Indonesi
an
Journa
l
of El
ect
ri
cal Engineer
ing
an
d
Comp
ut
er
Scie
nce
Vo
l.
23
,
No.
3
,
Septem
ber
2021
, pp.
1299
~
130
5
IS
S
N: 25
02
-
4752, DO
I: 10
.11
591/ijeecs
.v
23
.i
3
.
pp
1299
-
1305
1299
Journ
al h
om
e
page
:
http:
//
ij
eecs.i
aesc
or
e.c
om
An
inves
tigation
of
ine
rtia
co
nst
an
t in single
genera
tor on
transient
analysis
for an is
olated
electri
ca
l
n
etwork system
M.
Saifu
z
am
Jamr
i, M
uh
amm
ad Niz
am
Kam
arudin
,
Mohd
Lu
qman
Mohd
Jamil
Cent
re
for
Robo
t
ic
s a
nd
Industri
a
l
Autom
at
ion
(C
eRIA),
Univ
ersiti
T
ekni
ka
l
Ma
lay
sia
Mel
aka
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
Ma
y
9
,
2021
Re
vised
Ju
l
2
1
,
2021
Accepte
d
A
u
g
4
,
2021
An
isola
te
d
elec
tri
c
al
ne
twork
which
fed
b
y
an
i
ndepe
nden
t
gen
era
tor
for
a
low
volt
age
s
y
st
em
is
conside
rab
le
in
remote
a
nd
isla
ndic
ar
eas
.
Although
the
ne
twork
s
y
s
te
m
has
le
ss
co
m
ple
xity
in
te
r
m
of
sy
st
em
struct
ure
,
i
ts
stabi
lit
y
le
v
el
is
cru
cial
due
to
fr
eque
nc
y
d
y
n
amica
l
r
esponses.
An
infl
uence
of
i
nit
ial
stabi
l
ity
m
arg
in
on
fre
quency
st
ability
stud
y
during
c
onti
ngen
c
y
situa
ti
on
is
a
t
hing
rat
her
th
a
n
bei
ng
ignored.
Here
the
in
i
ti
al
t
ran
sien
t
response
inhe
re
ntly
d
el
iv
ers
important
info
such
as
sy
st
em
ine
rti
a
and
m
om
ent
ari
l
y
po
wer
def
ic
i
t.
In
thi
s
pap
er,
an
inve
stiga
t
ion
of
tra
nsien
t
stabi
lit
y
r
esponses
under
diffe
ren
t
in
ert
i
a
val
ues
is
ca
rri
e
d
out.
The
inve
stigation
is
ca
rr
ie
d
ou
t
b
y
m
odelling
the
isola
t
ed
s
y
stem
i
n
MA
TL
AB/S
imu
li
nk
envi
ronm
en
t
which
consists
of
stat
e
-
spac
e
m
at
hemat
ic
a
l
equa
t
ions.
It
i
s
c
onfirmed
that
th
e
gen
era
tor
s
y
st
em
ine
rt
ia
shap
e
s
the
in
it
i
a
l
slope,
spee
d
dro
op
an
d
oscillatio
n.
For
a
ver
ifica
ti
on
purpose,
th
e
infl
u
ence
of
s
y
stem
in
ert
i
a
is
a
lso
anal
y
zed
using
bode
di
agr
am
in
which
s
y
stem
gain
and
fre
qu
ency
m
arg
in are e
v
al
ua
t
ed.
Ke
yw
or
ds:
Fr
e
qu
e
ncy
devi
at
ion
s
In
e
rtia
constan
t
Iso
la
te
d el
ect
rical
syst
e
m
Stat
e
-
sp
ace m
odel
Transi
ent sta
bili
ty
This
is an
open
acc
ess arti
cl
e
un
der
the
CC
B
Y
-
SA
l
ic
ense
.
Corres
pond
in
g
Aut
h
or
:
Mohd Sai
fu
za
m
b
in Jam
ri
Ce
ntre fo
r
R
obotics an
d Ind
ust
rial
A
ut
o
m
ation
(CeR
IA)
Faculty
of Elec
tric
al
Engineer
ing
Un
i
v
ersit
i Te
knikal M
al
ay
sia
Mel
aka
Hang T
ua
h
Jay
a, 76
100 D
ur
ia
n
T
unggal
, Me
la
ka,
Mal
ay
sia
Em
a
il
: sai
fu
zam
@u
tem
.ed
u.m
y
1.
INTROD
U
CTION
D
u
e
t
o
c
o
s
t
,
o
p
e
r
a
t
i
o
n
,
a
n
d
m
a
n
a
g
e
m
e
n
t
w
i
s
e
[
1
]
-
[
3
]
,
a
n
i
s
o
l
a
t
e
d
e
l
e
c
t
r
i
c
a
l
n
e
t
w
o
r
k
w
i
t
h
l
o
w
v
o
l
t
a
g
e
s
y
s
t
e
m
b
a
s
e
d
i
s
c
om
m
o
n
l
y
a
c
h
o
i
c
e
t
o
s
e
r
v
e
c
o
n
s
u
m
e
r
s
i
n
t
h
e
r
e
m
o
t
e
a
n
d
i
s
l
a
n
d
i
c
a
r
e
a
s
.
I
t
c
o
n
s
i
s
t
s
o
f
d
i
s
p
a
t
c
h
a
bl
e
g
e
n
e
r
a
t
i
o
n
a
n
d
n
o
n
-
d
i
s
p
a
t
c
h
a
bl
e
r
e
n
e
w
a
b
l
e
e
n
e
r
g
y
t
y
pi
c
a
l
l
y
,
l
e
a
d
i
n
g
t
o
a
n
i
n
d
e
p
e
n
d
e
n
t
a
n
d
a
u
t
o
n
om
o
u
s
o
p
e
r
a
t
i
o
n
i
n
r
e
g
u
l
a
r
b
a
s
i
s
.
