Power systems modelling and fault analysis: theory and practice

Power systems modelling and fault analysis......Page 4
Copyright page......Page 5
Contents......Page 8
List of electrical symbols......Page 18
Foreword......Page 20
Preface......Page 22
Biography......Page 25
1.2 Structure of power systems......Page 26
1.3.1 General......Page 27
1.3.3 Design, operation and protection of power systems......Page 28
1.4.2 Types of faults......Page 29
1.4.3 Causes of faults......Page 30
1.4.4 Characterisation of faults......Page 31
1.5 Terminology of short-circuit current waveform and current interruption......Page 33
1.6.2 Mechanical effects......Page 37
1.7.2 Single-phase systems......Page 40
1.7.3 Change of base quantities......Page 43
1.7.4 Three-phase systems......Page 44
1.7.5 Mutually coupled systems having different operating voltages......Page 45
1.7.6 Examples......Page 50
2.1 General......Page 53
2.2.1 Balanced three-phase voltage and current phasors......Page 54
2.2.2 Symmetrical components of unbalanced voltage or current phasors......Page 56
2.2.4 Definition of phase sequence component networks......Page 59
2.2.5 Sequence components of unbalanced three-phase impedances......Page 61
2.2.6 Sequence components of balanced three-phase impedances......Page 64
2.2.8 Examples......Page 65
2.3.2 Balanced three-phase to earth short-circuit faults......Page 68
2.3.3 Balanced three-phase clear of earth short-circuit faults......Page 70
2.3.4 Unbalanced one-phase to earth short-circuit faults......Page 72
2.3.5 Unbalanced phase-to-phase or two-phase short-circuit faults......Page 74
2.3.6 Unbalanced two-phase to earth short-circuit faults......Page 76
2.3.7 Unbalanced one-phase open-circuit faults......Page 80
2.3.8 Unbalanced two-phase open-circuit faults......Page 81
2.3.9 Example......Page 83
2.4.1 General......Page 84
2.4.2 One-phase to earth short-circuit faults......Page 85
2.4.3 Two-phase to earth short-circuit faults......Page 86
2.5.2 Simultaneous short-circuit faults at the same location......Page 88
2.5.3 Cross-country faults or simultaneous faults at different locations......Page 90
2.5.4 Simultaneous open-circuit and short-circuit faults at the same location......Page 91
2.5.5 Simultaneous faults caused by broken and fallen to earth conductors......Page 93
2.5.6 Simultaneous short-circuit and open-circuit faults on distribution transformers......Page 94
Further reading......Page 98
3.2.1 Background......Page 99
3.2.2 Overview of the calculation of overhead line parameters......Page 101
3.2.3 Untransposed single-circuit three-phase lines with and without earth wires......Page 114
3.2.4 Transposition of single-circuit three-phase lines......Page 121
3.2.5 Untransposed double-circuit lines with earth wires......Page 127
3.2.6 Transposition of double-circuit overhead lines......Page 133
3.2.7 Untransposed and transposed multiple-circuit lines......Page 148
3.2.8 Examples......Page 152
3.3.1 Background......Page 165
3.3.2 Cable sheath bonding and earthing arrangements......Page 167
3.3.3 Overview of the calculation of cable parameters......Page 170
3.3.4 Series phase and sequence impedance matrices of single-circuit cables......Page 179
3.3.5 Shunt phase and sequence susceptance matrices of single-circuit cables......Page 189
3.3.6 Three-phase double-circuit cables......Page 193
3.3.7 Examples......Page 195
3.4.1 Background......Page 198
3.4.2 Sequence π models of single-circuit overhead lines and cables......Page 200
3.4.3 Sequence π models of double-circuit overhead lines......Page 202
3.5 Sequence π models of three-circuit overhead lines......Page 205
3.6.1 Background......Page 207
3.6.2 Single-circuit overhead lines and cables......Page 208
3.6.3 Double-circuit overhead lines and cables......Page 209
3.7.1 Computer calculations of overhead line and cable parameters......Page 211
3.7.2 Measurement of overhead line parameters......Page 212
3.7.3 Measurement of cable parameters......Page 218
3.8.2 Cables......Page 222
Further reading......Page 223
4.2.1 Background......Page 225
4.2.2 Single-phase two-winding transformers......Page 227
4.2.3 Three-phase two-winding transformers......Page 238
4.2.4 Three-phase three-winding transformers......Page 249
4.2.5 Three-phase autotransformers with and without tertiary windings......Page 255
4.2.6 Three-phase earthing or zig-zag transformers......Page 267
4.2.7 Single-phase traction transformers connected to three-phase systems......Page 268
