Power System Analysis: Short-Circuit Load Flow and Harmonics

✍ Scribed by J. C. Das

• Publisher: Marcel Dekker
• Year: 2002
• Tongue: English
• Leaves: 844
• Series: Power Engineering 16
• Edition: 1
• Category: Library

✦ Synopsis

Timely reference combines theoretical and practical aspects of short-circuit currents in ac and dc systems, load flow, and harmonic analysis to provide a sound knowledge base for modern computer-based studies.

✦ Table of Contents

Power System Analysis: Short-Circuit Load Flow and Harmonics......Page 1
SERIES INTRODUCTION......Page 4
PREFACE......Page 6
CONTENTS......Page 8
CHAPTER 1: SHORT-CIRCUIT CURRENTS AND SYMMETRICAL COMPONENTS......Page 16
CONTENTS......Page 0
1.1 NATURE OF SHORT-CIRCUIT CURRENTS......Page 17
1.2 SYMMETRICAL COMPONENTS......Page 20
1.3 EIGENVALUES AND EIGENVECTORS......Page 23
1.4.1 SIMILARITY TRANSFORMATION......Page 24
1.4.2 DECOUPLING A THREE-PHASE SYMMETRICAL SYSTEM......Page 25
1.4.3 DECOUPLING A THREE-PHASE UNSYMMETRICAL SYSTEM......Page 29
1.5 CLARKE COMPONENT TRANSFORMATION......Page 30
1.6 CHARACTERISTICS OF SYMMETRICAL COMPONENTS......Page 31
1.7.1 CONSTRUCTION OF SEQUENCE NETWORKS......Page 35
1.7.2 TRANSFORMERS......Page 36
1.7.3 STATIC LOAD......Page 43
1.7.4 SYNCHRONOUS MACHINES......Page 45
1.8 COMPUTER MODELS OF SEQUENCE NETWORKS......Page 50
PROBLEMS......Page 51
BIBLIOGRAPHY......Page 53
CHAPTER 2: UNSYMMETRICAL FAULT CALCULATIONS......Page 54
2.1 LINE-TO-GROUND FAULT......Page 55
2.2 LINE-TO-LINE FAULT......Page 57
2.3 DOUBLE LINE-TO-GROUND FAULT......Page 58
2.4 THREE-PHASE FAULT......Page 60
2.5.1 TRANSFORMER CONNECTIONS......Page 61
2.5.2 PHASE SHIFTS IN WINDING CONNECTIONS......Page 62
2.5.3 PHASE SHIFT FOR NEGATIVE SEQUENCE COMPONENTS......Page 63
2.6 UNSYMMETRICAL FAULT CALCULATIONS......Page 68
2.7 SYSTEM GROUNDING AND SEQUENCE COMPONENTS......Page 76
2.8.1 TWO-CONDUCTOR OPEN FAULT......Page 79
2.8.2 ONE CONDUCTOR OPEN......Page 80
REFERENCES......Page 86
CHAPTER 3: MATRIX METHODS FOR NETWORK SOLUTIONS......Page 87
3.2 BUS ADMITTANCE MATRIX......Page 88
3.3 BUS IMPEDANCE MATRIX......Page 93
3.3.1 BUS IMPEDANCE MATRIX FROM OPEN-CIRCUIT TESTING......Page 94
3.4 LOOP ADMITTANCE AND IMPEDANCE MATRICES......Page 96
3.5 GRAPH THEORY......Page 97
3.6.1 PRIMITIVE NETWORK......Page 101
3.6.2 INCIDENCE MATRIX FROM GRAPH CONCEPTS......Page 102
3.7 ALGORITHMS FOR CONSTRUCTION OF BUS IMPEDANCE MATRIX......Page 104
3.7.1 ADDING A TREE BRANCH TO AN EXISTING NODE......Page 105
3.7.2 ADDING A LINK......Page 107
3.7.5 REMOVAL OF A COUPLED BRANCH......Page 109
3.8.3 DOUBLE LINE-TO-GROUND FAULT......Page 118
PROBLEMS......Page 128
BIBLIOGRAPHY......Page 130
