Kothari D.P., Nagrath I.J. Modern Power Systems Analysis
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@
!no.*
Full
load
ri,iection
technique
for
;
,,
improving
system
stability
500
Fusion
23
Gauss
elimination
623
constants)
Generator
(see
Synchronous
generator)
Generator
load
model
296
Generator
operating
cost
243
Geometric
mean
distance
(GMD)
mutual 55
self
55
Geometric
mean
radius
(GMR)
55
Governors,
characteristics
298
dead
band
32I
free operation
301
model
with
GRC
32I
Gradient
method
272
Graph
connected
189
linear
189
oriented
189
.
theory
189
Greenhouse
effect
16
Growth
of
installed
capacity
in
India
30
Growth
of
power
systems
in
India
29
HVDC
572
Hydraulic'amplifier
292
Hydroelectric
power
generation
l7
Hyperbolic'functions
142,
143
Ideal
transformer
99
Illconditioning
229, 545
Impedance
driving
point 187
transfer
187
Impedance
diagram
98
Incidence
matrix
(see
Bus
incidence
matrix)
Incident
waves
I44
lncremental
fuel
cost
244
Incremental
transmission
loss
260
Inductionmotors
122,344
lnductance
definition
45
due
to
internal
flux
46
mutual
46
of
composite
conductor
lines
54
of
double
circuit
threc-phase
line
66
of single
phase
two
wire
line
50
of
three-phase
lines
59
Inequality
constraints
on control
variables
274
Inertia
constant
436
Infinite
bus
Ll2
Infinite line
145
Inner
product 607
Input-output
curve
of
a unit
243
Interrupting
capacity
of
breakers
345
Interconnected
power systems
10
Interference
with
communication
circuits
6l-63
Irrverse
of matrix
6L3
Iterative
algorithm
for
NR
method
for
load
flow studies
218
Jacobian
matrix
2I4,272
elements
of
2I4,629
Kalman
filtering
approach
583
application
to
short
term
load
forecasting
583
Kimbark,
E.W.
508
Kinetic
energy
435
Kirchhoff's
current
law
(KCL)
186.
Kirchmayer,
Leon
K. 325
Kron,
G.
265
Kuhn Tucker
theorem
(theorY)
632
Lagrangian
function
279,
632
Lagrange
multiplier
219, 632
Laplace
transformation
294
Leakage
reactance
331
Leakance
129
Lcast
squares
estimation
532
the basic
solution
532
Linear
graph
(see
GraPh)
Line charging
current
(see
capacitance)
Link
190
Line-to-line
(LLXault
402
Line
compensation
L-. -^-:^^ ^^-^^l+^-- 1?O /'lOQ
uy ugrrrrJ
ualP4r/rturJ
r t
7,
1/v
by
shunt
capacitors
179,498
Load
angle
(see
also
power angle;
torque
angle)
1
10
bus 198
oontro
I
I
compcnsation
557
delta
connected
374
representation
122
symmerrical
(balanced)
lO7
unbalanced
394
Loading
capability
557
Load
factor
3
Load
flow problem
196
Load
flow
methods
comparison
of
229
continuation
599
decoupled
222
FDLF
223
Gauss
205
Gauss-Seidel204
Newton-Raphson
213
decoupled
223
rectangularversion
Z2I
Load
forecasting
9
Load
forecasting
techniques
estimation
of
average
and
trend
terms
577
estimation
of
periodic
components
581
incorporation
of
weather
variables
5g3
time
series
approach
592
autoregressive
models
Sgz
autoregressive
moving-average
models
582
Load
frequency
conrrol
(LFC)
and
economic
dispatch
control
305
decentralizedcontrol
323
digital
322
single
area
case
29I
two
area
307
with
cRC
320
Load
management
33
Load prediction
on-line
techniques
586
A Dflt A ^^)^r^ Eoz
Al\llYl.l1
rrluugllt
Joo
non-dynamic
model
596
time
varying
model
5g6
'
long
term
587
using
econometric
models
5g7
Long
transmission
line
equations
l4Z
cvaluntion
of
ABCD
con$tsnts
l42
hypcrbolic
form
of
l4Z
generation
260
assumptions
in
calculating
266,269
equation
for
267
Maintenance
32
Magnetohydrodynamic
(MHD)
generation
23
Magnetomotive
force
around
closed
path
47
MATLAB
examples
651
introduction
to
640
programs
652
programming
640
Matrices
addition
of
610
associative
law
6l
l
commutative
law
611
equality
of
610
multiplication
of
611
associative
law
6lI
distributive
law
611
singular
and
nonsingular
(see
also
matrix)
610
Matrix
definition
'607
diagonal
608
element
of
607
identity
609
null
608
symmetric
609
