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Index
AC exciter, 365, 369, 371–374, 379–380
Alternate solution method, 425–427
Ancillary services, 193, 195, 221, 224
Artificial intelligence methods, 201, 202
ASVG, 308–312
Asymptotically stable, 490, 492, 509
ATC1, 248–250, 252–253
ATC2, 248–250
Augmented matrix, 23–26, 67, 93, 98
Automatic generation control (AGC), 76,
250, 251, 406, 534
Automatic voltage regulator (AVR), 333,
352, 357, 363, 375, 377, 378, 534–536
Available transfer capabilities (ATC), 196,
222–224, 241–249, 253
Axiomatic definitions of probability, 131
Bayes’ formula, 132
Binomial distribution, 136, 244, 245
Bipolar system, 258
Blackout, 114, 129, 152, 178, 179, 191
Branch addition method, 56, 57, 64, 65
BX algorithm, 106
Cascading outages, 179–180
CBM, 242
Characteristic equation, 520
Characteristic polynomial, 520
Classical model, 351, 352, 384, 399, 425,
434, 454, 457, 459, 463, 511
Common mode failures, 114
Compensation method, 38, 113–119, 460
Conditional probability, 131, 139, 158
Congestion management, 196, 218, 222–223
Constant e0q model, 351, 352
Contingency ranking, 123–124, 127
Continuation power flow (CPF), 243
Continuous random variable, 132–137, 162,
173, 244
Convergence characteristic, 73, 89, 106,
112, 216
Convergence condition, 89, 104, 109, 112
Convergence of the Monte Carlo simulation,
146
Convergence property, 100, 112, 113
Converter, 258–262, 264–270, 272, 273,
276–286, 289, 294–301, 326, 329, 331,
392, 479, 480, 505, 507
Converter basic equations, 261, 267, 278,
282, 283, 285, 289
Converter bridge, 259, 260, 280
Converter control, 260, 279, 285, 289, 297
Converter equivalent circuits, 273–276
Converter transformer, 259, 261, 267,
276–286, 294, 296–298
Convolution of random variable, 135
Coordinate transformation, 338, 432, 448,
494, 496, 499
Correction equations, 81, 83, 87, 89, 94,
103–106, 109
Correction equations of fast decoupled
method, 104–107
Critically stable, 490, 492
Cumulant method, 162
Cumulative probability, 141–144, 154, 188
Current decomposition, 229, 230, 234
Damping ratio, 523, 536, 537, 540
Damping winding, 335–336, 351, 352, 354,
356, 370, 536
555
d axis open-circuit sub-transient time
constant, 346, 347, 349, 350, 359,
465–467, 494
d axis open-circuit transient time
constant, 346
d axis subtransient reactance, 344–351,
356, 359, 360, 363, 432, 465–467, 475,
485, 494
d axis synchronous reactance, 344–351,
356, 358, 359, 401, 431, 432, 453, 465
d axis transient reactance, 344, 345,
347–352, 356, 359, 370, 374, 401,
432–434, 448, 453, 454, 465–467,
475, 494
DC exciter, 365–367, 369, 370, 378,
379, 494
DC load flow, 114, 119–127, 150, 154
DC network equations, 285, 286, 297
Decaying mode, 523
Decremental bidding prices, 224
Difference equations, 419–423, 464, 466,
470, 472, 474, 475, 483, 484, 487
Differential-algebraic equations, 407, 425,
427–429, 454, 472, 492, 530
Discrete random variable, 132–135,
163, 173
Distribution factor, 229, 230, 235–238, 240,
241, 243
Distribution function, 132–135, 137, 138,
141, 149, 166, 172, 173, 178, 245
Dominant eigenvalue, 527–529
dq0 coordinate system, 335
dq0 transformation, 338
Dynamic load model, 397–403
Dynamic ordering scheme, 46–48
Edgeworth series, 162, 166, 167
Effect of saturation, 357
