Indonesian J
ournal of Ele
c
trical Engin
eering and
Computer Sci
e
nce
Vol. 2, No. 3,
Jun
e
201
6, pp. 501 ~ 50
9
DOI: 10.115
9
1
/ijeecs.v2.i3.pp50
1-5
0
9
501
Re
cei
v
ed Fe
brua
ry 18, 20
16; Re
vised
May 7, 201
6; Acce
pted Ma
y 19, 201
6
Dynamic Stability Analysis of Generator with Power
System Stabilizers Using Matlab Simulink
Mariz
a
n Sulaiman
1
, Ha
y
f
a
a
Mohamme
d Huss
ein*
2
, Rosli Omar
3
, Zulhis
y
a
m
Salleh
4
F
a
cult
y
of Elec
trical Eng
i
ne
eri
ng, Univ
ersiti T
e
knik
al Mal
a
ysi
a
Melak
a
Han
g
T
uah Ja
ya, 7610
0 Dur
i
a
n
T
unggal, Mel
a
ka, Mala
ys
ia
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: marizan@
ute
m
.edu.m
y
1
, ha
yfa
a19
70@
ya
h
oo.com
2
A
b
st
r
a
ct
The dy
nam
i
cs
in s
i
ngle
m
a
chine
been connected to
an infinite power syst
em
bus
is analy
z
ed
in
this pap
er. This analysis re
q
u
ires certai
n a
m
o
unt of
system mod
e
li
ng le
vel. The ma
in compo
nents of
the
system
m
o
dels are excitation system
, synchronous
m
a
c
h
in
e and the
Power System Stabili
z
e
r. T
he
Simuli
nk /Matlab are us
ed
as the progr
a
m
mi
ng to
o
l
for analy
z
i
n
g thi
s
system perf
o
rmanc
e. Desi
g
n
opti
m
i
z
at
ion
ar
obust PSS
b
a
s
ed
on
ge
netic
al
gorith
m
(GA) ap
proac
h
ha
s be
en
i
m
pr
ov
ement. A
pro
p
er
design
is required for this
power system
stabil
i
z
er (
PSS) perfor
m
ance using the particle sw
ar
m
opti
m
i
z
at
ion
(P
SO) to archi
e
v
e
this. T
h
e
n
t
he i
m
pl
eme
n
t
ed
o
f
th
e mo
del
a
n
d
re
sp
on
se
o
f
th
e d
y
nam
i
c
system is be
en
analy
z
e
d
. The
desig
ned w
i
th
out PSS show
ed an u
nacc
e
p
t
able syste
m
respo
n
se sinc
e a
s
shown in the
simulation res
u
lts, system r
e
spon
se with
PSS prov
en t
o
have improv
ements
and P
SS
succeeding in
stabili
z
i
ng
an
unstable system
. Therefor
e th
is leads to st
ability of the performanc
e of the
gen
erator.
Ke
y
w
ords
: dy
nam
i
c stability,
pow
er system
stabili
z
e
r, genetic algor
ithm
(GA), particle sw
arm
opti
m
i
z
a
t
i
on
Copy
right
©
2016 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
Powe
r syste
m
stabilizers
has b
een co
mmonly
used
to provide ad
ditional su
ppl
ementa
r
y
control sig
nal
s into the AVR dampi
ng o
u
t the o
scillat
i
ons of ele
c
tromec
hani
cal
of generators i
n
the power
systems. The CPSS (conventional
PSS) is general
ly des
igned based
on “linear
model
of syst
em” fo
r
spe
c
i
f
ic ope
ratin
g
point.
Tho
u
g
h
, most
powe
r
sy
stem
s a
r
e funda
ment
ally
nonlin
ear an
d chan
ge
s a
t
operating
point much
durin
g a “da
ily cycle”. Hence, the CPSS
perfo
rman
ce
may be
significa
ntly degra
ded
un
der va
riation
s
cau
s
ed
b
y
vibrant ti
me
cha
r
a
c
teri
stics an
d n
onlin
e
a
r of th
e po
wer
syst
em
ele
m
ents. T
o
ob
tain a hi
gh-p
e
rformi
ng PS
S
for wide
ra
ng
es of con
d
itions
of ope
rat
i
ng,
so
me
co
ntrol strate
gi
es are
b
een
introdu
ce
d.