4.2.8 Variation of transformer's PPS leakage impedance with tap position......Page 270
4.2.9 Practical aspects of ZPS impedances of transformers......Page 271
4.2.10 Measurement of sequence impedances of three-phase transformers......Page 274
4.2.11 Examples......Page 279
4.3.1 Background......Page 286
4.3.2 PPS, NPS and ZPS modelling of QBs and PSs......Page 288
4.3.3 Measurement of QB and PS sequence impedances......Page 293
4.4.1 Background......Page 297
4.4.2 Modelling of series reactors......Page 298
4.4.3 Modelling of shunt reactors and capacitors......Page 300
4.4.4 Modelling of series capacitors......Page 303
4.5.1 Background......Page 308
4.5.2 PPS, NPS and ZPS modelling......Page 309
4.6.1 Background......Page 310
4.7.2 Three-phase modelling of reactors and capacitors......Page 311
4.7.3 Three-phase modelling of transformers......Page 312
4.7.4 Three-phase modelling of QBs and PSs......Page 322
4.7.5 Three-phase modelling of static load......Page 324
Further reading......Page 325
5.1 General......Page 326
5.2 Overview of synchronous machine modelling in the phase frame of reference......Page 327
5.3.1 Transformation from phase ryb to dq0 frame of reference......Page 329
5.3.2 Machine dq0 equations in per unit......Page 331
5.3.3 Machine operator reactance analysis......Page 333
5.3.4 Machine parameters: subtransient and transient reactances and time constants......Page 335
5.4.1 Synchronous machine sequence equivalent circuits......Page 339
5.4.2 Three-phase short-circuit faults......Page 340
5.4.3 Unbalanced two-phase (phase-to-phase) short-circuit faults......Page 349
5.4.4 Unbalanced single-phase to earth short-circuit faults......Page 353
5.4.5 Unbalanced two-phase to earth short-circuit faults......Page 357
5.4.6 Modelling the effect of initial machine loading......Page 362
5.4.7 Effect of AVRs on short-circuit currents......Page 364
5.4.8 Modelling of synchronous motors/compensators/condensers......Page 367
5.4.9 Examples......Page 368
5.5.1 Measurement of PPS reactances, PPS resistance and d-axis short-circuit time constants......Page 373
5.5.2 Measurement of NPS impedance......Page 377
5.5.4 Example......Page 378
5.6.1 General......Page 382
5.6.2 Overview of induction motor modelling in the phase frame of reference......Page 383
5.7.1 Transformation to dq axes......Page 387
5.7.3 Operator reactance and parameters of a single-winding rotor......Page 388
5.7.4 Operator reactance and parameters of double-cage or deep-bar rotor......Page 389
5.8.1 Three-phase short-circuit faults......Page 393
5.8.2 Unbalanced single-phase to earth short-circuit faults......Page 400
5.8.3 Modelling the effect of initial motor loading......Page 402
5.8.4 Determination of motor's electrical parameters from tests......Page 403
5.8.5 Examples......Page 408
5.9.1 Types of wind turbine generator technologies......Page 410
5.9.3 Modelling of small speed range wound rotor induction generators......Page 413
5.9.4 Modelling of doubly fed induction generators......Page 414
5.9.5 Modelling of series converter-connected generators......Page 418
Further reading......Page 421
6.1 General......Page 422
6.2.1 Simulation of short-circuit faults......Page 423
6.2.2 Simulation of open-circuit faults......Page 425
6.3.2 Passive short-circuit analysis techniques......Page 427
6.3.4 Estimation of dc short-circuit current component variation with time......Page 428
6.4 Time domain short-circuit analysis techniques in large-scale power systems......Page 429
6.5.1 Single short-circuit source connected by a radial network......Page 430
6.5.2 Parallel independent short-circuit sources connected by radial networks......Page 433
6.5.3 Multiple short-circuit sources in interconnected networks......Page 437
6.6.2 General analysis of balanced three-phase short-circuit faults......Page 442
6.6.3 General analysis of unbalanced short-circuit faults......Page 453
6.6.4 General analysis of open-circuit faults......Page 460
6.7.2 Three-phase models of synchronous and induction machines......Page 463
6.7.3 Three-phase analysis of ac current in the phase frame of reference......Page 466
6.7.4 Three-phase analysis and estimation of X/R ratio of fault current......Page 470
6.7.5 Example......Page 473
Further reading......Page 475
7.2.1 Background......Page 476
7.2.2 Analysis technique and voltage source at the short-circuit location......Page 477
7.2.3 Impedance correction factors......Page 478
