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References

549

[342]Extensible Markup Language, W3.ORG, http://www.w3.org/XML

[343]Wasynczuk, O., Man, D.T., Sullivan, J.P.: Dynamic Behavior of a Class of Wind Turbine Generators during Random Wind Fluctuations. IEEE Transactions on Power Apparatus and Systems 100(6), 2837–2845 (1981)

[344]Watson, L.T., Billups, S.C., Morgan, A.P.: HOMPACK: A Suite of Codes for Globally Convergent Homotopy Algorithms. ACM Transactions on Mathematical Software 13, 281–310 (1987)

[345]Watson, N., Arrillaga, J.: Power Systems Electromagnetic Transients Simulation. The Institution of Engineering and Technology, London (2003)

[346]Weber, J.D., Overbye, T.J.: Voltage Contours for Power System Visualization. IEEE Transactions on Power Systems 15(1), 404–409 (2000)

[347]Weidlich, A.: Engineering Interrelated Electricity Markets - An Agent-Based Computational Approach. Physica-Verlag, Heidelberg (2008)

[348]Wiegmann, D.A., Overbye, T.J., Hoppe, S.M., Essemberg, G.R., Sun, Y.: Human Factors Aspects of Three-Dimensional Visualization of Power System Information. In: Proceedings of the IEEE PES General Meeting, Montreal (July 2006)

[349]Working Group H-7 of the Relaying Channels Subcommittee of the IEEE Power System Relaying Committee, Synchronized Sampling and Phasor Measurements for Relaying and Control. IEEE Transactions on Power Delivery 9(1), 442–452 (1994)

[350]Working Group on a Common Format for Exchange of Solved Load Flow Data, Common Format for the Exchange of Solved Load Flow Data. IEEE Transactions on Power Apparatus and Systems 92(6), 1916–1925 (1973)

[351]Wu, F., Zhang, X., Ju, P.: Small Signal Stability Analysis and Control of the Wind Turbine with the Direct-Drive Permanent Magnet Generator Integrated to the Grid. Electric Power Systems Research 79(12), 1661–1667 (2009)

[352]Wu, Y., Debs, A.S., Marsten, R.E.: A Direct Nonlinear Predictor-Corrector Primal-Dual Interior Point Algorithm for Optimal Power Flow. IEEE Transactions on Power Systems 9(3), 876–883 (1994)

[353]Xie, K., Song, Y.-H., Stonham, J., Yu, E., Liu, G.: Decomposition Model and Interior Point Methods for Optimal Spot Pricing of Electricity in Deregulation Environments. IEEE Transactions on Power Systems 15(1), 39–50 (2000)

[354]Xu, W., Mansour, Y.: Voltage Stability Analysis Using Generic Dynamic Load Models. IEEE Transactions on Power Systems 9(1), 479–493 (1994)

[355]Yao-Nan-Yu: Electric Power System Dynamic. Academic Press, New York (1983)

[356]Z´arate-Mi˜nano, R., Conejo, A.J., Milano, F.: OPF-based Security Redispatching Including FACTS Devices. IET Generation, Transmission & Distribution 2(6), 821–833 (2008)

[357]Zhang, F., Cheng, C.S.: A Modiﬁed Newton Method for Radial Distribution System Power Flow Analysis. IEEE Transactions on Power Systems 12(1), 389–397 (1997)

[358]Zhong, J., Bhattacharya, K.: Toward a Competitive Market for Reactive Power. IEEE Transactions on Power Systems 17(4), 1206–1215 (2002)

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550	References

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Index

A
Abel	159
Absolute stability		195
Accelerating area		184
Adams-Bashforth’s method			193
Aggregation variable 160, 188
Anderson-Fouad’s model 331
Anti-windup limiter		517
Area	249
Arnoldi’s iteration		170, 177
Asynchronous machine see Induction
machine
ATLAS	36
Automatic voltage regulator			355, 376
type I, 363
type II, 364
type III, 366

AVR, see Automatic voltage regulator

B
Batch script 476
Battery energy system		391, 394
Bifurcation point	108, 158, 161
BLAS 36, 41, 72, 282, 502
Boltzmann’s constant		390
Bus
ac model, 247, 249
dc model, 379
frequency, 270, 311, 312
Butcher’s tableau	193, 194

