In
te
r
n
ation
a
l Jou
rn
al
o
f Po
we
r
Elec
tron
ic
s an
d
D
r
ive S
y
stem
(IJ
PED
S
)
V
o
l.
10, N
o.
2, June
2
01
9, pp.
900~
9
0
8
IS
S
N
: 2088-
86
94,
D
O
I
:
10.11
59
1
/ij
ped
s
.
v10
.
i
2.pp
9
00-
90
8
900
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/IJ
PED
S
A
review on optimal pl
a
c
e
m
e
nt
and sizing of
cust
o
m pow
e
r
devices/FACTS d
e
vices in
electrical power system
s
V. Tej
as
w
i
n
i
, D. Susitra
El
ectr
i
cal
E
nigineerin
g, Sat
hyaba
m
a Institu
te of
S
c
ience and Te
ch
nol
og
y,
I
ndi
a.
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
ce
i
v
e
d
Sep 6,
2018
Re
vise
d N
ov
1
9
,
201
8
A
c
c
e
pte
d
F
eb 15,
2
0
1
9
P
o
w
e
r
l
o
ss
redu
cti
on,
i
m
p
ro
vement
o
f
voltag
e
p
rofi
le,
s
y
stem
r
e
l
i
abilit
y
and
sy
st
e
m
s
ecu
rity
a
re
t
he
i
m
p
ortant
obj
ecti
v
es
t
h
a
t
mo
ti
vat
e
d
res
earchers
to
u
s
e
cus
t
o
m
p
ow
er
d
evi
ces/F
A
C
TS
d
ev
ices
i
n
p
o
w
er
s
y
s
t
e
ms.
T
h
e
e
xis
t
in
g
power
quality
p
robl
ems
such
a
s
po
wer
l
o
sses,
v
oltage
i
nst
a
b
i
l
i
t
y,
voltag
e
pro
f
il
e
pro
b
l
e
m
,
l
oad
abi
l
ity
i
ssu
es,
en
erg
y
l
o
sses,
r
eliabilit
y
pro
b
lem
s
e
t
c
.
are
c
a
u
s
ed
d
u
e
t
o
con
t
i
nuo
us
l
o
a
d
g
r
owt
h
a
nd
o
ut
a
g
e
o
f
c
o
m
p
o
nen
ts
.
T
h
e
si
gni
f
i
c
a
nt
q
ual
ities
of
c
ustom
power
d
evices
/
FACT
S
devices
s
u
ch
a
s
power
lo
ss
red
u
cti
on,
i
m
p
ro
vem
e
nt
o
f
v
o
l
t
ag
e
p
r
of
il
e,
s
ys
te
m
reli
abil
it
y
and
s
y
st
em
secu
rit
y
h
ave
m
o
tivat
ed
r
esearchers
i
n
t
h
i
s
a
r
ea
an
d
to
i
mplem
e
nt
t
h
e
se
dev
i
ces
i
n
po
wer
sy
stem.
T
h
e
op
timal
p
lacem
en
t
and
s
i
zi
ng
o
f
t
h
es
e
d
e
vi
ces
are
d
e
t
e
rmi
n
ed
b
as
ed
o
n
econ
o
m
ical
v
i
a
b
i
lity,
requ
ired
q
ual
i
t
y
,
r
el
iabil
ity
and
avail
a
bilit
y.
I
n
publ
i
s
hed
l
i
t
e
r
a
t
u
res,
d
i
fferent
a
l
g
ori
t
hm
s
are
im
plem
en
t
e
d
f
o
r
o
p
t
i
m
a
l
p
l
acem
ent
o
f
t
h
e
se
d
ev
ices
b
ased
on
d
i
f
f
e
rent
con
d
i
t
i
ons
.
In
t
his
pap
e
r,
t
he
pub
li
sh
ed
lit
eratu
r
es
on
th
is
f
i
e
l
d
are
com
p
rehens
iv
ely
revi
ewed and
e
lab
o
rate com
pari
so
n
of
v
ari
o
u
s
a
l
go
rit
h
ms
i
s
com
p
are
d
.
Th
e
inf
e
rence
of
t
his
ex
tens
iv
e
co
m
p
a
r
ati
v
e
anal
ysis
is
p
resented.
I
n
t
h
i
s
r
e
s
e
a
r
c
h
,
M
e
t
a
h
e
u
r
i
s
t
i
c
m
e
t
h
o
d
s
a
n
d
s
e
n
s
i
t
i
v
e
i
n
d
e
x
m
e
th
ods
a
re
us
ed
f
o
r
d
eterm
i
n
i
ng
the
optim
al
l
o
c
a
tio
n
an
d
s
i
zi
ng
of
c
usto
m
po
wer
dev
i
ces
/F
ACT
S
d
ev
ices.
Th
e
c
o
m
b
ina
t
io
n
of
t
hese
t
wo
m
eth
o
d
s
a
re
a
l
s
o
im
plem
en
t
e
d an
d p
r
esen
ted.
K
eyw
ord
s
:
Cust
om
power
dev
ic
es
/
F
ACT
S
dev
i
ce
s,
D-
S
T
ATCOM
,
Loca
t
i
o
n
a
nd s
i
zi
n
g
,
Power
system
netor
k,
SVC,
TCSC.
UPQC,
Co
pyri
gh
t © 2
019 In
stit
u
t
e
of Advanced
En
gi
neeri
n
g
an
d
S
c
ien
ce.
All
rights
res
e
rv
ed.
Corres
pon
d
i
n
g
Au
th
or:
V
.
Te
jasw
in
i
,
Elec
tric
a
l
Eni
g
i
ne
er
in
g,
S
a
t
hya
bam
a
I
nstit
u
t
e
of S
c
i
en
ce
and
Tec
h
n
o
l
o
g
y
(
D
e
e
m
e
d
t
o be
U
n
iv
e
r
sity
),
Che
n
na
i.
T
am
i
l
na
d
u
,
India
.
Em
ail:
t
e
jusa
t
e
esh
kuma
r
@gm
a
il.com
1.
I
N
TR
OD
U
C
TI
O
N
In
r
ece
nt
y
ea
rs,
d
u
e
t
o
i
ncr
e
a
s
i
ng
l
o
ad
d
e
m
a
nd
o
f
e
lec
t
r
i
c
i
t
y
,
t
h
e
s
i
zi
n
g
a
nd
c
o
m
p
lex
i
ty
o
f
e
l
e
c
tri
c
power
s
ys
tem
s
a
re
h
ig
hly
i
n
cr
eased.
There
f
ore
a
sta
b
le
,
relia
b
l
e
an
d
uni
nt
e
rru
pt
ed
powe
r
q
u
a
li
ty
w
it
h
t
h
e
minim
u
m
p
o
w
e
r
losse
s
i
s
a
ve
ry
d
iffere
nt
t
as
k
i
n
p
ow
e
r
s
ys
tem
s
[1].
I
nc
rea
s
in
g
loa
d
d
em
and
m
a
y
l
e
ad
t
o
vo
lta
ge
i
ns
t
a
b
ili
t
y
i
n
b
u
ses
a
n
d
e
x
ce
ssi
ve
pow
er
f
low
s
i
n
bra
n
c
hes
[
2
].
M
or
eo
ver
,
b
e
cause
o
f
o
u
ta
ge
o
f
com
p
o
n
e
n
t
s
t
h
e
re
m
ay
b
e
a
chanc
e
o
f
p
o
w
e
r
conges
t
i
o
n,
s
t
a
tic
a
n
d
d
yna
mic
ins
t
a
b
i
lit
ie
s
[3].
T
o
com
p
ensa
te
pow
er
l
osse
s
a
n
d
m
a
in
ta
in
v
olta
ge
s
w
ith
in
t
he
lim
it
se
r
i
es
v
ol
t
a
g
e
re
gul
at
o
r
s
and
sh
unt
c
ap
a
c
i
t
o
r
s
are
u
s
e
d
,
bu
t
these
two
de
v
i
ces
h
a
v
ing
som
e
d
i
s
a
d
v
a
nta
g
es
t
ha
t
a
r
e
series
v
o
l
t
a
g
e
r
eg
u
l
a
t
o
r
s
op
erat
es
i
n
st
ep
b
y
st
ep
ma
nner
so
t
hat
i
t
h
a
v
e
sl
ow
r
esp
onse
an
d
it
c
an’t
g
e
n
era
t
e
r
eac
tive
pow
e
r
.
