4.15), polarization corresponds to a charge density that is exponentially tending to an end value, and this is also described in the network model by the RCcharging of an additional capacitance Ci via a resistance Ri with the time constant Formation of vacuum field
H0 E
Polarization
+
Conduction current
J
Pi (t)
Current density
Charge density
Figure 4.11: Phyisical processes in a dielectic after application of a step field.
C
R
f
Charging the additional capacitance
Ri·Ci ,
(4.16)
Figure 4.12 (center). Since several polarization mechanisms are generally effective, they must be summed up according to Eq. (4.12). In the network model, this corresponds to the parallel connection of RCelements with different indices i or different parameters Ri and Ci and different time constants Wi. Dissipation factor
Conduction losses
Ci Charging the vacuum capacitance
=
tan G
R
i
Wi
Polarization losses
Steadystate conduction current
Figure 4.12: Network model of the dielectric.
f, Z
fi f
E (t)
Charging current impulse
ip(t)
ip(t) Polarization current
Permittivity Capacitance
Step field
E (t) = E·V (t)
Delayed charging of the additional capacitance C i
C~ H
Steadystate conduction current t
Figure 4.13: Dielectric system response in the time domain.
Ci + C0
Ci
C0
C0 fi Figure 4.14: Dielectric parameters in the frequency domain.
f, Z
4.1 Polarization in the Time and Frequency Domain
The polarization current as a response to the step field in the time domain can be directly assigned to the elements of the network model, as in Figures 4.12 and 3. It contains all the information that is necessary to form a dielectric equivalent circuit: The integration of the initial current gives the charge and therefore the initial capacitance C0: 1 't ³ ip (t ) dt V 0
C0 ('t )
(4.17)
Note: However, this is only the vacuum capacitance if the integration interval is chosen to be so short that no polarization phenomenon has yet been included. This is practically impossible. It is therefore better to speak of the “initial capacitance” (or “highfrequency capacitance”) C0('t), whose magnitude depends on the considered time interval 't and on the included polarization mechanisms.
The direct current resistance Rf results from the stationary end value of the polarization current ip(f): Rf
=
V/ ip(f)
(4.18)
Note: According to the standards (e.g. [157]) the measurement of volume “resistance” is performed with varying and sometimes very short measuring durations. This is of no physical significance, since not only the resistive conduction current flowing through Rf is recorded but also the polarizing current in an unknown state of transition, i.e. also the charging current of the additional capacitances Ci is recorded. Improved methods for determination of end values of resistance or conductivity can be found in Section 4.2.2.3 and 6.4.1.2.
The polarization equivalent circuit elements Ri and Ci representing polarization phenomena can likewise be determined from the polarization current: for t = 't, the initial current impulse has decayed and the polarization current is largely the charging current of the still uncharged capacitance Ci flowing through the resistance Ri. The steadystate current component through Rfmust be subtracted:
271
ment Ri, a parallel connection of multiple resistances Ri is used. The capacitance Ci can be determined from the time constant of the current decay according to Eq. (4.16), but only if a single polarization mechanism dominates. If several polarization mechanisms overlap, the sum of additional capacitances can be determined from the total charge that has flowed by integration of the charging current:
¦ Ci i
1 f ³ [i p (t ) i p (f)] dt V 't
(4.110)
Complete dielectric equivalent circuits can be determined by socalled “curve fitting”, i.e. by approximation of the measured polarization currents ip(t) with the help of exponential functions which have to be simulated with associated RCelements [229], [230].
Until now it has been assumed that the decreasing polarization currents must be interpreted as charging currents of additional capacitances Ci and not as time variable conductivities (which is conceivable, for example, in the case of oil with ion drift processes, Sections 4.2.2.2 and 4.3.2.3). Both of these options can be distinguished by measuring the depolarization current or the discharge or relaxation current id(t) after disconnecting the voltage and short circuiting the test object. For a linear system according to Figure 4.12, the depolarization current is supplied from the fully charged capacitances Ci (if charging time was long enough) and corresponds to the time profile of the charging current ip. It thus indicates the charge stored through polarization.
(4.19)
The proportion of the conduction current as well as the conductivity are derived from the difference of currents that are shifted in time relative to one another ip(t) and id(t+tL), see Figure 4.28 and Eq. (4.26d).
If multiple polarization mechanisms must be considered, then instead of an individual ele
Note: Polarization current measurements are used inter alia to determine material properties for insulation designs. Section 7.2 Another important application is
Ri
V ip ('t ) ip (f)
272 the dielectric diagnosis of operating equipment, in which circuit elements are calculated from current measurements to draw conclusions regarding the wetting or ageing state of an insulation, Section 6.4.7.6.
4.1.2 Description in the Frequency Domain By analogy with the description of dielectric properties in the time domain, treatment in the frequency domain is also possible based on Figures 4.11 and 2: The transformation of Eqs. (4.14) and (5) into frequency domain gives a complex polarization P and a complex permittivity H*, Section 4.2.4. The real part essentially describes the dependence of capacitance C or permittivity H on the frequency f or the angular frequency Zrespectively, Figure 4.14 (bottom). The imaginary part describes an additional phase shifting G being induced by dielectric losses. Phase angle between voltage (stimulation) and current (response) is M = 90°  G. The losses are generally specified by the dissipation factor tan G which equals the ratio of dissipation losses to capacitive reactive charging power, Figure 4.14 (top) and Eq. (4.213). The recording of these parameters (especially the complex permittivity) against frequency results in the dielectric system response in the frequency domain. The parameters of the frequency domain traditionally have great significance for describing dielectrics. The relationships are explained in detail in Section 4.2.3. The frequency dependences can be explained clearly with the help of Figures 4.11 and 2: At very high frequencies, the dipoles cannot follow the rapidly varying field and only the vacuum field is created. In the network model, this corresponds to a dominant displacement current through C0. A capacitance measurement for high frequencies, therefore, would give only the value C0 which often comes close to power frequency capacitance. The dissipation factor tends to zero, Figure 4.14.
4 DIELECTRIC SYSTEM CHARACTERISTICS
At very low frequencies, all dipoles can follow the field with no delay. As a result, the electrodes are additionally charged. In the network model, this corresponds to a charging of all capacitances C0+Ci or C0+6iCi. A capacitance measurement for very low frequencies would thus give the value of the sum of capacitances, Figures 4.14. The dissipation factor tends towards infinity, as in the ratio of dissipation losses to reactive power, the reactive power 2 ZC0V tends towards zero, and the ohmic 2
losses V /Rf largely remain constant. In the case of medium frequencies, the dipoles lag in following the field and perform mechanical work that is supplied to the medium as heat (the socalled dielectric losses or dissipation of heat). In the network model, this corresponds to the losses of the charging current in Ri. The capacitance measurement would result in a mean value. The dissipation factor shows a maximum of polarization losses in the transition region, Figures 4.14.
4.2 Dielectric Parameters In the following sections, dielectric parameters that are important in practice, such as permittivity Hr (Section 4.2.1), conductivity N (Section 4.2.2), dissipation factor tan G (Section 4.2.3) and complex permittivity H* (Section 4.2.4) are considered for insulating materials. The measurement of dielectric parameters is described in Section 6.4.1. Widely different substances are grouped under the collective term insulating materials, which exhibit a common characteristic: relatively low conductivity, Figure 4.21. However, conductivities are still significantly different for gaseous, liquid and solid insulating materials. Gases possess nearly ideal dielectric properties, although the electric strength is low: Besides the extremely low conductivity N the
4.2 Dielectric Parameters
273
constant permittivity Hr  1 and the low losses must especially be mentioned.
x
The electric strength is lower for AC voltage stress than for DC voltage stress and impulse voltage stress.
Liquid and solid dielectrics are characterized by a few common attributes:
x
The conductivity is, generally, 3 to 6 orders of magnitude higher than for gases.
4.2.1 Permittivity Hr
x
Permittivities are generally higher than 2 and lower than 7 for common insulating materials. However, there are substances with significantly higher values, Figure 4.22.
x
Permittivity, conductivity and losses are dependent on temperature, frequency and stress duration.
The occurrence of relative permittivities Hr > 1 through polarization of charge carriers and electrical dipoles in insulating materials has already been explained in detail in Section 2.4.1.2. Here, guide values for technically important materials and their basic dependences on different parameters are compiled.
x
The losses increase with the temperature and are greater for AC voltage than for DC voltage.
N S/m
10
9
10
6
10
Conductor materials Resistance metals
3
1 10
3
10
6
10
9
10
12
10
15
10
18
Semiconductors Water
Liquid and solid dielectrics (insulating materials) Gaseous dielectrics
Figure 4.21: Electrical conductivity for conductors, semiconductors and insulating materials.
4.2.1.1 Polarization Mechanisms
Materials which exhibit neither significant orientation polarization nor lattice polarization have permittivities in the range of 2. This includes, for example, mineral oil and many thermoplastic synthetic materials with symmetric nonpolar molecules, Figure 4.21. Several organic insulating materials with complex and stronger polarizable molecules and groups have higher permittivity of up to about Hr = 7 owing to orientation polarization. Important examples are cellulose, duroplastic cast resin (e.g. epoxy resin) and a series of thermoplastic synthetic materials. Extreme values are attained, for example, for water (Hr = 81) or glycerin Hr = 40). In many inorganic insulating materials, lattice polarization leads to largely increased permittivity of up to Hr = 10. In dielectrics with interfaces orthogonal to the electric field (for example in capacitors or in transformers with pressboard barriers in oil), in materials with fillers (e.g. epoxy resin with quartz powder) and in mixed dielectrics, interfaces between partial capacitances with different time constants HN occur (see Figure 2.116). For very low frequencies, only partial capacitances with the higher resistances are charged so that it results in a high capacitance
274
4 DIELECTRIC SYSTEM CHARACTERISTICS
or a high resultant permittivity. Owing to the charges accumulated at the interfaces, we refer to interfacial polarization (see Figure 2.423).
connection of the partial capacitances is effective, Figure 4.23.
4.2.1.2 Frequency Dependence (Dispersion)
The decay of the different polarization mechanisms takes place in steps for different frequencies, starting from the interfacial polarization through the orientation polarization and the lattice polarization to atomic polarization, Figure 4.23. In particular, the decay of orientation polarization can occur in multiple steps depending on the size and mobility of the molecular groups that are polarized.
Fig 4.23 shows the fundamental profile of permittivity Hr and polarization losses against frequency from the electrical engineering viewpoint and the optics for different polarization mechanisms. The profiles correspond to the relationships explained in the example of a single polarization mechanism in the Section 4.1.2 and Figure 4.14. In mixed dielectrics with interfacial polarization (that is with polarity reversals of the more resistive insulating layers), ohmic losses occur with increasing frequency since the more resistive layers are charge reversed via the resistances of the more conductive layers. Finally the total capacitance, the resultant permittivity and the losses decrease again, if the displacement current through all layers dominates the conduction current, so that the series
81 Water 40 Glycerin 8 7
Oilpaper
6
6
5
5 Ricinus oil
 
PCB ' (prohibited)
2
2.2 Mineral oil
8
Polyvinylidenefluoride (PVDF)
7
Polyamide (PA 6)
Resins and fillers 8
Calcium carbonate (Chalk) 7 Dolomite, Mica 5.8 Epoxy resin (filled)
5
(1.2 g/cm³)
2.7 Silicon oil
2
n
2.8 Paper (1.2 g/cm³, not impregnated)
(4.21)
is applicable, but only if frequency or wavelength coincide.
(1.53 g/cm³)
3.3 Ester fluids 3
Hr =
6.1 Cellulose
4.4 Mineral oil paper
4
Note: For very high frequencies, the frequency dependence (dispersion) is no longer described through the permittivity Hr as a function of frequency, but only with the quantities of optics as a refractive index against the wave length. Basically, the relationship
Thermoplastics
Hr Liquids
With increasing frequency, the dipoles can no longer follow the field with no lag and the permittivity decreases, Figure 2.45.
PVC with softeners
4.5 Polyamide (PA 12) 4 PVC pure 3.5 Polyimide (PI) 3.2 Polycarbonate (PC) 2.4 Polyethylene (PE) 2.2 Polypropylene (PP) 2 PTFE ("Teflon")
5
RBP Resin bonded paper
4
Quartz powder
3.5 Epoxy resin (unfilled) 3 SIR Silicon elastomer
Inorganic materials < 10 Alkalifree Eglasses
7
Mica
 6 
Porcelain
3.8 Quartz glass
Gases 1
1.0 Gases
Figure 4.22: Permittivities of technically important materials at technical frequencies (up to 1 MHz) under atmospheric standard conditions (T = 20 °C, p = 1 bar) as orientation values.
4.2 Dielectric Parameters
Hr
275
Electrical Optics engineering
Permittivity Interfacial polarization
Refractive index
n2
n
H r = n2
Orientation polarization Latttice polarization Atomic or deformation polarization 1 0
1
Hz
kHz
MHz Wavelength
GHz m
mm
Heating Joule's heating during recharging of partial capacitances
μm IR
Polarization losses
Frequency nm Licht
UV
Xrays
J rays
Absorption of light Sluggish dipoles lag in following the field
Crystal lattice in resonance
Atoms are excited
Figure 4.23: Dispersion (frequency dependence) of permittivity and polarization losses from the electrical engineering viewpoint (left side) and the optics viewpoint (right side), schematic representation.
Example: Water In the visible light region, water has a refractive index n 2 = 1.333. This corresponds to a permittivity Hr = n = 1.8. However, for low (electrotechnical) frequencies, owing to pronounced orientation polarization of water molecules Hr = 81. In the micrometer wave region, large polarization losses occur which can be used in socalled “microwave” chambers for dielectric heating of water based media.
4.2.1.3 Temperature Dependence
The temperature dependence of permittivity Hr is primarily caused by orientation polarization, see Figure 2.45. With increasing temperature, the “frozen” dipoles at first become mobile, so that orientation polarization can be effective. The permittivity frequently increases in multiple steps, corresponding to the “defrosting” of different polarization mechanisms, Figure 4.24. At the same time, the increase of temperature can also lead to changes of the conductivities and to the inception of interfacial polarization.
The steps in the profile of the permittivity Hr correspond to maxima of the dissipation factor tan G, which however, can often no longer be or can only poorly be identified in the cumulative curve, Figure 4.24. At higher temperatures, the influence of the strongly increasing conductivity is dominant. For further increases in temperature, the thermal agitation disturbs the orientation of the dipoles, and Hr again decreases, Figure 4.24. Increases in the permittivity often result from a transformation of the material structure, for example close to the glass transition temperature Tg. Example: Epoxy resin The thermosetting epoxy resin loses its considerable mechanical strength above the glass transition temperature Tg without melting. As a result of the softening, polar molecule groups become more mobile and Hr distinctly increases. Depending on the epoxy resin, Tg lies above approximately 100 °C. Even for temperature increases from 20 °C to 80 °C, there is an increase in permittivity by up to 20 %.
276
4 DIELECTRIC SYSTEM CHARACTERISTICS
4.2.1.4 Field Strength Dependence
Often, permittivity, conductivity and dissipation factor increase with increasing field strength. Note: For example, for unfilled epoxy resins, even for field strengths of approx. 42 kV/mm (that is, for about 20 to 50 % of the breakdown field strength), an increase in the permittivity by about 10 to12 % is observed (T = 20 °C); at 80 °C these values are increased to about 15 to 20 % [16]. By using fillers, the field strength dependences can be reduced.
In liquid dielectrics (e.g. in mineral oil) there are significant field strength dependences of conductivity and dissipation factor, already at low field strengths. This is caused by the fielddependent processes of charge carrier drift, charge carrier generation in the volume and charge carrier injection at the electrodes, see Section 4.3.2.3.
4.2.1.5 Mixed Dielectrics
In layered dielectrics and in mixtures of substances, the resultant permittivity Hr res can be calculated from the permittivities of the components.
Hr ( T )
3 2
1
Hr res =
d /{d1/Hr1 + .... + dn/Hrn}
(4.22)
For mixtures of substances, the resultant permittivity is derived from the relative percentage by volume v1 to vn as an approximation according to the empirically substantiated Lichtenecker’s law of mixtures: ln Hr res = v1·ln Hr1 + .... + vn·ln Hrn
(4.23)
Note: With the help of Eqs. (4.22) and (3), the temperature coefficient of Hr res can be determined from the temperature coefficients of the material components by differentiation with respect to the temperature T. By selection of materials with positive and negative coefficients, compensation of temperature dependences is thus possible. This is applied during the production of temperature stable capacitors.
Eqs. (4.22) and (3) are applicable under the assumption of a predominantly dielectric displacement field. For very slowly changing processes (or for highly conductive mixture components), higher capacitances and higher resultant permittivities result when the more conductive partial capacitances can be regarded as being short circuited (interfacial polarization). In Eq. (4.22), this extreme case can be considered with Hr k o f. In Eq. (4.23), Hr k o f does not give any meaningful result.
T
4.2.2 Conductivity N
tanG
4 1
For a layered dielectric with n layers and with interfaces orthogonal to the field, Hr res results from the resultant capacitance, Eq. (2.428):
2
3
Figure 4.24: Temperature dependences of permittivity and dissipation factor for a material with three different polarization mechanisms (1 to 3) and with increase in conductivity (4).
T
In the strict sense, conductivity refers to socalled direct current conductivity (DC conductivity), which according to Section 4.1.1, Eq. (4.18) and Figure 4.13, can be determined from the end value of the socalled polarization current, which is a steadystate conduction current. Conductivities in the broader sense that are determined (prematurely) from polarization currents after finite measuring periods, should actually be termed as “apparent conductivities”, since their cal
4.2 Dielectric Parameters
277
culation still includes polarizing current components that aren’t conduction currents. For stresses with DC voltage, for transition processes and for low frequency AC voltages, the formation of electric fields is (co)determined by the conductivities N, if the conduction current cannot be neglected against the displacement current (see Section 2.4.4). Moreover, the conductivity leads to losses in the case of AC voltages, which at higher temperatures, often dominate compared to polarization losses (see Section 4.2.3). Conductivity is caused by freely mobile charge carriers and is comparatively low in insulating materials, Figure 4.21. For the multitude of the conduction processes, differentiation into ionic conduction and electron conduction (Ntype conduction) is common [16].
tion can increase the conductivity of gases by many orders of magnitude and this can be utilized in the radiation measurements. Under standard atmospheric conditions, at very low field strengths, an initial conductiv14 14 ity of Ninitial = 2.5·10 to 5·10 S/m for air is mentioned [16], [24]. This value results from the equilibrium between the generation and recombination of charge carriers. It is valid only for so long as there is no saturation, i.e. as the flowing current remains clearly below the generation rate for new charge carriers. For atmospheric air in the vicinity of the Earth’s surface, the generation rate amounts to wn/wt = 1 / s cm³. The elementary charge e = 19 1.6·10 As and the air gap width d give rise to a saturation current Jsat
= e (wn/wt) d = 1.6·10
4.2.2.1 Conductivity in Gases
In gases, a very low conductivity is seen owing to a low number of ions that are created owing to collision ionization caused by radiation (see Section 3.2 and Figure 3.21). Radia
N S/m
10
Water (deionized and without atmospheric contact)
9
(wet)
10
12
(PA 6)
Resin bonded paper
Polyamide (PA 12)
Mineral oil Porcelain
(dry) (filled)
10
15
Oil paper
Epoxy resin (unfilled)
Polyethylen
10
18
(WepriBoard)
19
A/cm² d/ cm.
(4.24)
If d = 10 cm, this current corresponds to an approximation value according to Eq. (3.21). The current attains the saturation current, according to Esat = Jsat /Ninitial, even at field strength values in the range of V/m that are much below the relevant values for insulation. At higher field strengths, according to N = Jsat/ E, conductivities must be estimated with the constant saturation current value which gives rise to extremely low values (Figure 4.25) and extreme nonlinearity. Note: The conductivity of gases increases greatly owing to ionization. This can be induced, for example, by photoionization caused by radiation, by collision ionization at high field strengths (from approx. 2.5 kV/mm in normal atmosphere, see Section 3.2) or by thermal ionization at high temperatures (for example, in the vicinity of spark plugs in combustion engines).
Pressboard (Transformerboard)
Amber Quartz Gases
Figure 4.25: Conductivities at room temperature (orders of magnitude [2], [16], [82], without taking diverse parameters into consideration, see text).
4.2.2.2 Conductivity in Liquids
Ionic conduction dominates in liquids. Positive and negative ions are formed owing to dissociation of impurities. Free electrons play a role only at high field strengths; at low field strengths they are attached to molecules or they recombine with positive ions.
278
4 DIELECTRIC SYSTEM CHARACTERISTICS
During step voltage response measurements on liquids, there are a falling current profiles, Figure 4.26. Here they do not relate to linear polarization processes, according to Figures 4.12 and 3, but to a timevariant conductivity due to ion drift and charge accumulation close to the electrodes, cf. Section 4.3.2.3. Note: For insulating oils, depolarization current measurements often supply very small currents after only a few seconds. But after polarity reversal, higher currents are measured again. That is, the charge carriers wer accumulated as space charge close to the electrodes, and without applied voltage, they can be hold by the mirror charges on the electrodes for long periods. With the voltage applied already after a few seconds a low residual current is measured. It must therefore be attributed to a low residual conductivity [270], [271], [456], [486], cf. Section 4.3.2.3..
At lower field strength, insulating oils show an initial conductivity that results from the equilibrium between generation and recombination of charge carriers. Since in an alternating field, overall there is no removal of charge carriers, the initial conductivity is retained and we refer to it as AC conductivity, too. For an applied direct voltage, the charge carriers migrate to the electrodes and they are accumulated there. Charge carrier density and conductivity decrease, Figure 4.26. That is, the number of freely mobile ions decreases
steadily after some time. The transit time W is dependent on the ion mobility μ, the oil gap width d and the field strength E:
W
d/ (μ · E)
(4.25)
Thus, the conductivity of the liquid is not only dependent on temperature (by way of the ion mobility μ) but also on time, field strength and oil gap width! Example: For E = 1 kV/mm, d = 2mm and at room temperature, a transit time of W = 6 s was measured for a new insulating oil [271]. In HVDC insulations, viewed in the field direction, there are significantly larger oil gaps in the centimeter range and hence transit times in the range of a few minutes are possible.
After the removal of ions, for an applied constant field strength which leads to the permanent removal of ions, a new equilibrium is set at a lower level of conductivity and this is also described as DC conductivity, Figure 4.26. This conductivity end value is extremely dependent on field strength, as an intensely increased creation of new charge carriers is initiated for field strengths above 2 to 3 kV/mm [82], [271], Figure 4.27. The implied minimum of conductivity results from the opposing effects of a depletion of charge carriers and the generation of free charge carriers with increasing field strength, see also Section 4.3.2.3 and Figure 4.36. Note: In used oils, increased conductivities occur owing to acids and metal ions that have been delivered by
i, N Constant conductivity without depletion of charge carriers AC conductivity
12
10 Transit time
DC conductivity Steadystate current
W
ms
11
10
Charge carrier depletion and built up of space charge
(Orientation of dipoles)
μs
=
s
min
h
d
Time t
N S/m 13
10
2
4
6
8
E / kV/mm
Also see Figure 4.34 and 5
See also Figure 4.35
Figure 4.26: Reduction in current and conductivity with the stress duration in an insulating liquid.
Figure 4.27: Field strength dependence of mineral oil conductivity at room temperature [82], [271].
4.2 Dielectric Parameters
279
electrodes. Thus, the described changes in conductivity can sometimes be masked.
Section 4.3.2.3 describes the nonlinear conduction behavior by equivalent circuits and by multiphysics approaches, Figures 4.35 and 4.36.
100
i (t)
Polarization current
pA
i p(t)
10
Depolarization current
i d(t) 1 10
4.2.2.3 Conductivitiy in Solids
W
In solids too, charge transport at low field strengths takes place predominantly by ionic conduction. For high field strengths close to the electric strength limit (breakdown strength), also electron conduction is involved. In step voltage response measurements, at room temperature, the conductivity can often be identified as a steadystate end value only after very long times of several hours, days or even weeks since the currents are still dominated by polarization phenomena even after long measuring periods. At higher temperatures, the end values are identified earlier. By assuming linear system properties, the material characteristics can yet be determined from the step function response by approximating the current profile for t > 0 with exponential functions that are correlated with RCelements (curve fitting), see Figure 4.28 as well as Section 4.1.1 with Figure 4.12. Thus, the entire information is incorporated in a single measurement. ip (t )
V Rf
t
V ¦( e Wi ) i Ri
(4.26)
vCi (tL )
V (1 e
tL
Wi
)
tL, exponentially decaying depolarization current components occur and these are dependent on the attained charge status and these comprise system properties with the exception of DC resistance Rf, which is short circuited during depolarization: t t
id (t )
L vCi (tL ) W i ¦( e ) Ri i
(4.26b)
If the polarization current and the depolarization current are shifted by tL relative to each other and added, the related current components compensate each other partially: ip (t ) id (t tL )
The current component V/Rf caused by the conductivity corresponds to a theoretical end value ip(f), which can be developed more precisely with the help of depolarization current id(t): After the charging time t = tL, the equivalent capacitances Ci are charged by polarization current components to differently high fractions of the diagnostic voltage V:
100
If
(4.26a)
t
t
vCi (tL ) W V V ¦( e Wi e i) Rf R R i i i (4.2 6a)
t t
L V V Wi ¦( e ) Rf i Ri
(4.26c)
Eq. (4.26c) represents a significantly better approximation for the end value of the polarization current caused by conductivity than Eq. (4.26), since the exponential terms result in smaller values. For very long measuring peri
280
4 DIELECTRIC SYSTEM CHARACTERISTICS
ods and charging times, that is for t+tL >> Wi, the exponential terms can be largely neglected and the following is valid as an approximation: ip (t ) id (t tL ) 
V Rf
If
samples, on the basis of preliminary laboratory examinations for new material [234], [231], an exponential relationship is assumed, according to which the end value of DC conductivity
(4.26d)
If the magnitudes of the consecutive currents ip(t) and id(t) are mutually shifted by the charging time tL on the time axis, the described systemtheoretical relationship can be recognized, Figure 4.28. The sum (or the difference of the magnitudes) of the two currents, which are mutually shifted by tL, allows an improved estimation for the end value of the polarization current, even at earlier times t, Figure 4.28 (top). Note: The conductivity end value can also be calculated by the charge difference method (CDM): charges result from the integration of the measured currents. The charge difference forms approximately a straight line increasing with time, and the gradient converges relatively rapidly towards the conductivity end value, Section 6.4.1.3, Figure 6.4.15, [427], [392], [428]. This type of conductivity determination is advantageous for diagnostic measurements for which there is not enough time as well as for overlying disturbances which can averaged out by integration. Note: In Figure 4.28, slower polarization processes are represented by RCelements. The vacuum capacitance C0 and quickly changing polarization processes, which cannot be recorded for a step function response measurement with finite rise time, are summed in the socalled geometrical capacitance Cgeo, see Figure 4.32.
a) Oilimpregnated cellulose products Oilimpregnated cellulose is an important group of materials, which are used in the form of impregnated insulation paper (OIP oilimpregnated paper) and also as pressboard. For dry materials, the conductivities determined according to Eq. (4.26d) are only slightly dependent on the field strength in the range of 1 to approx. 20 kV/mm. For higher field strengths, an increase in conductivity by about 20 % at 30 kV/mm was observed, perhaps caused by the nonlinear characteristic of the insulating oil. [271]. The conductivity of impregnated paper increases with the water content w. For wetted
N board (f) 
N oil (f) K1
K2 e
w K3
(4.27)
is dependent both on the water content w of the board or paper as well as on the conductivity of the impregnating oil Noil(f), Figure 6.4.74. This corresponds to a conduction current along moisturized fibers and background conductivity due to oilfilled capillaries. Note: The constants K1 = 300, K2 = 0.00018 pS and K3 = 0.714 % are guideline values only for new materials at room temperature. For other temperatures, a temperature correction, according to Eq. (4.29) is necessary.
Water content and ageing products or deterioration products do not only increase conduction currents but also polarization currents. Depending on the polarization mechanism, the increase occurs in the time range of seconds, see Figure 6.4.79, or even after very long periods [392], see Section 6.4.7.6 b). Thus, not only conductivity but also RC elements for the description of polarization according to the Figures 4.12 or 4.28 must be adapted depending on the state of the material.
b) Highly polymerized substances In highly polymerized substances such as polyethylene, polypropylene or epoxy resin, the conductivity is comparatively very low, Figure 4.25. Freely moving ions are present in much lower concentration than in oilimpregnated pressboard or paper. Freely moving electrons are not available even for high field strengths. Charge transport is rather affected by socalled “hopping” of electrons from one trap to the next. This results in extremely reduced charge carrier mobility. Note: Since no regular crystal structure is generally present, the energyband model with valence band and conduction band is not applicable to high polymer insulating materials. Owing to irregularities in the crystalline structure, there are a large number of traps between the unoccupied conduction levels, in which the electrons
4.2 Dielectric Parameters are no longer attached to a specific atom, and the occupied valence levels. The traps are partly occupied by electrons (donor states) and are also partly unoccupied. For current conduction, the electrons must not be raised from the low lying valence levels to the conducting levels. Electrons in traps are raised to the conduction level and can again settle down in other traps. Under the effect of the field, “hopping” occurs in the direction of the field. Note: In composite materials, a higher conductivity is possible even for high polymer basic material if, for example, fibers that are admixed with it are conductive either intrinsically or owing to wetting. In silicone materials, based on the admixture of lower molecular components (silanes), ionic conductivity can be present to a certain extent.
281
served [271]. Probably, available ions here are exhausted by the field with no new ions being formed. In the case of higher field strengths, the conductivity in liquids increases owing to additional ions as a result of dissociation processes and by injection of electrons from the cathode, Figure 4.27. In mineral oil, the increase is from field strengths of about 2 kV/mm at 20 °C and from about 0.8 kV/mm at 70 °C. Significantly higher values are applicable for synthetic insulating liquids [16]. As an approximation, an exponential law with positive exponent m is applicable for constant temperature:
N =
c) Porcelain Porcelain and ceramics, depending on the mixture components used, can exhibit differently high ionic conductivities which are generally quite large in comparison with other insulating materials, Figure 4.25. 4.2.2.4 Influence of Field Strength and Temperature
The order of magnitude of conductivities can be stated only very inaccurately for different materials, Figure 4.25. The conductivity is dependent on the parameters stress duration, field strength, temperature, water content, purity, and material composition. Therefore, the conductivity can easily fluctuate over some orders of magnitude, despite of apparently similar conditions. Determining reliable values presents a serious problem, especially in field calculations for HVDCtransmission devices [7], [10], [82], [271] (see Section 2.4.4). With time, charge carrier depletion in an insulating material volume results from the withdrawal of mobile charge carriers for the electrodes. It can be observed as time dependence of electrical conductivity, especially for fluids, see Section 4.2.2.3. Therefore, it is often difficult to compare the conductivity values. With increasing field strength, the conductivity is at first constant. For liquids, even conductivity minima at 1 to 2 kV/mm are ob
N0·(E/E0)
m
(4.28)
In solid insulating materials, the field strength dependence is significantly weaker. For increasing temperature, the ion mobility and the number of electrons raised to the conduction levels exponentially increase. For both ionic conduction as well as for electron conduction, the socalled Arrhenius equation
N =
W/kT
Nf·e
(4.29)
can be determined with the material specific activation energy W and with the Boltzmann constant k = 1.3807·1023 J/K. In a logarithmic representation, straight lines result, Figure 4.29. With the help of the presented examples, the following statements can be made:
x
The increase in conductivity with temperature can amount to 4 to 5 orders of magnitude between ambient temperatures and operating temperatures.
x
Conductivities of different substances can vary by several orders of magnitude.
x
The conductivity ratio between different substances can vary substantially with increasing temperature.
This results in serious technical consequences: Example 1: Thermal stability: The exponential increase in conductivity leads to an exponential increase in dielectric power loss, and hence in unfavorable thermal conditions a thermal breakdown according to Figure 3.53 can be initiated (see Section 3.5.2). Insulations
282
4 DIELECTRIC SYSTEM CHARACTERISTICS
with relatively high losses (e.g. resinbonded paper, various resins), poor heat dissipation (solid, unfilled insulating materials), greater insulation thickness (for voltages of a few 100 kV) and high ambient temperatures (e.g. in hot transformer oil) are crucial.
Example 2: Field displacement in pressboard barriers at DC voltage: In layered dielectrics, pressboard barriers of transformerboard under oil are extremely highly stressed by fields orthogonal to the interfaces. The barriers must practically insulate the entire voltage, whereas the oil gaps are largely unloaded, Figure 2.423. Example 3: Barrier systems for a direct voltage bushing: Fig 2.428 shows a bushing in a barrier system of poorly conductive pressboard (transformerboard) in more conductive oil. According to Figure 4.29, the conductivity ratio between oil and pressboard amounts to about 1000:1 at room temperature. A uniform potential distribution in the axial direction thus results in the oil gap. At an operating temperature of 100 °C, the conductivity ratio reduces to about 30:1. The potential grading effect of barriers is thus greatly reduced. The radial resistance must be maintained high enough, even at operating temperatures, by using an adequate number of barriers. Temperature gradients can cause problems as they can lead to conductivity gradients and field displacements.
4.2.3 Loss or Dissipation Factor tan G For a dielectric at AC voltage, the current I of the voltage V leads by an angle of approximately M  90°, Figure 4.210. Owing to polarization losses and conductivity losses, the phase angle M deviates by a “loss angle" G from 90°. The current component IG (“inphase current", “active current”) is in phase with V and results in the real power that is dissipated in the dielectric, i.e. the dielectric power loss PG. The current component IC leads V by 90° and results in capacitive reactive power QC. According to Figure 4.210, the loss angle G is defined by the loss factor (dissipation factor):
10
10
S/m
12 Oil (1) 14
10
16 20
10
PG =
V·IG
(4.211)
QC =
V·IC
(4.212)
and
PG QC
tan G
10
filled (5)
Epoxy resin
(4.210)
the loss (dissipation) factor is also given by
Wepriboard (2)
N
.
With the power quantities
8
10
IG IC
tan G
.
(4.213)
The loss factor (dissipation factor) tan G therefore also specifies the ratio of dielectric power
Transformerboard (3)
unfilled (4)
I 40
60
80
100
120
140
T /°C Figure 4.29:Temperature dependence of apparent conductivity at E = 0.5 kV/mm (low field area). (1) Mineral oil, steadystate values [82]. (2), (3) Pressboard (Wepri board and Transformerboard), steadystate values [82]. (4), (5) Epoxy resin (unfilled and filled), 5 minutes values [16]. Note: The steadystate conductivity values are much lower than the 5 minutes conductivity values. Note: BisphenolA epoxy resin with liquid dicarboxilic acid anhydride hardeners and aminic accelerator (4), filled with 350 parts per weight of Al2O3.
I
C
I
V Complex plane
G
QC
P
C, H r
tan G
G
V
M
I I
G
G
I
C
Figure 4.210: Description of lossy dielectrics with active current, power loss and loss factor (dissipation factor) using the complex AC calculation methods and phasor diagrams.
4.2 Dielectric Parameters
283
tan G
Oilimpregnated paper with moisture (water) Polyamide 10 %
1
(PA 6)
10 %
10
1
Mineral oil
6 %
(wet)
1% 1‰
10 10
2 3
2 % 1 % (dry)
0.1%
4
(dry)
(filled & wet)
PVC Pressboard Paper Polyethylene VPE LDPE
Silikonöl
10
(PA 12)
Epoxy resin
(unfilled)
Resinbonded paper Porcelain Steatite Mica
PTFE
Quartz glass
Figure 4.211: Dissipation factors (loss factors) at power frequency (50 Hz) and room temperature.
loss PG to capacitive reactive power QC in a dielectric. If the capacitive reactive power is known, the dielectric power loss can be directly stated with the dissipation factor: PG =
(tan G)·QC
(4.214)
Note: In the English language, the quantities loss angle G, loss factor tan G, dissipation factor cot M and power factor cos M are used for the description of dielectric losses, Figure 4.210. tan G and cot M are identical, and for a small angle G, even the power factor cos M can be compared, Table 4.21. Table 4.21: Description of dielectric losses:
G
0.0573° 0.573° 5.71° 45° Loss angle tan G Loss factor 3 2 0.1 1 10 10 cot M Dissipation factor 3 2 0.0995 0.707 10 10 cos M Power factor
Nevertheless, dissipation factor is a very common wording in high voltage engineering, and it will be used predominantly in this book, instead of loss factor. The dissipation factor tan G is a material parameter, which according to Eq. (4.213) is determined by the polarization losses and the conductivity losses, Figure 4.210. The dissipation factors are greater than is to be expected on the basis of DC conductivity. In the case of liquids, this is because AC conductivity is lar
ger than the DC conductivity (see Figure 4.26). Especially for solids, the dissipation factor includes additional polarization losses that occur largely owing to orientation polarization and interfacial polarization. Figure 4.211 shows that substances which have relatively high permittivity owing to orientation polarization (for example, PVC, polyamide, epoxy resin, cellulose, resinbonded paper, see Figure 4.22), also exhibit relatively large (polarization) losses. Moisture results in a great increase in losses owing to water molecules that can be easily polarized as well as owing to an increase in conductivity. This is especially crucial for moisture sensitive substances such as paper, pressboard, polyamide and reinforced and filled synthetic materials. This results in strong dependences on the parameters such as frequency and temperature, Figures 4.213 and 2.45. The dissipation factor increases with the conductivity and hence possibly also with the field strength. On inception of strong partial discharges there is a sudden increase in losses (“partial discharge bend”), and some decacades ago, this was considered as a rough indicator for the occurrence of partial discharges. This is still of practical importance in partial
284
4 DIELECTRIC SYSTEM CHARACTERISTICS
E
D
V,E
Complex plane
I
J
Conduction (loss) current density
H 0 H r*E
Total current density
J+ j Z D
J =NE
Polarisation (loss) current density
D=
M
jZ D Displacement current density
Z H 0 H r" E
H 0 H r' E
G  j H 0 H r" E
j Z H 0 H r' E
Figure 4.212: Description of lossy dielectrics with conduction losses and polarization losses by means of phase shift of field quantities in a complex phasor diagram (for AC voltage).
dischargeresistant insulations of generators and resinbonded paper bushings. Generally, materials with low dissipation fac2 tors (generally under 10 = 1 %) are used for high voltage insulations, in order to avoid thermal instabilities and thermal breakdowns. In that connection, it must be noted that increased operating temperatures prevail in devices, which also lead to distinctly increased losses. It is a problem that the dissipation factor values measured at ambient temperature still do not give any indication of dissipation factors and thermal stability at increased operating temperatures. Along with the material properties, the insulation design and heat transmission conditions also play a decisive role in evaluating the thermal stability, see Section 3.5.2.
4.2.4 Complex Permittivity For a material with losses owing to conductivity and orientation polarization, it is assumed that the electrical polarization P(t), according to Eqs. (2.47) and (4.14), shows a lag in following the electric field E(t). For a single polarization mechanism with the relaxation time W, and for example assuming a step field E(t) = Estat·V(t), an exponential approximation to the stationary end value is obtained, Eq. (4.15).
Note: Polarization P should not be confused with the power loss PG
In the alternating electric field, the phase lag in polarization is expressed by a phase shift between the electric field E(t) or the voltage v(t) and the electrical displacement density D(t). That is, in a (complex) phasor diagram, the complex phasor for the r.m.s. value D lags in phase with regard to the complex phasors for the r.m.s. values E or V, Figure 4.212. Note: By assuming a uniform field or by taking very small field areas into consideration, the vectorial character of field quantities E, D and J needs not be considered.
Formally, the phase lag of D can be described with a decomposition into two phasors H0Hr' E and jH0Hr" E. The first phasor corresponds to the standard displacement density that is not out of phase. the second phasor lags by 90° corresponding to the multiplication with –j. With the approach D = H0 Hr* E
(4.215)
the phase displacement is thus described by a complex permittivity
Hr* =
Hr'  j·Hr" .
(4.216)
The real part Hr' equals the standard (relative) permittivity Hr; the imaginary part Hr" can be correlated with the polarization losses via the
4.2 Dielectric Parameters
285
phasor diagram of current densities, Figure 4.212: The displacement current density jZD which leads D by 90° is composed of purely capacitive component jZ H0Hr' E and polarization (loss) current density Z H0Hr" E . With the conduction (loss) current density phasor J = N E, total current density J + jZ D results. According to Figure 4.212, the dissipation factor (loss factor) is given by tan G
=
(N + ZH0Hr")/(ZH0Hr')
=
tan GL + tan GPol .
(4.217)
The dissipation factor components that have to be assigned to the conductivity losses and polarization losses are tan GL
=
N/(ZH0Hr')
and
(4.218) tan GPol
=
Hr"/Hr' .
