In
d
o
n
e
sian
Jou
r
n
al of
Ele
c
tr
i
c
a
l
En
g
in
e
erin
g
a
n
d
C
om
pu
ter S
c
ien
ce
Vol.
14, No.
1, April 2019,
pp.
346~352
ISSN: 2502-
4752,
DOI
:
10.115
91/ijeecs.
v
14.
i
1
.
pp346-352
346
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
a
e
score
.
com
/
j
o
u
r
na
l
s
/
i
n
d
e
x
.
p
hp/
i
j
eec
s
Multistage artific
ial imm
une system
for static V
AR
compensator planning
S. C
. Mohd N
a
s
i
r
1
,
M
. H.
M
a
n
s
or
2
,
I.
M
usirin
3
,
M
. M. O
th
man
4
, T.
M
. Kuan
5
,
K.
K
ami
l
6
,
M. N
.
Abd
u
ll
ah
7
1,
2
,
5,
6
Dep
a
rtm
e
nt
of
Elect
rical P
o
w
e
r
E
ngin
eerin
g, Coll
e
ge of
En
g
i
neer
ing
, Un
i
v
e
r
s
i
t
i
T
e
n
a
ga Nasi
o
nal, Selan
go
r,
M
a
la
y
s
ia
3,4
Faculty of E
l
ec
t
r
ical
E
ngi
n
eeri
n
g,
U
niversiti
T
e
knol
ogi M
ARA,
S
el
a
n
go
r, M
alay
si
a
7
Facul
t
y o
f
E
lectrical
and
E
l
ect
ro
nic E
ngineering,
Uni
vers
iti
Tu
n
Hus
s
ei
n
O
nn,
J
oho
r,
M
a
l
ay
si
a
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
Re
ce
i
v
e
d
Ju
n
7
,
2018
R
e
v
i
s
e
d
Oct
10
, 2
0
18
Ac
ce
p
t
ed
No
v
2
5
,
2
018
Int
e
rconn
ected
n
et
work
o
f
transm
is
si
on
and
d
i
stri
bu
ti
on
li
nes
l
ead
t
o
losses
in
t
he
s
ys
tem
a
n
d
wea
k
eni
n
g
th
e
vol
t
age
stability
i
n
the
sys
t
e
m
.
Inst
a
lling
Sta
tic
V
AR
C
o
m
pe
n
s
a
t
or
(
S
V
C
)
i
n
p
o
w
e
r
s
y
s
te
m
h
a
s
kn
own
to
i
mp
ro
ve
t
h
e
sy
st
e
m
b
y
minim
i
z
i
n
g
t
he
t
ot
a
l
l
os
s
and
im
p
r
o
v
e
th
e
vo
lt
age
p
r
o
fi
le
o
f
the
syst
e
m
.
This
p
a
p
er
p
resent
s
t
h
e
appli
cati
o
n
of
M
ultistage
A
r
t
i
f
ici
a
l
I
m
mune
S
y
s
t
e
m
(
M
A
IS)
t
echni
qu
e
to
d
eterm
i
ne
o
ptim
al
s
ize
o
f
S
V
C
.
Th
e
p
e
rform
a
nc
e
o
f
t
hi
s
te
c
h
n
i
qu
e
is
t
e
s
te
d
o
n
t
h
e
I
EE
E
14
-Bus
R
e
l
i
ability
T
es
t
S
y
s
t
e
m
(
RT
S
)
.
T
h
e
o
p
t
i
mizat
ion
res
u
l
t
s
sh
o
w
t
hat
th
e
pro
p
o
s
ed
M
ul
ti
stag
e
Artif
i
cia
l
I
mm
u
n
e
S
y
st
em
(
M
A
IS
)
tech
ni
que
g
ives
b
ett
e
r
s
o
l
u
tion
o
f
S
V
C
com
p
ensat
o
r
pla
n
ni
ng
p
ro
bl
e
m
c
om
p
a
red
t
o
s
in
g
l
e
st
age
A
r
tificia
l
Imm
u
ne
S
y
s
t
e
m
(
AIS
)
i
n
term
s
of
l
ow
er
t
ota
l
s
y
s
tem
loss
a
n
d
i
m
p
ro
ved
m
in
i
m
um
vo
lt
age m
a
g
n
it
u
d
e.
K
eyw
ord
s
:
Mu
lt
ist
a
ge
a
r
t
i
f
icia
l
imm
une
system
S
t
atic
V
A
R
co
m
pensa
t
or
To
tal sy
stem
l
oss
min
i
m
i
z
a
t
i
o
n
V
o
l
t
a
g
e
pr
ofi
l
e
im
provem
e
n
t
Co
pyri
gh
t © 2
019 In
stit
u
t
e
of Advanced
En
gi
neeri
n
g
an
d
Scien
ce.
All
rights
res
e
rv
ed.
Corres
pon
d
i
n
g
Au
th
or:
M.
H
.
M
a
nsor,
D
e
pa
rtme
nt
o
f
El
e
c
t
rica
l
P
o
w
e
r Engi
nee
r
i
n
g
, Col
lege
o
f En
gi
nee
r
ing ,
U
n
i
v
ersi
ti
T
e
n
aga
N
a
si
o
n
a
l
4
30
00
K
a
jan
g
,
S
e
lang
or,
Mala
ys
ia.
Em
ail:
mhe
l
m
i
@u
n
i
te
n
.
ed
u.
my
1.
I
N
TR
OD
U
C
TI
O
N
Ele
c
t
rica
l
p
o
wer
syste
m
s
are
com
p
le
x
sys
t
em
s
c
onsi
s
t
i
ng
o
f
l
a
rg
e
num
be
r
of
g
e
n
e
r
at
i
ng
un
i
t
s
an
d
i
n
t
e
rc
onn
e
c
t
e
d
n
e
t
w
o
r
k
of
t
ran
s
mi
ssio
n
a
n
d
d
i
st
ri
bu
tio
n
l
i
ne
s.
F
u
rthe
rm
o
r
e,
t
he
p
ow
er
d
em
and
is
i
nc
rea
s
in
g
at
a
n
a
l
arm
i
n
g
r
a
t
e
da
y
by
d
ay,
a
s
a
r
e
s
ult
o
f
w
h
i
c
h
t
he
u
til
i
t
i
e
s
a
r
e
bei
ng
c
o
mpe
lle
d
to
o
p
e
rate
t
he
ir
gene
ra
ti
n
g
u
n
i
t
s
a
nd
tra
n
sm
is
si
on
l
ine
s
a
t
t
h
eir
m
a
ximum
c
a
pa
ci
t
y
[
1
]
.