CHAPTER 4: CURRENT INTERRUPTION IN AC NETWORKS......Page 131
4.1 RHEOSTATIC BREAKER......Page 132
4.2 CURRENT- ZERO BREAKER......Page 133
4.3 TRANSIENT RECOVERY VOLTAGE......Page 135
4.3.1 FIRST POLE TO CLEAR FACTOR......Page 136
4.4.1 FOUR-PARAMETER METHOD......Page 140
4.4.2 TWO-PARAMETER REPRESENTATION......Page 141
4.6 INTERRUPTION OF LOW INDUCTIVE CURRENTS......Page 142
4.7 INTERRUPTION OF CAPACITIVE CURRENTS......Page 145
4.8 PRESTRIKES IN BREAKERS......Page 148
4.9 OVERVOLTAGES ON ENERGIZING HIGH-VOLTAGE LINES......Page 149
4.9.1 OVERVOLTAGE CONTROL......Page 150
4.10 OUT-OF-PHASE CLOSING......Page 151
4.11 RESISTANCE SWITCHING......Page 152
4.12 FAILURE MODES OF CIRCUIT BREAKERS......Page 154
PROBLEMS......Page 157
BIBLIOGRAPHY......Page 159
5.1 TOTAL AND SYMMETRICAL CURRENT RATING BASIS......Page 160
5.2 ASYMMETRICAL RATINGS......Page 162
5.4 CAPABILITIES FOR GROUND FAULTS......Page 163
5.5 CLOSING–LATCHING –CARRYING INTERRUPTING CAPABILITIES......Page 164
5.7 SERVICE CAPABILITY DUTY REQUIREMENTS AND RECLOSING CAPABILITY......Page 168
5.7.1 TRANSIENT STABILITY ON FAST RECLOSING......Page 169
5.8 CAPACITANCE CURRENT SWITCHING......Page 170
5.9 LINE CLOSING SWITCHING SURGE FACTOR......Page 175
5.10 OUT-OF-PHASE SWITCHING CURRENT RATING......Page 177
5.11 TRANSIENT RECOVERY VOLTAGE......Page 178
5.12.1 MOLDED CASE CIRCUIT BREAKERS (MCCBS)......Page 183
5.12.3 LOW-VOLTAGE POWER CIRCUIT BREAKERS (LVPCBS)......Page 184
5.13.1 CURRENT-LIMITING FUSES......Page 188
5.13.3 HIGH-VOLTAGE FUSES......Page 190
PROBLEMS......Page 191
REFERENCES......Page 192
CHAPTER 6: SHORT-CIRCUIT OF SYNCHRONOUS AND INDUCTION MACHINES......Page 194
6.1.3 TRANSIENT REACTANCE......Page 195
6.1.7 ZERO SEQUENCE REACTANCE......Page 196
6.2 SATURATION OF REACTANCES......Page 197
6.4 SYNCHRONOUS MACHINE BEHAVIOR ON TERMINAL SHORTCIRCUIT......Page 198
6.4.1 EQUIVALENT CIRCUITS DURING FAULT......Page 201
6.4.2 FAULT–DECREMENT CURVE......Page 205
6.5 CIRCUIT EQUATIONS OF UNIT MACHINES......Page 209
6.6.1 REACTANCE MATRIX OF A SYNCHRONOUS MACHINE......Page 213
6.6.2 TRANSFORMATION OF REACTANCE MATRIX......Page 215
6.7 PARK’S VOLTAGE EQUATION......Page 217
6.8 CIRCUIT MODEL OF SYNCHRONOUS MACHINES......Page 218
6.9 CALCULATION PROCEDURE AND EXAMPLES......Page 219
6.9.1 MANUFACTURER’S DATA......Page 227
6.10 SHORT- CIRCUIT OF AN INDUCTION MOTOR......Page 229
PROBLEMS......Page 231
BIBLIOGRAPHY......Page 232
REFERENCES......Page 233
7.1 TYPES OF CALCULATIONS......Page 234
7.2 IMPEDANCE MULTIPLYING FACTORS......Page 235
7.2.1 LOW-VOLTAGE MOTORS......Page 236
7.4 TYPES AND SEVERITY OF SYSTEM SHORT-CIRCUITS......Page 237
7.5.3 AC AND DC DECREMENT ADJUSTMENTS......Page 238