S
hun
t
c
a
p
ac
i
t
ors
ca
n’
t
gen
e
r
a
te
con
t
in
uou
s
re
acti
v
e
pow
e
r
,
so
t
o
c
o
mpe
n
sa
te
t
hese
d
ra
w
b
ack
p
ow
e
r
elec
tro
n
ic
b
ase
d
c
u
s
t
o
m
p
o
w
e
r
dev
i
ce
s/F
A
CT
S
de
vi
c
e
s
a
r
e
use
d
i
n
pow
e
r
s
ystem
s
[
4].
G
e
ner
a
ll
y
cu
st
om
power
d
ev
ice
s
,
whi
c
h
ar
e
near
ly
sam
e
a
s
FA
CTS
devices,
t
h
i
s
a
re
u
se
d
t
o
s
o
l
ve
p
ro
blem
s
like
p
o
w
er
i
n
t
e
r
ruptio
n
a
nd
p
oor
p
ow
er
qua
li
ty
i
n
pow
er
s
yste
m
ne
tw
ork
.
H
o
wever
cust
om
p
ower
d
e
v
ices
a
nd
FA
C
T
S
de
vice
s
are
share
a
co
m
m
on
t
e
c
h
n
i
ca
l
base,
t
h
ese
de
vi
c
e
s
h
ave
dif
f
er
ent
perform
ance
r
es
ul
ts.
T
h
e
FAC
T
S
d
e
v
i
c
e
s
a
r
e
u
s
e
d
i
n
t
h
e
t
r
a
n
s
m
i
s
s
i
o
n
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
A rev
i
e
w
o
n
o
p
tim
al
p
l
ac
em
e
n
t
an
d sizi
ng
of
cus
t
om
p
o
we
r dev
i
ce
s/
FA
CT
S .
.
. (V.
T
e
jaswin
i)
90
1
syste
m
,
w
h
ile
c
us
tom
pow
e
r
d
e
v
i
c
es
a
re
u
se
d
i
n
d
is
trib
uti
o
n
[5]
.
C
u
s
t
o
m
p
o
w
e
r
d
e
v
i
c
e
s
a
r
e
e
s
p
e
c
i
a
l
l
y
effec
t
i
v
e
i
n
t
he
system
r
e
li
a
b
il
it
y an
d
pow
er
qua
l
ity.
Cust
om
pow
er
de
v
ic
es
/F
A
C
T
S
devices
h
av
i
ng hi
g
h
i
ns
t
a
l
l
a
t
i
o
n cos
t
,
how
ever these devices are
u
sed
i
n
b
ot
h
t
r
an
smi
ssi
on
a
nd
d
i
s
t
r
i
b
u
tio
n
s
y
st
ems
b
e
ca
u
s
e
of
t
h
e
b
e
tte
r
perf
orm
a
nce
o
f
t
he
se
d
e
v
ic
es,
i
n
v
iew
o
f
th
i
s
i
t
i
s
nece
s
s
a
r
y to
d
eterm
i
n
e
t
he
o
p
t
i
m
al p
l
a
ce
me
nt of C
u
st
o
m
Po
w
e
r
d
ev
i
ces/
F
AC
TS d
e
v
i
c
es
[
6
]
.
C
u
sto
m
pow
er
d
e
v
ic
es/
F
A
C
TS
d
evice
s
a
re
m
ore
effec
tive
de
vic
e
s
to
m
i
n
im
i
z
e
po
w
e
r
losses,
v
ol
t
a
ge
s
t
a
b
i
l
i
t
y
m
a
r
g
i
n
enha
nc
em
en
t, cos
t
of
e
ne
rg
y sa
v
i
n
g
s,
i
m
p
ro
vin
g
relia
b
i
l
ity
and
se
cur
i
t
y
o
f
th
e power sys
t
e
m.
F
ACTS device
s
are
DVR
,
D
S
TATC
OM,
UP
QC,
UP
F
C
,
S
V
C
et
c.
T
h
e
re
e
x
i
st
l
ess
resear
ch
w
ork
on
o
p
t
ima
l
l
oca
t
ion
a
n
d
si
z
i
ng
of
c
usto
m
pow
e
r
d
ev
ic
e
s
i
n
the
di
stri
bu
tio
n
s
y
ste
m
r
a
t
he
r
tha
n
r
esea
rch
w
o
rk
on
op
tim
al
p
l
a
ce
me
nt
o
f
F
A
CTS
dev
i
ce
s
i
n
t
he
t
ra
ns
mission
s
yste
m
s
[
7].
F
i
g
u
re
s
1
&
2
sh
ow
s
the
re
prese
n
ta
ti
o
n
o
f
C
u
s
t
o
m
P
ow
e
r
D
e
vice
s
/
F
A
CT
S
de
vi
c
e
s
i
n
p
ow
er
s
yst
e
m.
T
h
i
s
pa
pe
r
pre
s
en
ts
m
e
t
a
h
u
r
istic
m
e
t
ho
ds
f
or
d
is
t
r
i
b
u
t
i
on
a
n
d
transm
i
s
s
i
on
s
y
ste
m
,
further
sens
iti
vi
ty
i
n
d
e
x
me
t
h
o
d
s
ar
e
re
vi
ew
ed
i
n
de
t
a
il.
F
ina
l
l
y
a
n
o
v
e
r
al
l
rev
i
ew
w
il
l
repr
esente
d
for
fut
u
re
r
ese
a
rch w
i
l
l
b
e
su
gge
ste
d
.
F
i
gure
1.
O
ptim
al
p
l
a
ce
me
nt
o
f F
A
CTS
de
v
i
ces
i
n
t
r
ansm
issi
on sy
st
ems
F
i
gure
2.
O
pt
i
m
al plac
e
m
e
n
t
of cos
t
um
pow
er
devic
es i
n d
i
stri
bu
ti
on
sy
s
t
e
ms
2.
REVIE
W
OF
RE
S
E
AR
CH
ON CU
S
T
OM
P
OW
ER/FACTS
DE
VICES ALL
O
CATIO
N:
A
ll
e
x
is
t
i
n
g
m
eth
o
d
s
for
op
ti
m
a
l
a
llo
ca
ti
on
o
f
Cus
t
om
p
o
w
er/F
A
C
TS
d
evic
e
s
c
a
n
b
e
div
i
de
d
in
t
o
c
a
t
e
go
ri
e
s
.
M
e
t
a
-h
e
u
ri
st
i
c
m
et
hod
s,
s
e
n
si
ti
vit
y
i
nd
e
x
m
e
t
ho
d
s
a
nd
Comb
ina
t
io
n
o
f
s
e
n
s
i
t
i
vi
ty
a
p
p
roac
h
a
n
d
meta-heuristics
.
2.1.
Meta-h
e
u
ristic met
h
o
ds
These m
e
t
h
o
d
s are
e
fficie
n
t and
fle
x
ible
m
et
ho
ds. D
i
sc
rete
a
nd
co
nst
r
a
i
nt
o
pt
i
m
i
z
at
ion
pro
b
l
e
ms
c
a
n
be
e
as
i
l
y
s
o
l
v
ed
b
y
usi
n
g
Me
ta-
h
eur
i
stic
a
ppr
oac
h
es
[
8
]
.
P
r
oble
m
s
r
e
l
a
t
e
d
t
o
m
u
l
t
i
m
odal,
m
ul
ti
ob
jec
t
i
v
e
fu
nc
ti
o
n
s ca
n a
l
s
o
b
e
sol
v
e
d
by
us
i
n
g
the
s
e m
e
tho
d
s.
2.1.
1. A
l
gor
i
t
h
m
s
for
tran
smiss
i
on
s
yst
e
ms
I
n
[
9]
J
a
n
2
01
9,
P
.
Lok
e
nder
Re
d
d
y,
G
.
Y
e
sura
tn
a
m
i
n
t
e
r
d
i
c
t
e
d
m
odif
i
e
d
B
act
er
i
a
l
fora
gin
g
alg
o
ri
t
h
m
for
op
t
i
ma
l
re
act
i
v
e
p
o
wer
dis
p
atch
p
ro
bl
em
.
