Preface ...................................................... xiii
1 Introduction of circuit theory-based approach and
numerical electromagnetic analysis ......................... 1
A. Ametani
1.1 Circuit theory-based approach: EMTP ........................ 1
1.1.1 Summary of the original EMTP ........................ 1
1.1.2 Nodal analysis ...................................... 2
1.1.3 Equivalent resistive circuit ........................ 4
1.1.4 Sparse matrix ....................................... 7
1.1.5 Frequency-dependent line model ...................... 8
1.1.6 Transformer ......................................... 9
1.1.7 Three-phase synchronous machine .................... 10
1.1.8 Universal machine .................................. 11
1.1.9 Switches ........................................... 13
1.1.10 Surge arrester and protective gap (archorn) ........ 16
1.1.11 Inclusion of nonlinear elements .................... 18
1.1.12 TACS ............................................... 20
1.1.13 MODELS (implemented in the ATP-EMTP) ............... 22
1.1.14 Power system elements prepared in EMTP ............. 24
1.1.15 Basic input data ................................... 24
1.2 Numerical electromagnetic analysis ........................ 36
1.2.1 Introduction ....................................... 36
1.2.2 Maxwell's equations ................................ 37
1.2.3 NEA method ......................................... 38
1.2.4 Method of Moments in the time and frequency
domains ............................................ 38
1.2.5 Finite-difference time-domain method ............... 41
1.3 Conclusions ............................................... 42
References ................................................ 42
2 EMTP-ATP .................................................. 47
M. Kizilcay and H.K. Hoidalen
2.1 Introduction .............................................. 47
2.2 Capabilities .............................................. 48
2.2.1 Overview ........................................... 48
2.2.2 Built-in electrical components ..................... 48
2.2.3 Embedded simulation modules TACS and MODELS ........ 49
2.2.4 Supporting modules ................................. 50
2.2.5 Frequency-domain analysis .......................... 52
2.2.6 Power flow option - FIX SOURCE ..................... 52
2.2.7 Typical power system studies ....................... 53
2.3 Solution methods .......................................... 53
2.3.1 Switches ........................................... 53
2.3.2 Non-linearities .................................... 58
2.3.3 Transmission lines ................................. 58
2.3.4 Electrical machines ................................ 62
2.4 Control systems ........................................... 63
2.4.1 TACS ............................................... 63
2.4.2 MODELS ............................................. 65
2.4.3 User-definable component (type 94) ................. 65
2.5 Graphical preprocessor ATPDraw ............................ 66
2.5.1 Main functionality ................................. 67
2.5.2 Input dialogues .................................... 68
2.5.3 Line and cable modelling - LCC module .............. 68
2.5.4 Transformer modelling - XFMR module ................ 70
2.5.5 Machine modelling - Windsyn module ................. 72
2.5.6 MODELS module ...................................... 73
2.6 Other post- and pre-processors ............................ 73
2.6.1 PlotXY program to view and create scientific
plots .............................................. 74
2.6.2 ATPDesigner - design and simulation of electrical
power networks ..................................... 74
2.6.3 ATP Analyzer ....................................... 77
2.7 Examples .................................................. 78
2.7.1 Lightning study - line modelling, flashover and
current variations ................................. 78
2.7.2 Neutral coil tuning - optimization ................. 82
2.7.3 Arc modelling ...................................... 84
2.7.4 Transformer inrush current calculations ............ 88
2.7.5 Power system toolbox: relaying ..................... 93
References ................................................ 99
3 Simulation of electromagnetic transients with EMTP-RV .... 103
J. Mahseredjian, Ulas Karaagac, Sébastien Dennetière
and Hani Saad
3.1 Introduction ............................................. 103
3.2 The main modules of EMTP ................................. 103
3.3 Graphical user interface ................................. 104
3.4 Formulation of EMTP network equations for steady-state
and time-domain solutions ................................ 106
3.4.1 Modified-augmented-nodal-analysis used in EMTP .... 106
3.4.2 State-space analysis .............................. 112
3.5 Control Systems .......................................... 114
3.6 Multiphase load-flow solution and initialization ......... 116
3.6.1 Load-flow constraints ............................. 118
3.6.2 Initialization of load-flow equations ............. 119
3.6.3 Initialization from a steady-state solution ....... 119