Figure 4.213 represents the profile of dissipation factor tan G and relative permittivity Hr = Hr' against frequency and against temperature. The analytical derivation, assuming a lag in dipole orientation according to Eq. (4.14), results in [25] 2
Hr' = Hf + (Hstat  Hf)/[1 + (ZW) ] and
(4.219) 2
Hr" = ZW·(Hstat  Hf)/[1 + (ZW) ] . In this, the decrease in Hr' with frequency can be noticed. The lossdetermining component Hr" has a maximum at the frequency f = 1/W. Instead of a theoretical derivation, the presented curves should be made physically plausible. Frequency dependences: At low frequencies, the dipoles follow the field practically without any lag, and depending on
the temperature this results in a static permittivity Hstat, Figure 4.213 (top left), see also Figure 4.23. Above the frequency f = 1/W, the dipoles can no longer follow the rapidly changing field and the permittivity falls to Hf. The polarization losses have a maximum in the frequency range of f = 1/W, because although the dipoles can still follow the field, impacts and other interactions cause a lag (phase shift) with a withdrawal of energy. In the case of lower frequencies f > W, the dipoles cannot move at all, Figure 4.213 (bottom left). With increasing temperature, the dipoles become more mobile, the relaxation time W decreases and the loss maximum is shifted to higher frequencies. The conductivity losses must be superimposed on the polarization losses. Owing to Eq. (4.218), the dissipation factor tan GL infinitely increases with decreasing frequency Z o 0 because the ratio of power loss to reactive power increases accordingly. Temperature dependencs: The permittivity increases at first with increasing temperature because the dipoles become more mobile. For this, with increasing frequency, ever higher temperatures are necessary to make the “frozen” dipoles sufficiently mobile, Figure 4.213 (top right). With further increasing temperature, the thermal agitation disturbs the orientation of dipoles and hence the permittivity again decreases. In the range of increasing dipole mobility, a maximum of polarization losses results, Figure 4.213 (bottom right). The superimposed conductivity losses with the conductivity N(T) according to Eq. (4.29) lead to an exponential increase in the dissipation factor with temperature. According to Eq. (4.218), a greater increase must be expected at lower frequencies.
286
4 DIELECTRIC SYSTEM CHARACTERISTICS
Practical curves:
Harmonics:
Practical curves often comprise a superimposition of various polarization mechanisms. Thus, they are related more to the representation in Figure 4.24. Moreover, there are large differences between different materials, different material states (e.g. ageing, moisture) and different insulation designs (interfacial polarization). Loss maxima and step levels in the permittivity profile can frequently no longer be clearly identified.
Often, not only the dissipation factor at a certain frequency has to be considered: harmonics in the network can lead to significant reactive currents and losses. Also power electronic switching impulses with steep switching edges always exhibit a pronounced harmonic spectrum with high amplitudes Vi. In these cases, the total dielectric power loss results from the superposition of loss components resulting from the individual harmonics, wherein the insulating material is considered as linear.
Note: For the practically important oilimpregnated paper, the dissipation factor reduces for increasing temperatures up to about 50 °C and beyond that it again sharply increases. This “bathtub curve” has a favorable impact on the thermal stability of oilimpregnated insulations at increased operating temperatures.
Unfortunately, the dissipation factor minimum disappears for wetting and ageing of insulation owing to which wetting and ageing represent a risk for the thermal stability of insulations.
Hr ' Hr Hstat
{
Dipoles do not lag behind the field
Hf
1
f
(4.220)
i 0
2
Since the reactive power ZiC·Vi increases proportionally to the frequency Zi, the associ
Hr ' Hr
Dipole become more mobile ("defrosted")
f1< f2< f3
Dipole sind unbeweglich ("eingefroren")
Thermal agitation disturbs the orientation of the dipoles
1
T At higher frequencies, the transition range with increasing dipole orientation is shifted to higher temperatures with higher dipole mobility.
At higher temperatures, the transition range with decreasing dipole orientation is shifted to higher frequencies due to the increased dipole mobility.
tan G
f
¦ ( tan G )i (ZiC Vi2 )
Dipoles can no longer follow the fast changing field
T1 < T 2 < T3
PG 0 PG 1 PG 2 .....
PG
tan G
T1 < T2 < T 3
f1< f2< f3
Rise due to conductivity
Rise due to conductivity
f
T
1/W 1 1/W 2 1/W 3 Figure 4.213: Basic dependence of relative permittivity and loss factor (dissipation factor) on the parameters temperature and frequency for a dielectric with orientation polarization (schematic, see Figure 2.45).
4.3 Description of Dielectrics
287
ated loss components also increase. In addition, the dissipation factor (tan G)i often also increases with frequency, especially since various polarization mechanisms normally overlap, which is not represented in Figure 4.213. Thus, for high harmonic content, unexpectedly high thermal stresses can occur owing to dielectric losses, along with the risk of thermal instability (thermal breakdown), see Section 3.5.2. Example: The oilpaper capacitors formerly used for reactive current compensation were thermally capable of coping with the losses for the fundamental component f = 50 Hz. However, the increasing harmonic content in the network has led to an intolerable thermal load. As a result, the oilpaper dielectric has been replaced by low loss synthetic dielectrics.
I
Rs Rp
V
Parallel equivalent circuit
tan G
Cs
V
Series equivalent circuit
Parallel equiv. c.
Series equiv. c.
tan G aZ
tan G aZ
only for very low frequencies
only for very high frequencies
Formal conversion values are valid only for the frequency under consideration
Z0
'Wp
³ V ip (t ) dt
(4.221)
With the switching frequency, the number of switching processes for each time unit and from that, the power loss is calculated. For a dissipation factor assumed to be independent of frequency, a power loss created by a square wave voltage is about four times greater than that created by a sinusoidal voltage of equal frequency [284].
4.3 Description of Dielectrics Simple equivalent circuits of capacitances and resistances can only describe the properties of dielectrics in an incomplete way.
I
Cp
Note: In the case of rectangular switching impulses, the losses can be computed from the harmonic spectrum according to Eq. (4.220). An alternative would be a calculation in the time domain, by computing the loss energy 'Wp created by the polarization during a switching operation. The loss energy is calculated from the polarization current:
f, Z
Figure 4.31: Parallel equivalent circuit and seriesequivalent circuit (top) with conversion at a fixed frequency (bottom).
Nevertheless, the classic parallel and series equivalent circuits (Section 4.3.1) are still a valuable calculating aid if restricted to one frequency or a narrow frequency range. The flaw in simple equivalent circuits lies in their inability to correctly simulate complex physical interrelationships. Extended materialrelated equivalent circuits, which can be determined from dielectric systems responses in time domain or frequency domain, offer a better simulation of dielectric properties (Section 4.3.2). For the description of insulation systems of various materials, multiple equivalent circuits must be combined in a geometryoriented arrangement (Section 4.3.3).
4.3.1 Classic Parallel and Series Equivalent Circuits Parallel and series equivalent circuits consist of a single equivalent capacitance and a single equivalent resistance respectively, Figure 4.31. The dissipation/ loss factors, according to Eq. (4.210), result from the ratio of real power (that is converted into resistance) to
288
4 DIELECTRIC SYSTEM CHARACTERISTICS
reactive power (that is assigned to the capacitance). For the parallel equivalent circuit tan G =
PG/ QC 2
2
=
[V / Rp] / [ZCp·U ]
=
1/(ZCpRp) .
(4.31)
Note: The hyperbolic decrease in the dissipation factor with frequency ~ 1/Z included in the above would only be physically correct for materials whose losses can be assigned exclusively to a constant conductivity. Generally, this may only be assumed for very low frequencies. In the limiting case of Z approaching zero, even the reactive power approaches zero, but the power loss remains finite owing to the ever available conductivity, so that the dissipation factor tends towards infinity. Practically, this is important below mHz.
The series equivalent circuit leads to tan G =
PG/ QC 2
2
=
[Rs·I ] / [I / ZCs)]
=
ZCsRs .
The physical interpretation of a series equivalent circuit consists of an ideal capacitor that is connected through a series resistance which is not negligible. In particular, the capacitor impedance 1/(ZCs) decreases very sharply at high frequencies and Rs increases owing to the skin effect and may no longer be ignored. The losses of any dielectric at one fixed frequency can be formally described by both the series equivalent circuit and the parallel equivalent circuit. However, the elements of the equivalent circuits, that is, Cp and Rp and Cs and Rs respectively, are applicable only for the considered frequency. A change in the frequency without adjusting the circuit elements leads to incorrect results! For a specific frequency Z0, a conversion of the elements of both the equivalent circuits is possible by equating the complex impedances Zp = 1/[1/Rp + jZCp] and Zs = Rs + 1/(jZCs) and the dissipation factors, according to Eqs. (4.31) and (2). From both the conditions, the following results for the equivalent capacitances
(4.32)
Note: The linear increase of dissipation factor with the frequency ~ Z present in the above would only be physically correct for arrangements whose losses can be exclusively assigned to a constant series resistance, for example on the basis of supply lines or contact resistances. However, this is not the case with pure dielectrics.
This means that both the equivalent circuits are not capable of correctly describing the frequency dependence of the dissipation factor, Figures 4.31 and. 4.212. However, the parallel equivalent circuit enables the physically correct description of conductivity losses. Therefore, for very low frequencies, there is a correlation with the actual profiles.
and
2
Cp
=
Cs / (1 + tan G)
Cs
=
Cp·(1 + tan G)
2
(4.33)
as well as for the equivalent resistances
and or
1 / (ZCp·tan G)
Rp
=
Rs
=
(tan G) / (ZCs)
Rp
=
Rs (1 + 1/ tan G) .
(4.34)
2
The equivalent capacitances Cs and Cp are therefore, not exactly equal. In practice, however, the difference is usually negligible in the case of dielectrics with dissipation factors tan 1 G < 10 .
4.3 Description of Dielectrics
289
In a dielectric with low losses, the parallel equivalent resistance Rp is very large, according to Eq. (4.34). Very small values are obtained for the series equivalent resistance Rs.
For a PE cable with Ra/Ri = e, H’ = Hr·H0 = 2.3·8.85
Several equations can be used for the calculation of power loss PG of a dielectric:
Vm, linetoline in kV
Under the condition Cp  Cs  C, generally the following is applicable, according to Eq. (4.210) PG = QC tan G
2
= ZC V tan G .
(4.35)
In the equivalent circuits 4.31, the following results for the power loss 2
PG = V / Rp
2
and
PG = Rs·I .
(4.36)
For the power loss density, according to Eq. (4.35), considering an infinitesimal volume 'Vvol = 'A·'x with uniform field E = 'V/'x, the generally applicable relation is pG
= 'PG/ 'Vvol 2
=
Z(H''A/'x)(E 'x) (tan G) / ('A 'x)
=
Z H0 Hr' (tan G) E
=
Z H0 H r" E .
2
2
(4.37)
Example: Coaxial cable By means of the power loss density pG, the dielectric heat generation (power dissipation) P of a coaxial cable (length l, outer and inner radii Ra and Ri) can be calculated by integration over the volume of the cable. The electric field strength E in Eq. (4.37) is expressed by Eq. (2.321):
P
³³ pG d Vvol
Vvol
Z H ' (tan G ) V 2 R ln 2 a Ri
Ra
³
1
Ri r
2
2ʌ r l d r
2 ʌ l Z H ' (tan G ) V 2 R ln a Ri (4.37a)
4
pF/m and tan G = 10 , the following dielectric power dissipation at f = 50 Hz is given in dependence on the voltage V (r.m.s. linetoground voltage): 12
24
36
123 245 420
V, linetoground in kV 6.93 13.9 20.8 71.0 141 242 P/l in W/km
0.19 0.77 1.74 20.3 80.4 236
It is interesting to note that the absolute value of the dielectric power dissipation does not depend on the absolute value of the cable diameter, but on the ratio of the radii only. For a highquality polymericinsulated cable, the dielectric losses are very small and can often be neglected in comparison with the ohmic loss in the conductor. For an oilpaperinsulated cable with Hr = 4.4 and tan G = 3
3·10 , the dielectric power dissipation is approximately sixty times greater than that calculated above, and it can further increase during the ageing of the cable.
4.3.2 Description of Dielectric Material Properties Generally, more complex dielectric material properties can be described by means of the dielectric sytem response according to Eq. (4.11). For practical applications, it is used for determination of materialrelated equivalent circuits or physical description models that represent dielectric properties much better than simple parallel or series equivalent circuits according to Section 4.3.1. Important applications of equivalent circuits for the description of materials are in the area of dielectric diagnostics. Under this, one seeks to draw conclusions regarding the magnitude of the equivalent elements from dielectric measurements and correlate them with the material properties, in order to make statements about the insulation condition and the ageing condition, Section 6.4.7. Another application is the description of high voltage DC fields and the related transition processes in which slow polarization occurs
290
4 DIELECTRIC SYSTEM CHARACTERISTICS
and which can substantially influence the currents and fields, Section 7.2.1. Solid materials can often be regarded as linear and are modeled with the help of dielectric equivalent circuits (soclled materialrelated equivalent circuits), Section 4.3.2.1 and 4.3.2.2. Liquid insulating materials generally exhibit a distinct nonlinear behavior and therefore must be described with suitable functional relationships, Section 4.3.2.3. 4.3.2.1 Linear Polarization Equivalent Circuit for Solid Materials
For linear materials, a linear equivalent circuit for describing different polarization mechanisms can be developed by expanding the basic parallel equivalent circuit, Figure 4.31 and 4.32. Many solid materials behave largely linearly with respect to field strength and
C0
Vacuum capacitance
R1
R
R
C1
C
C
W1
Geometric or high frequency capacitance
Cgeo = H r C0
i
i +1
i
207,000
120,000
100 kV/mm). For production samples of high voltage and extrahigh voltage cables of crosslinked polyethylene XLPE (l = 100 m), strengths for Ebd50% of 40 to 50 kV/mm (r.m.s. value for
The processing of polyethylene during the manufacture of cable insulations is carried out by extrusion, Figure 5.33 (top right). The internal conducting layer, insulation and external conducting layer are applied on the conductor in a triple extrusion head, Figure 5.33 (bot
Its nonpolar, symmetrical molecule results in low permittivity (Hr = 2.3) and very low losses 4
Clean room Material reservoir Thermoplastic granulat
Material dispenser Heating Extruder Pneumatic sifter Magnetic separator
Conductor
Coating of the conductor by extrusion (schematic) Melting with optical monitoring
Conductor
Triple extruder with filter modules Drive
Lubricating agent Cross linking tube
Cooling tube
Cable lead Scanning of cable lead with xrays Drive
Figure 5.33: Manufacturing a high voltage XLPE cable lead by triple extrusion in a horizaontal procedure.
5.3 Highly Polymerized Plastics
313
tom). While manufacturing extremely stressed extra high voltage cables, special quality assurance measures are applied [325]. The thermoplastic granulate is purified under clean room conditions by pneumatic sifters and magnetic separators. Melting and compaction as well as optical detection of particles in the melt are carried out in the extruder. Additional safety can be ensured by using filter modules at the outlet of the extruder. Owing to low permanent temperature resistance and the creepage of the material under mechanical and thermal stress, a threedimensionally crosslinked polyethylene (XLPE) is used in cables. Cross linking takes place after extrusion of thermoplastic insulation, for example by electron bombardment. This results in a thermosetting condition at ambient temperature and an elastomeric condition at higher temperatures with a certain degree of residual mechanical strength, see Section 5.3.3.5. The stability of shape of polymer molecules that are crosslinked to each other, which prevents the creepage of the material, is of special significance. Permanent temperature resistance increases to about 90 °C. Cross linking can occur through the direct effect of radiation or through reaction with peroxides that are added to the polyethylene. The temperature of about 200 °C necessary for the reaction can be attained, for example, by heat supply through steam, nitrogen or ultrasound. H
Cl
Cl
H
Cl
Cl
C
C
C
C
C
C
H
H
H
H
H
H
Vinyl chloride
Polyvinyl chloride (PVC)
Figure 5.34: Polymerization of vinyl chloride. H
CH 3
H
H
CH 3
C
C
C
C
C
C
H
H
CH 3
H
H
H
Propylene
CH 3
Polypropylene (PP)
Figure 5.35: Polymerization of propylene.
For the socalled horizontal method, the cable core is drawn through the heated horizontal tube with the help of an internal lubricant. In the tube, crosslinking takes place with admixed peroxides [325], Figure 5.33. The service life of polyethylene insulations is often reduced owing to socalled “water trees”. This refers to conductive treeshaped structures which are formed by electrochemical processes under the effect of the electric field and in the presence of diffused moisture. The growth of the “tree” in the direction of the field ultimately leads to the formation of finer discharge channels (so called “electrical trees”) and leads to insulation breakdown, see Section 7.1.1.2. For insulations that are exposed to UV radiation, embrittlement occurs owing to crosslinking reactions. Dark, absorbing fillers (e.g. carbon black) are therefore admixed for outdoor applications, e.g. in cable sheaths. 5.3.2.2 Polyvinyl Chloride (PVC)
Vinyl chloride prepared from ethylene and chlorine is catalytically polymerized under pressure to form polyvinyl chloride (PVC), Figure 5.34. This gives rise to a more brittle plastic that has a permittivity of Hr = 4 owing to the polar Cl atoms. By admixing polar flexibilizers, which interact with the polar Cl atoms, a flexible and elastic mixture is obtained. This greatly increases the permittivity and dissipation factor. For a cable mixture with a flexibilizer portion of 20 to 25%, Hr = 5.3 and tan G = 30 to 50% approximately. Typical operating field strengths are under 3 kV/mm. Owing to the high losses, PVC is used as a dielectric only in the low voltage range, currently only up to 10kV for shorter medium voltage cable runs. Cable sheaths are manufactured from PVC also for higher voltages. In PVC, ageing due to the flexibilizer diffusing out is a problem. In the event of fire, corrosive gases (e.g. hydrochloric acid HCl) are formed.
314
5 INSULATING MATERIALS
5.3.2.3 Polypropylene (PP)
Polypropylene (PP) is obtained by polymerization of propylene (propene), Figure 5.35. This involves the methyl side groups (CH3) pointing outwards in a twisted chain sequence. Thus, a higher degree of regularity is attained which favors the crystallization and leads to a largely nonpolar character of the chain molecule. The space required by the side groups is responsible for a relatively low density [49], [89]. The electric strength and the dielectric prop3 erties (Hr = 2.3 tan G < 10 ) are comparable with polyethylene. The thermal resistance is distinctly better than that for other bulk plastics such as PE, PVC and polystyrene (PS): The crystallite melting point lies at 160 to 168 °C, and hence continuous use up to 105 °C and a temporary stress up to 150 °C are possible. Low temperature flexibility is limited to about 20 °C. Along with high dimensional stability under heat, especially a relatively high degree of hardness, rigidity and strength at lower density must be mentioned. Polypropylene exhibits a low water adsorption and is highly resistant to chemicals. In chlorinated and aromatic oils, a swelling occurs on heating.
PP Paper PP Paper PP
Thin insulating films for capacitor dielectrics are at first extruded with a sheet die and are cooled down as a 13 mm thick film on a roller. By extreme extension in the longitudinal and transverse directions, the molecules are aligned and the mechanical properties are vastly improved. Insulating films can also be manufactured by blowing or casting. A rough surface or imprinting creates impregnation channels for the layers of films and these enable the penetration of impregnating agents, Figure 5.36 (bottom). By diffusion, even cavities enclosed on all sides, e.g. formed by closely lying aluminum foils, are impregnated. Paper layers are no longer required as an impregnating wick for low viscosity impregnating agents and an adequate “spacefactor” (> 10%). For AC voltage, the films in the allfilm dielectric can be more heavily stressed because electrically weaker paper is not present. Also for DC voltage, significantly better volume utilization is achieved in allfilm dielectric, since the electric field is forced out of the paper owing to difference in conductivity. Note: The permissible field strengths are especially oriented towards field distortion at the edges of the conductive foils; see Figures 2.420, 21 and 30. They must be determined for real production samples by durability tests. Operating field strengths for multilayer dielectrics with dtotal = 50 μm can be in the range of 20 to 30 kV/mm (50 Hz, r.m.s. values). Transient strengths are two to three times higher. Thus, lower values are more applicable to paper dielectrics and higher values to allfilm dielectrics.
Polypropylene is also suitable as a construc
O
PP
C
PP
C
O N
PP
Figure 5.36: Impregnation of a mixed dielectric (top) and an "allfilm" dielectric (bottom).
O Imide group
S O Diphenyl sulfone group
Figure 5.37: Components of polyimide (left) and polysulfone (right).
5.3 Highly Polymerized Plastics
tion material, e.g. for housings (casings) owing to its good mechanical properties. It can be processed by injection molding or extruded. PP parts can be joined by heated tool welding or hot gas welding. Reinforced PP modifications are available for increased mechanical stresses. 5.3.2.4 Hightemperature Resistant Thermoplastics
Polymers of pure CH compounds can no longer be used for temperatures that are distinctly above 100 °C. Significantly higher temperatures for continuous use are obtained in the case of polymers which, along with benzene rings, also comprise oxygen atoms, nitrogen atoms or sulfur atoms, Figure 5.37. Polyimides (PI) comprise the socalled imide group. They can be temporarily stressed up to 300 °C and are suitable for continuous use temperatures of 250 °C. Polyimide films are used in highly thermally loaded capacitor di3 electrics (Hr = 3.5 tan G = 3·10 ). Polyamide imides (PAI), which comprises additional amide groups, have a continuous use temperature of 220 °C and additionally exhibit a high ultimate tensile strength. Polysulfones (PSU), and the Polyethersulfones (PES) derived from it, can be used for up to 150 °C and 200 °C respectively. 5.3.2.5 Polyamides (PA) and Aramides
Polyamides are formed by polycondensation of dicarboxylic acids and diamines with the separation of water: HOOC  R  COOH + H2N  R  NH2 o ......  OC  R  CO  NH  R  NH  ..... + H2O This pertains to a group of different thermoplastic substances that are characterized by
315
comparatively high mechanical tensile strength, toughness and abrasion resistance. Therefore, they are often used as fiber reinforced material for insulating, mechanically loaded parts such as bracings, threaded rods, screws, nuts or casings. Their operation is possible even at very low temperatures. The types of polyamides are characterized by the length of the carbon chains in the compositions of chain molecule (PA 6 to PA 12). The polar carbon amide groups CONH that form the links, increase the permittivity, the dissipation factor, water absorption and the melting temperature according to their relative proportions in the molecule: PA 6 Hr = 7
tan G = 300 ‰ water absorption 4 %
PA 12 Hr = 4.5 tan G = 50 ‰ water absorption. >1 %
Owing to the high water absorption, the dimensional stability of the molded components is adversely affected by swelling. The melting temperatures lie between 220 °C (PA 6) and 178 °C (PA 12). Owing to the beginning softening, the continuous temperature resistance is restricted to values between 75°C (PA 6) and 65°C (PA 12). Mechanical and thermal properties can be improved through fiber reinforcement. Polyamides are not used for the highest electrical stresses owing to their high water absorption, high losses and the relatively high 10 11 conductivity (10 S/m for PA 6 to 10 S/m for PA 12). For aramides, R must be replaced by benzene rings in the above reaction equation. Aramide fibers attain high tensile strengths and they are stable up to about 300 °C. Aramides are used for the manufacture of pulp moldings ("Nomex®Board" [82]) and aramide papers. In the case of high thermal loads, they can fulfill the function of cellulose containing insulations, e.g. in transformers. The electrical properties of oilimpregnated materials are comparable with paper or pressboard.
316
5 INSULATING MATERIALS
5.3.2.6 Polytetrafluoroethylene (PTFE)
Extremely temperature resistant polytetrafluoroethylene (PTFE) is obtained by the polymerization of tetrafluoroethylene, Figure 5.38. The trade name is, for example, “Teflon®” (Du Pont). This is a thermoplastic material that does not melt in the conventional manner on attaining the crystal melting temperature. At 380 °C, the viscosity of the melt is still so high that the standard processing methods for thermoplastics cannot be applied. Thermal decomposition starts at a temperature above 400 °C. For manufacturing the molded parts, the PTFE in powder form must be sintered at about 380 °C in a gellike condition. Cavities can be reduced by simultaneous pressurization, but they cannot be totally eliminated. The production of extruded parts (profiles, conductor insulations) is possible with a paste of PTFEpowder and lubricating agent, generally benzene (paste extrusion). After the extrusion the lubricating agent is evaporated and the PTFE is sintered. PTFE products are very expensive owing to poor processability and complex production methods.
Because of low intermolecular forces, the material flows even under low mechanical loads. PTFE is therefore suitable as a lubricating agent and as a sealant in threaded joints ("Teflontape"). Mechanically loaded parts must be fiber reinforced. The regular structure of the molecule leads to very low permittivity of solids and liquids at comparable density (Hr = 2.05). The dissipa4
tion factor is very low (tan G = 10 ). Both the properties remain constant over a wide range of frequencies since there is no orientation polarization. Hence, PTFE is used in high fre
quency engineering for connectors, bushings and capacitor dielectrics. PTFE exhibits creepage resistance and arc resistance, but owing to its porosity it is very sensitive to partial discharges. Therefore, the continuous dielectric strength amounts to only 2 to 6 kV/mm. The use of PTFE in high voltage engineering is restricted to special applications in which a high operating temperature (up to 260 °C) or noninflammable substances are necessary. Other options for application are available owing to the resistance of PTFE to chemicals and weather influences. Note: There are still more fluorinebased polymers that can be more easily processed but their properties do not entirely correspond to the properties of PTFE [16], [88], [89]. Significantly different dielectric properties are seen in polyvinylidenefluoride (PVDF) with a permittivity Hr = 8 and a dissipation factor tan G = 0.1 (at 1 MHz). PVDF has a high mechanical strength and toughness. It melts at 175 °C and can be thermoplastically processed. It is used for wire sheathings and cable sheathings as well as for films.
5.3.2.7 Polymethylmethacrylate (PMMA), Acrylic Glass
The thermoplastic polymethylmethacrylate (PMMA) or the acrylic glass is obtained by the polymerization of methacrylic acid methyl ester (methyl methacrylate) H 
CH3 
C = C F
F
F
F
F
F
C
C
C
C
C
C
F
F
F
F
F
F
Tetrafluoroethylene
Polytetrafluoroethylene PTFE
Figure 5.38: Polymerization of Tetrafluoroethylene.


H
CO  O  CH3
and this is known by the commercial name “Plexiglas®”. Despite moderate dielectric properties (Hr = 3.8 and tan G = 6 % at 50 Hz), owing to excellent light transmitting capacity it finds some uses, even in electrically stressed
5.3 Highly Polymerized Plastics
environments, for example for viewing glasses, transparent appliances, optically high quality components or as light conductors.
5.3.3 Thermosetting Materials and Elastomers Thermosetting substances and elastomers are obtained by a crosslinking reaction between the molecule chains. That is, a firm spatial network is formed in which the molecules are chemically linked to each other, and this can no longer be broken down by heating as in the case of thermoplastics, therefore melting or liquefaction is no longer possible. The crosslinking can take place directly in the course of the chemical hardening reaction (such as for resins or silicone elastomers) or subsequently in the case of thermoplastic substances which are crosslinked by adding chemicals or through electron bombardment (such as for crosslinking of thermoplastic PE to XLPE). In this case, the thermosetting or elastomeric condition results generally during the manufacturing process of the insulation components. Below the glass transition temperature the molecule chains, in addition to the crosslinking, are strongly bonded by intermolecular forces; to an extent they are “frozen” and in the socalled thermosetting (duroplastic) condition; the material is hard and brittle. On heating way above the glass transition temperature, the intermolecular forces are overcome, causing the thermoplastics to attain the liquid state. However, in the case of thermosetting materials the chemical cross linkages continue to be intact so that only a softened elastomeric state is obtained. On cooling down, the molecules return to their original position, the substance exhibits the property of contour accuracy or of shape memory. The wellknown flow of thermoplastic substances under mechanical stress is prevented by the cross linking. Therefore, elastomers are especially well suited to applications with continu
317
ous mechanical stress (sealants, cable entrance fittings, cable joints, shrinkable sleevings). During the processing of more rigid thermosetting materials below the glass transition temperature, there are considerable restrictions, such as a subsequent change in form is no longer possible or is possible only by mechanical finishing. On the other hand, there are also other processing options which open up extensive areas of application for the thermosets as cast resins and as adhesives: x
The user can change the processability and molding material properties by the formulation of the reaction components. This is done, for example, by the addition of fillers, dyes or accelerators.
x
Molding material can be cured at comparatively low temperatures, sometimes even at room temperature. Thus, all types of casting are possible, e.g. for structural components, cable joints or transformer windings. Moreover, there are many applications such as coatings, sheathings and finishing (varnishing). Epoxy resins are also especially suitable for adhesive bonding.
x
Composite materials can be made directly by the manufacturer of a device. Examples are the production of fiber reinforced parts (e.g. GRP), production of resinimpregnated insulations based on paper or other fibrous materials, as well as application of silicone shields to other insulation bodies.
Epoxy resins have a special position among the thermosetting insulating materials. Further, polyurethanes and silicone resins as well as various elastomers and shrinkable sleevings are also of importance. 5.3.3.1 Epoxy Resins (EP)
Epoxy resins are polymer compounds which consist of the socalled epoxy groups with a braced three ring system, Figure 5.39. Owing to their instability, these groups can be used for building up macromolecules and for spatial
318
5 INSULATING MATERIALS
crosslinking. By breaking up the three ring system and transposing Hatoms, links are formed to adjacent molecules without the lower molecular reaction products being formed (polyaddition). Epoxy resins are thus especially suitable as casting resins for the manufacture of high quality insulation parts. Owing to the reactivity of epoxy groups, epoxy resin is also applicable as an adhesive.
Viscosity
T1 mPa·s Limiting viscosity
Pot lives t T1
The resin wellestablished in electrical engineering is based on a monomer compound of 2 moles phenol with 1 mole acetone and is therefore, named as bisphenol A. Cycloaliphatic resins free from aromatic compounds have a high resistance to creepage currents (tracking resistance) and are considered for outdoor insulators. However, they have not gained acceptance in preference to the classic porcelain and to hydrophobic silicone composite insulators. Further, there is a series of special resins for higher thermal stresses, for flame resistant molding materials or for flexible materials.
The reaction resin reacts after mixing it with the hardener ("hardener component") with the formation of spatial cross links to a thermosetting molding material. Generally amines and anhydrides are used as hardening agents. For aminecured systems, for example, diamines with two NH2 groups form bonds between resin molecules
O
R
C
C H
H
H
+
OH H
R
C
C
H
H
X
H
X
Bonding of two molecules by breaking the three ring system of the epoxy group
Figure 5.39: Reaction of the epoxy group.
> T3
1500 (EP unfilled) 15000 (EP filled)
a) Resin and hardener Reaction resin that is not yet crosslinked ("resin component") is produced by stepwise synthesis of macromolecules from monomers and the formation of new epoxy groups. Depending on the chain length, the reaction resin is liquid ("liquid resin") or solid ("solid resin") at room temperature and must first be melted for further processing.
> T2
t T2
t T3
t
Figure 5.310: Isothermal rise in viscosity till the limiting viscosity within the pot life (schematic). by reacting with the reactive epoxy groups according to Figure 5.39. Aliphatic amine hardeners can be used even at room temperatures, but they give rise to low glass transition temperatures of only about 50 °C. Cycloaliphatic and aromatic amines react at increased temperature and give rise to glass transition temperatures of up to 100 °C and 160°C respectively. A popular anhydride hardener is phthalic anhydride, which must first be melted. Therefore it is particularly used for solid resins. Other anhydride hardeners can be processed already at moderately increased temperature.
b) Reaction process After mixing the resin and hardener, the hardening process begins and this leads to an increase in the viscosity, and this in turn restricts the processing time. For a comparison of reaction resin masses, the isothermal viscosity rise (that is, for constant temperature) until attaining the limiting viscosity index is observed. The time required for this is termed as "pot life", Figure 5.310. The higher the temperature of the resin mass, the thinner is the resin liquid at the beginning of the hardening process and the shorter is the pot life. That is, the available processing time is shortened by increasing the temperature. Curing of the reaction resin mass is associated with a chemical reaction shrinkage that is caused by closer packing of chemically linked molecules. Figure 5.311 represents the increase in volume of liquid reaction resin mass and the cured material against temperature. The gelling line lies between the liquid state
5.3 Highly Polymerized Plastics
319
and the cured state. At first the shrinkage occurs in the liquid phase (AB) and can be balanced by the resin mass flowing in. After gelling this is no longer possible; the rigid body shrinks further owing to ongoing crosslinking processes which are not yet completed (BC). Thus, mechanical stresses are built up. After successful chemical curing, further physical cooling shrinkage occurs owing to a fall in temperature to the service temperature (CD). From Figure 5.311 it is clear that a temperature increase during curing owing to reaction heat (AB'C') leads to a reduction in the proportionate shrinkage in the free flowing phase. This increases the mechanical stresses owing to the greater shrinkage in the solid phase. For large castings, isothermal curing (ABC) at the lowest possible temperature must be the aim. Design and production technology must take the characteristics of shrinkage into consideration to avoid stress cracks. For unfilled resins, the reaction shrinkage can amount to up to 3%. Note: The reaction shrinkage for liquid resins is larger than that of solid resins, since a considerably larger number of smaller molecules must be crosslinked. The cooling shrinkage, on the other hand, is greater for solid resins owing to higher processing temperatures. An
Volume Liquid mass
Gelling A line
Curing shrinkage in the liquid phase
B' B
Curing shrinkage in the solid phase
C' C Hardened material
Cooling shrinkage
D
effective method for reducing the shrinkage is the use of mineral fillers (e.g. quartz powder). Mechanical stresses can occur if free shrinkage in the gelled state is obstructed in the mold. Demolding in the gelled, but not yet cured condition may help in this respect. A complete curing must be achieved by a subsequent tempering.
Curing is an exothermic reaction, that is, heat is released and this causes the reaction to proceed more rapidly within a larger volume than at the cooled surface. Therefore, effective heat removal must be provided. Note: The generation of heat depends on the number of reacting epoxy groups. Their number can be significantly reduced by using fillers and by using long chain solid resins.
c) Fillers Mineral fillers can be included up to a degree of filling of 55 to 65 percent by weight. Higher degrees of filling are not possible, since then the complete embedding and wetting of filler particles in the resin matrix is not guaranteed. Fillers are used less for a reduction in the cost of the molding material but they can help in improving a number of properties: Fillers reduce the reaction shrinkage and the generation of heat during the curing reaction. Thus actually makes the production even of large castings possible. Crystalline quartz powder is the standard filler, and this helps in increasing the mechanical strength and thermal conductivity. Adsorption of moisture at the grain surfaces is a problem and this can be overcome by silanization of quartz powder. Quartz powder cannot be used in SF6installations owing to the formation of conductive SiF compounds under the effect of decomposition products of SF6 (hydrofluoric acid).
Temperature
Dolomite (CaMg carbonate) and aluminum oxide are suitable for SF6 installations; however, they lead to reduced mechanical strength.
Figure 5.311: Components of shrinkage during the curing and hardening of reaction resin mass and during cooling down of the hardened material [90].
A number of other fillers can be used to achieve special properties, such as aluminum
20 °C
Tg
320
hydroxide Al(OH)3 for high tracking resistance and flame retardance (by separation of water of crystallization), amorphous quartz powder or glass beads for low thermal expansion, aluminum oxide Al2O3 for high thermal conductivity, fibrous fillers (short glass fibers, Wollastonite) for better crack resistance, as well as aluminum hydroxide or chalk for good mechanical machinability. Note: Specially improved properties must often be bought with other disadvantages, such as with poorer mechanical properties or with poorer flow of the reaction mixture (for fibrous fillers).
d) Technology Accurately weighed components (resin, hardener, accelerator, fillers, dye and additives) must be mixed under vacuum to ensure adequate degassing and to obtain void free products, Figure 5.312. For thinfilm degassing, a spiral conveyor feeds the reaction resin mass into a mixer tube to an end cone on which the mass can be degassed in a thin layer of large area. In the case of solid resins, for anhydride hardeners, as well as for highly filled and highly viscous preparations, a heating process must be carried out to attain a satisfactorily low viscosity for processing. For classical vacuum casting, the degassed mixture is sucked out in the absence of air into a mold that is evacuated and treated with parting agent, Figure 5.313. A resin reserve remains in the inlet connections and in the riser to compensate the volume shrinkage in the liquid phase. With the help of specific temperature gradients, a reaction is controlled in such a way that the gelling starts as far away as possible from the connecting sleeves (point A) so that the liquid resin mixture can flow as long as possible. After gelation, the reaction shrinkage in the solid phase leads to detachment from the mold walls and leads to shrink coating of molded components. Generally, filled resins are used for avoiding stress cracks.
5 INSULATING MATERIALS
Vacuum pump
Conveyor sprial drive
End cone
Mixing tube (heated) with conveyor spiral and mixing screw
Stirrer
Valve Figure 5.312: Mixing and degassing of reaction resin mass through thin film degassing. Vacuum pump
Mixer (pressurized)
Riser Two part mold
A Heating plate Figure 5.313: Example of the encapsulation of a high voltage resistance with a filled reaction resin compound under vacuum.
Note: The function of the riser in an evacuated mold can be fulfilled by a free resin surface. Through a given temperature gradient, the gelling process progresses from bottom to top. The cured component, e.g. an insulator, must then be mechanically reworked to the specified dimension.
A typical application of vacuum casting is the casting of larger components in small numbers
5.3 Highly Polymerized Plastics
321
of units, such as the encapsulation of windings for drytype transformers. Under the pressure gelation process, the reaction resin mass is gelled in a comparatively hot mold at a pressure of 2 to 5 bars. Thus, the gelation begins very quickly and extensively at the mold wall. Owing to high pressure, the resin mass is pushed out of the mixer while still in the semiliquid condition. Short molding cycles are possible even for larger castings owing to rapid gelation at higher temperatures. The effort for the pressureresistant design of molds and mixers is especially worthwhile for the automatic production of components in larger numbers of units. Unfilled cast resin must be used for vacuum impregnation since fillers would lead to rapid blockages in narrow impregnating channels such as in filters. Moderate mechanical properties, large shrinkage and intense exothermic reaction of unfilled resin are only put up with for electrically highly stressed parts, e.g. for windings of larger electrical machines and generators, for spools and dry (oil free) bushings, Figures 5.314, 15. Large machine parts are impregnated in an autoclave under vacuum in an impregnating bath. The liquid reaction resin mass with anhydride hardeners is set up to be so inert that the impregnating bath continues to be usable for a few years. Curing is done by heat supply and by the action of an accelerator within the material to be impregnated, Figure 5.314. Bushings made of resinimpregnated paper (RIP) are manufactured as cylindrical crepe paper windings that are several meters long and contain metallic foils. The crepe paper is dried and impregnated in the axial direction under vacuum, Figure 5.315. This involves several extreme conditions and they necessitate perfect process control: The pot life of the reaction resin mass must be long enough to enable complete filling of the mold and impregnation of the paper winding. During the exothermic curing reaction, the heat generated by the unfilled masses must remain within
Impregnating bath
Figure 5.314: Vacuum impregnation of a stator winding in an inert impregnating bath. Resin preparation
Vacuum
Resin surface
Crepe paper winding
Mold Conductor tube or mandrel Figure 5.315: Vacuum impregnation of large crepe paper windings for RIP bushing insulation core.
controllable limits. During shrinkage in the liquid phase, the resin is replenished in the axial direction through the channels in the crepe paper. After the gelation, the winding is detached from the external mold and it shrinks on the conductor tube in the radial direction. e) Fiber reinforced epoxy resins Fiber reinforced components for high voltage engineering, such as tubes, composite insulators or switch rods must form a void free, moisture resistant, stress resistant and durable
322
bond between the fibers and the resin matrix. Silanization acting as a size is necessary for this. The components can be manufactured using a vacuum impregnation process for example. High quality tubes can also be manufactured using the filament winding (FW) procedure. Using this method, glass fiber rovings soaked with reaction resin mass are coiled on a mandrel such that the mechanical stress on the fibers under load produces tension. The resin is cured subsequently. f) Adhesives Singlecomponent adhesives based on epoxy resin are used in the form of an already mixed powder which is melted and cured under the effect of heat. Note: Heat cured powder reaction resin mixtures can also be used for powder coating of electrode surfaces. Thus, the hot components are dipped in an atmosphere of powder for a specific duration.
Twocomponent adhesives are obtained in prefabricated containers in the correct mixture ratio. Largescale application is in two component mixers with static mixer tubes, Figure 5.316. Important applications are, for example, the attachment of porcelains to large housing insulators for bushings and instrument transformers, or the attachment of insulators with metallic armatures. While designing the adhesive joints, it must be noted that these may only be provided for pressure load, tensile stress or combined tensile and shear stress. Peeling stresses and nonuniform tensile loads must be avoided. The longterm stability and hydrolysis resistance of important adhesives must be determined through proper endurance tests at increased mechanical stress, similar to that while determining electrical service life time lines. g) Electrical properties The electrical and dielectric properties of epoxy resins depend strongly on the type of reaction resin mixture and on many production parameters.