transpose
of
609
unit
508
zero
(see
a/so
Bus
admittance
matrix:
Bus
impedance
matrix;
motri^^^\ zAo
rrElr
rvgJrf
Ul.,O
Medium
transmission
line
137
Method
of
images
g3
Methods
of
voltage
control
173
Mini
hydel
plants
18
Micro
hydel
plants
lg
Model
generator
load
42
of speed
governing
system
2g3
turbine
Z9S
Modil'icd
Euler's
method
for
stability
analysis
495
Losses
as
function
of
Modification
of Z for network
BUS
changbs
360
Mutual
(transfer)
admittance
I87
Mutual
coupling
46
National
Thermal Power Corporation
(NTPC)
4r
Negative sequence
components
370
Negative
sequence
impedance
383
of
passive
elements 383
of
synchronous
machines 386
table
334
of
transformers
390
of transmission
lines 390
Negative
sequence
networks
in fault analysis
399
examples
409
of
power
systems
386
of unloaded
generators
388
of Zr*
elements
417
Network
branch
190
model
formulation
for SLFE
185
node 90
observability
545,
549
primitive
191
Nodes
190
Node
elimination
technique
for stability
study
444
Nominal-
t
circuit of
medium
transmission
line
138
Nominal-T
representation
of medium
transmission
linc
137
Non-linear
programming
problem
632
Non-linear
programming
technique
279
Nuclear
reactors
2I
Objective
function
270, 27I,
275
Off-nominal
turn
(tap)
ratio or
off-nominal
tap
setting
234
One
linc
diugrtnr
98
On-line
-+^+^ ^.+1.-^+i^- <AA
Jlctlly\,DLlllldllutl
J1a
techniques
for
non-stationary
load
prediction
586
ARMA
models
5E6
rime
r-ar1-ing mcxlel
-s36
Apaaror
a 370
Wn
l cstrrdla
310
ft'dmrl
hrsd
fltrrr'
srrludon
:?0
Optimal
(two
area) load frequency
control 310
Optimal
ordering
I89, 627
Cptimal
operation
of
generators
on a bus
Optimal
operating
strategy
242
Optimal
reactive
power
flow
problem
272
Optimal
scheduling
of hydrothermal
,
system
276
Optimal
unit commitment
250
Optimal
security
constrained
unit
commitment
256
Optimum
generation scheduling
259
Optimum
real
power
dispatch
(sZe
optimum
generation
scheduling)
Parameter
estimation
552
Parameters
of overhead
lines
45
Patton, A.D.
254,256
Penalty
factor
260,275
Penalty
function
270,
275
Percent
value
99
Per
unit system
change of base
101
definitioir
of
99
selection of
base
100
Performance
chart
of synchronous
machines
119
Performance
index
GI)
316
Phase constants
143
Phase
shift in star-delta
transformers
377
Planning
commission
4L
z'-equivalent
for long line
152
for medium
length
line 138
zrmodel for
transformer
with
off-nominal
turns ratio
234
Plant
capacity tactor
4
Plnnt
use
factor
4
Photovoltaic
generation
2l
Pilct vulve
292
Point-by-point
solution
of swing
equation
481
Positive sequence
components 370
Positive
sequence
impedance
of
pa-ssive
elements
i8l
of
syfrrwus
nrchirc,s
3E3
table
334
of transformer
of
transmission
Positive sequence
in fault studies
390
lines 389
networks
398
of Zsu5 elements
417
Power
accelerating
46?
angle
437
_
apparent 106
by
symmetric components
374
complex
105
factor 105,
1 12, Il5
flow through a
transmission
line 158
in three-phase
circuits
Il2
maximum transmitted
I59
real and
reactive
(see
also Reactor
power;
Real
power
)
106
Power
angle curve 1I5,444
Power system
compensation
556
engineer
39
state
estimation 538
structure
10
studies 39
Primitive impedance
(admittance)
matrix I92
Primitive network
(see
Network)
I9l
Propagationconstant
l4l
Proportional
plus
integral
control 303
Proximity effect
7 L
Pumped storage
scheme
18
Qurdrrturc
axis
synchronous
reactance
I17
Rcuctivc
powcr
106
control of flow:
by machine
excitation ll3,
I14
injection
of 175
<ll' synchronous
machincs
with
ovcr
cxcitutiou
l
14
with
under
excitation
114
-- -l--r! --- ,r^:-^ ^,,:rl^ ....1r--.^- l--,..l 144
t-ctauunsntp
wil,u vurruBc rcvsl L I J
sign of l06
Real
power
106
f'ormulas for 159, 160
in sr nchrtrn(lus
nt&('hin('s I l-5. I l9
Real
dme
computer
control of
Ww'q
$-r-Silems
6Y
direct
axis
118.