In
o
rder
t
o
impr
ove
t
he
p
ow
e
r
s
ystem
opera
tio
n,
F
lexi
b
l
e
A
C
T
r
a
n
s
missi
on
S
y
s
t
e
m
s
(F
A
C
T
S
)
dev
i
c
e
s
are
u
se
d
in
r
e
cen
t
y
e
a
r
s.
R
ea
ct
i
v
e
p
o
w
e
r
cha
nge
s
pr
o
duc
ed
b
y
l
o
a
d
v
a
r
iat
i
o
n
s
a
nd
l
i
n
e
s
w
itc
h
i
n
g
c
a
n
c
a
u
s
e
ad
ver
s
e
effec
t
s
on
s
y
stem
vol
ta
ge
s
t
a
bi
l
i
t
y
and
the
i
n
te
rc
onne
c
t
e
d
s
ys
tem
se
curit
y
[2]
.
The
r
e
a
r
e
se
ve
ra
l
t
y
pes
o
f
F
A
C
TS
d
e
v
i
c
es
s
uc
h
as
S
ta
t
i
c
S
ync
h
r
o
no
u
s
C
ompe
nsa
t
or
(
S
T
A
T
CO
M
)
,
S
t
atic
V
A
R
C
om
pen
s
at
or
(
S
V
C),
U
n
ifie
d
P
o
w
e
r
F
l
ow
C
on
tro
l
l
e
r
(
U
P
FC
),
C
o
n
v
e
rtib
le
S
e
r
i
e
s
C
o
mpe
n
sat
o
r
(CS
C
),
I
nter
-phase
P
ow
e
r
F
low
Co
n
t
r
o
l
l
e
r
(
IP
F
C
),
S
tatic
S
ynchr
o
nou
s
S
e
ri
es
C
on
t
r
ol
l
e
r
(
S
S
S
C
)
,
Th
y
r
i
s
to
r
Con
t
ro
lle
d
S
e
ries
C
om
pe
nsa
t
or
(
TCS
C
),
T
hyr
ist
o
r
Co
ntr
o
l
l
e
d
P
ha
s
e
S
h
i
f
tin
g
Tra
n
sf
orm
e
r
(TCP
S
T
)
and
S
upe
r
Co
n
duc
t
i
n
g
M
a
g
ne
tic
E
ne
rg
y
S
t
or
ag
e
(S
MES
)
[
3].
A
m
ong
the
t
y
p
e
s
o
f
F
A
C
T
S
d
e
v
i
c
e
s
,
S
V
C
i
s
t
h
e
prom
ine
n
tly
u
s
e
d
b
y
t
he
G
r
i
d
S
y
st
e
m
O
pe
rators
(
G
S
O
s
).
O
ne
o
f
t
h
e
rea
s
on
s
for
this
i
s
SV
C
is
c
hea
p
e
r
t
han
ot
her
F
A
CTS
dev
i
ce
s
e
s
pe
ci
all
y
S
TA
T
C
O
M
a
n
d
T
CS
C.
H
ow
e
v
er,
S
V
C
i
s
st
i
ll
ve
r
y
e
xpe
n
s
i
v
e
in
p
rice
t
h
u
s
its
opt
im
al loc
a
t
i
o
n a
nd s
i
ze
i
n the
ne
tw
or
k m
u
st be
o
p
tim
all
y
a
s
ce
rt
ai
n
e
d
[
3
].
F
o
r
t
h
e
pa
st
d
eca
de,
re
sear
cher
s
an
d
ele
c
t
r
i
c
a
l
e
n
g
i
n
e
ers
have
i
n
tro
duce
d
m
a
n
y
op
t
i
miza
tio
n
tech
n
i
q
u
es
f
or
t
he
S
V
C
p
la
nn
in
g.
T
he
se
t
e
c
h
n
i
que
s
i
n
c
l
ud
e
m
a
the
m
a
t
i
ca
l
m
e
th
ods
l
i
k
e
l
i
nea
r
p
ro
gra
m
m
i
ng,
qua
dra
tic
p
r
o
gram
m
i
n
g
a
n
d
h
e
u
r
i
s
t
ic
m
eth
o
d
s
l
i
ke
E
vo
l
u
ti
onar
y
P
rogr
am
min
g
(
EP
),
P
a
r
ticle
S
w
a
rm
Evaluation Warning : The document was created with Spire.PDF for Python.
Ind
ones
i
a
n
J
E
lec
En
g & Co
mp
S
c
i
IS
S
N
: 2502-
47
52
Mu
l
t
is
tage
ar
t
ific
i
a
l immune s
y
stem f
o
r sta
t
ic
VAR compe
n
sat
o
r
p
l
an
n
i
ng (S. C.
M
ohd
N
a
sir)
34
7
Opti
m
i
za
t
i
on
(
PSO)
[
4
]
and
A
r
ti
f
i
cial
I
m
m
une
S
ystem
(A
IS
)
.
A
I
S
is
a
c
om
pu
ta
ti
ona
l
p
a
r
a
di
gm tha
t b
e
lo
n
g
to
the
c
o
mp
ut
at
i
o
nal
i
n
te
l
l
i
ge
nc
e
fam
i
l
y
i
ns
pire
d
b
y
t
he
b
io
log
i
c
a
l
im
mu
ne
s
yste
m
[5].
T
he
A
IS
u
se
s
an
i
de
a
glea
ne
d
from
i
m
munol
o
gy
in
o
rder
t
o
de
ve
l
op
sys
t
em
s
capa
b
l
e
o
f
p
e
rfor
ming
differe
n
t
tas
k
s
in
v
a
r
io
u
s
a
r
eas
of
r
ese
a
rc
h
[6
].
A
IS
i
s
a
divers
e
are
a
o
f
res
e
a
r
ch
t
h
a
t
a
t
t
e
mpt
s
t
o
b
ri
dg
e
i
m
mu
nol
o
g
y
a
n
d
e
ngi
ne
e
r
i
n
g
deve
l
ope
d
t
h
rou
g
h
t
he
a
ppl
ica
t
i
o
n
o
f
t
ec
hn
ique
s
suc
h
a
s
ma
them
a
t
i
c
a
l
an
d
c
o
mp
u
t
at
i
ona
l
mo
de
lin
g
of
imm
uno
log
y
.
A
I
S
h
a
s
pro
v
e
n
c
a
p
a
b
le
o
f
s
o
l
v
ing
m
a
ny
p
ow
e
r
s
ys
tem
p
rob
l
em
s
suc
h
a
s
eco
n
o
m
i
c
d
i
s
p
at
c
h
pro
b
lem
,
d
i
s
tr
i
b
u
t
e
d
ge
n
era
t
i
on p
l
ac
em
en
t p
r
o
b
le
m
and r
eac
tive
p
o
w
e
r
pl
ann
i
ng.