H
o
w
e
v
e
r
,
i
t
s
s
y
s
t
e
m
b
e
h
a
v
i
o
r
i
s
e
a
s
i
l
y
di
s
t
u
r
b
e
d
d
u
e
t
o
t
h
e
m
i
x
e
d
e
n
e
r
g
y
s
o
u
r
c
e
s
w
h
i
c
h
i
n
h
e
r
e
n
t
l
y
di
s
t
u
r
b
s
n
e
t
w
o
r
k
s
t
a
b
i
l
i
t
y
l
e
v
e
l
.
T
h
e
d
y
n
a
m
i
c
a
l
b
e
h
a
v
i
o
r
o
f
t
h
e
g
e
n
e
r
a
t
i
o
n
s
y
s
t
e
m
m
u
s
t
b
e
b
a
l
a
n
c
e
d
a
n
d
e
n
s
u
r
e
d
w
i
t
h
i
n
t
h
e
p
e
r
m
i
s
s
i
b
l
e
l
e
v
e
l
t
o
a
v
o
i
d
s
e
v
e
r
e
s
y
s
t
e
m
f
r
e
q
u
e
n
c
y
d
e
v
i
a
t
i
o
n
s
[
4
]
-
[
7
]
.
I
t
s
h
o
u
l
d
b
e
n
o
t
e
d
t
h
a
t
n
e
t
w
o
r
k
t
r
a
n
s
i
e
n
t
s
t
a
bi
l
i
t
y
i
s
n
o
t
o
n
l
y
d
e
p
e
n
d
o
n
e
n
e
r
g
y
b
a
l
a
n
c
e
d
b
e
t
w
e
e
n
s
u
p
p
l
y
a
n
d
d
e
m
a
n
d
,
b
u
t
i
t
a
l
s
o
d
u
e
t
o
a
n
i
n
f
l
u
e
n
c
e
f
r
om
g
e
n
e
r
a
t
i
o
n
s
i
de
i
.
e
.
a
g
e
n
e
r
a
t
o
r
s
y
s
t
e
m
[
8
]
-
[
1
0
]
.
Thus,
generat
or
sp
eci
ficat
io
n
fa
ct
or
s
houl
d be
counted
whe
n deali
ng w
it
h
c
on
ti
nge
ncy p
la
nn
i
ng.
A
re
view
on
fr
e
qu
e
ncy
sta
bi
li
t
y
and
c
on
t
r
ol
has
bee
n
s
umm
arized
[
11]
.
I
nv
e
sti
gations
on
the
influ
e
nce
of
frequ
e
ncy
l
oad
con
t
ro
l
on
po
wer
syst
em
network
fe
d
by
m
ul
ti
ple
distribu
te
d
ge
ner
at
ors
a
re
repor
te
d
in
[
12]
-
[
18]
.
In
[
19
]
-
[22],
the
tran
sie
nt
sta
bili
ty
was
analy
zed
by
m
eans
of
vi
rtual
inerti
a
con
t
ro
l
wh
e
n
the
netw
ork
is i
nteg
rate
d
with a
wind t
urbine
syst
em
. Th
e m
et
ho
d
to
stud
y t
he
e
ff
ec
t of
synt
hetic
iner
ti
a
and
virtu
al
ine
r
ti
a fo
r
ph
otovol
ta
ic
syst
e
m
w
as d
isc
us
se
d
in
[
23]
an
d
[
24]
. A
n
a
naly
sis on p
ower
syst
em
ang
l
e
durin
g
tra
ns
ie
nt
wa
s
discusse
d
in
[
25]
.
F
urt
her
m
or
e,
in
fluen
ce
s
of
va
riat
ion
of
f
requ
ency
bala
ncin
g
a
nd
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2502
-
4752
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci,
Vo
l.
23
, N
o.
3
,
Se
ptem
ber
2
02
1
:
12
99
-
130
5
1300
con
t
ro
l
a
ppr
oa
ches
on
t
he
dy
nam
ic
al
fr
eq
uen
cy
be
ha
vior
a
re
in
vestig
at
ed
[
26]
-
[
28]
.
For
a
giv
e
n
loa
d
var
ia
ti
ons,
the
autom
at
ic
gen
erati
on
c
ontr
ol
(AGC)
would
re
su
lt
sig
ni
ficant
influ
e
nc
e
on
the
dynam
ic
al
netw
ork’s f
re
quency
res
pons
e
.
In
t
his
pap
e
r,
an
in
vestigat
io
n
of
dynam
ic
a
l
fr
e
qu
e
ncy
re
s
pons
es
on
th
e
transient
sta
bili
ty
wh
en
a
n
inerti
a
const
an
t,
H
var
ie
s
is
presente
d.
T
he
inv
e
sti
gation
de
al
s
with
syst
em
fo
rm
ulati
on
and
d
eri
vations
for
an
isolat
ed
power
syst
e
m
fed
by
sing
le
generato
r.
Obser
vation
on
the
i
nf
lue
nc
e
of
H
on
the
transie
nt
phe
nom
ena
would be
the
oret
ic
al
ly
ad
van
t
ageous
in
t
he
e
arly
stage
of g
e
ner
at
or
sel
ect
ion
.
2.
RESEA
R
CH MET
HO
D
Figure
1
s
how
s
the
il
lustrati
on
of
t
he
ge
ne
rator
s
upplyi
ng
isolat
ed
loa
d
to
be
stu
dy.
The
net
wor
k
consi
sts
of
one
ge
ner
at
or
syst
e
m
and
c
onne
ct
ed
loa
ds
.
T
he
m
at
he
m
at
ical
m
od
el
that
has
bee
n
der
iv
ed
wa
s
div
ide
d
int
o
f
our
m
ai
n
par
ts
wh
ic
h
are
ro
ta
t
ing
m
ass,
pr
im
e
m
ov
er
,
sp
ee
d
gove
rnor
a
nd
load.
Each
pa
rt
was
m
od
el
ed
sepa
r
at
el
y and
a
ugm
ented
al
l t
og
et
her to
bec
om
e
a sin
gle m
od
el
.
Figure
1.
Ge
ne
rator s
upplyi
ng isolat
ed
l
oad
2.1
.