Eigensolution, 489, 492, 493, 510, 519, 521,
526, 527, 530, 531
Eigensolution analysis, 489, 492, 519
Eigenvalue sensitivity, 524–525,
531–534, 541
Eigenvalue sensitivity analysis,
533–534
Electromagnetic torque, 361–363
Electromechanical oscillations, 492, 493,
536, 540
Energy management system (EMS), 243,
457
Enumeration method, 159, 183, 244
Equilibrium point, 490–492, 509
Equivalent circuits of transformer, 9–11
ETC, 242
Euler method, 409, 412–417, 419, 421, 422,
424, 425, 447, 450, 452
Excitation system, 334, 363–365, 375–381,
407, 430, 446, 463, 464, 469, 472, 473,
494, 495, 498, 511, 535, 536, 540
Expected energy not supplied (EENS), 152,
155, 156, 159
Extended OPF problems, 224
Factor table, 27–31, 34–37, 39, 40, 42–44,
105, 108–111, 114–116, 118, 292, 295
FACTS, 9, 222, 224, 255–258, 260,
301–302, 325, 407, 436, 463, 464, 475,
502, 510, 534
Fast decoupled method, 72, 77, 88, 101–113,
118, 120
Feasible solution, 182–189, 199, 202, 256
Field winding, 335, 336, 350–352, 359, 363,
364, 369–371, 398, 400
Financial transmission right (FTR), 222
Firing angle, 260, 262, 264–269, 271–274,
279, 280, 299–302, 304, 305, 314, 316,
318, 372, 374, 476
Flat start, 89, 289
Fractional frequency transmission system
(FFTS), 255
Gauss elimination, 22–27, 31, 43, 44, 89, 93,
94, 434, 447, 448, 450
Genetic algorithm (GA), 73, 201, 243
Gibbs sampler, 157–159
Governing system, 361, 362, 381, 382,
386–389, 391–393, 407, 430, 446, 463,
464, 472, 473, 475, 496, 498
Gram-Charlier series expansion, 162, 166,
170, 173
Harmonic voltages, 259, 260
Hermite polynomial, 167, 168
Hessenberg matrix, 527
Homopolar connection, 258
Householder matrix, 528, 529
556 Index
HVDC, 255, 256, 258–261, 272, 276, 279,
281, 299, 300, 341, 372, 430, 436, 437,
464, 475, 479, 485–487, 493, 503, 510,
534, 535
HVDC dynamic mathematical models,
299–301
Hydraulic turbine, 381–388, 406, 496
Ideal synchronous generator, 336–338
Implicit integration methods, 419–424
Incidence matrix, 4–7, 9, 122, 247
Incremental bidding price, 224
Independent operator (ISO), 193–196, 222,
223, 226, 227
Independent power producers (IPPs), 228,
235
Initial condition, 143, 157, 234, 315,
354, 408
Initial value problem, 407, 420, 421, 425
Interarea oscillation, 535, 536, 541
Interior point method (IPM), 200–202, 207,
208, 216, 219
Inverse power method, 529–532
Inverter, 259, 260, 266, 272–274, 279, 280,
284–286, 289, 299, 301, 308–310, 319,
320, 326, 437, 438, 481, 483, 484, 503,
504, 506, 507
Jacobean, 72
Jacobean matrix, 72
Lagrangian function, 187, 204
Lagrangian multipliers, 202, 207, 216, 221
Linear optimal excitation controller
(LOEC), 364
Linear programming, 151, 198–200,
223, 243
Load flow, 71–127, 130, 150, 151, 154,
155, 161–162, 168–173, 175, 176,
178, 189
Load model, 140, 141, 394–397, 399, 400,
403, 500, 501
Local-mode oscillation, 535, 536
Location marginal price (LMP), 222
Loop current method, 2
Loss allocation, 229, 231–235, 238, 240
Loss of load probability (LOLP), 145, 151,
155, 159–161
Lower boundary point, 186, 188
Lyapunov linearized method, 489–491
Market clearing price (MCP), 195
Markov chain, 139, 156, 157, 159, 160
Markov chain Monte Carlo (MCMC)
simulation, 156–159
Markov process, 138–140
Mathematical expectation, 134, 173
Mean value, 134, 137