The
m
a
i
n
obje
c
tive
f
u
nc
tio
ns
a
r
e
m
inimiz
a
t
i
o
n
of
rea
l
p
ow
e
r
l
o
s
s
an
d
v
o
l
ta
ge
s
t
a
bi
l
ity
L
-in
d
e
x
t
hi
s
me
th
od
i
s
t
e
sted
o
n
IEE
E
3
0
bus
s
yste
m
.
I
n
[10]
D
e
c
2
01
8,
Sa
l
m
an
a
nd
A
l
i
use
d
g
e
n
e
tic
a
lgor
ithm
to
d
e
t
e
r
m
i
ne
t
he
o
p
tim
al
l
o
cat
io
n
a
n
d
si
zi
ng
o
f
UPFC
.
Th
e
ma
i
n
o
b
j
e
ct
iv
e
fu
n
c
t
i
on
s
are
vo
lt
ag
e
p
r
o
f
il
e
i
m
pro
v
eme
n
t
,
powe
r
l
o
s
s
e
s
r
ed
uc
ti
on,
t
r
eatm
e
nt
o
f
p
o
w
e
r
flow
i
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
Pow
El
ec &
D
ri
S
yst
,
Vol
.
10,
N
o.
2
, June 2019: 900
–
90
8
90
2
over
l
oa
de
d
t
r
ansm
i
s
s
i
on
l
i
n
e
s
a
n
d
m
i
n
imiz
e
t
o
t
a
l
c
o
st
o
f
pow
er
sy
st
e
m
.
In
[
11
]
Aug
20
18
,
S
i
rot
e
K
hu
nki
t
t
i
,
A
p
irat
S
iri
t
ara
t
iw
a
t
P
r
opose
d
H
ybr
id
D
A
-
P
S
O
O
p
t
i
miza
t
i
o
n
A
lgor
i
t
h
m
to
s
ol
ve
m
ult
i
o
bjec
tive
op
t
i
m
a
l
pow
er
f
l
o
w
(O
P
F
)
prob
lem
s
i
n
a
p
o
w
e
r
system
.
Thi
s
n
e
w
h
ybr
id
D
A
-P
S
O
a
lgor
it
hm
p
ro
vi
d
e
s
e
x
plo
r
a
tio
n
pha
se
o
f
D
A
a
n
d
t
h
e
e
x
pl
o
ita
tio
n
pha
se
o
f
P
S
O
,
to
i
mpr
o
ve
i
t
s
p
e
r
fo
rma
n
ce
f
o
r
f
in
d
i
ng
sol
u
tio
n
of
t
he
O
P
F
pro
b
lem
s
. The
m
ain ob
je
c
t
i
v
e
is to m
i
n
i
m
i
ze
f
ue
l
ca
st
a
n
d
t
ra
ns
m
i
ssion
l
osses.
In
[
12]
S
e
p
201
6,
E
lazim
a
n
d
A
l
i
use
d
C
uc
k
o
o
s
ear
c
h
a
lg
ori
t
h
m
t
o
f
i
nd
o
pti
m
a
l
l
o
c
a
t
io
n
of
S
T
A
T
CO
M
in mult
i
m
issi
on pow
er
s
yste
m.
I
t
is
i
ns
p
i
r
e
d
fr
om
l
i
f
e
o
f
ba
rds.
B
y
using
S
T
ATCOM
t
h
e
ov
e
r
al
l
vo
lta
ge
p
r
o
fi
le
a
n
d
s
ys
tem
loa
d
a
b
i
l
i
t
y
c
a
n
b
e
i
m
pro
v
e
d
.
P
V
c
ur
ve
s
a
r
e
used
t
o
d
e
t
e
rm
i
n
e
l
o
c
a
t
i
o
n
o
f
S
T
A
T
CO
M
an
d
CS
a
l
gori
t
h
m
is
u
se
d
to
s
olve
o
pt
i
m
iza
t
i
on
p
r
o
b
l
e
m
s
.
Co
mp
are
to
GA,
C
S
p
r
o
v
i
d
es
good
dam
p
i
ng
cha
r
a
c
t
e
r
s
to
t
he
s
y
s
tem
osc
i
l
l
a
t
i
o
n
s
over
a
w
i
de
r
a
n
ge
o
f
l
o
ad
i
n
g
c
o
n
d
it
io
ns.
In
[
13]
2
0
16,
S
ai
R
am
and
V
e
n
k
a
n
na
i
mple
me
nt
e
d
P
S
O
a
dapt
i
v
e
G
S
A
hybri
d
a
l
g
o
r
ithm
a
n
d
i
t
i
s
u
s
e
d
t
o
f
i
n
d
t
h
e
o
p
t
i
m
a
l
l
o
c
a
t
i
o
n
,
pow
er
r
ati
n
g
s
o
f
the
F
A
CTS
dev
i
ce
s
base
d
on
vo
l
t
ag
es
a
n
d
m
in
im
u
m
po
w
e
r
losses.
G
ravi
ta
t
i
o
n
a
l
c
o
n
s
t
a
nts
are
optim
i
z
e
d
by
us
in
g
P
S
O
a
l
g
or
it
hm
t
o
im
prove
t
he
s
ea
rchi
ng
p
erfor
m
ance
o
f
the
GS
A.
U
P
F
C
&
IP
F
C
a
re
use
d
f
or
s
ys
te
m
st
a
b
ili
ty
a
na
ly
sis.
V
o
lta
ge,
pow
er
l
oss
va
l
u
es
ca
n
be
c
a
l
c
u
l
a
te
d
by
p
l
a
c
in
g
IP
F
C
i
n
b
e
t
w
e
e
n
tw
o
b
u
sse
s
an
d
ma
gnit
udes
of
v
o
l
t
a
ge
,
p
o
w
e
r
loss
c
a
n
be
e
val
u
a
t
ed
b
y
pl
a
c
in
g
U
P
F
C
i
n
betw
ee
n
tw
o
bus
se
s.
P
S
O
-G
S
A
p
rovide
s
be
tter
sta
b
i
l
ity
m
argi
n
a
nd
r
e
d
u
ci
n
g
p
ow
er
l
os
se
s
c
o
m
p
ar
e
to
GA
&
G
S
A.
I
n
[14
]
M
ar
ch
20
1
6
,
S
u
sa
nta
and
R
oy
dev
e
lo
pe
d
c
h
em
ic
al
r
e
a
c
tio
n
o
p
t
i
m
iza
t
i
o
n
for
op
t
i
ma
l
loc
a
t
i
on
of
S
TA
TCO
M
,
in
order
to
s
o
l
ve
o
p
t
ima
l
r
ea
ct
io
n
pow
e
r
d
is
p
a
t
c
h
pro
b
lem
s
.
S
T
A
T
CO
M
can
m
i
nim
i
ze
transmission
l
oss
e
s
and
vo
lta
ge
d
e
v
ia
ti
ons
a
n
d
i
m
p
ro
ve
s
v
o
l
ta
ge
p
rofi
le,
vo
lt
a
g
e
s
t
ab
i
l
i
t
y
of
t
he
s
ys
tem
.
T
hi
s
C
R
O
m
e
th
od
i
s
m
or
e
efficie
n
t t
h
an
P
S
O
and
DE.
In
[
1
5
]
20
16,
I
m
p
erialis
tic
c
om
pet
i
t
i
ve
a
lgor
it
hm
i
nsp
i
r
e
d
f
o
rm
s
oc
io
-
poli
t
i
c
al
p
hen
o
m
e
no
n
of
impe
ria
list
i
c c
o
m
puta
t
i
o
n is use
d for
o
p
t
i
m
a
l
des
i
gn o
f
S
TA
TCO
M
i
n po
w
e
r system
s. O
pt
i
m
iza
t
i
o
n p
r
oble
m
s
c
a
n
b
e
s
ol
v
e
d
b
y
u
si
ng
I
C
.
T
h
e
p
ropo
sed
ICA
STATCOM
p
r
ov
id
e
s
g
o
o
d
d
a
m
p
i
ng
c
hara
cteris
t
i
c
to
t
he
syste
m
o
sc
i
llat
i
o
n
s
an
d
als
o
i
mpr
ove
s
o
v
er
all
vo
lta
ge
p
rof
ile
,
system
l
oad
a
b
i
lit
y.
