Transformer Design Prins - W. Appln to Core-Form Pwr Transformers

TABLE OF CONTENTS......Page 0
TRANSFORMER DESIGN PRINCIPLES: With Applications to Core-Form Power Transformers......Page 1
CONTENTS......Page 3
PREFACE......Page 9
1.1 HISTORICAL BACKGROUND......Page 10
1.2 USES IN POWER SYSTEMS......Page 12
1.3 CORE-FORM AND SHELL-FORM TRANSFORMERS......Page 18
1.4 STACKED AND WOUND CORE CONSTRUCTION......Page 19
1.5 TRANSFORMER COOLING......Page 24
1.6 WINDING TYPES......Page 26
1.7 INSULATION STRUCTURES......Page 29
1.8 STRUCTURAL ELEMENTS......Page 33
1.9 THREE PHASE CONNECTIONS......Page 38
1.10 MODERN TRENDS......Page 45
2.1 INTRODUCTION......Page 48
2.2 BASIC MAGNETISM......Page 51
2.3 HYSTERESIS......Page 55
2.4 MAGNETIC CIRCUITS......Page 58
2.5 INRUSH CURRENT......Page 63
2.6 TRANSFORMER CIRCUIT MODEL WITH CORE......Page 75
2.7 PER UNIT SYSTEM......Page 89
2.8 VOLTAGE REGULATION......Page 91
3.1 INTRODUCTION......Page 95
3.2 IDEAL TRANSFORMERS......Page 96
3.2.1 Ideal Autotransformer......Page 100
3.3 LEAKAGE IMPEDANCE FOR 2-WINDING TRANSFORMERS......Page 102
3.3.1 Leakage Impedance for a 2-Winding utotransformer......Page 106
3.4 LEAKAGE IMPEDANCES FOR 3-WINDING TRANSFORMERS......Page 107
3.4.1 Leakage Impedances for an Autotransfonner with Tertiary......Page 112
3.4.2 Leakage Impedance between 2 Windings Connected in Series and a Third Winding......Page 117
3.4.3 Leakage Impedance of a 2-Winding Autotransformer with XLine Taps......Page 118
3.4.4 More General Leakage Impedance Calculations......Page 121
3.5 TWO WINDING LEAKAGE REACTANCE FORMULA......Page 122
4.1 INTRODUCTION......Page 126
4.2 SYMMETRICAL COMPONENTS......Page 128
4.3 FAULT ANALYSIS ON 3-PHASE SYSTEMS......Page 134
4.3.1 3-Phase Line to Ground fault......Page 136
4.3.2 Single Phase Line to Ground Fault......Page 137
4.3.3 Line to Line Fault......Page 138
4.3.4 Double Line to Ground Fault......Page 139
4.4 FAULT CURRENTS FOR TRANSFORMERS WITH 2 TERMINALS PER PHASE......Page 140
4.4.1 3-Phase Line to Ground Fault......Page 142
4.4.2 Single Phase Line to Ground Fault......Page 143
4.4.4 Double Line to Ground Fault......Page 144
4.4.5 Zero Sequence Impedances......Page 145
4.5 FAULT CURRENTS FOR TRANSFORMERS WITH 3 TERMINALS PER PHASE......Page 147
4.5.2 Single Phase Line to Ground Fault......Page 150
4.5.3 Line to Line Fault......Page 151
4.5.4 Double Line to Ground Fault......Page 152
4.5.5 Zero Sequence Impedances......Page 153
4.6 ASYMMETRY FACTOR......Page 154
5.1 INTRODUCTION......Page 156
5.2 THEORY......Page 157
5.3 DETERMINING THE B-FIELD......Page 173
5.4 DETERMINING THE WINDING FORCES......Page 174
5.5 GENERAL METHOD FOR DETERMINING INDUCTANCES AND MUTUAL INDUCTANCES......Page 176
5.6 RABINS’ FORMULA FOR LEAKAGE REACTANCE......Page 182
5.7 RABINS’ METHOD APPLIED TO CALCULATE SELF AND MUTUAL INDUCTANCES OF COIL SECTIONS......Page 189
6.1 INTRODUCTION......Page 192
6.2 FORCE CALCULATIONS......Page 195
6.3 STRESS ANALYSIS......Page 197
6.3.2 Axial Bending Stress per Strand......Page 200
6.3.3 Tilting Strength......Page 204
6.3.4 Stress in Tie Bars......Page 208
6.3.5 Stress in the Pressure Rings......Page 215
6.3.6 Hoop Stress......Page 216
6.3.7 Radial Bending Stress......Page 218
6.4 RADIAL BUCKLING STRENGTH......Page 226
6.5 STRESS DISTRIBUTION IN A COMPOSITE WIRE-PAPER WINDING SECTION......Page 236
6.6 ADDITIONAL MECHANICAL CONSIDERATIONS......Page 242
7.1 INTRODUCTION......Page 244
7.2 THEORY......Page 245
7.3 STEIN’S CAPACITANCE FORMULA......Page 252
7.4 GENERAL DISK CAPACITANCE FORMULA......Page 259
7.5 COIL GROUNDED AT ONE END WITH GROUNDED CYLINDERS ON EITHER SIDE......Page 260
7.6 STATIC RING ON ONE SIDE OF DISK......Page 263
7.7 TERMINAL DISK WITHOUT A STATIC RING......Page 264
7.8 CAPACITANCE MATRIX......Page 265
7.9 TWO END STATIC RINGS......Page 268
7.10 STATIC RING BETWEEN THE FIRST TWO DISKS......Page 272
7.11.1 Analytic Formula......Page 273
7.11.2 Circuit Model......Page 277