7.5.4 FAULT FED FROM REMOTE SOURCES......Page 241
7.5.5 FAULT FED FROM LOCAL SOURCES......Page 242
7.5.6 WEIGHTED MULTIPLYING FACTORS......Page 245
7.6 NETWORK REDUCTION......Page 246
7.6.1 E/X OR E/Z CALCULATION......Page 247
7.8 HIGH RATIOS (DC TIME CONSTANT GREATER THAN 45MS)......Page 248
7.9.1 ANSI EMPIRICAL CALCULATION PROCEDURE......Page 250
7.10 EXAMPLES OF CALCULATIONS......Page 251
7.10.1 DERIVING AN EQUIVALENT IMPEDANCE......Page 271
7.11 THIRTY- CYCLE SHORT-CIRCUIT CURRENTS......Page 276
7.12 DYNAMIC SIMULATION......Page 277
PROBLEMS......Page 278
REFERENCES......Page 280
8.1.1 BREAKING CAPABILITY......Page 282
8.1.5 INITIAL SYMMETRICAL SHORT-CIRCUIT CURRENT......Page 283
8.1.8 STEADY-STATE CURRENT......Page 284
8.1.9 HIGHEST SHORT-CIRCUIT CURRENTS......Page 285
8.3 FAR-FROM-GENERATOR FAULTS......Page 286
8.3.1 NONMESHED SOURCES......Page 288
8.3.2 MESHED NETWORKS......Page 289
8.4.1 GENERATORS DIRECTLY CONNECTED TO SYSTEMS......Page 290
8.4.2 GENERATORS AND UNIT TRANSFORMERS OF POWER STATION UNITS......Page 291
8.4.4 SHORT-CIRCUIT CURRENTS FED FROM ONE GENERATOR......Page 292
8.4.6 SHORT-CIRCUIT CURRENTS IN MESHED NETWORKS......Page 295
8.5 INFLUENCE OF MOTORS......Page 296
8.5.3 STATIC CONVERTER FED DRIVES......Page 297
8.6 COMPARISON WITH ANSI CALCULATION PROCEDURES......Page 298
8.7 EXAMPLES OF CALCULATIONS AND COMPARISON WITH ANSI METHODS......Page 300
PROBLEMS......Page 315
REFERENCES......Page 316
CHAPTER 9: CALCULATIONS OF SHORT-CIRCUIT CURRENTS IN DC SYSTEMS......Page 317
9.1 DC SHORT-CIRCUIT CURRENT SOURCES......Page 318
9.2.1 IEC CALCULATION PROCEDURE......Page 319
9.3 SHORT-CIRCUIT OF A LEAD ACID BATTERY......Page 321
9.4 DC MOTOR AND GENERATORS......Page 327
9.5 SHORT-CIRCUIT CURRENT OF A RECTIFIER......Page 333
9.6.1 IEC METHOD......Page 339
9.7 TOTAL SHORT- CIRCUIT CURRENT......Page 340
9.8 DC CIRCUIT BREAKERS......Page 341
REFERENCES......Page 342
CHAPTER 10: LOAD FLOW OVER POWER TRANSMISSION LINES......Page 343
10.1 POWER IN AC CIRCUITS......Page 344
10.2 POWER FLOW IN A NODAL BRANCH......Page 346
10.2.2 VOLTAGE REGULATION......Page 348
10.3 ABCD CONSTANTS......Page 349
10.4.1 MEDIUM LONG TRANSMISSION LINES......Page 351
10.4.2 LONG TRANSMISSION LINE MODEL......Page 354
10.4.3 REFLECTION COEFICIENT......Page 356
10.4.4 LATTICE DIAGRAMS......Page 357
10.4.6 SURGE IMPEDANCE LOADING......Page 358
10.5 TUNED POWER LINE......Page 360
10.6 FERRANTI EFFECT......Page 361
10.7 SYMMETRICAL LINE AT NO LOAD......Page 362
10.8 ILLUSTRATIVE EXAMPLES......Page 364
10.9 CIRCLE DIAGRAMS......Page 367
10.10 SYSTEM VARIABLES IN LOAD FLOW......Page 371
PROBLEMS......Page 373
BIBLIOGRAPHY......Page 374