5 INSULATING MATERIALS
The electric strength of epoxy resin in general is dealt with in Section 3.5 (Figure 3.55, Table 3.52). A description of dielectric properties is given in Chapter 4 (Figures 4.22, 5, 9, 11). Guide values for permittivity at room temperature and power frequency are Hr = 3.5... 4 for unfilled materials and Hr = 5.8 for filled materials (approx. 40 weigth percent Al2O3). Depending on the filler substance, other (generally lower) values are obtained. Dissipation factors for unfilled materials are 2 less than 10 and slightly higher for filled materials. They increase sharply with temperature (rise in conductivity, as well as polarization losses near the glass transition temperature) and can lead to thermal instability in the case of thick, electrically and thermally heavily stressed insulations. Moisture adsorption on nonsilanized surfaces of fillers or glass fibers causes a sharp increase in losses and results in a sharp fall in electric strength in the case of fiber reinforced materials. 5.3.3.2 Polyurethanes (PU)
Linear urethanes with thermoplastic properties are obtained by polyaddition of diisocyanates
Component "A"
Component "B"
Mechanically coupled dosing pumps (reciprocating pumps) Mixing block
Static mixing tube Outlet
Figure 5.316: Principle of a twocomponent mixer (simplified).
5.3 Highly Polymerized Plastics
323
and diols (dihydric alcohols): O=C=N R N=C=O + HO X OH o O=C=N R (NH)(CO)O X OH Under this, the bonding urethane group (NH)(CO)O results from the transposition of an H atom without the elimination of lower molecular reaction products. Cross links are possible via NH groups as well as by using isocyanates with three O=C=N groups. Polyols (polyhydric alcohols) such as ricinus oil (castor oil) are used as a reaction agent. Polyurethanes are substances with thermosetting or elastic properties. Although they offer a very wide range of materials and they can be formulated for specific properties, their use in the high voltage engineering field has remained comparatively low until now. The reasons for this are as follows: Isocyanates react with moisture with the formation of CO2 gas which can lead to cavity formation. This problem can be overcome by the addition of zeolites that absorb water or by processing without air contact in a twocomponent mixer. After the preparation of the reaction resin mass, the reaction takes place relatively rapidly even at low temperatures, hence the available processing period is short. Polyurethanes are, thus well suited to castings at room temperature. However, using a mixing plant is recommended owing to short pot lives. The thermal resistance is comparable with the thermal resistance of coldcuring epoxy resins. Generally, maximum operating temperatures of 50 °C to 120 °C are attained. However, special polyurethanes have even much higher glass transition temperatures. The electrical properties are slightly poorer than those of epoxy resins. Guide values at room temperature [88] are for a thermosetting PU
Hr
= 4
(1 MHz), 2
tan G = 2·10 (1 MHz), 11 N = 10 S/m
and for a PU elastomer
Hr
= 7
(1 MHz), 2
tan G > 5·10 (1 MHz), 10 12 N = 10 ..10 S/m. Positive properties of polyurethanes are high tracking resisitance, high toughness and high elasticity. Foamed elastic polyurethanes exhibit the property of compressibility. They are used as finepored foam for subsidiary insulations, for example, between epoxy resin core and housing insulator in a bushing for compensating thermal expansions. Electric field strength, pore size and type of gas must be matched to each other so that no discharges are ignited in accordance with Paschen’s law. Typical applications of polyurethanes are in the low voltage range, e.g. for castings of assembly components, insulation parts for moist interior rooms or for foams. Moreover, wires are insulated with PU varnishs. In the medium voltage range, elastic PU casting compounds for cable fittings are used as standard.
5.3.3.3 Phenolic Resin and Resinbonded Paper (RBP)
Phenolic resins are obtained by polycondensation with the elimination of water, Figure 5.32. Phenolic resins are a classic, but obsolete substance of high voltage engineering that was used up to the voltage level 220kV. By impregnating paper with liquid resin, processing into plates, rolled laminated tubes or bushings and subsequent curing at increased temperature, oilfree insulation parts could be manufactured for the first time from socalled resinbonded paper RBP (commercial name e.g. "Pertinax"). However, to avoid stress cracks in large scale insulations, the papers were not completely impregnated so that mechanical stresses could be reduced by the delamination of paper layers. In such insulations, since they are not completely free from air, partial discharges must be taken into consideration. However, they last a relatively long
324
time owing to the relatively high partial discharge resistance of the phenolic resin. Resinbonded paper has a relatively high per11 mittivity (Hr  5), high conductivity (H  10 S/m) and high losses (tan G  0.1). The given values relate to T = 20 °C and f = 1 MHz. The shortduration electric strength is comparable with the strength of other high polymer insulating materials. Insulating components made of resinbonded paper are not always gastight and oiltight parallel to the paper layers. Infiltrating oil can reimpregnate the available cavities and thereby lead to a rise in the capacitance of the insulation. Owing to the effect of partial discharges, yellow "Xwax" is thus formed by decomposition and crosslinking of oil molecules. While dissecting electrically highly stressed resinbonded paper insulations, often interesting, widely branched discharge traces are seen between the paper layers. Today, void free resinimpregnated paper RIP insulation is state of the art. However, resinbonded paper RBP bushings are still in use. 5.3.3.4 Elastomers and Shrinkable Sleevings Elastomers are spatially crosslinked macromolecules which return to their initial position without experiencing any permanent change in shape, even after a mechanical extension, owing to their contour accuracy and their shape memory. Popular substances are, for example, ethylene propylene rubber (EPR) or silicone elastomers. Elastomers, when compared to thermoplastics, have a very wide elastic range in which the extension is reversible, since the crosslinking of molecules does not allow mutual relative displacement. Insulation systems with high mechanical flexibility are thus possible, e.g. flexible cables that are not laid in a fixed position. Furthermore, elastomers can be compressed or extended for long periods without losing their restoring forces
5 INSULATING MATERIALS
through material flow processes. Along with the usual technical applications, such as for sealing, this is especially important for cable joints and cable entrance fittings, which must contact the cable insulation with adequate surface pressure to guarantee the high voltage strength of the joints, Section 7.1.4.4. Note: Such joints generally contain a lubricating agent to compensate for unevenness and to fill voids.
Cable insulations are manufactured from extruded thermoplastic polyethylene by subsequent spatial crosslinking, Section 5.3.2.1 Thus, a thermosetting crosslinked polyethylene (XLPE) is obtained, which does not melt at increased temperatures but changes to an elastomeric condition. Hence, even at increased operating temperatures of up to 90 °C, the flow of the material is inhibited. A special form of elastomers is shrinkable sleevings. They are elastic only at increased temperature, that is, above the glass transition temperature. They are stretched in that state by compressed gas and subsequently cooled down below the glass transition temperature. In this way, the stretched condition is frozen since the intermolecular forces no longer allow any change in the position of the molecules. Only when heated, these bonds are released and the sleeving shrinks to the original dimensions, which are predetermined by the spatial crosslinking of macromolecules (contour accuracy, shape memory). While manufacturing shrinkable sleeving, at first a tube is extruded from thermoplastic material (for example, from polyethylene PE). Subsequently spatial crosslinking takes place, e.g. by bombardment with electrons. Owing to this, the bonds of hydrogen atoms are broken, giving rise to free valences and this enables the polymer molecules to crosslink with one another. At room temperature, such a crosslinked sleeving still has thermosetting properties owing to intermolecular forces. By heating above the glass transition temperature, the sleeving becomes elastic and can be stretched to the desired dimension by compressed gas. After cooling down in the stretched condition,
5.3 Highly Polymerized Plastics
it is again frozen into the thermosetting condition. The user can change the stretched sleeving into the elastic state again by heating, in which the sleeving tries to shrink to its original dimensions. During this socalled heatshrinking technique, the sleeving largely adapts itself to form fit the body to be shrinkwrapped, but no permanent force is exercised on the substrate after cooling down. In contrast, there is a socalled coldshrinking technique, whereby the sleeving is made of permanent elastic material (e.g. of silicone elastomer). It is mechanically widened on a supporting base (e.g. a plastic spiral or mandrel) and is applied to the body to be shrinkwrapped by removing the supporting base. A certain amount of residual extension of the sleeving remains, which leads to a permanent surface pressure on the substrate and which, along with the lubricating agent, allows joints of very high voltage strength.
5.3.4 Silicones 5.3.4.1 Properties of Silicones
The chemical relationship of the silicon atom with the carbon atom allows the formation of analogous compounds with exceptional properties. The simplest monomer compounds are the methanerelated silane and the long chain silanes derived from it, Figure 5.317. Polymer silicone compounds, for example, are obtained from methyl silanols by polycondensation. That is, two OH groups are attached to form an oxygen bridge O with the elimination of H2O, Figure 5.317. Silicones are macromolecules made of a very stable inorganic skeleton with Si and Oatoms that is surrounded by organic groups R, Figure 5.317. The monomer structural unit R2SiO formally corresponds to a ketone R2CO, and hence the macromolecule is referred to as "silicoketone" or as "silicone" [49].
325
By spatial crosslinking (vulcanization), thermosetting silicone resins and also silicone elastomers (SIR, silicone rubber) are obtained. Silicone elastomers are exceptionally elastic, extensible and have a very high contour accuracy. Their properties are greatly influenced by the degree of crosslinking and by mineral fillers that are added to resins and elastomers, generally with percentages ranging from 30 to 70 %. In high voltage engineering, the following groups of materials are especially important: 1. Silicone resins are spatially heavily crosslinked thermosetting materials whose glass transition temperature lies above the working temperature. They are used as temperature resistant substances. 2. Silicone elastomers (socalled "silicone rubbers") are spatially less strongly crosslinked so that the glass transition temperature lies below the working temperature and an elastomeric (extensible) condition exists. Areas of application are hydrophobic insulators (Section 5.3.4.2), contour accurate and permanently elastic insulation bodies (Section 5.3.4.3) as well as insulations and sheathing for flexible cables. 3. Silicone gels are spatially crosslinked only to a very small extent and have a higher pro
C
H
H
H Methane
H
Si R
Si
H HO
H Silane (silicomethane, hydrosilicon)
R O
CH 3
H
H
Si R
O
OH
CH 3 Methyl silanol R
R
R O
Si
Si
O
R
Si R
Silico ketone or "silikone" respectively Figure 5.317: Monomer and polymer silicon compounds as well as alalogies between carbon chemistry and silicon chemistry.
326
5 INSULATING MATERIALS
portion of silicone fluid. This results in a sticky state with greater spreading power and higher breakdown strength, and hence they are well suited to electrically highly stressed joints or interfaces (Section 5.3.4.3).
ample, oil impermeability can be attained with fluorinated silicone elastomers. In the case of silicone gels, this property has a positive effect, since the trapped gas in seams can escape by diffusion. [472].
4. Silicone pastes (socalled “silicone grease”) are spatially no longer crosslinked; however, the chain length of the molecule is so large that a pastelike condition exists. They can be used, for example, in filling electrically stressed joints or for applying to porcelain insulator surfaces for (temporarily) increasing the hydrophobicity.
The permittivity of unfilled silicones is Hr = 2.8 to 3, with fillers between 3 and 6, in special cases it is even at 15 to 20. The dissipation factor tan G amounts to about 0.5 to 1 % and 13 11 the conductivities are between 10 and 10 S/m for unfilled and filled materials. Owing to the nonpolar properties of molecules, the dielectric properties vary significantly less with temperature than for other elastomers. Silicones are generally tracking resistant and have high breakdown strength that is comparable with other polymers.
5. Silicone liquids (so called “silicone oils”) are no longer crosslinked for short chain lengths and hence a liquid state exists. They can be generally used as a substitute for mineral oil, Section 5.4.3.2. For cost reasons, however, this happens only when it is necessary owing to technical requirements (temperature resistance, fire protection). Silicones that are crosslinked can be differentiated as RTV silicone, i.e. room temperature vulcanization silicone, and HTV silicone, i.e. hightemperature vulcanization silicone or heatcuring silicone respectively. HTV silicone has been preferred in the past owing to its better mechanical properties. RTV silicones have improved so much in their properties in the meantime that they are increasingly used at low temperatures owing to their simpler processability (LSR liquid silicone rubber). It is common practice to use a twocomponent mixer system for the components A and B which react by polyaddition, Figure 5.316. Silicones are not inflammable and can be used over a wide range of temperature (60 °C to 180°C) without any significant change in properties. Silicones are highly resistant to chemicals, weather influences and ageing. The widemeshed crosslinking of silicone elastomers allows a comparatively high diffusion of gases, water vapor or oil molecules. Hence, the suitability of silicones as sealing material must be tested in each case. For ex
Note: By filling with carbon black, conductive mixtures are obtained and these can be used in cable fittings for potential grading electrode contours.
5.3.4.2 Hydrophobic Insulators Surface hydrophobicity must be mentioned as an excellent property, Figure 5.318. Silicones are thus the ideal material for outdoor insulations under conditions of severe pollution. Precipitation forms isolated water droplets, which are held together on polluted surfaces by the surface tension of water, Figure 5.318 (top right and middle). Comparable porcelain surfaces, on the other hand, are hydrophilic, water flows to form a large area of moist film, Figure 5.318 (top left). The contact angle 4 [92] is suitable for the quantification of hydrophoby: a large contact angle is obtained for hydrophobic surfaces, whereas easily wettable surfaces lead to small contact angles and the drops run to form a film. When a drop runs on to the insulator surface, the contact angle can be differentiated as the advancing angle 4a and the receding angle 4r. The latter determines whether the flowing drop leaves behind a moist film. Moist films can bridge over large stretches of the insulator and initiate a pollution flashover.
5.3 Highly Polymerized Plastics Note: An additional option for qualitative estimation of hydrophobicity is a simple flashover test: a plate like 3 material sample (125 x 125 x 5 mm ), which has been wetted earlier in an aqueous saline solution (N = 100 μS/cm) is placed between two plate electrodes (D = 70 mm) following a defined dripping period (1 min) and stressed several times with AC voltage until flashover occurs [9], [57]. The results can be useful in identifying significant differences depending on the surface condition. The flashover test is thus even suitable for comparative evaluation of different prestresses and different methods of surface treatment.
327 Note: Dew on the silicone surfaces can be a reason for corona discharge. A socalled dewdrop corona occurs at the dew drops which are distorted to form peaks due to the field forces. The dewdrop corona can be avoided by limiting the field strengths to 0.3 to 0.5 kV/mm
Silicone sheds have the ability to prevent the formation of continuous films, even under intense rain, and to facilitate isolated drops rolling off, Figure 5.319. The surface resistance is maintained at a high level, a continuous moist film does not form. Porcelain insulators that are coated with silicone paste (“silicone grease”) exhibit a similar characteristic. On the other hand, the surface resistance of clean porcelain surfaces collapses by many orders of magnitude at relatively low rain intensities and the individual drops flow together to form a tight water film [7], [9], [10]. Experiments have shown that several weeks of pollution on porcelain surfaces under outdoor conditions leads to the breakdown of hydrophobicity even for much lower rain intensities. The performance of silicone surfaces has not changed [57]. Long term experience has proved that silicone sheds, even after many decades, retain their hydrophobic character even under the conditions of industrial pollution [9], [93]. The hydrophobicity extends even to the deposited dirt layer. The lowmolecular components of silicone which diffuse out and which are formed within the shed material are held responsible for this. The hydrophobicity on the stressed areas can be temporarily reduced by flashovers, corona discharges or treatment with aggressive solutions. However, lowmolecular components that diffuse out lead to an automatic regeneration. With the help of silicone liquid (“silicone oil”), the hydrophobicity can be immediately restored [9], [57].
4a
4r
Receding angle
Advancing angle
Figure 5.318: Drop formation on the surface of a hydrophobic siliconeshed insulator (top right, middle and bottom) in comparison to the formation of a moist film on the hydrophilic surface of a comparable porcelain (top left) [9], [57]. Photo insulators: HSP Hochspannungsgeräte GmbH, Troisdorf.
328
5 INSULATING MATERIALS
[471], Section 3.2.6.4.
The excellent surface properties of silicone give rise to the question of whether the usual creepage distance of 2.5 to 5 cm/kV for porcelain (related to the r.m.s. value of the applied operating voltage, see Section 3.2.6.4) can be shortened. Long term investigations with silicone sheds on bushing insulators for more than a decade have shown that even in severely polluted, humid and salty atmospheres, without intermediate cleaning, reliable operation with creepage distances between 1.7 and 2 cm/kV is possible [57], [93]. Despite this, creepage distances are often designed according to the guidelines approved for porcelain. It must also be noted that corona discharges can occur for local field strengths that are too high when there is dew on the surface [471] (see above). Note: In the case of HVDC bushings above 500 kV, the application of bushings with silicone sheds is often considered as the only secure way to avoid flashovers under nonuniform rain [8], [93], see Figure 2.429.
Important applications of silicone elastomers are as insulators fit for outdoors (insulator rods, housing insulators for instrument transformers and bushings), pushon cable fittings with potential grading and thermally resistant flexible cable insulations. Different methods can be applied for manufacturing composite insulators, Figure 5.320. In each case, the surface of the fiber –reinforced tube or rod must be treated with a bonding agent (primer), and this guarantees a permanent and hydrolysis resistant chemical bonding between the substrate and the sheds. Note: The vulcanization and bonding of silicones can be hampered by chemicals (e.g. by amines for adhesives and epoxy resins) and by their vapors.
Individual prefabricated sheds are vulcanized with a RTV silicone (crosslinking at room temperature) on the pretreated surface of the insulator tube and on the already applied sheds, Figure 5.320a. Using individual sheds allows a high degree of flexibility with respect to spatial dimensions and the choice of mate
R/ :
D l
13
R
10
l
12
10
11
10
HTV silicone elastomer
10
10
Porcelain with silicone paste
9
10
8
10
Porcelain (cleaned)
7
10
Rain intensity
6
10
10
20
30
40
mm/min
Figure 5.319: Resistance of cylindrical surfaces (D = 70 mm, l = 188 mm) for vertical rain (conductivity 100 μS/cm).
rial (HTV silicone or RTV silicone) owing to lower molding costs. The sheds can also be directly cast in a top opening mold with RTV silicone on a pretreated insulator tube, Figure 5.320b. After gelation, the mold migrates downward into the position for casting the next shed. Great flexibility with respect to spatial dimensions is obtained by using very simple molds. The cast of the complete insulator on the pretreated substrate needs expensive, longitudinally divided molds, Figure 5.320c. The flexibility is thus severely restricted, but it results in very short cycle times that enable batch production of larger numbers of units. For longer insulation lengths, many successive castings are conducted. The parting seam of the mold running longitudinally must be subsequently smoothened if possible to avoid the accumulation of dirt. Note: Composite insulators are impressive not only owing to their excellent surface properties. They also have a much lower weight compared to porcelain. Moreover, greater safety is also provided, e.g. in the case of an internal short circuit or for devices filled with
5.3 Highly Polymerized Plastics
329
SIR A
SIR A + B
SIR B
Figure 5.320: Manufacture siliconeshed composite insulators on a glassfiber reinforced insulating tube or insulating rod: a) Application of prefabricated HTV or RTVsheds. b) Casting of individual sheds with a RTV casting compound in a mold migrating downwards. c) Casting of a complete insulator in a single split mold.
a)
b)
compressed gas: there are no sharpedged porcelain pieces if the housing insulator bursts [57], [93], Figure 7.1.24.
5.3.4.3 Other Applications of Silicones
In cable entrance fittings and in cable joints, conductive silicone is used for a potential grading ground electrode (deflector), which is cast in insulating silicone, Figure 5.321. The flexibility of the silicone enables close and permanent contact to the surface of the uncovered cable insulation while pushingon the “grading cone”. The permanent elastic properties of the silicone elastomer enable the continuance of a permanent mechanical stress, which takes care of the necessary contact pressure on the uncovered cable insulation. A high
c)
quality joint over a long period of time is only made possible by the permanent elasticity of the SIR. Note: The contacting of the deflector with the outer semiconductive layer (insulation screen) of the cable insulation and the quality of the joint, which is highly stressed in the normal and tangential directions, are of particular significance.
Other applications of permanently elastic elastomers have been described under Section 5.3.3.4. The properties of silicone gel for electrically highly stressed interfaces and joints are also of interest: owing to its high degree of stickiness, adhesion is good on many substrates. Owing to the low degree of crosslinking in the gel, crosslinking with the substrate is often even
E t1 Cable sheath
(1)
E t2
(2) Cable insulation Conductor
Figure 5.321: Potential grading in a cable entrance fitting through a ground electrode (socalled "deflector") made of conductive silicone (1) and a "grading cone" made of insulating silicone (2).
330
possible. The voids formed by the surface roughness can be completely filled for forcefit connections under pressure, owing to the high proportion of silicone liquid in the gel. Furthermore, the trapped gas can easily diffuse out under sufficient contact pressure so that a high quality interface is obtained. Breakdown tests for twocomponent systems of basic material (silicone elastomer, polyethylene, epoxy resin and porcelain) with a silicone gel have shown that the longitudinally stressed interface with the polymeric basis materials has an electric strength that can correspond to (at least) the strength of the pure gel [472]. Only the interface with the porcelain corresponds to standard high voltage engineering expectations and is of lower strength, since apparently the roughness here is greater and the adhesion is lower [472].
5.3.5 Nanodielectrics 5.3.5.1 Introduction
Substances with special properties determined by nanosized fillers have been in use for a long time without the relationship between the properties and nanofillers being known. Historical examples are Roman glasses, whose fascinating optical properties were created by nanoparticles of gold, or oriental sword blades whose carbon content in the form of nanotubes gave rise to excellent mechanical strengths. It th only became known towards the end of 20 century that the properties of a basic material can be drastically changed by relatively low quantities of nanostructured fillers. Since then, efforts have been made specifically to develop so called “nanocomposites” with improved properties. For this, particles with dimensions of a few 10s of nm are mixed with a proportion of very few weight percents of up to about 10 %. Note: The nanostructuring of nanoparticles can be threedimensional (particles in the form of powder),
5 INSULATING MATERIALS twodimensional (rods, tubes) or onedimensional (plates).
Surprisingly, this achieved exceptional changes in properties that are completely unknown for fillers in the μm range. At first, there was greater interest in the resultant high mechanical strength or high thermal resistance. As early as 1994, Lewis had described the consequences of nanostructuring for dielectrics by a drastic enlargement of the microscopic interfaces and had used the term “nanometric dielectrics” [448]. Inorganic nanoparticles, as fillers in polymers, have the ability to cause a socalled nanostructuring of the surrounding polymer molecules and effect large improvements of the electrical and dielectric properties [416] [487]. The interfaces between the nanoparticles and the polymers and the reduced distances to the neighboring particles play a special role in this. Properties that were not attainable until now for dielectrics are thus attained, e.g. hydrophobicity and selfcleaning surfaces, reduced buildup of space charge, better resistance against treeing and erosion or higher resistance to partial discharges. Nanocomposites, therefore, possess a special innovation potential also in high voltage engineering. Wellknown inorganic materials are used as fillers, such as aluminum oxide Al2O3, silicon dioxide SiO2, titanium dioxide TiO2, magnesium oxide MgO or socalled layered silicates LS. Popular polymer materials such as polyamide PA, polypropylene PP, crosslinked polyethylene XLPE, epoxy resin EP or silicone elastomers SIR are considered as basic materials (matrix). Therefore, the special properties of nanodielectrics arise primarily from the small diameter of the filler particles and not necessarily from special materials. Manufacturing procedure requires the mixing of particles with diameters in the nm range into organic polymers in the liquid phase, such as resin components or thermoplastics. For this, a few percentages by weight must be homogeneously and completely dispersed. This is technologically very complex and expen
5.3 Highly Polymerized Plastics
331
Polymer R
R
Si
Si
O H H O
O H
H O H
H O
Silane linkages
M
M Filler
Figure 5.322: Silane linkages between filler particles and polymer molecules.
sive, but very important since the desired property improvements can only be attained by optimal distribution of the nanoparticles. Note: The use of nanoparticles is still at a very early stage and many physical and chemical interdependencies are not yet completely known. The probable risks of handling nanoparticles, therefore, should not be simply ignored. Still, high chemical activity exists in many cases owing to extremely large particle surfaces and the small particles can penetrate deep into the biological systems down to the level of individual cells [449]. The medical and pharmaceutical sciences want to use these properties, specifically for new therapy approaches.
5.3.5.2 Principle of Nanostructuring
Nanoparticles, like other fillers, can form a compound with the polymer matrix, e.g. through silanes, Figure 5.322. The special feature here is the large particle surface area, which leads to comparatively wideranging and comprehensive structuring or selforganization of the surrounding polymer molecule chains parallel or perpendicular to the surface, Figure 5.323. The range of the structuring imparted by the particle surface area can amount to a few 100 nm. For the common filler particles in the μm range, this has no effect on the actual basis material (matrix material), since the distances also lie in the μm range and thus are much greater than the range of the structuring, Fig
ure 5.324 (top). With nanoparticles, on the other hand, even the distance of the particles is in the order of magnitude of 100 nm, so that the structured layers in the environment of the particle comprise a large part of the total volume, Figure 5.324 (bottom). Thus, the material on the whole acquires completely new properties. Note: An interactive zone with multiple charge double layers is formed at the surface of a nanoparticle with a diameter of about 10 to 50 nm (Tanaka model [416]): comparatively large bonding forces act on a first layer that is a few nm thick. Deep traps are formed in the second layer of about 10nm thickness. Local microscopic volumes in a third layer of several 10s of nm thickness act as traps for charge carriers and ions. The interactive zones at the particle surfaces not only lead to structuring of the surrounding polymer matrix, but also influence the injection of charge carriers at high local field strengths at the electrodes (Schottky emission).
The structuring imparted by the particles results, for example, in a firm and regular structure of the base material. Polymer chains are immobilized and the glass transition temperatures are shifted. This can manifest itself in higher mechanical strength, in higher thermal resistance, in larger resistance against erosion and in changed electrical properties. 5.3.5.3 Dielectric Properties
The typical electrical and dielectric properties of nanocomposites are substantially
Figure 5.323: Alignment of polymer chain molecules parallel or perpendicular to the surface of nanoparticles (selforganization, schematic).
332
5 INSULATING MATERIALS
changed in comparison with amorphous polymers without structuring [487]. For the application as dielectrics, the following effects are significant: 1.) Increasing the resistance against partial discharges, treeing and erosion as well as the tracking resistance. Owing to the forces in the interactive zones, segmented structures occur from nanoparticles (nanosegmentation) and quite strong bonding forces exist between these (first and second layer). The eroding effect of electrical discharges takes place at first in the spatially limited areas with weaker bonds (third layer).
2.) Reducing the space charge buildup. The negative extensions of the charge double layers of the structured arrangement of nanoparticles increase the potential thresholds at the electrodes for charge carrier injection. The microscopic field stress enhancements caused by space charges are distinctly reduced because of this.
1st layer, 2nd layer, 3rd layer,
~ nm ~ 10 nm ~ 100 nm
3.) Improved strength.
or
unchanged
breakdown
4.) Partly slight reduction of permittivity owing to reduced interfacial polarization and because of immobilization of polymer chains. 5.) Changes in the dissipation factor with temperature and frequency caused by the complex structure of the interfaces and owing to shifts in glass transition temperatures. 6.) Increase or decrease in conductivity. Depending on whether the nanoparticles used act as ion traps or contribute to ionic impurities, charge carrier densities are decreased or increased.
5.3.5.4 Applications
For most of the applications in high voltage engineering, the high costs of nanocomposites are not yet in reasonable proportions to the attainable improvements. However, there is potential for numerous applications and this will increasingly lead to practical applications. Table 5.3.51: Possible applications for nanocomposites [416], [460]
Unstructured base material (matrix) Micrometer particle
Application Motor windings High voltage machine windings Cast resin transformers AC cables
Material Polyimides Epoxides
Advantages PD resistance PD resistance
Epoxides
Capacitors DC cables
PP PE, XLPE
PD resistance, thermal resistance Resistance against treeing Voltage strength Reduction of space charges Tracking resistance, hydrophobicity Space saving
External tion
Insula
Switchtgears
Nanometer particles Figure 5.324: Incomplete structuring of base material by micrometer particles (top) and extensive tructuring by nanometer particles (bottom), schematic representation.
XLPE
SIR PE, Epoxides
Example: A possible application example is enameled wires in converterfed motors, which are subjected to quickly rising repetitive impulses. Partial discharges in the air filled cavities can lead to a progressive erosion of insulation for conventional wires. Wires in which the partial discharge resistance of 15μm thick polyesterminide insulation was significantly increased by nano
5.4 Insulating Liquids
333
Figure 5.41: Compensation of thermal expansion of insulating liquids: a) Hermetically sealed housing (tank) with rectangular cross section. b) Hermetically sealed housing with metallic expansion cell or bellow. c) Hermetically sealed housing with gas cushion. d) Open housing with expansion tank (compensator) and dryer.
a)
b)
particles based on layered silicates (phyllosilicates) have been reported in literature [459]. Even with filling ratios between 1 and 5 %, service life extensions of several orders of magnitude were attained.
5.4 Insulating Liquids The main task of insulating liquids is the impregnation of cavities of all types with a medium that has an electric strength as high as possible. Compared to gases, liquids have the advantage of significantly higher electric strength even under normal pressure. Even the field displacement in the liquid is less owing to higher permittivity. Additionally, in transformers insulating liquids must remove the occuring ohmic heat losses convectively. Note: Earlier, insulating liquids were also used as extinguishing media in circuitbreakers (“switchgear oils”). This application, however, has been pushed to the background since the introduction of compressed gasblast circuitbreakes and vacuum circuitbreakers. Only onload tap changers in transformers operate in oil.
5.4.1 Technology of Insulating Liquids The application of insulating liquids requires proper handling with respect to structural design, processing, impregnation and condition monitoring during operation:
c)
d)
The structural design of a device must take the thermal expansion of the insulating liquid and of other materials present in the device into consideration. The volume expansion coefficient of insulating liquids amounts to ap4 proximately 7 to 10·10 /K. That is, for a temperature enhancement of 100 K, the volume increases by 7 % or even by 10 %.
Rectangular housing cross sections or cooling ribs with walls that can be arched are often used in oilfilled, hermetically sealed capacitors and medium voltage distribution transformers, Figure 5.41a. In hermetically sealed devices with cylindrical cross sections such as in bushings, the volume is compensated by compressible expansion cells or expansion bellows, Figure 5.41b. The same purpose is fulfilled by a compressible gas cushion, e.g. of nitrogen, which has a lower volume, Figure 5.41c. However, the electric strength in this case is reduced owing to the gas dissolving in oil; see Figure 3.4.26 (curves 2 and 4). But the exsolution of gas bubbles from mineral oil with temperature variations under standard conditions is not to be expected [94]. Note: Devices with gas cushions (bushings, capacitors, and instrument transformers) shall not be inclined or may only be inclined to the extent that the gas cannot reach the impregnated insulations ("active parts") and cannot settle there. This is generally applicable even during transportation.
Large transformers compensate the thermal expansion via an expansion tank, which is in
334
contact with the atmosphere via a dryer, Figure 5.41d. Before filling a device, the insulating liquid must be subjected to drying and degassing. For this, the liquid is led into a degassing column under vacuum at increased temperature through a pack of Raschig rings, on which the liquid in thin layers can be degassed over a long period of time (thinfilm degassing) [47], Figure 5.42. The conditions must be chosen in such a way that highly volatile fractions are not distilled off. Mineral oil can be dried at 50 2 to 60 C and 10 mbar to a residual water content of 0.5 to 5 ppm.
5 INSULATING MATERIALS
esses. The parameters to be observed depend on the type and the application of insulating liquid.
5.4.2 Mineral Oil Mineral oils are the most frequently used insulating oils. As low viscosity oils, they are useful in the filling of transformers (transformer oils), impregnation of oil cables (cable Vacuum pumps Degassing column
Note: Along with the degassing of oil, it must also be ensured that insulation to be impregnated is dried. Cellulosebased insulations can hold large quantities of water (depending on the drying state from less than 0.5 to 6 %).
Impregnation process is generally started with a vacuum phase, so that there is no trapped gas any more, Figure 5.42. Then, the insulating liquid is led in. The actual “impregnation” is achieved by a subsequent pressurization. Therefore, the wording “vacuum impregnation” is not quite correct; it should better be replaced by “vacuumpressure impregnation”.
If the housing cannot be completely evacuated (e.g. for mechanical reasons), impregnation based on the capillary effect can still be considered in the case of fibrous insulations. However, the liquid level may only be increased so slowly that there is no occlusion of larger volumes of gas. Even after the impregnation, small gas bubbles can be dissolved in the liquid by diffusion if the bubbles are in contact with a sufficiently large volume of liquid. Voidfree impregnation can be proven by a sensitive partial discharge measurement. Owing to slow diffusion and dissolution processes, this can sometimes only be successfully tested after a waiting time of several days. Insulating liquids in large devices must be subject to a diagnosis on a regular basis to enable the documentation of parameters such as moisture, ageing and any discharge proc
Viewing glass
Tank Capacitor
Figure 5.42: Processing of insulating oil and impregnation of a capacitor (schematic).
H2 H
H
H
H
C
C
C
C
H
H
H
H
C
C
H2
H2C H2
Paraffins
C H2
C
C H2
C
H2
Naphthenes
H C
H
HC
CH
H
H
C
HC
CH
C
C =C
C
H
H
H
C H Aromatics (benzene ring)
H
Olefines
Figure 5.43: Basic constituents of insulating mineral oil (transformer oil).
H
5.4 Insulating Liquids
oils), capacitors, instrument transformers and bushings, as well embedding compact high voltage equipment (e.g. impulse generators, power supplies for lasers and Xray machines). Note: The depletion of reliable crudeoil reservoirs led to the development of gastoliquid oil (GTL) made of natural gas by FischerTropsch synthesis. It guarantees constant properties, high ageing stability and very low electric conductivity. Classic mineral oils are obtained from crude oil by refining, hydrogenation and if necessary, by the addition of inhibitors. They comprise the following as basic components (Figure 5.43): x
paraffins (chain molecules without double bonds) and isoparaffins (with branching),
x
naphthenes (circular hydrocarbons without double bonds),
x
aromatic compounds (hydrocarbons with benzene rings), as well as
x
olefins (chainlike or circular molecules with double bonds).
Long chain paraffins obstruct the flow of oil at low temperatures. Insulating oils that must also be suitable for low temperatures, therefore contain a higher proportion of naphthenes. Olefins are chemically vulnerable owing to unsaturated double bonds and greatly reduce the ageing stability of the oil. Olefins should not be present in substantial quantities in insulating oil. Also Aromatic compounds lead to accelerated ageing on exposure to oxygen and light. They can oxidize to polar molecules, can add ions or other molecules, can also chemically bond once the double bonds are broken or can cross link with one another. Aromatic compounds also even have the advantageous property of gas absorbing behavior, i.e. the molecules adsorb hydrogen under the effect of partial discharges (see Section 3.4.3). Gas absorbing aromatic oils are therefore often used in hermetically sealed insulations that are electrically highly stressed (e.g. for capacitors and bushings with very high field strengths at the
335
edges of metallic foils). Special ageing resistant oils are preferred in transformers owing to the influx of air, to higher temperatures and to the catalytic effect of conductor materials. Ageing stability is achieved by naphthenebased oils and chemical inhibitors. Note: After refining at 180 to 200 °C, the mineral oil comprises, depending on the origin of the oil, especially paraffins and naphtenes as well as a larger proportion of monocyclic and polycyclic aromatic compounds (approx.. 20 %). By hydrogenation, the double bonds of aromatic compounds can be saturated by the addition of hydrogen and are thus converted into considerably more stable naphthenes. A steam pressure of 50 to above 100 bars is built up at increased temperature for this and the reaction must be catalytically accelerated. For producing special gas absorbing oils, monocyclic aromatic compounds can again be added which are slightly more ageing resistant than the originally available aromatic mixture. The reduced ageing stability of gas absorbing oils can be improved again by the addition of inhibitors, but this is used up through oxidation during the course of time, especially under the effect of oxygen. Since insulating oil is obtained from natural mineral oil, even small quantities of sulfur are present in it at first. The socalled corrosive sulfur can attack the conductor materials. Therefore it is now common practice to eliminate the corrosive sulfur from the oil.
The ageing of mineral oil largely takes place through different oxidation mechanisms that require the presence of oxygen and the effect of heat, radiation or partial discharges, Figure 5.44. Copper catalytically accelerates the reaction; therefore, it should not be laid as a bare conductor in the oil. The dissipation factor increases irreversibly owing to the integration of polar OHgroups. Acids and insoluble oil sludge are formed. The oil resinifies owing to cross links over oxygen bridges. Water is produced as a condensation product and reduces the electric strength. A particularly dangerous reduction in electric strength is caused by the formation of socalled Xwax: under the effect of partial discharges or of very high alternating electric field strengths, any available oxygen oxidizes the oil molecules. These are then crosslinked under prolonged stress. An insoluble wax as well as hydrogen gas are formed; the gaseous form can be separated and destroys the electric
336
5 INSULATING MATERIALS
strength. Xwax is observed, for example, in older oil cables, at the metallic foil edges in AC capacitors and impulse capacitors, in delaminated resinbonded paper bushings with infiltrated oil as well as in incompletely impregnated insulations. The following methods can be used for the analysis of oil condition:
Breakdown measurements can only identify heavy wetting of oil. The direct determination of moisture through titration (Karl Fischer titration) is more significant. However, the cellulosebased insulation frequently extracts the moisture from oil and hence high moisture
Mechanism a) Breaking double bonds and addition of polar groups (oxidation): + ½ O2
C =C
C
+ ½ O2
H
C
H
O2
+ C
O
H
+
+
C
C H 2O
Moreover, the ageing condition can also be determined from neutralization of free acids (neutralization number) or free and bonded acids (saponification number) by potassium hydroxide. An oil change is generally recommended when the neutralization value for 1 g of oil exceeds the value of 0.5 mg of KOH.
Note: Gasinoil analysis, i.e. the analysis of gases dissolved in oil, does not give any direct
Consequences
Measures *)
Dissipation factor irreversibly increases due to polarization losses.
Use of oils with low percentage of unsaturated hydrocarbons (olefines).
C
*) see below Dissipation factor increases due to polarization losses. Decomposition products, acids, oil sludge.
OH
c) Oxidation and polycondensation (effect of PD, UV or light): C
Ageing (Oxidation) of oil can also be recognized from enhanced values of the dissipation factor tan G, Figure .5.45.
Crosslinking and gumming.
OH
b) Oxidation of oil molecules (effect of PD, UV or light): C
values occur only in extreme cases.
The breakdow strength reduces due to the synthesis of water, conductivity and dissipation factor increase, see Figures 3.34, 4.25 und 4.210. Crosslinking leads to formation of oil sludge and gumming.
OH + C
O
H C
crease in volume and gas formation (hydrogen) through crosslinking.
C
+
H2
*) General measures:
By drying of oil, breakdown strength, conductivity and dissipation factor can (partially) be regenerated. *) see below
d) Xwax formation (high alternating field strengths, effect of PD): 1.) Bonding of oxygen through oxi Irreversible increase in polarization dation of oil molecules, see b). losses due to oxidation. 2.) Subsequent crosslinking: Gumming, formation of Xwax, deC
Regeneration through fuller's earth treatment is only possible to a limited extend. *) see below
Paritial discharge free design. Voidfree impregnation. Use of gasabsorbing oils.
*) see below Closure against influx of air or access to oxygen and moisture, as well as measures against the effects of PD, UV, light and catalysts (copper). Application of inhibitors which break the oxidation chain.
Figure 5.44: Ageing of mineral oil by oxidation processes.
5.4 Insulating Liquids
337
are at lower risk of ageing and hence even the use of gasabsorbing oils with a high content of aromatic compounds is possible.
1
10
2
10
The electric strength and dielectric properties of mineral oil have already been described in Section 3.4 and Chapter 4. In particular, see Figures 3.31, 3.4.12, 3.4.21, 2, 4, 5 and 6, Table 3.4.21 and 3.4.31 and Figures 4.22, 5, 6, 7, 9 and 11.