7.11.3 Experimental Methods......Page 283
7.11.4 Results......Page 284
7.12 MULTI-START WINDING CAPACITANCE......Page 288
8.1 INTRODUCTION......Page 292
8.2 PRINCIPLES OF VOLTAGE BREAKDOWN......Page 293
8.3 INSULATION COORDINATION......Page 305
8.4 CONTINUUM MODEL OF WINDING USED TO OBTAIN THE IMPULSE VOLTAGE DISTRIBUTION......Page 310
8.5.1 Circuit Description......Page 320
8.5.2 Mutual and Self Inductance Calculations......Page 324
8.5.3 Capacitance Calculations......Page 326
8.5.4 Impulse Voltage Calculations and Experimental Comparisons......Page 327
8.5.5 Sensitivity Studies......Page 333
9.1 SIMPLE GEOMETRIES......Page 336
9.2.1 Physical Basis......Page 344
9.2.2 Conformal Mapping......Page 345
9.2.3 Schwarz-Christoffel Transformation......Page 349
9.2.4 Conformal Map for the Electrostatic Field Problem......Page 351
9.2.4.1 Electric Potential and Field Values......Page 356
9.2.4.2 Calculations and Comparison with a Finite Element Solution......Page 363
9.2.4.3 Estimating Enhancement Factors......Page 367
9.3 FINITE ELEMENT ELECTRIC FIELD CALCULATIONS......Page 370
10.1 INTRODUCTION......Page 376
10.2 NO-LOAD OR CORE LOSSES......Page 377
10.2.2 Interlaminar Losses......Page 382
10.3.1 I2R Losses......Page 386
10.3.2 Stray Losses......Page 387
10.3.2.1 Eddy Current Losses in the Coils......Page 390
10.3.2.2 Tieplate Losses......Page 394
10.3.2.3 Tieplate and Core Losses Due to Unbalanced Currents......Page 404
10.3.2.4 Tank and Clamp Losses......Page 411
10.3.2.5 Tank Losses Due to Nearby Busbars......Page 414
10.3.2.6 Tank Losses Associated with the Bushings......Page 419
10.3.3 Winding Losses Due to Missing or Unbalanced Cross-Overs......Page 425
11.1 INTRODUCTION......Page 436
11.2 THERMAL MODEL OF A DISK COIL WITH DIRECTED OIL FLOW......Page 438
11.2.1 Oil Pressures and Velocities......Page 440
11.2.2 Oil Nodal Temperatures and Path Temperature Rises......Page 445
11.2.3 Disk Temperatures......Page 447
11.3 THERMAL MODEL FOR COILS WITHOUT DIRECTED OIL FLOW......Page 448
11.4 RADIATOR THERMAL MODEL......Page 451
11.5 TANK COOLING......Page 455
11.6 OIL MIXING IN THE TANK......Page 457
11.7 TIME DEPENDENCE......Page 460
11.8 PUMPED FLOW......Page 461
11.9 COMPARISON WITH TEST RESULTS......Page 462
11.10 DETERMINING M AND N EXPONENTS......Page 467
11.11 LOSS OF LIFE CALCULATION......Page 469
11.12 CABLE AND LEAD TEMPERATURE CALCULATION......Page 473
11.13 TANK WALL TEMPERATURE CALCULATION......Page 480
11.14 TIEPLATE TEMPERATURE CALCULATION......Page 482
11.15 CORE STEEL TEMPERATURE CALCULATION......Page 485
12.1 INTRODUCTION......Page 488
Separate compartment......Page 489
Plus—Minus (Reversing)......Page 490
12.4.1 Resistive Switching......Page 491
12.4.2 Reactive Switching with Preventative Autotransformer......Page 493
Fixed volts/turn......Page 495
Variable volts/turn......Page 496
12.5.2 Autotransformers......Page 497
The Series Voltage Regulator......Page 500
The Series (booster) Transformer......Page 501
12.6 GENERAL MAINTENANCE......Page 502
13.1 INTRODUCTION......Page 505
13.2 BASIC PRINCIPLES......Page 509
13.3 SQUASHED DELTA PHASE SHIFTING TRANSFORMER......Page 513
13.4 STANDARD DELTA PHASE SHIFTING TRANSFORMER......Page 520
13.5 TWO CORE PHASE SHIFTING TRANSFORMER......Page 525
13.6 REGULATION EFFECTS......Page 532
13.7 FAULT CURRENT ANALYSIS......Page 534
13.7.1 Squashed Delta Fault Currents......Page 538
13.7.2 Standard Delta Fault Currents......Page 541
14.1 INTRODUCTION......Page 549
14.2 GEOMETRIC PROGRAMMING......Page 551
14.3.1 Characterization of the Minimum......Page 558
14.3.2 Solution Search Strategy......Page 567
14.3.3 Practical Considerations......Page 573
14.4 APPLICATION TO TRANSFORMER DESIGN......Page 574
14.4.1 Design Variables......Page 575
14.4.2 Cost Function......Page 576
14.4.3 Equality Constraints......Page 579
14.4.4 Inequality Constraints......Page 583
14.4.5 Optimization Strategy......Page 584
REFERENCES......Page 588