T
h
i
s
p
a
p
e
r
p
r
o
p
o
s
e
s
t
o
u
s
e
M
u
l
t
i
s
ta
ge
A
rtific
ial
I
m
m
une
S
ystem
(MA
I
S
)
t
echn
i
que
t
o
s
o
lve
S
V
C
p
l
ann
i
n
g
p
r
oble
m
.
M
A
I
S
i
s
a
n
e
w
t
ech
niqu
e
th
at
d
ev
el
op
ed
f
ro
m
t
h
e
m
odi
fica
ti
on
of
t
he
o
ri
g
i
nal
A
I
S
t
e
c
h
n
i
q
u
e
.
D
i
f
f
e
r
e
n
t
f
r
o
m
t
h
e
o
r
i
g
i
n
a
l
A
I
S
,
M
A
I
S
h
a
s
m
u
l
t
i
p
l
e
s
ta
ge
s
of
t
he
s
a
m
e
p
r
oce
s
se
s
of
c
l
o
n
i
ng,
muta
ti
on
a
n
d
sele
ct
io
n.
T
he
pur
pose
of
t
h
i
s
m
odi
fica
t
i
o
n
is
t
o
mak
e
t
he
p
o
ssib
l
e
so
l
u
t
i
on
b
ro
a
d
e
r
t
han
the
ori
g
ina
l
A
IS
te
c
hn
i
q
ue
. S
ubse
que
ntl
y
, th
i
s w
i
l
l
i
nc
rea
s
e
t
h
e
ac
c
u
ra
cy
o
f
th
e re
su
l
t
s
p
rod
u
ced
a
s t
h
e
nu
mbe
r
o
f
com
p
aris
on
i
n
cre
a
sed.
T
he
i
m
p
l
e
me
n
t
a
t
ion
of
M
A
I
S
t
o
s
ol
ve
S
V
C
p
l
a
n
n
in
g
pr
ob
le
m
is
e
xp
la
ine
d
i
n
de
ta
i
l
s
in t
he
n
e
x
t sec
tio
n.
I
t
is fou
n
d
t
ha
t
the pr
opose
d
MA
I
S
is super
i
or
tha
n the
or
i
g
i
n
a
l A
I
S
to sol
ve
S
V
C
p
la
nn
i
n
g pr
ob
lem
.
M
A
I
S
g
i
v
e
s
b
e
t
t
e
r
s
o
l
u
t
i
o
n
i
n
t
e
r
m
s
o
f
l
o
w
e
r
t
o
t
a
l
s
y
s
t
e
m
l
o
s
s
a
n
d
impr
ov
e
d
m
i
n
i
m
u
m
v
o
l
t
a
ge
m
a
gni
tu
de
com
p
are
d
t
o or
i
g
i
n
al
A
IS.
2.
PROBLE
M
FORMULATIO
N
P
r
ior
to
t
he
e
m
p
l
o
ym
en
t
o
f
M
A
I
S
,
t
he
o
pt
ima
l
l
oca
t
i
o
n
of
t
he
S
V
C
uni
ts
w
a
s
f
o
und
u
si
ng
vol
t
a
ge
dev
i
a
t
i
o
n
in
de
x
.
V
olta
ge
d
e
v
ia
ti
on
i
nde
x
(V
D
I)
is
a
n
in
d
i
c
a
t
o
r
use
d
t
o
deter
m
i
n
e
h
o
w
m
u
ch
t
he
b
us
v
o
l
tag
e
ma
gni
tude
h
a
s
d
e
v
i
a
ted
from
its
r
e
f
er
ence
v
a
l
ue.
A
p
o
w
e
r
syste
m
i
s
c
ons
i
d
e
r
e
d
t
o
have
g
o
o
d
v
o
l
t
a
ge
p
rofi
le
if
it
has
l
o
w
v
o
l
t
a
g
e
de
v
i
a
t
i
o
n
i
nde
x
va
lue
.
T
he
f
orm
u
la
o
f
v
o
l
ta
ge
d
e
v
ia
ti
o
n
i
nde
x
is
a
s
show
n
i
n
e
q
u
a
t
io
n
(1).
∆
,
,
(1)
wh
ere
,
i
s t
h
e ref
e
re
n
c
e v
o
lt
ag
e a
t
ℎ
bus [8]
The
sea
r
ch
f
o
r
t
he
o
p
tim
al
l
oca
tio
n
a
n
d
s
i
z
e
i
s
ba
sed
o
n
t
w
o
o
b
je
c
tiv
e
fun
c
ti
ons,
w
h
i
c
h
ar
e
to
m
i
n
i
m
i
z
e
t
o
t
a
l
s
y
s
t
e
m
l
o
s
s
a
n
d
t
o
i
m
p
r
o
v
e
m
i
n
i
m
u
m
v
o
l
t
a
g
e
m
a
g
n
i
tu
de
.
Th
is
s
t
u
dy
c
o
n
s
i
ders
s
i
n
g
l
e
ob
jec
t
i
v
e
op
ti
miz
a
t
i
on,
w
hic
h
m
e
a
ns on
l
y o
n
e
ob
jec
tive
fu
nct
i
on
i
s op
t
i
mize
d at
a
t
im
e.
a.
Objective
Fu
nction
1:
T
o
m
inimize tot
a
l
s
y
s
t
em
l
oss
The
t
o
ta
l sys
t
e
m
l
oss
ca
n be
calc
u
l
a
t
e
d usi
n
g
the fo
llow
i
n
g
e
qu
ati
on:
2
co
s
co
s
(2)
wh
ere
a
nd
a
re
t
he
numbe
r
o
f
line
s
a
n
d
buse
s
,
re
spect
ive
l
y;
i
s
the
r
e
sist
a
n
ce
of
l
ine
;
is
the
cur
r
en
t
thr
o
u
g
h
l
i
n
e
;
a
nd
are
t
h
e
vol
ta
ge
m
a
gni
tud
e
and
a
n
g
le
at
node
,
re
specti
v
e
l
y;
and
ar
e
the
m
a
g
n
i
t
u
de
an
d
a
n
g
le
o
f t
h
e
line
adm
i
t
t
a
n
ce
be
t
w
ee
n bus
and
bus
,
respectivel
y
[8].
b.
Ob
j
ec
t
i
v
e
Fu
n
c
tion
2
: To i
mp
rove
m
in
i
m
u
m
volta
ge
ma
g
n
i
t
u
d
e
(3)
F
o
r
this
s
e
c
o
n
d
o
bj
e
c
t
iv
e
fu
n
c
ti
o
n
,
it
i
s
e
ns
ure
d
t
ha
t
t
h
e
mini
mum
v
o
lt
a
g
e
m
a
gn
itu
de
o
f
the
system
is
i
mpr
ove
d a
f
t
e
r
t
h
e
ins
t
a
l
l
a
ti
on o
f
S
V
C
s
i
n
t
he p
ow
e
r
syst
e
m
a
s
s
how
n i
n
e
qua
t
i
o
n
(
3).
c.