T
h
e
appli
c
ation o
f
adaptive control techni
que
s
and robu
st contro
l methods a
nd have be
en
mentioned for PSS des
ign. Due to
the requirement of informat
ion
on s
y
s
t
em
s
t
ates
or the
func
tion t
r
ans
f
er form in the PSS des
i
gning, it
is
rather
diffic
u
lt
finding
a dy
namic lineariz
e
d
model
for the
syste
m
. Fu
rt
herm
o
re,
in
real
system
s
of ele
c
tri
c
p
o
wer
who
s
e
time p
a
ra
mete
rs
vary, the onli
ne a
pplicatio
n of id
entifier for t
he te
chniqu
es of a
daption
in
which
the
syst
em
para
m
eters
a
r
e b
een
esti
mated, might
be difficult
a
nd the fixed
controlle
r bei
ng mo
re fe
asible
and
pro
per for the
p
r
a
c
tical implem
ent
ations.
Lo
w f
r
equ
en
cy an
d sm
all ma
g
n
itude
oscilla
tions
often remained for an ex
tensiv
e time in power
systems. T
h
es
e
types of oscillations were
controlled
by
co
ntrollin
g t
he ex
citation
sig
nal
of a
u
t
omatic volta
ge
reg
u
lator
of the
gene
rator.
The tuning and location
of PSS
were found to be important pa
ram
e
ters to suppress low
frequency
oscillations [1],[2]. Auto
matic voltage
regul
a
tors have
been
utilized i
n
power
syst
ems
sin
c
e 1
960’
s.
Oscillation
at low freque
nci
e
s of
0.2 to
2.
5 Hz may o
ccur in th
e sy
stem du
e to la
rge
disturban
ce
s
like p
h
a
s
e-to
-groun
d fault
s
in a tr
an
smissi
on lin
e. Powe
r sy
ste
m
stabili
ze
rs are
use
d
in the addition of da
mp to the system th
roug
h modulatio
n of excitation sy
stem by addi
ng a
comp
one
nt to the electri
c
al
torque that p
hases
with the spe
ed devi
a
tion [3].
The PSS being a device that provides ad
ded
supplementary l
oops control
to the
automatic vol
t
age regul
ato
r
s
syste
m
an
d/or that
of the
system
of turbin
e g
o
ve
rning
ge
nerating
unit. This is
con
s
id
ere
d
the most co
mmon metho
d
s of enha
n
c
ing for b
o
th
the small si
gnal
stability (“steady-state”)
and the large-signal
stability (“tr
ansi
ent”). PSS are
oftenly used as
economi
c
and effective damping means of such
oscil
l
ations [4]. The PSS is connected directly
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ISSN: 25
02-4
752
IJEECS
Vol.
2, No. 3, Jun
e
2016 : 501
– 509
502
to the AVR f
o
r
synchronous g
enerators in
addition; the fund
erm
ental
aim of the
PSS-AVR
control ex
cita
tion configu
r
a
t
ion is
providi
ng vo
ltage
re
gulation
and
dampin
g
. So
me techniq
ues
are been
proposed in order tune
and
desi
gn
sche
mes of PSS–AVR properly [5]. Basically
the
function
of p
o
we
r
system
stabili
ze
r i
s
extending
th
e sta
b
ility lim
its
of gene
rat
o
r excitation
by
modulatin
g to
provid
e d
a
m
p
ing fo
r o
s
cill
ations of
the machi
ne roto
rs syn
c
h
r
on
o
u
s
i
n
relation
to
anothe
r. Furt
herm
o
re th
e
advanceme
n
t in the
bio-in
spi
r
ed a
nd evolution
techniq
u
e
s
like
Particle
-Swarm Optimi
zati
on (PS
O
)
an
d Ge
netic
Alg
o
rithm
s
(GA)
have le
ad to
a ne
w
app
ro
ach
in solvingco
m
plex optimi
z
ation
proble
m
s. Th
e a
d
v
antage
of u
s
i
ng GA te
ch
ni
que
s i
s
that i
t
is
indep
ende
nt of the compl
e
xity of
the performan
ce in
d
e
x con
s
ide
r
e
d
. Typically these oscillati
ons
con
c
e
r
n ari
s
e approximately in the frequen
cy ran
g
e
s
of 0.2 to
2.5 Hz, also these o
scill
ations
might limit the tran
smition
ability for th
e po
wer ina
d
equate
dampi
ng [6]. The a
dded
sig
nal
s
are
gene
rally
d
e
r
ived
from deviation excitation sy
st
em, speed
of deviation
or the
po
wer
acceleration.
