Transformer Engineering Copyright © 2004 by Marcel Dekker, Inc. POWER ENGINEERING 1. Power Distribution Planning Reference Book, H.Lee Willis 2. Transmission Network Protection: Theory and Practice, Y.G.Paithankar 3. Electrical Insulation in Power Systems, N.H.Malik, A.A.Al-Arainy, and M.I.Qureshi 4. Electrical Power Equipment Maintenance and Testing, Paul Gill 5. Protective Relaying: Principles and Applications, Second Edition, J. Lewis Blackburn 6. Understanding Electric Utilities and De-Regulation, Lorrin Philipson and H.Lee Willis 7. Electrical Power Cable Engineering, William A.Thue 8. Electric Systems, Dynamics, and Stability with Artificial Intelligence Applications, James A.Momoh and Mohamed E.El-Hawary 9. Insulation Coordination for Power Systems, Andrew R.Hileman 10. Distributed Power Generation: Planning and Evaluation, H.Lee Willis and Walter G.Scott 11. Electric Power System Applications of Optimization, James A.Momoh 12. Aging Power Delivery Infrastructures, H.Lee Willis, Gregory V.Welch, and Randall R.Schrieber 13. Restructured Electrical Power Systems: Operation, Trading, and Volatility, Mohammad Shahidehpour and Muwaffaq Alomoush 14. Electric Power Distribution Reliability, Richard E.Brown 15. Computer-Aided Power System Analysis, Ramasamy Natarajan 16. Power System Analysis: Short-Circuit Load Flow and Harmonics, J. C.Das 17. Power Transformers: Principles and Applications, John J.Winders, Jr. 18. Spatial Electric Load Forecasting: Second Edition, Revised and Expanded, H.Lee Willis 19. Dielectrics in Electric Fields, Gorur G.Raju 20. Protection Devices and Systems for High-Voltage Applications, Vladimir Gurevich 21. Electrical Power Cable Engineering: Second Edition, Revised and Expanded, William A.Thue 22. Vehicular Electric Power Systems: Land, Sea, Air, and Space Vehicles, Ali Emadi, Mehrdad Ehsani, and John M.Miller 23. Power Distribution Planning Reference Book: Second Edition, Revised and Expanded, H.Lee Willis 24. Power System State Estimation: Theory and Implementation, Ali Abur and Antonio Gómez Expósito 25. Transformer Engineering: Design and Practice, S.V.Kulkarni and S.A.Khaparde ADDITIONAL VOLUMES IN PREPARATION Copyright © 2004 by Marcel Dekker, Inc. Transformer Engineering Design and Practice S.V.Kulkarni S.A.Khaparde Indian Institute of Technology, Bombay Mumbai, India NEW Y ORK • BASELMARCEL DEKKER, INC. Copyright © 2004 by Marcel Dekker, Inc. Transferred to Digital Printing 2005 Although great care has been taken to provide accurate and current information, neither the author(s) nor the publisher, nor anyone else associated with this publication, shall be liable for any loss, damage, or liability directly or indirectly caused or alleged to be caused by this book. The material contained herein is not intended to provide specific advice or recom- mendations for any specific situation. Trademark notice: Product or corporate names may be trademarks or registered trademarks and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress. ISBN: 0-8247-5653-3 Headquarters Marcel Dekker, Inc., 270 Madison Avenue, New York, NY 10016, U.S.A. tel: 212–696–9000; fax: 212–685–4540 Distribution and Customer Service Marcel Dekker, Inc., Cimarron Road, Monticello, New York 12701, U.S.A. tel: 800–228–1160; fax: 845–796–1772 Eastern Hemisphere Distribution Marcel Dekker AG, Hutgasse 4, Postfach 812, CH-4001 Basel, Switzerland tel: 41–61–260–6300; fax: 41–61–260–6333 World Wide Web http://www.dekker.com The publisher offers discounts on this book when ordered in bulk quantities. For more information, write to Special Sales/Professional Marketing at the headquarters address above. Copyright © 2004 by Marcel Dekker, Inc. All Rights Reserved. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage and retrieval system, without permission in writing from the publisher. Current printing (last digit): 10 9 8 7 6 5 4 3 2 1 Copyright © 2004 by Marcel Dekker, Inc. Foreword It is a great pleasure to welcome this new book from Prof. S.V.Kulkarni and Prof. S.A.Khaparde, and I congratulate them for the comprehensive treatment given in the book to nearly all aspects of transformer engineering. Everyone involved in or with the subject area of this book, whether from academics or industry, knows that the last decade has been particularly dynamic and fast changing. Significant advances have been made in design, analysis and diagnostic techniques for transformers. The enabling factors for this technological leap are extremely competitive market conditions, tremendous improvements in computational facilities and rapid advances in instrumentation. The phenomenal growth and increasing complexity of power systems have put up tremendous responsibilities on the transformer industry to supply reliable transformers. The transformer as a system consists of several components and it is absolutely essential that the integrity of all these components individually and as a system is ensured. A