Rotatin
g mass
m
od
el
This
m
od
el
is
relat
ed
to
the
beh
a
vior
of
th
e
ro
ta
ti
on
towa
rd
s
t
he
m
echan
ic
al
tor
qu
e
a
nd
el
ect
rical
tor
qu
e
which
s
at
isfie
d
the
law
of rotat
ion
2
2
=
−
(1)
No
te
d
that
,
,
and
are
the
c
om
bin
ed
inerti
a
co
ns
ta
nt,
m
echan
ic
al
ro
t
or
a
ng
le
,
m
echan
ic
al
tor
qu
e
an
d
el
ect
rical
tor
qu
e
r
especti
vely
.
M
ulti
plyi
ng
t
he
s
ynch
ron
ou
s
s
pe
ed
i
n
m
echani
cal
te
r
m
to
t
he
bo
t
h
side
s
of
t
he
(
1)
an
d
a
pp
ly
ing
the
tra
nsfo
rm
ation
to
th
e
ro
t
or
a
ngle
wi
th
gen
e
rato
r
pole
,
it
will
tur
ne
d
the equat
io
n
i
nt
o
po
wer relat
e
d
to
the elect
ri
cal
an
gle
as
fo
l
lows
:
2
2
2
=
−
(2)
is t
he
i
ner
ti
a c
on
sta
nt in
the
ki
netic
en
er
gy
=
2
⁄
. Su
bs
ti
tuti
ng
into (2) y
ie
lds,
2
.
2
.
=
−
(3)
In
(
3)
desc
ribe
s
the
beh
a
vior
of
ge
ner
at
or
rot
or
represe
nted
in
f
reque
ncy
dev
ia
ti
ons
with
re
sp
ect
t
o
tim
e
and
note
d
that
2
2
=
.
Di
vid
in
g
the
(
3)
with
the
base
powe
r
a
nd
c
onve
rting
t
he
to
th
e
synch
ron
ous
s
peed
relat
ed
to
el
ect
rical
wi
th
ge
ner
at
or
pole
,
t
he
e
quat
ion
will
t
urne
d
i
nto
the
generali
ze
equ
at
io
n
t
hat c
omm
on
ly
call
e
d
as
a s
wing e
quat
ion i
n pe
r u
nit.
2
.
=
−
(4)
No
te
d
t
hat
is
the
pe
r
unit
in
erti
a
co
ns
ta
nt
and
the
only
pa
ram
et
er
that
aff
ect
t
he
behavio
r
of
f
requ
enc
y
dev
ia
ti
ons
oth
e
r
tha
n defici
t
powe
r betwee
n m
echan
ic
al
and elec
tric
al
po
wer.
2.2
.
Pri
me
m
ov
er
m
od
el
Pr
im
e
m
ov
er
is
the
so
urce
of
the
m
echan
ic
al
power
f
or
the
ro
ta
ti
ng
m
ass
syst
e
m
.
The
m
o
st
eff
ect
ive
way
to
m
od
el
t
he
pr
im
e
m
ov
er
is
by
relat
in
g
it
s
beh
a
vior
wi
th
the
ste
am
tu
rb
i
ne
syst
em
.
The
m
od
el
is
r
el
at
ed
to
the
m
echan
ic
al
power
outp
ut
to
the
ste
a
m
po
sit
ion
.
T
hi
s
work
us
e
d
t
he
sim
ple
pr
im
e
m
ov
er
m
od
el
that ca
n be
app
roxim
at
ed
with a single
ti
m
e c
on
sta
nt
res
ulti
ng in
t
he follo
wing tra
nsfer
f
un
ct
io
n
;
Evaluation Warning : The document was created with Spire.PDF for Python.
Ind
on
esi
a
n
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E
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c Eng &
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m
p
Sci
IS
S
N:
25
02
-
4752
An
i
nvesti
gati
on
of inerti
a co
nst
an
t i
n
sin
gle
gen
e
ra
t
or
on tr
an
sie
nt
analysis f
or
…
(
M.
Sai
fuzam J
amri
)
1301
=
1
+
1
(5)
Convertin
g
the
transf
e
r
f
unct
ion
(5)
into
t
he
diff
e
re
ntial
equ
at
i
on
will
m
a
ke
the
pri
m
e
m
ov
er
m
od
el
beco
m
e
co
m
patible
to
augm
ent
with
the
ro
ta
ti
ng
m
ass
m
od
el
in
(4
)
.
By
app
ly
ing
the
inv
erse
Laplace
trans
form
ation
,
the
final e
qu
at
ion
f
or
t
he pri
m
e
m
ov
er m
odel
can be
wr
it
te
n
as
foll
ows
=
1
(
−
)
(6)
2.3
.
G
overn
or
model
Wh
e
n
the
loa
d
dem
and
sud
de
nly
increase
d,
the
el
ect
rical
load
powe
r
e
xc
eeds
the
m
echan
ic
al
powe
r
and
re
su
lt
in
g
the
powe
r
de
fici
ency.
The
am
ount
of
powe
r
def
ic
it
will
influ
ence
the
am
ou
nt
of
kin
et
ic
energy
store
d
in
the
r
otati
ng
syst
em
.
The
reducti
on
in
kin
et
ic
ene
rg
y
will
aff
ect
the
tur
bin
e
s
pe
ed
an
d
co
ns
e
quently
the
ge
ner
at
or
f
reque
ncy
goin
g
to
fall
.
A
s
a
co
nclusion,
the
s
peed
go
ve
rnor
syst
em
is
de
pends
on
the
el
ect
rical
load
dem
and
.
This
change
in
s
pee
d
is
sense
d
by
the
tur
bin
e
go
vern
or
an
d
act
to
adjust
the
tur
bin
e
input
val
ve
to
cha
ng
e
t
he
m
echan
ic
al
po
wer
outp
ut
to
br
i
ng
t
he
s
pe
ed
to
a
ne
w
s
te
ady
-
sta
te
le
ve
l.
The
equ
at
io
n w
hich
d
irect
ly
d
es
cri
bes
t
he
s
peed g
ov
e
r
nor beha
vi
or is de
picte
d i
n (7).