I
n
[1
6]
2
01
5,
R
e
zae
e
Jaorde
hi
d
e
v
e
l
ope
d
Brai
ns
tor
m
o
pt
im
i
z
a
t
i
o
n
al
g
o
rithm
for
o
p
tim
a
l
p
l
ace
me
nt
o
f
F
A
CTS
de
vice
s,
i
t
i
s
heur
ist
i
c
a
l
gori
t
hm,
w
h
ic
h
is
i
n
s
p
i
re
d
from
B
rai
n
s
t
ormin
g
p
roc
e
ss
in
human
b
ei
ng
.
SV
C
an
d
TC
SC
d
e
v
i
ces
are
used
f
or
v
o
l
tage
p
ro
fi
l
e
e
nh
a
n
ce
me
nt,
over
l
o
a
d
m
i
n
im
i
zat
i
o
n
and
l
o
ss
re
du
ctio
n.
C
ompa
r
e
t
o
enha
nc
em
en
t
G
A
,
P
SO
a
nd
D
E
,
this
B
S
O
A
pr
ov
i
d
e
s
b
e
tter
v
o
lta
ge
p
r
o
f
i
l
e
a
n
d
l
e
s
s
p
o
w
e
r
l
o
s
s
e
s
.
I
n
[
1
7
]
2
014
,
Th
a
n
h
lo
ng
,
Ji
a
n
u
sed
mi
ni
c
ut
a
lg
ori
t
h
m
f
o
r
f
i
ndin
g
t
h
e
loc
a
tio
n,
q
uan
t
i
t
y
an
d
s
i
ze
o
f
T
C
S
C
.
I
t
impro
v
e
s
s
ys
te
m
loada
b
il
i
t
y
t
h
ro
ug
h
cha
n
gi
ng
li
ne
r
e
acta
n
c
e
by
in
st
al
l
i
ng
t
h
e
T
CS
C
on
t
ran
s
missi
on
l
i
n
e.
Th
is
m
e
t
ho
d
i
m
proves
s
y
s
t
e
m
l
oada
b
i
li
ty,
m
i
nim
i
z
e
t
he
i
ns
tal
l
a
t
i
o
n
co
st
a
nd
r
e
duce
se
ar
ch
s
pa
ce.
T
h
i
s
w
i
ll
be
t
es
t
e
d on I
EEE 6
bus
,
13
bu
s,
and 118 bus system
s
.
In
[
1
8
]
S
e
p
2
0
1
3
,
Edw
a
r
d
a
nd
Ra
j
a
se
kar
pro
pose
d
a
n
enha
nce
d
b
ac
t
e
rial
f
or
ag
i
ng
alg
o
ri
t
h
m
to
deter
m
i
n
e
s
u
it
able
l
oca
tio
n
and
s
i
zi
n
g
f
or
S
VC
a
n
d
T
C
SC
d
e
v
ices
,
i
n
o
r
d
er
t
o
m
i
n
i
m
i
ze
pow
e
r
f
l
o
w
pro
b
lem
s
e
n
h
a
n
ce
d
EBF
A
i
s
c
o
mbi
n
a
t
io
n
of
B
F
an
d
N
e
l
d
e
r-Me
a
d
a
l
g
or
ithm
so
it
is
c
a
lle
d
a
s
h
ybr
id
a
l
g
o
r
i
t
h
m
.
C
o
m
p
a
r
e
B
F
,
E
B
F
p
r
o
v
i
d
e
s
b
e
t
t
e
r
o
p
t
i
m
a
l
p
a
r
a
m
e
t
e
r
s
e
l
e
ct
i
o
n
,
r
ed
u
c
e
s
t
h
e
g
en
e
r
at
ion
co
st
a
nd
impro
v
e
s
v
ol
ta
ge
s
ta
b
i
l
ity
l
im
it.
In
[
1
9
]
2013
,
S
a
fa
ri
a
nd
A
hm
ada
i
an
p
ro
pose
d
h
o
n
ey
b
ee
m
a
t
i
n
g
op
tim
iza
t
i
o
n
a
l
g
o
r
i
t
h
m
for
o
p
t
i
ma
l
de
si
g
n
o
f
S
T
A
T
CO
M
.
I
t
is
i
ns
pir
e
d
from
bird
s’
l
i
f
e
.
T
his
pr
o
pos
ed
me
tho
d
p
ro
v
i
d
e
s go
od
dam
p
i
ng
char
ac
ter
i
s
t
i
c
s to
l
ow
f
re
qu
ency
o
sc
i
llat
i
o
ns an
d
i
mprov
e
s
syst
e
m
s
t
a
b
ili
t
y
.
In
[
20
]
20
11
,
ES
a
l
i
a
nd
S
.M
a
bd
E
l
azi
n;
in
t
r
o
in
t
r
o
d
u
ced
a
n
i
m
p
r
ove
d
ba
cter
i
a
l
sw
a
r
m
opt
imiza
tio
n
alg
o
ri
t
h
m
f
o
r
coor
dina
t
e
d
de
si
gn
o
f
P
SSs
a
nd
T
CSC
i
n
a
m
ulti
m
a
c
h
ine
p
o
w
e
r
sys
t
em
.
T
h
is
B
S
O
i
s
hy
br
id
alg
o
ri
t
h
m
a
n
d
it
is
c
omb
i
nat
i
on
of
B
F
and
P
S
O
.
O
ver
a
w
i
de
r
a
n
g
e
o
f
l
oa
d
co
nd
uc
t
i
ons
t
he
c
o
o
rd
i
n
ate
d
des
i
g
n
p
rob
l
e
m
s
of
P
S
S
&
T
CS
C
is
e
xc
it
ed,
tha
t
p
ro
bl
e
m
c
ons
ider
a
s
o
p
ti
mi
z
a
t
i
on
p
ro
bl
e
m
.
B
S
O
p
r
ov
id
es
b
e
tt
e
r
d
a
m
pi
ng
c
h
a
ra
ct
e
r
isti
cs
t
o
syst
e
m
o
sc
i
l
l
a
t
i
on
s
ove
r
wi
d
e
r
a
nge
o
f
l
o
a
d
c
on
d
u
c
t
i
o
n
s
a
nd
di
ffere
n
t
di
st
urba
nces.
Whe
n
c
om
par
e
t
o
BF
&
P
S
O
,
BS
O
prov
i
d
es
f
as
ter
an
d
m
ore
efficie
n
t
con
v
erge
nce,
p
reve
nt
trap
pi
n
g
s in l
o
c
a
l
a
re
as.
2.1.
2. A
l
gor
i
t
h
m
s
for d
i
strib
u
tion
S
yste
ms
In
[
2
1
]
A
p
r
201
9,
S
r
i
de
r
and
P
r
akash
pro
pos
ed
w
ha
le
o
pt
i
m
iza
t
io
n
al
gor
ithm
for
fi
nd
i
n
g
o
p
t
i
m
a
l
loca
t
i
o
n
a
n
d
s
iz
ing
o
f
the
D
G
.
Mai
n ob
jec
t
i
v
e
func
tio
n is m
in
im
iza
tio
n of
pow
e
r
loss
an
d
cos
t
w
i
t
h
m
ax
i
m
um
v
o
l
t
a
g
e
s
t
a
b
i
l
i
t
y
i
n
d
e
x
,
t
h
i
s
m
e
t
h
o
d
i
s
t
e
s
t
e
d
f
o
r
I
E
E
E
6
9
b
u
s
s
y
s
t
e
m
.
I
n
[
2
2
]
F
e
b
2
0
1
8
,
M
.
L
a
x
m
i
d
e
v
i
Ra
ma
na
iah,
M
.
D
a
m
odar
Re
ddy
in
tro
d
u
c
e
s
m
ot
h
fla
m
e
opt
imiz
a
t
ion
m
e
t
h
od
t
o
de
term
i
n
e
t
h
e
op
t
i
m
a
l
loca
t
i
o
n
o
f
U
P
Q
C
i
n
distr
i
b
u
t
i
o
n
system
.