Thi
s
i
s
archeived by i
n
serting th
e “st
abilizing signal
into
the excitation
syst
em
voltage reference
summi
n
g
poi
nt jun
c
tion. The
devi
c
e
arran
gem
ent is to p
r
ov
ide the
sig
n
a
l
is
calle
d po
we
r
system
stabili
zer”. Fu
rthe
rmore, tuni
ng
of scaling fa
ct
ors is ve
ry im
portant
becau
se
a ch
ang
e of
scaling fa
ct
ors
ca
n affe
ct the st
a
b
ility, oscillatio
n
and d
a
mpin
g of the sy
ste
m
[7,[8].The parameter tuning of the PSS has
been
know to be
a complex exerc
i
s
e
becoming
the
subj
ect of
m
any re
se
arch
es [5]. In
co
nvent
ional P
SS tuning fo
r large
po
we
r sy
stem
s th
e
methodol
ogie
s
a
r
e in
ade
quate,
since
they produ
ce occa
sion
ally
adverse
effects on othe
r
oscillatory
m
odes for the dampi
ng, especially
the
once associated wi
th exciters and t
he
oscillation
s
shaft torsional.
Using
re
du
ced o
r
de
r m
o
d
e
ls of
the po
wer
sy
stem could sig
n
ifica
n
tly
spe
ed-up the
pro
c
e
ss of P
SS tuning [9].
2. Rese
arch
Metho
d
In this work, the re
sea
r
ch methodol
ogy will be discu
s
sed in de
pth in the followi
ng su
b-
se
ct
ion
s
.
2.1. Stabiliz
ing Signal
Signal
wa
sho
u
t be
comin
g
a filter hig
h
-p
as
s p
r
eventin
g the
steady
cha
nge i
n
sp
eed from
being m
odifie
d
by the volta
ge field. Th
e
wa
sho
u
t time value of the
“co
n
sta
n
t
T
w
” sho
u
ld al
wa
y
s
be high e
n
ough all
o
win
g
asso
ciated
“sign
a
ls
wi
th oscill
ation
s
sp
eed
” in
rotor pa
ssi
n
g
unchan
ged. The
T
w
value may not critical a
nd
ca
n be a
n
ywh
e
re
within th
e ran
ge 1 to
20
se
con
d
s fro
m
the "wash
o
u
t
function," viewp
o
int.
The
main con
c
e
r
n is that, it should b
e
ma
de
long eno
ugh
in order to pass the “sta
bilizing
si
gn
a
l
s at frequen
cie
s
of relatively unchan
g
e
d
intere
st”, b
u
t
again
not
so
l
ong th
at coul
d result
to u
n
desi
r
abl
e volt
age
gen
erato
r
ex
cursio
ns
due
to
stabili
ze
r a
c
tion
s
d
u
rin
g
the co
nditio
n
s of sy
stem
-islan
ding.
Id
e
a
lly,
the stabi
lizer shoul
d no
t
respon
d to t
he
system
-wi
de freque
ncy
variation
s
.
F
o
r “the
l
o
cal mode oscillat
i
ons” within
t
h
e
rang
es 0.8 t
o
2.0 Hz, th
e wa
sho
u
t of 1.5 seco
nd
s is con
s
ide
r
ed satisfa
c
t
o
ry. From lo
w-
freque
ncy vie
w
poi
nt of osci
llations inte
r area, a “c
o
n
st
ant wa
sho
u
t time of 10 se
cond
s or hig
h
e
r”
is con
s
ide
r
ed
desi
r
a
b
le, si
nce th
e
con
s
tants lo
we
r-ti
m
e re
sult i
n
the sig
n
ifica
n
t
phase le
ad
at
lower frequencies.
