Power Systems Electromagnetic Transients Simulation

Contents......Page 6
List of figures......Page 14
List of tables......Page 22
Preface......Page 24
Acronyms and constants......Page 26
1.1 Introduction......Page 28
1.2 Classification of electromagnetic transients......Page 30
1.3 Transient simulators......Page 31
1.4.2 Method of difference equations......Page 32
1.5 Historical perspective......Page 33
1.7 References......Page 36
2.2 Continuous systems......Page 38
2.2.1.1 Successive differentiation......Page 40
2.2.1.2 Controller canonical form......Page 41
2.2.1.3 Observer canonical form......Page 43
2.2.1.4 Diagonal canonical form......Page 45
2.2.1.5 Uniqueness of formulation......Page 46
2.2.2 Time domain solution of state equations......Page 47
2.2.3 Digital simulation of continuous systems......Page 49
2.2.3.1 Example......Page 54
2.3 Discrete systems......Page 57
2.4 Relationship of continuous and discrete domains......Page 59
2.6 References......Page 61
3.2 Choice of state variables......Page 62
3.3.1 The transform method......Page 64
3.3.2 The graph method......Page 67
3.4 Solution procedure......Page 70
3.5 Transient converter simulation (TCS)......Page 71
3.5.1 Per unit system 45......Page 72
3.5.2 Network equations......Page 73
3.5.3 Structure of TCS......Page 76
3.5.4 Valve switchings......Page 78
3.5.5 Effect of automatic time step adjustments......Page 80
3.5.6 TCS converter control......Page 82
3.6 Example......Page 86
3.7 Summary......Page 91
3.8 References......Page 92
4.1 Introduction......Page 94
4.2.2 Inductance......Page 95
4.2.3 Capacitance......Page 97
4.2.4 Components reduction......Page 98
4.3 Dual Norton model of the transmission line......Page 100
4.4 Network solution......Page 103
4.4.1 Network solution with switches......Page 106
4.4.2 Example: voltage step applied to RL load......Page 107
4.5 Non-linear or time varying parameters......Page 115
4.5.2 Compensation method......Page 116
4.5.3 Piecewise linear method......Page 118
4.6 Subsystems......Page 119
4.7 Sparsity and optimal ordering......Page 122
4.9 Summary......Page 124
4.10 References......Page 125
5.2 Exponential form of the difference equation......Page 126
5.3 z-domain representation of difference equations......Page 129
5.4 Implementation in EMTP algorithm......Page 132
5.5 Family of exponential forms of the difference equation......Page 139
5.5.1 Step response......Page 141
5.5.2 Steady-state response......Page 143
5.5.3 Frequency response......Page 144
5.6 Example......Page 145
5.7 Summary......Page 147
5.8 References......Page 148
6.1 Introduction......Page 150
6.2 Bergeron’s model......Page 151
6.2.1 Multiconductor transmission lines......Page 153
6.3 Frequency-dependent transmission lines......Page 157
6.3.1 Frequency to time domain transformation......Page 159
6.3.2 Phase domain model......Page 163
6.4 Overhead transmission line parameters......Page 164
6.4.1 Bundled subconductors......Page 167
6.5 Underground cable parameters......Page 169
6.6 Example......Page 173
6.8 References......Page 183
7.1 Introduction......Page 186
7.2 Basic transformer model......Page 187
7.2.1 Numerical implementation......Page 188
7.2.2 Parameters derivation......Page 189
7.2.3 Modelling of non-linearities......Page 191
7.3 Advanced transformer models......Page 192
7.3.1 Single-phase UMEC model......Page 193
7.3.1.1 UMEC Norton equivalent......Page 196
7.3.2 UMEC implementation in PSCAD/EMTDC......Page 198
7.3.3 Three-limb three-phase UMEC......Page 199
7.4 The synchronous machine......Page 203
7.4.1 Electromagnetic model......Page 204
7.4.2 Electromechanical model......Page 210
7.4.2.2 Multimass representation......Page 211
7.4.3 Interfacing machine to network......Page 212
7.4.4 Types of rotating machine available......Page 216
7.5 Summary......Page 217
7.6 References......Page 218
8.1 Introduction......Page 220
8.2 Transient analysis of control systems (TACS)......Page 221
8.3 Control modelling in PSCAD/EMTDC......Page 222
8.3.1 Example......Page 225
8.4.1 Transducers......Page 232
8.4.2 Electromechanical relays......Page 235
8.4.4 Microprocessor-based relays......Page 236
