2012 • 728 Pages • 3.79 MB • English

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Transformer Engineering Design, Technology and Diagnostics Second Edition S.V. Kulkarn i S .A . Khaparde

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CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2013 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business International Standard Book Number-13: 978-1-4398-5418-1 (eBook - PDF) Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com Version Date: 20120803

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ª º Preface to the second edition xi Foreword to the first edition xiii Preface to the first edition xv Acknowledgments xix 1 Transformer Fundamentals 1 1.1 Perspective 1 1.2 Applications and Types of Transformers 5 1.3 Principles and the Equivalent Circuit 11 1.4 Representation of a Transformer in a Power System 21 1.5 Open-Circuit and Short-Circuit Tests 23 1.6 Voltage Regulation and Eficiency 26 1.7 Paralel Operation of Transformers 34 References 36 2 Magnetic Characteristics 37 2.1 Construction 38 2.2 Hysteresis, Eddy, and Anomalous Losses 44 2.3 Excitation Characteristics 48 2.4 Over-Excitation Performance 50 2.5 No-Load Loss Test 51 2.6 Impact of Manufacturing Proceses 58 2.7 Inrush Current 60 2.8 Influence of the Core Construction and Winding Connections on No-Load Harmonic Phenomenon 71 2.9 Transformer Noise 73 2.10 Rotational Core Losses 76 References 78 Contents

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3 Impedance Characteristics 83 3.1 Reactance Calculation 84 3.2 Different Approaches for Reactance Calculation 91 3.3 Analytical Methods 94 3.4 Numerical Method for Reactance Calculation 96 3.5 Impedance Characteristics of Three-Winding Transformers 104 3.6 Reactance Calculation for Zigzag Transformers 109 3.7 Zero-Sequence Reactances 115 3.8 Stabilizing Tertiary Winding 129 References 132 4 Eddy Currents and Winding Stray Losses 135 4.1 Field Equations 136 4.2 Poynting Vector 141 4.3 Eddy Curent and Hysteresis Loses 145 4.4 Efect of Saturation 148 4.5 Eddy Losses in Transformer Windings 150 4.6 Circulating Current Loss in Transformer Windings 165 References 176 5 Stray Losses in Structural Components 179 5.1 Factors Influencing Stray Loses 181 5.2 Overview of Methods for Stray Loss Estimation 192 5.3 Core Edge Los 194 5.4 Stray Loss in Frames 195 5.5 Stray Los in Flitch Plates 197 5.6 Stray Los in Tank 202 5.7 Stray Loss in Bushing Mounting Plates 208 5.8 Evaluation of Stray Loss Due to High Current Leads 210 5.9 Measures for Stray Loss Control 217 5.10 Methods for Experimental Verification 225 5.11 Estimation of Stray Losses in Overexcitation Condition 227 5.12 Load Los Measurement 229 References 235 6 Short-Circuit Streses and Strength 243 6.1 Short-Circuit Curents 244 6.2 Thermal Capability during a Short-Circuit 251 6.3 Short-Circuit Forces 252 6.4 Dynamic Behavior under Short-Circuits 260 6.5 Failure Modes Due to Radial Forces 265 6.6 Failure Modes Due to Axial Forces 271

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6.7 Failure Modes Due to Interactive (Combined Axial and Radial) Forces 279 6.8 Efect of Prestres 280 6.9 Short-Circuit Test 281 6.10 Effect of Inrush Current 283 6.11 Split-Winding Transformers 283 6.12 Short-Circuit Withstand 285 6.13 Calculation of Electrodynamic Force between Parallel Conductors 289 6.14 Design of Clamping Structures 291 References 293 7 Surge Phenomena in Transformers 299 7.1 Initial Voltage Distribution 299 7.2 Ground Capacitance Calculations 304 7.3 Capacitance of Windings 305 7.4 Inductance Calculation 320 7.5 Standing Waves and Traveling Waves 322 7.6 Methods for Analysis of Impulse Distribution 325 7.7 Computation of Impulse Voltage Distribution Using State Variable Method 328 7.8 Winding Design for Reducing Internal Overvoltages 336 References 343 8 Insulation Design 349 8.1 Calculation of Stresses for Simple Configurations 350 8.2 Field Computations 355 8.3 Factors Affecting Insulation Strength 357 8.4 Test Methods and Design Insulation Level (DIL) 372 8.5 Insulation between Two Windings 375 8.6 Internal Insulation 377 8.7 Design of End Insulation 379 8.8 High-Voltage Lead Clearances 382 8.9 Statistical Analysis for Optimization and Quality Enhancement 385 References 387 9 Cooling Systems 393 9.1 Modes of Heat Transfer 394 9.2 Cooling Arrangements 397 9.3 Dissipation of Core Heat 402 9.4 Dissipation of Winding Heat 403 9.5 Aging and Life Expectancy 406

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9.6 Direct Hot Spot Measurement 411 9.7 Static Electrification Phenomenon 412 9.8 Recent Trends in Computations 414 References 416 10 Structural Design 419 10.1 Importance of Structural Design 419 10.2 Different Types of Loads and Tests 420 10.3 Classification of Transformer Tanks 422 10.4 Tank Design 425 10.5 Methods of Analysis 427 10.6 Overpressure Phenomenon in Transformers 432 10.7 Seismic Analysis 433 10.8 Transformer Noise: Characteristics and Reduction 436 10.9 Transport Vibrations and Shocks 442 References 442 11 Special Transformers 445 11.1 Rectifier Transformers 445 11.2 Converter Transformers for HVDC 451 11.3 Furnace Transformers 458 11.4 Phase Shifting Transformers 463 References 467 12 Electromagnetic Fields in Transformers: Theory and 471 Computations 12.1 Perspective 472 12.2 Basics of Electromagnetic Fields Relevant to Transformer Engineering 476 12.3 Potential Formulations 502 12.4 Finite Element Method 516 12.5 FEM Formulations 528 12.6 Coupled Fields in Transformers 538 12.7 Computation of Performance Parameters 552 References 564 13 Transformer–System Interactions and Modeling 569 13.1 Power Flow Analysis with Transformers 569 13.2 Harmonic Studies 580 13.3 Ferroresonance 583 13.4 Arc Furnace Application 587

