This document provides an index of terms related to power system dynamics, modeling, stability, and control. It includes over 200 entries ranging from specific component models like boiler-turbine-generator systems to concepts like electromechanical oscillations, bifurcations, and blackouts analysis. The index serves as a reference guide for the topics, methods, and models covered in the associated handbook on electrical power system dynamics.

1. INDEX
IEEE type AC5A excitation system model, 101
AC alternator supplied rectifier excitation, 98
Active and reactive powers and voltage,
relationship, 342
sensitivity coefficients, 346
short line model, 343
shunt admittance, 346
transmission lines reactance, 345
Adams–Bashforth–Moulton integration
formulae, 606
Adams–BDF method, 614
Adams type methods, 606
Additive model, 666
ADE dynamic model, 694
Adiabatic process, 140
Admittance matrix, 732, 908
AGC (automatic generation control) actions, 293
Algorithms, 33, 72, 210, 369, 416, 596, 603,
605, 614, 628, 629
Analog digital (A/D) converter, 743, 750
Angular stability, 469
Aperiodic instability, 478
Approximate method, 690
Asymmetric three-phase system, 758
Asymptotically stable, 587
Automatic generation control (AGC) principles
and modeling, 137, 328
in multiarea systems, 332–335
area control error (ACE), 333
in a single-area (isolated) system, 329
tie-line control, frequency bias, 329
two-area AGC tie-line model, 329, 330
Automatic load shedding systems, 823, 825
Automatic tap changing system, 680
Automatic voltage regulators (AVRs), 514, 516,
676, 892
controls, 347
Autoreclosing, 738
Autoreclosure function, 772
Backup protection, 741–742
Backward differentiation formulae, 611
Bifurcations
global bifurcations, 707–708
Hopf bifurcation, 704–705
Neimark-Sacker bifurcation, 708
saddle-node bifurcation, 705–706
singularity induced bifurcation,
706–707
Binary digital (B/D) converter, 744
Biquadratic equation of voltages, 667
Blackouts analysis, 835–847
Boiler
Boiler–turbine–generator, 146
power plant control modes, 147
pressure effects, model, 146
steam chest and high-pressure piping,
147–148
Boundary controlling unstable (BCU)
method, 601
Brayton cycle, 139
Breaker failure protection, 753, 772
Breaker IED (BIED), 752
Buchholz protection, 761
Busbar differential protection, 770, 774
Busbar protection, application issues for,
770–771
differential protection, 768–770
line differential protection, application
issues, 771
Bus participation factors, 714
Bypass circuits for induced negative field
current, 109
Cascading overload, mechanism, 843
Cascading system, 856
Ceiling voltage, 94
Center of inertia, 628, 634
parameters of the equivalent, 634–638
929
Handbook of Electrical Power System Dynamics: Modeling, Stability, and Control. Edited by Mircea Eremia and
Mohammad Shahidehpour.
Ó 2013 by The Institute of Electrical and Electronics Engineers, Inc. Published 2013 by John Wiley & Sons, Inc.

2. CENTREL and European system (UCTE), 292,
293, 832
grids, 805
load frequency control, 294–295
primary control, 295
secondary control by AGCs, 295–296
self-regulation of load, 296
tertiary control, 296
schematic map, 832
security rules, 833
typical small frequency deviation responses
in, 293
Circuits
open- and short-circuit characteristics,
67–69, 71
synchronous generator, 18, 43
terminals of a simple R-L circuit, 46–55
Classical frequency protection, 762
Clustering algorithm, 630
Coefficient matrix, 590
Coherency estimation, 623–631
Coherency indices, 625–628
Coherent motion, 625, 628, 634
Combined-cycle power plants, 158–159
black-start-up, 877–888
energization maneuvers analysis, 878–879
islanding maneuvers analysis, 879–886
islanding tests description and
experimental results, 886–888
model block diagrams, 160–166
IEEE model, 163
Rowen’s model, 162–163
subsystems of the combined-cycle power
plant, 161
Combined heat and power (CHP), 834
station, 892
Communication, 775, 780
Compensation impedance, 106
Complete system matrix, 480
structure of, 480
Complex load model, 621, 661
Compound source-rectifier exciter, 103
Comprehensive method, flowchart, 604
Computer simulators description, 888–896
combined-cycle power plant simulator,
892–896
gas turbine model and validation, 889
steam group repowered with gas turbine,
888–892
steam section modeling and validation,
889–892
Constant-step methods, 604
Controlling unstable equilibrium points
(CUEPs), 601, 603
Conventional transformers (CIT), 748, 749
Critical clearing angle, 645
Critical clearing time, 599, 621
Critical fault clearing time, 577, 580, 648
definition, 571
Critical machine ranking (CMR) method,
581–582
Critical voltage, 730
Cross-magnetizing phenomenon, 72–73
Current differential functions, 768–772
Current injection vector, 908
Cyclic fold bifurcation, 708
Damper effect, 651
Damping. See also Electromechanical oscillations
impact of loads and power flows on, 527–535
improvements, 546–550
limitation on PSS gains, 561–564
PSSs on excitation control, 553–561
theory of small shift poles, 550–553