CHAPTER 11: LOAD FLOW METHODS: PART I......Page 375
11.1 MODELING A TWO-WINDING TRANSFORMER......Page 376
11.2 LOAD FLOW, BUS TYPES......Page 381
11.3.1 GAUSS ITERATIVE TECHNIQUE......Page 382
11.3.2 GAUSS–SEIDEL ITERATION......Page 385
11.3.4 GAUSS –SEIDEL Y MATRIX METHOD......Page 386
11.4.1 ILL-CONDITIONED NETWORK......Page 392
11.4.3 CONVERGENCE SPEED AND ACCELERATION FACTOR......Page 394
11.5 GAUSS–SEIDEL Z MATRIX METHOD......Page 398
11.6 CONVERSION OF Y TO Z MATRIX......Page 399
PROBLEMS......Page 403
BIBLIOGRAPHY......Page 405
12.1 FUNCTION WITH ONE VARIABLE......Page 406
12.2 SIMULTANEOUS EQUATIONS......Page 408
12.3 RECTANGULAR FORM OF NEWTON-RAPHSON METHOD OF LOAD FLOW......Page 410
12.4 POLAR FORM OF JACOBIAN MATRIX......Page 412
12.4.1 CALCULATION PROCEDURE OF NEWTON-RAPHSON METHOD......Page 413
12.5 SIMPLIFICATIONS OF NEWTON-RAPHSON METHOD......Page 420
12.7 FAST DECOUPLED LOAD FLOW......Page 423
12.8 MODEL OF A PHASE-SHIFTING TRANSFORMER......Page 426
12.9.1 PO NETWORK......Page 428
12.10 LOAD MODELS......Page 430
12.11 IMPACT LOADS AND MOTOR STARTING......Page 437
12.11.1 MOTOR STARTING VOLTAGE DIPS......Page 438
12.12 PRACTICAL LOAD FLOW STUDIES......Page 439
PROBLEMS......Page 448
REFERENCES......Page 449
CHAPTER 13: REACTIVE POWER FLOW AND CONTROL......Page 450
13.1 VOLTAGE INSTABILITY......Page 451
13.2.1 ZO COMPENSATION......Page 457
13.2.3 COMPENSATION BY SECTIONALIZATION OF LINE......Page 458
13.2.4 EFFECT ON MAXIMUM POWER TRANSFER......Page 460
13.2.5 COMPENSATION WITH LUMPED ELEMENTS......Page 461
13.3 REACTIVE POWER CONTROL DEVICES......Page 462
13.3.1 SYNCHRONOUS GENERATORS......Page 463
13.3.2 SYNCHRONOUS CONDENSERS......Page 465
13.3.3 SYNCHRONOUS MOTORS......Page 467
13.3.4 SHUNT POWER CAPACITORS......Page 468
13.3.5 STATIC VAR CONTROLLERS......Page 469
13.3.6 SERIES CAPACITORS......Page 473
13.4 SOME EXAMPLES OF REACTIVE POWER FLOW......Page 475
13.5 FACTS......Page 482
13.5.1 SYNCHRONOUS VOLTAGE SOURCE......Page 483
13.5.2 STATIC SYNCHRONOUS COMPENSATOR (STATCOM)......Page 484
13.5.3 STATIC SERIES SYNCHRONOUS COMPENSATOR......Page 486
13.5.4 UNIFIED POWER FLOW CONTROLLER......Page 488
PROBLEMS......Page 491
REFERENCES......Page 492
CHAPTER 14: THREE-PHASE AND DISTRIBUTION SYSTEM LOAD FLOW......Page 493
14.1 PHASE CO-ORDINATE METHOD......Page 494
14.2.1 CONDUCTORS......Page 496
14.2.2 GENERATORS......Page 498
14.2.3 THREE-PHASE TRANSFORMER MODELS......Page 500
14.2.4 LOAD MODELS......Page 505
14.3 DISTRIBUTION SYSTEM LOAD FLOW......Page 506
14.3.2 DISTRIBUTION SYSTEM AS A LADDER NETWORK......Page 508
14.3.3 OPTIMAL CAPACITOR LOCATION......Page 511
REFERENCES......Page 514