7.2.4 Asynchronous motors and static converter drives......Page 481
7.2.5 Calculated short-circuit currents......Page 483
7.2.6 Example......Page 487
7.3.1 Background......Page 488
7.3.2 Representation of machines and passive load......Page 489
7.3.3 Analysis technique......Page 490
7.3.4 Calculated short-circuit currents......Page 491
7.3.5 Implementation of ER G7/4 in the UK......Page 492
7.4.2 Representation of system and equipment......Page 494
7.4.3 Analysis technique......Page 495
7.4.4 Calculated short-circuit currents......Page 496
7.5 Example calculations using IEC 60909, UK ER G7/4 and IEEE C37.010......Page 498
7.6.1 Short-circuit ratings......Page 504
7.6.2 Assessment of circuit-breakers short-circuit duties against ratings......Page 506
Further reading......Page 508
8.2.1 Theory of static network reduction......Page 510
8.2.2 Need for power system equivalents......Page 512
8.2.3 Mathematical derivation of power system equivalents......Page 514
8.3.1 Representation of power generating stations......Page 521
8.3.2 Representation of transmission, distribution and industrial networks......Page 522
8.4.1 Superposition analysis and initial ac loadflow operating conditions......Page 523
8.4.2 Effect of mutual coupling between overhead line circuits......Page 524
8.4.3 Severity of fault types and substation configuration......Page 526
8.5 Uncertainties in short-circuit current calculations: precision versus accuracy......Page 528
8.6.2 Probabilistic analysis of ac short-circuit current component......Page 532
8.6.3 Probabilistic analysis of dc short-circuit current component......Page 534
8.6.4 Example......Page 540
8.7.1 Background......Page 541
8.7.3 Theory of quantified risk assessment......Page 542
8.7.4 Methodology of quantified risk assessment......Page 543
Further reading......Page 544
9.2.1 Background......Page 545
9.2.3 Substation splitting and use of circuit-breaker autoclosing......Page 546
9.2.4 Network splitting and reduced system parallelism......Page 548
9.2.6 Increasing short-circuit fault clearance time......Page 549
9.2.9 Example......Page 550
9.3.2 Opening of unloaded delta-connected transformer tertiary windings......Page 552
9.3.4 Upgrading to higher nominal system voltage levels......Page 553
9.3.8 Examples......Page 554
9.4.2 Earthing resistor or reactor connected to transformer neutral......Page 556
9.4.3 Pyrotechnic-based fault current limiters......Page 557
9.4.4 Permanently inserted current limiting series reactor......Page 558
9.4.6 Limiters using magnetically coupled circuits......Page 559
9.4.8 Passive damped resonant limiter......Page 561
9.4.9 Solid state limiters using power electronic switches......Page 563
9.4.10 Superconducting fault current limiters......Page 564
9.4.12 Applications of fault current limiters......Page 568
9.4.13 Examples......Page 571
Further reading......Page 574
10.1 Background......Page 575
10.2.1 Step, touch, mesh and transferred potentials......Page 576
10.2.2 Electrical resistance of the human body......Page 577
10.2.3 Effects of ac current on the human body......Page 578
10.3.2 Equivalent resistance to remote earth......Page 580
10.4.2 Equivalent earthing network impedance of an infinite overhead line......Page 586
10.5 Analysis of earth fault ZPS current distribution in overhead line earth wire, towers and in earth......Page 588
10.7 Overall substation earthing system and its equivalent impedance......Page 592
10.8 Effect of system earthing methods on earth fault current magnitude......Page 593
10.9 Screening factors for overhead lines......Page 594
10.10.2 Single-phase cable with metallic sheath......Page 596
10.10.3 Three-phase cable with metallic sheaths......Page 598
10.11 Analysis of earth return currents for short-circuits in substations......Page 601
10.12 Analysis of earth return currents for short circuits on overhead line towers......Page 602
10.13 Calculation of rise of earth potential......Page 604
10.14 Examples......Page 605
10.15.1 Background......Page 609
10.15.2 Electrostatic or capacitive coupling from power lines to pipelines......Page 610
10.15.3 Electromagnetic or inductive coupling from power lines to pipelines......Page 613
10.15.5 Examples......Page 620
Further reading......Page 628
A.1 Theory and analysis of distributed multi-conductor lines and cables......Page 630
A.2.1 General......Page 633
A.2.2 Data......Page 634
C......Page 644
E......Page 645
I......Page 646
P......Page 647
S......Page 648
T......Page 649
Z......Page 650