transformer is a complex three-dimensional electromagnetic structure, and it is subjected to variety of stresses, viz. dielectric, thermal, electrodynamic, etc. In-depth understanding of various phenomena occurring inside the transformer is necessary. Most of these can now be simulated on computers so that suitable changes can be made at the design stage to eliminate potential problems. I find that many of these challenges in the design and manufacture of transformers, to be met in fast changing market conditions and technological options, are elaborated in this book. There is a nice blend of theory and practice in almost every topic discussed in the text. The academic background of the authors has ensured that a thorough theoretical treatment is given to important topics. A number of landmark references are cited at appropriate places. The previous industry experience of S.V.Kulkarni is reflected in many discussions in the book. The various theories have been supported in the text by reference to actual practices. For example, while deliberating on various issues of stray loss estimation and control, the relevant theory of eddy currents has been first explained. This theoretical basis is then used to explain various design and iii Copyright © 2004 by Marcel Dekker, Inc. manufacturing practices established in the industry to analyze and minimize the stray losses in the windings and structural components. The design and manufacturing practices and processes have significant impact on the performance parameters of the transformers, and the same have been identified in the text while discussing various topics. Wherever required, a number of examples and case studies are given which are of great practical value. The knowledge of zero-sequence characteristics of transformers is very important for utilities. It is essential to understand the difference between magnetizing and leakage zero-sequence reactances of the transformer. These two types of zero-sequence reactances are explained in the book for three-phase three-limb, three-phase five-limb and single-phase three- limb transformers with numerical examples. One may not find such a detailed treatment to zero-sequence reactances in the available literature. The effect of tank on the zero-sequence reactance characteristics is lucidly explained. The discussions on the sympathetic inrush phenomenon, part-winding resonance, short-circuit withstand characteristics and noise reduction techniques should also be quite useful to the readers. With the increase in network complexity and severity of loads in some cases, the cooperation between the transformer manufacturers and users (utilities) is very critical. The design reviews with the involvement of users at various stages of contract should help in enhancing the reliability of transformers. I am happy to note that such areas of cooperation are identified at appropriate places in the text. The book propagates the use of modern computational tools for optimization and quality enhancement of transformers. I know a number of previously published works of the authors in which Finite Element Method (FEM) has been applied for the stray loss control and insulation design of the transformers. The use of FEM has been aptly demonstrated in the book for various calculations along with some tips, which will be helpful to a novice in FEM. The book is therefore a major contribution to the literature. The book will be extremely helpful and handy to the transformer industry and users. It will be also useful for teaching transformers to undergraduate and postgraduate students in universities. The thorough treatment of all-important aspects of transformer engineering given will provide the reader all the necessary background to pursue research and development activities in the domain of transformers. It is anticipated that this book will become an essential reference for engineers concerned with design, application, planning, installation, and maintenance of power transformers. H.Jin Sim, PE VP, Waukesha Electric Systems Past Chairman, IEEE Transformers Committee iv Foreword Copyright © 2004 by Marcel Dekker, Inc. Preface In the last decade, rapid advancements and developments have taken place in the design, analysis, manufacturing and condition-monitoring technologies of transformers. The technological progress will continue in the forthcoming years. The phenomenal growth of power systems has put tremendous responsibilities on the transformer industry to supply reliable and cost-effective transformers. There is a continuous increase in ratings of generator transformers and autotransformers. Further, the ongoing trend to go for higher system voltages for transmission increases the voltage rating of transformers. The increase in current and voltage ratings calls for special design and manufacturing considerations. Advanced computational techniques have to be used that should be backed up by