Oper
ationa
l C
o
n
s
traint
s
The
tw
o o
b
j
ec
t
i
ve
fu
n
c
t
i
ons a
re
s
ubje
c
t
ed
t
o
the
fo
ll
ow
i
ng
o
p
er
a
tio
na
l
con
s
t
r
ai
nts:
2.3.
1 Re
a
l
a
nd
Reac
t
ive
Power
Balan
ce
Cont
raints
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2502-
4752
I
n
do
n
e
si
an
J
E
l
e
c
E
n
g
&
C
o
m
p
S
ci
, V
o
l
.
1
4
,
No. 1, April 2019 :
346 –
3
52
34
8
The
ba
l
a
nce
o
f
a
ct
i
v
e
an
d
r
e
ac
t
i
ve
p
owers
must
b
e
sa
tis
fi
ed
a
t
e
ach
b
us.
Rea
l
a
nd
rea
c
ti
ve
pow
e
r
bala
nc
e w
ith r
espec
t
t
o a
bus c
a
n
be
form
ula
t
ed
a
s:
′
co
s
′
si
n
(4)
′
si
n
′
si
n
(5)
wh
ere
a
nd
a
re
t
he
g
ener
ate
d
acti
v
e
and
r
eac
tive
p
o
we
rs,
respec
tive
l
y
;
a
nd
a
r
e
t
h
e
loa
d
act
i
v
e
an
d
re
acti
v
e
p
o
w
ers
at
node
,
re
spe
c
ti
ve
ly.
The
co
n
duc
ta
n
c
e,
′
a
n
d
s
u
s
c
e
p
t
a
n
c
e
,
′
repr
esent the
re
al a
nd im
agi
n
ary com
pone
n
t
s of elem
e
n
t
′
of
the
[
′
] ma
trix, respec
tive
l
y,
obta
i
ned b
y
modi
fyi
n
g
t
he
init
ia
l
noda
l a
d
mit
t
a
n
ces
m
a
t
rix w
h
en
i
ntro
duc
ing
the
S
V
C
[1
0].
2.3.
2V
o
l
t
a
ge S
tab
i
l
i
ty C
on
strain
t
The
v
o
l
t
a
g
e
ma
gn
itu
de
a
t a
ll
busse
s
ar
e e
n
su
r
e
d
to
b
e w
i
t
h
in t
h
e
lim
its of
±
5
% of
i
t
s
n
o
m
inal va
l
ue
.
V
,
V
,
V
,
(6)
3.
IMPL
E
M
EN
TATION
O
F
MAIS
T
O
FI
N
D
TH
E
S
I
ZE OF
S
VC
S
Th
e
l
o
cati
o
n
of
S
VC
u
nit
s
a
re
d
et
ermi
n
e
d
b
y
u
si
ng
v
ol
t
a
g
e
d
evi
a
t
i
on
inde
x
before
t
h
e
M
A
I
S
is
em
plo
y
e
d
t
o
fi
nd
t
he
o
ptim
al
s
ize
of
t
he
S
V
C
u
n
i
t
s
.
F
o
r
the
IEE
E
1
4
-
B
us
R
e
lia
b
ili
ty
T
est
Sys
t
em
(
RTS
)
a
s
show
n
in
F
ig
ur
e
1,
i
t
w
a
s
dec
i
de
d
t
o
i
nsta
l
l
onl
y
t
h
r
e
e
S
V
C
un
i
ts
b
ase
d
o
n
its
s
ize.
T
he
l
o
c
ati
ons
o
f
t
h
e
SVC
un
its a
re
at
b
u
s
e
s
tha
t
h
av
e hig
h
e
st
VDI v
a
l
ues
.
F
i
gure
1.
14-B
u
s
Re
li
a
b
i
l
i
t
y
Test S
yst
e
m
[9
]
Tab
l
e
1.
V
ol
ta
g
e
D
e
v
ia
tio
n
Inde
x
at Base
Con
d
i
t
i
on
Bu
s
Vol
t
age
d
e
v
i
a
t
i
on
Ind
e
x
at e
a
c
h
b
u
s
1
0.
0036
2
0.
0020
3
0.
0001
4
0.
0002
5
0.
0006
6
0.
0049
7
0.
0031
8
0.
0081
9
0.
0097
10
0
.
0097
11
0
.
0066
12
0
.
0034
13
0
.
0032
14
0
.
0039
Evaluation Warning : The document was created with Spire.PDF for Python.
Ind
ones
i
a
n
J
E
lec
En
g & Co
mp
S
c
i
IS
S
N
: 2502-
47
52
Mu
l
t
is
tage
ar
t
ific
i
a
l immune s
y
stem f
o
r sta
t
ic
VAR compe
n
sat
o
r
p
l
an
n
i
ng (S. C.
M
ohd
N
a
sir)
34
9
The
proce
ss
of
M
A
I
S
t
o
f
i
n
d
t
h
e
opt
im
al
s
iz
e
o
f
t
he
t
hr
ee
S
V
C
u
ni
t
s
i
s
show
n
in
F
ig
u
r
e
2.
F
irstl
y
,
three
i
n
itia
l
va
lue
s
w
er
e
gene
rated
ra
n
dom
ly.
These
t
h
re
e
val
u
e
s
repr
esen
t
thr
ee
con
t
rol
varia
b
les
o
f
S
V
C
un
its t
o
be ins
t
a
lle
d.
T
he
s
e
r
ies of ra
n
d
o
m
nu
mbe
r
,
is
g
e
ner
a
ted b
y
u
nif
o
r
m
d
istri
b
u
t
ion
numbe
r [1
0]:
=
r
an
d(a
,
b
)
*o
ff
_set
+
mi
n_s
et
(7)
wh
ere;
i
=
1,
2
and 3
a
=
n
um
ber
of
r
ow
b
=
n
um
ber
of
c
ol
umn
o
ff_s
e
t
=
m
axim
um
r
an
ge
n
um
ber
tha
t
ca
n
be
ac
h
i
e
v
ed
m
in_
s
et
=
m
in
i
m
um
range
n
u
m
ber
Th
e
ra
ndo
m
nu
mb
e
r
g
en
era
t
e
d
u
sing
t
h
e
u
n
i
fo
rm
d
i
s
t
r
ib
ut
ion
n
u
m
b
e
r
w
i
l
l
b
e
a
ss
igne
d
a
s
t
he
s
ize
of
the
SV
C
uni
t
s
.
Since
it
w
a
s
dec
i
de
d
to
h
a
v
e
three
SV
Cs
i
nsta
lle
d,
t
hus
t
h
r
ee
v
a
r
iables
n
am
ely
,
a
nd
are
gene
rate
d
to
r
epre
se
n
t
t
he
s
i
z
e
of
S
V
C
a
t
b
u
s
8,
9
a
n
d
10
r
e
s
pec
t
iv
el
y.