Aged oil
tan G 3
10
New oil
4
10
30
30 T /°C
60
Figure 5.45: Dissipation factors of aged transformer oil and of new transformer oil [23].
information about the condition of the oil, but it indicates the defects in the device. For example, it can distinguish between electric arcs, partial discharges, overheating in different temperature ranges and decomposition of cellulose [95]… [100]. This and other methods of analytical and electrical diagnostics are described in Section 6.4. The regeneration of aged mineral oils is possible to a limited extent. Dissolved gases and moisture can be completely eliminated by drying or degassing. Polar components which increase losses can be partially absorbed by a specially prepared bleaching clay (fuller’s earth, aluminum silicate). Gumming (resinification) and Xwax formation can no longer be reversed. Ageing of insulating oils is a major problem in highly thermally stressed transformers in which the oil is in contact with the atmospheric oxygen through the expansion tank. Preventive measures against ageing are the encasement of copper based conductors, the utilization of oils with ageing stability having low content of aromatic compounds as well as the use of inhibitors, which break the oxidation chain and get attached to the oil molecule. Inhibitors are consumed over time and must be replenished. Oils in hermetically sealed devices (bushings, capacitors, converters, hermetically sealed transformers and apparatus)
5.4.3 Synthetic Insulating Liquids Synthetic insulating liquids are generally applied owing to special properties that are not provided by mineral oils. 5.4.3.1 Polychlorinated Biphenyls (PCB)
Polychlorinated biphenyls were used as fire resistant insulating liquids and cooling liquids in transformers and as impregnating agents of higher permittivity (Hr = 4 .... 6 at 20 °C and 50 Hz) in capacitors. They can be bioaccumulated and are difficult to biodegrade. Moreover, under the effect of great heat, highly toxic decomposition products (dioxins) are formed. Hence, the production of PCB was stopped in the Federal Republic of Germany in 1983 for example. Existing devices had to be replaced or filled with nonhazardous liquids while observing limiting concentrations. Disposal is carried out by high temperature incineration. 5.4.3.2 Silicone Liquids ("Silicone Oils")
Silicone liquids consist of linear polymers of limited length without spatial crosslinkages. The macromolecule consists of an inorganic skeleton with Si and O atoms that is enclosed by methyl groups, for example, Figures 5.317 and 5.46. Often silicone liquids are also called “silicone oils”. Silicone liquids are characterized by a high flash point (> 300 °C according to ASTM D
338
5 INSULATING MATERIALS
92) and a high fire point (> 335 °C). These values are twice as high as for mineral oils. Moreover, silicone liquids are chemically stable and thus ageing resistant. Even in the presence of air, at 150°C silicone liquids have practically unlimited stability [88]. Compared to mineral oil, thermal transmission properties are not so favorable; the volumetric thermal 3 expansion coefficient is higher (10 /K). Physiologically, toxicologically and ecologically, polydimethylsiloxane (n = 35) is considered as nonhazardous; it decomposes in the environment into nonhazardous decomposition products of water, carbon dioxide and silicic acid [101]. Similar to mineral oils, the classification is according to the German water polluting category WGK 1 (mild water pollutant) for example.
At Hr = 2.7 (20 °C)... 2.3 (200 °C), the permittivity is slightly higher than that for mineral oil. The dissipation factor varies only slightly over a wide frequency and temperature range (up to 10 MHz and up to 200 °C respectively) 4 and is very low at tan G = 1 ... 2·10 . Silicone liquids have a slightly lower electric strength than mineral oils. Moisture has a similar strength reducing influence. Lower electric strength for larger oil gaps is a disadvantage for their application in high voltage transformers. Owing to its high pricing, silicone liquid is only used as an insulating liquid when it is necessary on the basis of thermal stress or as fire protection. Furthermore, silicone pastes made of silicone liquid with silicic acid are useful for hydrophobizing of porcelain sur
CH 3 O
Si CH 3
CH 3 O
Si CH 3
CH 3
CH 3 O
Si CH 3
Figure 5.46: Polydimethyl siloxane.
O
Si CH 3
faces. However, the effectiveness is limited in time. Instead of regular renewal, using a SIR composite insulator is often preferred, see Section 5.3.4.
5.4.3.3 Other Organic Liquids
Synthetic insulating liquids for transformers are preferred over mineral oil, especially when thermally resistant, flameretardant or environmentally compliant substances that are not hazardous to water are required. Along with silicone liquids, ester liquids [102] which have already been tried and tested in distributing transformers are especially considered. Pentaerythritol tetraester C(CH2  O  CO  R)4 (e.g. "Midel 7131" [101], [103]) is produced by esterification of the tetraalcohol pentaerythritol and monocarboxilic acids [488]. As compared to mineral oil, higher permittivity Hr = 3.3 and a slightly higher dissipation factor 3 tan G > 10 are observed. Owing to thermal ageing at 150 °C, tan G increases within 2000 h by about a factor of 10. The electric strength is at comparable values. However, owing to a high water absorption capacity (2700 ppm at 20 °C), it is only dependent on water content to a very small extent up to 500 ppm. This also applies to the dissipation factor. It must be noted that there are a low pour point of 50 °C and high values of flash point (257 °C) and fire point (310 °C) which are almost double the values of typical mineral oils. Insulating liquids for capacitors are today less used in the impregnation of paper, but are increasingly used for the impregnation of very lowloss film dielectrics (allfilm dielectrics) with lower permittivity. The high permittivities of polychlorinated biphenyls (PCB) are therefore no longer necessary. Frequently demanded properties are a low viscosity for the impregnation of films placed one upon another, a high electric strength for withstanding
5.4 Insulating Liquids
339
strengths up to 100 kV/mm (1 Minute, 50 Hzr.m.s. value, in the area of the uniform field at d = 50 μm). This implies that electric strengths that are about twice as high as those in mineral oilimpregnated paper can be attained.
Winding on mandrel (circular winding)
Stacking in insulation frame
Loose flat pressing (flat winding)
Drying and vacuum impregnation
Repressing
Figure 5.47: Production of allfilm capacitors with synthetic liquids (schematic).
the high edge field strengths at the metallic foil edges and a high gasabsorbing capability. For a long time, polyisobutylene ....  CH2  C(CH3)2  .... has been used as a chemically resistant impregnating agent for cables, capacitors and metal paper (MP) capacitors. It has similar properties to mineral oil (Hr = 2.2). The viscosity depends on the chain length [88].
Thermally stable, low viscosity insulating liquids with a high gas absorption capacity comprise benzene rings, i.e. they have an aromatic character. Examples of this are mentioned as dodecyl benzene from the series of alkyl benzenes, phenylxylylethane (PXE), monoisopropylbiphenyl (MIPB), benzyl neocaprate (BNC), ditolylether (DTE, "Baylectrol 4900", from Bayer) as well as mixtures of mono benzyl toluene and dibenzyl toluene (M/DBT, "Ugilec", "Jarilec", from Prodelec) [16], [104] to [107]. Furthermore, there are also fluorinated and chlorinated insulating liquids. Capacitors with allfilm dielectrics are mainly used as compensation capacitors owing to their low losses for AC voltage. They are considerably less sensitive to increased power loss for distortions than paper insulated capacitors. Allfilm dielectrics with synthetic insulating liquids can be stressed partially with field
Note: The dielectric strength in capacitors is not determined by the field strengths in the homogeneous area of the dielectric, but by the sharply increased field strengths at the edges of the conductive foils, see Figure 2.420.
Owing to a compact method of construction, employing expensive insulating materials is useful even for other applications, such as for grading capacitors, impulse capacitors or measuring capacitors. By choosing suitable insulating materials, the temperature dependence of precision capacitors can be partly compensated. The impregnation of allfilm capacitors requires a raw or punched film surface and a loose assembly of the capacitor winding to ensure an adequate “space factor” for a surface covering penetration of the impregnating agent, Figure 5.47. Circular windings that were wound on a mandrel are pressed into loose flat windings with adequate space factor after the removal of the mandrel. Several flat windings are stacked in an insulating frame, electrically connected via inserted metal strips (reed contacts), dried under vacuum and impregnated under vacuum, see Figure 5.42. The capacitor pile is pressed in the impregnated condition. A paper insulated capacitor can be pressed already after drying since the fibrous structure of the dielectric ensures the absorption of the liquid, see Figure 5.36 and Section 5.3.2.3.
5.4.4 Vegetable Oils and “Natural Ester Liquids” In the initial stages of high voltage engineering, resin oils were used as voltage resistant impregnating agents for transformers [81]. But owing to their low ageing stability and their inclination to gumming, they were very soon
340
replaced by mineral oils. Nevertheless, there are still a few applications of vegetable oils for insulation, Section 5.4.4.1. Note: Nowadays, vegetable oils are mainly used as raw materials for the manufacture of wire enamels and impregnating resins, based on polyester resins and polyurethane resins. Linseed oil, wood oil, soya oil, ricinus oil and turpentine oil are used for this [88].
Meanwhile, there is a strongly increasing interest in socalled natural ester liquids which are made of renewable raw materials (seed oils) and which provide a number of very favorable properties such as biodegradability, noninflammability, no hazard to water, low viscosity and sufficient electric and dielectric properties as well as sufficient ageing stability, Section 5.4.4.2. 5.4.4.1 Vegetable Oils Ricinus oil has until now been an important electrical insulating material for DC voltage capacitors and impulse capacitor. High permittivity at Hr = 4.5 is advantageous for capacitive energy storage of high energy density for this. Moreover, impulse capacitors with ricinus oilpaper insulation have an about ten times longer service life than capacitors with mineral oilpaper insulation. The field strength reduction at the sharp foil edges for impulse stresses owing to the higher permittivity is considered responsible for this. Moreover, it is assumed that the viscous ricinus oil cannot be as easily eliminated as the viscous mineral oil owing to electrostatic alternating forces on the metallic foils, and hence the formation of partial vacuums and gas bubbles is hindered. Furthermore, ricinus oil could have higher resistance to partial discharges occurring during the impulse discharges at the foil edges. However, the erosion of insulation for impulse discharges is also greatly determined by the resistance of the paper or the film to partial discharges.
The dissipation factor of ricinus oil is about 5 times higher than the dissipation factor of mineral oil. The dielectric properties are also strongly temperature dependent. Hence, ricinus oil is not used for AC voltage stresses but more for DC voltage stresses and impulse
5 INSULATING MATERIALS
voltage stresses as well as for insulation in physical devices and in laboratories [22]. Ricinus oil must be dried, filtered and treated with fuller’s earth and activated carbon. Owing to high viscosity, impregnation is possible only at increased temperatures. The advantage is that the high viscosity prevents the leakage of an impregnated winding at room temperature. Ricinus oil solidifies at 10 to 18 °C and therefore cannot be used at low temperatures. Meanwhile, even rapeseed oil is also considered as insulating liquid for high voltage devices owing to the growing interest in renewable and biodegradable raw materials. The electric strength corresponds to approximately that of mineral oil at the same relative moisture, whereby the water absorption capacity of rapeseed oil is more than a factor of 10 greater than that of mineral oil. The requirements for the breakdown strength of new oils are fulfilled. The dissipation factor is about a factor of 10 greater than that of mineral oil. Thus, the dissipation factors at 90°C are far above the (for mineral oil!) stipulated value of 0.5% [399]. Experiments with a 20kV/250 kVA distributing transformer have in principle shown the suitability of rapeseed oil as a cooling medium and insulating medium [400]. Note: In the comparative ageing tests on the transformerboard that was impregnated with mineral oil or with ageing stabilized rapeseed oil, the boards impregnated with rapeseed oil and the associated oil unexpectedly aged slower than the conventional comparative samples [401]. However, based on the structure of rapeseed oil, a comparatively lower ageing stability was expected.
5.4.4.2 Natural Ester Liquids
Pure vegetable oils (seed oils) are biodegradable, difficult to inflame and not hazardous to water. Unfortunately, viscosity is comparatively high and ageing stability is insufficient for many applications. These drawbacks can be overcome by the socalled “natural ester fluids”. The denomination as “natural ester fluid” might be misunderstood, the final product is
5.4 Insulating Liquids
not natural, it is a result of chemical processing, but the raw materials are natural seed oils. Easily available seed oils (e.g. rapeseed, soya, sunflower) are used as renewable raw materials. From these, a triester is produced by esterification of trialcohols and fatty acids. A further processing allows the generation of monoesters by a transesterification reaction. The final product consists of monoesters, of triesters or of mixtures from monoesters, triesters, seed oils and inhibitors [488], [489], [490]. Depending on the raw materials and process technology, properties of natural ester fluids can vary in a wide range. Low viscosity and good lowtemperature behavior can be achieved by a high percentage of unsaturated fatty acids. Improved oxidation stability is possible by a high percentage of saturated fats. An optimized balance of different seed oils and additives provides insulating liquids that have a high environmental safety, high fire safety, compatability with transformer materials, sufficient oxidation stability, low viscosity, low pour point and good electrical properties [489]. Therefore, natural esters are already widely used in distribution transformers, especially for environmentally sensitive applications. The usage for high voltage transformers as well as for retrofitting of aged transformers is possible and is tested. However, natural ester fluids are not completely equivalent to mineral oils; there are the following basic similarities and differences [489] [290] [491] [292]: x
The breakdown strength is comparable, but a higher sensitivity to electrode surface area is reported (area effect).
x
Dissipation factor (a few percent at 90 °C) and acidity are higher and increase significantly during ageing.
x
Natural esters are less stable with respect to oxidation, protection against the access of oxygen might eventually be necessary.
341
x
Natural esters dissolve much more water than mineral oil (approximately 200 to 1000 ppm at 20 °C), therefore, new equilibrium diagrams for liquid and solid insulations have to be established [492].
x
The viscosity is higher, therefore natural ester fluids are less efficient for the convective heat transfer in transformers.
x
The pour point is higher, therefore the lowtemperature limit has to be chosen accordingly.
x
The flash point is higher.
x
The biodegradability is much better, i.e.degradation is faster.
In any case, the limits of the individual (natural) ester formulation have to be considered carefully.
5.4.5 Water Water has a high electric strength for voltage stresses of very short duration, and it complies with the impulse voltagetime characteristics of other liquid insulating materials. Êbd50 amounts to about 40kV/mm for a breakdown time of 1 μs and falls to about 20 kV/mm for a breakdown time of 10 μs. For stresses of long duration, water is heated and vaporized even at low field strengths owing to its high conductivity, and this initiates the breakdown [22]. Water has a high permittivity at Hr = 81 owing to its highly polar molecule. Under completely deionized conditions, the conductivity due to the dissociation of water molecules amounts to 7 about N = 10 S/m, and this corresponds to a selfdischarge time constant W = HN = 7 ms. In contact with air, the conductivity increases owing to the dissolution of CO2 and the formation of dissociated carbonic acid up to 4 about N = 10 S/m, and this corresponds to a selfdischarge time constant W = HN = 7 μs. Therefore, energy can only be stored in water
342
insulated capacitors for a very short period of time. Note: Breakdown strength and specific resistance can be distinctly increased by mixing with ethylene glycol [475]. The bivalent alcohol C2H4(OH)2, known as an antifreeze compound and a solvent, is highly polarizable like water but does not form ions. For a proportion of approx. 70 %, the breakdown strength increases by 6 about 39 %, conductivity decreases from 8 10 ·S/m to 6 2.5·10 S/m and permittivity falls from about 80 to 68.5 [475]. As per Eq. (2.113), an increase in the energy density by approx. 48 % is associated with it. An increase in the selfdischarge time constants through reduced conductivity and lowering of the freezing point is also of advantage. The toxicity of ethylene glycol must be considered.
An important application is the highpower impulse technology (pulsed power technology) described in Sections 2.6.3.3, 6.2.3.7 and 7.4.2. Under this, very compact water insulated lines are charged within about a few μs from conventional capacitor batteries by oscillation. At a voltage maximum, the lines are discharged within a few 10 ns as a travelling wave. This results in an extreme space and time compression of the stored energy that is required for basic physical research and for ignition impulses in nuclear fusion experiments [14], [15], [40], [42], [43], [108]. Water is also used as a switching medium in spark gaps. By discharging an energy storage capacitor, the electrically stored energy can be quickly transformed into the energy of an acoustic shock wave in a water insulated spark gap. In medical technology, this is useful for destroying renal stones, in production technology for material transformation and in recycling for separating material fractions. Moreover, the pulse power technology described above is also used for water insulated pointtopoint spark gaps (made of rods). The breakdown time depends on the distance of the electrodes and on the magnitude and profile of the applied voltage. Furthermore, in high voltage engineering, water resistors are used for current limitation and as filter elements in high voltage circuits or as load resistors in impulse voltage circuits. Ow
5 INSULATING MATERIALS
ing to the corrosion hazard at the electrodes and to the probable separation of gas, the use of transparent pipes or tubes is recommended. The conductivity should be adjusted in a defined manner by the release of small quantities of salt (for copper electrodes, for example, with copper sulfate CuSO4). During the design stage, the adequate removal of resultant heat must be ensured. Water is also used for potential grading for cable tests in cable test terminations, Figure 5.48. Under this, the resistance must be adjusted in such a way that there is no overloading of the voltage source and the heat losses can be dissipated.
5.4.6 Liquefied Gases For the utilization of superconductivity in power engineering (see Section 7.5), an impregnating agent suitable for low temperatures is necessary [111]. All the technically applied insulating liquids today can only be used for temperatures above approx. 60 °C. For use at lower temperatures, liquefied insulating gases such as sulfur hexafluoride (LSF6, liquid SF6), nitrogen (LN2, liquid N2) and helium (LHe, liquid He) are available for example. For LN2 and LHe, strengths that can be compared with other liquid insulating materials are specified [109], Tab. 5.41. Table 5.41: Breakdown strengths of liquid gases at normal pressure given as 63% value (peak value). Breakdown probabilities under 1% must be expected to occur at about half of the specified values [109]. Arrangement
Êbd63 (LHe)
Êbd63 (LN2)
Spheretoplane (D = 50 mm, d = 1 mm) AC (60 Hz) DC positive DC negative
39.0 54.5 50.9
68.5 kV/mm 72.4 kV/mm 74.4 kV/mm
Coaxial cylinders (L = 100 mm. d = 2.3 mm) AC (60 Hz) DC positive DC negative
19.7 20.4 19.2
23.1 kV/mm 23.9 kV/mm 24.0 kV/mm
5.4 Insulating Liquids
343
LN2 d=
LSF6
05 mm
Êbd = 80 kV/mm
90 kV/mm
Guarding toroid on the high voltage side
1 mm
55 kV/mm
90 kV/mm
2 mm
40 kV/mm
90 kV/mm
Water resistor
5 mm
30 kV/mm
90 kV/mm
10 mm
25 kV/mm

20 mm
19 kV/mm

XLPE cable insulation Conductor
Outer semiconductive layer Guarding toroid at the ground side
Cable
The strength of liquefied insulating gases is heavily dependent upon pressure. Strengths are specified for LSF6, which approximately correspond to that of gaseous SF6 with the same density as that which occurs for the respective pressure above the liquid [22]. The use of hightemperature superconductivity enables insulation with LN2, whose boiling point is 77K under normal pressure. This enables the heat removal capacity to be reduced approximately by a factor of 100 in comparison with LHe with a boiling point of 4.2 K. For the volume effect and area effect, exponents (0.148 and 0.172 according to [109]) were determined that are smaller than the exponents assumed for the distance effect in insulating oil (approx. 0.37), Figure 3.4.26. For LN2, the following is given as the empirically determined distance effect 331], [332].
Figure 5.48: Cable test termination (schematic).
Ebd(DC) = (29 kV/mm) · (d/mm) Breakdown is initiated by thermal gas bubbles [110]. This leads to a pronounced volume effect and area effect, as well as to a large dispersion of breakdown field strengths. Therefore, low breakdown probabilities of < 1 % must only be expected at much lower field strengths (about half of the above mentioned values) [109]. For a larger range of flashover distances, the following breakdown field strengths Êbd (peak values) are given in a spheretoplane arrangement (D=50mm), for LN2 under normal pressure and for LSF6 at 22 bars [22]:
0.2
(5.4.61)
The breakdown is initiated by thermal gas bubbles at the electrode surfaces and in the volume. In contrast to insulating oil, bubble formation in LN2 is unavoidable: While operating close to the boiling point, it is not only the heating at quenching (loss of superconductivity), but probably even the AC losses in operation (which cannot be totally avoided even for superconductivity, see Section 7.5) that leads to bubble formation at the conductor surface. The design of the insulation, therefore, must also take into consideration the presence of bubbles that can be noticed from a distinct reduction in the breakdown voltage,
344
5 INSULATING MATERIALS
V / kV (DC) 60
Breakdown voltage d
40 Natural convection of LN2 20 Start of boiling
D
Bubble motion determined by the field forces Bubble motion determined by buoyant forces Heating power
Figure 5.49: Influence of thermal gas bubbles on the breakdown behavior of LN2 in a cylindertoplane arrangement with d=2mm and D=10mm. The grounded, horizontally placed cylinder was heated [332].
Figure 5.49. The bubbles deform under the effect of the electric field and form chains [332]. Thus, the electric strength approximates to the value of gaseous nitrogen (GN2), very rapidly for small gaps (< 0.5 mm) and slightly slower for larger gaps (> 1 mm) with intensified heating and intensified bubble formation [333]. Approximately comparable profiles were determined for the strength for AC, DC positive and DC negative (for peak values, see also [333]). In the case of impulse voltage, a fundamentally different characteristic is seen: during the liquid phase  similar to insulating oil  the impulse strength is far above the AC strength (a factor of 1.5 relative to the AC peak value and 2.2 relative to the AC r.m.s. value [333]), but the strength reduces in the gas bubble phase to the value of the gas strength, so that there is no significant difference between impulse strength and ACstrength, Figure 5.410. There is no distortion of the gas bubbles for impulse voltage stress, and hence the decease is slower, i.e. only for higher heating power. But basically it is ascertained that thermal gas bubbles especially lead to loss of high impulse voltage strength!
The effect of bubbles in LN2 is less hazardous than in insulating oil: however, owing to a low permittivity of Hr = 1.44 in spherical bubbles, the field stress enhancement amounts to only about 11 % (for AC and impulse voltages). Furthermore, the gas density of bubbles in the low temperature range at about 77 K is approx. 3.8 times higher than at the room temperature of 293 K. According to Paschen’s law, this leads to a significantly higher electric strength owing to correspondingly reduced free path lengths, Section 3.2.2.4. Measurements have been reported, according to which even the ACstrength in LN2 in the range of 0.5 to 1 mm, approximately follows Paschen’s law for GN2 at 77 K (Êbd = 12.5 kV/mm for d = 1 mm [333]). Other sources also recommend the strength of nitrogen gas at 77 K to be chosen as the limiting value [334] (AC r.m.s. value: 6.4 kV/mm, LI peak value: 15 kV/mm, for d = 10 mm in each case). Measures for increasing the electric strength would include preventing the formation of bubbles by having operating temperatures far below the boiling point (the lower limit is the melting point of nitrogen at 63 K) as well as by increasing the pressure, which delays boiling and increases the strength [335].
60
Û Vbd50% / kV (Peak values) LI 1.2/50 μs pos./neg.
Horizontal cylinder (grounded and heated) vertical plane
40 AC
DC pos./neg.
20 Initial boiling point Heating power
Figure 5.410: Reduction of AC voltage strength and loss of impulse voltage strength under the effect of thermal gas bubbles in LN2 in a cylindertoplane arrangement with d=1 mm, D = 10 mm and l= 20 mm [333].
5.5 Fibrous Materials
5.5 Fibrous Materials Impregnated paper and impregnated pressboard consisting of fibrous materials are used as dielectrics and dielectric barriers in capacitors, cables, bushings, instrument transformers and transformers. Plates, tubes and other molded components are largely used in transformer construction as dielectric barriers. Fibrous materials are one of the most important insulating materials of high voltage engineering. The properties must always be considered with regard to an impregnating agent, Figure 5.51. In combination with mineral oils or other insulating liquids, high electric strengths can be attained by impregnation of cavities and pores between the fibers. Without impregnation, fibrous materials possess unacceptably low strengths. Note: Although the strength of papers can also be increased by compressed gases, it is less common. The high impregnability of gases allows the use of electrically resistant foils with lower permittivity and accordingly less field displacement into the gasfilled gaps.
The main component of paper and pressboard is cellulose (Section 5.5.1), for which shortterm temperatures up to 120 °C can be allowed, but this ages unacceptably fast for operating temperatures above 90 °C. Higher temperatures are possible with synthetic fibrous materials (Section 5.5.2).
5.5.1 Paper and Pressboard Paper and pressboard acquire their electric strength only by impregnation with insulating oil, Section 5.5.1.1. The actual insulating materials are therefore not paper and pressboard, but oilimpregnated paper OIP and impregnated pressboard. Dielectric properties are dependent on a series of different parameters, Section 5.5.1.2. Significant reductions in strength are possible as a result of ageing and absorption of water (or moisture resp.), therefore condition assessment is of great significance for OIP, Section 5.5.1.3. The special
345
features of OIP dielectrics must be taken into consideration during manufacturing and processing, Section 5.5.1.4. 5.5.1.1 Electric Strength
The high electric strength of impregnated fibrous materials depends on the barrier effect of fibers, which subdivide the volume into a large number of very closely placed oil gaps or pores with high electric strength, Figure 3.4.26. For a theoretical assessment of partial discharge inception field strengths in oilfilled pores of impregnated paper or pressboard, see Eq. (3.4.21), case (1) and (2), Table 5.51. Table 5.51: Theoretically estimated partial discharge inception field strengths (r.m.s. values) in the oil filled pores of impregnated paper or pressboard. Oil condition
degassed
gassaturated
EPDI
EPDI
kV/mm
kV/mm
1 μm
270
220
3 μm
180
148
10 μm
115
95
30 μm
76
64
Pore width
Under this, pore widths in the range of 1 ... 3 μm are associated with thin, highly compressed insulating papers, and pore widths of 10 … 30 μm are associated with less strongly compressed, thicker materials. These inception field strengths in the pores are attained owing to field displacement even for lower mean field strengths. In the ideal case, a spherical oil filled pore, according to Figure 2.422 and Eq. (2.438), increases the field strength in oil by about 25% relative to the surrounding cellulose. This implies that the following is valid:
Efiber
245 kV), Tables 6.12 and 3. Note: Other or extended specifications can be made for specific operating equipment for the respective conditions to be covered, e.g. see Section 7.1.3.5 (Transformer Tests). In special cases even tests with DC voltages, with nonpowerfrequency AC voltages or with special impulse voltage shapes are necessary, such as for example for HVDC transmission components, DCvoltage operated devices, cables or impulse capacitors, see Figure 2.2.4.
6.1.4.2 High Voltage Tests
Depending on the function of the insulation, high voltage tests for the proof of dielectric strength require the application of test voltages between phase and earth (phasetoearth or linetoground insulation), between energized conductors (phasetophase or linetoline insulation) or between different points of the grid (longitudinal insulation), Figure 6.13. In threephase AC systems, the linetoline insulation is the insulation between the phases in most of the cases. In the follwing, test voltages are described for threephase AC systems. L3
L2 Phasetophase (linetoline) insulation Phasetoearth (linetoground) insulation Longitudinal insulation Figure 6.13: Insulations in a threephase AC system that have to be tested, phase L1 is chosen as an example.
L1
Generally, high voltage equipment is characterized by a socalled nominal voltage Vn, e.g. by Vn = 380 kV or 400 kV. Due to the requirements of insulation coordination, the rating of the insulation is determined by the highest voltage for equipment Vm within the considered group of similar nominal voltages, that is Vm = 420 kV for the example mentioned above [498]. The standardized withstand voltages for high voltage tests according to Tables 6.12 and 6.13 are related to this value, and the tests should show the compliance of the insulation with the rated voltage Vr. The general standard IEC 600711 gives the following possibilities, x x x x
shortduration AC voltage tests, switching impulse voltage tests, lightning impulse voltage tests and combined voltage tests.
Tests for steepfront impulse voltages should be specified in the standards for special devices. For the insulation levels specified in the standards, in the case of non selfrestoring insulations, it is a socalled assumed conventional withstand voltage, for which no breakdowns are permitted. In the case of selfrestoring insulations (e.g. pure gas gaps), a statistical withstand voltage with a specific number of breakdowns can be allowed. Verification is achieved by high voltage tests in the form of type tests, routine tests or special tests based on test programs given in the standards or agreements. Lower test voltages are often stipulated for repeat tests, e.g. after long lasting operation. For a reference voltage, different test voltage levels that correspond to different degrees of safety are mentioned. The selection of the test voltage level is based on the amplitude of the overvoltages to be expected, which can vary, e.g. based on the neutral point treatment. Moreover, different rated withstand voltages apply depending on the operating equipment. For example, higher values are stipulated for isolating distances than for high voltage de
6.1 Quality Assurance
363
vices (insulators, bushings, power transformers, instrument transformers, cables, …). Requirements for neutral point insulations and insulations in rotating machines are lower. In many cases, a higher withstand voltage must be proven for the internal insulation of an equipment than for the external insulation which often can flash over without causing irreversible damage. Details are obtained from the specialist literature [498] and from the applicable standards and specifications agreed between the manufacturer and customer. 6.1.4.3 Surge Arresters
a) Application of surge arresters Using surge arresters for the protection of operational resources is especially required, if 1.) Protective spark gap
Vpl
lightning overvoltages or high switching overvoltages are to be expected. The protection parameters of arresters must be coordinated with the electric strength of the insulation [124], Figure 6.14. The protection levels Vpl and Vps for lightning impulse voltages and switching impulse voltages must be much below the rated withstand voltages of the insulation to be protected, so that overvoltages are definitely limited to values for which there is only a negligibly small probability of an electrical breakdown of insulation in the network. Here we refer to protective ratio. Note: Besides, the protection level must be significantly higher than the permanent operating voltages, in order to avoid a faulty response or overheating owing to leakage currents. The selection of a surge arrester thus represents an optimization task; some usable data are presented as an extract in Table 6.14 [124].
A protection level is defined by the maximum 3.) Metaloxide arrester
2.) Valvetype, nonlinearresitortype or sparkgap arrester SiC
ZnO
v
v
v
Rated withstand voltage (insulation level)
Rated withstand voltage (insulation level)
Rated withstand voltage (insulation level)
Vso
Vso Sparkover voltage Vm
Impulse current (kA)
Vex Short V m
circuit current
v,i response characteristics
Vres
Vres Vr
Extinction voltage
Vex= Vr
Operating voltage
8/20 μs Impulse current (kA)
Rated voltage 8/20 μs Operating voltage Impulse Leakage current current (μA ... mA) (kA)
Vm
i
i
i Vso
Sparkover voltage or Vres residual voltage
Vres Residual voltage
Network protection
Vex Extinction voltage
Vr
No
No
Leakage current
Protection level
Vso Sparkover voltage
Extinguishing Permanent current
Figure 6.14: Functional principles of different overvoltage protection elements.
Rated voltage
364
6 TESTING, MEASURING AND DIAGNOSIS
voltage occurring at the arrester. This is either the sparkover voltage Vso of spark gaps or the maximum residual voltage Vres occurring during the leakage impulse current, which results as a voltage drop at the nonlinear resistors, Figure 6.14. Note: In the context of insulation coordination, the values Vso and Vres respectively can be considered as representative over voltages at the location of the arrester. Thus, they are always significantly below the rated switching impulse withstand voltages and rated lightning impulse withstand voltages which are applied to verify the insulation level of the insulation to be protected, as in Figure 6.12. Note: Generally, arresters are installed between the conductor and ground. The protection levels Vpl and Vps thus correspond to the representative linetoground overvoltages. Note: In the case of overvoltages that increase rapidly, arresters have only a protection zone that is limited in terms of line length, Section 2.6.3.2. For this, according to Figure 2.617 and Eq. (2.622), higher representative overvoltages Vrp can occur depending on the transit time W between the arrester and the object to be protected and depending on the rate of rise in the overvoltage wv/wt. These overvoltages can be above the sparkover voltage or the residual voltage and above the lightning impulse voltage level Vpl of the arrester [123]: Vrp
Vmax
Vpl 2 'v Vpl 2 W
wv wt
(6.16)
Therefore, a short, lowinductance connection of the surge arrester is required. Data about the coordination withstand lightning impulse voltage Vcw resulting from Vpl and about a protection zone Lp derived from a lightning strike rate and an acceptable error rate are specified in the standards, [124].
Overvoltage impulses give rise to large pulsed leakage currents. The currentcarrying capacity or the energy consumption capacity of an arrester is thus classified by a nominal discharge current (8 μs /20 μs for front and back). 5 or 10 kA are recommended for range I (Vm over 1 to 245 kV) and 10 or 20 kA are recommended for range II (Vm over 245 kV) [124].
b) Types of surge arresters The task of surge arresters is to limit transient lightning overvoltages and switching overvoltages, Figure 6.14. 1.) A coarse protection can be attained through protective spark gaps, Figure 6.14 (left). They are often found in the form of metal parts (socalled arcing horns) on both sides of outdoor insulators, in which the critical task is to keep the arc away from the insulator surfaces in the event of an insulator flashover. For very fast transient overvoltages the sparkover voltage results from the impulse voltagetime characteristic of the highly nonuniform electrode arrangement, with possibly greater spark formation time in accordance with Figure 3.222. It is also disadvantageous that the subsequent current and the arc driven by the line voltage, are generally not selfquenching, but must be detected by the power system protection as current to ground and must be disconnected by power circuitbreakers. Note: For this type of overvoltage protection, it must be noted that rapid voltage breakdowns can become a risk to operating equipment. Hence, spark gaps are not recommended as surge arresters in IEC 600995 [124].
2.) Better protection is offered by a valvetype arrester (nonlinearresistortype arrester or a sparkgap arrester), in which a nonlinear resistor made of silicon carbide SiC is connected in series with a spark gap, Figure 6.14 (center). The sparkover voltage Vso is determined by the spark gap. After the breakdown and during the leakage impulse current, the nonlinear resistance of the SiC restricts the voltage to a residual voltage of Vres. During the subsequently arising permanent power frequency voltage, the current decreases so much owing to the nonlinear SiC resistance characteristic that the arc in the spark gap extinguishes below the extinction voltage Vex. Normal operating voltage can then be applied over the extinguished spark gap. The extinction spark gap is necessary because exces
6.2 Generation of High Voltages
365
sively large currents and thermal stresses would occur in the SiC at a permanently applied operating voltage. Table 6.14: Parameters of metaloxide arresters for networks with grounded neutral point, used in Germany [124] Nominal voltage
Continuous voltage
Rated voltage
VN
min. kV
kV
Vc
min. kV
10 20 30 110 220 220* 380 380*
8 16 24 75 160 160 260 260
12 24 36 126 216 240 360 396
*
Vr
Residual voltage Vres for Nominal Switching leakage impulse impulse current current max. kV max. kV
35 70 105 310 530 600 900 1000
260 440 500 750 830
For generator transformers
Note: In the case of nonlinearresistortype arresters, the extinction voltage Vex is used as rated voltage Vr to which the other characteristic values are related to [309].
3.) Metaloxide arresters comprise nonlinear resistors of zinc oxide ZnO which can be permanently subjected to a continuous voltage Vc without a spark gap and without the arrester being thermally overloaded by resistive (leakage) currents, see Figure 6.14 (right) and Table 6.14. The nonlinear performance is very much more pronounced than for SiC, and hence only currents below 1 mA flow at normal operating voltages. A response voltage is not defined, since if an overvoltage occurs the nonlinear characteristic is followed according to the leakage current amplitude up to a residual voltage Vres, which defines the protection level at which the voltage is limited by the arrester. The magnitude of the residual voltage is, however, dependent on the gradient of the voltage rise. With the disappearance of the overvoltage, the current also falls to the lower initial value in accordance with the v,icharacteristic and an extinction spark gap is not necessary.
Note: The rated voltage Ur is the r.m.s. value of a power frequency voltage, to which the arrester can be exposed for 10s. This value is close to the bend in the v,icharacteristic, and hence can be compared with the extinction voltage of nonlinearresistortype arresters with spark gap. Note: For long columns of arresters (for high voltages), parasitic currents through stray capacitances must be considered: similar to capacitive voltage dividers, they lead to an unequal voltage distribution along the longitudinal capacitances of the arrester column. Thus, the tablets of ZnO stacked on one another act in different regions of the nonlinear v,icharacteristic and can possibly be thermally overloaded. Corrective measure is possible through field grading in the vicinity of the arrester (external grading) or through grading capacitors (internal grading).
6.2 Generation of High Voltages In the following sections, the generation of high AC voltages, DC voltages and impulse voltages for test purposes is described. The methods discussed for the generation of high test voltages are applicable in other technical fields too. High voltage test fields and high voltage test laboratories are generally an electromagnetically shielded room and/or a hall to maintain the background noise level at a minimum during partial discharge measurements; they also include high voltage sources for three basic test voltages, namely AC voltages, DC voltages and impulse voltages. Owing to the large flashover distances necessary for air, high test voltages also require large hall dimensions, Figure 6.21. Note: Test voltage sources up to 3200 kV for lightning impulse voltages and 1500 kV for DC voltages and 1200 kV for AC voltages are necessary for the new voltage levels 1000 kV AC (UHVAC Ultra High AC Voltage) and 800 kV DC (UHVDC Ultra High DC Voltage).
In any case, i.e. regardless of the size of the test facility, working with high voltages requires special safety measures that are to be found in the respective updated and applica
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6 TESTING, MEASURING AND DIAGNOSIS
Figure 6.21: Shielded UHV ultra high voltage test laboratory with 1200 kV AC voltage cascade, 1500 kV DC voltage generator and 3200 kV impulse voltage generator, hall dimensions 35 x 50 x 30 m3 (b x l x h), photo HSP Hochspannungsgeräte, Troisdorf/Highvolt, Dresden, year of construction 2007.
ble standards and they also require special qualifications and training for the personnel. Depending on the purpose of the high voltage equipment, there are different specifications, such as for test fields, for switchplants or for high voltage supplies in devices.
Important safety elements in a high voltage test laboratory are the barricading of the high voltage room with protection against contact and adequate safety clearances between parts that conduct high voltage and ground potential as well as marking the areas through warning labels and warning lights indicating the switching status. Barricades and other grounded parts of the installation must be connected to the grounding system of the laboratory in a reliable and visible manner. For this, a radial grounding arrangement of unsheathed ground wires in which a broken wire could be identified anywhere is established. The entries of the highvoltage room must be included in a safety circuit, whose opening leads to immediate deactivation of the high voltage source.
Automatic grounding switches can further enhance safety. Before entering the high voltage room, the high voltage source must be visibly switched off in two stages with the help of the power circuitbreaker and the disconnector. Then the installation parts on the high voltage side must be manually grounded with the help of an earthing stick. The earthin stick must subsequently be connected to the high voltage generator to make a permanent and visible grounding connection before starting work on the plant. Instrument leads or control wires which lead into the high voltage room and which could displace the high voltage potential outwards must have a grounded sheath and are to be protected by surge arresters. Capacitors and other capacitances can still carry charge, even after disconnecting the high voltage source, or can be recharged by recov
6.2 Generation of High Voltages
367
ery voltages even after a temporary shortcircuit. Especially with regard to DC voltage generators, capacitances form one of the largest safety risks. It is therefore recommended (but not sufficient) to provide a rapid discharge through discharge resistances or automatic grounding switches. Furthermore, capacitances must always be reliably and continuously shortcircuited. In the case of a series connection of capacitors, this is applicable even to the individual partial capacitances. Establishing a grounding connection is not sufficient if a direct short circuit of all partial capacitances is not simultaneously guaranteed. Note: Risks due to charged capacitors exist especially for improper handling of electrical devices, which include high voltage direct current supplies.
6.2.1 Generation of AC Voltages 6.2.1.1 Principles of Generation Test voltage values are always specified as peak values divided by
2
since peak values are decisive for breakdown [133]. In the case of sinusoidal voltages, division by 2 allows a comparison with the r.m.s. values of the operating voltage. Different principles are provided for generation of high AC test voltages, Figures 6.2.11 and 6.2.12. Singlephase test objects of low capacitance (e.g. insulators, bushings, grading capacitors, components of singlephased encased switchgear, instrument transformers, voltage dividers, surge arresters) are tested with singlephase test transformers; the supply is generally from the low voltage network at power frequency, Section 6.2.1.2, Figure 6.2.11 and Figure 6.2.12 (left). Special designs allow the testing of groundfree test objects or the generation of voltages balanced to ground. Very high test voltages can be attained by the cascaded arrangement of comparatively small, insulated test transformers, Section 6.2.1.3. Appreciable voltage rises sometimes occur in the case of capacitive loads and in noload operation, Section 6.2.1.4. For test objects with high capacitances (e.g. cables, large enclosed switchgear and capacitors with large capacitances), the common test transformers and test voltage sources are often too weak owing to high capacitive reactive power, and they are very heavy to transport or not even available. For onsite tests, high voltage generation by transportable series resonance test systems with high voltage reactor coil is possible, whereby either the frequency of the supply voltage or the inductance of the reactor coil (adjustablegap inductor) must be tuned to resonance. The resonance should be in a range, which must still be considered as “close to operating frequency”, Section 6.1.2.5, Figure 6.2.12 (center).
Figure 6.2.11: 500 kV/ 125 kVA test transformer with oilfilled tank and with porcelain bushing in the HV test laboratory of Hochschule WürzburgSchweinfurt.
Note: Generally, the compensation of capacitive reactive power is also possible through parallel compensation (parallel resonance test systems). However, a high voltage test transformer is also necessary for this, along with the high voltage compensation reactor. The application of a series resonance system is thus generally the more economical solution.
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6 TESTING, MEASURING AND DIAGNOSIS
Singlephase test transformer for test objects of lower capacitance (generally for power frequency f = 50 or 60 Hz).
Singlephase series resonance test system for test objects of higher capacitance with excitation transformer (left), high voltage inductor (center) and cable with termination (right). The circuit is tuned to resonance via the frequency or the adjustablegap inductance.
Threephase testing of a power transformer with induced AC voltage in the high voltage winding through excitation of the low voltage winding with increased frequency (generally 100 or 120 Hz).
Figure 6.2.12: Generation of high AC test voltages with test transformers (left), series resonance systems (center) and through the AC voltage induced in the test object (right).