In
l
ar
ge
d
is
tri
b
uti
on
s
y
s
t
em
s
U
P
Q
C
’s
s
te
ady
sta
t
e
c
o
mpe
n
sa
tio
n
ca
pab
i
lit
y
ha
s
gi
ve
n
a
solu
ti
o
n
f
or
p
ro
v
i
d
i
ng
r
ea
ctive
pow
e
r
c
o
m
p
ensat
i
o
n
.
Mai
n
o
bjec
ti
ves
ar
e
t
o
r
e
a
l
powe
r
lo
ss
r
ed
uc
t
i
o
n
,
v
o
lta
ge
p
rof
ile
i
mpr
ove
me
nt.
I
n
[
23]
N
ov
2
0
17,
Laxm
i
&
Damodar
used
G
ray
Wolf
op
tim
iza
t
i
o
n
for
o
p
t
im
al
a
l
l
o
c
ati
o
n
of
U
P
Q
C
i
n
D
istri
b
ut
i
o
n
s
y
s
t
e
m.
T
hi
s
g
r
ay
w
ol
f
opti
m
i
z
a
t
ion
i
n
spired
by
the
h
u
n
ti
ng
m
e
c
ha
nism
o
f
g
r
ey
w
ol
ves.
T
he
m
a
i
n
ob
jec
t
i
v
e
f
u
n
c
t
i
on
i
s
t
o
r
edu
c
e
power
l
o
ss
and
v
o
lt
ag
e
profi
l
e
i
m
pro
v
e
m
e
nt
o
f t
h
e
sy
ste
m
.
This c
an be
tes
t
ed
on
st
a
nda
nd I
EEE 33 and 69
bus
s
ystem
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
A rev
i
e
w
o
n
o
p
tim
al
p
l
ac
em
e
n
t
an
d sizi
ng
of
cus
t
om
p
o
we
r dev
i
ce
s/
FA
CT
S .
.
. (V.
T
e
jaswin
i)
90
3
In
[
2
4
]
a
n
othe
r
resea
r
ch
w
ork
2
0
1
5,
h
a
r
m
o
n
y
s
ea
rc
h
al
g
o
r
ithm
is
u
se
d
t
o
f
in
d
opt
im
al
l
oca
tio
n
&
si
z
i
ng
of
D
S
T
A
T
CO
M.
T
h
i
s
alg
o
ri
t
h
m
is
i
nsp
i
re
d
from
i
mprov
i
sat
i
o
n
p
r
o
c
e
s
s
i
n
m
u
s
i
c
.
T
h
e
m
a
i
n
o
b
j
e
c
t
i
v
e
is
t
o
m
i
n
i
m
i
ze
t
ota
l
p
ow
er
l
osses.
T
hi
s
m
e
th
o
d
i
s
tes
t
ed
o
n
IE
E
-3
3
bu
s
sys
t
em
.
H
a
rm
ony
a
l
g
ori
t
h
m
w
i
l
l
reduc
e
p
o
w
e
r
l
o
sses
m
o
re
t
h
a
n
imm
une
a
l
gor
it
hm.
In
[2
6]
2
0
1
4
D
ev
i
and
G
e
tha
n
jal
i
i
n
tro
duc
e
d
P
S
O
f
or
f
i
nd
i
n
g
t
h
e
o
p
t
i
m
a
l
l
o
c
a
t
i
o
n
an
d
si
z
i
ng
o
f
DG
a
n
d
DS
TATC
O
M
,
i
n
o
r
d
e
r
t
o
r
e
d
u
c
e
p
o
w
e
r
l
o
s
s
e
s
&
i
m
p
r
o
v
e
vo
lta
ge
p
rofi
le.P
SO
i
s
i
n
s
p
ired
b
y
fis
h
s
c
h
o
o
l
i
ng
a
nd
b
ird
fl
oc
k
s
.
Th
e
st
ud
y
i
s
d
on
e
w
i
t
h
f
iv
e
di
ff
ere
n
t
c
a
s
e
s.
In
a
ll
c
as
es
p
erf
o
rma
n
ce
o
f
DG&DST
A
TC
OM
c
an
b
e
ana
l
y
z
e
d
b
y
u
s
in
g
LS
F
me
tho
d
.
I
n
[27]
2
01
4
ta
her
,
A
f
sar
i
u
se
d
im
m
u
n
e
a
lgor
it
hm
f
o
r
o
p
timi
z
a
tio
n
pr
ob
l
e
ms
o
f
D
S
TA
T
CO
M
i
n
r
ad
ia
l
d
i
s
t
ri
but
io
n
sys
t
em
.
It
r
educ
e
s
pow
er
l
osse
s,
c
ost
of
D
S
T
A
T
CO
M
a
n
d
i
m
pro
v
e
v
olta
ge
o
f
b
u
ses.
C
om
pare
t
o
G
A
,
I
A
p
rov
i
des
mi
n
i
mu
m
DST
A
TCOM si
z
e a
n
d
C
P
U t
i
m
e.
In
[
2
8
]
20
1
3
,
Maso
u
d
a
n
d
A
za
h
use
d
f
i
r
efl
y
a
l
g
ori
t
hm
t
o
f
i
nd
op
t
i
m
a
l
loca
t
i
o
n
a
nd
siz
i
n
g
o
f
D
S
TA
TCO
M
i
n
d
i
s
t
r
i
bu
t
i
o
n
s
yste
m,
f
or
pow
er
qua
lit
y
e
n
ha
ncem
en
t.
A
n
e
w
l
y
d
e
f
i
n
e
d
o
b
j
e
c
t
i
v
e
f
u
n
c
t
i
o
n
i
s
in
t
e
rd
ic
ted,
w
hi
c
h
i
nc
lude
t
o
t
a
l
h
ar
mo
ni
c
dis
t
ort
i
o
n
,
vol
tage
d
e
v
ia
t
i
o
n
s
a
nd
t
o
ta
l
in
v
e
s
t
m
e
n
t
c
o
s
t
o
f
D
S
TA
TCO
M
.
Th
is
f
i
r
efl
y
a
l
g
ori
t
hm
p
ro
v
i
de
s
bet
t
er
r
e
s
ults t
ha
n
G
A
and
P
S
O.
I
n
[2
9]
20
12,
A
bas
an
d A
f
sari
use
d
D
iffe
ren
t
ial
e
v
a
l
uat
i
on
a
l
gor
it
hm
t
o
d
e
ter
m
ine
op
t
i
m
a
l
l
o
c
at
i
on
o
f
U
P
Q
C
co
nside
r
i
ng
i
t
s
siz
e
.
In
t
h
e
radia
l
d
is
t
r
ibu
t
io
n
sys
t
em
,
Objec
tiv
e
f
unc
t
i
on
de
fine
d
f
o
r
vo
lt
a
g
e
an
d
c
u
rr
ent
p
r
ofi
l
e
im
prove
me
nt,
p
o
w
e
r
lo
ss reduc
tio
n, m
i
n
im
i
zat
i
on o
f
i
nves
t
me
nt c
os
t. Com
pare
d w
i
t
h
I
A
a
nd
GA,
D
C con
v
er
ge
s
faster & smot
h
er
,
it
p
r
o
v
i
des m
i
n
i
m
u
m
UP
Q
C
s
i
z
e,
CP
U
t
im
e and o
b
j
ec
t
i
ve
func
tio
n.
2.2.
S
e
n
s
itive
ap
p
r
oach
In
s
e
n
sit
i
v
e
app
r
o
ach
o
r
me
th
od
,
fi
rst
an
i
nd
e
x
i
s
e
xpl
a
i
n
e
d
a
n
d
co
mp
ut
at
ion
fo
r
di
ff
e
r
en
t
po
t
e
nt
i
a
l
l
o
c
a
ti
on
s
of
C
u
s
to
m
po
we
r
d
e
vi
ce
s/
FACTS
d
e
vi
c
e
s
de
t
e
rmi
n
ed
b
ase
d
on
t
he
c
o
m
pute
d
i
nd
ice
s
,
m
o
st
com
m
onl
y
tw
o
ty
pes
of
i
n
d
i
c
e
s
a
re
u
se
d
for
alloc
a
t
i
on
pro
b
lem
s
tho
s
e
in
dice
s
are
volta
g
e
s
ens
i
t
i
v
i
t
y
i
nde
x,
pow
er
loss
ind
e
x.