oscillation problems, 478
d-axis, 10
Damping coefficients, 15, 595, 648
Data acquisition system, 747
sensors, 748–751
DC exciter model, 97
Decision algorithm, 780
Defense actions, 851–854
Definite minimum time lag (IDMT) function,
760
Definite time lag (DTL) function, 760
Degree of criticality of machine (DCM), 581
Degrees of closeness, 629
Delay times, 767
Differential-algebraic equations (DAEs), 702
Digital communication methods, 768
Dimo-REI method, 616
Directional line protection, 765
use as busbar protection, 766
Directional overcurrent protection, 765
Direct methods assessment, 572–603
direct methods based on Lyapunov’s theory,
587–603
equal area criterion, 572–580
extended equal area criterion (EEAC),
580–582
single-machine equivalent (SIME) method,
582–587
Direct/normal logic, 678
Dispersed mode, 714
Distance protection, 766
Distributed protection
differential object protection functions, 774
directional object protection functions, 775
930 INDEX

3. Distribution power systems, principle
structures, 754
Distribution systems, 757, 758
Disturbance impact indices, 617, 620, 621
study, 617–621
Droop, 297
Dynamic equivalents, 614–638
center of inertia, parameters of the
equivalent, 634–638
coherency estimation, 623–631
coherency indices, 625–628
clustering, 628–631
disturbance impact index, 617
study, 617–621
equivalencing criteria, 631–634
mutual motion equation of a pair of
machines, 623–625
system element
significance estimation, 621–623
system, mathematical description
simplification, 617–621
system structural connectivity, index of,
621–622
Dynamic frequency response, 297
Dynamic load characteristics, 661
Dynamic load restoration process, 665
Dynamic matrix, 478
Dynamic security assessment (DSA) system,
474–475
Eigenvalue analysis, 916
Eigenvalue sensitivity, 550
Electrical power market, liberalization, 868
Electric connectivity, 622
Electric distance, 618–619
Electric power systems, 291, 599, 614, 621,
625, 631, 643
Electromagnetic power, 574, 575, 650
Electromagnetic torque, 11
Electromagnetic transients program (EMTP),
900, 901, 904
Electromechanical equations, 610, 919
Electromechanical loops, block
diagram, 516
Electromechanical oscillations, 478, 483, 486
assessment of periods, 493
damping of, 501–503, 545–546
eigenvalue analysis, 500–501
factors affecting, 501
local, 502
low-frequency, 502
undamped, 502
interarea or low-frequency, typical cases,
564–568
oscillation amplitudes, 489–493
oscillation modes, 486–488
participation factors, 489–493
poles and zeros associated with, 492
properties, 492
qualitative shift following transit decrease,
533
Electromotive forces, 622, 643
Emergency isolation plan, 802
Emergency state, 790
Equal area criterion, 572–580, 647
Equivalent generators, 632, 634
Equivalent system configuration, 636
EUROSTAG software, 611, 613, 614
Excitation limiters, 107
Excitation systems, 93–112
Explicit integration formulae, 606
Explicit methods, 604
Extended equal area criterion (EEAC),
580–582
Fault clearing time, 579
Fault direction detection
principle, 764
Fault impedance, 764
Fault ride-through capability, 223–225
active stall-controlled wind turbine, 225
blade pitch angle control, 225–226
pitch angle-controlled wind turbine, 225–226
torsional oscillations damping controller,
226
Field forcing, 94
Field-shorting circuits, 109
First energy (FE) system, 793, 795, 900
operators, 801
First-order delay model, 720
First-swing instability, 572
First-swing stability, 573
Flexible AC transmission systems (FACTS),
802, 842, 849
Floquet multipliers, 707, 708
Fossil-fired power generation plants, 827
Fossil fuels, 144
Fourier spectrum, 902
Four-machine two-area test system, 923
Frequency-adaptive companion model, 910
Frequency-adaptive model, of single-phase line
model, 913
Frequency-adaptive simulation of transients
(FAST) processes, 902, 925, 926
Frequency collapse, mechanism, 842
Frequency deviations in practice, 293–294
Frequency error, 877
Frequency local integrator (FLI), 874
INDEX 931

4. Frequency stability, 467–468
Fuel metering valve (FMV), 892
Gas turbines (GTs) model, 864, 888, 893
angular speeds, 883
mechanical powers, 884
operation modes, 881
power plant arrangement, typical, 140
shaft angular speed transients, 885
Gear–Hindmarsh method, 611, 612, 613
Gear type integration formulae, 608
Gear type methods, 607
General steam system model, 151–152
generic turbine model, 151
including IVeffects, 152
Generator
synchronous, 9
Generator-line-load configuration, 688
Generator motion coherency, 615, 636
Generators
coherency indices, 627
connected to infinite system with
intermediate load, 527
doubly fed induction generator, 190–191
dynamic slip-controlled wound rotor
induction generator, 189
generator capability curves, 526
induction generator, 185–188
parallel operation of, 298–299
permanent magnet synchronous generator,
192
axial flux machines, 192, 193
with boost chopper, 193
drive trains, 194
from high-speed to low-speed generators,
194
with PWM converter, 193