T
he
r
a
n
ge
o
f
r
a
nd
om
numbe
r
of
the
S
V
C
un
its’
size
i
s
b
e
t
w
e
e
n
-
10
0
MV
A
R
t
o
1
00
MV
A
R
.
The
S
V
C
u
ni
t
s
c
a
n
e
i
t
he
r
in
j
e
c
t
ing
or
a
b
s
or
b
i
n
g
the r
eac
t
i
ve
p
o
w
er
to or
f
rom t
h
e
b
u
ses
respe
c
t
i
v
e
l
y.
Eq
ua
ti
ons
(
3),
(4),
(
5)
a
nd
(6)
a
r
e
use
d
t
o
e
n
sur
e
t
he
r
a
n
d
o
m
n
um
bers
g
e
n
era
t
e
d
a
bi
de
t
he
p
rob
l
em
c
o
nst
r
a
i
nt
s.
T
twe
n
ty
i
nd
ivi
d
ual
s
o
f
co
nt
rol
va
ri
ab
l
e
s
are
g
e
n
e
r
ate
d
b
a
s
e
d
on
t
h
e
ca
l
c
u
l
a
t
ed
f
i
t
ne
ss,
wh
ic
h
ca
n
be
t
o
t
al
s
ys
te
m
loss
o
r
m
i
nim
u
m
vo
l
t
age
m
a
gni
t
ude.
T
h
e
s
e
in
di
vi
du
a
l
s
a
r
e
st
o
r
ed
i
n
t
h
e
po
pul
a
t
i
o
n
p
ool
.
S
ubseq
ue
n
t
l
y
,
the tw
e
n
ty
i
n
d
i
v
i
d
ual
s
ar
e
c
loned b
y
t
e
n
.
U
n
l
i
ke
t
he
s
ingle
sta
g
e
A
I
S
,
M
A
I
S
c
l
one
s
the
p
o
p
u
l
at
i
o
n
w
ith
m
u
l
t
ip
l
e
s
ta
ges.
B
efore
the
c
l
on
in
g
proce
s
s,
t
he
i
nit
i
a
l
p
o
pula
tio
n
are
dec
o
m
p
ose
d
i
n
t
o
fo
ur
s
ub-
po
p
u
la
t
i
o
n
s,
w
hic
h
c
on
t
a
in
s
five
i
nd
iv
id
ua
ls.
A
f
ter
tha
t
,
the
sub
-
po
p
u
la
tio
ns
w
i
ll
u
n
d
ergo
c
l
on
i
ng,
m
ut
a
t
i
o
n
a
n
d
se
le
ct
ion
proc
e
s
ses.
T
he
M
A
TLA
B
pro
g
ra
mm
ing code
for
clo
ni
n
g
pr
oc
ess is a
s
show
n in e
qua
tion
(8
).
Cl
on
e_
k =
r
e
pm
at (
A,
[
i, j
]
)
(8)
wh
ere;
k
= num
b
er
of
s
t
age
A
=
subj
e
c
t
to
c
lo
n
e
i
=
c
lone
t
he
r
o
w
j
=
c
lone
t
he
c
o
l
umn
F
o
r
t
h
e
mut
a
ti
o
n
p
ro
c
e
ss,
G
a
u
ssi
a
n
M
u
t
a
t
i
o
n
te
ch
ni
qu
e
is
u
sed
t
o
pro
duc
e
the
o
f
f
s
p
ri
ng.
T
h
e
G
a
ussia
n
M
u
t
a
t
i
o
n equa
ti
on
is a
s show
n in
e
qua
t
i
o
n
(9).
,
,
0
,
(
9
)
wh
ere;
,
=
m
ut
at
e
d
p
aren
t
(o
ff
sp
rin
g
)
,
=
p
a
r
e
n
t
s
=
Gau
ssi
an
rand
o
m
v
a
r
i
a
b
l
e
wi
t
h
mea
n
a
nd
va
r
ianc
e
=
mu
t
at
ion
sc
al
e, 0
<
<
1
= m
a
xim
u
m
ran
d
om
num
ber
for
eve
r
y va
ria
b
le
= m
i
n
i
m
u
m
rand
om
numbe
r for e
v
ery
varia
b
le
= f
i
tness
for
t
h
e
r
a
n
do
m
nu
m
b
e
r
=
ma
x
i
mu
m
f
i
tn
e
s
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2502-
4752
I
n
do
n
e
si
an
J
E
l
e
c
E
n
g
&
C
o
m
p
S
ci
, V
o
l
.
1
4
,
No. 1, April 2019 :
346 –
3
52
35
0
F
i
gure
2.
F
low
Char
t
for
M
A
IS
T
ec
hn
i
que
A
t
t
he
e
nd
o
f
e
ach
s
tage,
f
i
ve
b
e
s
t
i
n
div
i
d
u
a
l
s
a
r
e
pro
duc
e
d
m
a
de
u
p
o
f
t
w
e
nt
y
i
n
d
i
vid
u
a
l
s.
T
he
b
e
s
t
tw
en
ty i
n
d
i
v
i
d
ual
s
a
re
t
hen u
nde
r
go c
o
n
v
e
r
genc
e te
st
t
o
fi
nd t
h
e
glo
b
a
l
o
ptim
a.
C
o
n
v
erge
nce
c
r
iteri
on
i
s
sp
ecifie
d
w
he
n
the
va
lue
o
f
d
i
ffe
re
nc
e
b
e
t
w
e
e
n
t
h
e
2
0
th
a
nd
the
1
st
i
n
d
i
vid
u
a
l
i
s
l
e
s
s
th
an
0
.0
0001
f
o
r
e
a
c
h
fi
tne
ss.
M
a
t
h
e
mat
i
ca
l
l
y
,
t
h
e
c
onve
rg
e
n
c
e
c
ri
t
e
ri
o
n
o
f
f
i
t
n
ess
of
t
ot
al
syste
m
l
oss
an
d m
i
ni
m
u
m
b
u
s
vo
lta
ge
a
re
as
show
n i
n
e
q
u
a
tio
n
(1
0) a
nd e
qua
t
i
o
n
(
11)
r
espec
t
i
v
e
l
y
.
,
,
0
.0
00
1
(
10)
∆
∆
,
0
.000
1
(
11)
4.
RESUL
T
S A
N
D
DIS
CUS
SION
A
s
m
e
n
t
i
o
n
e
d
i
n
t
h
e
p
r
e
v
i
o
u
s
s
e
c
t
i
o
n
,
t
h
e
r
e
a
r
e
t
w
o
o
b
j
e
c
t
i
v
e
f
unc
ti
ons
t
es
te
d
for
the
M
A
I
S
op
tim
iza
t
i
o
n. The ob
j
ec
tive
func
tio
ns a
re t
o m
i
nim
i
z
e
to
t
a
l
sys
tem
l
o
ss a
n
d t
o
im
p
ro
ve
m
inimum
bus
v
o
ltage
.