C
C language		33–37, 39, 42, 72, 91,
	117, 121
C++	33–35, 37, 121, 491
C#	33, 37
Canonical model			464
Cardan 85
Center of inertia			270, 342, 343
Chaotic motion			182
Cholesky’s factorization 37, 502
Chopper		406

CIM, see Common information model COI, see Center of inertia

Command line 475

Common information model 464, 467 Commutation margin 397

Constant power generator, see PQ generator

Constant power load, see PQ load

Constitutive equations		9, 11
Continuation power ﬂow		38, 40, 103,
117, 129, 265, 512
Continuous Newton’s method 96
Convex hull	484
Corrector step	121

Coupling device, see Transmission line CPF, see Continuation power ﬂow Crank-Nicolson’s method 196

Critical clearing time	183
Current-injection model	187

CVXOPT, VIII, 41, 43, 91, 121, 227, 234, 239, 241, 285, 497, 505, 529

Cygwin	529
CYME	460,	462

552

Dahlquist

A-stable deﬁnition, 195 theorems, 195, 197

Davidenko’s method 126, 127, 214

Dc machine 384 compound connection, 386 separate winding, 385 series connection, 386 shunt connection, 386

Dc power ﬂow 61, 92, 95, 101, 512

DDSG 453, 455
Decelerating area	184
Degradation matrix	160

Delaunay’s triangulations 485 Delphi 37, 40

Demand

bid function, 301, 302 daily proﬁle, 302, 303 power ramp, 303, 304

DFAG 449, 452

Direct-drive synchronous generator, see DDSG

Direct methods 108

Dominant eigenvalue	170
Dommel’s method	211, 212, 382

Doubly-fed asynchronous generator, see DFAG

Dynamic shaft

synchronous machine, 343, 344 wind turbine, 446, 448

Enterprise resource planning 485 Euler

backward method, 196, 198, 202, 206, 512

forward method, 96, 97, 99, 100, 180

modiﬁed method, 194 Excitation, see Automatic voltage

regulator

Exponential recovery load 313, 320 Extinction angle 397

	Index
F
FACTS	188, 267, 282, 384, 401, 413,
434, 524

Fast Decoupled Power Flow, see FDPF FDPF 86, 90, 91, 101, 512

Ferranti’s e ect 396
Flexible ac transmission system, see
FACTS
FORTRAN	34, 36, 37, 42, 55, 56, 72,
248, 289, 505
FOSS, see Free open source software
Free open source software		491
Free software	490
Frequency dependent load		313, 316,
317

Frequency regulation, see Turbine governor

Fuel cell, see Solid oxide fuel cell

Galvanic insulation 401 Gauss

distribution function, 439 language, 38

Gauss-Seidel’s method 61, 70, 74, 85, 90, 91, 101

Generator

capability curve, 292, 293 o er function, 293, 296 power ramp, 299, 301 power reserve, 298

reactive power payment function, 296, 297

Genericity 158

Geographical information system 485 GIS, see Geographical information

system
GMRES	85, 86, 90, 91, 101
GNU Octave 34, 37, 38, 40, 42, 492
Gnuplot	37
G¨odel’s theorem 467
Goderya’s algorithm		287–289
Gram-Schmidth orthonormalization
170
Graphical interface		475
Ground	381

Index
H
Hamming’s method	193
Hard limit 516
Hermite’s function	439
Hermitian matrix	74, 170, 175

High voltage dc transmission system,

	see HVDC
Homotopy methods				114, 117
Hopf bifurcation			120, 162, 214, 215,
	258, 346, 361, 367, 373
HVDC		165, 282, 395, 400
Hybrid automaton				11
Hybrid dynamical system					11, 186
Hybrid transient simulator					187
I
Ideal generator			381
IEEE, VIII, 27, 174, 530
Induction machine				325, 348, 353
double cage, 351
mechanical model, 349
order I, 349
order III, 350
order V, 351
single cage, 350
Inductor model			9
Inﬁnite bus, see Slack generator
Integrator clamping				519
Interior point method				142, 152
InterPSS		40, 42, 461, 463
Inverse iteration			172, 177
Inverse time characteristic					308
IPython		529
Iwamoto’s method				84, 85, 99, 100,
	512
J
Jacobi’s method			70, 74, 90, 91, 101
Java	33–35, 37, 38, 40, 42, 472, 487,
	491
Jimma’s load			313, 322
Jordan’s canonical form					171
K
Kiss rule		466
Kronecker’s operator				98