transverse flux machines, 192
wind turbine, architecture, 192, 193
phasor diagram of a generator
connected to infinite system, 518
squirrel cage induction generator, 188–189
advantages and disadvantages, 189
unloaded (See Synchronous compensators)
wind turbine, categories, 185
wound rotor synchronous, 191–192
advantages, 192
Generic Object Oriented System Event
(GOOSE), 744
Global coherency, 616
Global index, 733
Global positioning system (GPS), 744, 849
Gorev’s stability criterion, 625, 626
Governor droop on regulation, effect of, 298
Governor modeling, 302–303
with droop, 303–304
hydraulic governor modeling, 304–306
Graphical–analytical method, 572
Grid blackouts, 789–860
analysis of blackouts, 835–847
August 14, 2003 Northeast United States and
Canada blackout, 793–805
August 10, 1996 Northwest U.S. blackout
causes of, 803–804
December 19, 1978 national blackout in
France, 819–820
defense and restoration actions, 850–856
description, 792
economical and social effects, 847–848
European incident of November 4, 2006,
832–835
initiating events, 838
January 12, 2003 blackout in Croatia, 812–814
January 17, 1995 Japan blackout after
Hanshin earthquake, 826–830
January 12, 1987 Western France blackout,
820–821
July 12, 2004 Greece blackout, 816–817
July 2, 1996 Northwest U.S. blackout,
817–818
March 13, 1989 hydro-quebec system
Blackout response to geomagnetic
disturbance, 822–826
May 25, 2005 blackout in Moscow, 814–816
mechanisms, 841–847
periods of, 840
recommendations for preventing blackouts,
849–850
September 23, 2003 Eastern Denmark and
Southern Sweden blackout, 810–812
September 28, 2003 Italy blackout, 805–810
some lessons learned, 835
survivability/vulnerability of electric power
systems, 856–859
types of incidents, 840–841
Grid voltage and reactive power
automatic voltage control
by generator line drop compensation,
385–391
of generator stator terminals, 379–385
at power plant, 391–399
control methods, 374–377
voltage–reactive power automatic control,
378–379
voltage–reactive power manual control,
377–378
932 INDEX

5. by network topology modification, 378
by reactive power flow, 378
GRTN operator, 807
Heat recovery steam generator (HRSG), 878,
888, 894
Hierarchical voltage control in world, 429
Brazilian hierarchical voltage control
system, 442
French power system hierarchical voltage
control, 429–435
Italian hierarchical voltage control system,
435–442
Hierarchical voltage regulation, 399
primary voltage regulation, 402–405
secondary voltage regulation (SVR)
architecture and modeling, 405–417
control areas, 418
pilot nodes/control areas, 418–420
procedure to select control generators,
420–422
tertiary voltage regulation (TVR), 417–418
structure of hierarchy, 399–401
High-pressure (HP)
collector, 883
feedwater, 869
High-speed cascading, 796, 812, 836, 850
High-voltage direct current (HVDC) links, 2
Hilbert transform, 920
Hydraulic power plants, 169–171
elements of water system for, 169–170
functional block diagram, 171
penstock, 169
water admission valve, 170
water hammer, 170
water supply system, 169
Hydraulic governor, 304–306
Hydro prime mover systems, 171–174
Hydro turbine governor control systems, 174
actuator, 176
set point controller, 174–175
permanent speed droop, 174–175
speed regulation, 175
IEEE ST1-Type exciter with PSS input, 113
IEEE type DC1A—DC commutator exciter
model, 96
IEEE type ST2A—compound source-rectifier
exciter, 104
IEEE type ST1A potential source-controlled
rectifier exciter model, 102
IEV 448-12-05, 740
Impedance protection, 766–768
distance protection, 766–768
special impedance-based functions, 768
Implicit functions theorem, 659
Implicit method, 605
Implicit trapezoidal rule, 609–611
Inadequate reactive power reserve, 837
Independent system operators (ISOs),
794, 804
Induction motor, 115–133
electromagnetic model, 131–133
electromechanical model, 129–130
general equations, 116
rotor, 115
steady-state operation, 123–129
theory/modeling of, 114
design and operation issues, 114–116
Inertia, 297
Inertia and synchronizing power coefficients,
483–486
Inertia center coordinates, 616
Inertial variables, 571
Infinite bus (IB), 645
Insensitivity domain of regulator, 677
Instrument transformers, 748–749
Integration methods, 605
considerations, 603–608
implicit trapezoidal rule, 609–611
mixed Adams-BDF method, 611–614
Runge–Kutta methods, 608–609
Intelligent electronic devices (IEDs), 737, 740,
753
based (numerical) busbar protection
systems, 771
Interarea/low-frequency electromechanical
oscillations, 564–568
Intermediate generator bus, 684
Internet protocol (IP), 744
Isentropic efficiency, 166
Isolated area modeling, and response, 301–302
Jacobian matrix, 603, 612, 669, 696, 699, 708,
710, 712, 716
Kinetic energy, 13
Kirchhoff’s law, 770, 775
node, 769
Lagrange extrapolation polynomials, 608
Large electric power systems assessment,
638–645
LaSalle’s invariance principle, 588
Leakage effects, 911
Least squares approximation, 585
INDEX 933

6. Lienard vector equation, 593
