Transformer Engineering

weiqun2008

Contents
Foreword Jin Sim iii
Preface v
Acknowledgements ix
1 Transformer Fundamentals 1
1.1 Perspective 1
1.2 Applications and Types of Transformers 5
1.3 Principles and Equivalent Circuit of a Transformer 11
1.4 Representation of Transformer in 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 36
2.2 Hysteresis and Eddy Losses 42
2.3 Excitation Characteristics 44
2.4 Over-Excitation Performance 46
2.5 No-Load Loss Test 46
2.6 Impact of Manufacturing Processes on Core Performance 54
2.7 Inrush Current 56
2.8 Influence of Core Construction and Winding
Connections on No-Load Harmonic Phenomenon 67
2.9 Transformer Noise 69
References 72
xi
Copyright © 2004 by Marcel Dekker, Inc.
3 Impedance Characteristics 77
3.1 Reactance Calculation 78
3.2 Different Approaches for Reactance Calculation 85
3.3 Two-Dimensional Analytical Methods 88
3.4 Numerical Method for Reactance Calculation 90
3.5 Impedance Characteristics of Three-Winding Transformer 98
3.6 Reactance Calculation for Zigzag Transformer 103
3.7 Zero-Sequence Reactance Estimation 108
3.8 Stabilizing Tertiary Winding 121
References 123
4 Eddy Currents and Winding Stray Losses 127
4.1 Field Equations 128
4.2 Poynting Vector 133
4.3 Eddy Current and Hysteresis Losses 137
4.4 Effect of Saturation 139
4.5 Eddy Loss in a Transformer Winding 141
4.6 Circulating Current Loss in Transformer Windings 155
References 166
5 Stray Losses in Structural Components 169
5.1 Factors Influencing Stray Losses 171
5.2 Overview of Methods for Stray Loss Estimation 182
5.3 Core Edge Loss 184
5.4 Stray Loss in Frames 185
5.5 Stray Loss in Flitch Plates 187
5.6 Stray Loss in Tank 192
5.7 Stray Loss in Bushing Mounting Plates 197
5.8 Evaluation of Stray Loss Due to High Current Leads 199
5.9 Measures for Stray Loss Control 206
5.10 Methods for Experimental Verification 214
5.11 Estimation of Stray Losses in Overexcitation Condition 216
5.12 Load Loss Measurement 218
References 224
6 Short Circuit Stresses and Strength 231
6.1 Short Circuit Currents 232
6.2 Thermal Capability at Short Circuit 239
6.3 Short Circuit Forces 240
6.4 Dynamic Behavior Under Short Circuits 247
6.5 Failure Modes Due to Radial Forces 251
6.6 Failure Modes Due to Axial Forces 254
xii Contents
Copyright © 2004 by Marcel Dekker, Inc.
6.7 Effect of Pre-Stress 260
6.8 Short Circuit Test 260
6.9 Effect of Inrush Current 261
6.10 Split-Winding Transformers 262
6.11 Short Circuit Withstand 264
6.12 Calculation of Electrodynamic Force Between
Parallel Conductors 268
6.13 Design of Clamping Structures 270
References 272
7 Surge Phenomena in Transformers 277
7.1 Initial Voltage Distrubution 277
7.2 Capacitance Calculations 282
7.3 Capacitance of Windings 286
7.4 Inductance Calculation 298
7.5 Standing Waves and Traveling Waves 300
7.6 Methods for Analysis of Impulse Distribution 303
7.7 Computation of Impulse Voltage Distribution
Using State Variable Method 306
7.8 Winding Design for Reducing Internal Overvoltages 314
References 321
8 Insulation Design 327
8.1 Calculation of Stresses for Simple Configurations 328
8.2 Field Computations 333
8.3 Factors Affecting Insulation Strength 335
8.4 Test Methods and Design Insulation Level (DIL) 348
8.5 Insulation Between Two Windings 351
8.6 Internal Insulation 353
8.7 Design of End Insulation 356
8.8 High-Voltage Lead Clearances 358
8.9 Statistical Analysis for Optimization and Quality Enhancement 361
References 362
9 Cooling Systems 367
9.1 Modes of Heat Transfer 368
9.2 Cooling Arrangements 370
9.3 Dissipation of Core Heat 375
9.4 Dissipation of Winding Heat 376
9.5 Aging and Life Expectancy 380
9.6 Direct Hot Spot Measurement 384
9.7 Static Electrification Phenomenon 385
References 387
Contents xiii
Copyright © 2004 by Marcel Dekker, Inc.
10 Structural Design 389
10.1 Importance of Structural Design 389
10.2 Different Types of Loads and Tests 390
10.3 Classification of Transformer Tanks 392
10.4 Tank Design 395
10.5 Methods of Analysis 397
10.6 Overpressure Phenomenon in Transformers 401
10.7 Seismic Analysis 403
10.8 Transformer Noise: Characteristics and Reduction 404
References 409
11 Special Transformers 411
11.1 Rectifier Transformers 411
11.2 Converter Transformers for HVDC 417
11.3 Furnace Transformers 424
11.4 Phase Shifting Transformers 428
References 433
12 Recent 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 443
12.6 Monitoring and Diagnostics 445
12.7 Life Assessment and Refurbishment 449
References 449
Appendix A: Fault Calculations 453
A1 Asymmetrical Fault with No In-Feed from LV Side 454
A2 Asymmetrical Fault with In-Feed from LV Side 457
Appendix B: Stress and Capacitance Formulae 459
B1 Stress Calculations 459
B2 Capacitance Calculations 467

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