3.7 Implementation ........................................... 120
3.8 EMTP models .............................................. 120
3.9 External programming interface ........................... 121
3.10 Application examples ..................................... 122
3.10.1 Switching transient studies ....................... 122
3.10.2 IEEE-39 benchmark bus example ..................... 124
3.10.3 Wind generation ................................... 126
3.10.4 Geomagnetic disturbances .......................... 128
3.10.5 HVDC transmission ................................. 130
3.10.6 Very large-scale systems .......................... 132
3.11 Conclusions .............................................. 132
References ............................................... 132
4 PSCAD/EMTDC .............................................. 135
D. Woodford, G. Irwin and U.S. Gudmundsdottir
4.1 4 Introduction ........................................... 135
4.2 Capabilities of EMTDC .................................... 138
4.3 Interpolation between time steps ......................... 139
4.4 User-built modelling ..................................... 141
4.5 Interfacing to other programs ............................ 142
4.5.1 Interfacing to MATLAB/Simulink .................... 142
4.5.2 Interfacing with the E-TRAN translator ............ 143
4.6 Operations in PSCAD ...................................... 145
4.6.1 Basic operation in PSCAD .......................... 145
4.6.2 Hybrid simulation ................................. 146
4.6.3 Exact modelling of power system equipment ......... 148
4.6.4 Large and complex power system models ............. 148
4.7 Specialty studies with PSCAD ............................. 149
4.7.1 Global gain margin ................................ 150
4.7.2 Multiple control function optimizations ........... 150
4.7.3 Sub-synchronous resonance ......................... 150
4.7.4 Sub-synchronous control interaction ............... 151
4.7.5 Harmonic frequency scan ........................... 152
4.8 Further development of PSCAD ............................. 152
4.8.1 Parallel processing ............................... 152
4.8.2 Communications, security and management of
large system studies .............................. 153
4.9 Application of PSCAD to cable transients ................. 154
4.9.1 Simulation set-up ................................. 155
4.9.2 Parameters for cable constant calculations ........ 158
4.9.3 Cable model improvements .......................... 161
4.9.4 Summary for application of PSCAD to cable
transients ........................................ 165
4.10 Conclusions .............................................. 166
References ............................................... 166
5 XTAP ..................................................... 169
T. Noda
5.1 Overview ................................................. 169
5.2 Numerical integration by the 2S-DIRK method .............. 169
5.2.1 The 2S-DIRK integration algorithm ................. 170
5.2.2 Formulas for linear inductors and capacitors ...... 172
5.2.3 Analytical accuracy comparisons with other
integration methods ............................... 174
5.2.4 Analytical stability and stiff-decay comparisons
with other integration methods .................... 176
5.2.5 Numerical comparisons with other integration
methods ........................................... 177
5.3 Solution by a robust and efficient iterative scheme ...... 184
5.3.1 Problem description ............................... 187
5.3.2 Iterative methods ................................. 188
5.3.3 Iterative scheme used in XTAP ..................... 194
5.3.4 Numerical examples ................................ 195
5.4 Steady-state initialization method ....................... 205
5.5 Object-oriented design of the simulation code ............ 207
References ............................................... 208
6 Numerical electromagnetic analysis using the FDTD
method ................................................... 213
Y. Baba
6.1 Introduction ............................................. 213
6.2 FDTD method .............................................. 214
6.2.1 Fundamentals ...................................... 214
6.2.2 Advantages and disadvantages ...................... 217
6.3 Representations of lightning return-stroke channels
and excitations .......................................... 217
6.3.1 Lightning return-stroke channels .................. 217
6.3.2 Excitations ....................................... 220
6.4 Applications ............................................. 221
6.4.1 Lightning electromagnetic fields at close and
far distances ..................................... 221
6.4.2 Lightning surges on overhead power transmission
lines and towers .................................. 227
6.4.3 Lightning surges on overhead power distribution
lines ............................................. 233
6.4.4 Lightning electromagnetic environment in power
substation ........................................ 236
6.4.5 Lightning electromagnetic environment in