experimental verification to ensure quality of design and manufacturing processes. Some of the vital design challenges are: stray loss control, accurate prediction of winding hot spots, short-circuit withstand capability and reliable insulation design. With the increase in MVA ratings, the weight and size of large transformers approach or exceed transport and manufacturing capability limits. Also, due to the ever-increasing competition in the global market, there are continual efforts to optimize the material content in transformers. Therefore, the difference between withstand levels (e.g., short circuit, dielectric) and corresponding operating stress levels is diminishing. Similarly, the guaranteed performance figures and actual test values are now very close. All these factors demand greater efforts from researchers and designers for accurate calculation of various stress levels and performance figures for the transformers. In addition, strict control of manufacturing processes is required. Manufacturing variations of components should be monitored and controlled. Many of the standard books on transformers are now more than 10 years old. Some of these books are still relevant and widely referred for understanding the theory and operation of transformers. However, a comprehensive theoretical basis together with application of modern computational techniques is necessary to face the challenges of fast-changing and demanding conditions. This book is an effort in that direction. The principles of various physical phenomena occurring v Copyright © 2004 by Marcel Dekker, Inc. within a transformer are explained elaborately in the text, which could also be used in a course at the undergraduate or postgraduate level. Wherever required, adequate references have been cited so that readers can explore the phenomena in more depth. In fact, a large number of very useful references (more than 400) is one of the hallmarks of this book. Some of the references—classic sources that date back to the early part of the last century—explain many of the theories useful in transformer engineering. Some most recent works are also discussed to give readers a feel for the latest trends in transformer technology. The first author worked in the transformer industry for 11 years before joining academia. He has vast experience in the design and development of transformers, from the small distribution range to 400 kV class 300 MVA ratings. He had ample opportunity to investigate problems in transformer operations and sites. A few case studies and site investigations in which he was actively involved have been incorporated at appropriate places in the text. Also, he found that some aspects of transformer engineering had not been given adequate treatment in the books available. Hence, the emphasis of this book is on these aspects: magnetizing asymmetry, zero-sequence reactance characteristics, stray losses and related theory of eddy currents, short-circuit forces and withstand, part winding resonance phenomena, insulation design, and design aspects of transformers for rectifier, furnace and HVDC applications. The book will be particularly useful to: (1) Transformer designers and researchers engaged in optimization and quality-enhancement activities in today’s competitive environment (2) Utility engineers who would like to learn more about the system interaction aspects of transformers in an interconnected power system to improve on specifications and employ diagnostic tools for condition monitoring (3) Undergraduate and postgraduate students who wish to integrate traditional transformer theory with modern computing practices In Chapter 1, in addition to the transformer fundamentals, various types of transformers in a typical power system are explained along with their features. There is a trend to use better materials to reduce core losses. Often the expected loss reduction is not obtained with these better grades. The design and manufacturing practices and processes that have significant impact on the core performance are highlighted in Chapter 2. The three-phase three-limb core has inherent magnetizing asymmetry that sometimes results in widely different no- load current and losses in three phases of the transformer during the no-load loss measurement by the three-wattmeter method. It is shown that one of the three wattmeters can have a negative reading depending on the magnitude of asymmetry between phases and the level of excitation. Although the inrush current phenomenon is well understood, the sympathetic inrush phenomenon— in which the magnetization level of a transformer is affected by energization of vi Preface Copyright © 2004 by Marcel Dekker, Inc. another interconnected transformer—is not well known. The factors influencing the phenomenon are elucidated in the chapter. The phenomenon was investigated by the first author in 1993 based on switching tests conducted at a site. Chapter 3 is devoted to