There
f
ore
,
t
he
r
esults
o
f
MAI
S
t
o
de
ter
m
ine
the
size
o
f
t
h
e
i
n
s
t
a
l
l
e
d
S
V
C
u
n
i
t
s
a
r
e
d
i
v
i
d
e
d
i
n
t
o
t
w
o
p
a
r
t
s
base
d o
n
i
ts o
b
j
ect
i
v
e func
t
i
o
n
s
.
F
o
r the
s
e
t
w
o o
b
je
c
t
i
v
e
func
t
io
ns, t
h
e
l
oca
t
ion
s
o
f t
h
e
SV
C uni
ts ar
e
at b
u
ses
8,
9
a
n
d
1
0.
T
h
e
se
l
ocat
i
o
n
s
a
re
d
e
t
erm
i
ned
from
t
he
V
D
I
v
a
l
ue
s
o
f
all
bu
se
s
wh
ere
th
e
th
ree
SVC
u
n
it
s
are
place
d at
t
he
b
uses
t
ha
t
ha
ve
h
i
ghe
s
t
V
D
I
v
alue
s.
a.
Minimizin
g
Total Syst
e
m
L
o
ss as t
he O
bj
ect
i
ve Fu
n
ct
i
o
n
The
re
su
l
t
s
of
t
o
t
a
l
s
ys
t
e
m
loss
a
nd
mi
n
i
mum
vol
t
a
ge
m
agni
t
ude
pro
duc
e
d
b
ef
ore
a
nd
a
f
te
r
t
h
e
op
tim
iza
t
i
o
n fo
r
the
first o
b
j
e
c
t
i
v
e
func
t
i
o
n
a
r
e
ta
b
u
l
a
t
e
d
in
Ta
ble
2.
Ta
b
l
e
2.
V
alue
s
of T
ota
l
S
yst
e
m
Loss a
nd M
i
n
i
m
u
m
V
o
lt
age
Ma
gn
it
u
d
e
for
Minim
i
z
i
ng
the T
o
ta
l
System
Loss
Te
c
hniq
u
e
To
t
a
l
S
y
s
t
e
m
L
o
ss (MW)
Mi
n
i
mu
m
V
o
ltage
Magn
itude
(
p
.
u)
Pre
-
optim
iza
tion
(wit
hout
S
V
C
)
13.
56
1
.
0100
Post-o
ptim
i
z
at
ion
(
u
si
ng
A
I
S
te
c
hnique
)
13.
48
1
.
0100
Pos
t
-
o
pti
m
i
z
a
tion
(usin
g
M
AIS
te
c
hnique
)
13.
46
1
.
0093
B
a
se
d
o
n
t
h
e
T
ab
l
e
2
,
M
A
IS
p
ro
du
ced
t
he
l
o
w
es
t
t
o
t
a
l
sy
st
em
l
o
s
s
c
o
m
p
are
d
t
o
pr
e-op
t
i
miz
a
tio
n
and
A
I
S
re
sult
s,
w
hich
i
s
13.
46
M
W
.
H
o
w
e
ver
,
f
or
t
h
i
s
o
b
j
e
c
t
i
ve
f
unc
t
i
o
n
,
the
m
i
n
i
m
u
m
vol
tage
m
a
g
n
i
t
u
d
e
pro
duce
d
b
y MA
IS
i
s slide
l
y low
e
r th
a
n
p
r
e
-op
t
imiza
t
i
o
n and A
I
S
results. Thi
s
val
ue is st
i
l
l
a
cce
p
t
a
b
l
e
a
s
th
e
most mi
n
imum
va
l
ue
a
ll
ow
ed
i
s
0.9
5
p
.
u
. It i
s
f
ou
nd
tha
t
S
V
C
u
n
i
t
s
i
nst
a
ll
ati
o
n c
a
n
h
e
lp
t
o
mi
ni
mi
z
e
t
he
t
o
t
al
Evaluation Warning : The document was created with Spire.PDF for Python.
Ind
ones
i
a
n
J
E
lec
En
g & Co
mp
S
c
i
IS
S
N
: 2502-
47
52
Mu
l
t
is
tage
ar
t
ific
i
a
l immune s
y
stem f
o
r sta
t
ic
VAR compe
n
sat
o
r
p
l
an
n
i
ng (S. C.
M
ohd
N
a
sir)
35
1
syste
m
l
oss
a
n
d
b
y
u
si
ng
MA
IS
t
ec
hniq
u
e
t
o
f
i
nd
the
op
t
i
m
a
l
siz
e
of
t
he
S
V
C
u
nits
w
ill
le
ad
t
o
be
tter
r
e
su
lts
com
p
are
d
t
o AI
S
t
e
chn
i
que.
Tab
l
e 3.
Loc
at
ions
a
nd S
i
zes
o
f
SVC
Un
i
t
s
B
ased
o
n
Obj
e
c
t
iv
e
Fu
nc
t
i
o
n
of
Mi
nim
i
z
i
n
g
t
he
T
ota
l
S
yst
e
m
Loss
Si
z
e
o
f
SV
C
(
M
VA
R)
T
e
c
h
ni
qu
e
SV
C l
o
c
a
t
i
o
n
Bu
s
8
Bus
9
Bus
1
0
AIS
34.
35
35.25
2
.
7
9
M
A
IS
-
25.
8
3
32.28
15.
29
I
t
c
an
b
e
seen
f
r
o
m
Ta
b
l
e
3.
t
ha
t
a
ll
th
e
thr
ee
S
V
C
uni
ts
s
up
pl
i
e
d
rea
c
t
i
ve
p
ow
er
t
o
t
h
e
sys
t
em
.
H
o
w
e
ve
r,
f
or
M
A
I
S
,
only
S
V
Cs
a
t
b
u
s
9
and
bus
10
su
pp
l
i
ed
r
ea
ct
ive
pow
e
r
a
nd
S
V
C
at
b
us
8
a
bsor
bed
rea
c
ti
ve
p
ow
er
o
f 25.
8
3
MV
A
R fr
o
m
t
he
sys
t
e
m.
D
iffer
e
nt tec
hni
q
ue
l
e
a
ds
t
o
differ
en
t
size
of
S
V
C
uni
ts.
Ta
ble
4.