Unless thi
s
i
s
compensated f
o
r
elsewher
e, it will
reduce the torque
comp
one
nt synchroni
zing
at the freque
ncie
s of in
ter area. Th
e e
ffect of desy
n
ch
roni
zin
g
is
harmful
to transient stability of in
ter
area as it causes the
area
s
swingi
ng further apart foll
owing
the disturban
ce[10],[11].
2.2. Infinite Bus to Single Machine
Connec
t
ion
The synchro
n
ous gen
erato
r
expe
rien
ce and
the
pe
rio
d
of oscillato
ry could
be
cl
assified
into the
pe
rio
d
of tran
sient
and
dyn
a
mic pe
riod
o
r
ste
ady state.
From the
a
s
su
mption thi
s
st
ator
voltage linea
r “equatio
n of
′
” that is prop
ortional to the main linka
g
e
flux windin
g
could b
e
found
[4, 7].
∆
′
1
′
∆
1
′
∆
(1)
∆
∆
∆
′
(2)
′
′
(3)
Evaluation Warning : The document was created with Spire.PDF for Python.
IJEECS
ISSN:
2502-4
752
Dynam
ic Stability Analysi
s
of Generator with PSS Usi
ng …
(Ha
y
faa
Moham
m
ed
Hu
ssein)
503
Whe
r
e the
is gap stato
r
air RMS voltage
, synch
r
ono
u
s
gen
erato
r
“li
neari
z
e
d
term
inal voltage”
∆
is given by:
∆
∆
∆
′
(4)
Note that the c
o
ns
tants
K
1
,
K
2
,
K
3
,
K
4
,
K
5
and
K
6
are been d
epe
ndent on the
system
operation con
d
itions a
nd p
a
ram
e
ter.
G
e
nerally,
K
1
,
K
2
,
K
3
and
K
6
are be
en po
si
tive, wherea
s
K
4
is al
ways
positive except
R
e
is high.
Nonethel
ess,
K
5
is a po
sitive for
the
lo
w an
d the m
edium
loadin
g
and t
he extern
al i
m
peda
nce. Neverthele
s
s, if
loading a
nd
external im
pe
dan
ce b
e
com
e
s
high
K
5
will becom
e
Ne
gat
ive.
∆
′
1
′
∆
1
∆
(5)
∆
1
2
∆
∆
∆
(6)
∆
∆
∆
(7)
whe
r
e the
is Lapla
c
e Op
erato
r
. The system of exci
tation repre
s
entation is sh
own in Figure1
[4, 7, 10]
Figure 1.
Simple excitation
system mo
de
l
The linea
ri
ze
d equatio
n of the excitation
syst
em is giv
en by the followin
g
equati
on [4]:
∆
∆
∆
(8)
2.2.1. Sy
nchronous Ma
c
h
ine Model
The Synch
r
o
nou
s ma
chin
e model
s, wh
ich a
r
e con
s
i
s
ting of de
ca
y loop flux, and torq
ue
angle lo
op are being impl
e
m
ented in Ma
tlab/ Simulink as sh
own in Figure 2 [4, 7].
The ope
ratin
g
con
d
ition is
listed bel
ow [
4
], where K5
< 0 ope
rating
conditio
n
:
K1= 0.983
1, K2= 1.092, K
3
= 0.38
64 K4
= 1.474
6, K5= - 0.11
03 K6
= 0.447
7, H=6 se
c,
DT = 5
se
c, TE = 0.25, KE
= 0.075
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 25
02-4
752
IJEECS
Vol.
2, No. 3, Jun
e
2016 : 501
– 509
504
Figure 2.