The reduction of capacitive reactive power can also be achieved by applying voltages of very low frequency (VLF, f = 0.1 Hz) [128], [129], [130]. The voltages are, for example, sinusoidal or they exhibit a squarewave voltage with a halfwave oscillation for charge reversal (the socalled cosinesquare voltage), Section 6.2.1.6. The VLF test can be carried out onsite with light, mobile systems. They are therefore set up for laid medium voltage cables as an alternative to the DC voltage test that is no longer considered relevant. Threephase and singlephase power transformers cannot be tested at power frequency (50 or 60 Hz) because owing to the saturation of the iron core, the voltages cannot be increased significantly above the voltages occurring during operation. As per the law of induction, significantly higher induced test voltages vind = w)wt
and
Vind = Z)
(6.2.11)
are only possible with increased frequency, since the magnetic flux ) must be restricted owing to iron saturation. It is a standard practice to feed the transformer on the lowvoltage side with doubled frequency, and the high
voltage side insulation is then tested with the induced AC voltage, Figure 6.2.12 (right) [131]. Testing with the induced AC voltage of increased frequency can in principle be applied to all types of power transformers, test transformers and instrument transformers, Section 7.1.3.5. 6.2.1.2 Test Transformers
Test transformers generate high and (to the extent possible) distortion free test voltages at comparatively small powers. Test transformers and power transformes are very different, based on design and construction, Table. 6.2.11. Test transformers are generally designed to be singlephase. They have a relatively large transformation ratio. Owing to the high voltages to be insulated, comparatively large insulation gaps, and therefore even large magnetic leakage fluxes or large relative shortcircuit voltages vsc occur. The ironcore is designed in such a way that the flux density remains in an approximately linear region of the magnetization characteristic.
6.2 Generation of High Voltages
369
Table 6.2.11: Characteristic features of power transformers and test transformers
Power transformers
Test transformers
Voltage transformation during transmission of (large) power Generally, threephase (Figure 6.21, right) Large Lower, e.g. 123 kV/20 kV = 6.15 e.g. 20 kV/ 0.4 kV = 50 Design for high durability under operating conditions with high thermal stress and ageing Lesser, due to lower voltages to be insulated
Voltage transformation for generating higher test voltages
Task Structure Nominal power Transmission ratio Insulation
Stray inductance
vsc = 5%.....15% Maximum saturation degree of magnetization characteristic for weight reduction
Iron core
Permanent operation, mostly below the nominal apparent power
Operation
Singlephase test transformers can be manufactured with different insulation systems. In Figure 6.2.13, the respective arrangements of the lowvoltage winding (narrow) and highvoltage winding (broad) on the limb of the iron core are illustrated. In order to avoid unnecessary insulation gaps, the windings are interlaced in such a way that minimum possible potential difference is obtained between them and relative to the core. For oilfilled transformers, the winding insulation consists of oilimpregnated paper and pressboard, Figures 6.2.13 a), b) and d). Gasimpregnated windings or windings cast with resin can be insulated with polymeric films, Figure 6.2.13 e) and c). Note: In the case of windings cast with resin (encapsulatedwinding drytype transformer), a completely cavity free insualtion can hardly be attained, and thus they can generally only be employed free of partial discharges for voltages up to about 100 kV, and therefore are only suitable for the medium voltage range.
Conductive housings (tank construction) require high voltage bushings or partition insu
Generally singlephase (see Figure 6.21 left) Comparatively low Larger, e.g. 500 kV/0.4 kV = 1250 e.g. 100 kV/0.23 kV = 434.8 Design for withstanding high voltages with low thermal stress and slower ageing Comparatively high, owing to thicker insulation between primary voltage winding and secondary voltage winding vsc = 15%.....25% Low saturation degree of magnetization characteristic in linear region in order to achieve distortionfree and linear transformation Short test intervals (overload is possible), partial permanent operation
lators, Figure 6.2.13 a), b) and e), that can be absent for insulating housings (insulating housing construction), Figure 6.2.13 c) and d). However, insulating enclosures have poorer heat dissipation to the surroundings. Gasinsulated switchgear (GIS) can be tested with directly flangemounted and encased transformers [132]. The low weight of SF6impregnated transformers is advantageous for onsite tests, Figure 6.2.13 e). The stray capacitance of the high voltage electrode (across the winding) to the housing and core can be used along with a lowvoltage measuring electrode for voltage measurements and partial discharge measurements [125]. If the iron core is laid at ground potential, then the entire high voltage must be insulated within the high voltage winding and against the core. These stesses can be halved if the high voltage winding is divided and the core is laid at halfpotential, Figures 6.2.13 b) and c). For onesided grounding of the high voltage winding, the core and housing are at half
370
6 TESTING, MEASURING AND DIAGNOSIS
a)
b)
c)
Oil Cast resin
Oil
Test transformer in steel tank, core at ground potential
Test transformer in steel tank (left) and with resinencapsulated windings (right), both with divided high voltage winding and core at half potential
d)
e)
Test transformer in insulating tube, core at ground potential
GIS  test transformer in pressureproof steel tank, core at ground potential
Oil
SF 6
SF 6
Figure 6.2.13: Connection and assembly of test transformers with oil insulation, cast resin insulation and compressedgas insulation.
the potential of the high voltage and must be insulated against ground. Connections for low voltage windings, which are at the potential of the respective high voltage connections, are fed out through the bushings within the (hollow) high voltage winding termination. For onesided grounding of the high voltage winding, see Figures 6.2.13 b) and c), this can be used for a low voltage side excitation of the transformer. Note: The symmetrically constructed transformer even facilitates the generation of a voltage balanced to ground if the core is laid at ground potential. Thus, a low voltage winding at core potential is necessary for excitation. However, this is not illustrated in Figure 6.2.13.
6.2.1.3 Cascade Arrangement
Voltages of individual transformers are connected in series by the cascaded arrangement of test transformers, Figures 6.2.14a and 4b. Thus, highest AC test voltages of up to several MV can be generated with comparatively compact test transformers.
The whole transformers are insulated against ground according to their housing potential. High voltage windings (H) are connected in series. The radii of curvature of shields and electrodes must increase stagebystage owing to increasing voltage. In the first stage, the low voltage excitation takes place with an excitation winding (E) lying inside the HV winding and being connected to the core potential. An coupling winding (C) lying outside the HV winding and being connected to high voltage potential supplies the current for the excitation winding in the second stage. The lines between coupling winding 1 and excitation winding 2 are led within the inner conductor of the bushing at high voltage potential. The excitation winding of the third stage is supplied with power from the coupling winding of the second stage. The relative shortcircuit voltage of the cascade rises sharply with an increase in the number of stages. Higher thermal stress on the lower stages is also a disadvantage. Hence, the number of
6.2 Generation of High Voltages
371
V
P EHC
V
2P
Figure 6.2.14a: Generation of very high AC test voltages in a threestage cascade assembly.
EHC
3P
E: Excitation windings H: High voltage windings C: Coupling windings
V
EHC
stages is restricted to three in practice for most of the cases. Note: Cascade connections can even be set up from test transformers with two connections that are symmetrical to the core, Figures 6.2.13 b) and c). Both the low voltage windings that lie on the outer side of the HV winding are at the potential of the associated high voltage connection, and they can therefore be used as excitation winding and as coupling winding.
6.2.1.4 Capacitive Voltage Rise in Transformers Test transformers are largely capacitively loaded by the capacitances of the insulation arrangements to be tested, by capacitive voltage dividers and by coupling capacitors for partial discharge measurements. Owing to winding capacitances, even in noload operation, there exists a certain amount of capacitive load. Thereby, along with the relatively large stray inductance of test transformers, substan
tial capacitive voltage rises (resonant overvoltages) can result, Figure 6.2.15. For a large capacitive load current I, the magnetization current through the main inductance, the core losses and thus the magnetizing impedance can be neglected. The capacitive voltage rise thus results from a simplified transformer equivalent circuit diagram which consists of the leakage impedance ZL = RW + jXL only and which is related to the high voltage side. ZL can be determined in a shortcircuit test. RW is the sum of the winding resistances converted with the voltage transformation ratio a = VN2/VN1: 2
RW = RW1·a + RW2
(6.2.12)
LL and XL respectively is the sum of the converted stray inductances and leakage reactances respectively:
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6 TESTING, MEASURING AND DIAGNOSIS
Figure 6.2.14b: Twostage AC voltage cascade for 1200kV with coupling capacitor and telescope electrode (from right to left), see Figure 6.21. from HSP Hochspannungsgeräte, Figure Troisdorf/Highvolt, Dresden
2
2
LL = LV1·a + LV2
(6.2.13)
2
XL = XV1·a + XV2
(6.2.14)
Due to the capacitive load C2, the complex resonance voltage ratio K is 1
1
V2/V1' = (jZC2) /[RW + jZLL + (jZC) ] and the magnitude is 2
(6.2.15) 2
2 1/2
K = V2/V1' = [(1Z LLC2) + (ZRWC2) ]
.
Owing to the capacitive voltage rise, the magnitude of the generated secondary voltage cannot generally be concluded from the magnitude of the preset primary voltage, i.e. an independent measurement of secondary voltage is always necessary. Example: Test transformer with capacitive load The following test transformer is considered: a = V2N/V1N
= 100 kV/220 V = 454.5
a = I1N/I2N
= 22.7 A/50 mA
RW1 = 0.5 :,
With Eq. (6.2.12), RW is = 124 k:. In the shortcircuit test, the current I2N = 50 mA is driven by the voltage V´sc1 = vsc ·100 kV = 14.4 kV. This corresponds to an
2
2.) Maximum possible load capacitances for full high voltage V2 = 100 kV shall be calculated for continuous operation (I = IN) and transient overload (I = 2·IN). The capacitances are calculated from V2max/I2max = 1/(ZCmax): Cmax = 1.6 nF for I = 50 mA (permanent operation) and Cmax = 3.2 nF for I = 100 mA (transient overload). 3.) For the range of C = 0 to 3 nF, the capacitive voltage rise K and the maximum permissible primary voltages V1 are specified. With Eq. (6.2.15), the following values are obtained for different load capacitances:
Simplified transformer equivalent circuit diagram (leakage impedance only) for a test transformer with capacitive load jXLI
R WI
RW2 = 20.66 k:, vsc = 14.4 %
1.) At first, the elements of the transformer equivalent circuit diagram related to the high voltage side must be determined:
2
impedance ZL = 288 k:. From ZL = RW + XL , the elements XL = 260 k: and LL = 827 H are determined.
LL V 1'
I
R WI jXLI
V2
V 1'
RW V2
C2 I
90°
Figure 6.2.15: Voltage rise caused by capacitive load of a test transformer.
6.2 Generation of High Voltages C/nF
K
V2 /kV V´1/kV V1 /V
0 1 100 100 220
0.5 1.04 100 96 211
1 1.09 100 92 202
1.5 1.14 100 88 193
2 1.19 100 84 185
373 2.5 1.25 100 80 176
3 1.31 100 76 168
3.5 1.37 100 73 161
4) For a load capacitance C = 6 nF, the maximum possible high voltage and the related primary voltage shall be determined. The voltage rise factor K = 1.78 for C = 6 nF. In continuous operation (I = IN), the following is valid and
V2 = I2N/(ZC)
= 26.5 kV
V1 = v2/(a·K)
= 32.8 V.
For transient overload (I = 2·IN), the maximum values are twice as large: V2 = 56 kV and V1 = 65.6 V Note: Generation of high frequency high voltage with ironfree Tesla transformer is likewise based on a resonant overvoltage. A capacitance C1 is discharged across a spark gap and across the low voltage winding in an oscillating manner. C1, the stray capacitance C2 at the high voltage side and the stray inductance of the transformer determine the resonance frequency. Each discharge event is followed by a highfrequency oscillation package in the range of about 10 to 100 kHz. The oscillation decays owing to the damping of the resonant circuit.
6.2.1.5 Series Resonance Test Systems
Series resonance test systems are especially used for single phase onsite tests on the test objects with high capacitance, such as for installed cable runs, Section 7.1.15, for onsite assembled gasinsulated switchgear and for gasinsulated transmission lines (GIL), Section 7.1.1.3. The quality control of the installation and the assembly respectively or the assessment of the insulation condition and the verification of availability are carried out by withstand voltage tests and partial discharge tests. Thus, the onsite testing concept follows the basic concepts of insulation coordination, i.e. the test stresses shall be representative of the operating stresses [121], [122], [123], [133], and [375]. However, the direct usage of test transformers for test objects with high capaci
tance is not possible owing to the power supply required. Example: For a cable with a length of l = 10 km and with a capacitance of C’ = 250 nF/km, at a test voltage of V = 400 kV (r.m.s. value) and f = 50 Hz, a capacitive 2 reactive testing power of S = (2Sf) (C’l) V = 126 MVA is obtained. Such a power is not available at the medium voltage level and the low voltage level.
This problem can be technically and economically solved with a series resonance test system. In a series resonance circuit of a reactor inductance and a test object capacitance, a high test voltage results from a resonant overvoltage, Figure 6.2.12 (center) and 6. For tuning to resonance, either the inductance of the high voltage reactor (via an adjustable gap in the magnetic circuit) or the frequency of the supply voltage (via a frequency converter) is tuned, [125], [126], [127], [355]. The resonance circuit can be supplied with a low voltage VE and a low power by an excitation transformer: in the case of resonance, the reactor inductance supplies the capacitive reactive power required by the test object capacitance, the voltage source only has to cover the very low power loss of the resonance circuit, which is produced in an equivalent series
Variable inductance j X RI
RSI
RSI
V2
I LR
RS Damping
VE
C2 V2 Test object
Variable frequency I
j X RI
VE
90°
Figure 6.2.16: Generation of high AC voltages in series resonance with variable inductance (reactor) or variable frequency (30 to 300 Hz) for test objects with high capacitive reactive current.
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6 TESTING, MEASURING AND DIAGNOSIS
resistance RS, Figure 6.2.16: 2
PS = RS I = VE I
(6.2.16)
The series resonance system can thus manage with a very low power input. However, the excitation transformer and the reactor coil must be designed for the high capacitive reactive current (charging current) I. Furthermore, the high voltage reactor is generally lighter than a comparable transformer. Moreover, it can be modularly transported and can be connected in series (or parallel) onsite, in order to attain the maximum possible test voltages (or currents). Figures 6.2.17 and 9 show the corresponding cascading. In the case of resonance, the following is applicable:
Z0
1 LR C2
2 ʌf 0
(6.2.17)
According to Eq. (6.2.15) and (6.2.17), the resonance ratio V2/VE is
K
V2 VE
1
Z0C2 RS
.
(6.2.18)
It corresponds by Eqs. (6.2.16) and (8) to the quality factor q of the resonance circuit and to the ratio of the capacitive reactive power S2 to the power loss of the resonance circuit respectively:
q
S2 PS
1 I2 Z0C2 RS I
2
V2 VE
K
(6.2.19)
The quality factor or the resonance ratio that can be attained are determined by the losses of the test circuit, which especially result from the winding resistances and from the iron losses of the reactor, because the test objects generally have very low losses. For reactors with variable inductance, the values are about q = 50, whilst for reactors with fixed inductances, q = 100 to 200 is specified [379].
A great advantage of resonance test systems is that in the event of a breakdown in the test object, the resonance circuit is detuned, the high voltage immediately disappears and the short circuit current remains very low since it is driven only by the weak excitation transformer and is also limited by the reactor. a) Variable inductance Adjustable reactors can be built in, for example, insulating housing design: the twoleg core is divided and comprises an oil gap that can be adjusted by an insulated spindle, Figure 6.2.12 (center). The winding is divided between the upper and lower legs; the core is at half potential and is externally shielded by ringshaped electrodes. The reactors can be assembled in series in selfsupporting manner because of their modular design, Figure 6.2.17. Thus, modular resonance test systems are possible for very high voltages [126], [127]. In the case of a constant test voltage frequency Z0, the ratio of maximum to minimum test object capacitance is obtained in accordance with Eq. (6.2.17) from the adjustable ratio of inductances, which amounts to about 20:
C2max/C2min = LRmin/LRmax
(6.2.110)
Note: A variable inductance can be implemented in the form of a variable low voltage inductance that can be looped into the high voltage circuit through a test transformer. However, it is a disadvantage that an additional transformer is required. Note: Cable test illustrated in Figure 6.2.17 is conducted with a cable test termintionl in which the space between the uncovered bare cable insulation and the housing insulator is filled with slightly conductive water for resistive potential grading, Sections 5.4.5 and 7.1.1.5, Figure 5.48.
b) Variable frequency An innovation in high voltage test techniques are series resonance circuits that are tuned via the variation in frequency with the help of frequency converters for fixed inductance. Fixed inductances are highly reliable and have low losses, so that a very high quality factor or a very advantageous ratio of input power to
6.2 Generation of High Voltages
375
testing power of approximately 1:100 to 1:200 is obtained.
but can be extended further by series and parallel connection of reactors.
By changing the frequency, there is a deviation to some extent from the power frequency of 50 or 60 Hz. However, today a larger range of frequencies from a few 10s of Hz to a few 100 Hz is considered as “close to the operating frequency” [355]. IEC 600603 provides a frequency range of 10 to 500 Hz [390], while IEC 62067 restricts the frequency range for tests on cables with a nominal voltage above 150 kV to fmin = 20 Hz to fmax = 300 Hz [356]. In the case of a fixed inductance LR , the ratio of maximum to minimum test object capacitance, in accordance with Eq. (6.2.17), is obtained from the ratio of adjustable frequencies:
Note: The weight of a test system plays a major role for the mobile application. For systems with fixed inductance and with variable frequency, particularly low values of approx. 1 kg/kVA with regard to the 50 Hz testing power result. The optimization of the overall system is the reason for this: the design of reactor core for a lower frequency (e.g. 30 instead of 50 Hz), indeed leads to an increased weight in iron, but it can also be compensated by a lower test reactive power. The fixed reactor has no movable parts and can therefore be made lighter and more compact than a variable reactor. Furthermore in a fixed reactor the magnetic circuit can be designed to be optimal and with lower leakage flux by subdividing into many subgaps. Ultimately, a regulating transformer can be dispensed with owing to the supply of power through a frequency converter.
2
2
1/LR = Zmin C2max = Zmax C2min C2max/ C2min = (fmax/ fmin)
2
(6.2.111)
That is, a frequency ratio of 300 Hz/ 20 Hz = 15 results in a capacitance range of C2max/ 2 C2min = 15 = 225 that can be used for tests. This range is adequate in many practical cases,
I
LR
C2
f
VE
V2
Figure 6.2.17: Generation of high AC voltages in a series resonance system with adjustable inductances or adjustable frequencies, high voltage reactors in series connection, schematic (left) and a 1700 kV 3 A  50 Hz series resonance system with reactors, compressedgas capacitor and coupling capacitor, photo Haefely Test AG/ Hipotronics Inc. (right).
Figure 6.2.18 shows the example of a mobile test system with a high voltage reactor in a tank construction [355]. With this, similarly to oil transformers with steel tanks, effective cooling and permanent operation at high power over a long period are possible. A filter circuit against supplyside interferences, a coupling capacitor for partial discharge measurements and the test object are
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6 TESTING, MEASURING AND DIAGNOSIS
Reactor Excitation transformer Operating chamber Control unit Frequency converter
Oiloutdoor bushing, entry fitting or oilgas bushing connetion to filter coupling capacitor test object
Figure 6.2.18: Mobile resonance test system with variable frequency for 90 A and 150 kV [355] (schematic).
6.2.1.6 Requirements for Test Voltages in Laboratories and Onsite
Figure 6.2.19: Mobile resonance test system with series connection of reactors [357] (schematic).
connected to the bushing, see Section 6.4.2. The advantage is that the series resonance test circuit already forms a filter. However, the circuit is excited by the frequency converter with rectangular voltages whose broad frequency spectrum cannot be completely filtered out. Since the four switching impulses of the source are known, they can be considered for the evaluation of a partial discharge measurement in the time domain. [379]. Instead of oiloutdoor bushings, even oilgas bushings or entry fittings can be used, resulting in hermetically sealed onsite test systems. For the extension of the range of test voltages, similar reactors can be positioned on post insulators and connected in series [357], Figure 6.2.19. For a cascading of reactors, however, the insulating housing construction is preferred, which allows the direct stacking of reactors. Moreover, the weight can be reduced by replacing the oil insulation by SF6 Note: The many advantages of frequencyvariable resonance test systems can be expected to lead to an increasing expansion of onsite use, and in special cases even for stationary use.
During onsite tests, even with the above mentioned test voltage sources, the requirements of IEC 60 0601 for AC test voltages often cannot be fulfilled. Owing to this, in practice, considerable variations have been developed with respect to type of voltage, voltage waveform, frequency, tolerances and test procedures. The new standard IEC 60 0603 shall, therefore formulate (general) requirements that can be economically implemented onsite [375], [390], Table 6.2.12 and Figure 6.2.110. Devicespecific standards can thus comprise additional refinements or limitations. Onsite tests on cables are described in Section 7.1.1.5 with Table 7.1.11. A test in accordance with operating conditions should be conducted, as far as possible, close to the operating frequency (AC). For all the test stresses varying from the operating conditions, it must be asked whether the test provides representative results. A strong dependence of the shortduration withstand voltage with frequency was shown for VPE cable samples [377], Figure 6.2.110. Therefore, for VLF tests and DC voltage tests, considerably higher withstand voltages must be expected. Owing to this, the magnitude and duration of the test voltage stress are graded according to the frequency, see Section
6.2 Generation of High Voltages
377
7.1.1.5, table 7.1.11. However, since the frequency dependence apparently corresponds to a change of breakdown mechanism, fixed relations of test voltage values for significantly different frequencies unfortunately cannot be specified. Investigations on artificially damaged cable test objects made of crosslinked polyethylene (XLPE), however, have shown a high selectivity of breakdown voltage at f = 0.1 Hz for mechanical damage and for “water trees” [376]. Moreover, ample experience with VLF tests for medium voltage cables is available which enables a condition estimation of the aged cable.
V / kV
400
Em / kV/mm
DC
VLF
AC
300
200
200 100 100 0
The decision about the type of test voltage that must be applied is therefore greatly dependent on the query to be answered: a proof of withstand voltage in accordance with operation conditions requires a frequency close to the operating frequency. Diagnostic statements are also possible in other frequency ranges.
1 1 0,1 1000 100
0 1
10 100 1000
f / Hz
Figure 6.2.110: Withstand voltages determined for XLPE cable samples as a function of test voltage frequency [377].
a) DC voltage tests In the past, DC voltage tests with high test levels (for cables 4 V0) were common for oilfilled cables and paperinsulated massimpreg
Different types of test voltages are discussed in the following sections:
Table 6.2.12: Requirements for laboratory tests and onsite tests for AC voltage equipments [375], [390]. Note: Test voltage levels see Table 7.1.15. Note: Impulse voltage tests see Section 6.2.3. a) DC voltage Frequency f DC ( no longer Ripplefactor common for AC Tolerance for test voltage voltage operating equipment)
Measurement uncertainty
Tests in laboratory (test field)
Onsite tests
IEC 60 0601
IEC 60 0603 *) devicespecific variations
DC voltage 1 min)
DC voltage 1 min)
+3%
+5%
Frequency f b) Very low frequency voltage VLF
0.01 – 1 Hz
Sine to rectangle, test voltage is peak value (sometimes r.m.s. value*) +5%
Voltage wave form Tolerance for test voltage Measurement uncertainty
Not common
Frequency f c) Damped AC voltage DAC (Oscillating voltage)
+5% 20 – 1000 Hz
Damping
< 40 % for each period
Tolerance for test voltage
+5%
Measurement uncertainty
+5%
Frequency f d) AC voltage close Sinusoidal Vˆ / V r.m.s. to operating frequency (power freTolerance for test voltage quency) Measurement uncertainty
45 – 65 Hz 2 +5%
10 – 500 Hz (cable 20 – 300 Hz*) 2 + 5 % (or 2 + 15 % and 0.98 Vˆpos Vˆneg 1.02 )
+ 1 % (< 1 min), + 3 % (> 1 min)
+ 3 % (< 1 min), + 5 % (> 1 min)
+3%
+5%
378
nated cables, as well as for electrical machines, since even large capacitances could be tested with transportable equipment at low input power and meaningful conclusions about the insulation condition could be made, Table 6.2.12 a), Figure 6.2.111 a). However, it was shown for XLPE cables that the DC voltage test is not sensitive even at high test levels for many of the very serious errors. This is because eroding partial discharges can occur with a high repetition rate for operational AC voltages but not for DC voltages. On the other hand, DC voltages could be hazardous for the test object owing to space charge built up, Section 7.1.1.5. These differences can also be explained by the fact that the field distributions in the insulation are determined by permittivities for operational AC voltages and by conductivities and transition processes for DC voltages. Consequently, completely different stresses can occur during testing and during operation, see Section 2.4.4. Note: Tests with DC voltages for HVDC applications are described separately, Section 6.2.2 and 7.2.
b) Very Low frequency (VLF) voltages For voltages with very low frequencies, space charge build up should be avoided by the periodic changes in polarity, Table 6.2.12 b), Figure 6.2.111 b). In addition, eventual defects can be identified by partial discharges with low repetition rates. However, it is not always clear whether the capacitive field distributions for the power frequency also occur during testing in the very low frequency range between 0.01 Hz and 1 Hz. This depends on the selected frequency, on the conductivities of the materials and on the geometrical structure of the insulation, Section 2.1.4.3. Note: In addition to the voltage test, it is recommended to evaluate the global ageing condition of cable insulations by comparative or voltage dependent dissipation ( or loss) factor measurements at 0.1 Hz [378]. The significance of dissipation factor measurements is debatable, and hence, socalled isothermal relaxation current analysis (IRCanalysis) is recommended as an alternative [223], [224], Section 6.4.7.4.
6 TESTING, MEASURING AND DIAGNOSIS
VLF withstand voltage testing for the very low frequency f = 0.1 Hz is developed for onsite testing the laid medium voltage cables, which generally takes place at three times the nominal voltage (phase to ground voltage) 3 V0 with a test duration of 1 h, Section 7.1.1.5 with Table. 7.1.11. All voltage waveforms between sine wave and rectangular wave are allowed and the test voltage is the peak value [375], [390], Table 6.2.12b). In practice, a sinusoidal AC voltage and the socalled cosinerectangular voltage are mainly used, Figure 6.2.111 b). Note: At 0.1 Hz, the capacitive charging power (reactive power) is smaller by a factor of 500 than at 50 Hz, so that the test equipment is very compact and can be transported in very compact cable measuring coaches. These generally include the equipment for voltage tests with 0.1 Hz and with DC voltages as well as extensive measurement equipment for the acoustic and electrical runtime location of cable defects, for cable diagnosis as well as for dielectric measurements (dissipation factor measurements and partial discharge measurements). Note: The sinusoidal 0.1 Hz test voltage can, for example, be generated by slowly increasing and decreasing of voltages from two different sources with positive and negative polarity. The cosinerectangular voltage is generated by charging the cable capacitance from a DC voltage source. After about 5 s, a reactor is connected in parallel so that an oscillation process is initiated, this approximately corresponds in duration to the power frequency. At the negative voltage peak, a switch disconnects the oscillating circuit and the cable retains the charge state with opposite polarity. The lossrelated voltage reduction is balanced by a DC voltage source. After another 5 s, the next oscillating charge reversal of the cable is performed.
c) Damped AC voltage Damped AC voltages can be generated onsite by charging the test object capacitance from a DC voltage source with subsequent discharge via an inductance, Table 6.2.12 c), Figure 6.2.111 c). A decaying, damped oscillation, a socalled “oscillating voltage” occurs and its frequency, likewise, can be set in the range of f = 20 to 1000 Hz “close to the operating frequency”. This results in field distributions of the test object that correspond to the fields at operating frequency; however, the stress is not
6.2 Generation of High Voltages
379
continuous and has only a transient, pulsed character. Ignition delay for inception of partial discharge, or the change in partial discharge intensities with the stress duration, therefore cannot be observed. In addition, the prior DC charging of the test object does not correspond to the operating stress. Test voltage is the peak value Vp and it is identical with the charging voltage.
can be employed [375], [390], Table 6.2.12 d), Figure 6.2.111 d). The test voltage is the peak value divided by 2 .
d) AC voltage
6.2.2 Generation of DC Voltages
With the help of series resonance testing systems, it is possible to test even test objects with large capacitance with continuous AC voltages close to the operating frequency, Section 6.2.15. For this, it is assumed that capacitive field distributions present in operation are also present within the permitted frequency range of 10 to 500 Hz (for cables 20 to 300 Hz, see Section 7.1.1.5, Table 7.1.11) and that no changes occur in the breakdown processes [377], Figure 6.2.110. Therefore, test systems with corresponding variable frequency
High DC voltages serve as test voltages for HVDC components and cables as well as supply voltages for various technical applications, such as video terminals, Xray equipment, electron microscopes, capacitor chargers, dust precipitators (electrostatic precipitators), paintspraying devices and surface coating devices.
Continuous AC voltage tests close to the operating frequency are most comparable with the test stresses in the laboratory and with the operating stresses.
High DC voltages are obtained from AC voltages by rectification (Section 6.2.2.1), mostly in connection with a voltage multiplier circuit (Section 6.2.2.2). In the case of lower voltages,
a) Direct voltage (DC voltage) t VLF sine 0.1 Hz VLF cosine rectangular 0.1 Hz 5s
10 s t
0s b) VLF voltage 0.01 bis 1 Hz A few ms V1 V2
t Vp
20 to 1000 Hz c) Damped AC voltage (DAC)
d) AC voltage 10 to 500 Hz
Figure 6.2.111: Test voltage waveshapes for onsite tests.
t
380
6 TESTING, MEASURING AND DIAGNOSIS
supply is often via a switchedmode power supply (Section 6.2.2.3). Using electrostatic generators is restricted to special applications at very high voltages (Section 6.2.2.4). Direct voltages are often superimposed by periodic functions. Therefore, IEC 600601 [133] defines the arithmetic mean value as the DC test voltage. ____
V
v(t )
(6.2.21)
The ripple Gv = 0.5(vmax  vmin) is described by the ripple factor (“ripple factor”) Gv/V= = 0.5(vmax  vmin)/V= .
Stray capacitances to AC voltage side
Transformer connection
Stray capacitances to ground
Figure 6.2.22: Linearization of potential distribution in the reverse blocking state by grading capacitors parallel to the highvoltage rectifiers.
(6.2.22)
It should not be more than 3% for DC voltage tests. 6.2.2.1 Highvoltage Rectifier
Highvoltage rectifiers always consist of a series connection of several semiconductor diodes whose reverse voltage is restricted to a few kV. This is a problem for potential distribution in the reverse blocking state, since an unequal voltage distribution would lead to overstress and destruction of individual diodes. Voltage distribution determined largely by undefined junction capacitances and blockingstate currents can be made more uniform by parallel grading capacitors and grading resistors for the grading of timevarying voltages and steadystate DC voltages respectively, Figure 6.2.21. In forward direction, i.e. in the coducting state, the diodes are protected by series resistors.
Symbol
Figure 6.2.21: Capacitively and resitively graded highvoltage rectifier.
For spatially extended rectifiers that are used for very high voltages of many 100 kV, a nonlinear voltage distribution along the series connection of the individual rectifiers occurs, owing to undefined stray capacitances to the groundside and to the AC voltage side, Figure 6.2.22. Voltage distribution can be lineraized by parallel grading capacitors. For this, sufficiently large longitudinal currents must be present, relative to which the transverse currents over the stray capacitances are negligible. 6.2.2.2 Rectifier Circuits
AC voltage sources available in high voltage laboratories are often supplemented with a capacitively graded rectifier and a smoothing capacitor to form a halfwave rectifier circuit, Figure 6.2.22 and 3 (top): After connecting the AC voltage, the capacitor is charged to the peak value vˆ during the positive half wave. The charging current must be restricted to the permissible value by a series resistor. Full charging within a quarter period presumes a small charging time constant RC > W1  RFCL. The parameters front time T1 and time to halfvalue T2, which are defined for lightning impulse voltages, are proportional to the time constants W1 and W2: T1 =
Tf =
K1·W1
(6.2.35)
T2 =
Th =
K2·W2
(6.2.36)
Impulse voltage wave form
K1 K2
1.2/5
1.2/50
1.2/200
250/2500
1.49
2.96
3.15
2.41
1.44
0.73
0.70
0.87
Lightning impulse voltage impulses can be generated with the standardized parameters by appropriate dimensioning of the circuit elements. Equations that are only slightly different are applicable for the two basic circuits, which differ in the position of the discharge resistance, Figure 6.2.33 with Eq. (6.2.33a,b,c). The maximum amount of charging voltage V0 is restricted by the sparkover voltage of the switching spark gap G1. Generally, the electrode distance is set so wide that the gap does not break down spontaneously. Thus, it is purposefully ignited by a trigger impulse that generates an ignition spark at a trigger electrode and thereby triggers the main discharge, Figure 6.2.35. The trigger generator must be at the potential of an electrode or an additional coupling capacitor must be used. Note: Below the breakdown voltage of a spark gap, a limited voltage range exists in which the field strengths
Constants K1 and K2 are dependent on the impulse voltage wave form, Table 6.2.32.
Main discharge Ignition spark Trigger electrode
v(t) ~ (e
V Û v(t)
W1
t / W 1
V0
Charging circuit
) ~e
Storage capacitance
t / W 2
W2 t
Figure 6.2.34: Double exponential impulse voltage.
Trigger impulse
Switch (thyratron)
Trigger impulse
Figure 6.2.35: Triggering of the main discharge in a spark gap by an ignition impulse.
6.2 Generation of High Voltages
391
are still adequate for triggering by an ignition impulse [108]. It is best to determine the triggering range for a given arrangement empirically. The voltage at the spark gap should be chosen at the center of the triggering range to maintain the minimum possible probabilities of a spontaneous breakdown on the one hand and of an ignition failure on the other hand.
According to Eq. (6.2.33a), the voltage efficiency is K = CD/ (CD + CL) = 91 %. Therefore, at V0 = 140 kV, an impulse voltage peak value Vˆ = K ·V0 = 127 kV is obtained. A higher voltage efficiency K 1 is obviously obtained only under the condition
Note: Instead of triggering by an ignition spark, it is also possible to shift the potential of an intermediate electrode to such an extent that the main discharge is triggered [108].
The energy stored capacitively in CD is described as socalled “impulse energy”, and it amounts to about W = 100 J for V0 = 140 kV. The impulse energy is largely transformed into ohmic heat losses in the elements RF and RT, and to a smaller extent also into losses in the spark resistance of the switching spark gap G1 as well as in the capacitors and in the test object.
Chopped impulse voltages are generated by a chopping spark gap G2. The chopping time Tc is adjusted either by the electrode distance or is also determined by triggering. Even the parameters of switching impulse voltages result from the time constants W1 and W2. For time to crest (time to peak) and time to halfvalue (tail time), the following is approximately applicable, Tcr
W1W 2 W ln 2 W 2 W1 W1
T2
W 2 ln
(6.2.37)
and 2
K
(6.2.38)
under the assumption T2 = Th > 10·Tcr [135]. Example: Dimensioning of an impulse circuit A discharge capacitor CD = 10 nF (V0 = 140 kV) and a capacitive voltage divider with a highvoltage capacitance CV = 200 pF are provided for an impulse circuit setup. The impulse circuit elements shall be dimensioned according to basic circuit 1 in such a way that a lightning impulse voltage 1.2/50 is generated at a test object capacitance CT = 800 pF. The time constants W1 = 405 ns and W2 = 68.5 μs result from T1 = 1.2 μs and T2 = 50 μs with Eq. (6.2.35) and 6 as well as Table 6.2.32. The total load capacitance is CL = CV + CT = 1 nF. Thus the discharging resistance (tail resistance) RT is obtained from Eq. (6.2.33c) as RT = W2/ (CD + CL) = 6.2 k:. The damping resistance (front resistance) is RF = W1(1/CD + 1/CL) = 450 : according to Eq. (6.2.33b).
CD >> CL .
(6.2.39)
Often, the properties of the test object change the form of the impulse voltage to such an extent that the permissible tolerances are no longer maintained: large test object capacitances increase the rise time constant W1, but the influence on the wave tail time constant W2 is weak for comparatively large discharge capacitances. The front time is adjusted by changing the damping resistor RF. In a modular system, for example, the given resistances can be used in series connections and parallel connections. When using a tapetype resistor web, there is generally the option to make adjustments by bridging sections. Note: Resistor webs are made woven of insulating fabric tapes with meandershaped continuous resistance wires of large length. High voltage resistors consist of series connections of many lowinductance partial resistors that can be immersed in oil or embedded in cast resin to increase the voltage strength.
6.2.3.3 Multistage Impulse Voltage Generators
The voltage of a singlestage impulse circuit is mainly restricted to approximately 100 to 300 kV by the voltage rating of the components. Multistage generators according to Erwin Marx, socalled Marx generators, are used for higher impulse voltages. By parallel charging of stages, shortduration series connection of the discharge capacitors and series discharging, a temporary multiplication of voltage occurs, Figures 6.2.36 and 6.2.37.
392
6 TESTING, MEASURING AND DIAGNOSIS
Impulse generator with sparkgap column
Test object
Chopping spark gap
Voltage divider
R Fe
RV
v (t)
Charging device
R'C
Triggering
R'Fi
CV
R'T CT
C'D
Storage oscilloscope
Figure 6.2.36: Multistage impulse generator or "Marx generator" with related impulse circuit, see Fig. 6.2.37.
Charging of discharge capacitances CD' takes place in a parallel connection on two bus bars via charging and discharging resistors RC' and RT'. Therefore, the charging device needs only be dimensioned for the singlestage voltage V0. All discharge capacitances CD' are connected in series by igniting the switching spark gaps. For n stages, the summated charging voltage V06
=
n·V0
(6.2.310)
is available at the generator head in a resulting discharge capacitance CD
= (1/n)·CD'
(6.2.311)
The resultant load capacitance consists of the sum of the test object capacitance and voltage divider capacitance: CL
= CT + CV
(6.2.312)
Note: Voltage divider capacitance CV is often chosen to be large compared to the test object capacitances, which therefore have only a weak influence on the front time. The load capacitance CL  CV is charged via the resultant (fronttime) damping resistance RF, which is the sum of the internally distributed damping resistances RFi', the concentrated external damping resistance RFe and the resultant damping resistance of the voltage divider RV: RF
= n·RFi' + RFa + RV (6.2.313)
The discharge capacitances are discharged via the resistances R'T and R'C with the switching spark gaps ignited. If RC' >> RT' is selected, the resultant discharging resistance (tail resistance) is given by RT
= n·RT'.
(6.2.314)
6.2 Generation of High Voltages
393
Figure 6.2.37: Top:Tenstage impulse generator (summated charging voltage 1000kV) with direct voltage supply (left) and damped capacitive impulse voltage divider (right) in the high voltage test laboratory of Hochschule WürzburgSchweinfurt. Right: UHV impulse generator (summated charging voltage 3200 kV) with impulse voltage divider (left) and chopping spark gap (right), Picture HSP Hochspannungsgeräte, Troisdorf/ Highvolt, Dresden.
For the calculation, Eqs. (6.2.31) to (3) can be applied with the resultant parameters (CD, CL, RF, RT) or with the parameters of the individual stages (CD', CL' = n·CL, RF' = RF/n and RT'). Multiplication circuits are possible for both basic circuits 1 and 2. Note: Modern impulse generators are frequently designed to be modular, i.e. the stages can be connected in different combinations, in series or parallel. This results in greater flexibility for adaptation of the generator to different test objects as well as for onsitetests.
All spark gaps must be adjusted in such a way that they do not automatically ignite for an applied direct voltage V0. Fireing of the generator is caused by triggering the lowest spark gap that connects the two first discharge capacitors in series. Thereafter, the doubled loading voltage occurs at the second spark gap and owing to high overvoltage, it results in a rapid breakdown. Here it is assumed that the
stray capacitances to ground temporarily maintain the upper electrode of the second spark gap approximately at ground potential. The other spark gaps are progressively ignited from bottom to top by everincreasing overvoltages. The arrangement of discharge gaps one above the other in a spark gap column should ensure that the UVradiation emitted by the first discharge generates start electrons at the electrode surfaces of the higher spark gaps and thereby minimizes the ignition delay time and statistical dispersion (“jitter”). Note: Complete ignition of impulse generators can be improved by additional capacitors to ground in the lower stages if the stray capacitances are not adequate for reliable ignition. For large generators, simultaneous triggering of multiple successive stages is often useful to achieve reproducible ignition with less dispersion. Finally, for extreme requirements regarding jitter, potentialfree laser triggering is possible.
394
6 TESTING, MEASURING AND DIAGNOSIS
Note: Dirt on the electrode surfaces frequently causes nontriggered spontaneous ignitions. It is therefore recommended to burn away any dirt by multiple test triggers and to check for reliable operation.