CHAPTER 15: OPTIMIZATION TECHNIQUES......Page 515
15.1 FUNCTIONS OF ONE VARIABLE......Page 516
15.2 CONCAVE AND CONVEX FUNCTIONS......Page 517
15.3 TAYLOR’S THEOREM......Page 518
15.4 LAGRANGIAN METHOD, CONSTRAINED OPTIMIZATION......Page 520
15.5 MULTIPLE EQUALITY CONSTRAINTS......Page 522
15.6 OPTIMAL LOAD SHARING BETWEEN GENERATORS......Page 523
15.7 INEQUALITY CONSTRAINTS......Page 525
15.8 KUHN–TUCKER THEOREM......Page 526
15.9 SEARCH METHODS......Page 527
15.9.2 POWELL’S METHOD OF CONJUGATE DIRECTIONS......Page 528
15.10.1 METHOD OF OPTIMAL GRADIENT......Page 529
15.11 LINEAR PROGRAMMING—SIMPLEX METHOD......Page 531
15.13 DYNAMIC PROGRAMMING......Page 536
15.14 INTEGER PROGRAMMING......Page 538
REFERENCES......Page 539
16.1 OPTIMAL POWER FLOW......Page 540
16.1.1 HANDLING CONSTRAINTS......Page 541
16.2 DECOUPLING REAL AND REACTIVE OPF......Page 542
16.4 GENERATION SCHEDULING CONSIDERING TRANSMISSION LOSSES......Page 543
16.4.1 GENERAL LOSS FORMULA......Page 545
16.4.2 SOLUTION OF CO-ORDINATION EQUATION......Page 547
16.5 STEEPEST GRADIENT METHOD......Page 551
16.5.1 ADDING INEQUALITY CONSTRAINTS ON CONTROL VARIABLES......Page 552
16.5.2 INEQUALITY CONSTRAINTS ON DEPENDENT VARIABLES......Page 553
16.6.1 FUNCTIONAL CONSTRAINTS......Page 554
16.6.2 LAGRANGIAN FUNCTION......Page 555
16.6.3 THE HESSIAN MATRIX......Page 556
16.6.5 PENALTY TECHNIQUES......Page 557
16.6.7 ALGORITHM FOR THE COUPLED NEWTON OPF......Page 558
16.8 SUCCESSIVE LINEAR PROGRAMMING......Page 560
16.9 INTERIOR POINT METHODS AND VARIANTS......Page 562
16.9.1 KARMARKAR INTERIOR POINT ALGORITHM......Page 563
16.9.3 PRIMAL–DUAL IP METHOD......Page 564
16.10 SECURITY AND ENVIRONMENTAL CONSTRAINED OPF......Page 566
REFERENCES......Page 567
CHAPTER 17: HARMONICS GENERATION......Page 569
17.1 HARMONICS AND SEQUENCE COMPONENTS......Page 571
17.4 THREE-PHASE WINDINGS IN ELECTRICAL MACHINES......Page 572
17.5 TOOTH RIPPLES IN ELECTRICAL MACHINES......Page 574
17.7 TRANSFORMERS......Page 575
17.8 SATURATION OF CURRENT TRANSFORMERS......Page 579
17.10 SUBHARMONIC FREQUENCIES......Page 580
17.11.1 SINGLE-PHASE BRIDGE CIRCUIT......Page 581
17.11.2 THREE-PHASE BRIDGE CIRCUIT......Page 587
7.11.3 DIODE BRIDGE CONVERTER......Page 595
17.12 SWITCH-MODE POWER (SMP) SUPPLIES......Page 596
17.13 ARC FURNACES......Page 597
17.14 CYCLOCONVERTERS......Page 599
17.15 THYRISTOR-CONTROLLED REACTOR......Page 601
17.17 PULSE WIDTH MODULATION......Page 603
17.19 PULSE BURST MODULATION......Page 606
17.20 CHOPPER CIRCUITS AND ELECTRIC TRACTION......Page 607
17.22 LIGHTING BALLASTS......Page 609
PROBLEMS......Page 610
REFERENCES......Page 611
CHAPTER 18: EFFECTS OF HARMONICS......Page 612