2.2.
1. V
ol
t
age
s
en
sitivit
y
i
n
d
ex
To
d
e
t
e
r
min
e
o
pti
m
al
l
o
cati
o
n
of
C
usto
m
po
wer
d
e
vi
ces/
F
ACTS
d
e
v
ic
es,
vo
lta
ge
s
t
a
bi
l
ity
i
nd
e
x
(VS
I
)
i
s
calc
u
l
a
t
e
d
for
d
i
ffe
r
ent
buse
s
,
the
bus
w
h
i
c
h
i
s
h
a
vi
n
g
h
i
g
h
es
t
V
S
I
va
lue
t
h
e
n
t
ha
t
bus
c
ho
sen
for
cus
t
om
power
d
ev
ice
s
/F
AC
T
S
de
v
i
c
e
pl
a
c
e
m
ent.
a)
A
l
g
o
ri
t
h
m
s
for
Tra
nsmission
S
y
stem
s
In
[
30]
2
0
1
6
,
m
ute
g
i
&
K
i
hat
o
p
ro
po
se
d
a
v
o
lta
ge
s
ta
b
i
l
ity
b
ase
d
m
et
ho
d
to
f
in
d
opt
im
al
p
l
a
ce
me
nt
of
F
A
C
TS
d
e
v
ic
e
s
i
n
t
h
e
w
eak
&
h
ea
vi
ly
l
oa
de
d
b
u
s
e
s
for
v
o
lta
ge
s
ta
b
ili
ty
i
m
p
r
ovem
e
n
t
t
w
o
v
o
l
tag
e
st
a
b
il
it
y
in
dice
s,
n
am
ely
t
h
e
F
a
st
v
o
l
tage
s
t
a
bi
lit
y
inde
x
&
th
e
li
ne
s
tab
ili
ty
i
n
d
e
x
a
re
u
se
d
t
o
d
e
t
er
mine
b
e
s
t
loca
t
i
o
n
o
f
F
A
CTS
de
vic
e
s.
I
n
[3
1]
2
01
5,
A
lba
s
t&
A
hm
a
d
P
ropo
sed
,
vol
tage
s
e
n
si
ti
vit
y
b
ase
d
m
et
ho
d
i
s
use
d
t
o
de
t
e
rm
i
n
e
op
t
i
ma
l
l
o
c
a
tio
n
o
f
U
P
Q
C
for
se
curi
ty
c
o
n
stra
ine
d
v
olta
ge
s
ta
b
i
l
i
t
y
impr
o
v
em
ent.
I
ni
ti
a
lly
the
vo
lta
ge
s
t
a
bil
i
t
y
o
f
al
l
b
u
s
es
w
a
s
d
e
t
erm
i
ned
by
ca
lc
ula
t
in
g
vol
t
a
g
e
c
o
l
l
a
pse
p
r
ox
imi
t
y
i
ndi
c
a
t
e
s
(VCPI
)
,
V
S
I
&
LLS
I
v
a
l
u
e
s
a
nd
m
os
t
u
n
sta
b
le
b
us
w
a
s
s
elec
te
d
for
U
P
F
C
p
lacement.
3
9
bus
system
s
i
s
u
s
e
d
f
o
r
tes
tin
g
of
r
esu
l
t
s
.
Plac
em
ent
of
u
n
i
fie
d
pow
er
f
low
c
o
n
t
ro
llers
t
o
im
pro
v
e
d
yn
am
i
c
vol
tage
s
tab
i
lit
y
u
s
ing
pow
er
s
ys
t
e
m
var
i
a
b
l
e
b
a
s
e
d
v
ol
ta
ge
s
t
a
b
i
l
i
t
y
i
n
d
i
c
e
s.
I
n
[32]
20
14
,
nu
rd
i
n
a
nd
fat
h
in
p
ro
po
se
d
sen
s
i
tiv
it
y
ana
l
ys
is for
p
la
ce
me
nt of shu
n
t
D
V
R
c
om
pe
n
s
at
or & S
TA
TCO
M
i
n
th
e p
o
we
r
sy
st
e
m
.
R
eac
t
i
v
e
po
w
er l
o
sse
s
ca
n
be
r
e
duc
e
d
b
y
us
ing
S
T
A
T
CO
M
a
n
d
v
o
l
t
a
g
e
i
n
st
abi
l
ity
c
a
n
b
e
preve
n
t
e
d
b
y
u
s
i
n
g
sh
u
n
t
D
V
R
com
p
en
sat
o
rs.
Thr
ee
se
ns
iti
vi
ty
i
n
d
i
ces
a
r
e
u
se
d
na
me
ly
,
vol
tag
e
s
t
ab
i
l
i
t
y
i
nde
x,
v
o
l
t
a
ge
s
e
n
s
iti
v
ity
i
nde
x
,
ang
l
e
sens
it
iv
i
t
y
i
n
de
x to se
l
e
c
t
bes
t bus
l
oc
a
tio
ns
f
or
s
h
u
n
t
D
V
R
com
p
ens
a
tor
an
d S
T
ATCOM
.
b)
A
l
g
o
ri
t
h
m
s
for
D
istrib
u
t
i
o
n Sys
t
e
m
In
[
33]
2
0
1
8
,
B
u
shr
a
W
e
q
ar
,
M
o
h
d
T
a
u
se
e
f
K
ha
n
use
d
v
ol
ta
ge
s
t
a
b
il
it
y
i
nde
x
a
nd
lo
ss
se
ns
it
iv
ity
fa
ct
or,
t
o
d
e
t
er
m
i
ne
t
he
o
p
tim
al
l
oc
a
t
i
o
n
a
nd
s
i
ze
o
f
D
G
a
nd
D
S
TA
TCOM.
This
i
s
tested
o
n
33-
b
u
s
r
adial
di
stri
b
u
t
i
on
s
ystem
.
cha
n
ges
i
n
v
ol
ta
ge
p
rofi
le
a
nd
a
c
tiv
e
p
o
w
e
r
l
o
sse
s
w
e
re
c
om
pa
re
d
be
f
o
r
e
a
n
d
a
fte
r
in
sta
l
lat
i
on o
f
t
hese d
ev
ice
s
.
O
p
tim
al
p
lac
e
m
ent
o
f
D
G
,
D
STA
T
CO
M
re
duce
s
t
he
p
ow
e
r
l
osses a
n
d im
prove
s
the
vo
l
t
a
g
e
pro
f
ile.
In
[
34]
2
0
15,
P
enk
i
t
a
M
ehta,
P
r
a
ghnes
h
B
ha
t
t
a
p
r
e
s
e
n
t
s
t
h
e
a
n
a
l
y
s
i
s
f
o
r
s
e
l
e
c
t
i
o
n
o
f
t
h
e
bes
t
D
.
G
unit
s
f
rom
differe
n
t
cate
gor
i
e
s
in
D
istri
but
i
on
s
y
stem
s
for
v
o
lta
ge
s
ta
b
ili
ty
i
m
p
ro
vem
e
nt
a
nd
loss
reduc
tio
n.
V
ol
tage
s
tab
i
lit
y
ind
i
ce
s
a
r
e
use
d
t
o
in
ves
t
i
g
a
t
e
th
e
im
pac
t
o
f
loca
t
i
o
n
D
.
G
u
n
its
f
or
t
he
p
ow
er
l
o
s
s
es
,
vo
lt
ag
e
p
r
o
f
il
e
a
n
d
vo
lt
ag
e
st
ab
ili
t
y
.
In
[
35
]
2
014
J
a
i
n
a
nd
G
u
p
t
a
use
d
v
o
l
t
a
ge
s
e
n
sit
i
vit
y
i
n
d
e
x
for
deter
m
i
n
e the
op
t
i
ma
l
p
l
ac
e
m
ent
of
D
S
T
A
T
CO
M to
e
nha
nce th
e vol
t
a
g
e
p
r
o
f
i
l
e
&
r
e
d
u
c
e
power
losses.