Line differential protection, for T-line, 770
Line voltage drop effect, 345
Load compensation, 105–107
Load drop anticipator (LDA) relay, 882
Load exponential model, 663
Load flow feasibility (LFF) methods, 689
to predict voltage collapse, 691–692
Load frequency control (LFC), 833, 834
Loading capability chart
curves, 685
of synchronous generator, 91
Loading margin, 698–701
Load modeling, 660–667
dynamic models, 664–667
exponential model, 662
generic model, 665
polynomial, 663
load characteristics, 660–662
mathematical model, 661
static models, 662–664
Load restoration process, 682, 683
dynamic process, 666
Load scheduler, scheme, 875
Load shedding, 718
Load stability, 660
Local backup protection concept, 742
Local bifurcations, 704
Local coherency, 616
Local frequency integrator (LFI),
878, 893
Localized variation mode, 714
Local parameterization technique, 700, 701
Logical Nodes (LN), 744, 773, 780
Long-term transient processes, 628, 638
Lossless single-phase line, 913
Loss of synchronism, mechanism, 844
Lyapunov function, 588, 589, 592, 593, 594,
598, 601, 625, 644
Lyapunov matrix equation, 590
Lyapunov stability theory. See Lyapunov’s theory
Lyapunov’s theory, 587–603
direct methods based on, 587–603
determination of equilibrium, 594–596
extension, 596–601
Lyapunov function designing, 590–594
Lyapunov’s method, 587–603
potential energy boundary surface (PEBS)
method, 601–603
Magnetically coupled inductances, 910
Magnetic flux equations, 23
Magnetic poles, 12
Magnetic saturation, 66–73
Magnetomotive force, 10
Mathematical model, 82–90
interconnection of synchronous generator to
electrical grid, 87–90
synchronous generator, 83
Matrix of coherency indices, 630
Maximum angle deviation, 584
Maximum transmissible powers, 729, 731
Mean time to failure (MTTF), 739
MEDRING power system, 568
Merging Unit (MU), 745, 750
Microprocessor-based IEDs, 751
Minimum voltage criteria, 686, 687
Mixed Adams-BDF method, 611–614
general Gear–Hindmarsh method,
611–614
Modal analysis method, 716
Modeling in dynamic state, 73–90
Moment of inertia, 13
Motion coherency index, 626
Motion noncoherency, 617
Multifunctional relays, integrate protection
functions in, 773
Net transfer capacity (NTC), 473, 805
New information and communication
technology (NICT), 856
Newton–Raphson method, 595, 596, 600, 605,
610, 611, 696, 701
Nodal admittance matrix, 712, 907
No-load operating conditions, 711
Nonconventional instrument transformers
(NCIT), 748, 749
Noninertial variables, 571
Nonsingular matrix, 706
Nordsieck vector, 611, 612
North American Electric Reliability Council
(NERC) standards, 868
for power and frequency control, 296
regions, 292, 293
Nuclear power plants, types on circuits,
167–168
Nuclear reactor, 144
characteristic elements, 167
Numerical protection device
principle diagram, 743
Numerical relays, 751
Numerical technology, 780
advantages, 743
impact, 742
Object protection, 766, 771
OMIB
equivalent identification, 586–587
934 INDEX

7. parameters, 582
rotor angle, 583
On-load tap changers (OLTC), 341,
676–683, 681
automatic tap changing effect on possible
operating points, 678–679
on-load tap changing dynamics modeling,
676–678
on-load tap changing influence on voltage
stability, 679–683
transformers, 366, 369
turns ratio, 367
On-load tap changing, 724
regulation, 679
transformer (See On-load tap changing
transformers)
On-load tap changing transformers, 352, 677
applications of, 366–371
determination of current operating tap,
362–363
generalities, 352–355
primary/secondary
connections of, 352
windings, 353
single-phase equivalent circuits, 352, 354
star–delta connections, 354
static characteristic of transformer, 363–366
switching technologies, 355–362
Operating zones, 674
Operation in islanding conditions, 336–338
Ordinary differential equations (ODEs), 702
Oscillations
curves, 571
damping, 514, 525
frequency, 521–522
interarea, 522–524
Overcurrent protection, characteristics, 760
Overexcitation limiter (OEL), 107
Parametric resonance, 707
Park equations, 27–33
Park transformation, 24–27, 920
Participation factor, 714
Pascal’s triangle array, 612
Performance index (PI), 689
regulator, 895
Periodic instability, 477
Phase shifting transformers, 372
Phasor diagram, 659
with damper winding neglected, 76, 77
transient model, 81
Phasor measurement units (PMU), 849,
886, 887
Phasor measuring functions, 775
Pole slipping function, 768
Pole, small shift of, 552
Polynomial load models, 664
Positive-sequence diagram, 614
Potential energy, 601, 626
Potential energy boundary surface (PEBS)
method, 601–603
Potential source-rectifier exciter employing
controlled rectifiers, 101
Power-angle characteristics, 46
Power control concepts, 197–200
aerodynamic forces, 198
active stall control, 200
pitch control, 199–200
stall control, 198–199
wind turbine, 198
Power factor, 670, 721, 730
Power flow (PF)
computations, 478, 479
security limits, 472
stability limit, 472
thermal limit, 472
voltage limit, 472
Power system protection, 737–784