Arrangement of impulse circuit elements is carried out in accordance with Figure 6.2.36 in such a way that the impulse generator is connected directly to the test object. The voltage divider must be connected in a separate circuit starting from the test object to record the voltage at the test object as accurately as possible. To avoid oscillations and inductive coupling impedances, the high voltage connections and ground connections must be made while keeping insulation distances at the shortest paths possible. Reference conductors are arranged radially to a central reference point and are grounded centrally, Figure 6.2.36, Section 6.3.8. Note: Highvoltage conductors must not be provided with large radii of curvature as for DC voltages and AC voltages. Owing to very shortduration transient voltage stress, the dielectric strength can be ensured by adequate distances.
6.2.3.4 Overshoot and Back Swing
Owing to parasitic properties of the test circuit or the test object that is connected, the impulse voltage waveform can considerably be distorted and it can be deviate from the doubleexponential function according to Eq. (6.2.34). Mainly the overshoot in the front of the voltage curve (a), the definition of a test voltage amplitude (b) and the back swing in the tail of the voltage curve (c) is a matter of concern.
L Circuit CD
RF
1 μH/m
CL
CCircuit Figure 6.2.38: Damping of an impulse circuit by the resultant damping resistance.
a) Overshoot In the case of spatially extended impulse circuits, i.e. especially for multistage generators, appreciable circuit inductances and oscillations occur. They can be ignored in to a first approximation if there is at least a critical damping of the circuit. By the damping resistance (front resistance) RF. For a simple RLC series resonant circuit, this results in a damping condition in accordance with Figure 6.2.38: L Circuit (6.2.315) RF > 2 · CCircuit
The series connection of the discharge capacitance and the load capacitance must be considered as the circuit capacitance. The circuit inductance can be roughly estimated from the length of the electric circuit of the oscillating circuit with 1 μH/m, see Figure 6.2.36 with a boldly drawn discharge circuit. The damping resistance (front resistance) includes the internal and external damping resistances as well as the voltage divider resistance RV, if the divider capacitance represents the major proportion of the load capacitance. Example: Spatial extension of an impulse circuit The maximum possible spatial extension of the impulse circuit shall be estimated for the example (CD = 10 nF, CL = 1 nF, RF = 450 :) calculated in Section 6.2.3.2. The effective capacitance results from the series connection of CD and CL to CCircuit = 0.909 nF. For RF, a possible damping by a divider resistance is not considered, since the load capacitance is concentrated largely in the test object capacitance (CT = 0.8 nF). LCircuit < 46 μH is obtained with RF = 450 : from Eq. (6.2.315). This corresponds approximately to a maximum circuit length of l < 46 m.
For large impulse generators or high load capacitances (with accordingly small damping resistances), compliance with the damping condition according to Eq. (6.2.315) can lead to difficulties. Note: Following the response of the chopping spark gap, a high frequency oscillation occurs at first in the
6.2 Generation of High Voltages
395
circuit of the test object and the chopping spark gap, and it is only very poorly damped.
obsolete) procedure that the test voltage amplitude Vˆt below 500 kHz must be inferred from the extreme value Vˆ of the oscillating
b) Test voltage amplitude
e
voltage and above that from the peak value Vˆb of an averaged curve (base curve), Figure 6.2.39 (below, grey curve), does not correspond to the continuous breakdown behavior of insulations in dependence on stress duration.
The exact performance of an impulse circuit can only be determined by network analysis. However, the knowledge of all relevant equivalent netework elements is generally not given for that. Therefore, it is a practical difficulty to determine the test voltage amplitude from a measured impulse voltage curve which contains superimposed oszillations to a greater or lesser extent, Figure 6.2.39 (top left). Thus, significant differences 'v between the extreme value Vˆe of the measured curve and the peak value Vˆ of the doubleexponential base curve ac
Therefore, IEC 600601 describes the following evaluation procedure based on a continuous curve [133], [489], Figure 6.2.39: The recorded oscillating impulse voltage vrec(t) is approximated by a doubleexponential base curve vb(t) according to Eq. (6.2.34). The difference between recorded curve and base curve is the residual curve vr(t), it represents the superimposed oscillating content, Figure 6.2.39 (top left). This oscillating content is filtered according to the socalled kfactor
b
cording to Eq. (6.2.34) can occur. The previously used discrete (and meanwhile
Test voltage curve acc. to IEC 600601 (with oscillating content after damping)
Recorded impulse voltage curve (with oscillations) v rec
'v
v rec
vb Base curve Ûe U V U V Ût U V Ûb
Calculation of the difference in the time domain vr
v rf
t
0.5
t Filtered residual curve v rf (oscillating content after damping)
Transformation into the frequency domain 1
Base curve Superposition in the time domain
Residual curve v r (oscillating content)
Vr
vb
vt
Filtering in the frequency domain
Transformation into the time domain V rf
Old method (discrete)
V rf k (f) = Vr
500 k
Improved method (continuous)
f / Hz
0 10 k
100 k
1M
10 M
Figure 6.2.39: Method for the determination of the test voltage curve from a measured impulse voltage with superimposed oscillations. Damping of the ocillating content according to Eq. (6.2.316) and IEC 600601.
396
6 TESTING, MEASURING AND DIAGNOSIS
curve k(f) = 1 / (1 + 2.2·(f / MHz)2)
(6.2.316)
in the frequency domain, and this results in a frequncydependent damping. Note: This filter characteristic represents the characteristic of breakdown voltage as a function of stress duration which was empirically determined for many insulating materials. Corresponding investigations have been performed, for example, with the basic high voltage materials such as air, SF6, popyethylene and oil [293]. Accordingly, for a slow overshoot with correspondingly long stress duration (f > 500 kHz), the oscillating contents are completely damped (k = 0).
The test voltage curve vt(t) with the amplitude Vˆt is calculated by superposition of the base curve vb(t) and the filterd residual curve vrf(t) in the time domain, Figure 6.2.39 (top right). G1 V0
RF RH
CD
L'L
v (t) R'2 = a² R 2
CL
Impulse circuit
R'W
Test object (transformer)
a R2
v (t) 40 μs
60 μs
Û V V 0.5 Û t
(b)
T2(a)
T2(b) (a)
R2 > 0 R2 = 0
V  0.5 Û
Figure 6.2.310: Lightning impulse voltage test of a singlephase transformer (a) with a damping of backswing by a resistive termination of the lowvoltage winding (b).
Note: The test voltage curve that is calculated according to the describe procedure is also used for the determination of the time parameters (front time Tf = T1 and time to halfvalue Th = T2 or tail time Tt resp.). Note: A simplified manual calculation of the test voltage amplitude can be based on the fundamental oscillation of the oscillation spectrum: depending on the frequency of the fundamental oscillation, it is weightened with the appropriate kfactor and then it is superimposed to the base curve. However, components of higher frequencies are not regarded in this case.
c) Back swing During the impulse voltage testing of transformers, particularly large changes in the wave tail of the impulse voltage occur, since the low short circuit impedance of the transformer is parallel to the discharging resistor if the low voltage winding of the transformer is shortcircuited, Figure 6.2.310 (top). In particular, the leakage inductance LV' = LL' of the transformer leads to “backswings” that must be restricted to 50 % [52]. The winding resistance of the transformer RW' is not enough for this in most of the cases. The impulse voltage waveform must be given a profile conforming to the standards by connecting a resistance R2 to the lowvoltage winding, whose value is multiplied with the square of the transformation ratio a for a transformation to R2' on the highvoltage side, Figure 6.2.310 (bottom). Note: The complex structure of transformer windings, in conjunction with the impulse circuit, leads to resonances that manifest themselves as intense superimposed oscillations in the impulse voltage waveform v(t), cf. to Section b).
6.2.3.5 Impulsecurrent Generators
Impulse currents are frequently used in association with impulse voltages for test purposes and they are generated similarly to impulse voltages by discharging capacitive energy storage capacitors. They should therefore be discussed briefly in this context. For double exponential impulse currents, the front time T1 and the time to halfvalue (tail
6.2 Generation of High Voltages
397
time) T2 are standardized. The tolerance range is +10 %. However, the front line must be defined through the 90% and the 10% point of the curve profile for the definition of front time! Back swing may not exceed 20% of the peak value; the amplitude of oscillations at peak current must remain under 5%. Standardized exponential impulse currents are, for example, 8/20 and 4/10, the numbers respectively specify the front time and time to halfvalue (tail time) in μs. Overvoltage protection devices (spark gaps, arresters) must be tested with exponential impulse currents with regard to their current carrying capacity following to their response. Moreover, tests for electromagnetic compatibility (EMC) of complex systems such as aircraft require the simulation of lightning strikes by impulse currents. Exponential impulse currents are generated from capacitor banks, in which discharge capacitors are connected in parallel and charged up to voltages of approximately 100 kV. Discharging takes place in parallel via minimal length paths of equal length via a switching spark gap and the test object (load), Figure 6.2.311. Owing to the circuit inductance, the current does not follow an ideal exponential function. It is rather a damped oscillation of a series resonance circuit. For the relationship between the current parameters T1, T2 and Î and the network elements of the impulse current circuit, refer to the relevant literature [16]. Triggering
L G CD
R RS
RL
Current measuring shunt
Figure 6.2.311: Generation of exponential impulse currents from a capacitor bank (schematic).
Rectangular or longduration impulse currents shall represent discharge currents, which, after the response of the overvoltage protection devices, are fed from long cables charged to operating voltage. The duration Td for which the current is larger than 0.9·Î is standardized. Td is largely in the range from 500 to 3200 μs [16].
Rectangular impulse currents and longduration impulse currents are generated by discharging LC lattice networks, whose capacitances have been charged in advance. Thus, an electrically long line is simulated by concentrated components, Figure 6.2.312. The rectangular impulse current simulates the traveling wave process to be emulated. Note: Strictly speaking, power frequency shortcircuit currents up to the 100 kA range with currentflow durations in the seconds range are not impulse currents. They are fed from the rotating mass of highperformance motorgenerator sets or from highcapacity highcurrent transformers.
6.2.3.6 Combined Test Circuits
Many electrical power engineering equipments are stressed both by high voltages as well as by high currents. Corresponding highpower test sources are impossible to implement with reasonable technical effort. Instead of this, one applies combined test circuits to generate high currents and high voltages in separate lowpower circuits. With the help of a control unit, the time sequence of current stress and voltage stress is aligned in such a way that the stresses correspond to the conditions in service or according to the test requirements, Figure 6.213 and 14. The response behavior of overvoltage protection devices is checked with impulse voltages. The discharge capacity is tested by the immediately subsequent feedin of an impulse current, Figure 6.2.313. Switching devices must be capable of interrupting a specific power frequency current and
398
6 TESTING, MEASURING AND DIAGNOSIS
of insulating the recurrent voltage across the switching contacts that open. The currentbreaking capacity is tested with socalled “synthetic test circuits”, in which a motorgenerator set supplies the power frequency current which is to be interrupted. Interrupting the current through the test object is followed by triggering of the impulse voltage circuit, which simulates the recurrent voltage by an oscillating voltage in a RLCcircuit, Figure 6.2.314. Triggering
L CD
G
RS
RL
Current measuring shunt Figure 6.2.312: Generation of rectangular impulse currents by discharging lattice networks (schematic). Impulse current circuit Triggering
Impulse voltage circuit Test object G
Figure 6.2.313: Testing an overvoltage arrester with impulse voltage and impulse current (schematic). Impulse current circuit Impulse voltage circuit Test object
M
G
"Current off": triggering Figure 6.2.314: "Synthetic test circuit" for testing the breaking capacity of switches (schematic).
6.2.3.7 Special Impulse Generators
Many technical applications require impulses that do not correspond to the impulse voltages that are standardized for insulation tests. A few examples are given in the following sections: a) Rectangular impulse voltages help in determining system properties or transmission properties of measuring systems by stepresponse measurements. Generally, voltages are relatively low, since it is not important to test the insulation but only to achieve a sufficiently high signal level. High voltages are only necessary for testing nonlinearities.
In the case of lower voltages, it is possible to use electronic function generators. Higher rectangular voltages of up to a few 100 V are generated by the parallel connection of charged capacitances to the test object. A low inductivity assembly and adequate damping of oscillations must be ensured for this. Rectangular voltages in the kV range can be generated with line generators (cable generators), see Section 2.6.3.3 and Figure 2.618. For this, a charged line is connected to the load through a lowinductive switch. Discharging the line by traveling waves ideally leads to a rectangular voltage impulse. According to the equivalent transmissionline circuit in Figure 2.68, the risetime constant for a resistive load R is practically exclusively determined by the inductance L of the switch and the characteristic (line) impedance Z, i.e. the following is applicable: W = L/(R + Z). For a capacitive load C, such as for a capacitive voltage divider, C is exponentially charged with the time constants W = ZC if the inductance can be neglected. Depending on the voltage, electronic switches, relays with mercury contacts, switching tubes (thyratrons) or switching spark gaps are used as switches. b) Very rapidly rising impulses in the ns range are used for the simulation of electromagnetic wave fields for testing of the electromagnetic compatibility (EMC) of devices and systems.
6.2 Generation of High Voltages
For example, the immunity to the socalled nuclear electromagnetic pulse (NEMP, HEMP high altitude electromagnetic pulse), that is expected for a nuclear explosion outside the earth’s atmosphere, is tested with a double exponential impulse whose rise time Tr is = 4 ns and whose time to halfvalue on wave tail T2 is = 200 ns [41]. The test object is exposed to the transient electromagnetic wave field in a parallelplate line, Figure 6.2.315. The supply is from a charged capacitor bank that in principle belongs to an impulse voltage circuit (discharge capacitance CD). The unavoidable inductance of the discharge circuit LD prolongs the attainable rise time too much. A socalled secondary circuit is therefore necessary, which can be designed to be of considerably low inductance, since significantly smaller insulation distances and overall dimensions are possible owing to the only shortduration voltage stress. That is, LT 50 μs), since the impulse voltagetime characteristics remain flat down to the μs range. For a sphere gap grounded on one side, a polarity effect for impulse voltages results from field distortions at larger flashover distances only, because the field strength at the grounded electrode is reduced owing to the surrounding grounded structures and is increased at the voltage electrode (asymmetry relative to ground). Note: According to Section 3.2.5.2, it might be assumed that the breakdown voltage for a positive voltage electrode (or “point”) should be lower than for a negative electrode. However, the opposite is observed in reality, Table 6.3.11. For this, better starting conditions for electron avalanches at the negative point are important since the first avalanche leads to a breakdown in a weakly nonuniform field (streamer mechanism). For impulse voltages, no fielddistorting spacecharge cloud can be formed.
Some disadvantages of the sphere gap are the collapse of the measured voltage during breakdown and the dispersion of the individual breakdown values, which necessitates preionization (with UV light or laser light) and forming a mean value of many breakdown values. Before a measurement, any deposited dirt must be burnt away by cleaning breakdowns until reproducible, less dispersed values are obtained. Additionally, there is neither a direct nor a continuous voltage display. The sphere gap mainly helps in check measurements, i.e. if another measuring system has to be checked. Under this, the voltage is repeatedly increased until breakdown for an exactly known distance d. Owing to deionization of the gap, the interval between the breakdowns must be at least 30 s. An average breakdown value is obtained from the readings
6.3 High Voltage Measurement Techniques
403
of the measurement system to be checked. It can be compared to the voltage value that is associated with the distance d and the prevailing atmospheric conditions.
impulse voltage and of 1.5 % for a switching impulse voltage. Alternatively, the breakdown mean value can be determined according to the upanddown method with at least 20 impulse voltage stresses in 1 % steps, Figure 3.1.1b).
Note: For measuring an AC voltage, the voltage is increased slowly ten times until breakdown. The resulting standard deviation of the displayed values must not exceed 1%.
Measurements for direct voltages are problematic since dust deposits can lead to large dispersions. Therefore, using a rodtorod spark gap provides better results, Section 6.3.1.2. For measurements with a sphere gap, a constant air flow of 3 m/s is recommended if necessary, as well as a very large number of breakdowns until a stable value is achieved.
For the measurement of an impulse voltage, the amplitudes of successive impulses are increased in steps of approx. 1 % of the expected breakdown value until breakdown. The trials repeated for ten times should result in a standard deviation of 1 % for a lightning
The table value (standard value) Vˆbd50(0) is valid under the standard atmospheric condi
Tabelle 6.3.11: Peak values of 50 % breakdown voltage on unipolar grounded sphere gap in kV for different sphere diameters D and flashover distances d for DC voltage, AC voltage and negative impulse voltage (left columns) as well as positive impulse voltage (right columns) under standard atmospheric conditions (T = 20 °C, p = 1013 mbar = 1013 hPa = 760 Torr). The impulse voltages are valid for times to halfvalue on wave tail longer than or equal to 50 μs; the polarity effect for positive impulse voltages is marked by numbers in italics (see the note in the text). Numbers presented in bold correspond to the values of the uniform field and are valid also for larger sphere diameters D. Measurement uncertainties are assumed for AC voltage and impulse voltage for d < D/2 at ±3 % and for DC voltage for d < 0.8·D/2 at ±5 %, the values presented in brackets rerfer to larger, unexplained dispersions.
0,5 1 1,5
= 5 cm D = = 10 cm D = = 15 cm D= = ~ = ~ = ~ + + + 17,4 17,4 16,8 16,8 32,0 32,0 31,7 31,7 45,5 46,2 45,5 45,5
2 2,4 3
57,5 59,5 65,5 69,0 (75,5) (81,0)
4 5 6
(88,5) (97,5) 105 109 123 130 (138) (148)
7 8 9
(150) (163)
d cm
10 12 14 16 18 20
59,0 69,5 84,0
59,0 70,0 85,5
70,0 85,5 110 133 152
111 136 158
169 178 (185) (196) (198) (212) (209) (226) (229) (249)
Area with increased dispersion and externally influenced field
= 50 cm D= = ~ +
= 75 cm D= = ~ +
Detailed tables are given in the relevant standards [142], [143]
= 100 cm D= = ~ +
86,0
2 2,4 3
V Û
bd50(0)
86,0
d cm 0,5 1 1,5
Area with almost uniform field
kV
112 137 161
112 138 163
138 164
138 164
184 206 226
187 211 233
189 214 239
189 214 239
190 215 240
190 215 240
241
241
244 254 275 291 (302) (323)
263 309 353
263 311 357
265 315 363
265 315 363
266 318 366
266 10 318 12 366 14
(326) (350) (347) (374) (366) (395)
392 429 460
402 442 480
410 453 492
411 458 505
414 462 510
414 16 462 18 510 20
585 695 (835)
595 710 875
600 24 725 30 900 40
515 540 565 (585) (620) 665 (670) (715) (800)
24 30 40 50 60 70
70,0 85,5
= 25 cm D= = ~ +
4 5 6 7 8 9
(895) (940) 1010 1040 50 (970) (1020) (1110) (1150) 60 (1200) (1240) 70
404
6 TESTING, MEASURING AND DIAGNOSIS
tions temperature
T0 = 20 °C,
atmospheric pressure
p0 = 1013 mbar
and 3
absolute humidity
h0 = 8.5 g/m ,
and it must be converted to the applicable peak value Vˆbd50 under the given atmospheric conditions (T, p, h). Changes in the air density and the humidity are corrected. The dependence of the breakdown on pressure and temperature results directly from Paschen’s law, Section 3.2.2.4. An increased air humidity leads to an increased electron affinity and thus to an increase in the breakdown voltage. A simplified conversion, which ignores the slight curvature of the Paschen curve, assumes proportionality between breakdown voltage and relative air density GThe absolute humidity h is considered by applying a correction factor k: Vˆbd50  Vˆbd50(0) · G · k
G k
(6.3.12)
p 273 K T0 · p0 273 K T 1 0.002 ·(
h/gm
G
3
 8.85)
Note: Owing to long years of painful experience in practical training, it shall be mentioned that measured values are given on the left and standard (table) values are given on the right hand side of Eq. (6.3.12)! Note: Conversion to standard conditions in nonuniform field is described in Section 3.2.5.5
The sphere gap was formerly often used as a simple and clear calibration tool for other measurement systems. However, the measurement uncertainty of 3 % (for a confidence interval of 95 %) that can be attained for AC voltages and impulse voltages or 5 % for DC voltages is no longer adequate for a reference system according to the standards, see Table 6.11. However, the application as a measuring system for AC voltages and impulse volt
ages, predominantly for check measurements, is possible if a standard deviation of 1% is attained for AC voltages and lightning impulse voltages and a deviation of 1.5% is attained for switching impulse voltages. The measurement uncertainty can be reduced a little more by an individual calibration of a sphere gap with an accordingly suitable reference measuring system. A breakdown provides a very clear and direct proof of voltage stress. Therefore, sphere gaps still have great practical value for quick and indicative check measurements. Note: Sphere gaps can also be used as protective gaps, as chopping spark gaps and as modifiable capacitances in high voltage laboratories. There are vertical and horizontal sphere gaps.
6.3.1.2 Rodtorod Spark Gap
Since the accuracy of the sphere gap for DC voltages is distinctly poorer than for AC voltages and impulse voltages, the vertical or horizontal rodtorod spark gap is recommended for relatively high DC voltages, [142], [143], Figure 6.3.12. The rods must have a rectangular and sharpedged cross section (side length 15 to 25 mm) so that corona discharges and an exactly reproducible breakdown behavior occur. For flashover distances between 250 and 2500 mm, there is a largely linear relationship that is explained by the growth of the streamer discharges: Vˆbd50(0) = 2 kV + d·0.534 kV/mm·
(6.3.13a)
Note: Under 120 kV, this relationship is no longer valid since the streamer discharges are initiated only above 120 kV.
With respect to the air density, correction of the standard value is carried out in accordance with Eq. (6.3.12). Similar to Eq. (3.270b), a considerably larger influence of humidity is observed here than in the uniform field of a sphere gap:
6.3 High Voltage Measurement Techniques
k
1 0,014 ·(
h/gm
405
3
 11) (6.3.13b)
G
Eq. (6.3.1) is valid in the humidity range from 3 1 to 13 g/m and allows a voltage determination with an estimated uncertainty of 3 % for a confidence interval of not less than 95 % [142], [143]. Note: There are tests that have detected even smaller standard deviations (< 1 %) and measurement uncertainties (±2 %) [144]. For round rods (D = 20 mm) and rounded off rod ends, the following is applicable: Vˆbd50 = G·[V0 + d·5.1 kV/cm]· 3
[0.051·(8.65 + h/g/m )]
0.25
(6.3.14)
Here, V0 is 20 kV for positive DC voltages, V0 is 15 kV for negative DC voltages and h lies between 4 and 20 g/m³.
6.3.2 Electrostatic Voltmeter
Figure 6.3.12: Rodtorod spark gap for the measurement of high DC voltages, rectangular rod crosssection.
Return spring (Spring const. D) Mirror Small field plate (Area A)
Fel E
V d Rogowski electrodes Projection plane of light pointer with scale graduation Figure 6.3.21: Electrostatic voltmeter (voltmeter according to Starke and Schröder).
250 < d
< 2500
in mm
i.e. in a uniform field for example, an eccentrically supported small plate is deflected so far by the force of the field until the field force corresponds to the force of a return spring. Using a mirror, the deflection x is displayed by projection of a pointer image on a scale divided into voltage values. With equilibrium of forces 2
Fel = 0.5 H0 A V /d = FSpring = D·x , the deflection is proportional to the square of the voltage and inversely proportional to the square of the electrode distance: 2
2
x ~ V /d Light source
< 5000
> 2000
2
Electrostatic voltmeters provide an absolute voltage measurement, that is, voltage measurement can be traced back to measurement of other physical quantities (force and distance), Figure 6.3.21. In a computable electric field,
> 1000
(6.3.21)
The reading for DC voltages is independent of the polarity. In the case of AC voltages, the system cannot follow the pulsating force owing to its mass inertia, and hence the mean value of the square of the voltage is displayed. This is therefore a true r.m.s. measurement that is independent of the voltage waveform. Displaying impulse voltages is not possible. High accuracy (up to 0.1%) is only achieved in the upper section of the voltage measuring scale owing to the squarelaw dependence of the reading on the voltage; the accuracy falls steeply for lower voltages. A selection of the measuring range is possible in accordance with Eq. (6.3.21) by changing the electrode distance d. The exceptional property of electrostatic voltmeters lies in their extremely low feedback to
406
the voltage source via the very high insulation resistance and via the comparatively low capacitance between the electrodes. Electrostatic voltmeters can therefore be used for the measurement of DC potentials, even in the case of highresistive arrangements and high internal impedances of the voltage source. A compact construction with a closed housing is designed for up to a few 10 kV. Above 100 kV, rounding off the electrode edges gives rise to such large dimensions that compressedgasinsulated designs are used. Electrostatic voltmeters are precision instruments with sensitive adjustment mechanics and projection optics. Generally, they are used only under the controlled conditions of a laboratory.
6.3.3 Field Sensors 6.3.3.1 Electrically Short Sensors
Classic field sensors record timevarying electric and magnetic field strengths by a displacement current coupled in a sensor surface or by a rotational voltage induced in a sensor loop, Figure 6.3.31 (top, left and right). Here, the sensors are assumed to be spatially concentrated or “electrically short”, so that lumped circuits with lumped equivalent network elements can be specified, Figure 6.3.31 (bottom). Broadband measurement of extremely rapidly varying processes is possible through appropriate small sensor dimensions. For a known field geometry, such as in uniform or coaxially symmetric fields, conclusions about the voltage, the current or the electromagnetic wave processes can be drawn from the measured variables. Important applications are, for example, the broadband measurement of fast transients and partial discharge impulses in gas insulated switchgear, the directional coupler technique for directionally selective measurement of partial discharge impulses and interference impulses [215] or the measurement of pulse forming processes of pulse power technology [5], [145], [146], [147], [148].
6 TESTING, MEASURING AND DIAGNOSIS Note: The sensitivity of the capacitive and magnetic sensors to unwanted magnetic and capacitive coupling is reduced with the help of a symmetrical structure, Figure 6.3.31.
Since the signals are proportional to the time derivatives of field quantities, generally they must be integrated. Integration can be performed actively by broadband integration amplifiers or by numerical integration of the digitized signals. However, in the case of extremely rapidly varying processes for a capacitive sensor, direct passive integration by a defined sensor capacitance CS that shall be only loaded with a high impedance RS is recommended. For a magnetic sensor, the selfinductance LS of the magnetic sensor loop along with a lowimpedance load RS can be used for passive integration, Figure 6.3.31 (bottom). Note: The capacitive sensor with a capacitive load CS can also be interpreted as a capacitive voltage divider, if the coupling of the displacement current is described by a highvoltage stray capacitance CHV, Figure 6.3.31 (bottom center).
D (t)
B (t)
Load
Load
D·A C HV B·A D·A
D·A
LS
u (t) CS R S Capacitive sensor
CS R S Capacitive highvoltage divider
RS Magnetic sensor
Figure 6.3.31: Coupling of displacement current in a capacitive sensor surface and induction of a rotational voltage in a magnetic sensor loop (top, left and right) with equivalent network representations (bottom).
6.3 High Voltage Measurement Techniques
407
6.3.3.2 Electrically Long Sensors
In the case of extremely rapidly changing field variables or spatially extended sensors, such as Rogowski coils, the runtime events in the sensor must also be considered [145], [146]. That is, the sensor itself must be understood as a system with distributed parameters or as an “electrically long” traveling wave line with the characteristic impedance Z, Figure 6.3.32, also see Section 2.6. It could be proven that even electrically long sensors are suitable for measuring extremely rapidly varying processes if they are operated either with a very highimpedance load (R >> Z for capacitive sensors) or with a very lowimpedance load (R > Z
x
u Screen
tions. The spatial field distribution along the sensor contour in the xdirection can then be determined for a known time function by numerical deconvolution [5].
D (t) Z R 90°, characteristics are not unique since Eq. (6.3.33) is a periodic function. For a measurement, it must therefore be tracked in which section of the characteristic the measurement is made, Figure 6.3.36.
Polarizer generates linearly polarized light
EL
=
Electric field inducese an optical axis: induced birefringence
E
EL A
Figure 6.3.35: Elektrooptical field strength measurment through induced birefringence.
Elliptically polarized light results from phase shifting.
I1
Polarizer (Analyzer)
x I2 Intensitymodulated light
410
6 TESTING, MEASURING AND DIAGNOSIS
dependence of the angle of rotation D on the magnetic flux density B:
1
D
I2 I max
'M
S E
Figure 6.3.36: Characteristic of a simple Kerr cell.
Note: Intensity variations do not only arise from phase shifts but also from intensity variations of the light source or from (slow) changes in the optical path. Therefore, the intensity signal containing the field strength information must be related to a reference signal obtained, for example, by means of a beam splitter.
The characteristic illustrated for the quadratic Kerr effect in Figure 6.3.36 is analogously also applicable to the linear Pockels effect, but the maxima and minima follow at equal intervals, because the phase shift increases linearly with the field strength in accordance with Eq. (6.3.32). b) Induced optical activity For optically active materials, the plane of polarization of traversing light is rotated. Here, there are material causing anticlockwise or clockwise rotation (direction of view against the direction of light). This natural optical activity can be used interalia for determining the concentration of solutions (e.g. sugar solutions). Note: Optical activity can be described by different phase velocities for two oppositely rotating circularly polarized waves, which on superimposition always result in linearly polarized light, but with rotated direction of polarization. Analogously to the double refraction (birefringence) of linearly polarized waves dicussed above, this is described as circular double refraction (circular birefringence).
In some materials (e.g. in quartz or in lightconducting fiber optic glasses), optical activity can be induced parallel to the direction of propagation by magnetic fields, Figure 6.3.37. This socalled Faraday effect shows a linear
= V·l·B.
(6.3.34)
Here, V is the socalled Verdet constant (and not a voltage). With two crossed polarizers, the modulation of the polarization state can be converted into an intensity modulation, whereby minimal intensity is obtained at D = 0 and maximum intensity is obtained at D = S/2. Also in this case, a quadratic relationship is applicable: I 2/ I1
2
sin D
=
(6.3.35)
With Eq. (6.3.34), this forms a nonlinear characteristic that is not unique. Figure 6.3.36 is likewise applicable; however, the maxima and minima follow at equal intervals, because the angle increases linearly with magnetic flux density B in accordance with Eq. (6.3.34). c) Analysis of characteristic curves Crossed polarizers according to Figures 6.3.35 and 7 are suitable, for example, for cells for intensity modulation in which the full range between maximum and minimum intensity is to be used. For measuring purposes, especially for small phase shifts or for small angles of rotation, nonlinearity and low sensitivity are a disadvantage. Improved evaluation options are described in the following sections. Induced optical activity: If in Figure 6.3.37, the analyzer is turned back by 45°, this acts as
Laser
Polarizer
B
Rotation of the plane of polarization
D
B Faraday effect Figure 6.3.37: Induced optical activity.
Analyzer
411
6.3 High Voltage Measurement Techniques
an additional rotation of the plane of polarization by +45°. In accordance with Eq. (6.3.35), the working point shifts into the area of half intensity I 2/ I 1
= sin (45°+D)  ½+D 2
(6.3.36)
and into the linear region of the characteristic with the highest sensitivity, Figure 6.3.38. Note: For magnetooptical current transformers very long effective lengths in the field direction and large angles of rotation D can be attained by winding optical wave guides, so that multiple maxima and minima are passed through. Signals must be numerically evaluated. Another option is that a reference current must be set by a control circuit in such a way that the rotation of the plane of polarization caused by the field to be measured is reversed (compensated) in a second Faraday cell.
Induced birefingence: A linearization that is comparable with Eq. (6.3.36) and an increase in sensitivity of the optical characteristic are possible, even for induced birefringence (Kerr effect and Pockels effect), if the working point is adjusted for half the intensity and maximum gradient according to Eq. (6.3.33) for one of the components by a phase shift by 'M = 90° :
I2/I1 = sin (45°+'M/2)  ½+ 'M/2 2
(6.3.37)
The adjustment of this working point is not made by rotation of the analyzer, but by a socalled O/4 plate, which effects a phase displacement of orthogonal light components by a quarter of the wavelength, that is by the abovementioned 90°, and thus generates circularly polarized light. I2 I max
Note: Unfortunately, even for linearized optical characteristic, the Kerr effect is still nonlinear, Eq 6.3.31. Therefore, for slowly changing fields, it is recommended to superimpose on the field to be measured a known alternating field with the angular frequency Z The fundamental component of the light intensity with Z is then directly proportional to the field strength [366]: For the measurement of a DC field E0, the Kerr cell characteristic can be linerarized by modulation with a commparatively weak sinusoidal field E1= Ê1·sin(Zt) which is superimposed to the measured field [494], [495]. The resulting field E = E0 + E1 gives the intensity 2
2
I2 ~ E = (E0 + E1) = 2
2
2
E0 + 2 E0 Ê1·sin(Zt) + Ê1 ·sin (Zt) . (6.3.38) The three components with the different frequencies Z = 0, Z and 2Z can be separated by means of filters. The second term is proportional to the measured quantity E0 and the third term can be used as a reference signal.
d) Applications While using electrooptical sensors it must be noted that the signals can also be superimposed by the mechanical elastooptic effect (birefringence induced by mechanical stresses). Electrooptical sensors must, therefore, be protected against mechanical stresses and vibrations. Further, it must be noted that the constants in Eqs. (6.3.31), (2) and (4) do not only depend on the material but also on the wavelength of the light used and on the temperature, so that according corrective calculations may be necessary. In optical systems, fluctuating intensities (caused by the light source) or changes in the optical path (caused by contaminations or ageing) must be monitored and compensated (drift compensation). This is simpler to implement for short periods in testsetups than in instrument transformers for current and voltage, from which a very high longterm stability (durability) is expected.
1
0.5
S 4
S 2
D
Figure 6.3.38: Linearization of the characteristic.
Note: Options for drift compensation are optical reference paths, modulation of light intensity, regulated compensating circuits as well as methods for determin
412 ing phase shifts 'M and Dindependently of intensity.
6 TESTING, MEASURING AND DIAGNOSIS angles
of
rotation
Owing the to difficulties mentioned, application options of electrooptical effects are still restricted to a few special cases: Magnetooptic measuring transformers were developed based on the Faraday effect in optical fibers [368], see Section 6.3.5.2 with Figure 6.3.5.3 (c), Kerr cells with larger Kerr constants (e.g. in nitro benzene) are used for the switching and modulation of light flux. Potentialfree field strength measurements are feasible with Pockels cells [152]. The Kerr effect is often the only option for the measurement of electric field distributions in transparent insulating liquids, such as in insulating oil or in water. Here, the application spectrum extends from the measurement of stationary or slowly changing fields in HVDC insulation and for electrostatic charges [366], [367], [494], [495] up to very rapidly changing periodic or transient fields of pulsed power technology in the ns range [153].
arity of the components used with respect to the voltage. High voltage and low voltage sections of a divider may not change with temperature (or only in the same manner), so that the divider ratio is maintained even for temperature fluctuations. Note: Temperatureindependent capacitances occur in compressedgas capacitors. For other capacitor dielectrics, a certain amount of compensation is attained by the combination of materials with positive and negative temperature coefficients. For special requirements, the room temperature may have to be maintained constant.
The large extent of a high voltage divider leads to distributed stray capacitances towards ground and high voltage electrodes. Thereby, the dynamic system behavior changes in an undefined manner and is also generally dependent on frequency, see Section 6.3.4.3. The dynamic response characteristic of voltage dividers is especially important for the proper transfer of fast impulse voltage signals. It is generally determined not by frequency response measurements but by step response measurements, Figure 6.3.41.
6.3.4 Voltage Dividers Generally, high voltages are divided by many orders of magnitude (e.g. from the MV range into the 100 V range) by voltage dividers down to a level which facilitates reading with measuring instruments, oscilloscopes and transient recorders or further processing in electronic circuits and computers. A highvoltage divider always consists of a highvoltage arm (highvoltage section) and a lowvoltage arm (lowvoltage section) in series.
v 2 (t )/ V2 1
T1
T2
Tr 6.3.4.1 Response Characteristic
The extrapolation of the divider ratio calibrated at low voltage by many orders of magnitude to the high voltage level requires line
T3
T4 90 %
10 %
Figure 6.3.41: Stepresponse measurements at a voltage divider with concentrated and with distributed step generator (top left and right). Overshooting and aperiodic profile of stepresponse function with definition of a response time and a rise time (bottom).
t
6.3 High Voltage Measurement Techniques
The stepfunction fed into the head of the divider generates an aperiodic or slightly overshooting stepresponse. For this, the overshooting must not exceed 5%. In high voltage measurement techniques, sometimes the rate of rise is characterized by the response time Tresp and this is defined as the difference of the areas under the ideal step function and under the normalized stepresponse function g(t) = v2(t)/V2: f
Tresp
³ >1 g (t )@ dt
(6.3.41) However, the response time is not sufficient for the characterization of of dynamic system properties, as already shown by examples with negative response times, e.g. if there is a high overshooting. A better characterization is given by the rise time Tr between the 10 % and 90 % amplitude values [141]. For multiple independent elements of a measurement setup, (e.g. step function generator, divider, attenuator and oscilloscope) individual rise times are added geometrically: 2
2 1/2
Tr = [Tr1 + Tr2 + ... + Trn ]
(6.3.42)
Note: Here a socalled Gaussian system is assumed, whose attenuation increases quadratically with the frequency. This assumption is fulfilled with satisfactory precision for many cascade connections with lowpass characteristics [141].
Example: Stepresponse measurement Stepfunction generator, divider, attenuator and oscilloscope each exhibit a rise time of 1 ns. According to Eq. (6.3.42), the rise time of the recorded signal is Tr = 2 ns.
For exponentially increasing voltagetime characteristics, e.g. for RC elements and LR elements, the rise time Tr corresponds to 2.2 times the time constant W: Tr = 2.2·W
In Gaussian systems, for rise time and 3 dB bandwidth B, the applicable relationship is Tr·B = 0.35.
(6.3.44)
Note: For dividers with extremely low rise times, the electromagnetic radiation emanating directly from the step function generator gives rise to distortions in the stepresponse. They can be suppressed if the divider is situated in the cylindrical phase plane of the TEM wave which is generated by spatially distributed and synchronized step function generators [18], [19], Figure 6.3.41 (top right).
T1 T2 T3 ...
2
413
(6.3.43)
6.3.4.2 Divider Designs
a) Resistive voltage divider Resistive voltage dividers are exclusively suitable for DC voltage measurements, Figure 6.3.42 (a). Owing to stray capacitance to ground, a RC lattice network occurs with a distinct lowpass behavior. For resistances on the highvoltage side in the G: range and stray capacitances in the 10 pF range, the magnitude of the divider ratio
r = V2/V = R2/(R1 + R2)
(6.3.45)
decreases considerably even for frequencies of a few 10 Hz. The divider is no longer suitable for network frequency AC voltages. Note: For a more accurate conclusion, a quantitative analytical estimation of the frequency response by complex calculation with a simplified equivalent circuit is possible, Section 6.3.4.3 includes an example.
b) Resistivecapacitive voltage divider Resistivecapacitive voltage dividers (compensated resisitve voltage dividers) according to Figure 6.3.42 (b) are in principle suitable for all types of voltages if they fulfill the compensation condition
R1C1 = R1'C1' = R2C2 .
(6.3.46)
The compensation condition implies that the resistive and capacitive divider ratios of the two parallel divider columns must be equal, Figure 6.3.43 (curve 2). Ideally, a frequency
414
6 TESTING, MEASURING AND DIAGNOSIS
independent divider ratio r or a rectangular stepresponse results. r = v2(t)/v(t)
2
= R2/(R1 + R2)
2 3
(6.3.47)
Capacitive divider ratio
If the compensation condition is not fulfilled, a frequencydependent divider ratio or a step response with exponential transition processes results, Figure 6.3.43 (curves 1 and 3).
Despite good dynamic system behavior, high voltage dividers for very high voltages are not designed as compensated ohmic dividers, because two highvoltage divider columns are necessary for this. Often there is also no requirement for such a divider since test devices
The divider is only conditionally suited for impulse voltage measurements, since the un(c)
(d)
Lp R'1
R'1
C'1 C'1
v2
R2 Resistive divider
R2
C2
C2
Resistivecapacitive divider
Capacitive divider
t
damped capacitive column along with the measuring circuit inductance can lead to resonances, which must be suppressed by additional external damping resistances, see section d).
Note: During the design process of the divider, the parallel capacitances C1’ must be chosen to be so large that the stray capacitances to ground are negligible.
(b)
C 2 is too large
Figure 6.3.43: Step responses of a compensated resistive voltage divider for the cases of undercompensation (1), compensation (2) and overcompensation (3).
Note: If C2 is too small, we have undercompensation, since C1 is not adequately compensated. In the first instant, the capacitive divider ratio is effective and it results in a voltage step that is too high. If C2 is too large, we have overcompensation, Figure 6.3.43 (curve 3). The capacitive divider ratio gives a very low initial voltage.
(a)
Ohmic divider ratio
1
= C1/(C1 + C2)
v
C 2 is too small
v (t)
(e)
RS
Parasitic measuring circuit inductance
R'1
Lp
C'1
C'1
v
u C2 Capacitive divider with series resistance
(f)
R2 C2 Damped capacitive divider
Field sensor
DC voltage AC voltage (Impulse voltage)
Impulse voltage Fast Transients
Figure 6.3.42: Designs of highvoltage dividers and their suitability for different types of voltages.