Memory requirement, 71, 72, 89, 149
Midterm and long-term stability, 405
Mixed programming, 198, 200
Modal analysis, 523, 537
Model of load curtailment, 150–151, 153
Modified Euler’s method, 412–417, 421,
425, 447, 450, 452
Monopolar system, 258
Monte Carlo simulation, 130, 145–149, 152,
153, 155, 157, 159, 244–248, 250
MSC, 306
Multi-fold outages, 114
Multiple bridge, 276
Multistep or multivalue algorithms, 411
Mutual admittance, 3, 4, 14, 19, 21
Mutual inductance, 337, 338, 340, 343,
357, 366
Newton-Raphson method, 22, 72, 76,
79, 81, 87–90, 93, 100, 172, 173,
175, 198
N-l checking, 123–124
Nodal admittance matrix, 1, 4, 7, 13–22,
48–50, 72, 104, 247
Nodal impedance matrix, 1, 48–64, 72,
122, 123
Nodal self-admittance, 3, 4
Node power equations, 76–78, 284
Node voltage method, 2
Nondamping winding model, 351, 352
Nonlinear algebraic equation, 71, 426
Nonlinear optimal excitation controller
(NOEC), 364
Nonlinear programming, 196, 198–199
Nonoscillatory mode, 523
Non-periodic instability, 523
Normal distribution, 137–138, 140–141,
146, 167, 168, 244–246, 250
Index 557
Numeral characteristics of random variable,
133–135
Numerical stability, 421, 424, 425, 430, 462
One-step transition probability, 139, 140
Open access same-time information system
(OASIS), 243–244
Operation risk, 129
Optimal ordering schemes, 43
Optimal power flow (OPF), 1, 38, 196–203,
207, 209, 216–224, 226, 227, 243, 257
Ordinary differential equations, 299, 407,
408, 424
Orthogonal matrix, 499, 526, 527
Oscillation analysis, 493, 534, 537, 540
Outage analysis, 122, 123, 127
Outage table, 142–144, 150, 188
Parallel computing algorithms, 73
Park’s transformation, 335, 338–340
Participation factor, 525–526, 541
Participation matrix, 525
Per unit equations, 282, 340–341, 343, 401
Phase shifting transformer, 1, 11, 13, 16, 18,
20, 38, 301, 322, 325
Piecewise solution method, 72
Polar form of the nodal power
equations, 77
Potier voltage, 357, 360
Power exchange (PX), 193–195, 252, 309,
535
Power flow tracing, 196, 228–241
Power market, 114, 129, 193–196,
222–224, 241, 242, 248, 253, 256
Power method, 527–532
Power rectifier, 371, 373, 379, 380
Power system stabilizers (PSS), 364, 365,
377, 407, 468, 469, 471, 495, 533, 535,
541
P-Q decoupled method, 72, 73, 107, 113,
290, 291, 294
PQ nodes, 76, 85, 90, 109, 111
Predictor-corrector method, 462
Prime mover, 142, 360–362, 381, 382, 406,
407, 430, 446–448, 463, 466, 472,
473, 496
Probabilistic load flow, 130, 161–178
Probabilistic model of load, 140–141
Probabilistic models of transformer and
generator, 142
Probability density function, 133–135, 137,
138, 171, 177–179
Probability of stochastic events, 130–132
Proportional-integral-differential (PID),
364, 388, 392
Pseudo-random numbers, 149
12-pulse converter, 277, 278
PV nodes, 76, 83, 85, 88, 105, 109, 110
q axis sub-transient reactance, 344
q axis synchronous reactance, 340, 344
q axis transient reactance, 344, 356
QR method, 511, 518, 526–527, 531
Quadratic programming, 198, 199
Quasi-steady state model, 480–484, 493
Random process, 138, 139, 159
Random variable, 130, 132–139, 143,
145–148, 151, 162–164, 166–168,
170–173, 244, 245
Random variable’s moment, 163
Real-time balancing market (RBM), 223,
224
Rectangular form of the nodal power