18.1.1 PULSATING FIELDS AND TORSIONAL VIBRATIONS......Page 613
18.1.3 INCREASE OF LOSSES......Page 614
18.1.4 EFFECT OF NEGATIVE SEQUENCE CURRENTS......Page 615
18.1.5 INSULATION STRESSES......Page 616
18.1.7 EFFECT OF CABLE TYPE AND LENGTH......Page 617
18.2 TRANSFORMERS......Page 618
18.2.1 UL K FACTOR OF TRANSFORMERS......Page 621
18.3 CABLES......Page 622
18.4 CAPACITORS......Page 623
18.5.1 PARALLEL RESONANCE......Page 624
18.5.2 SERIES RESONANCE......Page 626
18.7 EMI (ELECTROMAGNETIC INTERFERENCE)......Page 628
18.8 OVERLOADING OF NEUTRAL......Page 629
18.10 CIRCUIT BREAKERS AND FUSES......Page 630
18.11 TELEPHONE INFLUENCE FACTOR......Page 631
PROBLEMS......Page 632
REFERENCES......Page 633
CHAPTER 19: HARMONIC ANALYSIS......Page 634
19.1.1 FREQUENCY DOMAIN ANALYSIS......Page 635
19.1.2 FREQUENCY SCAN......Page 636
19.1.4 PHASE ANGLE OF HARMONICS......Page 637
19.1.5 NEWTON–RAPHSON METHOD......Page 638
19.1.6 TIME DOMAIN ANALYSIS......Page 639
19.1.7 SWITCHING FUNCTION......Page 640
19.2.3 FILTER REACTORS......Page 641
19.2.4 TRANSFORMERS......Page 642
19.2.5 INDUCTION MOTORS......Page 643
19.2.6 GENERATORS......Page 644
19.4 SYSTEM IMPEDANCE......Page 645
19.5 THREE-PHASE MODELS......Page 646
19.5.1 UNCHARACTERISTIC HARMONICS......Page 647
19.6 MODELING OF NETWORKS......Page 648
19.6.2 DISTRIBUTION SYSTEMS......Page 649
19.6.4 SENSITIVITY METHODS......Page 650
19.7 POWER FACTOR AND REACTIVE POWER......Page 652
19.8 SHUNT CAPACITOR BANK ARRANGEMENTS......Page 655
19.9 STUDY CASES......Page 659
PROBLEMS......Page 677
REFERENCES......Page 678
20.1 MITIGATION OF HARMONICS......Page 679
20.2 BAND PASS FILTERS......Page 680
20.3 PRACTICAL FILTER DESIGN......Page 683
20.4 RELATIONS IN A ST FILTER......Page 693
20.5 FILTERS FOR A FURNACE INSTALLATION......Page 696
20.6 FILTERS FOR AN INDUSTRIAL DISTRIBUTION SYSTEM......Page 698
20.7 SECONDARY RESONANCE......Page 699
20.8.1 Q FACTOR......Page 701
20.9 DOUBLE-TUNED FILTER......Page 702
20.10 DAMPED FILTERS......Page 704
20.10.1 SECOND-ORDER HIGH-PASS FILTER......Page 706
20.11 DESIGN OF A SECOND-ORDER HIGH-PASS FILTER......Page 708
20.12 ZERO SEQUENCE TRAPS......Page 709
20.13 LIMITATIONS OF PASSIVE FILTERS......Page 711
20.14.1 SHUNT CONNECTION......Page 713
20.14.2 SERIES CONNECTION......Page 714
20.14.4 COMBINATION OF ACTIVE FILTERS......Page 715
20.15 CORRECTIONS IN TIME DOMAIN......Page 716
20.16 CORRECTIONS IN THE FREQUENCY DOMAIN......Page 717
20.17 INSTANTANEOUS REACTIVE POWER......Page 719
20.18.1 PHASE MULTIPLICATION......Page 721
20.18.4 ACTIVE CURRENT SHAPING......Page 723
REFERENCES......Page 725
A.1.1 SETS......Page 727
A.1.2 VECTORS......Page 728