airborne vehicles ................................. 236
6.4.6 Lightning surges and electromagnetic environment
in buildings ...................................... 238
6.4.7 Surges on grounding electrodes .................... 238
6.5 Summary .................................................. 239
References ............................................... 239
7 Numerical electromagnetic analysis with the PEEC method .. 247
Peerawut Yutthagowith
7.1 Mixed potential integral equations ....................... 250
7.2 Formulation of the generalized PEEC models ............... 252
7.2.1 Derivation of the generalized PEEC method ......... 252
7.2.2 Circuit interpretation of the PEEC method ......... 257
7.2.3 Discretization of PEEC elements ................... 258
7.2.4 PEEC models for a plane half space ................ 259
7.3 Some approximate aspects of PEEC models .................. 260
7.3.1 Center-to-center retardation approximation ........ 260
7.3.2 Quasi-static PEEC models .......................... 262
7.3.3 Partial element calculation ....................... 262
7.4 Matrix formulation and solution .......................... 266
7.4.1 Frequency domain circuit equations and the
solution .......................................... 267
7.4.2 Time-domain circuit equations and the solution .... 269
7.5 Stability of PEEC models ................................. 272
7.5.1 +PEEC formulation ................................. 273
7.5.2 Parallel damping resistors ........................ 273
7.6 Electromagnetic field calculation by the PEEC model ...... 274
7.7 Application examples ..................................... 277
7.7.1 Surge characteristics of transmission towers ...... 277
7.7.2 Surge characteristics of grounding systems ........ 284
References ............................................... 286
8 Lightning surges in renewable energy system components ... 291
K. Yamamoto
8.1 Lightning surges in a wind turbine ....................... 291
8.1.1 Overvoltage caused by lightning surge
propagation on a wind turbine ..................... 291
8.1.2 Earthing characteristics of a wind turbine ........ 300
8.1.3 Example of lightning accidents and its
investigations .................................... 308
8.2 Solar power generation system ............................ 318
8.2.1 Lightning surges in a MW-class solar power
generation system ................................. 319
8.2.2 Overvoltage caused by a lightning strike to
a solar power generation system ................... 339
References ............................................... 354
9 Surges on wind power plants and collection systems ....... 359
Y. Yasuda
9.1 Introduction ............................................. 359
9.2 Winter lightning and back-flow surge ..................... 361
9.3 Earthing system of wind turbines and wind power plants ... 362
9.3.1 Earthing system of WTs ............................ 362
9.3.2 Earthing system in WPPs ........................... 363
9.4 Wind power plant models for lightning surge analysis ..... 363
9.4.1 WPP model ......................................... 363
9.4.2 Model for winter lightning ........................ 365
9.4.3 Model for surge protection device (SPD) ........... 365
9.4.4 Comparison analysis between ARENE and PSCAD/
EMTDC ............................................. 367
9.5 Mechanism of SPD's burnout incidents due to back-flow
surge .................................................... 368
9.5.1 Analysis of the surge propagations in WPP ......... 368
9.5.2 Detail analysis on surge waveforms ................ 369
9.6 Effect of overhead earthing wire to prevent back-flow
surge .................................................... 370
9.6.1 Model of a collection line in a WPP ............... 371
9.6.2 Observation of waveforms around SPDs .............. 372
9.6.3 Evaluation of the possibility of the SPD's
burning out ....................................... 373
9.6.4 Evaluation of potential rise of earthing system ... 376
9.7 Conclusions .............................................. 377
Symbols and abbreviations ................................ 377
Acknowledgments .......................................... 378
References ............................................... 378
10 Protective devices: fault locator and high-speed
switchgear ............................................... 381
T. Funabashi
10.1 Introduction ............................................. 381
10.2 Fault locator ............................................ 381
10.2.1 Fault locator algorithm ........................... 382
10.2.2 Fault locator model description using MODELS ...... 383
10.2.3 Study on influence of fault arc characteristics ... 385
10.2.4 Study on influence of errors in input devices ..... 389
10.3 High-speed switchgear .................................... 393
10.3.1 Modeling methods .................................. 395
10.3.2 Comparative study with measurement ................ 395
10.3.3 Influence of voltage sag magnitude ................ 397
10.4 Conclusions .............................................. 400
References ............................................... 400
