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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