basic protection properties and resulting
requirements, 739
IEC 61850, 744–745
main operative requirements, 740–742
adaptive protection, 741
backup protection, 741–742
reliability, 740
remarks about features, 742
selectivity, 740
speed and performance, 741
protection chain, 746–753
protection functions, 759–773
current differential functions, 768–772
directional protection, 764–766
with fault direction detection, 764–766
frequency protection, 761
impedance protection, 766–768
with improvement of selection by
communication, 763–764
with improvement of selection by time
delays, 762–763
on limits of locally measured values, 759–764
limit supervision and protection, 761–762
overcurrent and time overcurrent
protection, 760
overload protection, 760–761
protection-related functions, 772–773
voltage protection, 761
INDEX 935

8. Power system protection (Continued )
single protection functions to system
protection, 773–780
adaptive protection, 774
distributed protection, 774–775
general recommendations for protection
application, 776–779
security and dependability, 779
single function and multifunctional relays,
773–774
wide area protection, 775–776
state-of-the-art protection, advantages,
742–744
task of protection, 738–739
three-phase systems properties, 755–759
symmetrical components, 755–759
unbalance, 756–758
Power systems, 1, 669, 672, 695, 705, 718,
719, 789
components modeling, 909–923
electromagnetic and mechanical machine
equations, 918–919
multiphase lumped elements, 909–910
stator current, real and imaginary parts
calculation, 920–921
synchronous machine in dq0 domain,
918–923
transformer, 911–912
transmission line, 912–918
distribution power systems, 754
instantaneous and phasor signals bridging,
901–903
limiting state for, 857
network modeling, 903–909
direct construction of nodal admittance
matrix, 906–909
network branches, companion model for,
903–906
operating states, 790
protection (See Power system protection)
services, categories, 473
ancillary services, 473
system services, 473
stability (See Power system stability)
stabilizer (See Power system stabilizers
(PSSs))
survivability, 857
transmission power systems, 754
principle structures, 755
Power system stability, 453
classification, 453–454
based on dynamics, 455
frequency stability, 467–468
importance of security, 469–475
dynamic security assessment, 474–475
physical security, 470
power flow security limits, 472–473
power system states, 470–471
reliability of bulk power system, 470
services to meet power system security
constraints, 473–474
large-disturbance rotor angle stability/
transient stability, 461–462
parallelism between voltage stability, and
angle stability, 469
rotor angle stability, 454, 456–460
small-disturbance (or small-signal) rotor
angle stability, 460–461
voltage stability, 462–467
Power system stabilizers (PSSs), 110–112, 478,
804, 850
on excitation control, 478
base case and theory, 553–556
general case, 556–561
general block diagram, 555, 560
limitation on, 561–564
modal characteristics, 478
on voltage loop, 561, 562
Power system states, 470, 471
Predictor–corrector methods, 606, 607, 700
computation technique, 701
Preemergency condition, 624
Primary frequency control, 537
block diagrams for assessing effect of,
538
combined-cycle power plants, 541
contribution of jPV in interconnected power
systems, 544
conventional thermal units, 539–540
electromechanical oscillations, 541
damping of, 538
gas turbines to, 541, 542
HVDC links, 545
stabilizing and destabilizing effects, 539
thermal unit, 540
Primary voltage control, 523, 536–537
contribution of, 514
to damping, physical interpretation, 548
evaluation of, 536
Private communications system
with strong aseismic design, 830
Protection
electrical values, 748
nonelectrical values, 748
types, 748
values measured for, 748
936 INDEX

9. Protection chain, 746–753
circuit breaker, 752–753
copper wires vs. serial links, 746
data acquisition from sensors, 748–751
data handling features, 751
data sending to actuators, 751–752
hardwired, 746
power supply, 753
process interface, 712
protection data processing, 751
with serial links, 747
supervision, 746–747
transmission/distribution power system
structures, 753–755
trip decision, information, 751
values measured for, 748
Protection coordination, 778
Protection functions, 777
characteristics, 760
identification, 780–784
IEC designation, 781
logical nodes names, 781
sorted according to objects protected,
759–773
current differential functions, 768–772
directional protection, 764–765
directional protection improvement by
communication, 765–766
frequency protection, 761
impedance protection, 766–768
on limits of locally measured values,
759–764
limit supervision and protection, 761–762
overcurrent and time overcurrent
protection, 760
overload protection, 760–761
protection-related functions, 772–773
protection with fault direction detection,
764–766
protection with improvement of selection
by communication, 763–764
protection with improvement of selection