Matlab/Simulin
k model for Synch
r
on
ou
s m
a
chi
n
e
2.2.2. Excita
tion Sy
stem
Excitation
syste
m
is
de
scrib
ed
b
y
Equation (4
) and Equ
a
tio
n
(8). Th
ese impleme
n
tent
ed
Equation
s
are done in Mat
l
ab / Simulink as sh
own in Figure 3.
Figure 3. Excitation sy
ste
m
of simulin
k layout [4]
2.3. Implementation of
Pow
e
r S
y
stem
Stabiliz
er
The PSS model present
ed in Equation (9) is
implemented in Matlab / Si
mulink as
s
h
own in Figure
4, been t
he in
put s
i
gnal of deviation to PSS speed and the V
PSS output s
i
gnal
being the auxiliary signal fo
r the excitation system.
.
10
10
1
.
1.
1
2.
1
.
3
.
1
4
.
1
(9)
Figure 4. Implementation of PSS in s
i
mulink
[4]
Table 1
shows PSS
param
eters
been designed by the GA (Geneti
c Algorithm
). A PSO
is being used in this paper
in order to tune parameters of
PSS as described in previous
sections, presenting the PSS param
eters been designed by a PSO.
Evaluation Warning : The document was created with Spire.PDF for Python.
IJEECS
ISSN:
2502-4
752
Dynam
ic Stability Analysi
s
of Generator with PSS Usi
ng …
(Ha
y
faa
Moham
m
ed
Hu
ssein)
505
Table 1. PSS parameters
des
ign [4]
paramete
r
s
T
1
T
2
T
3
T
4
K
PS
S
T
R
GA
1.4557
0.6143
1.0083
0.1005
2.1783
0.02
PSO 0.3730
0.1096
0.7910
0.0819
7.1144
0.02
2.3.1. Simula
tion Model for Sy
nchronous Machin
e
The si
mulati
on of dynam
ic sta
b
ility analysi
s
is
ba
sed
on reference [4]. Figure 5
(
a
)
sho
w
s Synch
r
ono
us M
a
chi
ne Mod
e
l wit
h
Excitati
on
System Automatic Voltage
Regul
ator
(A
VR)
without
connected PSS to show An
gular Speed, Angular Position
,
Torque V
a
riat
ion and V
o
ltage
Variation
whe
n
con
n
e
c
ted to Single Ma
chine Infinite Bus (SMIB).
Figure 5(a). Simulin
k
model for
syn
c
hrono
us m
a
chin
e with ex
citation sy
ste
m
automatic
voltage regul
a
tor (AVR) wi
thout PSS
Figure 5(b)
shows Synchr
onous Machine M
odel
conn
ected
wi
th PSS desi
gned
by
Geneti
c
Algorithm (GA) for
simulatio
n
test of
Angular Speed, Angul
a
r
Position, To
rque Va
riatio
n
and Voltage
Variation
whe
n
con
n
e
c
ted to Single Ma
chine Infinite Bus (SMIB).
Figure 5 (b). Simulink model
for synchronous ma
chine model connected
with PSS and GA
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IJEECS
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e
2016 : 501
– 509
506
Figure 5(c)
shows Synchron
ous Machine M
odel
with
connect
ed PSS desi
gned by
Particle S
w
a
r
m Optimization (PSO
) to
sho
w
Ang
u
la
r Speed, Ang
u
lar Po
sition,
Torq
ue Va
ri
ation
and Voltage
Variation
whe
n
con
n
e
c
ted to Single Ma
chine Infinite Bus (SMIB).
Figure 5(c). S
i
mulink m
odel
for synchro
n
ous
ma
chi
ne
model conn
e
c
ted with PS
S and PSO
3. Results a
nd Analy
s
is
Figure 6 sho
w
s va
riation
of the angul
a
r
po
si
tion an
d the ang
ular spee
d in
cre
a
sin
g
the
torque
for ne
gative of K5.
This sy
stem
has be
co
m
e
unsta
ble;
h
o
wever,
the
tra
n
sie
n
ts have also
become
more with
the
n
egative K5
whe
r
ea
s t
h
e
po
sition
of the hi
ghe
r a
n
gular is attai
ned
without the PSS “Power S
y
stem Stabilizer”.