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13.5 Geomagnetic Disturbances 589 13.6 Sympathetic Inrush Phenomenon 589 13.7 Internal Resonances Due to System Transients 591 13.8 Very Fast Transient Overvoltages 592 13.9 Transients in Distribution Transformers 592 13.10 Low-, Mid-, and High-Frequency Models of Transformers 593 References 605 14 Monitoring and Diagnostics 611 14.1 Conventional Tests 613 14.2 Disolved Gas Analysis 616 14.3 Partial Discharge Diagnostics 617 14.4 Degre of Polymerization and Furan Analysis 626 14.5 Time Domain Dielectric Response Methods 627 14.6 Frequency Domain Dielectric Response Method 639 14.7 Detection of Winding Displacements 644 14.8 Acesories 655 14.9 Other Diagnostic Tests/Instruments 657 14.10 Life Asesment and Refurbishment 659 References 659 15 Recent Trends in Transformer Technology 665 15.1 Magnetic Circuit 666 15.2 Windings 666 15.3 New Insulating Liquids 668 15.4 Advanced Computations 669 15.5 Transformers for Renewable Energy Applications 671 15.6 Applications of Power Electronics 672 15.7 Other Technologies 674 15.8 Trends in Monitoring and Diagnostics 676 References 678 Appendix A: Sample Design 681 Appendix B: Vector Groups 701 Appendix C: Fault Calculations 705 Appendix D: Stress and Capacitance Formulae 711 Index 721

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ª º Preface to the Second Edition There have been considerable advancements in various aspects of transformer engineering since the publication of the first edition in 2004. Improvements can be clearly seen in computational capabilities and monitoring/diagnostic techniques. Such new developments and encouraging feedback received on the first edition prompted the authors to embark on the task of writing the second edition. Three new chapters have been introduced in the second edition, Electromagnetic Fields in Transformers: Theory and Computations, Transformer–System Interactions and Modeling, and Monitoring and Diagnostics. The chapter on Recent Trends in Transformer Technology has been completely revised to reflect the latest and emerging trends in the various facets of the transformer technology. Chapter 6 on short-circuit strength aspects has been updated to bring more clarity on failure mechanisms involving buckling, tilting, and spiraling phenomena. Various factors of safety are defined along with procedures for calculating them. An appendix explaining a step-by-step procedure for designing a transformer is added, which should be beneficial to engineers in the transformer industry and the student community. A few improvements have been incorporated in the other chapters as well. Understanding the basics of electromagnetic fields is an essential prerequisite for doing advanced computations. Chapter 12 explains the field theory relevant to transformer engineering in a simple manner. Concepts from vector algebra and vector calculus are first explained followed by corresponding examples which help understand the behavior and distribution of fields inside transformers. Properties of insulating and magnetic materials used in transformers are explained from a fundamental electromagnetic perspective. Finite element method (FEM) is widely used for analysis and optimization of

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transformers. While using commercial software, the knowledge of the FEM theory helps researchers and practicing engineers solve complex problems and easily interpret field solutions. The theory of FEM is explained through the solution of one-dimensional and two-dimensional problems that represent typical electrostatic and magnetostatic fields encountered in transformers. After explaining static, time-harmonic and transient formulations, advanced coupled field computations involving electromagnetic fields and external networks/other physical fields are elaborated. Brief theory/procedures for dealing with hysteresis and magnetization/magnetostrictive forces are also given at the end. The second new chapter covers relevant theory and explanations required for understanding the effects of transformer–system interactions. The chapter starts with the modeling aspects of transformers essential for steady-state analysis of power systems. The usefulness of magnitude-regulating and phase- shifting transformers is demonstrated through examples. The section on harmonics briefly covers their sources and effects, followed by modeling strategies for analyzing them. Ferroresonance phenomena can be detrimental to transformers; the system conditions causing ferroresonant conditions are enumerated. Adverse effects of arc-furnace loads and geomagnetic disturbances are explained later. Internal resonances due to system transients including very fast transient overvoltages are also described. Effects of switching operations involving vacuum circuit breakers on distribution transformers are highlighted. At the end, low-, mid-, and high-frequency models of transformers used for transient studies/investigative analysis are elaborated. A considerable amount of research and development efforts by the academic community, utility engineers, and transformer specialists have led to the availability of advanced diagnostic tools. After summarizing conventional tests on oil and windings, the chapter Monitoring and Diagnostics comprehensively covers techniques for detecting partial discharges (PD), insulation degradation, and winding displacements/deformations. Methods based on electrical, acoustic, and ultra high frequency signals are practiced for PD diagnostics. Dielectric response methods used for the condition assessment of insulation are categorized into time domain and frequency domain methods. Background theory for understanding these two types of approaches is described along with diagnostic procedures. Finally, frequency response analysis, used widely for detection of winding irregularities, is thoroughly explained. Thus, the focus of the second edition is also on diagnostic aspects and transformer–system interactions, and therefore, it is expected to help readers comprehend operational/maintenance issues and solutions in addition to the intricacies of transformer design and the applications of advanced numerical field computations. S. V. Kulkarni S. A. Khaparde (For comments and suggestions, contact: [email protected])

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Foreword to the First Edition 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 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 a variety of stresses, 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 discussed 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. Various theories have been supported in the text by reference to actual practices.

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