=
1
(
−
−
)
(7)
wh
e
re
re
pr
e
se
nts
the
slo
pe
of
the
cu
r
ve
in
t
he
s
pee
d
gove
r
nor
c
harac
te
ris
ti
cs
as
sho
wn
in
Fi
gure
2
w
hich
relat
ed
to
the devia
ti
on
of f
re
qu
e
ncy w
it
h
re
sp
ect
to
po
wer change
d.
Noted
that
t
his
m
ath
em
atical
m
od
el
do
e
s
no
t c
onside
r
th
e auto
m
at
ic
g
ener
at
io
n
c
ontr
ol
(
A
GC).
Figure
2.
S
pee
d gove
rnor cha
racteri
sti
c
2.4
.
L
oad m
odel
The
loa
d
on
a
powe
r
syst
em
consi
sts
of
va
r
ie
ty
of
el
ect
rical
dev
ic
es.
It
c
an
be
di
vid
e
d
i
nto
2
ty
pes
wh
ic
h
a
re
fr
e
quency
i
ndepe
ndent
l
oa
ds
s
uc
h
as
li
gh
ti
ng
a
nd
heati
ng
loa
ds
,
an
d
fr
e
que
ncy
de
pe
ndent
load
s
su
c
h
as
m
oto
r
loads
.
The
sen
sit
ivit
y
of
su
c
h
loads
is
dep
e
ndin
g
on
thei
r
s
peed
-
loa
d
c
harac
te
risti
cs
and
can
be
appr
ox
im
at
ely d
efi
ned b
y
,
=
+
(8)
wh
e
re
is
the
non
-
f
reque
ncy
sensiti
ve
loa
d
cha
ng
e
a
nd
is
the
f
re
qu
e
nc
y
sensiti
ve
loa
d
c
hange.
is
expresse
d
as
th
e p
e
rcen
t c
ha
nge in
loa
d divi
ded b
y t
he perc
ent ch
a
nge i
n
f
reque
ncy.
2.5
.
S
tate
space
represen
tat
ion
In
(
4),
(6),
(
7)
and
(
8)
can
be
wr
it
te
n
into
the
sta
te
-
sp
ace
represe
ntati
on
as
sh
ow
n
in
(9).
From
the
equ
at
io
n,
the
s
ta
te
var
ia
bles
a
re
∆
,
∆
and
∆
w
hile
the
in
pu
t
sta
te
is
the
loa
d
de
m
and
∆
.
N
oted
that
the sym
bo
l
∆
use
d
in
these
equ
at
ion
s is t
o rep
resen
t t
he devi
at
ion
s
of the
sta
te
.
̇
=
+
(9)
The
m
at
rix
an
d
is ar
range
d
a
s sho
wn in (1
0) a
nd
(
11).
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
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Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci,
Vo
l.
23
, N
o.
3
,
Se
ptem
ber
2
02
1
:
12
99
-
130
5
1302
=
[
0
1
2
⁄
0
0
−
1
⁄
1
⁄
−
⁄
0
−
1
⁄
]
(10)
=
[
−
1
2
⁄
0
0
]
(11)
3.
RESU
LT
S
A
ND
D
IS
C
USS
ION
The
m
ai
n
obj
e
ct
ive
of
this
w
ork
is
t
o
in
ves
ti
gate
the
in
flu
ences
of
dy
na
m
ic
al
fr
equ
e
nc
y
respo
ns
e
towa
rd
s
the
m
ulti
far
io
us
ine
r
ti
a
con
sta
nt
va
lue.
The
is
olate
d
powe
r
syst
e
m
netwo
r
k
w
as
m
od
el
ed
wi
th
the
relat
ion
t
o
the
swing
e
qu
at
io
n
an
d
au
gm
ented
with
the
t
urb
ine
an
d
gove
rnor
syst
e
m
.
The
tur
bin
e
syst
e
m
was
m
od
el
ed
as
a
non
-
re
heat
tur
bin
e
ty
pe
w
hile
the
ref
ere
nce
power
in
the
gove
rnor
syst
e
m
is
al
ways
e
qu
al
to
zero
s
o
t
hat
t
he
netw
ork
m
od
el
does
no
t
consi
der
as
r
equ
i
red
in
AGC
.
T
hus,
the
s
yst
e
m
will
on
l
y
exp
e
rience
t
he
pr
im
ary
con
tr
ol
in
it
s
loa
d
fr
e
qu
e
ncy
c
ontrol
m
echan
ism
.
The
par
am
et
ers
of
the
is
olate
d
powe
r
syst
em
m
od
el
are
sh
own
i
n
Ta
ble
1.
N
oted
that
t
he
value
of
i
nert
ia
con
sta
nt
w
as
arb
it
ra
rily
va
ried
durin
g
the
sim
ulati
on
in
acco
rd
a
nce
with
th
e
ty
pical
gen
er
at
or
with
no
n
-
r
eheat
tur
bin
e
s
yst
e
m
and
the
resu
lt
s
wer
e
in
pe
r
unit
.
The
m
od
el
was
te
ste
d
a
nd
ve
rified
un
der
3
inerti
a
c
onst
ant
c
onditi
on
s
with
s
udde
n
0.3
pe
r
un
it
of loa
d de
viati
on
.
T
hen the
dynam
ic
al
f
reque
ncy res
po
ns
es
were
a
naly
zed and
i
nv
e
s
ti
gated.
Table
1.
Param
et
ers
of is
olate
d powe
r
syst
e
m
m
od
el
Para
m
eters
Valu
e
Sp
eed regu
latio
n
,
R
0
.05
Frequ
en
cy
-
sen
sitiv
ity
,
D
0
.6
Inertia c
o
n
stan
t,
H
Varied
(2.5
–
6
.0
)
Go
v
erno
r
ti
m
e
con
stan
t,
0
.2
Turb
in
e ti
m
e
con
stan
t,
0
.3
3.1
.
Simul
at
io
n results
for
f
requenc
y
d
ynamic
al
beh
av
i
or
Figure
3
s
how
s
the
dy
nam
ic
a
l
fr
e
qu
e
ncy
res
pons
es
unde
r
t
he
diff
e
ren
t
i
ne
rtia
const
ant
value
a
nd
0.3
per
unit
load
de
viati
on
.