6.3 High Voltage Measurement Techniques
for AC voltages, DC voltages and impulse voltages are generally already equipped with special dividers. Besides, two separate dividers can be used more flexibly. Compact high voltage probes of up to several 10 kV are designed as compensated voltage dividers. Spatially separated highvoltage and lowvoltage sections of C1/R1 and C2/R2 are connected via a matched coaxial line, which includes a distributed resistance for attenuation of travelingwave oscillations. The probe is balanced with a seriesconnected signal shaping network [141]. The probe forms a mached unit with the actual head, the connecting line and the termination network, lengthening of the connecting cable is generally not possible. Note: Other areas of application of the compensated divider are compact structures in devices with low voltages or secondary dividers of high bandwidth in the low voltage range.
c) Capacitive dividers Capacitive voltage dividers, Figure 6.3.42 (c), can not be used for DC voltage measurements, since a completely undefined resistive divider ratio results from undefined insulation resistances and from the load impedance. Capacitive dividers are especially suitable for AC voltage measurements in a wide frequency range, because although stray capacitances bring about a change in the magnitude, there is no frequency dependence of the divider ratio
r = v2(t)/v(t)
= C1/(C1 + C2)
(6.3.48)
In the case of impulse voltage measurements, similar to compensated dividers, sufficient external damping of the measuring circuit must be ensured, see section d). Owing to their simple construction, capacitive dividers are generally used in small, e.g. singlestage impulse circuits up to the 100 kV range. d) Capacitive divider with series resistor Capacitive voltage dividers lead to relatively weakly damped measuring circuits whose inductances increase with the height of the di
415
vider. For critical damping, a damping resistor whose resistance depends on the measuring circuit inductance and the divider capacitance is necessary according to Figure 6.2.38 and Eq. (6.2.315), see Figure 6.3.42 (d). Example: For a divider with 500 pF and a circuit inductance of 20 μH (that corresponds to a measuring circuit length of about 20 m), a damping resistance of RD > 100 : is obtained.
It must be noted that a damping resistance RD and a divider capacitance C1 form a RCelement whose rise time Tr = 2.2·RDC1
(6.3.49)
must be much shorter than the rise time of the impulse voltage to be measured. Example: In the abovementioned example, a rise time of the divider of Tr = 2.2·RDC1 = 110 ns results, and this is still adequate for the measurement of a lightning impulse voltage of 1.2/50 μs. Nevertheless, fast transients or traveling waves in the ns range can no longer be measured.
e) Damped capacitive dividers Damped capacitive dividers (Seriesdamped capacitive dividers, “Zaengl dividers”) are the typical impulse voltage dividers for high and highest voltages. Damping resistors are integrated into the divider column in a distributed arrangement in series with the capacitors, Figure 6.3.42 (e), not only to damp the inductance of the low voltage circuit, but also to suppress traveling waves that could be formed on a long undamped divider column. At high frequencies, the ohmic divider ratio is effective owing to low capacitive impedances, and the capacitive divider ratio is effective at low frequencies owing to high capacitive impedances. If the compensation condition
R1C1 = R1'C1' = R2C2
(6.3.410)
is met, a divider ratio independent of frequency theoretically results. Damped capacitive dividers with distributed resistances therefore (if they fulfill the compensation condition) have a
416
6 TESTING, MEASURING AND DIAGNOSIS
significantly higher upper cutoff frequency than capacitive dividers with concentrated series resistors. Damped capacitive dividers cannot be used for DC voltage measurements since no defined parallel resistances exist, similarly to capacitive dividers. The lower cutoff frequency is determined by the discharging of C2 through the coupling circuit.
I/I0 = 0.79 is obtained. That is, the error already amounts to 21%.
Only the purely capacitive divider remains independent of frequency, even under the effect of stray capacitances, because the entire
Toroid
f) Field sensors
C'G1
Very fast traveling wave processes and fast transients can be measured with field sensors that are integrated into the ground electrode and which take up the displacement current components of electromagnetic waves, Figure 6.3.42 (f). Field sensors are described in detail in Section 6.3.3.
C'G2 .... .... C'Gn
Z 1 /n ~
Z /2 CE·2/3 ~ 1
Z 1 /n ~
~
Z 1 /2
Z 1 /n ~
~
Z2
Z1 ~
V
Z 1 /n ~ Z 1 /n ~ Z2
V2
~
Z2 ~
V2
6.3.4.3 Stray Capacitances
The large extent of a high voltage divider leads to distributed stray capacitances to ground, through which currents are carried over to ground, bypassing the low voltage section, Figure 6.3.44. Thus, the transmission ratio changes in an undefined manner and is also largely frequency dependent.
Figure 6.3.44: High voltage divider with distributed stray capacitances to ground (lattice network structure), as well as equivalent circuits with and without concentrated stray capacitances to ground.
V R/ 2
Example: Ohmic divider with stray capacitance to ground Instead of the divider ratio, the current I through the divider column is calculated taking into consideration a stray capacitance to ground that is assumed to be concentrated. Here the comparatively small low voltage resistance can be ignored, Figure 6.3.45 (top). The analysis of the network with the help of a complex calculation leads to the following current magnitude:
I
V R 1 (
Z CR 4
.
(6.3.411)
Stray capacitance to ground
Highvoltage resitances C
I Z is similar to openended line termination, at which the traveling voltage wave is reflected with doubled value 2·v2(t)/2 = v2(t), so that the original amplitude occurs again. The returning wave is absorbed nearly without reflection at the input side by (ZR2)+R2 = Z, because C2 exhibits a very low impedance. Note: By charging the oscilloscope input capacitance (approx. 15 pF) via the cable impedance (approx. 50 :), the rise time of the measurement system is increased by a proportion of approximately 1.7 ns that is to be added in accordance with Eq. (6.3.42).
Connection of the highvoltage section
To the coaxial measuring tap or to the secondary divider
Figure 6.3.47: Lowinductive design of a capacitive divider's lowvoltage arm.
For slowly changing processes, the capacitive divider ratio is effective. Thus, the cable capacitance CC lies parallel to C2 and this slightly distorts the divider ratio. C2 is chosen to be so large in the μF range that standard cable lengths do not have any undue distortion. A discharge with a time constant in the range of seconds takes place via R  1 M:, so that even very slowly changing processes can be measured. Other coupling circuits are given in the specialist literature [141].
High voltage hall Figure 6.3.48: Coupling of a highimpedance oscilloscope to the lowvoltage arm of a damped capacitive divider via a measuring cable with an additional shield as a bypass for the defined conduction of cablesheath currents.
R'1 C'1 R2 C2
Lowinductive cylindrical capacitor elements with frontal contact areas
Z R 2 Z Measuring cable Bypass for cablesheath currents
Shielded measuring cabin Oscilloscope
R >> Z
6.3 High Voltage Measurement Techniques
419
6.3.5 Instrument Transformers Instrument transformers serve as operating equipment of the electrical supply network primarily for recording the voltages and currents at operating frequency. They must be measured in the normal operating condition of the network with a precision defined by the accuracy class. Moreover, disturbances in the network (overvoltages/undervoltages, shortcircuit currents) must be detected.
Resinencapsulated m.v. voltage transformer
SF6
Instrument transformers are designed to be single phase; three units are required for three phase systems. Instrument transformers are increasingly manufactured with siliconeshed composite isolators and with oilfree dielectrics (cast resin or film insulation with SF6), since the explosion of oilfilled equipment with porcelain insulators can lead to considerable consequential damages. 6.3.5.1 Voltage Transformers
a) Inductive voltage transformers Inductive voltage transformers are comparable with test transformers that are excited on the highvoltage side and are loaded on the lowvoltage side with a measurement impedance, Figure 6.3.51. For adequate loading, the capacitive voltage rise (resonant overvoltage) is negligible. Voltage transformers are operated at operating voltage in the approximately linear region of the magnetization characteristic. From the transmission ratio, the high voltage V1 is obtained:
V1 = V2·n1/n2
(6.3.51)
Recording the r.m.s. value is of importance here. It was previously implemented by a true r.m.s. responding instrument; today the r.m.s. value is determined by the evaluation of the digital signal. The upper cutoff frequency of the inductive voltage transformer amounts to a few kHz in the mediumvoltage range and for
Kern
Voltage transformer module in a GIS
Oilinsulated h.v. voltage transformer with outdoor bushing
Figure 6.3.51: Inductive voltage transformers.
highvoltage transformers it decreases to a few 100 Hz. Inductive voltage transformers are largely used in the medium voltage range, frequently in dry construction as resinencapsulated transformers, Figure 6.3.51 (top left). There are also voltage transformers for the highvoltage range that are insulated with films and SF6 and are used in gasinsulated switchgear, Figure 6.3.51 (bottom left). Classic oilinsulated voltage transformers consist of a transformer insulated with oil and paper in a deadtank construction and an outdooroil bushing, Figure 6.3.51 (right). b) Capacitor voltage transformer
At high voltages, iron cores and windings of inductive voltage transformers are very large, therefore it is more economical to use capacitior voltage transformers together with inductive transformers in resonance circuits (resonance capacitor transformers), Figure 6.3.52 (left). The high voltage V1 is divided by a capacitive divider down to a medium voltage V2 in the range of approx. 10 to 30 kV. The measurement devices with the load resis
420
6 TESTING, MEASURING AND DIAGNOSIS
tance R are connected as socalled burden via a reactor (inductance L) and an inductive voltage transformer. The inductive transformer can thus be designed as a compact mediumvoltage transformer. The inductance L and the capacitance C1+C2 form a resonance circuit at the fundamental power frequency of the network f0. In the case of resonance 1/2
f0 = 1/{2S [L(C1+C2)] },
(6.3.52)
the voltage VR is independent of the magnitude of the burden (load) R so that the reading is basically independent of the number of measurement devices connected in parallel: VR/V1 = C1/(C1 + C2)
(6.3.53)
Note: Eq. (6.3.53) can be derived from the equivalent circuit in Figure 6.3.52 (bottom right) by complex calculation with the condition Eq. (6.3.52). For illustration purposes, noload operation (R' o f) for which a capacitive divider ratio results owing to the lack of a load is considered. For the loaded divider (R' < f) a voltage decrease is to be expected and it is directly balanced by a resonance overvoltage.
The fact that the output signal was independent of the load and the possibility to even sup
ply the older protective relays with higher power consumption was of great advantage in the days of analog power system management. Pure capacitive voltage transformers (dividers) can supply only very highimpedance loads with lower power consumption. Hence, the signal that has been capacitively divided must be further processed electronically. Thus, a constant load for the divider, a higher bandwidth for recording the signal as well as unlimited options for further processing of signals with respect to power system management and with respect to network protection are achieved. An inductive voltage transformer is no longer required. Capacitive, resistive or compensated voltage transformers (dividers) can be used even in the medium voltage range, Figure 6.3.52 (top right). For example, it is possible to encapsulate a cylindrical capacitor or resistor elements in an epoxyresin support insulator [363], [364]. Thus, the transformer or divider does not take up its own space and can contribute to the simplification of mediumvoltage switching systems. Along with an electronic evaluation unit, the lowvoltage elements are connected to the lower side of the insulator.
6.3.5.2 Current Transformers C1
a) Inductive current transformers
C2 C1
Mediumvoltage support insulator with capacitance
C1 C2
L
L
R' C2
R VR
V1 V2
V R'
Capacitor voltage transformer with resonance circuit Figure 6.3.52: Capacitor voltage transformer.
Inductive current transformers must carry the conductor(s) at highvoltage potential as primary winding via a transformertype current transformation unit, Figure 6.3.53 (a), (b). If the conductor is directly fed through a circular closed iron core, the primary winding consists of only one turn. The inductive current transformer is thus comparable to a Rogowski coil (but with an iron core), see Figure 6.3.71. The secondary winding at lowvoltage potential consists of many turns. It supplies the transformed current into the secondary circuit and this must not be interrupted (!) to prevent overvoltages and therefore has to be protected with overvoltage arresters.
6.3 High Voltage Measurement Techniques Note: Short circuit currents are often indicated to be too low owing to saturation of the iron core and owing to the suppression of the direct current component.
b) Current transformers with highvoltage insulation
In medium voltage applications, it is common to use compact and dry inductive current transformers that are embedded in cast resin (resinencapsulated current transformers). Moreover, Rogowski coils and inductive magnetic field sensors with electronic signal integration can be integrated in components of switchgear assemblies, for example in cable connectors [365]. In high voltage applications, the high voltage difference between the primary winding and the secondary winding at ground potential places particularly high demands on the insulation within the current transformer. In the case of classic crossedringcore transformer, the conductor is fed into the grounded tank and out again with the help of a capaci
421
tively graded bushing, Figure 6.3.53 (a). The bushing is thus thermally loaded by the doubled primary current. Within the transformer, the high voltage is to be insulated between primary winding and the core, tank and secondary winding. The classic insulation system is oilpaper with a bushing insulator made of porcelain. At the socalled topassembly current transformer, the tank with the inductive transformer is at the highvoltage potential and forms the head of the transformer, Figure 6.3.53 (b). The core and secondary winding are at ground potential and must be insulated against the tank and conductor (primary winding) at highvoltage potential. The supply wires for secondary windings are fed into the head with an inverse capacitively graded bushing that is only loaded by secondary current. Films that have been impregnated with SF6 and siliconeshed composite insulators are implemented as the insulation system. In this way, exploding porcelain and burning oil are prevented in the event of damage.
Inductive LV transInductive Opticalfibre coil transformer
Shunt electrooptical
Optical fibre
Inverse bushing
Bushing
former
transducer
LWL digital
Optical fibre Inductive transformer Transmitter and analyzer (a) Crossedringcore transformer
(b) Topassembly current transformer
Figure 6.3.53: Current transformers.
(c) Optical current transformer
Receiver and optoelectrical transducer (d) Hybridoptical current transformer
422
c) Transformers without highvoltage insulation
With respect to insulation technology, favorable conditions for the installation of current transformers are found in bushings and gas insulated switchgear. Here the conductor is fed centrally through the circular iron core and the secondary winding without interruption. The current transformer is placed in an area that is shielded from the electric field, such as above the grounded grading layer of the bushing, Figure 6.4.83, or in an ring groove in the outer conductor of a coaxial arrangement, Figure 6.3.71. The transformer must have an adequate internal diameter to be able to accommodate the bushing or the conductor insulated by the SF6 gas. d) Current transformers with potential separation
Modern options for potential free signal transmission allow completely new currenttransformer concepts. Current signals can be recorded directly on the conductor at the highvoltage potential and, for example, can be transmitted via optical waveguides across any potential differences to a receiving unit at any position, Figure 6.3.53 (c), (d). A magnetooptical current transformer, for example, can be employed with a coil shaped optic fiber wound around a conductor [368]. The magnetic field parallel to the fiber causes a rotation of the plane of polarization of the polarized light. The angle is proportional to the length of the light path and the strength of the magnetic field (Faraday effect). This rotation can be recorded by various methods; in the simplest case, the modulation of the polarization condition is converted with the aid of an optical polarizer and analyzer into an intensity modulation [141], see Section 6.3.3.5. While designing the current transformer, compensation for intensity fluctuations in optical system and for temperature influences on the optical properties must be carried out. Moreover, it must be noted that even mechanical loads and vibrations can influence optical properties. The
6 TESTING, MEASURING AND DIAGNOSIS
high bandwidth of the analog optical transmission is an advantage. An auxiliary power supply at highvoltage potential is not necessary. Hybridoptical current transformers measure the current at the highvoltage potential with a conventional inductive current transformer (for alternating current) or with a current–sensing resistor or measuring shunt (for direct current). Thus, the measurement signal is provided with precision and reliability known for conventional current transformers and without any problems with regard to insulation. The electrical signal is transmitted in digitized form over the optical path to the receiver at ground potential. The need to supply the electronics at highvoltage potential with auxiliary power is a disadvantage. For this purpose, optical, capacitive or inductive transmission procedures are considered.
6.3.6 Measurements of R.m.s. Value, Peak Value and Harmonics The peak value that is significant for breakdown is primarily to be recorded during measurements in the high voltage laboratory. The measurement of r.m.s. values is important in the power supply network. Various circuits are available for this along with series impedances, capacitances, transformers and dividers. A few examples are given in the following sections. Resistive and capacitive series impedances along with r.m.s.responding current measurement instruments are used in measuring the r.m.s. value of power frequency AC voltages. Ohmic series resistors are also suitable for measuring DC voltages. With capacitive series impedances, it must be noted that in the case of voltages having harmonic distortions, incorrectly high values are shown since the harmonic contents of the voltage drive disproportionately large currents owing to their higher frequencies:
Ik = k·Z0C·Vk
(6.3.61)
6.3 High Voltage Measurement Techniques
C
v (t)
i C (t) Figure 6.3.61: Measurement of peak value of AC voltages according to ChubbFortescue.
I
For series impedances, hazardous contact voltages can occur on the lowvoltage side if the current path is interrupted. An overvoltage protective circuit must prevent this. The circuit according to ChubbFortescue enables the measurement of the peak value vˆ for periodic AC voltages, Figure 6.3.61. The current iC(t) that is impressed by the capacitive series impedance is proportional to the derivative of the voltage with respect to time: iC(t) = C·wv/wt
(6.3.62)
The reading iM of a movingcoil instrument corresponds to the mean value of the rectified current that is developed by integration of the positive halfwave oscillation between t = 0 and t = T/2: iM
1 T / 2 wv ³ C wt dt T 0
ˆ C v ³ dv (6.3.63) T vˆ
Here the instants t = 0 and t = T/2 correspond to the current zero and the negative and positive maxima of the voltage respectively. Proportionality between the displayed mean value of the rectified current and the voltage peak value results from Eq. (6.3.63): iM = C·f·2· vˆ
423
While using voltage dividers, the peak value can be measured by peak detection and peak value storage. Here, charging a measurement capacitor CM via a diode prevents the decrease in stored measurement voltage for a decreasing divider voltage, Figure 6.3.62. This principle can generally be used for AC voltages and impulse voltages. The described basic circuit according to Davis, Bowdler, and Standring is subjected to systematic errors due to the discharging of CM, the parallel connection of C2 and CM in the recharging phase and the parallel connection of the discharging resistance RD and the low voltage capacitance C2. Therefore, a series of improved circuits, such as a twobranch circuit (with an equalizing branch) for AC voltage measurements according to Rabus, circuits with nocurrent, controlled charging by active components or sample and hold elements with operational amplifiers for the storage of nonrecurrent processes are available [141]. Note: Reading electronic peak voltage measurement devices is often sensitive to unwanted electromagnetic coupling by impulse voltages. Besides ensuring the necessary electromagnetic compatibility, the displayed peak value must also be definitely checked using the oscillographic recording of the impulse voltage profile.
The possibilities of digital signal processing also include the calculation of r.m.s values and peak values from the signaltime characteristics recorded with high bandwidth. This can also be used for examining the harmonic distortion spectrum in the supply network by
v (t)
(6.3.64)
Note: If the voltage profile shows intermediate maxima, additional current zeros occur and result in a faulty reading. Note: The diode that is antiparallel to the measurement branch obstructs the charging of capacitance C.
v 2 (t) C2
C1 RD
RM
v M  ûv2
CM
Figure 6.3.62: Basic circuit for peak detection and peak value storage in a measurement capacitor.
424
6 TESTING, MEASURING AND DIAGNOSIS
Fourier analysis, which is gaining importance since the increasing number of power electronic consumers and operating equipments lead to nonsinusoidal currents and voltage drops at the network impedances. Owing to this, the recommended "voltage quality" is possibly impaired [154]. Transition processes in the network to some extent lead to increased deviations from the stationary operating condition [155] and must be recorded by relevant broadband measurements with transient storage.
6.3.7 Current Measurement Measurement of currents with inductive current transformers in the power supply network was described in Section 6.3.5.2. Current probes, whose magnetic circuit can be opened like tongs to enclose a conductor at low voltage, are based on the same principle. Depending on the type of the magnetic material used and the connected signal amplifier, even large bandwidths are possible. Socalled Rogowski coils are inductive current transformers that can be used even for extremely rapidly changing currents. Here, according to the theory of electrically long magnetic sensors, it must be ensured that the coil with the surrounding shield forms a travelingwave line with constant characteristic impedance, which is operated in short circuit mode and for which the magnetic coupling is uniformly distributed over its circumference, Fig
ure 6.3.32, Section 6.3.3.2, [5], [145], [146], [149], [150]. This implies that a Rogowski coil arranged concentric to the current conductor can measure current profiles, whose rise times are considerably shorter than the propagation time along the coil, Figure 6.3.71. For the commonly undefined arrangement, the current rise times must be considerably longer than the propagation time along the coil, so that the signal is not superimposed by transient oscillations based on spatially nonuniform signal coupling. Rapidly varying currents can also be measured with current measuring resistors (shunts). However, the problem here is that current path and measuring circuit are often coupled not only by the ohmic measuring resistance but are also magnetically coupled so that measuring voltage is not proportional to the current. It is therefore recommended to use coaxially symmetric current measuring shunts, in which the measuring tapping is placed in the center of a cylindrical resistor tube in a space free of magnetic field, Figure 6.3.72. Current is returned via a coaxially symmetric arrangement on a mounting flange. The rise time of the shunt is restricted by the effect of the current displacement. That is, a current step can be noticed within the tube with a delayed rise in voltage at the measuring tapping. Rise times can be achieved in the ns range for very thin tubes of resistance alloys.
Flange
' v (t) Schielding tube
B (t)
i (t)
Figure 6.3.71: Toroidal Rogowski coil without iron core, with slitted shield and with concentric current conductor for the measurement of rapidly varying currents i(t).
i (t)
Coaxial signal cable
B (t) Space, free of magnetic field with central measuring tapping Tubular resistance Figure 6.3.72: Coaxial current measuring shunt without electromagnetic induction in the measuring circuit.
6.3 High Voltage Measurement Techniques
425
Note: For low resistive shunts, only a low signal level results in a possibly severely disturbed electromagnetic environment. Therefore, it can be necessary to use an additional cable shield (e.g. in the form of a flanged tube) as a bypass for cable sheath currents.
that will not be dealt with here [41], [141]. In the following section, only a few important EMC measures in high voltage laboratories are discussed, Figure 6.3.81.
Currents can also be measured with the help of magnetooptical methods (Faraday effect). In many crystals, such as in quartz, the optical activity is induced by magnetic fields, which then leads to a rotation of the polarization plane of polarized light, Section 6.3.3.5 and 6.3.5.2. In particular, the option to implement potentialfree sensors is an advantage. An optical Rogowski coil can be formed with the aid of optical waveguides that are wound around the conductor that conducts the current, Section 6.3.3.5 b).
6.3.8 Electromagnetic Compatibility (EMC)
High voltage testing fields are electromagnetically shielded in order to carry out sensitive partial discharge measurements at low background noise level. Supply lines and control lines are guided via leadin filters. Before measuring a partial discharge, the background noise level must be checked by measurement. Values around 1 pC can be achieved with good shielding. Under the conditions of industrial test fields as well as for onsite measurements, optimal shielding is not always achievable. In many cases, electromagnetic compatibility can only be achieved through narrowband partial discharge measurement in a slightly disturbed frequency domain. Interferencefree partial discharge measurement is discussed in detail in Section 6.4.2.5.
High voltage measurement technology has always meant the assurance of electromagnetic compatibility in an especially strongly disturbed environment. Therefore, experiences and knowledge of the high voltage measurement techniques form an important foundation of modern, generally applicable EMCphilosophy. The electromagnetic compatibility is by itself a large independent special discipline
For impulse voltage measurements, the shielded room serves as a protective shield for sources of interference from the environment. Within the room, coupling through electromagnetic fields is reduced by separations of large dimensions. It is a rule of thumb that the distance of the devices should be approximately equal to their height. Coupling impedances are prevented by a common mass point
Electromagnetically shielded room
Decoupling by distance Divider
Transformer Impulse generator
Control room or shielded cabin Test object Coaxial cable
Bypass for cable sheath currents Central mass point
Figure 6.3.81: Ensuring electromagnetic compatibility for impulse voltage tests (schematic).
Line filter
426
with very short connection lines. In particular, the connection of the divider parallel to the test object must be made so that no voltage drops occur at the supply lines on the ground side or on the high voltage side. Cables must be led from the hall on short paths such that no looping occurs in which induced voltages can drive cable sheath currents. I.e. cables must be bundled and must be laid as directly as possible on the shielding structures. Cable sheath currents cause voltage drops at the coupling impedances of the cable sheath, which can completely distort the measurement signal especially at low signal levels. Therefore, if possible, a large signal level is chosen within the room and the signal is once again divided outside the shielded room, if necessary. Cable sheath currents can also cause electromagnetic influences outside the shielding. Therefore, it is often necessary to lay an additional cable shield as a bypass for the cable sheath currents. On the input side, it is directly connected to the reference conductor (i.e. to the common mass point). On the other side, the bypass must have such a good circumferential contact with the shielding of the room that the cable sheath currents pass to the shielding practically completely.
The amount of interference coupling into a cable can be ascertained by preliminary tests with signal conductors that are short circuited (and possibly also interrupted) on the input side.
6.4 Diagnosis and Monitoring Along with high voltage tests for verification of withstand voltages, diagnostic methods are absolutely essential to obtain more differentiated conclusions about the condition of a device and respectively, its insulation. This, at first, pertains to ordinary type tests, routine tests and service tests. Reliable conclusions are particularly important, especially for decade
6 TESTING, MEASURING AND DIAGNOSIS
long aged equipment, which on the one hand must be taken out of the network in advance before the occurrence of a crucial damage, and which on the other hand, owing to its high replacement value, should not be replaced before the expiry of its technically probable lifetime. Ultimately, also the investigation of damages requires a suitable set of diagnostic tools. The informative value of the diagnostic methods still does not come up to the questions posed in many cases. This especially pertains to the question of the expected remaining service life of a device. Important methods are the dielectric measurements of classic parameters such as capacitance and dissipation factor at power frequency, conductivity and the dielectric system response (Section 6.4.1). Partial discharge measurements (Section 6.4.2), chemical analyses (Section 6.4.3), insulating material tests (Section 6.4.4) as well as optical and acoustic methods (Section 6.4.5) also come under this. New methods for determining system properties (Section 6.4.6) and dielectric diagnoses (Section 6.4.7) have now become increasingly valid and significant. Diagnostics are generally carried out in the plant or in the high voltage test field. Increasingly onsite diagnoses ("offline diagnosis") are also being carried out. Moreover, the interest in “online diagnosis” is also on the rise and even in permanent “online monitoring” during operation (Section 6.4.8), especially for valuable or strategically important equipment, such as large transformers or bushings [156].
6.4.1 Dielectric Measurements 6.4.1.1 Dissipation Factor and Capacitance
Dissipation factor and capacitance are materialspecific and devicespecific parameters. Compliance with specified values is checked by measurements. Trend analyses provide details about changes. For example, increases in
6.4 Diagnosis and Monitoring
Measuring arm
427
Reference arm
Cx
Null indicator
R3
R4
HV side
a
C4
Top left:
Basic circuit.
Top right:
Regulation of shield potential for the prevention of displacement currents to the ground side that could load the bridge (and compensation of the earth stray capacitances respectively).
Bottom right:
Arithmetic compensation for earth stray capacitances of given values (such as cable capacitances).
bushing capacitance or capacitor capacitance indicate breakdowns of partial capacitances. For resinbonded paper bushings, a rise in capacitance can even be caused by oilimpregnation of the not entirely voidless insulation body. Loss of impregnating agent or a disconnected contact can be indicated by a fall in capacitance. Increased dissipation factors, for example, occur owing to infiltrating moisture and as a result of structural changes owing to ageing, see Section 4.2.3.
Null indicator
R3
Basic circuit
LV side
only the internal shields are presented
with voltage controller
b
Figure 6.4.11: Measuring bridge for capacitance and dissipation factor (socalled Schering bridge):
CN
Rx
High voltage side Low voltage side
Reference arm
Cx
CN
Rx
a
Measuring arm
b
R4
C4
Automatically regulated shield potential
Cx R x
Connections for
with earth stray capacitances
C'3
a
CN
Null indicator
R3
R4
b
C'4
C4
Shield at earth potential
Note: With a rise in voltage, the inception of intense partial discharges becomes noticeable also through a rise in dissipation factor. Determining partial discharge inception via the “partial discharge kink” of the dissipation factor graph is, however, very insensitive and was in practice only during the initial stages of high voltage engineering.
The classic basic circuit for determining capacitance and dissipation factor is the Ctan G measuring bridge according to Schering ("Schering bridge”), Figure 6.4.11 (top left).
428
6 TESTING, MEASURING AND DIAGNOSIS
It is distinguished from common AC measuring bridges by the fact that the test object (Cx, tan Gx) is realistically stressed with high voltage, while all trimming elements are at low voltage. CN is a very low loss, high voltage capacitor, for example a gasinsulated high voltage capacitor, with exactly known capacitance (standard or reference capacitor). The balanced condition of the bridge, at which the null indicator shows no voltage, is
Zx / Z3
= ZN / Z4 ,
(6.4.11)
and it can be evaluated best with a series equivalent circuit for Zx: Zx / Z3 =
1 jZCx R3
Rx
ZN · Y4
1 1 ( jZ C 4 ) jZCN R4
The following results from the real part and the imaginary part Rx
= R3·C4/CN ,
Cx
= CN·R4/R3
(6.4.12)
and tan G x = Z CxRx = Z C4R4 . Under this, ground stray capacitances can lead to inaccurate results. In particular, the cables between the bridge and the high voltage components have capacitances C3’ and C4’. They are in parallel to the bridge impedances Z3 and Z4, Figure 6.4.11 (bottom right). However, the following remedial measures are available: 1. Doubleshielded cables and housings are used. External shields remain grounded, internal shields are dynamically maintained at the potential of the bridge points a and b of the balanced bridge by an electronic voltage controller. Thus, in the absence of a potential difference between the
internal shielding and the inner conductors (bridge points a and b), displacement currents do not flow. Displacement currents between internal and external shields are fed by the voltage controller and they do not load the bridge. 2. Even without voltage controller, the shielding and bridge points a and b can be brought to the same potential by manual trimming of a third bridge arm (“auxiliary arm according to Wagner”), so that the stray capacitances remain ineffective [141]. If an ungrounded high voltage source is available, a single grounded shielding can also be used. 3. Further, there is the option to compensate the phase displacement angle caused by ground stray capacitances with a RLCnetwork in arm 3. 4. If the ground stray capacitances are defined and known, what is mostly the case for coaxial measuring cables, an arithmetic correction of the result is made. From the balancing condition (6.4.11), with 1/Z3 = Y3 = 1/R3 +jZ C3’ and 1/Z4 = Y4 = 1/R4 + jZ (C4 + C4’) and in accordance with Figure 6.4.11 (bottom right) to a good approximation tan G x
= Z CxRx 
Z C4+C4’) R4  Z C3’R3
is obtained. With the balanced value tan G x0 = ZC4R4 in accordance with Eq. (6.4.12), the following is obtained for the dissipation factor correction: tan G x
= Z CxRx  tan G x0 + Z C4’R4 
Z C3’R3 (6.4.13)
The capacitance measurement value in accordance with Eq. (6.4.12) is hardly influenced by the stray capacitances.
6.4 Diagnosis and Monitoring
429
Along with the basic circuit according to Schering, different variants were developed [141]. For example, there are special bridge circuits for large capacitances, for large dissipation factors and for grounded test objects. The universal Ctan G measuring bridge allows simplified balancing with a complex comparator, with which the balancing is performed in dependence on the magnitude and phase angle of the diagonal bridge voltage Vab. Moreover, there are bridges with current comparators. In addition to manually balanced bridges, there are also automatically balancing versions. Computerbased measuring systems work according to the principle of a vectorial impedance measurement in the frequency domain, Figure 6.4.12. The dissipation factor tan įx that is sought is thus determined from the currents in the measurement arm and in the reference arm, i.e. from the phase displacement įx of the fundamental modes. For this purpose, for example, analog current signals recorded in both the arms are integrated, digitalized, fiberoptically fed into a digital signal processor (DSP) and processed further with a discrete Fourier transform (DFT) [204]. Depending on the speed and precision of the A/D Measurement arm
Reference arm
Measurement signal A
Z t
A D
D Fiber optic transmission
Reference signal
Capacitances and dissipation factors can also be determined from resonance frequency and damping of oscillating circuits. For this, a charged capacitance, for instance, is discharged in oscillation (“oscillating voltage”). It is an advantage that even very large capacitances, such as in cables, can be measured. The accuracy is, however, not comparable with a bridge measurement, since other imperfect elements with losses (circuit inductance, switching elements) are included in the measurement result. For determining permittivity, an accurately defined field geometry is necessary, in which the field distortions at the edges must be avoided by a guardring arrangement, Figure 6.4.13. Relative permittivity is obtained as the quotient of the measured insulating material capacitance and the calculated (or measured) vacuum capacitance:
H r = Cx/C0
i (t)
G
conversion and the capacity of the processor, high precision and extremely short measuring durations can be achieved, which in practice facilitates the automatic monitoring of dielectric parameters in real time. The ability to calculate other parameters, such as capacitances, series resistances or parallel resistances, dissipation factor, power factor, power loss, voltage and frequency is an additional advantage.
(6.4.14)
Coaxial guardring arrangements are used in compressed gas insulated reference capacitors (socalled compressedgas capacitors) and in test vessels for liquid insulating materials. Plane guard ring arrangements are used for testing flat insulating material samples.
DSP
6.4.1.2 Insulation Resistance, Conductivity PC
Figure 6.4.12: Computerbased measurement of the dissipation factor from the phase difference of the currents in the measurement arm and reference arm (as in [204]).
Insulation resistance RIn between two electrodes results from a resistance network which emulates different materials and surfaces. Usually, a parallel connection of the volume resistance RV and the surface resistance RS, is considered:
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6 TESTING, MEASURING AND DIAGNOSIS
RIn =
RV + RS
(6.4.15)
The values are determined by the conductivity of the material and by the surface condition. The volume resistance is accordingly dependent on stress duration, field strength, temperature and water content (see Section. 4.2.2). Typical values can be referred from Figures 4.25 to 9. Surface resistance is heavily dependent on the type, quantity, distribution, and wetting of pollution layers (see Section. 3.2.6.4 and 5.3.4). It is specified as resistance between opposite edges of a square and typi6 13 cally lies between 10 and 10 :. First of all, the measurement of insulation resistance for devices gives an indication of the presence of isolating gaps. In the context of trend analyses, ageing and wetting of cellulosebased insulations or contamination of oils can be tracked, for example. Surface resistances give information about the hydrophobicity of differently contaminated, aged or treated surfaces for instance, Figure 5.319. With the help of guard ring arrangements, volume resistance and surface resistance of insulating material samples can be differentiated, Figure 6.4.14 (top and bottom resp.). While measuring the volume resistance between the
H: M: G:
High voltage electrode Measurement electrode Guard ring electrode
high voltage electrode and the measurement electrode, current flowing through RG is not measured and RS is parallel to the low impedance measuring device. Even while measuring the surface resistance between the measuring electrode and the guard ring electrode, the current over RG remains without any influence and RV is parallel to the low impedance measuring device. Note: The surface resistance can also be measured between two 10 cm long parallel bladeshaped electrodes that are pressed against the surface at a distance of 1 cm [157].
Similar to the determination of permittivity, a well defined field geometry in which field distortions at the edges and surface currents are prevented by a guard ring arrangement is also necessary for determining conductivities, Figure 6.4.14. The conductivity N and the resistivity U for plane arrangements
N
G
G M
(6.4.16)
are calculated from the volume resistance RD
1 d . N A
RV
G
V=
G
M
U
1 d . RD A
H
M
H
1
G
RS
RV
H
V= Figure 6.4.13: Plane insulation material sample with plane guard ring arrangement (left) and coaxial guard ring arrangements for testing liquids (center) and for a compressedgas capacitor (right).
I
RG
I
RG RS
Figure 6.4.14: Measurement of volume resistance (top) and surface resistance (bottom) in a guardring electrode arrangement.
6.4 Diagnosis and Monitoring
Solid insulating materials are usually measured on flat plateshaped samples in plane electrode arrangements. However, it is also possible, to apply electrodes and guard rings as conductive coatings on differently shaped bodies. For liquid insulating materials, there are measuring cells of two concentric cupshaped electrodes with a liquidfilled insulation gap. Similar to a compressedgas capacitor, a guard ring is found in the upper area, Figure 6.4.13. In conductivity measurements, it must be noted that the measured currents for solid insulating materials are influenced not only by its own direct current conductivity but also by polarization processes for long periods, Sections 4.2.2 and 4.3. Therefore, measurement must continue until the value of the direct current conductivity can be identified from a constant steadystate end value of the current. In practice, such an end value is often not attained, therefore measurement values are specified for different periods of measurement such as 1, 2, 5, 10, 50 and 100 minutes [157], [386]. Note: However, one should not come to the false conclusion that here it deals with real conductivity values or resistance values; they also include polarization current components. Therefore, it is better to use terms like “apparent conductivity” and “apparent insulation resistance” respectively. Note: A new method, the charge difference method (CDM), under which the conductivity end values can be estimated by the calculation of charge differences from the polarization current measurements and depolarization current measurements (PDCmeasurements), is described in Section 6.4.1.3 [427], [392], [428].
For liquids, the decrease in conductivity caused by ion drift in an electrical DC field plays an especially significant role, Section 4.2.2.2. Therefore, there is a special specification for the measurement of insulating liquids using trapezoidal AC voltages, with which the charge carrier depletion, which would be caused by the ionic drift, is prevented. With the rise in voltage, capacitive displacement current flows and conduction current flows during the stable phase at constant voltage.
431
This allows both the measurement of permittivity and the measurement of the initial value of conductivity without charge carrier depletion (i.e. the socalled AC conductivity) [270], [385]. However, this value is different from the steadystate values obtained after prolonged DC field stresses. 6.4.1.3 Dielectric System Response
Capacitance, dissipation factor and conductivity are parameters which describe only a small section of the dielectric system properties. It is more comprehensive to measure a complete dielectric system response, which in the case of a linear dielectric or insulation system, enables the establishment of a complete equivalent circuit, Figure 4.32, Section 4.3.2.1. The abovementioned classic parameters can be derived from it. These measurements are carried out on material samples in a guardring arrangement, through which it is ensured that only the current is measured which flows directly through the material and that the surface currents are made ineffective by discharging them via the guard ring, Figure 6.4.14 (top). System responses can be measured in both the time domain and the frequency domain, see Sections 6.4.7.6 and 6.4.7.7. Basically, both the measurements are equal; a conversion is possible in the case of a linear system. However, this prerequisite is not always fulfilled, e.g. for an oilinsulated or oilimpregnated arrangement with nonlinear insulating materials. a) Measurements in the time domain
For measurements in the time domain, a stabilized direct voltage is applied as a step function on the object to be measured. The polarization current ip(t) flowing through the object results from a capacitive charging current impulse directly after connecting; it is subsequently determined by the polarization mechanisms that are effective in the material and that subside with time, and it finally tends towards an end value that is determined by the conduc
432
6 TESTING, MEASURING AND DIAGNOSIS
tivity of the material. After a long period, the high frequency capacitance is charged, and moreover charge is stored at the interfaces and in the aligned dipoles. In the equivalent circuit according to Figure 4.32, these processes are physically correctly described by a capacitance, by RC elements for different polarization mechanisms and by a resistance for the conductivity.
After disconnecting the voltage and short circuiting the object, a depolarization current id(t) is flowing owing to the charge stored by the preceding polarization. In the equivalent circuit according to Figure 4.32, this corresponds to the charge stored in the RCelements. Even in the depolarization current, complete system information is contained, with the exception of information about the insulation resistance that is shortcircuited during depolarization. Note: Depolarization current measurements are not influenced by surface resistances since they are short circuited during the measurement. Owing to this, dielectric measurements are possible even for insulations on which no guard ring arrangement can be implemented (e.g. on cables). However, the signal no longer contains information about the conductivity.
The analysis of polarization currents and depolarization currents is known as PDC analy100 pA i
sis, Section 6.4.7.6. Note: A common task is the measurement of socalled direct current conductivity
N
1
I䌲 d · , V A
1 d · RV A
U
(6.4.17)
which can be determined from the end value If of the decreasing polarization current ip(t), i.e. theoretically only after an infinitely long time and in practice, often only after hours or days, Figure 6.4.15 (left), Section 6.4.1.2: ip(t) o If
(6.4.18)
Convergence occurs much faster when the difference in the magnitudes of the polarization current and the depolarization current ip(t) and id(t) is developed, since in both the currents redundant information about the polarization effects cancel out with opposite signs and because the conductivity component is present only in the polarization current, Figure 6.4.15 (left). For this comparison, the depolarization current must be shifted in time by the polarization duration tp or charging time tC as polarization current and depolarization current are not flowing simultaneously and the measurements are performed with the time shift tp = tC: ip(t) – id(t + tp)
o If
(6.4.19)
A new method, the socalled charge difference method CDM, is based on the integration of ip(t), giving the total charge qp(t) that has flowed, and on the integration 100 nAs q
80 pA 60 pA i
i i p d
p
(t)
q
d
( t + tp)
40 pA q p  qd
i ( t + tp) d 1000 s
q (t) p
t
3000 s
1000 s
t
3000 s
Figure 6.4.15: Polarization current measurement and depolarization current measurement on a material sample of oilimpregnated paper with the difference in the magnitudes of currents ip and id (left) as well as evaluation of current measurements by integration (right). qp is the total charge that has flowed, qd is the stored and released charge. The gradient of the charge difference function qp  qd is approximately proportional to the conductivity (charge difference method CDM [427]). Superimposed interferences (left) are averaged out by integration (right).