A.1.3 MATRICES......Page 729
A.2 CHARACTERISTICS ROOTS, EIGENVALUES, AND EIGENVECTORS......Page 731
A.2.2 CHARACTERISTIC VECTORS......Page 732
A.3.1 SIMILARITY TRANSFORMATION......Page 733
A.5 QUADRATIC FORM EXPRESSED AS A PRODUCT OF MATRICES......Page 734
A.6 DERIVATIVES OF SCALAR AND VECTOR FUNCTIONS......Page 735
A.7.1 BY CALCULATING THE ADJOINT AND DETERMINANT OF THE MATRIX......Page 736
A.8.3 TEST FOR CONSISTENCY AND INCONSISTENCY OF EQUATIONS......Page 740
A.9 CROUT’S TRANSFORMATION......Page 742
A.10 GAUSSIAN ELIMINATION......Page 744
A.11 FORWARD–BACKWARD SUBSTITUTION METHOD......Page 745
A.11.1 BIFACTORIZATION......Page 746
A.12 LDU (PRODUCT FORM, CASCADE, OR CHOLESKI FORM)......Page 748
BIBLIOGRAPHY......Page 750
B.2 INDUCTANCE......Page 751
B.2.2 TRANSPOSED LINE......Page 752
B.2.3 COMPOSITE CONDUCTORS......Page 753
B.4 THREE-PHASE LINE WITH GROUND CONDUCTORS......Page 754
B.5 BUNDLE CONDUCTORS......Page 756
B.6 CARSON’S FORMULA......Page 757
B.6.1 APPROXIMATIONS TO CARSON’S EQUATIONS......Page 759
B.7.1 CAPACITANCE MATRIX......Page 763
B.8 CABLE CONSTANTS......Page 766
B.8.1 CONCENTRIC NEUTRAL UNDERGROUND CABLE......Page 767
B.8.2 CAPACITANCE OF CABLES......Page 769
REFERENCES......Page 770
C.1 MODEL OF A TWO-WINDING TRANSFORMER......Page 771
C.1.2 SHORT-CIRCUIT TEST......Page 775
C.2.1 ADDITIVE AND SUBTRACTIVE POLARITY......Page 776
C.3 PARALLEL OPERATION OF TRANSFORMERS......Page 778
C.4 AUTOTRANSFORMERS......Page 780
C.4.1 SCOTT CONNECTION......Page 784
C.6 EXTENDED MODELS OF TRANSFORMERS......Page 785
C.6.1 MODELING THE HYSTERESIS LOOP......Page 787
C.6.2 EMTP MODELS......Page 788
C.8 DUALITY MODELS......Page 791
C.9 GIC MODELS......Page 794
C.10 REACTORS......Page 795
REFERENCES......Page 798
D.1 OPTIMAL ORDERING......Page 799
D.2 FLOW GRAPHS......Page 800
D.3 OPTIMAL ORDERING SCHEMES......Page 803
BIBLIOGRAPHY......Page 806
E.3 FOURIER SERIES AND COEFFICIENTS......Page 807
E.5 EVEN SYMMETRY......Page 810
E.6 HALF-WAVE SYMMETRY......Page 811
E.7.1 CONSTRUCTING FOURIER SERIES FROM GRAPHS AND TABLES......Page 812
E.8 COMPLEX FORM OF FOURIER SERIES......Page 814
E.9 FOURIER TRANSFORM......Page 815
E.10 SAMPLED WAVEFORM: DISCRETE FOURIER TRANSFORM......Page 818
E.10.1 LEAKAGE......Page 821
E.11 FAST FOURIER TRANSFORM......Page 822
REFERENCE......Page 823
F.1 HARMONIC CURRENT LIMITS......Page 824
F.2 VOLTAGE QUALITY......Page 826
F.3 COMMUTATION NOTCHES......Page 828
F.4 INTERHARMONICS......Page 831
F.5 FLICKER......Page 832
REFERENCES......Page 833
G.1 WAVEFORM WITHOUT RIPPLE CONTENT......Page 834
G.2 WAVEFORM WITH RIPPLE CONTENT......Page 836
G.3 PHASE ANGLE OF HARMONICS......Page 842
REFERENCES......Page 844