by time delays, 762–763
voltage protection, 761
Protection methods, summary, 779
Protection-related functions, 772–773
autoreclosing, 772
breaker failure protection, 772
synchrocheck, 773
Proximity indicator, 690
q-axis, 10
Quasistatic approximation system, 689
Radial networks
overcurrent delay times in, 763
overcurrent relays in, 763
Radial power system, characteristics, 463
Rankine cycle, 144
Reactance, of generator
leakage, 54
subsynchronoys, 54
synchronous, 54
transient, 54
Reactive capability limits, 90
loading capability chart, 90–92
V curves, 92
Reactive power compensation devices, 347
Reactive power equipment, 671
Reactive power, expression, 685
Reactive power–voltage control, 340
Reactive voltage compensation, 106
Recovery angle, 585
Recovery time, 665
Rectifier voltage output, 895
Reduced Jacobian matrix
modal analysis, 711–716
power system, V-Q variation modes,
712–714
voltage stability analysis, participation
factors definition, 714–716
branch participation factors, 715
bus participation factors, 714–715
generator participation factors,
715–716
Reflected gradient system (RGS), 603
Region of attraction, 676
Regulating transformers, 371
basic booster scheme, 371–372
in-phase regulating transformer (IPRT),
371
phase shifting transformers, 372–374
Reliability, 740
Remedial system actions (RAS), 293
Remote backup protection concept, 741
Restoration actions, 854–856
Restoration plan, 851
Restoration processes
after blackouts, 864–896
combined-cycle power plant, black-start-up,
877–888
energization maneuvers analysis,
878–879
islanding maneuvers analysis,
879–886
islanding tests description and
experimental results, 886–888
INDEX 937

10. Restoration processes (Continued )
computer simulators description, 888–896
combined-cycle power plant simulator,
892–896
gas turbine model and validation, 889
steam group repowered with gas turbine,
888–892
steam section modeling and validation,
889–892
system restoration stages, duration, tasks,
typical problems, 866–868
thermal power plant, black-start-up
capabilities, 869–888
capability of single steam group, 870–872
capability of steam group repowered by
gas turbine, 872–874
improvement, control system
modifications, 874–877
steam group repowered by gas turbine,
869–877
Restoration, system voltages, 719
Resynchronization process, 835
Robust and flexible power system, 829
Rotating excitation systems, 517
Rotating phasors, sinusoidal representation, 756
Rotating rectifier systems, 100
Rotor angle stability, 454
electromechanical oscillations, mechanical
analogy for, 458
illustration of a power transfer, 456
large-disturbance rotor angle stability/
transient stability, 461–462
power transferred from generator, 456
rotor angle oscillations, 459
small-disturbance/small-signal rotor angle
stability, 460–461
Rotor angle variations, 619, 620
curves, 650
for OMIB, 584
Rotor inductances, 22
Routh–Hurwitz conditions, 596
stability conditions, 590
Runge–Kutta methods, 605, 608–609, 648
rotor angle variation, 650
Sammis-Star line, 801
Sample and hold (S/H) process, 750
Sampled value (SV) service, 744
Scale-bridging line model, 912
Scale-bridging transients, computer simulation,
900–926
Scale-bridging transmission model, 913
Schur’s formula, 706, 711
Second-order dynamic model, 483
Selectivity, 740
Self-excited DC exciter, 97
Self starting-up processes, 640
Sensitivities analysis method
approach, 695–697
Sensitivity coefficients, 346
Sensitivity matrix, 690, 694, 696
Sensor, via supervision to actuator, 740
Sequence components model, 244
Sequence impedance of network components,
247–253
Sequence impedances, decoupling, 243
Sequential approach, 604
Sequential tripping, impact, 778
Serial connections, benefits, 746
Serial interface, 744
Shadowing method, illustration, 603
Shift frequency, 925
Short-circuit
applications, 277
short circuit fed from nonmeshed network,
280–282
short circuit in meshed network, 282–289
single-fed short circuit, 277–280
characteristics and consequences, 230–231
current components, calculation (See Short-
circuit current components, calculation)
currents
analysis, 229
characteristics, 232–236
initial symmetrical, 232
near generator, 235
reactance development, stages, 234
typical wave, 233
near-to-generator short circuit, 234
Short-circuit current components, calculation, 264
DC component of short-circuit current,
271–272
initial symmetrical short-circuit current, 264
peak, 269
phase-to-earth short circuit, 268–269
phase-to-phase short circuit, 267–268
three-phase short circuit, 264–267
peak short-circuit current, 269–271
steady-state short-circuit current, 273
three-phase short circuit in meshed
networks, 276–277
unbalanced short circuits, 277
symmetrical short-circuit breaking
current, 272
far-from-generator short circuit, 272
near-to-generator short circuit, 272–273
938 INDEX

11. Short-circuit currents calculation, 236
basic assumptions, 236–237
method of equivalent voltage source,
237–239
method of symmetrical components, 239
Simple Network Time Protocol (SNTP),