From
the
obser
vatio
ns
,
it
is
ob
viou
sly
seen
that
th
e
inerti
a
co
ns
t
ant
play
s
the
r
ole
in
weig
hting
t
he
gen
e
rato
r
sh
a
ft
.
It
can
be
pro
ved
by
lookin
g
to
the
siz
e
of
os
ci
ll
at
ion
s
durin
g
the
tra
ns
ie
nt
wh
e
re
the
high
er
inerti
a
c
onsta
nt
val
ue
will
resu
lt
in
le
ss
osc
il
la
ti
on
.
The
init
ia
l
slop
e
al
so
af
fected
sin
ce
th
e
inerti
a
const
an
t
is
t
he
on
ly
par
am
et
er
that
influ
e
nce
to
the
fr
e
quen
cy
dev
ia
ti
on
with
resp
ect
to
ti
m
e
and
com
plied
the
(
4).
L
ow
i
ner
ti
a
co
ns
ta
nt
m
ay
pu
t
t
he
ge
ne
rator
i
n
da
nger
be
cause
the
init
ia
l
drop
of
f
re
quency
decay
m
a
y
be
ou
t
of
per
m
issi
ble
range
wh
e
n
m
or
e
load
dem
and
de
viati
on
ha
pp
e
ne
d.
I
t
can
be
see
n
i
n
the
gr
a
ph
f
or
ine
rt
ia
co
ns
ta
nt
e
qual
to
2.5
,
the
unde
rs
hoot
ne
arly
reac
h
to
0.0
3
per
un
it
.
Table
2
sho
ws
t
he
su
m
m
ary of
th
e res
ults.
Figure
3.
Fr
e
quency
de
viati
ons
unde
r
m
ulti
far
io
us
ine
rtia
c
on
sta
nt
Evaluation Warning : The document was created with Spire.PDF for Python.
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci
IS
S
N:
25
02
-
4752
An
i
nvesti
gati
on
of inerti
a co
nst
an
t i
n
sin
gle
gen
e
ra
t
or
on tr
an
sie
nt
analysis f
or
…
(
M.
Sai
fuzam J
amri
)
1303
Table
2.
T
he
s
u
m
m
arizat
ion
of the tra
ns
ie
nt an
al
ysi
s
Inertia Co
n
stan
t
Un
d
ersh
o
o
t
Initial Slo
p
e
Settlin
g
ti
m
e
Oscillatio
n
Stead
y
-
stat
e
2
.5
8
9
.73
%
0
.06
7
.39
s
Hig
h
No
t inf
lu
en
ced
5
.0
3
5
.82
%
0
.03
4
.45
s
Mediu
m
6
.0
2
5
.66
%
0
.25
3
.69
s
Low
3.2
.
Sim
ulat
i
on
re
sults
f
r
om
bode pl
ot f
r
equenc
y
res
ponse
In
the
pr
e
vious
sect
ion
,
the
frequ
e
ncy
de
viati
on
s
r
esp
onses
with
res
pect
to
tim
e
wer
e
re
corde
d.
T
he
resu
lt
s
s
how
t
he
i
nfor
m
at
ion
ab
ou
t
tra
ns
ie
nt
sta
bili
ty
.
In
this
sect
io
n,
th
e
res
ults
we
re
plo
tt
ed
in
fr
e
quenc
y
respo
ns
e t
hrough
the
bode
gr
aph as s
how
n
i
n
Fi
gure
4.
Fro
m
the obser
vat
ion
,
the m
ulti
far
io
us
ine
rtia
constant
will
on
ly
influe
nce
the
gai
n
m
agn
it
ud
e
i
n
the
highe
r
fr
e
quency
ba
ndwi
dt
h
wh
il
e
the
ga
in
in
lowe
r
fr
e
qu
e
nc
y
band
width
is
rem
ai
n
un
c
hanged.
As
s
uch,
low
i
ner
ti
a
c
on
sta
nt
will
le
ad
to
the
high
er
de
viati
on
of
the
m
agn
it
ud
e
gai
n.
T
his
ph
e
no
m
eno
n
has
be
com
e
the
evid
ence
that
the
inerti
a
co
ns
ta
nt
par
am
et
er
does
not
per
t
urb
the
ste
ady
-
sta
te
.
Figure
4.
The
re
su
lt
s p
l
otted i
n fr
e
qu
e
ncy
re
sp
onse
(
B
od
e
diag
ram
)
3.3
.
Analysis
on
th
e
freq
ue
ncy tr
an
sie
n
t r
espo
n
se
The
tra
ns
ie
nt
of
t
he
dy
nam
i
cal
fr
eq
ue
ncy
respo
ns
es
ca
n
be
di
vid
e
d
int
o
th
ree
re
gion
s
wh
ic
h
are
dro
op
re
gion,
ada
ptati
on
re
gion
a
nd
sta
bi
li
ze
reg
io
n
re
sp
ect
ively
.
Fi
gure
5
s
hows
the
th
ree
regi
on
s
t
o
il
lustrate
th
e
lev
el
of
ge
ne
rato
r
respo
ns
es
w
he
n
the
syst
e
m
has
purt
ub
e
d
with
increase
d
of
loa
d
dem
and
.
The
dro
op
reg
i
on
s
hows
the
i
niti
al
neg
at
ive
sl
ope
respo
ns
es
with
the
m
axi
m
u
m
nad
ir
poi
nt
towa
rd
s
t
he
sud
de
n
change
d
in po
wer
def
ic
it
w
hi
le
the ad
aptat
io
n
re
gion is w
he
n
the turbi
ne
syst
e
m
starts
t
o
cha
nge an
d
cl
i
m
b
it
s
powe
r
from
th
e
init
ia
l
op
erati
ng
point
.
When
the
tur
bi
ne
syst
e
m
su
ccessfu
ll
y
m
eet
s
the
power
dem
and
,
th
e
total
power
de
fici
t
will
sta
rt
to
decr
ea
se
an
d
nea
rly
to
zer
o
an
d
this
phe
no
m
enon
can
be
cl
early
seen
in
the
sta
bili
ze
reg
i
on
wh
e
re
t
he
tra
ns
ie
nt
is
al
ready
reache
d
t
he
s
te
ady
-
sta
te
co
ndit
ion
.