6.4 Diagnosis and Monitoring of id(t+tp), giving the released charge qd(t+tp) that has been stored before, Figure 6.4.15 (right), [427] to [429]. The difference of charge magnitudes qp(t) – qd(t+tp) is approximately equivalent to the unstored charge that has been discharged as conduction current via the insulation resistance. From the gradient of the charge difference function, a good estimation for the conductivity end value can be derived quite early. Here it is particularly of advantage also that the interferences present in the current signals can be averaged out by the integration.
b) Measurements in the frequency domain
For measurements in the frequency domain, the object is subjected to a sinusoidal voltage until a steady state is achieved (at least four periods). An impedance is determined from the stationary current flowing through the object. By measurement at many different frequencies, the frequency dependence of the impedance is determined pointbypoint, and from this the frequency dependence of the complex permittivity H = H’  jH’’ as well as the magnitudes of the capacitance C and the dissipation factor tan G are calculated. Its analysis is described as frequency domain spectroscopy FDS, Section. 6.4.7.7. Note: A measurement in the time domain often appears to be more advantageous than in the frequency domain: 1. For measurements in the frequency domain, a large number of individual measurements are necessary to measure C, tan G and H = H’  jH’’ over a large frequency range. Here, for each individual measurement point one must wait for a steady state to be reached (i.e. at least four periods). Owing to this, very long measuring times are necessary, especially for very slowly changing proc3 4 esses in the range of 10 to 10 Hz. Instead of this, the measurement period in the time domain is only a fraction of this, since a single voltage step is sufficient for recording the complete system information. 2. For measurement in the time domain, it is simply possible to apply voltages of any magnitudes. As a result of this, there is great freedom with regard to the field strength load during the measurement and the insulation can be stressed similarly to the actual operational conditions, for example, for DC voltage insulation systems (HVDC) or for diagnostic purposes. Lower voltages are adequate for diagnostic examinations. In the frequency domain, on the contrary, it is extremely difficult to implement frequency variable voltage sources with large amplitudes. Therefore, the voltages must generally be restricted to the range of a few 100 V,
433 which is, however, often adequate for diagnostic measurements. 3. Processes in the time domain are often more directly accessible to the human imagination than processes in the frequency domain, for which an additional measure of abstraction is necessary. Note: The strong point of time domain measurement lies in the measurement of slowly changing processes and in the use of higher voltages. Frequency domain measurements are advantageous for very high frequencies, since corresponding time domain measurements would require extremely rapid voltage steps and very high sampling rates. Note: It is necessary to complete the measurement with a depolarization both in the time domain as well as in the frequency domain, in order to avoid influences on the subsequent measurements by the previous loading (memory effect). That is, in the frequency domain, the same number of both positive and negative periods must be passed through from zero crossing to zero crossing. In the time domain, the depolarization can be attained by an equivalent stress with opposing polarity or by a longterm short circuit.
6.4.2 Partial Discharge (PD) Measurement and Diagnosis The formation and clear interpretation of partial discharges from the viewpoint of gasdischarge physics has already been discussed in Section 3.6. Many practically relevant cases can already be assessed with the phaseresolved diagrams (phaseresolved pattern) described there, if the test voltage function corresponds to a distortionfree sinusoid, Figure 3.68. Here, the methods for measuredvalue acquisation, signal processing, evaluation and further computeraided diagnosis shall be described. The partial discharge measuring technique requires two different perspectives to be distinguished: according to one perspective, partial discharge measurement is used in the context of quality assurance during high voltage testing in order to confim specific and specified partial discharge levels according to standardized procedures [476], [477], the socalled IEC partial discharge measurement. On the
434
6 TESTING, MEASURING AND DIAGNOSIS
L
R PDfree test setup
PDfree test setup
Blocking impedance
Cc
Test transformer Test object
CT
Cc
CT
Coupling capacitor
CD
PDM
Test object CD
PDM
Figure 6.4.21: Parital discharge tests on grounded and earthfree test objects (left and right) with blocking impedance, coupling capacitor, coupling device (CD), partial discharge measuring device (PDM) and PDfree test setup.
other hand, partial discharge measurement is also an efficient instrument for diagnosis and research, which allows considerably more thorough analyses of insulation faults, often even with new and nonstandardized procedures or with measurement circuits or parameters that are not recommended according to the standards.
connected to the test transformer via a blocking impedance [476]. In the case of a partial discharge, a pulsed compensating current flows in the circuit of CC and CT. The partial discharge current impulse can be measured as voltage impulse using a coupling device (CD) that is situated either in the arm of the test object or in the arm of the coupling capacitor.
With the common partial discharge measuring technique in the kHzrange (Sections 6.4.2.1 to 6.4.2.4), the questions of interference signal suppression and partial discharge diagnosis must also be considered (Sections 6.4.2.5 and 6.4.2.6). The separation of several overlapping signal sources and sources of interference is also newly possible with synchronous multichannel partial discharge measurement (Section 6.4.2.7). In addition to the classic measuring procedure, the ultrahigh frequency UHF technique and a few nonelectrical methods are also of importance (Sections 6.4.2.8 and 6.4.2.9).
Note: Coupling out of partial discharge signals can also be performed at the measuring tap of a bushing; in this case, the bushing capacitance adopts the function of the coupling capacitor. Nonconventional coupling out using capacitive or magnetic sensors, Rogowski coils and antennae can also be considered if there is adequate sensitivity in the frequency domain under consideration and if calibration of the partial discharge measurement circuit is possible, see Section 6.3.3. They are the prerequisite for newer approaches to partial discharge analysis, e.g. for the analysis of impulse shape (timeresolved analysis) or for the analysis of extremely highfrequency components in the frequency spectrum of the signal, see Section 6.4.2.6. Further, field probes and antennae can be used onsite for the localization of partial discharges in stationary electrical equipment.
6.4.2.1 Partial Discharge Measurement Circuit
Note: Coupling devices are often networks with bandpass or highpass behavior, e.g. consisting of a parallel connection of inductance and resistance. Owing to this, an overload of the sensitive partial discharge measuring device by the power frequency voltage is avoided.
The measurement of partial discharge impulses requires a special measuring technique, Figure 6.4.21. A coupling capacitor with capacitance CC.is connected in parallel to the test object with capacitance CT which is also
Often, decoupling of the entire partial discharge circuit from the network side through a blocking impedance acting as lowpass filter (e.g. series connection of R and L) is helpful to suppress conducted interferences. Also, the
6.4 Diagnosis and Monitoring
435
parallel connection of transformer winding capacitances is prevented which would reduce the sensitivity of the measuring circuit, Figure 6.4.21 (left). Note: Damping of external interferences is also possible using a socalled bridge circuit, in which the coupling devices are present both in the arm of the test object as well as the arm of the coupling capacitor (socalled Kreuger bridge). External current impulses cause commonmode signals at both the coupling devices. Partial discharges in the test object (or in the coupling capacitor) lead to differentialmode signals.
The overall test setup must be free of partial discharges. That is, along with the use of appropriate devices (transformer, coupling capacitor), adequately rounded supply lines, toroids and fittings are necessary. Moreover, all metallic parts must be maintained at defined potential through contacting. Note: The partial discharge measurement circuit described here can be used for both AC voltage as well as DC voltage. Partial discharge impulses for DC voltage, however, occur essentially more rarely and irregularly than for AC voltage, since a discharged defect is recharged not by displacement currents but by much lower conduction currents. Therefore, the partial discharge measuring device cannot provide a continuous charge reading, but the charge of individual impulses must be recorded over time. A criterion for the withstanding of a DC voltage test is therefore, for example, charge and counting of individual impulses within a longer observation period. Note: Partial discharge measurement for DC voltage is to a large extent susceptible to external interferences and to interferences in the measurement setup. For AC voltage, individual current impulses are conspicuous in
C T = C S+ C 0 v (t)
C0 C Cav
CS vCav(t)
Figure 6.4.22: Simplified equivalent circuit for describing internal partial discharges in a test object.
view of regular and repetitive partial discharge impulses or they are averaged out. In the case of direct voltage, there is no comparable differentiating possibility and greater effort must be applied to the suppression (of interference) and shielding. In Section 6.4.2.7 c), a new method is described as to how interferences and partial discharge can be differentiated with synchronous multichannel measurement.
6.4.2.2 Apparent Charge, Partial Discharge Energy
a) Apparent charge
According to Figure 3.62, internal partial charges are described by an equivalent circuit and by the discharging of a cavity capacitance CCav on exceeding the ignition voltage or breakdown voltage Vbd, Figure 6.4.22. The real charge turnover
'Q = CCav·'vcav = CCav·Vbd
(6.4.21)
cannot be measured at the terminals of the test object. The voltage drop at the cavity 'vCav is identical to the ignition voltage Vbd of the cavity: 'vCav = Vbd. However, owing to the voltage division at CS and C0, it only causes a negligible small voltage dip at the terminals of the test object
'v = 'vCav·CS/(CS + C0) = Vbd·CS/CT (6.4.22) assuming that the test object is inductively decoupled from the rest of the measuring circuit during several nanoseconds. Note: In Figure 6.4.22 and in Eq. (6.4.22) it is assumed with CT = CS + C0 that the cavity has a significantly smaller thickness than the insulating material in series. In consequence, it is also assumed that the cavity capacitance CCav is significantly larger than the series capacitance CS and that CCav can be neglected in the series connection with CS.
This voltage dip according to Eq. (6.4.22) is so small that it cannot be measured directly. Instead of this, the charge that flows out from
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6 TESTING, MEASURING AND DIAGNOSIS
the coupling capacitor and recharges the test object is measured. For this purpose, the coupling device is regarded as the current measurement resistance and the signal is integrated in the partial discharge measuring device in order to calculate the charge that is flowed. During this, it is not important whether the current is measured in the arm of the coupling capacitor or in the arm of the test object, see Figure 6.4.21. This charge which can be measured, is described as the “apparent charge” QA = CT 'v = 'vCav·CS = 'Q CS/CCav
(6.4.23) for which it is assumed that the voltage dip 'v can be fully compensated by an constantvoltage source. This apparent charge QA is much smaller than the real charge turnover Q. Unfortunately, the relationship according to Eq. 6.4.23 is completely unknown, since the type, position and size of the defect are not known, thus there is no information about the "transmission ratio" CS/CCav. Despite this, the apparent charge QA has proven in practice its value as a parameter for the specification of partial discharge intensity. This is also theoretically comprehensible, since the apparent charge is related to the energy dissipation in the defect and to the size of internal cavities, cf. b) and c) [67]: b) Partial discharge energy
The energy dissipation WPD in the defect and the discharge frequency are responsible for the eroding effect of partial discharges.. The partial discharge energy can only be indirectly estimated from the parameters measured externally at the test object terminals on the basis of the following consideration: the energy dissipation is equal to the capacitive energy stored in the cavity capacitance CCav before the partial discharge event. On the assumption of a complete discharge of the cavity by ¨vCav, the following is approximately valid:
WPD
1 2  CCav 'vCav 2
1 'Q 'vCav 2
According to Eq. (6.4.23), ¨Q is related to the externally measurable apparent charge QA by the capacitive divider ratio CS/CCav . ¨vCav is likewise obtained via the capacitive divider ratio from the peak value of the externally measurable partial discharge inception voltage 2 VPDI or from the externally measurable voltage difference of the AC voltage ¨Vn,n+1 between two successive partial discharge impulses n and n+1. Thus, an expression that comprises only parameters that can be measured externally is obtained for the energy dissipation in the cavity: WPD
C C 1 ˷ · (QA Cav ) · ( 2 VPDI · S ) CS CCav 2
WPD
˷
1 2 · QA ·VPDI 2 1 ˷ · QA ·'Vn, n 1 2
(6.4.24)
The unknown capacitive divider ratio falls out, since charge parameters and voltage parameters are divided in inverse ratio. The partial discharge inception voltages are often comparable for devices of the same voltage level, so that the apparent charge can also be considered as a relative guide to the energy of the discharging impulse. c) Size of the cavity
According to Eq. (6.4.23) and (1), apparent charge also increases with the breakdown voltage of the cavity and thus with the flashover distance d and the size of the cavity: QA
'Q
CS CCav
~ Vbd
~d
CCavVbd
CS CCav
(6.4.25)
6.4 Diagnosis and Monitoring
d) Determination of limit values
Eq. (64.24) suggests that for high voltage levels (with high partial discharge inception voltages), lower apparent charges are acceptable than for lower voltage levels, if there is the same acceptable energy dissipation in the cavity [67]. This gradation is actually seen in current test practice. However, this has not resulted from the presented theoretical considerations, but over many decades of test experience. For the magnitude of acceptable partial discharge intensities, there are neither general specifications nor theoretical justifications. Generally, values from practical test experience are stated in the device specific standards. Mostly, during testing, the test voltage is applied. On reducing the voltage, the partial discharge intensity should not exceed the specified charge value QA for a defined voltage value (significantly above the operating voltage). During this, it must be ensured that in operation, partial discharges that could be ignited by an overvoltage are in any case extinguished again at the operating voltage. Generally, charge values that are accepted for a test for highly stressed insulations (operating field strength > 3 kV/mm) are between QA = 1 and 10 pC, if a sensitive insulating material such as polymeric films, epoxy resin or oilimpregnated paper is involved. Generator insulations with a high percentage of partial dischargeresistant mica can exhibit discharges in the range of 1000pC; 10000 pC is considered to be hazardous [67]. Glass and porcelain exhibit an even higher resistance to partial discharges. Corona discharges in air, and even on ceramic surfaces, are considered nonhazardous. Partial discharge tests for transformers are mandatory for voltages of Vm > 72.5 kV. The levels are 100 pC for 1.2 Vm/ 3 and 250 pC for the one hour PD measurement voltage of 1.58 Vr/ 3 or 1.5 Vm/ 3 , see Section 7.1.3.5 with Figure 7.1.314. These levels are consid
437
ered generous and values are generally well below them. It can be assumed that for an apparent charge of 500 pC, there is a serious problem in the transformer [206]. With regard to erosive ageing of insulating materials, both the discharge intensity QA and the discharge frequency N are important. In sensitive organic insulating materials, a charge rate of N QA = 2 nC/min = 33 pC/s  1 pC/ period
is considered safe. This value should be valid for both AC voltage and for DC voltage [207]. 6.4.2.3 Sensitivity and Calibration
a) Sensitivity
According to Eq. (6.4.22), the discharge of the defect leads to a voltage dip ¨v at the test object connections, which, in accordance with Eq. (6.4.23), can be compensated completely by the outflow of apparent charge QS from a constantvoltage source. But, since the coupling capacitor does not form an ideal voltage source, a voltage dip of 'v* remains. This implies that the entire apparent charge is not compensated, but only the measurable charge QM = CC·'v*.
(6.4.26)
For the charge balance, the following applies:
'v*(CC + CT) = QA = CT 'v .
(6.4.27)
For CC >> CT, 'v* approaches zero, i.e. it is a constantvoltage source. For CC > CT, QM is equal to QA. For smaller values of CC, QM also decreases. Especially for large test object capacitances (such as for
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6 TESTING, MEASURING AND DIAGNOSIS
capacitors, cables or layer windings of transformers), a significantly reduced sensitivity of the partial discharge measurement circuit must therefore be expected. Note: The relationship between QA and QM can be determined by an indirect calibration. Under this, current impulses of constant charge quantity are passed via the parallel circuit consisting of CC and CT, so that the partial discharge measurement device shows a signal corresponding to QM. If an equal current impulse is directly passed via the coupling device, the reading corresponds to the apparent charge QA. The ratio of the readings corresponds to the sought calibration factor
kc =
QA/QM = (CC + CT)/CC . (6.4.29)
The apparent discharge QA is used as a measurement parameter for quantification of partial discharges. A conclusion from QA about the actual charge turnover ¨Q in the defect would be desirable. Unfortunately, Eq. (6.4.23) provides only a basic relationship that cannot be practically evaluated, since the ratios of parameters and capacitances cannot be specified for an unknown defect. However, in general CS > QA can be assumed. b) Calibration
In practice nowadays, a direct calibration is carried out. That is, the current impulses of the calibration are fed with known charge quantity Q0 via the terminals of the test object and compared with the indicated charge value Qind. Generally, partial discharge measuring devices can be set in such a way that displayed charge values correspond to the supplied charge. During the measurement, the displayed charge corresponds to the apparent charge QA. While carrying out a calibration, a few important points must be considered [476]: 1. Calibration must be carried out without high voltage, but in the original and complete test circuit including the test object, since all the lumped capacitances and stray capacitances are also included in the sensitivity of the test circuit. Each change, therefore, requires a new calibration.
2. The calibrator itself shall be made up of a fast stepfunction generator connected in series with a capacitance C0 . With the step voltage V0, the charge Q0 = C0·V0 is coupled into the test object via C0. The calibrator thus simulates the capacitive coupling of partial discharge impulses from a defect. C0 must not be higher than 10 % of the test object capacitance, in order not to influence the setup too strongly. 3. The connection of the calibrator capacitance C0 should be done close to the high voltage terminal of the test object, so that the calibration charge is not partially lost via the stray capacitance of a supply line. 4. Charge values that approximately correspond to the partial discharges to be measured should be used for calibration. Here, however, it must be ensured that the calibration impulses are significantly larger than the background noise level. The frequency of the calibration impulses should be at least 2 for each period of the AC voltage. 5. The rise time Tr of the step voltage V0 must be so small that the calibration impulse exhibits a frequency spectrum whose limit frequency is higher than the limit frequency of the partial discharge impulses to be measured. With the common, rather lowfrequency filter settings of the partial discharge measuring devices (see Section 6.4.2.4), it is ensured that the partial discharge impulses and the calibration impulses have spectral amplitude densities that are comparable within the frequency band f1< ¨f < f2 which is used for the measurement. Note: These requirements are generally fulfilled with Tr < 60 ns. Tr < 0.03/f2 is applicable for broadband devices with f2 > 500 kHz.
6.4.2.4 Signal Processing and Signal Evaluation
Owing to complex system properties of the measurement circuit, current impulses that can be measured with the coupling device are
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mostly not of significance with regard to classic partial discharge diagnostics. Current impulses must be integrated to form the "charge" parameter. The “quasiintegration” undertaken for this purpose can be carried out by broadband and narrowband partial discharge measuring devices. Note: Interference voltage meters and radio interference meters (RIVmeters) were originally developed for communications engineering and they were used at the early beginnings of partial discharge measurement technique. Although they do no longer fulfill the requirements of IEC 60270, they can be used for orienting measurements and with great care, even for quantitative information.
Important parameters of classic diagnostics are the apparent charge QA (partial discharge intensity PDI), phase position with reference to the power frequency fundamental mode, the discharge frequency N, as well as the partialdischarge inception voltage and the partialdischarge extinction voltage (PDI and PDE), see Section. 3.6. The reading of a partial discharge measuring device is proportional to the apparent charge of the largest regularly recurring impulses. If the impulse frequency N falls below 2 impulses per 50 Hz period (i.e. less than 100 per s), the amplitudes in accordance with Table 6.4.21 are weighted with less importance. The inertia of earlier analogous pointertype instruments is thus replicated. Tab 6.4.21: Weighting of the reading of a partial discharge measuring device with respect to impulse frequency N. Impulse frequency N/s
1
2
5
10
50 >100
Reading in % + 5 %
40 60
81
90
99
100
Note: Following the radio interference meters, the socalled CISPR evaluation characteristic was in use in the past, Figure 6.4.24. It was based on the idea adopted from acoustics that a few large impulses should be rated just as high as many smaller ones. The damaging effect of partial discharges is, however, so complex that the application of this simple idea is not justified.
a) Broadband partial discharge measuring devices
The performance of broadband partial discharge measuring devices will first be explained with the example of an analog RCIntegration, Figure 6.4.23. For Rm >
Wi
(6.4.212)
The time constant W, however, should not be too large, so that successive impulses can be distinguished Practical values are in the μs range. The RC integration element can also be interpreted as a low pass in the frequency domain.
CT
v ~ Q (i) u û Figure 6.4.23: Broadband integration of a compensating current i(t) in a PD measuring circuit by a RC low pass.
(6.4.210)
W = R·C t
i (t)
Rm PD measuring circuit
CC W = R·C
v (t)
Broadband integration circuit (very much simplified)
440
The requirement for a large time constant W = R·C corresponds to the requirement for a low upper cutoff frequency of the low pass. For practical measuring devices, this lies in the 100 kHz range. Systems with significantly higher limit frequencies would no longer work as integrators, but would transfer the current impulse more or less unchanged. Note: Even for current impulses lasting for a longer period, the condition (6.4.212) is probably no longer fulfilled and hence an integration error can result.
Owing to the low signal amplitudes, active integration amplifiers were used in the past. Today, the input signal is immediately digitalized in totally digitalized measuring devices and then processed further in digital form. Thus, a high level of flexibility with regard to the integration procedures and further evaluations is obtained. Practical partial discharge measuring devices have no low pass characteristic, but have a bandpass characteristic for blocking network frequency and other low frequency signal components below approx. 10 kHz. According to IEC 60270, the upper cutoff frequency f2 should be at 500 kHz, the bandwidth ¨f between 100 kHz and 400 kHz and the lower cutoff frequency f1 between 30 kHz and 100 kHz. [476]. When determining the filter characteristic of the bandpass, the coupling device (with circuiting), connecting line and partial discharge measuring device must be regarded together as one unit, for which the resultant frequency response must be considered. Mostly damped oscillating impulse responses occur, and these no longer have a similarity with the shape of the original impulse. Only the amplitude is proportional to the apparent charge (quasiintegration) and polarity can be identified from the largest halfwave. Occasionally, tuning of the filters is inadequate and hence the information about the polarity of the impulse can be lost. The resolution for successive impulses is determined by the damping of the oscillations and generally is in the μs range.
6 TESTING, MEASURING AND DIAGNOSIS
b) Narrowband partial discharge measuring devices
Narrowband partial measuring devices have very intensely oscillating impulse responses. That is, the impulse response is in the form of a sine beat that rises and decays, whereby the frequency of the oscillation corresponds to the center frequency (midfrequency) fC of the filter. The duration of the oscillation is determined by the bandwidth ¨f. Information about the polarity of the impulse is thus completely lost. It can be shown that the amplitude of the oscillation is proportional to the charge of the exciting impulse [141], if the spectral amplitude density of the partial discharge impulses is constant in the frequency domain covered by the filter [477]. This implies that for the selection of the centre frequency, a frequency range must be selected in which the reading does not vary with the frequency. According to IEC 60270, the bandwidth 'f should be between 9 kHz and 30 kHz and the center frequency fC between 50 kHz and 1 MHz [476]. A common bandwidth is the value adopted from the CISPR [158] for interference voltage receivers (or radiointerference meters) ¨f = 9 kHz, which corresponds to an impulse resolution time of approx. 220 μs. Narrowband partial discharge measuring devices with tunable filters have the advantage that in an electromagnetically disturbed environment (such as in industrial production units), a frequency band with comparatively little disturbance can be selected. Poor resolution of rapidly successive pulses and loss of polarity information is a disadvantage. c) Interference voltage measuring devices
Historic precursors of partial discharge measuring devices are the interference voltage measuring devices (radiointerference meters) of communications engineering. These are tunable measurement receivers with bandpass characteristics, which are also suitable as narrowband partial discharge measuring devices for the quasiintegration of impulses. Their
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441
reading is a voltage VRIV in μV and not a charge in pC, as in partial discharge measuring devices. For calibrated interference voltage measuring devices, the following relationship is applicable VRIV
QM Rm 'f a / 2 .
(6.4.213)
Rm is the resistance of the coupling device, ¨f the bandwidth and QM the (measurable) charge flowing through Rm. The factor a increases with the frequency N of the impulses in accordance with a weighting characteristic, Figure 6.4.24. The interference voltage for N = 100 impulses per second (corresponding to one impulse per AC halfcycle) is the reference value with the weighting factor a = 1. The weighting characteristic results originally from a circuit with rectifier (for peakvalue storage), a resistivecapacitive network and a pointertype instrument with mechanical inertia. Example: For a bandwidth ¨f = 9 kHz, a coupling device Rm = 60 : a factor a = 1 (i.e. N = 100/s) according to Eq. (6.4.213), an interference voltage VRIV = 1 μV corresponds to a measurable charge QM = 2.62 pC. Note: The relationship between QM and QA can be determined by calibration in accordance with Eq. (6.4.29). However, the calibration is overall made difficult owing to different weighting characteristics according to Figure 6.4.24 and Table 6.4.21, since the reading pertains not only to the frequency of the partial discharge impulses to be measured, but also to the frequency of the calibrator impulses. The calibration is applicable only to the cases in which the frequencies coincide. In other cases, the charge values must be converted to the given frequencies. Interference voltage measurement devices with weighting functionality that can be turned off are therefore often more suitable. Note: The weighting characteristic takes into account the subjective perception that for radio reception, many small impulses cause similar interference to a few large impulses. Also for partial discharges, many small impulses can be likewise considered to be similarly damaging to a few large impulses. However, the processes of erosion breakdown are dependent on a number of hardly ascertainable parameters, so that the abovementioned qualitative dependence cannot be included in a weighting characteristic.
d) Digital partial discharge measuring devices
Because very quick and efficient computers are available, partial discharge measuring devices have now been completely implemented in digital form. This means that the signal measured at the coupling device is digitalized immediately and in realtime. Only then, it is digitally filtered, integrated and further processed. This has resulted in completely new options for partial discharge measurement, partial discharge analysis and the suppression of interference impulses, Section 6.4.2.7. For example, bandwidths, center frequencies and cutoff frequencies are completely freely adjustable; the distinction between narrowband and broadband devices and the restriction to a few center frequencies defined in the standards becomes obsolete; and timebased correlations between individual impulses can be determined. A wide electromagnetic interference signal spectrum can be monitored, so that frequency ranges can be chosen with minimum background noise levels. This is a great advantage for the onsite testing technique. 6.4.2.5 Interferencefree measurement
Partial discharge measurement circuits are designed for the sensitive measurement of the smallest impulses in the pC range. Therefore, they are also particularly sensitive to all types of interferences. Interferencefree measurement of partial discharges, therefore, is one of the major challenges of the practical applica2,0 1,0 a (N)
0,5 0,2 0,1 10 20
50 100 200 500 1000
N/
1 s
5000
Figure 6.4.24: CISPR weighting characteristic for interference voltage measuring devices. For high impulse frequency N > 1000/s, it can lead to erroneous displays due to lack of impulse resolution.
442
tion of high voltage measurement technology. Therefore, before a partial discharge measurement is performed with high voltage, it must first be checked without voltage whether the socalled background noise level is lower than the signal to be measured. Moreover, it must be verified that the the setup without a test object is free from partial discharges under voltage. In the following section, the most important sources of interference and appropriate countermeasures are listed: 1. External electromagnetic radiation can be damped over a broadband range by a high voltage room shielded on all sides. Background noise levels lower than 1 pC can be attained. 2. External conducted interferences, e.g. by power electronic switching impulses on the low voltage side of the power supply, are often damped by inductances and winding capacitances of the test transformer as well as by current limiting resistors on the high voltage side. If necessary, filters connected with low inductance to the hall shield must be used on the low voltage side. 3. Narrowband interference sources (e.g. transmission equipment) can be blocked with a narrowband partial discharge measuring device by adjusting the center frequency in an undisturbed frequency range. This is a helpful solution for onsite measurements, in which shielding is generally not possible. It is disadvantageous here that the information about polarity and impulse shape is lost. 4. Impulse interference sources with constant phase relationship can be gated out by choosing an appropriate time window. This option, available for many partial discharge measuring devices, is helpful for orienting measurements, but it is largely not accepted, since there is the risk that also the signals to be measured are blocked. 5. Metal parts at floating potential can be discharged periodically to the high voltage
6 TESTING, MEASURING AND DIAGNOSIS
side or the ground side. Only a good tidiness of the high voltage laboratory with well defined contacting of all conductive parts helps here. 6. Poor, loose or undefined contacts can cause the socalled “contact noise”that can be avoided by well defined, e.g. by screwed or wedged conductor connections. 7. Partial discharges in a test set up (at edges or points on the high voltage side or the ground side) must be prevented by adequately rounded shield caps. Directional microphones and lowlight amplifiers have proved useful as aids for fault location. Onsite partial discharge measurements in an electrical installation are especially difficult, since large external interferences can be eliminated neither by a hall nor by filters or shield caps. There are a number of approaches, but these do not allow the background noise level of a laboratory measurement to be achieved:
1. Partial discharges are measured with a bridge measurement, both in the leg of the test object and in a reference leg (instead of the coupling capacitor) and they are synchronously recorded [67]. Common mode signals must be assigned to external interferences, pushpull signals to the test object (or the coupling capacitor). 2. By the socalled directional coupler technique, i.e. by partial discharge measurement at two different points (e.g. left or right of a cable joint), it can be distinguished whether the impulse source is between or beyond the measuring points. In this way, both external interferences can be identified and localization or spatial demarcation of the partial discharge source is possible. For that purpose, currents and magnetic fields caused by the partial discharge impulses must be observed. External sources cause commonmode currents, sources between the measuring points cause pushpull currents. Broadband magnetic sensors or Rogowski coils can be
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443
used for the measurement of partial discharge currents [215], Section 6.37. 3. Many more methods are now available to attenuate narrowband and broadband interference sources with the aid of digital filters: By transformation in the frequency domain and adaptive filtering of interference lines, narrowband interference sources can be gated out. External (corona) interference sources can be separated from internal discharges by comparing two signals (e.g. a current signal and a voltage signal), in which one of the signals must be filtered in such a way that the transmission properties of both the channels correspond to each other. Interference is similarly suppressed as described in item no. 1, i.e. by calculating the difference. For current signals and voltage signals, the direction of interference propagation can be determined by calculating the product [215]. Another approach is the separation of random interference signals from the desired partial discharge signals by neural networks. For this, a timeresolved signal shape analysis is used. It requires a broadband output signal coupling and signal processing up to the VHF range, i.e. up to about 100 MHz, [249]. 4. New options for interference signal suppression are also offered by fully digital partial discharge measuring devices, in which the interference signal spectrum can be analyzed and the center frequency and bandwidth can be adjusted so that the lowest possible background noise level occurs, Section 6.4.2.4d). 5. Greater progress in interference signal suppression is attained by the synchronous multichannel partial discharge measurement, Section 6.4.2.7. Synchronously measured and related impulses can be identified by their characteristic amplitude relationships or time relationships and assigned to specific interference sources or
partial discharge sources. By this, selective blocking of individual interference impulses (socalled “gating”) is possible. 6.4.2.6 Partial Discharge Diagnosis
Owing to the complexity of the discharge processes, many partial discharge events evade direct physical interpretation according to Section 3.6.3. Modern data techniques could thus make progress by signal analysis, by statistical methods, by pattern recognition methods and by the correlation of synchronous impulses. The decisive breakthrough, namely the reply to the questions
x
“Where is the defect?”
x
“What type of defect is it?”
x
“How severe is its damaging effect?”
x
“How are multiple defects to be differentiated?”
x
“How does it impact durability?”
has not yet yielded a full response in the general form. Partial discharge diagnosis is, therefore, apparently an everlasting challenge for high voltage engineering research. A few approaches will be described in the following sections. Particular progress is represented by synchronous multichannel partial discharge analysis, and the following Section 6.4.2.7 is dedicated to this. a) Classic interpretation
Classic parameters of partial discharge diagnostics are the partial discharge intensity or the apparent charge, the inception voltages and extinction voltages and the phase position of partial discharge impulses. The partial discharge intensity refers to the socalled apparent charge QA that can be measured externally on the test object terminals. Actual maximum permissible values are derived on the basis of experiences. However it is not possible to make a general statement
444
about the magnitude and hazard of partial discharges within the insulation and about the expected sevice life, since the specific stresses on volumes or surfaces and the signal coupling paths in an (unknown) defect cannot be specified. Moreover, the readings of partial discharge measuring devices depend more on the amplitude of the strongest of the impulses and less on the frequency N which is also relevant for the ageing processes. The inception voltages and extinction voltages VPDI and VPDE serve as indicators of production defects and they shall show that, under operating conditions, no damaging discharges can take place. The problem with this is that the inception and extinction of a partial discharge must be defined by a possibly less significant intensity threshold. Additionally, a considerable ignition delay can often be found for closely localized defects [209]. In the case of a sinusoidal AC voltage, without appreciable distortion by harmonic oscillations, the phase position of the impulses gives important indications of the physical environment of the discharge for simple defect situations (e.g. internal/external discharge, contact to electrodes), Section 3.6.3, Figure 3.68. The phaseresolved partial discharge patterns are based on a deterministic physical approach which facilitates the understanding of the patterns. But on the other hand, it no longer meets the complexity of the situation in many cases. For example, by the superimposition of events from different defects, the clearness of partial discharge patterns is lost. Moreover, the interpretation often reflects subjective experiences and feelings. A frequent source of error is that for nonsinusoidal voltages, false conclusions can be drawn from the phase position of the impulses; and the phase positions can additionally be shifted owing to the buildup of space charges [214]. The possibilities for partial discharge interpretation for DC voltages are far more limited, since phase relationships cannot be established. Instead of this, it is recommended that time differences between successive impulses
6 TESTING, MEASURING AND DIAGNOSIS
are considered [465]. This allows basic types of defects to be distinguished, Section 3.6.3.2, but for the development of partial discharge interpretation methods that are illustrated in the following section, this has had no further significance: they are practically exclusively fixated upon AC voltage still. Only synchronous multichannel partial discharge measurement offers a new option, including for DC voltages, for associating the impulses with different defects and different interference sources, Section 6.4.2.7. b) Statistical approaches
Modern data techniques have opened up new options for processing large data quantities and for statistical partial discharge analyses. Statistical approaches for analysis systems are based on maximum possible acquisition of impulse data, on data reduction by the storage of some selected impulse parameters, on calculation of new parameters, on determination of distribution functions and on the comparison with reference databases. This allows probabilities for the presence of different types of defects or “degree of correlation” with known defects to be specified [74], [78], [79]. No physical explanation is provided for this, but only a statistically substantiated similarity is ascertained. Reference to discharge physics is often sought through phaseresolved patterns, in which socalled “cloud plots” are created by superposition of many periods. This enables the frequency of the discharges to be visualized additionnally by using a three dimensional image or by color gradation, [74] to [80], [204], [212], [213]. Note: There is also the possibility here of misinterpretation through harmonic distortion influences and space charge influences associated with the phaseresolved representation.
For digital evaluation, the partial discharge impulses must at first be recorded with high bandwidth and unaltered as far as possible, then digitalized, filtered and then must be stored in connection with other measurement values (voltage, time). This is restricted to a few impulse parameters to reduce the data
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volume. By numerical signal processing, along with the development of classic parameters (charge, phase position, frequency), other parameters (such as polarity, energy and amplitude) and time constants are developed. Owing to this, during the increasing and decreasing of the test voltage, an extensive data record is created, which is compressed by creating statistical distribution functions and which can be further processed based on different methods and approaches. This involves the important distributions impulse frequency against the phase angle or the impulse amplitude against the phase angle. It is, however, largely common to analyze a dozen different distributions. The availability of an extensive database with explicitly identifiable defects is a decisive factor for the validity of statistical analyses. Note: The reading of a classic partial discharge measuring device can thus be numerically simulated based on the recorded data.
The visualization of data records is often carried out with multidimensional histograms, in which, for example, parameters such as charge QA, frequency N and phase position M are represented three dimensionally as a socalled "M,Q,Npattern”. In the simplest form, these are socalled "cloud plots”, in which partial discharge events summed over several periods are represented as charge points against the phase position. The frequency N is represented in the third dimension either by the density of the cloud points, by a color gradation (see Fig
ure 6.4.25 center) or by three dimensional bars. Along with the subjective evaluation of partial discharge patterns, the aim is to ascertain the concurrence of measured data records with reference measurements by means of expert systems, in order to achieve an allocation to type of defect and location of defect. For this purpose, parameters and distribution functions are compared, correlations are determined and the methods of pattern identification or “fuzzy logic” are applied. One can also attempt to relate discharge parameters and types of defect via a neural network using a neuronal approach [75], [76], [77]. This allows the interpretation of partial discharges to be raised from the subjective level to the level of automated objective comparison. In many cases, this is a great advantage for test practice [210]. Partial discharge analysis systems generally do not give any absolute information about the type of defect, but determine a degree of correlation of the measured partial discharge data with previously measured references. An allocation to a defect category is possible for sufficiently large database with known defect instances. A statement about the hazard of the partial discharge or about the service life of the insulation is thus at most possible only very indirectly on the basis of operating experiences. The interpretation of phaseresolved patterns such as cloud plots or the M,q,npatterns is
2 û uv
v (M) , Q (M)
û uv
uv û
ûv 2u
A
uv û û uv Original data
'v
M
Phaseresolved histogram cloud plot, "phaseresolved pattern"
uv û 'v
'v n , n +1
0 û uv
'v n 1, n
Figure 6.4.25: Partial discharge diagnosis for a model body (cylindrical cavity 1 x 1 mm in epoxy resin) with original data (left), phaseresolved cumulative representation (center) and pulse sequence analysis (right).
2 û uv
446
associated with several fundamental problems: 1. The deterministic relationship between individual successive and related impulses is lost during the summation of several periods, as is still clearly identifiable in the original data of the example, Figure 6.2.45 (left). 2. Phaseresolved representations are not clear if the test voltage is distorted, especially when intermediate maxima occur. Then several rising and falling flanks of the voltage can occur, in which discharges of varying polarity result. The partial discharge pattern would be completely changed. 3. Phase position can also be shifted owing to superimposition of space charging fields. 4. Multiple defects are hardly kept apart without additional methods. Synchronous multichannel partial discharge measurement has now been proven as an efficient method for separation of multiple partial discharge sources. This method is able to assign the source of individual impulses and to resolve overlapping partial discharge patterns into individual pattern and to analyze them separately, Section 6.4.2.7. c) Pulse sequence analysis
The abovementioned difficulties do not occur with the pulse sequence analysis method, or appear only to a lesser extent. With a pulse sequence analysis, a deterministic relationship between successive impulses should be made noticeable by redefined discharge parameters, [211], [214]. The test voltage change ¨v between two partial discharge events is observed. Note: It is a socalled autocorrelation method, in which the measured impulses are correlated with each other and not with an external parameter (e.g. phase position).
For example, Figure 6.4.25 (left) shows internal discharges in a cavity, which “in accordance with the textbook” and analogous to
6 TESTING, MEASURING AND DIAGNOSIS
Figure 3.62 ignite in the area of the steepest voltage gradient wv/wt, always after passing through the same voltage difference ¨v. If the voltage difference between the events n and n+1 is applied over the voltage difference between the events n1 and n, points occur on the diagonals of the pattern for related, equally high voltage differences, Figure 6.425 (right). The position of the points is determined by the voltage difference ¨v. This voltage difference is characteristic of the defect and independent of the test voltage waveform. In contrast to the phaseresolved pattern (cloud plots), here sharp patterns occur, since neither the space charge induced phase displacements nor test voltage distortions play a role here. A second defect would be indicated by another voltage difference. If unrelated impulses appear successively, statistically dispersed voltage differences arise, similar to stochastic interference impulses. Then it can be identified that the impulses do not have a deterministic relationship with each other. Also pulse sequence analysis shows characteristic patterns that can be physically substantiated. While internal discharges occur in the pattern diagonals (see above), external discharges have very small voltage differences, and they are concentrated at the origin. Thus, pulse sequence analysis promises to give an additional contribution to defect detection. However, here also, the question of the life time of insulation under the effect of partial discharge erosion cannot be answered. Note: With pulse sequence analysis it could be shown that the sequence of partial discharge events is very much more deterministic than that which can be identified with statistical analysis. For example, the dispersion of the phase position of the impulses that had been assumed until now as coincidental could be attributed to a systematic cause i.e. could be attributed to superimposition of space charge fields. For the evaluation of voltage differences ¨v, therefore, many sharp partial discharge patterns occur that are not blurred by statistical averaging and which allow a new and more precise physical interpretation of events [214].
With the superposition of several defects, the ability to identify uniquely is often lost, simi
6.4 Diagnosis and Monitoring
larly to the phaseresolved representation. However, a unique identification can be achieved, even in the case of multiple partial discharge sources, by separation of impulses with the aid of synchronous multichannel partial discharge measurement, Section 6.4.2.7. d) Analysis of impulse shape
The analysis of the impulse shape requires a highly broadband signal recording to