745
Single-machine equivalent (SIME) method,
582–587
criteria and degree of instability, 585–586
method formulation, 583–585
OMIB equivalent identification, 586–587
Single machine infinite bus (SMIB) system,
503–512, 574, 575
characteristic equation of system, 507
damping/braking power (torque), 510
decelerating power variations, 507
electromechanical loop, 508, 511
electromechanical oscillation,
characterization, 511
stabilizing and destabilizing effects, 510
synchronizing power (torque), 510
Single-output/input systems, feedback, 550
Single-phase autoreclosing, 777
Single-phase transformer, 911
Single protection functions
to system protection, 773–780
adaptive protection, 774
distributed protection, 774–775
general guide, 776–779
security/dependability, 779
single function and multifunctional relays,
773–774
wide area protection, 775–776
Single-shaft gas turbine block diagram,
890
Singularity, induced bifurcation, 706–707
Slip-ring motor, 115
Slow oscillation mode, 567
Smallest singular value technique
VSI global index, 708–711
Small shift poles, theory of
modal synthesis, 550–553
Small-signal angle stability, 477
dynamic matrix, 481–482
Small-signal voltage stability assessment,
711
Special protection system (SPS)
actions, 293
start-up steam flow circuit, 890
steam pressure value, 874
Speed governor, 543
Spinning reserve, 336
Stability limits, qualitative curves, 526
Stamping method, 907
Standard emergency power imbalances, 642
Star-delta transformation, 529
Start-up circuit, once-through boiler block
diagram, 891
Start-up control mode, block diagram, 892
Start-up procedure, 872
State-space model, 720
STATic COMpensator (STATCOM), 351
Static excitation systems, 101, 517
Static load characteristics, 661
Static synchronous series compensator
(SSSC), 351
Static VAr compensator (SVC), 717, 823
Stationary rectifier systems, 98
Steady-state stability methods, 690
to predict voltage collapse, 693
Steam collector pressure transients, 885
Steam system configurations, 148
control valves (CV), 149
corresponding mathematical models,
149–151
intercept valve (IV), 149
main steam stop valve (MSV), 148
reheat stop valve (RSV), 149
Steam turbine (ST), 864
block diagram, 891
governing systems for, 152–153
digital electrohydraulic control, 157
electrohydraulic control, 155–157
mechanical hydraulic control, 153, 154
mechanical speed governor, 154
model, 895
power generation, 165–166
rotor
angular speeds, 883
mechanical powers, 884
speed governing systems, 157–158
structure, 138
Step-up unit transformers model, 896
Substation automation (SA), 738
Superheaters (SH) storage, 894
Supplier–consumer relationship, 342
Swing equation (SE), 13, 619
integration, 648
numerical integration, 577
Switching-on of braking resistors, 535
Switching technologies, 355–362
alternative solutions, types, 360–362
load tap changer, used in conjuction with,
358
mechanical tap changers, 356–357
INDEX 939

12. Switching technologies (Continued )
off- and on-load designs, 355–356
RMV-II load tap changer, 359
static switched tap changers, 360
thyristor substitution of mechanical
contacts, 360
vacuum interrupters, 358
vacuum switched tap changers, 357–358
Symmetrical components, 758, 761
three phases, transformation, 758
Symmetrical phasors, 759
Symmetrical voltages, characteristics,
245–247
Synchronous compensators, 368, 533
Synchronous generators, 9, 55, 582, 648
components, 9
electromechanical model, 13
electromagnetic model, 17
operational parameters, 55–59
phasor diagram, with damper winding
neglected, 76, 77
standard parameters, 59–66
terminal short circuit, behavior, 46–55
typical values of parameters, 65
Synchronous machine model, 922
under balanced steady state, 43
block diagram organization, 918
network interfacing, 922
Synchronous reactance
d-axis, 68, 73
q-axis, 42, 73
System characteristics, 658–660
and load modeling, 658–667
System dynamics, block diagram of, 297
and governor droop, 298
and load damping, 297
System Protection System (SPS), 775
System restoration service, 854
System restoration stages
duration, tasks, typical problems,
866–868
System separation, mechanism, 843
Tangent vector, 700
Taylor series, 696
expansion, 577–579, 581, 609
Terminal voltage transducer, 105
Thermal generation units, 821
Thermal governor modeling, 311, 315–328
gas turbine model, 312–315
general steam system model, 311–312
Thermal power plants, 143, 894
black-start-up capabilities, 869–888
improvement, control system
modifications, 874–877
single steam group, 870–872
steam group repowered by gas turbine,
869–877
boiler and steam chest models, 145–148
conventional steam-fired thermal power
plant, 144
digital electrohydraulic control
(DEHC), 157
electrohydraulic control (EHC), 155–157
general steam system model, 151–152
governing systems, for steam turbines,
152–153
mechanical hydraulic control (MHC),
153–155
prime mover and energy supply system,
elements of, 144, 145
Rankine cycle, 144
speed governing systems, general model,
157–158