reactance of transformers, which can be calculated by either analytical or numerical methods. Procedures for the calculation of reactance of various types and configurations of windings, including zigzag and sandwich windings, are illustrated. The reactance for complex winding configurations can be easily calculated by the finite element method (FEM), which is the most widely used numerical method. The chapter gives exhaustive treatment of zero-sequence characteristics of the transformers. Procedures for calculation of the magnetizing zero-sequence and leakage zero-sequence reactances of the transformers are illustrated through examples (such a treatment is unusual in the published literature). The effect of the presence of delta winding on the zero-sequence reactance is also explained. In order to accurately estimate and control the stray losses in windings and structural parts, an in-depth understanding of the fundamentals of eddy currents starting from the basics of electromagnetic fields is desirable. The treatment of eddy currents given in Chapter 4 is self-contained and useful for the conceptual understanding of the phenomena of stray losses in the windings and structural components of transformers described in Chapters 4 and 5, respectively. Stray losses in all the conducting components of the transformers have been given elaborate treatment. Different analytical and numerical approaches for their estimation are discussed and compared. A number of useful guidelines, graphs and equations are given that can be used by practicing engineers. A few interesting phenomena observed during the load-loss test of transformers are explained (e.g., the half turn effect). Various shielding arrangements for effective stray loss control are discussed and compared. Failure of transformers due to short circuits is a major concern for transformer users. The success rate during actual short-circuit tests is far from satisfactory. The static force and withstand calculations are well established. Efforts are being made to standardize and improve the dynamic short-circuit calculations. A number of precautions (around 40) that can be taken at the specification, design and manufacturing stages of transformers for improvement in short-circuit withstand are elaborated in Chapter 6. The various failure mechanisms and factors that determine the withstand strength are explained. Although methods for calculating impulse distribution are well established, failures of large transformers due to part-winding resonance and very fast transient overvoltages have attracted the attention of researchers. After an explanation of the methods for calculating series capacitances of commonly used windings, analytical and numerical methods for transient analysis are discussed in Chapter 7. The results of three different methods are presented for a typical winding. Methods for avoiding winding resonances are also explained. Chapter 8 examines in detail the insulation design philosophy. Various factors that affect insulation strength are summarized. The formulae given for bulk oil Preface vii Copyright © 2004 by Marcel Dekker, Inc. and creepage withstand are very useful to designers. Procedures for the design of major and minor insulation systems are presented. Chapter 9 deals with the thermal aspects of transformer design. After a description of the modes of heat transfer, various cooling systems are described. The insulation aging phenomenon and life expectancy are also discussed. A number of recent failures of large transformers have been attributed to the static electrification phenomenon, which is explained at the end of the chapter. Various types of loads and tests that determine aspects of structural design are discussed in Chapter 10. Tank-stiffening arrangements are elaborated. This material has been scarce in the available literature. Because of increasing environmental concerns, many users are specifying transformers with lower noise levels. Different noise level reduction techniques are discussed and compared. Chapter 11 is devoted to four special transformers: rectifier transformers, HVDC converter transformers, furnace transformers and phase-shifting transformers. Their design aspects and features, different from those of conventional distribution and power transformers, are enumerated. The text concludes by identifying current research and development trends. The last chapter is intended to give pointers to readers desirous of pursuing research in transformers. Even though the transformer is a mature product, there are still a number of design, manufacturing and power system interaction issues that continue to attract the attention of researchers. This book addresses many of these issues and provides leads to most of the remaining ones. It encompasses all the important aspects of transformer engineering including the recent advances in research and development activities. It also propagates the use of advanced computational tools such as FEM for optimization and quality enhancement of transformers. S.V.Kulkarni S.A.Khaparde Prefaceviii Copyright © 2004 by Marcel Dekker, Inc. [...]