T
his
tra
ns
ie
nt
phen
ome
no
n
was on
ly
c
over
ed wit
hin
10s
of ti
m
e interval b
ef
or
e
the
fr
e
quency
sta
te
d o
n
the
n
e
w o
perat
ing
po
i
nt.
Figure
5.
The
thr
ee
r
e
gions
of d
ynam
ic
al
f
re
qu
e
ncy
respo
nse
s to
wards s
udde
n
i
ncr
ease
d o
f
loa
d dem
and
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2502
-
4752
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci,
Vo
l.
23
, N
o.
3
,
Se
ptem
ber
2
02
1
:
12
99
-
130
5
1304
4.
CONCL
US
I
O
N
T
h
e
s
t
a
t
e
-
s
p
a
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s
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a
l
y
s
i
s
.
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r
om
t
h
e
o
b
s
e
r
v
a
t
i
o
ns
,
t
h
e
i
n
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s
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i
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a
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i
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o
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l
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d
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di
f
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l
u
e
o
f
i
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e
r
t
i
a
c
o
n
s
t
a
nt
p
a
r
a
m
e
t
e
r
m
a
y
i
n
f
l
u
e
n
c
e
o
n
l
y
t
o
t
h
e
i
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i
t
i
a
l
t
r
a
n
s
i
e
n
t
s
t
a
b
i
l
i
t
y
o
f
t
h
e
g
e
n
e
r
a
t
o
r
’
s
d
y
n
a
m
i
c
a
l
f
r
e
q
u
e
n
c
y
r
e
s
p
o
n
s
e
b
u
t
n
o
t
t
h
e
s
t
e
a
d
y
-
s
t
a
t
e
.
ACKN
OWLE
DGE
MENTS
The
a
uthor
s
grat
efu
ll
y ac
knowle
dge the
Ce
nter fo
r
R
obotics an
d Ind
us
tri
al
A
ut
om
at
ion
, Unive
rsiti
Tek
nik
al
Mal
a
ysi
a Me
la
ka
(C
eR
IA) fo
r
the
re
search
f
aci
li
ti
es an
d
s
uppo
rt,
to
the
Ce
nte
r
f
or Rese
arc
h
a
nd
Inn
ov
at
io
n
Ma
nag
em
ent (
CR
I
M) for
the
f
unding a
nd pu
blica
ti
on
facil
it
y.
REFERE
NCE
S
[1]
G.
R.
Prudhvi
K
um
ar,
D.
Satt
ia
n
ada
n,
and
K.
Vij
a
y
akumar,
“
A
s
urve
y
on
power
m
ana
gement
strat
eg
ie
s
of
h
y
b
r
i
d
ene
rg
y
s
y
stems
in
m
ic
rogrid,
”
I
nte
r
nati
onal
Jou
rnal
of
El
ec
tri
c
al
and
Computer
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JE
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A.
Avilé
s,
“
Sim
ula
ti
on
of
a
m
ic
rogrid
for
a
non
-
int
erc
on
nec
t
ed
zone
that
int
egr
at
es
r
ene
w
abl
e
energie
s,
”
I
nte
rnational
Jou
rnal
of
El
e
ct
ric
al
and
Comput
e
r
Engi
ne
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IJE
CE)
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S.
Sat
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a
na
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sh,
“
Design
of
H
y
brid
S
ola
r
W
ind
Ene
rg
y
S
y
stem
in
a
Microgr
id
with M
PP
T
Te
chni
qu
es,
”
Int
ernati
ona
l
Journal
of
E
lec
tric
al
and
Comp
ute
r E
ngineering
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IJE
CE)
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m
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A.
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A.
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z
m
in,
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Za
m
b
ri,
“
Freque
nc
y
cont
ro
l
r
ese
rve
via
m
ic
ro
gr
id
for
th
e
futur
e
re
newa
bl
e
Malay
sian
power
s
y
s
te
m
,
”
IE
EE
P
E
S
Asia
-
Pac
i
fi
c
Po
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Ene
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onfe
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y
e
en,
“
I
slandi
ng
oper
a
tion
of
h
y
brid
m
i
cro
grids
with
hi
gh
int
egr
at
ion
of
wi
nd
d
rive
n
c
age inducti
on
generators
,
”
Sustain
.
En
ergy
Techno
l. A
s
sess
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8
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N
.
N
.
A
.
B
a
k
a
r
,
M
.
Y
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H
a
s
s
a
n
,
M
.
F
.
S
u
l
a
i
m
a
,
M
.
N
.
M
o
h
d
N
a
s
i
r
,
a
n
d
A
.
K
h
a
m
i
s
,
“
M
i
c
r
o
g
r
i
d
a
n
d
l
o
a
d
s
h
e
d
d
i
n
g
s
c
h
e
m
e
d
u
r
i
n
g
i
s
l
a
n
d
e
d
m
o
d
e
:
A
r
e
v
i
e
w
,
”
R
e
n
e
w
.
S
u
s
t
a
i
n
.
E
n
e
r
g
y
R
e
v
.
2
0
1
7
,
p
p
.
1
6
1
-
1
6
9
,
d
o
i
:
1
0
.
1
0
1
6
/
j
.
r
s
e
r
.
2
0
1
6
.
1
2
.
0
4
9
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[7]
M.
Mehra
sa,
E
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Pouresm
ae
il
,
B.
N.
Jørgensen,
and
J.
P.
S.
Cat
al
ão
,
“
A
cont
rol
pla
n
for
the
sta
ble
oper
a
ti
on
of
m
ic
rogrids
durin
g
gr
id
-
conn
ecte
d
and isla
nd
ed
m
odes,
”
Elec
tr.
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wer
Syst. Res
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-
22
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2015
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Ng
y
armunta
Al
a
n
Aud
u,
Odaba
Alphae
us,
T
alat
u
Adam
u,
“
Eff
ec
t
of
Ine
r
ti
a
Con
stant
on
Gene
r
ator
Freque
nc
y
an
d
Rotor
Angle
,
”
E
ngine
ering
an
d
Appl
ie
d
Sc
ie
n
ce
s
.
vol
.