121
leakage, of transformers
101
of bundled conductors
inductive 67
quadrature
axis Ll7
subtransient
332
synchronous
111,332
transient
332
Reactance diagram
98
Reactive load forecast
587
Reclosure
474
Reference bus 198
Reflected
waves
144
Regulating transformers
(s
ee Transformer,
regulating)
Regulating constant
(R)
294
Regulation
of voltage
130
Reheat turbine model 295
Reliability
considerations
for
economic
dispatch 253
Reluctance
power
.
118
Repair rate 255
Reserve 254
\
Resistance of lines 7O
Rotating
VAR
generator
176
Rigid limits 275
Salient
pole
synchrono-us
generator
ll7
Saturated reactor 563
SCADA
634
Scalar
product
607
Sctrlnr and
v0ctor
functions
614
derivatives
of 614
Security analysis 256
Scnsitivity luctors
generation
shift factors
520
line
outage
distribution
factors
520
Seqtience
impedances
lirr
synchronous machines
3ti5
ol passive
elements
383
of
transformers 386
of transmission
lincs
3E5
table lbr
typical
values
of
334
Sequence
impedances
and
sequence networks
ul
ptr$
E'r s\stL'nl
iss
of syrrchrowus
mar.+tiffi
3t5
of
transformers
390
Reactance
i
lndex
lndex
Sequence
netviork
connections
for
unsymmetrical
faults
4OO,
403,4A5
Sequen,:e
networks
construction
of
sequence
networks
Short
circuit
current
limiters
499
Short
circuit
megavoltamperes
345
Short
circuit
ratio
(SCR)
498
Short
term
load
forecasting
estimating
of stochastic
component
583
innovation
model
approach
588
using
Kalman
filtering
approach
583
using
the periodic
load
model
581
Short
transmission
line
equations
12,9
Short
transmission
line
equivalent
circuit
129
Shunt
capacitors
effect
upon
voltage
regulation
132
for
power
factor
correction
133
for
voltage
control
175
Simulink
640
basics
648
example
648
Single
line-ro-ground
(LG)
fault
399
Skin effect
71
Slack
bus
198
Soft
limit
275
Solid
LG
fault
407
Sparse
matrix
188
Sparsity
188,
I
89,
623
Speed
changer
293
Speed governing
system
293
Speed
regulation
constant
(see
regulation
constant)
Spinning
reserve
245,
254
Stabiliry
analysis
for
multimachine
system
497
definition
433
dynamic
434
study
461
steady
state 454
transient,
defined
434
clearing
angle
466
clearing
time
466
critical
clearing
angle
467
critical
clearing
time
467
equal
area
criterion
461
point-by-point
merhod
4gl
some
factois
affecting
496
voltage
591
Stability
limit
steady
srate
456
Start
up
cost
250
Statcbm
562
State
electricity
boards
303
State
estimation
external
system
equivalencing
545
of
power
systems
538
the
injections
oniy
algorithm
540
the
line
only
algorithm
543
nonlinear
measurements
535
problems
of illconditioning
545
stochastic
component
583
State
variable
model
3lz
State
variables
199,312,
494
Static
load
flow equarions (SLFE)
198
Static
reserve
capacity
254
Static
VAR generator
175,
565
Static
VAR
sysrem
562,565
State-vector
198
Steady
stare
srabiliry
454-
Step-by-step
fofmulation
of bus
impedance
matrix
addition
of
a
branch
357
addition
of
a link
359
Stiffness
of
sy,nchroneus
machine
455
Steepest
descent
method
(see
Gradient
method)
Suboptimal
conrrol
318
Substation
bulk powcr
13
distribution
l3
Superconductingmachine
l4
Surge
impbdance (see
also
characteristic
impedance)
145
SVC
(Static
var
compensator)
562.565
Swing
bus
(see
Slack
bus)
Swing
curve
459,495
determination
using
modified
Euler's
marhn-| ,{ n<
tllvLtlvu
a7J
step-by-step
determination
of
481
Swing
equation
438,
480, 494
state
variable
form
495
Switching
single
pole
500
three
pole
500
Symmetric
marrix
609
Symmetrical
comPonets
definition
of
369
of
unsymmetrical
Phasors
372
power
in
terms
of
374
algorithm
for
large
sYstems
ustng
zBUs 350
selection
of
circuit
breakers
344
short
circuit
current
computation
through
the
Thevenin's
theorem
341
short
circuit
of
a synchronous
machine
on load
339
on
no
load 330
transient
on
a
transmission
line
320
Symmetrical
short
circuit
current
329,
331
Synchronising
power
coefficient
I
18, 308,
455
Synchronous
reactance
33
I
Synchronous
machine
armature
reaction
108
construction
108
dynamics
of
435
equivalent
circuit
lll
excitation
1 13
inertia
constants
of
435
leakage
reactance
331
ioad
angle
of
I
10
operating
(performance)
chart
ll9
-'
n(qr.