8.4.5 Circuit breakers......Page 237
8.4.6 Surge arresters......Page 238
8.5 Summary......Page 240
8.6 References......Page 241
9.2 Valve representation in EMTDC......Page 244
9.3 Placement and location of switching instants......Page 246
9.4 Spikes and numerical oscillations (chatter)......Page 247
9.4.1 Interpolation and chatter removal......Page 249
9.5 HVDC converters......Page 257
9.7.1 The static VAr compensator......Page 260
9.7.2 The static compensator (STATCOM)......Page 268
9.8 State variable models......Page 270
9.8.1 EMTDC/TCS interface implementation......Page 271
9.9 Summary......Page 275
9.10 References......Page 276
10.1 Introduction......Page 278
10.3 Extent of system to be reduced......Page 279
10.5.1 Frequency domain identification......Page 280
10.5.1.1 Time domain analysis......Page 282
10.5.1.2 Frequency domain analysis......Page 284
10.6.1 RLC networks......Page 289
10.6.2 Rational function......Page 290
10.6.2.1 Error and figure of merit......Page 292
10.7 Model implementation......Page 293
10.8 Examples......Page 294
10.10 References......Page 302
11.1 Introduction......Page 304
11.3 Harmonic assessment......Page 305
11.4 Phase-dependent impedance of non-linear device......Page 306
11.5 The time domain in an ancillary capacity......Page 308
11.5.1 Iterative solution for time invariant non-linearcomponents......Page 309
11.5.2 Iterative solution for general non-linear components......Page 311
11.5.3 Acceleration techniques......Page 312
11.6.2 Time step......Page 313
11.6.4 AC system representation......Page 314
11.7 Voltage sags......Page 315
11.7.1 Examples......Page 317
11.8 Voltage fluctuations......Page 319
11.8.1 Modelling of flicker penetration......Page 321
11.9 Voltage notching......Page 323
11.10 Discussion......Page 324
11.11 References......Page 327
12.1 Introduction......Page 330
12.2 Description of the hybrid algorithm......Page 331
12.3 TS/EMTDC interface......Page 334
12.3.1 Equivalent impedances......Page 335
12.3.3 Phase and sequence data conversions......Page 337
12.3.4 Interface variables derivation......Page 338
12.5 Interaction protocol......Page 340
12.6 Interface location......Page 343
12.7 Test system and results......Page 344
12.9 References......Page 346
13.1 Introduction......Page 348
13.2 Simulation with dedicated architectures......Page 349
13.2.1 Hardware......Page 350
13.2.2 RTDS applications......Page 352
13.3 Real-time implementation on standard computers......Page 354
13.3.1 Example of real-time test......Page 356
13.4 Summary......Page 357
13.5 References......Page 358
A Structure of the PSCAD/EMTDC program......Page 360
A.1 References......Page 367
B.1 s-domain identification (frequency domain)......Page 368
B.2 z-domain identification (frequency domain)......Page 370
B.3 z-domain identification (time domain)......Page 372
B.4 Prony analysis......Page 373
B.5 Recursive least-squares curve-fitting algorithm......Page 375
B.6 References......Page 377
C.1 Review of classical methods......Page 378
C.2 Truncation error of integration formulae......Page 381
C.3 Stability of integration methods......Page 383
C.4 References......Page 384
D.2 Lower South Island (New Zealand) system......Page 386
D.3 Reference......Page 392
E.1 Root-matching technique applied to a first order lag function......Page 394
E.2 Root-matching technique applied to a first orderdifferential pole function......Page 395
E.4 Difference equation by numerical integrator substitutionfor RL series branch......Page 396
F.1 Voltage step on RL branch......Page 400
F.2 Diode fed RL branch......Page 401
F.3 General version of example F.2......Page 403
F.4 Frequency response of difference equations......Page 414
G.1 State variable analysis program......Page 416
H.1 DC source, switch and RL load......Page 422
H.2 General EMT program for d.c. source, switch and RL load......Page 424
H.3 AC source diode and RL load......Page 427
H.4 Simple lossless transmission line......Page 429
H.5 Bergeron transmission line......Page 431
H.6 Frequency-dependent transmission line......Page 434
H.7 Utility subroutines for transmission line programs......Page 440
Index......Page 444