553

Lanczos’ method 170

LAPACK	36, 41, 121
Latex, VIII,	20, 33, 478, 491, 493
Leibniz 163

axiom, 13 monad, 226

Limit-induced bifurcation 111 Limit cycle 258

Line, see Transmission line

Line sections, see Transmission line

Linux

19, 20, 33, 476, 491, 492

LMP, see Locational marginal price Load tap changer, see Tap changer

Local parametrization				121
Locational marginal price					150
Loss of opportunity				296
LTC, see Tap Changer
LU factorization			7, 37, 63, 86, 91,
121, 163, 502
LUP factorization			120
Lyapunov
direct method, 179, 181–185
ﬁrst stability method, 157
function, 181, 182
M
Mac OS X		529
MacPorts		529
Manifold folding			160
Marconato’s model				330–332
MathCAD		38
Mathematica 34, 38
Matlab	34, 37–42, 72, 91, 117, 170,
461, 507
Matplotlib, VIII,			41, 48, 477, 481,
483, 497, 507, 509, 529
Matpower		40, 42, 460, 461
Maxima		38
Maximum power point tracking						405
Maxwell’s equations				11
Mehrotra’s predictor-corrector						142,
513
Mexican hat wavelet				435, 439, 440
Milne-Simpson’s method					193
Mixed load		313, 323, 324
Modelica		38, 40
Montecarlo simulation				466

554
Moore’s law 41
Multi-stage method	192
Multi-step method	193
Multi-swing instability		182, 206
N
N-1 contingency analysis		127

NCP, see Nodal congestion price NCSWT 448, 449

Newton 99

composite method, 153 continuous method, 101, 126, 127,

512

direction, 142, 145–148, 152, 153, 513

dishonest method, 85, 86, 88, 101, 192, 196

inexact method, 85, 86, 101

method, 12, 22, 28, 42, 43, 48, 61, 74, 82, 86, 90, 91, 101, 103, 109, 115, 121, 140, 141, 144, 190, 192, 196, 198, 200, 224, 250, 253–255, 268, 443, 512

robust method, 82, 84, 97, 101 very dishonest method, 192, 196

Nodal congestion price	150
Non-conforming load	313

Non-controlled speed wind turbine, see NCSWT

Nonlinear programming 113

Normal form	158
NumPy, VIII,	41, 121, 227, 483, 497,
505–507, 529

Observation window 309

Occam’s razor 466

Octave, see GNU Octave

OLTC, see Tap Changer

OpenDSS 39, 40
Open source software	490
OPF, see Optimal power ﬂow
Optimal Power Flow	131
Optimal power ﬂow	38, 40, 131, 153,

265, 291, 304, 512

OSS, see Open source software

					Index
Over-excitation limiter			355, 373, 375
OXL, see Over-excitation limiter					373
P
Park
model, 325, 326, 348
transformation, 325, 326
Participation factor			165
Partitioned-solution approach					192
Perl	34–37, 472
Perpendicular intersection				121
Phase shifter, see Phase shifting
	transformer
Phase shifting transformer				278, 279
Phasor measurement unit				309, 311
Php	34
PhST, see Phase shifting transformer
PI controller		518
Pitch angle		444
Pitch control		445
Plato	5
Plug bridge		308
PMU, see Phasor measurement unit
Power-injection model			189
Power method		170, 172, 177
Power system stabilizer				355, 369, 373
simpliﬁed model, 371
type I, 371
type II, 371
type III, 373
PQ generator		256, 257
PQ load 257, 259, 314, 316
Predictor step		117

Primary frequency regulation, see Turbine governor

Primary voltage regulation, see Automatic voltage regulator

Proprietary software		489
PSAT	42, 460, 461, 463
PSCAD	55
PSS 376
PSS, see Power system stabilizer
PV generator 250, 254, 327
Python, VII, VIII,		31, 33–37, 39–43,

49, 51, 54, 55, 57, 72, 73, 75, 78, 83, 89, 100, 119, 121, 131, 148, 160, 165, 170, 204, 221, 227–229,