V
alues
of To
t
a
l
S
yst
e
m
Loss a
nd M
i
nim
u
m
V
o
lta
ge
M
a
g
n
i
t
u
d
e
for
Im
provi
ng
the
Mi
n
i
mum
Vo
lt
a
g
e M
a
gnit
u
d
e
Te
c
hniq
u
e
To
t
a
l
Sy
s
t
e
m
L
o
ss (
M
W)
Mi
n
i
mu
m
V
o
l
t
a
g
e
Magni
t
u
d
e
(p.
u
)
Pre
-
optim
iza
tion
(wi
t
hout
S
V
C
)
13.56
1
.
0100
Post-o
ptim
i
z
at
ion (
u
si
n
g
AIS
te
c
hnique
)
13.49
1
.
0150
P
o
s
t
-
o
pt
im
i
z
a
tion
(usin
g
M
A
I
S
te
c
hnique
)
13.49
1
.
0200
Base
d
o
n
th
e
re
s
u
lts i
n Ta
ble 4.
t
he
m
i
n
im
u
m
vol
t
a
ge ma
gni
t
ude
of
t
h
e
s
y
s
t
e
m
i
m
p
r
ov
e
d
fro
m
1
.
010
p.u
b
e
fore
o
pt
i
m
iza
t
i
o
n
t
o
1
.
0
1
5
p
.
u
a
nd
1.
02
0
p.u
a
f
ter
i
t
i
s
op
t
i
m
i
ze
d
us
i
n
g
A
I
S
and
MA
IS
r
e
s
pe
ct
ive
l
y
.
The
t
o
tal
s
y
ste
m
l
oss
als
o
c
a
n
b
e
see
n
r
edu
c
e
d
f
rom
t
h
e
p
r
e
-
opt
imiza
t
i
o
n.
F
rom
Table
5
.
it
ca
n
be
s
e
e
n
t
h
a
t
bo
th
A
IS
a
nd
MA
IS
h
a
v
e
SV
C
u
n
its t
hat
a
b
sor
b
in
g
t
h
e
r
eac
tive
p
ow
e
r
.
F
o
r
A
I
S,
S
V
C
u
n
i
t
at b
us 8
a
bsor
bed
t
h
e
r
e
a
c
t
i
v
e
p
o
w
e
r
w
h
i
l
e
f
o
r
M
A
I
S
a
t
b
u
s
1
0
.
T
h
e
o
t
h
e
r
t
w
o
S
V
C
un
i
t
s
of
e
ach
t
ec
hn
ique
a
re
s
u
p
p
l
y
in
g
rea
c
ti
ve
p
ow
er
t
o
th
e
s
y
stem
.
Tab
l
e 5.
Loc
at
ions
a
nd S
i
zes
o
f
SVC
Un
i
t
s
B
ased
o
n
Obj
e
c
t
iv
e
Fu
nc
t
i
o
n
of
Im
p
r
ov
i
n
g
the
M
i
n
i
m
u
m
V
o
l
t
age
Ma
gn
i
t
u
d
e
Size
o
f
SV
C
(
M
VA
R)
T
e
c
h
ni
qu
e
SV
C
lo
c
a
t
i
on
Bu
s
8
Bus
9
Bu
s 1
0
AIS
-2
3.
3
0
3.
88
66.
19
M
A
IS
64.
94
50.59
-
67.
4
1
5.
CONCL
U
S
IONS
I
n
t
h
i
s
pa
pe
r,
M
A
I
S
opti
m
i
z
a
t
i
o
n
tec
h
ni
q
u
e
ha
s
be
en
u
se
d
t
o
a
c
h
i
e
ve
t
w
o
d
i
ffe
re
nt
o
b
j
ec
t
i
ve
fu
nc
ti
o
n
s
for
de
term
in
i
n
g
the
op
tim
al
s
ize
o
f
t
hre
e
S
V
C
u
nits
i
nst
a
lle
d
in
t
he
I
EEE
14-
B
u
s
Reliability
T
e
s
t
S
y
stem
(
RTS
)
.
The
l
o
c
a
t
i
on
s
of
t
he
S
V
C
u
n
its
w
ere
firstl
y
de
t
e
r
m
i
n
e
d
u
s
i
n
g
t
h
e
V
D
I
a
pproac
h
.
Whe
n
targe
t
i
n
g
on
e
of
o
b
j
ec
ti
ve
f
u
n
c
t
i
on,
t
he
o
th
e
r
o
b
j
e
c
tive
fu
nct
i
on
i
s
s
l
i
ght
ly
h
a
v
i
n
g
d
i
sa
dva
n
t
age
.
H
o
w
ever
,
f
o
cu
si
ng
o
n
eac
h
o
b
j
ect
i
v
e
wi
ll
h
el
p
t
h
e
Gri
d
S
y
s
tem
Op
e
r
at
o
r
s
(
G
SO
s)
t
o
c
o
mpa
r
e
and
dec
i
de
w
hic
h
ob
jec
t
i
v
e
ne
e
d
t
o
be
c
o
n
s
i
de
red
de
pen
d
i
n
g
o
n
t
he
c
urrent
s
i
t
ua
t
io
n
a
n
d
con
d
iti
on.
I
t
c
a
n
be
c
o
n
c
l
u
d
e
d
th
a
t
MA
IS
i
s
s
uper
i
or
t
han
the
or
ig
i
n
al
A
I
S
f
or
s
o
l
v
i
ng
s
ta
t
i
c
V
A
R
c
om
pe
ns
ator
p
lan
n
i
ng
pro
b
lem
in
t
e
r
m
s
o
f
gi
vin
g
l
ow
er
t
ota
l
s
yst
e
m
l
o
ss
and i
m
pro
v
i
n
g
m
i
n
i
mum
vo
lta
ge
m
a
g
n
i
t
ud
e
.
T
his
d
u
e
t
o
m
ul
t
i
pl
e
sta
g
e
s
o
f
t
h
e
sam
e
p
roce
sse
s
o
f
c
l
o
n
i
n
g,
m
ut
a
t
i
on
a
n
d
selec
t
io
n
i
n
M
A
I
S
that
inc
r
ea
se
t
h
e
p
ote
n
tia
l
of
p
r
o
d
u
ce
d
in
div
i
dua
ls i
n i
n
i
tia
l
p
o
pula
tio
n to
b
e se
l
e
cte
d
a
s the
fi
na
l o
pt
ima
l
s
o
l
ut
i
o
n
.
F
o
r
the
fu
t
u
re
d
ev
el
o
p
me
nt,
the
MA
IS
a
l
gor
ithm
ca
n
b
e
i
mpro
ve
d
b
y
re
pl
a
c
i
ng
t
he
G
a
u
ssi
an
Mu
t
a
tio
n t
e
ch
n
i
q
u
e
w
i
t
h
L
og
nor
ma
l
M
u
ta
t
i
o
n
t
ec
h
n
i
q
ue
o
r mutate
d
us
i
ng ot
her
o
p
t
im
iza
t
io
n
tec
h
n
i
q
u
e
s
s
uc
h
as
P
article
S
w
a
rm
O
ptimiza
t
i
o
n
(P
SO
)
or
K
ine
tic
G
a
s
M
o
l
ec
u
l
e
op
ti
m
i
z
a
t
i
o
n
(
K
G
M
O
)
t
o
prod
u
c
e
be
tter
offspr
in
g from
the
muta
t
i
on pr
oc
ess.