steam system configurations, 148–151
Th
evenin electromotive voltage, 727–728
Th
evenin’s theorem, 529, 530
Threshold value (TH), 689
Thyristor controlled series capacitors
(TCSC), 723
Thyristor-switched capacitor (TSC) reactors,
824
Time constants of synchronous machine, 61
Total transfer capacity (TTC), 472
Total vector error (TVE), 886
Tracked AC voltages, 901
Transfer function, amplitude
asymptotic plot, 554
Transformation equations, 759
Transformer differential protection, 769
Transient characteristics, 646
Transient energy function, 592
Transient short-circuit time constant, 75
Transient stability, 570–651
assessment, direct methods for, 572–603
direct methods based on Lyapunov’s
theory, 587–603
equal area criterion, 572–580
extended equal area criterion (EEAC),
580–582
single-machine equivalent (SIME)
method, 582–587
assessment, integration methods, 603–614
assessment of large electric power systems,
638–645
dynamic equivalents, 614–638
940 INDEX

13. Transmission capacity
net transfer capacity (NTC), 473
total transfer capacity (TTC), 472
Transmission lines, 912–918
equivalent circuit, 725
multiphase line model, 916–918
parameters, 924
single-phase line model, 912–916
and substations, 827–828
Transmission reliability margin (TRM), 805
Transmission substation equivalent circuit, 727
Transport Control Protocol (TCP), 744
Trapezoidal rule, 649, 910
Triangle approximation, 585
Triggering, 847
Turbines, 138
Francis turbine, 142
gas turbines, 139–140
hydraulic turbines, 140
impulse turbine, 140
James Francis’s turbine, 141
Kaplan propeller turbine, 143
propeller type turbine, 142
reaction turbines, 141
steam turbines, 138–139
turbine blading, 139
Two-machine systems, 595
Two-stage restoration plan, 866
Unbalanced phasors, 240
Underexcitation limiter (UEL), 108
Underfrequency load shedding, 336–338
Underfrequency protections, 842
Under load tap changer (ULTCs), 842
Unified power flow control (UPFC), 351
Universal pressure (UP) boiler, 870
Unsymmetrical fault calculations, 253–263
Variable-step methods, 604
V curves, 92, 93
Volosov’s algorithm, 637, 638
Voltage collapse, 702
criteria, overview, 688–695
mechanism, 842
Voltage control block (VCB), 112, 113, 477,
548
Voltage control loops, block diagram, 516
Voltage control strategy, 342
Voltage instability countermeasures, 716–733
Voltage instability mechanism, 674–688, 675,
676, 686
generated reactive power limitation effect,
683–686
interaction between electrical network and
load, 674–676
minimum voltage criteria, 686–688
on-load tap changer influence, 676–683
Voltage instability phenomenon, cause, 657
Voltage modal variations vector, 712
Voltage–reactive power support, 340
Voltage regulators, 102, 477, 821
Voltage response time, of excitation
system, 94
Voltage sensitivities, 672, 729
Voltage sensor, 745
Voltage stability, 462, 469, 657–733
load modeling, 660–667
dynamic models, 664–667
load characteristics, 660–662
static models, 662–664
long-term voltage stability, 465–466
short-term voltage stability, 465
small-disturbance voltage stability, 465, 658
static aspects, 667–674
operating points and zones, 670–674
steady-state solutions existence, 667–670
system characteristics, 658–660
voltage instability mechanisms, 674–688
generated reactive power limitation effect,
683–686
interaction between electrical network and
load, 674–676
minimum voltage criteria, 686–688
on-load tap changer influence, 676–683
Voltage stability assessment methods, 688–697,
689
bifurcations theory, aspects, 702–708
loading margin as global index, 698–701
reduced jacobian matrix, modal analysis,
711–716
sensitivities analysis method, local indices,
695–697
smallest singular value technique, VSI global
index, 708–711
voltage collapse criteria, overview, 688–695
Voltage stability index (VSI), 695, 711
Voltage stability limit, 723, 724
Voltage stability local indicator, 697
Volt/Hertz limiter model, 108, 109
V2–P2 system
characteristics, 668
reactive power compensation, 670
Wide-area control system (WACS), 804
Wide-area fault tolerant control system
(WAFTCS), 804, 810
INDEX 941

14. Wide-area measurement system (WAMS), 804,
849, 860
Wide-area monitoring and control systems
(WAMC), 849, 860
Wide area protection system (WAPS), 775, 780
physical setup, 775
Wide-area stability and voltage control system
(WACS), 849, 860
Wind energy, 179
converted into electrical energy,
phases, 179
wind energy converter, 180
Wind power
generation, characteristics, 181
aerodynamic profile of wind turbine’s
blades, 181–182
capacity factor, 184
mechanical power of wind turbine,
182–183
performance coefficient, 183–184
power curve, 183
Wind turbine generators (WTGs), 185
full-scale converter wind turbine, 218–223
modeling, 200
constant-speed wind turbine, 200–205
doubly fed induction generator wind
turbine system, 205–218
Wind turbine systems, 179–197
components, 179–180
nacelle, role of, 179–181
turbines concepts, 195
fixed-speed wind turbines, 195
variable-speed wind turbines, 195–197
Wound rotor, 115
942 INDEX