Index

233, 234, 248, 289, 472, 476, 482, 485, 487, 488, 492, 497, 509, 529, 530

Q
Q language		38
QR algorithm			170, 177
QR factorization			502
R
R language		34, 38
Rayleigh
distribution, 437
iteration, 172, 173, 177
quotient, 172
Reactor model			16
Region	249
Relay	307, 308
RLC models		382
Robustness		158
Rosenbrock		197

formula, 197, 198, 218 semi-implicit method, 197

Ruby 34

Runge-Kutta’s formula 99, 100, 192–195, 218, 512

Runge-Kutta-Fehlberg’s formula 194

Saddle-node bifurcation 109, 158, 161–163, 176

Sauer-Pai’s model 330, 331 Scala 33, 37

Schur’s factorization

120, 121, 502,

503
SciLab 38
Secant predictor	118
Seidel’s method	28
Seneca’s style, VIII
Shadow e ect	447, 456

Shaft, see Subsynchronous resonance,

Dynamic shaft
Shunt	260, 261
SIME method 179, 204, 206, 218
Simulink	38, 483
Simultaneous-solution approach		192
Singular value decomposition		174

555

Singularity-induced bifurcation 160 Skin 476

Slack bus, see Slack generator Slack generator 254, 256

SMES, see Superconducting magnetic

	energy storage
Solar photovoltaic cell				390, 391
control, 404
Solid oxide fuel cell				387, 388
control, 403
SSSC	413, 423, 428
Stability function 195
Stallman		490
Statcom		413, 419, 423, 524
Static Compensator, see Statcom
Static Synchronous Series
	Compensator, see SSSC
Static var compensator, see SVC
Stefan-Boltzmann’s constant					388,
	391, 394
Step length			218
Sti problem			195
Sub-synchronous resonance					345, 347
Superconducting magnetic energy
	storage		17, 391, 406, 408
Supply		293, 297
SVC	413, 416, 524
Swing bus, see Slack generator
Synchronous machine				67, 325, 355,
	361

Anderson-Fouad’s model, 331 center of inertia, 270, 342 classical model, 335

common equations, 328

constant emf behind the sub-transient reactance, 335

constant emf behind the transient reactance, 335

dynamic shaft, 343 magnetic equations, 329 Marconato’s model, 330

one d- and one q-axis equation, 334 one d- and two q-axis equation, 333 one d-axis model, 334

one d-axis model with stator ﬂux dynamics, 338

Saccomanno’s model, 338 saturation, 339 Sauer-Pai’s model, 330

556

simpliﬁed models, 332

stator electrical equations, 329 sub-synchronous resonance, 345 two d- and one q-axis equation, 332 two-axis model, 223, 225, 234, 241,

246, 334 System 249

Tangent vector 117 Tap changer

dynamic model, 275, 278 with embedded load, 317, 320

Tcl	34
TCSC	267, 413, 417, 419

TCUL, see Tap Changer Temperature map 482 Test equation 195

TG, see Turbine governor Thermostatically controlled load 313,

321, 322 Three-dimensional plot 484 Thyristor Controlled Series

Compensator, see TCSC Tie line, see Transmission line Time multiplier 308 Transformer 272, 281 Transient energy function 181 Transmission line 263, 271

Admittance matrix, 282 coupling, 271 distributed model, 268 frequency e ect, 270

Hessian matrix, 285
Jacobian matrix, 285
lumped model, 263
sections, 265
tie line, 267, 427
zero impedance, 271
Trapezoidal method	198, 202, 206,
211, 218, 512
Turbine governor	355, 360

ﬂyball governor, 9 isochronous governor, 9 type I, 358

type II, 359 Turn-o device 400

Two-dimensional plot 478, 507

			Index
U
UCTE	3
ULTC, see Tap Changer			275, 317
UMFPACK		36, 41, 503
Under-excitation limiter			355, 376
Uniﬁed PF controller, see UPFC
Unix	19, 20, 36, 481, 529
UPFC	413, 428, 433
UWPFLOW		39, 40, 42, 463
UXL, see Under-excitation limiter
V
Voltage dependent load			313
static model, 313, 315

with dynamic tap changer, 317, 320 Voltage regulation, see Automatic

voltage regulator	361
Voltage source converter	400, 403,
413

VSC, see Voltage source converter

Weibull’s distribution 435–437 Wind 435, 456

composite model, 438, 439 gust, 438

ramp, 438 turbulence, 438

Wind turbine	443
Windows 36, 39, 529
Windup e ect	517
Windup limiter	517

Xcode 529

Yorick 38

Zero impedance line, see Transmission line

ZIP load 313, 315, 316 Zone 249

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