ACKNOW
LEDG
M
E
N
T
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2502-
4752
I
n
do
n
e
si
an
J
E
l
e
c
E
n
g
&
C
o
m
p
S
ci
, V
o
l
.
1
4
,
No. 1, April 2019 :
346 –
3
52
35
2
The
a
u
th
ors
w
oul
d
like
to
a
c
k
n
o
w
l
e
d
ge
t
he
U
ni
versi
t
i
T
e
n
aga
N
a
s
i
o
na
l
(
UNITEN
)
for
the
f
i
nancial
su
pp
o
r
t
o
f
t
hi
s
p
r
oj
e
c
t
.
T
hi
s
re
se
arc
h
i
s
su
pp
o
r
t
e
d
by
UNITEN
u
nde
r
t
h
e
U
N
ITEN
I
nt
e
r
nal
Rese
arc
h
G
rant
(U
NI
IG
201
8)
w
i
t
h
p
r
o
j
e
c
t c
o
de: J
5
1
0
0
5
0
629
.
REFE
RENCES
[1]
S
.
R
.
Ola,
“
Reacti
v
e
P
o
wer
Flo
w
C
on
tro
l
U
sing
S
t
a
ti
c
VAR
C
om
pen
sator
t
o
I
mprove
V
oltage
S
t
a
bi
l
ity
i
n
Tran
smissi
on
S
y
s
t
em,
”
2
01
6.
[2]
L. A.
S
n
ider,
“An Intel
ligent
Vo
lt
age Co
ntroll
er for St
a
ti
c
VA
R
C
om
pen
s
at
ors,
”
p
p
.
2
39
–24
3,
1
9
9
4
.
[3]
A.
K
.
Mohant
y
and
A.
K
.
B
a
ri
k
,
“
Po
wer
Sys
t
em
S
tabi
lity
I
mprovem
e
n
t
Usin
g
F
A
C
TS
D
ev
ices,
”
I
n
t. J
.
Mo
d.
En
g
.
Res.
, vo
l
.
1,
n
o.
2
, pp
.
66
6
–
6
7
2
,
2
00
9.
[4]
M
.
G
iti
z
ad
eh,
M
.
S
h
i
dpil
e
hv
ar,
and
M
.
M
ardan
e
h,
“
A
n
e
w
m
e
thod
f
o
r
S
V
C
p
lacem
en
t
con
s
i
d
erin
g
F
S
S
li
mit
an
d
SVC
in
ve
s
t
me
nt
c
ost,”
Int
e
rn
a
tiona
l Jo
urn
a
l
o
f
Electr
i
ca
l P
o
wer a
n
d E
n
er
gy S
y
s
t
em
s
,
vo
l.
5
3
.
pp.
9
00–
90
8,
201
3.
[5]
J.
A
l
-
En
ez
i
,
M
.
Ab
bo
d,
a
nd
S
.
A
ls
harhan,
“Ar
tif
ic
ia
l
I
mmu
ne
S
y
s
tem
s
-mo
d
els,
a
lg
orit
h
m
s
and
ap
pli
cati
o
n
s
,”
In
t
.
J.
Res.
Rev.
App
l
.
Sci
.
,
vol.
3
,
n
o
.
M
ay
,
p
p.
1
18
–131
,
2
0
1
0
.
[6]
W.
O
n
g
s
a
kul
a
nd
P.
J
irapo
n
g
,
“
O
p
tim
a
l
A
l
l
o
c
a
t
io
n
of
F
A
C
TS
D
evi
c
es
t
o
Enhance
Total
Trans
f
er
C
apabi
lity
U
sing
Ev
ol
u
tion
a
ry
P
ro
gram
min
g
,
”
p
p
.
4
1
7
5
–
4
178
,
2
005.
[7]
M
.
H
.
M
a
nso
r
,
M
.
R
.
Irvi
ng,
a
nd
G.
A
.
T
a
y
l
or,
“
A
d
eco
mp
os
itio
n/
a
g
greg
ati
on
m
e
th
od
f
o
r
s
olvin
g
e
lect
rical
p
o
w
er
di
sp
atch
p
ro
b
l
em
s
,
”
in
2012
47t
h Interna
t
ional Uni
versities
P
o
wer
Eng
i
neeri
ng Conf
erence (
U
P
E
C
)
,
20
12,
p
p
.
1
–
7.
[8]
K.
P
.
Nguyen,
G.
F
ujita,
and
V
.
N
.
D
i
eu,
“CUC
KOO
S
E
ARC
H
A
LG
ORIT
HM
F
OR
O
PTI
M
AL
P
LA
C
E
MEN
T
AN
D
SI
ZIN
G
O
F
STATIC
V
AR
C
OMPEN
S
ATOR
I
N
LA
R
G
E
-
SCA
L
E
POWER
S
Y
S
TE
MS,
”
v
ol
.
6
,
n
o.
2
,
pp.
59
–6
8,
2
01
6.
[9]
D.
R
.
Tob
e
rgte a
nd
S.
Cu
r
tis,
Transmi
ss
i
o
n and
Distribut
i
on E
l
ect
rical
E
ngineering 3rd
Edition
. Newnes, 2013.
[10]
R
.
S
i
r
j
a
n
i
,
A
.
M
o
h
a
m
e
d
,
a
n
d
H
.
S
h
a
r
e
e
f
,
“
A
H
y
b
r
i
d
B
C
O
/
H
S
A
l
g
o
rithm
f
o
r
Opt
i
m
a
l
Placem
ent
and
Sizi
ng
o
f
S
t
atic
V
ar
C
o
m
p
e
n
s
at
ors
in
P
ow
er
S
ystems,
”
pp.
54
–
5
9
.
[11]
R.
S
i
r
jan
i
,
A.
M
o
h
am
ed,
and
H
.
S
h
a
reef
,
“O
ptimal
a
ll
ocatio
n
of
shu
n
t
V
a
r
co
mp
e
n
s
a
to
rs
i
n
power
s
y
s
t
e
ms
u
si
ng
a
no
vel
gl
oba
l
h
a
rmo
n
y
search
a
lg
ori
t
h
m
,
”
Int. J. Elect
r. P
o
wer
En
erg
y
Sys
t
.
,
v
o
l
. 43
,
n
o.
1
, p
p.
56
2
–
5
72
,
2
0
1
2
.
Evaluation Warning : The document was created with Spire.PDF for Python.