... Loss in Transformer Windings References 127 128 133 137 139 141 155 166 5 Stray Losses in Structural Components 5. 1 Factors Influencing Stray Losses 5. 2 Overview of Methods for Stray Loss Estimation 5. 3 Core Edge Loss 5. 4 Stray Loss in Frames 5. 5 Stray Loss in Flitch Plates 5. 6 Stray Loss in Tank 5. 7 Stray Loss in Bushing Mounting Plates 5. 8 Evaluation of Stray Loss Due to High Current Leads 5. 9 Measures... Insulation 12.4 Challenges in Design and Manufacture of Transformers 12 .5 Computer-Aided Design and Analysis 12.6 Monitoring and Diagnostics 12.7 Life Assessment and Refurbishment References 437 437 438 440 441 443 4 45 449 449 Appendix A: Fault Calculations A1 Asymmetrical Fault with No In-Feed from LV Side A2 Asymmetrical Fault with In-Feed from LV Side 453 454 457 Appendix B: Stress and Capacitance Formulae... Preface Acknowledgements iii v ix 1 Transformer Fundamentals 1.1 Perspective 1.2 Applications and Types of Transformers 1.3 Principles and Equivalent Circuit of a Transformer 1.4 Representation of Transformer in Power System 1 .5 Open-Circuit and Short-Circuit Tests 1.6 Voltage Regulation and Efficiency 1.7 Parallel Operation of Transformers References 1 1 5 11 20 23 25 33 34 2 Magnetic Characteristics... Winding Heat 9 .5 Aging and Life Expectancy 9.6 Direct Hot Spot Measurement 9.7 Static Electrification Phenomenon References 367 368 370 3 75 376 380 384 3 85 387 7 Copyright © 2004 by Marcel Dekker, Inc 268 270 272 306 314 321 xiv Contents 10 Structural Design 10.1 Importance of Structural Design 10.2 Different Types of Loads and Tests 10.3 Classification of Transformer Tanks 10.4 Tank Design 10 .5 Methods... 10.6 Overpressure Phenomenon in Transformers 10.7 Seismic Analysis 10.8 Transformer Noise: Characteristics and Reduction References 389 389 390 392 3 95 397 401 403 404 409 11 Special Transformers 11.1 Rectifier Transformers 11.2 Converter Transformers for HVDC 11.3 Furnace Transformers 11.4 Phase Shifting Transformers References 411 411 417 424 428 433 12 Recent Trends in Transformer Technology 12.1 Magnetic... Computations 8.3 Factors Affecting Insulation Strength 8.4 Test Methods and Design Insulation Level (DIL) 8 .5 Insulation Between Two Windings 8.6 Internal Insulation 8.7 Design of End Insulation 8.8 High-Voltage Lead Clearances 8.9 Statistical Analysis for Optimization and Quality Enhancement References 327 328 333 3 35 348 351 353 356 358 361 362 9 Cooling Systems 9.1 Modes of Heat Transfer 9.2 Cooling... Calculation 3 .5 Impedance Characteristics of Three-Winding Transformer 3.6 Reactance Calculation for Zigzag Transformer 3.7 Zero-Sequence Reactance Estimation 3.8 Stabilizing Tertiary Winding References 77 78 85 88 90 98 103 108 121 123 4 Eddy Currents and Winding Stray Losses 4.1 Field Equations 4.2 Poynting Vector 4.3 Eddy Current and Hysteresis Losses 4.4 Effect of Saturation 4 .5 Eddy Loss in a Transformer. .. Sachin Thakkar and Mr G D.Patil helped tremendously, and the excellent quality of the figures is due to their efforts Ph.D students Mr G.B.Kumbhar, Mr A.P.Agalgaonkar and Mr M.U.Nabi also contributed in the refining of some topics in the book Previously, S.V.Kulkarni worked in Crompton Greaves Limited in the area of design and development of transformers He sincerely acknowledges the rich and ample experience... Characteristics 2.1 Construction 2.2 Hysteresis and Eddy Losses 2.3 Excitation Characteristics 2.4 Over-Excitation Performance 2 .5 No-Load Loss Test 2.6 Impact of Manufacturing Processes on Core Performance 2.7 Inrush Current 2.8 Influence of Core Construction and Winding Connections on No-Load Harmonic Phenomenon 2.9 Transformer Noise References 35 36 42 44 46 46 54 56 67 69 72 xi Copyright © 2004 by Marcel... Stray Loss Control 5. 10 Methods for Experimental Verification 5. 11 Estimation of Stray Losses in Overexcitation Condition 5. 12 Load Loss Measurement References 169 171 182 184 1 85 187 192 197 199 206 214 216 218 224 6 Short Circuit Stresses and Strength 6.1 Short Circuit Currents 6.2 Thermal Capability at Short Circuit 6.3 Short Circuit Forces 6.4 Dynamic Behavior Under Short Circuits 6 .5 Failure Modes . Trends in Transformer Technology 437 12. 1 Magnetic Circuit 437 12. 2 Windings 438 12. 3 Insulation 440 12. 4 Challenges in Design and Manufacture of Transformers 441 12. 5 Computer-Aided Design and Analysis. Library of Congress. ISBN: 0- 824 7 -56 53-3 Headquarters Marcel Dekker, Inc., 27 0 Madison Avenue, New York, NY 10016, U.S.A. tel: 21 2–696–9000; fax: 21 2–6 85 454 0 Distribution and Customer Service Marcel. Power System 20 1 .5 Open-Circuit and Short-Circuit Tests 23 1.6 Voltage Regulation and Efficiency 25 1.7 Parallel Operation of Transformers 33 References 34 2 Magnetic Characteristics 35 2. 1 Construction