F
irst
vo
lta
ge
s
ta
b
ili
ty
i
n
d
e
x
v
al
ues
shou
l
d
c
a
l
c
u
l
a
te
f
or
a
l
l
b
u
s
e
s
,
in
o
rde
r
t
o
de
t
e
r
m
ine
u
n
s
t
ab
l
e
b
us
f
or
p
l
a
ce
m
e
nt
of
D
S
T
ATC
O
M
.
F
inally
t
he
r
esults
h
a
v
e
been
p
resented
f
or
I
EEE
3
3
b
u
s
s
ys
t
e
m.
I
n
[3
6]
2
01
2
H
u
ssa
in
a
n
d
V
i
sal
i
p
r
o
p
o
se
d
a
v
o
lta
g
e
s
e
n
sit
i
vit
y
b
ase
d
m
e
t
ho
d
for
d
e
ter
m
in
e
th
e
we
ak
est
b
u
s
o
f
di
st
ri
b
u
t
i
on
n
et
wo
rk
.
V
o
l
t
a
g
e
pr
ofile
i
s impro
v
e
d
b
y p
l
a
c
i
ng
D
S
T
A
T
CO
M
o
n
t
h
e
w
e
a
kes
t
b
u
s.
T
he
e
ffic
i
enc
y
o
f t
h
e p
r
o
pose
d
V
S
I
have bee
n tes
t
ed on
IEEE
33
bus s
ystem
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
Pow
El
ec &
D
ri
S
yst
,
Vol
.
10,
N
o.
2
, June 2019: 900
–
90
8
90
4
2.3.
Power los
s
ind
e
x
P
o
w
e
r
l
o
ss
i
nde
x
(P
LI)
is
a
n
o
t
h
er
a
ppr
oach
t
o
sele
c
t
s
u
i
ta
ble
l
oc
a
t
i
o
n
for
c
u
s
t
om
p
ow
e
r
dev
i
ce
s/F
A
CT
S
d
e
v
i
ces,
p
o
w
e
r
l
o
ss
a
re
c
alc
u
la
te
d
base
d
o
n
l
oa
d
fl
ow
s
tu
die
s
.
A
t
a
l
l
n
o
d
es
e
xc
ep
t
f
o
r
sour
c
e
no
de,
re
ac
t
i
ve
pow
e
r
i
s
inje
c
t
ed,
a
nd
the
t
o
ta
l
p
o
w
e
r
l
o
s
s
e
s
&
l
o
ss
r
e
d
u
ct
io
n
a
t
e
ach
n
o
d
e
ar
e
calc
u
la
te
d.
T
he
no
de
w
h
i
c
h
i
s
hav
i
ng
h
i
g
h
e
s
t
val
u
e
of
P
LI,
tha
t
n
o
d
e
w
i
l
l
b
e
th
e
bes
t
p
l
a
ce
for
i
n
sta
l
la
t
i
on
o
f
c
us
t
o
m
p
o
w
e
r
d
e
vi
c
e
/
F
AC
TS d
ev
i
c
es.
a)
A
l
g
o
ri
t
h
m
s
for
Tra
nsmission
S
y
stem
In
[
37]
A
pril
2
0
1
8
,
l
o
ss
s
en
siti
v
ity
i
nd
i
c
es
a
re
u
se
d
for
place
m
e
n
t
o
f
T
C
S
C
a
n
d
T
C
P
A
R
d
e
v
i
c
e
s
.
The
ob
jec
tive
fu
nc
ti
o
n
i
s
m
i
ni
m
i
za
ti
on
o
f
l
ine
l
o
sses
t
h
i
s
a
ppr
oach
i
s
im
pl
ement
e
d
on
I
EEE
57-
bus
s
ystem
.
In
[
38],
201
7
,
a
no
t
h
er
r
e
s
ear
c
h
w
ork,
pow
er
l
oss
se
ns
it
ivi
t
y
i
nde
x
is
u
s
e
d
t
o
de
t
e
rm
i
n
e
opt
im
al
p
la
ce
m
e
nt
p
f
STATC
O
M
the
n
o
p
t
i
m
al
p
a
r
amet
ers
se
t
t
i
n
g
o
f
S
TATC
OM
h
as
b
e
e
n
do
n
e
b
y
N
e
w
t
o
n
Ra
phs
o
n
p
ow
e
r
f
low
tech
n
i
q
u
e.
T
he
o
bjec
ti
ve
f
u
n
c
t
i
o
n
i
s
m
i
n
imi
z
a
t
i
o
n
of
s
yste
m
pow
e
r
l
osse
s,
t
h
i
s
a
p
proac
h
i
s
i
m
p
l
em
ent
e
d
o
n
14
b
us
t
e
s
t
s
y
s
t
em
,
bef
o
re
a
nd
a
f
ter
pla
c
i
ng
t
he
S
TA
TCO
M
,
v
o
l
t
a
ge
a
nd
p
ow
e
r
l
o
s
se
s
have
b
e
e
n
c
om
pare
d.
In
[
39]
2
0
1
3
,
Ma
ni
ka
nda
n
a
n
d
A
r
ul
p
ro
po
sed
pow
e
r
l
oss
i
nde
x
me
t
h
o
d
to
d
eterm
i
ne
o
p
t
im
al
p
lac
e
m
ent
o
f
T
C
S
C
a
n
d
U
P
F
C
,
f
o
r
c
o
n
t
r
o
l
l
i
n
g
p
o
w
e
r
l
o
s
s
a
n
d
e
n
h
a
n
c
i
n
g
t
h
e
u
s
a
b
l
e
c
a
pa
ci
ty
o
f
tra
n
sm
i
s
s
i
on
li
ne.
Tw
o
in
dic
e
s a
r
e
used na
m
e
l
y
p
o
w
e
r
loss
s
ens
i
t
i
vi
ty
i
n
d
e
x
and
se
ns
it
i
v
i
t
y
of o
ve
r loada
b
il
it
y i
n
dex (
S
O
L
).
b)
A
l
g
o
ri
t
h
m
s
for
D
istrib
u
t
i
o
n Sys
t
e
m
In
[
4
0
]
m
a
rc
h
201
7,
F
aha
d
,
Mo
hd
k
h
a
n
i
n
t
rod
u
ced
n
ew
m
etho
d
o
l
o
g
y
f
or
f
in
di
n
g
o
pti
m
al
p
l
a
cem
en
t
of
D
G
a
nd
D
S
TA
TCO
M
f
or
l
o
ss
re
d
u
ct
i
on
and
vo
lta
ge
p
rofi
le
i
mpr
o
ve
me
nt
.
Loss
se
ns
it
ivi
t
y
f
ac
t
o
r
(LSF
)
use
d
f
or
f
i
ndi
n
g
t
he
b
es
t
loca
t
i
o
n
o
f
D
G
.
A
ll
the
opera
t
i
o
n
a
l
a
n
d
s
ys
tem
con
s
trai
n
t
s
mu
st
b
e
c
ons
ider
e
d
a
n
d
verifie
d
t
o
fi
n
d
t
he
o
p
t
i
m
al
l
oc
a
tio
n
of
D
S
T
A
T
CO
M.
O
pt
i
m
al
s
ize
o
f
DG
and
D
S
TATCOM
c
an
b
e
deter
m
i
n
ed
b
y
us
i
n
g
direc
t
l
oa
d
fl
ow
a
nal
y
s
i
s.
I
n
[4
1]
2
01
6
A
t
m
a
Ra
m
G
upt
a
,
A
shw
a
ri
kum
ar
p
rop
o
se
d
“
perform
ance
a
nal
y
sis of
R
a
d
i
a
l
D
i
str
i
b
u
t
i
on w
i
t
h
U
P
Q
C
&
D
S
TA
TCO
M.
P
ropose
d
pow
er
l
oss
i
n
dex
m
e
t
h
o
d
f
o
r
find
in
g
o
p
ti
mal
l
o
cat
ion
o
f
D
STA
T
C
O
M
&
UOQC
i
n
rad
i
al
d
i
s
t
r
ib
u
t
i
o
n
s
y
ste
m
.
The
bus
w
hic
h
i
s
h
a
vin
g
the
m
i
ni
m
u
m
losse
s
,
th
at
bus
i
s
selec
t
e
d
a
s
t
h
e
ca
ndi
da
te
bus
f
or
U
P
Q
C
plac
em
en
t
an
d
opt
im
al
l
oca
t
i
o
n
o
f
D
S
TA
TCO
M
i
s
fo
un
d
by
P
L
T.