of
values
of
sequence
impedances
of
385
per
unit
reactance,
table
334
phasor
diagrams
112
T
circuit
of
medium
length
line
137
Taylor
series
expansion
213
TCUL
(tap
changing
under
load)
(see
transformers)
Thevenin's
theorem
in calculation
of
three-phase
fault
currents
341,
35O
in
caleulation
of unsymmetrical
fault
currents
416
Three
phase
circuits
power in
lO7
voltage and
current
in
107
Three
phase faults
(see
Faults)
Thyristor
controlled
braking
resistor
577.
Thyristor
controlled
phase
shifting
transformer
(TCPST)
572
Thyristor
controlled
reactor
(TCR)
563
Thyristor
controlled
voltage
regulator
t.T.rl!.f D \ {?t
\
r L
v r\,, J
t -
TSC)
564
Tie
line
power 307
Tolerance
206
Torque
angle
(see
also
Power
angle)
438
Tracking
state
estimation
of
power
systems
544
Transformers
control
(see
regulating
below)
231
off-norninal
tapes
234
per unit representation
of lOl
phase
shift
in
Y-A 377
phase
shifting
232
polarity markings
377
regulating
232
equivalent
circuit of
234
for
magnitude
control
232
for
phase
angle
control
233
sequence
impedances
of
385
TCUL
177.232
Triangularisation
and back
\
substitution
623
Transient
reactance
332
Transient
stability
definition
of
433
digital
computer
solution
method
610
equal
area
criterion
461
Euler
modified
method
495
multigeneratorcase
487
numcrical
solution
of swing
cquation
for single
generator case
480
Transmissioncapability
12
Transmission
level
l3
Transmission
loss
(see
Losses
as function
of
plant
generation)
'
Transmission
loss
formula
261
derivation
of
264
Transposition
of transmission
lines
60
tn lralanna nqnqnif
qnne
fl, I
lv
vslsrrvv
to
balance
inductance
6l
Tree 190
Tuned
power lines 15t
Turbine
fast
valving
499
Turbine
model
295
Turbine
speed
governing
system
292
Two-area
load
frequency
control
307
Two
reaction
theory
Il7
Unit
comrnitment
250
branch
and
bound
technique
250,
252
dynamic
programming
method
Z5l
reliability
(security)
considerations
253
securityconstrained
256
stait-up
consideration
Z5g
Unit
matrix
609
Unsyrirmetrical
faults
(see
also
Faults)
analysis
u,sing
Zsu5
rhbthod
416
symmetriCal
component
analysis
of
398
Use
of
computers
and
microprocessors
in power
systems',
39
VAR
(see
also
Reactive
power)
Variance
582
Vector
column
607
control
(see
control
vector)
disturbance
27l
equation
271
null
605
of
fixed parameters
Ig9
orthogonal
607
row
607
state
(see
State
vector)
sum
606
unit
606
Velocity
of
propagation
146
Voltage
collapse
528,
592
prevention
of
526,593,
600
control
by
transformers
i'77
control
by VAR
injecrion
I75
eff'ect
of capacitors
on
l3Z,
175
equations:
for
long
line
142
for
medium
transmission
lines
137
-t39
for
short
transmission
lines
l/g
stability
524,
592
methods
for
improVing
5Zg
Voltage
controlled
bus
198
Voltage
regulation
130
Voltage
stability
591
analysis
592,
5gl
criteria
of
596
with
IdVDC
links
599
Watts
(see qlso
Real power)
106
Wavelength
145
Waves,
incident
and
reflected
144,
I45
Weighted
least
squares
estimation
533
Weighting
marrix
534
Y"r,
(see
Bus
admittance
matrix)
Y-A
transfonners
96
phase
shift
in
377
single-phase
equivalent
of
96
zero
sequence
networ[s
of
397
Z^.,^
(see
Bus
impedance
matrix)
BUS
./'
Zero
sequence
components
371
Zero
sequence
impedance
of circuit
elements
384
of
synchronous
machines
384
table'
334
of
transformers
387
of
transmission
lines
3g5
Zero
sequence
networks
in
fault
studies
399
of delta
connected
loads
389
of
transformers
387
of
unloaded
generators
384
of
Y-connecred
loads
397
Index