11 Overvoltage protection and insulation coordination ....... 403
T. Ohno
11.1 Classification of overvoltages ........................... 403
11.1.1 Temporary overvoltage ............................. 404
11.1.2 Slow-front overvoltage ............................ 405
11.1.3 Fast-front overvoltage ............................ 406
11.1.4 Very-fast-front overvoltage ....................... 407
11.2 Insulation coordination study ............................ 408
11.2.1 Study flow ........................................ 408
11.2.2 Determination of the representative
overvoltages ...................................... 408
11.2.3 Steps following the determination of the
representative overvoltages ....................... 410
11.3 Selection of surge arresters ............................. 412
11.3.1 Continuous operating voltage ...................... 412
11.3.2 Rated voltage ..................................... 413
11.3.3 Nominal discharge current ......................... 413
11.3.4 Protective levels ................................. 413
11.3.5 Energy absorption capability ...................... 414
11.3.6 Rated short-circuit current ....................... 415
11.3.7 Study flow ........................................ 415
11.4 Example of the transient analysis ........................ 416
11.4.1 Model setup ....................................... 416
11.4.2 Results of the analysis ........................... 422
References ............................................... 428
12 FACTS: voltage-sourced converter ......................... 431
K. Temma
12.1 Category ................................................. 431
12.2 Control system and simulation modeling ................... 433
12.3 Application of STATCOM ................................... 434
12.3.1 Voltage fluctuation ............................... 435
12.3.2 Small-signal stability ............................ 436
12.3.3 Voltage stability ................................. 437
12.3.4 Transient stability ............................... 441
12.3.5 Overvoltage suppression ........................... 442
12.4 High-order harmonic resonance phenomena .................. 444
12.4.1 Overview of high-order harmonic resonance
phenomenon ........................................ 444
12.4.2 Principle of high-order harmonic resonance
phenomenon ........................................ 450
12.4.3 Field test ........................................ 453
12.4.4 Considerations and countermeasures ................ 455
References ............................................... 457
13 Application of SVC to cable systems ...................... 461
Y. Tamura
13.1 AC cable interconnection to an island .................... 461
13.2 Typical example of voltage variations in an island ....... 461
13.3 The required control function for the SVC ................ 463
13.4 V-I characteristics of the SVC ........................... 463
13.5 Automatic Voltage Regulator (AVR) of the SVC ............. 465
13.6 Transient analysis model ................................. 466
13.7 Control parameter settings survey ........................ 467
13.8 Comparison of the simulation results ..................... 469
13.9 The applied control parameters ........................... 472
13.10 Verification by the transient analysis .................. 473
13.11 Verification at the commissioning test .................. 475
13.12 Summary ................................................. 478
References ............................................... 479
14 Transients on grounding systems .......................... 481
S. Visacro
14.1 Introduction: power system transients and grounding ...... 481
14.2 Basic considerations on grounding systems ................ 482
14.3 The response of grounding electrodes subjected to
transients currents ...................................... 484
14.3.1 Introduction ...................................... 484
14.3.2 Behavior of grounding electrodes subjected to
harmonic currents ................................. 484
14.3.3 The frequency dependence of soil resistivity
and permittivity .................................. 488
14.3.4 Behavior of grounding electrodes subjected to
impulsive currents ................................ 492
14.3.5 The soil ionization effect ........................ 496
14.4 Numerical simulation of the transient response of
grounding electrodes ..................................... 497
14.4.1 Preliminary considerations ........................ 497
14.4.2 General results of the response of grounding
electrodes ........................................ 499
14.4.3 Grounding potential rise of electrodes subject
to lightning currents ............................. 501
14.4.4 Impulse impedance and impulse coefficient for
first and subsequent return-stroke currents ....... 502
14.5 Case example: analysis of the influence of grounding
electrodes on the lightning response of transmission
lines .................................................... 503
References ............................................... 508
Index ......................................................... 513
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