Figure 6.
Simulation re
sult
of angula
r
sp
eed, ang
ular
posit
io
n and t
o
rqu
e
for the
system
witho
u
t
PSS for 10% change in
step input
Figure 7 Shows the
com
p
arison
of angular
sp
eed
i
n
three cases without
PSS, with
PSS
desi
gned by GA and with
PSS desi
gned by PSO with WB=3.14.
Evaluation Warning : The document was created with Spire.PDF for Python.
IJEECS
ISSN:
2502-4
752
Dynam
ic Stability Analysi
s
of Generator with PSS Usi
ng …
(Ha
y
faa
Moham
m
ed
Hu
ssein)
507
Figure 7. Simulation re
sult
angul
ar
spee
d for 10% ch
ange in
step i
nput
Figure 8. Shows
the c
o
mparis
on of angular pos
i
tion in three c
a
ses
without PSS, wit
h
PSS designed by GA and with PSS designed by PSO with WB
=3.
14.
Figure 8.
Simulation re
sult
angul
ar po
siti
on for 10% chang
e in step
input
Figure 9 Shows the
com
p
arison of torque vari
ation in three
cases without PSS, with
PSS designed by GA and with PSS designed by PSO with WB
=3.
14.
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02-4
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IJEECS
Vol.
2, No. 3, Jun
e
2016 : 501
– 509
508
Figure 9.
Simulation re
sult
torque va
riati
on for 10% chang
e in step
input
Figure 10. Shows the com
pari
s
on of voltage va
riation in three cases without PSS, with
PSS designed by GA and with PSS designed by PSO with WB
=3.
14.
Figure 10. Simulation resu
lt voltage variation for 10%
chan
ge in st
ep input
4. Conclusio
n
Powe
r
syste
m
s a
r
e
bee
n
subj
ecte
d to
a variety of d
i
sturb
a
n
c
e
s
e
x
isting
such
as
slight
load
cha
nge
s that coul
d b
e
of effect to
the e
fficien
cy mostly lead
ing to un
stab
lilityof the entire
system.
Th
e disturban
ce
s can co
ul
d a
s
a re
sult of l
o
w fre
que
nci
e
s of u
nde
sired o
scill
ation
s
sin
c
e thi
s
m
o
stly affects the qua
ntity of t
he po
wer b
een tran
sferred th
ro
u
gh the lin
es of
transmission l
eading to
external
te
nsions to the m
e
chanical
shaft. In
order to
avoid thi
s
situati
on
the PSS is added to AVR
enhanci
ng the stability of t
he dynamic
ranges
and di
sturbance of
the
first few
cycl
es. Th
e control of sig
nal i
nput
to the P
SS is bee
n
selecte
d
be
co
ming the
sp
e
ed
deviation
of g
enerator (
∆ω
). The
re
sult f
o
r th
e a
nalysi
s
sho
w
s that
addin
g
the
P
SS has given
an
addition
al da
mping for the
oscill
atory of
the
system
bringi
ng ba
ck the normal
stable ope
rati
on
.
This PSS proposed design
enhances the res
ponse ti
me of system
while
providi
ng a better result
in dampin
g
for oscillation
when compa
r
in
g to similar d
e
sig
n
s by the
Genetic Algo
rithm (GA). T
he
main c
o
ntribution to des
ign an optimal PSS.
Part
ic
le Swarm optimiz
a
tion (PSO) is
used to
des
ign the PSS parameters
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IJEECS
ISSN:
2502-4
752
Dynam
ic Stability Analysi
s
of Generator with PSS Usi
ng …
(Ha
y
faa
Moham
m
ed
Hu
ssein)
509
Ackno
w
l
e
d
g
ment
The autho
rs extend their appre
c
iatio
n
to Universiti
Tekni
k
al M
a
laysia Mel
a
ka and
Ministry of
Highe
r E
ducation, M
a
laysia
fo
r supp
ortin
g
this re
se
arch un
der grant
FRGS/2/20
1
4
/
TK03/FKE/01/F0023
8.
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ces
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MR T
a
vakoli,
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uli,
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