3
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no
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1
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U.
Datt
a
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A.
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and
J.
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“
Bat
te
r
y
en
erg
y
storage
s
y
st
em
for
tra
nsient
fr
eq
uency
stabilit
y
e
nhanc
emen
t
of
a
la
rge
-
sc
ale
po
wer
s
y
st
em,”
Australasian
Unive
rs
it
i
es
Pow
er
Engi
n
ee
ring
Confe
ren
ce
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E.
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ez
,
a
nd
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afu
erte
,
“
Eff
ect
of
th
e
Control
of
Gene
rat
ors
and
Turb
i
nes
on
the
Tr
ansi
ent
Stab
il
i
t
y
of
a
Pow
er
S
y
stem,”
IEE
E
Latin Ame
rica
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an
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[11]
B.
Sabe
eh
and
C.
K.
Gan
,
“
Pow
er
S
y
stem
Fre
quenc
y
Stab
il
i
t
y
and
Contro
l:
S
urve
y
,
”
Inte
rnat
ional
Journal
of
Appl
ie
d
Eng
inee
ring R
ese
arch
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v
ol.
11
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no
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N
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K
.
K
u
m
a
r
a
n
d
I
.
E
.
S
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N
a
i
d
u
,
“
L
o
a
d
f
r
e
q
u
e
n
c
y
c
o
n
t
r
o
l
f
o
r
a
m
u
l
t
i
a
r
e
a
p
o
w
e
r
s
ys
t
e
m
i
n
v
o
l
v
i
n
g
w
i
n
d
,
h
yd
r
o
a
n
d
t
h
e
r
m
a
l
p
l
a
n
t
s
,
”
I
n
t
e
r
n
a
t
i
o
n
a
l
C
o
n
f
e
r
e
n
c
e
o
n
E
n
g
i
n
e
e
r
i
n
g
T
e
c
h
n
o
l
o
g
y
a
n
d
S
c
i
e
n
c
e
,
v
o
l
.
3
,
n
o
.
1
,
p
p
.
1
0
0
8
-
1
0
1
3
,
2
0
1
4
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[13]
S.
Ta
ka
y
am
a
an
d
R.
Ma
tsuhashi
,
“
Deve
lopment
of
m
odel
for
load
fre
quency
con
trol
in
power
s
ystem
with
la
rge
-
sca
le
in
te
gr
at
i
on
of
ren
ewa
ble
en
erg
y
,
”
IEE
E
Power
and
Ene
rgy
Confe
renc
e
,
2016,
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C.
Li
ang
,
P.
W
ang,
X.
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W
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Qin,
and
Y.
Ji
a,
“
Freque
nc
y
a
spec
ts
of
power
sy
st
em
oper
ati
onal
reliab
i
li
t
y
,
”
Inte
rnational
Confe
renc
e
on
Probabil
isti
c
Me
thods
Appl
ie
d
to
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er
Syste
ms
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[15]
M.
Jala
luddi
n
,
H.
V.
Saikumar,
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Bansil
al,
“
Perform
anc
e
evalua
ti
on
of
m
ult
i
m
ac
hine
power
s
y
stem
with
fu
z
z
y
base
d
power
s
y
s
te
m
stabi
l
izer,”
Inte
rnational
Co
nfe
renc
e
on
Te
c
hnologi
cal
Ad
va
nce
ments
in
Po
wer
and
Ene
rg
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il,
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ese
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“
Opera
ti
o
n
of
m
ult
imicro
grids,
”
Book
Ch
apte
r:
Mi
crogrids:
Archi
t
ec
tures
an
d
Control, N. Hatziargyriou,
Ed.
New
J
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n
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[17]
A.
Us
m
an
and
B.
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r
,
“
Sim
ula
ti
on
stud
y
of
loa
d
fre
qu
en
c
y
cont
ro
l
of
single
and
two
ar
ea
s
y
st
ems
,
”
IE
EE
Global
Hum
anitar
ian
Technol
og
y
Conf
ere
nc
e
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20
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[18]
S.
A.
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S.
H.
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nia,
“
Loa
d
fre
qu
ency
cont
rol
of
two
a
rea
interc
onn
ect
ed
power
s
y
ste
m
(die
sel
gen
erat
o
r
and
solar
PV
)
with
PI
and
F
GS
PI
cont
roll
er,”
16th
CS
I
Inte
rnational
Sympo
sium
on
Arti
fi
cial
Inte
lligen
ce and Signa
l Proce
ss
in
g
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st
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m
S
m
al
l
-
Signal
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Co
nsideri
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Loc
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uen
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d
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FIG
fre
quency
oscil
lation
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wind
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n
es
wit
h
virt
ual i
n
ert
i
a co
ntrol
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”
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nal
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g
,
“
P
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w
e
r
s
ys
t
e
m
a
n
g
u
l
a
r
s
t
a
b
i
l
i
t
y
a
s
a
f
f
e
c
t
e
d
b
y
t
h
e
r
e
d
u
c
e
d
i
n
e
r
t
i
a
d
u
e
t
o
w
i
n
d
di
s
p
l
a
c
i
n
g
s
yn
c
h
r
o
n
o
u
s
g
e
n
e
r
a
t
o
r
s
,
”
2
n
d
I
n
t
e
r
n
a
t
i
o
n
a
l
C
o
n
f
e
r
e
n
c
e
o
n
P
o
w
e
r
a
n
d
R
e
n
e
w
a
b
l
e
E
n
e
r
g
y
(
I
C
P
R
E
)
,
2
0
1
7
.
[24]
A
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Naz
ir
,
D
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S.
M.
Os
heba
,
and
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S.