equations, 78
Recursive formula, 143, 144, 410, 411,
419–421
Reliability of transmission system, 188–191
Right eigenvector, 520, 521, 523–525, 531,
533, 537–540
Rotor motion equation, 352, 360–362,
398–400, 464
Round-off error, 412, 424
Round rotor generator, 335, 336, 338, 340
Runge-Kutta method, 417–419, 421,
425, 464
Salient-pole generator, 335, 336, 340, 351
Sampling, 145, 147–150, 152, 155,
157–160, 253, 254
Saturation effect, 336, 337, 359, 366, 369
Saturation factor, 355, 366, 369, 370, 379
Schur decomposition, 526, 527
Self inductance, 337, 338, 340, 365, 366
Semi-dynamic ordering Scheme, 45, 46
Sensitivity method, 114, 246
558 Index
Simplified models for transient stability, 446
Simultaneous solution method, 425, 427
Single-step algorithm, 411
Slack node, 76, 83, 85, 90, 94, 174, 216,
247, 250
Small-signal stability, 489–493, 500,
506–518, 530, 536
Smoothing reactor, 259, 260, 264, 480
Sparse vector method, 22, 38–43, 460, 461
Sparsity techniques, 1
Spot pricing, 195, 196, 219–221
SPWM, 326
SSSC, 301, 302, 319–322, 326, 329, 331
STATCOM, 301, 302, 308–312, 319, 326,
329, 331
State matrix, 492, 509–511, 518, 519, 533
State space, 139, 145, 150
Static load model, 394–397, 399, 400, 500
Static ordering scheme, 44–46
Static security analysis, 73, 113–114, 189
Stationary exciter, 374, 375
Steady-state equations, 354, 356, 360,
437, 438
Steam turbine, 362, 381, 382, 389–393,
492, 493
Step-by-step integration, 408, 409
Step size, 143, 199, 408, 409, 411, 412,
420, 421, 423–426, 428, 454, 462–464,
466, 467
Stiff differential equations, 425
Stiff rotor, 360–362
Stochastic programming, 244
Stormer and Numerov integration formula,
462
Sub-synchronous oscillation, 493
Sub-transient parameter, 335, 344
SVR, 301, 302
Symmetric, 13, 16, 19, 32, 34, 38, 51, 102,
104, 105, 125, 261, 299, 308, 314
Synchronous generator, 334–340, 343, 344,
347–363, 365, 369–372, 398, 400–402,
493–496, 498, 500, 535
Synthesized impedance matrix, 440, 441,
444, 446, 486
System contingency, 124
System performance index, 124, 126, 127
Taylor series, 79, 81, 84, 86, 168, 169
TCPST, 301, 302, 322, 323, 325, 329
TCR. See Thyristor controlled reactors
TCSC, 301, 302, 313, 314, 316–319, 322,
325, 436, 437, 464, 477–479, 485, 487,
502, 503, 507, 508, 510
Telegen’s theorem, 124
Three rotor winding model, 351
Three-winding transformer, 10, 11
Thyristor controlled reactors, 302–307, 313,
316, 476, 478
Thyristor switched capacitors, 302
Time domain, 522
Torsional oscillations, 365, 492, 493
Torsional torque, 493
Transformation matrix, 170, 335, 340
Transient parameter, 335, 344
Transient stability, 357, 362, 400,
405–407, 425, 427–431, 435, 444, 446,
447, 450, 453, 457, 459, 463, 464, 480,
484, 537
Transmission open access, 193, 221
Transmission right, 222, 224
Trapezoidal rule, 419–421, 425–427,
464, 466, 470, 471, 474, 477–479,
482, 483
Triangular decomposition, 27–34,
530–532
TRM, 242
TSC, 302, 303, 305, 306
TTC, 224, 242, 243
Two winding model, 351–352
Uniform distribution, 136–137, 148–150,
154, 158, 251
UPFC, 301, 302, 325–331
Usage sharing problem, 234
Variance, 134–137, 140, 141, 145–147,
155, 157, 159, 160, 168, 245,
246, 394
Voltage regulators (AVR), 333, 352, 357,
363, 375, 377, 378, 534–536
XB algorithm, 106
Index 559