Mansour,
“
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l
in
ertia
i
m
pac
t
on
the
pe
r
form
anc
e
of
pho
tovol
taic
s
y
s
te
m
,
”
2019
IEE
E
Confe
renc
e
on
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r
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ec
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cs
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e
Ene
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y
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“
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d
e
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it
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pow
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s
y
stem
st
abi
l
ity
-
s
y
nt
h
etic
ine
r
tia
con
ce
p
ts
anal
y
sis,
”
2017
6
th
Inte
rnational
Y
o
uth
Conf
ere
nce
on
Ene
rgy
(
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ourc
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Co
ntro
l
and
Minim
iz
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”
I
nte
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va
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d
Re
search
in
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a
l,
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ct
roni
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I
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Riz
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an
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“
Achie
ving
Pow
er
Sy
st
em
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li
t
y
for
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Area
H
y
dro
Pow
er
S
y
stem
via
LQR
Te
chn
ique
s,
”
Inte
rnational
Journal
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ering
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[28]
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a
m
a
r
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i
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,
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M
o
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d
S
h
a
h
a
r
u
d
i
n
,
M
.
H
.
J
a
l
i
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d
.
S
.
R
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z
a
l
i
,
a
n
d
M
.
S
.
M
o
h
d
A
r
a
s
,
“
A
c
h
i
e
v
i
n
g
T
h
e
r
m
a
l
P
o
w
e
r
S
y
s
t
e
m
S
t
a
b
i
l
i
t
y
U
s
i
n
g
L
o
a
d
F
r
e
q
u
e
n
c
y
C
o
n
t
r
o
l
l
e
r
,
”
M
o
d
e
l
i
n
g
,
D
e
s
i
g
n
a
n
d
S
i
m
u
l
a
t
i
o
n
o
f
S
y
s
t
e
m
s
,
p
p
.
4
5
5
-
467
,
2
0
1
7
.
BIOGR
AP
HI
ES OF
A
UTH
ORS
M.
Saifu
z
am
J
amr
i
was
born
in
Octobe
r
1984.
He
rec
e
ived
his
bac
hel
or
degr
ee
i
n
El
e
ct
ri
ca
l
Engi
n
ee
ring
(Pow
er
El
e
ct
roni
cs
&
Drive
s)
from
Univer
siti
Te
kn
ik
al
Mal
a
y
s
ia
Mela
ka
,
Mal
a
y
s
i
a
in
2007
and
r
e
ce
iv
ed
the
M
aste
r
Degre
e
in
E
lectr
i
ca
l
Pow
er
En
gine
er
ing
from
Univer
siti
Te
knologi
Malay
sia
in
2009
.
He
is
cur
r
ent
l
y
w
orke
d
with
th
e
Univer
sit
i
Te
knik
al
Ma
lays
ia
Mel
aka
(UT
eM)
as
a
l
ec
tur
er
and
be
longs
t
o
Cent
r
e
for
Ro
boti
cs
and
Industria
l
Auto
m
at
ion
(CeRIA)
group.
His
in
te
r
est
is
in
powe
r
sy
stem
stud
y
and
m
ic
ro
-
grid
inc
ludi
ng
loa
d
f
req
uency
cont
ro
l
(LFC)
and
r
en
ewa
ble
ene
rg
y
i
nte
gra
ti
on.
He
i
s
cur
ren
t
l
y
per
suing
th
e
Ph
D
in
Univer
si
t
y
Te
kn
ina
l
Mala
y
sia
Mel
aka
un
der
Facu
lty
of
El
e
ct
ri
ca
l
Engi
ne
eri
ng.
Muhammad
Ni
z
am
Kamar
ud
in
was
born
in
S
el
angor
,
Malay
s
ia
.
He
re
ceive
d
the
B.
Eng
(Hons
.
)
El
ec
tr
ical
from
the
Univer
siti
Te
kno
log
i
MA
RA,
Malays
ia
n
in
2002,
and
M.Sc
in
Autom
at
ion
and
Control
from
th
e
Univer
sit
y
o
f
Newca
stle
Upon
T
y
ne,
Unite
d
Kingdom
in
2007.
He
rec
e
iv
ed
the
Doctor
o
f
Philosoph
y
in
El
e
ct
ri
ca
l
Engi
n
ee
ring
from
the
Univer
siti
Te
knologi
Malay
sia
in
2015.
He
is
cur
ren
t
l
y
wit
h
the
Univer
si
ti
Te
knik
al
Mal
a
y
s
ia
Mel
ak
a
(UTe
M).
He
is
the
m
ember
of
th
e
Board
of
Engi
nee
rs,
Malay
si
a
and
Instit
ute
of
Engi
ne
ers,
Malay
s
ia.
His
r
ese
arc
h
intere
st
s
inc
lude
non
linear
con
trol
s
a
nd
robust
cont
r
ol
s
y
stems
.
Befor
e
jo
ini
ng
UTe
M,
he
work
ed
as
a
T
ec
hn
ical
Eng
ine
er
at
t
he
m
agne
t
ron
d
epa
rtment
of
Sam
sung E
le
ct
ro
nic
s Mal
a
y
s
ia.
Mohd Luq
man
Mohd Jami
l
re
c
ei
ved
B
.
Eng
.
de
gre
e
from
th
e
Univer
siti
Te
kno
l
ogi
MA
RA
,
Shah
Alam,
Malay
s
ia,
in
2000
,
M.Sc.
degr
ee
f
rom
Univer
ist
y
of
Newca
stle
u
pon
T
y
n
e
,
U.K.,
in
2003,
a
nd
Ph.D.
degr
ee
from
The
Unive
rsit
y
of
Sheffi
eld,
Sheffi
el
d,
U.
K.,
in
2011
,
al
l
in
e
lectr
i
ca
l
engi
nee
r
ing.
He
is
cur
ren
tly
an
ac
ad
emici
a
n
in
Facul
t
y
o
f
El
ectrica
l
Engi
ne
eri
ng,
Un
ive
rsit
y
T
ekni
k
a
l
Malay
sia
Me
laka,
Mel
aka,
Mal
a
y
si
a.
He
is
al
so
an
ac
t
ive
rese
arc
h
er
in
Po
wer
El
e
ct
roni
cs
and
Drive
s
Rese
arc
h
Group
(PEDG
)
tha
t
esta
b
l
i
shed
under
the
sam
e
fa
cult
y
.
His
rese
arc
h
int
er
ests
inclu
de
the
design
,
cont
rol
and
a
naly
s
is
of
per
m
ane
nt
-
m
agn
et
m
ac
h
ine
s.
Evaluation Warning : The document was created with Spire.PDF for Python.