T
he
m
a
i
n
o
b
jec
tiv
e
is
t
o
r
e
duc
e
p
o
w
e
r
l
osse
s,
i
nve
stm
e
nt
c
os
t
a
nd
i
m
pr
ovin
g
voltage pr
o
file of
th
e sys
t
em
.
In
[
4
2
]
20
16
G
u
p
t
a
an
d
K
u
m
a
r
propose
d
s
e
n
s
iti
vi
ty
i
nd
i
c
e
s
f
or
o
p
t
i
m
al
l
oc
at
i
on
of
D
-S
TA
TCO
M
’s.
fa
st
v
o
lta
ge
s
t
a
bil
i
t
y
i
n
d
e
x
,
th
e
c
o
mbi
n
e
d
p
o
w
er
l
oss
inde
x
,
v
o
l
t
a
g
e
s
tab
i
l
ity
i
n
d
e
x
,
vo
lta
ge
s
ens
i
tiv
i
t
y
i
nde
x
and
pro
p
o
se
d
sta
b
il
it
y
i
nde
x
are
u
s
e
d
.
T
h
e
new
v
o
l
t
a
ge
s
ens
i
t
i
v
i
t
y
in
de
x
i
s
u
sed
to
d
ete
r
mine
t
he
o
pt
i
m
al
l
o
c
a
t
i
o
n
o
f
D
-
S
T
A
T
C
O
M
.
O
p
t
i
m
a
l
s
i
z
e
o
f
D
-
S
T
A
T
C
O
M
f
o
u
n
d
i
n
s
u
m
me
r
and
w
i
nte
r
t
im
es,
cons
i
d
e
r
l
oa
d
impro
v
e
m
e
n
t.
t
he
e
ffic
i
e
nc
y
o
f
d
i
f
fe
rent
s
e
n
s
i
t
i
v
i
t
y
-base
d
a
p
p
roac
hes
i
n
o
ptim
al
a
l
l
oca
t
io
n
of
D
-
S
T
A
T
CO
M’
s
w
e
r
e
c
ompar
e
,
and
the
i
m
pac
t
o
f
t
h
e
op
tim
al
p
lac
e
m
e
n
t
o
f
D
-
S
T
A
T
C
O
M
’
s
t
o
i
m
p
r
o
v
e
vo
lta
ge s
tab
i
lit
y
ma
rgin, r
educe
e
n
ergy
losse
s a
nd i
n
cr
ease
ene
rgy
co
s
t
sav
in
g
s
we
r
e i
n
ve
sti
g
at
ed
.
In
[
4
3
]
201
5,
pow
er
l
oss
ind
e
x
me
tho
d
i
s
u
s
ed
f
or
p
la
cem
ent
o
f
D
S
TA
TCO
M
i
n
r
a
dia
l
d
istri
b
u
t
io
n
syste
m
f
or
r
ed
uct
i
on
o
f
l
ine
losses
a
n
d
im
p
r
ovem
e
n
t
o
f
v
o
lta
ge
p
r
o
f
il
e
.
B
u
s
p
ara
m
e
t
ers
c
a
n
b
e
cal
cul
a
te
d
by
us
i
n
g
loa
d
f
l
o
w
me
t
h
o
d
s.
M
a
t
hem
a
tica
l
m
o
d
el
i
n
g
i
s
u
se
d
t
o
c
a
l
c
u
la
te
r
e
a
c
ti
v
e
p
o
w
e
r
i
n
j
e
c
t
i
o
n
o
f
D
S
T
A
T
C
O
M
f
o
r
a
l
l
h
e
b
u
s
e
s
.
B
a
s
e
d
o
n
r
e
a
c
t
i
v
e
p
o
w
e
r
v
a
l
u
e
s
o
p
t
i
m
a
l
l
oc
at
ion
of
D
S
T
A
T
CO
M
ca
n
be
selec
t
e
d
b
y us
i
ng P
L
I.
2.4.
C
omb
i
n
a
tion
of
meta-
h
eu
ristic
&
se
n
sitiv
i
t
y
ap
p
roac
h
In
s
o
m
e
re
sear
ch
w
ork,
s
e
n
s
itiv
i
t
y
i
n
dex
me
t
h
o
d
s
a
n
d
m
e
ta-
h
eur
i
st
i
c
t
ec
hn
i
q
ue
s
has bee
n
hy
b
ri
d
i
ze
d
and
a
p
p
l
i
e
d
to cus
tom
p
o
w
e
r
dev
i
ce
s
/
F
A
CT
S
devices
a
ll
oc
ati
o
n
pr
o
b
le
ms
t
o
ge
t
be
t
t
e
r
s
olu
t
i
o
ns
c
om
p
a
r
e
d
t
o
in
div
i
dua
l m
e
t
h
o
d
s.
a)
A
l
g
o
ri
thms for
Tr
a
nsm
i
ssi
on
S
y
stem
In
[
44]
F
eb
2
0
18,
S
rava
na
k
u
m
a
r
,
S
u
rya
k
ala
v
at
h
i
p
rop
o
se
d
a
new
me
tho
d
for
op
t
i
ma
l
p
l
a
cem
ent
o
f
TCS
C
&
o
p
t
i
m
a
l
t
u
n
in
g
of
g
e
n
era
t
or
s
i
n
pow
er
s
ys
te
m.
C
om
b
i
ne
d
i
nd
ex
i
s
u
s
e
d
f
o
r
o
p
t
i
m
al
g
en
e
r
a
t
o
r
rea
lloc
a
t
i
o
n
w
ith
o
p
t
i
m
al
p
la
ce
me
nt
o
f
TCS
C
.
Krill
H
e
rd
a
lgor
it
h
m
i
s
u
s
e
d
f
o
r
o
p
t
i
m
a
l
t
u
n
i
n
g
o
f
T
C
S
C
.
Com
b
i
n
e
d
i
n
d
e
x
ha
v
i
n
g
l
i
n
e
uti
liza
t
io
n
fa
ctor
(
LU
F
)
a
nd
fas
t
v
o
lt
ag
e
st
abi
l
i
t
y
ind
e
x
(FV
S
I
)
.
Th
e
ma
i
n
ob
jec
t
i
v
e
f
u
nc
tio
n
is
m
in
im
iz
ati
on
of
l
i
n
e
loss
an
d
vo
l
t
a
g
e
de
v
i
a
ti
on
.
In
[
45
]
2
0
1
5
,
g
ra
vi
t
a
ti
on
a
l
s
e
a
rc
h
alg
o
ri
t
h
m
is
p
r
e
sen
t
ed
t
o
de
t
e
rm
i
n
e
t
h
e
o
p
t
i
ma
l
p
l
ac
em
en
t
o
f
F
A
CTS
de
vice
s
(T
CS
C,
S
V
C
,
UP
F
C
).
V
ol
t
a
ge
s
e
c
u
r
i
t
y
i
n
d
e
x
(
V
S
I
)
,
l
i
n
e
s
e
c
u
r
i
t
y
i
n
d
e
x
(
L
S
I
)
a
r
e
u
s
e
d
f
o
r
p
e
r
f
orm
a
nc
e
ana
l
ys
is.
T
h
e
m
a
in
a
im
i
s
t
o
r
educ
e
pow
er
l
osse
s
and
en
ha
ncem
ent
o
f
s
ystem
se
curi
ty.
I
n
[
4
6
]
201
2,
a
ne
w
m
e
tho
d
i
s
pro
pose
d
f
or
o
p
t
i
m
a
l
place
me
nt
o
f
TCS
C
a
n
d
S
TA
TCO
M
i
n
po
w
e
r
sy
stem
.
R
eal
pow
er
f
lo
w
se
nsit
i
v
it
y
inde
x
a
n
d
com
b
i
n
a
tio
n
vo
lta
ge
s
e
n
s
i
tivi
t
y
i
n
d
e
x
a
r
e
u
sed
for
fi
nd
in
g
op
tim
al
p
l
a
c
e
m
e
n
t
of
T
CSC
a
nd
STATCOM.
T
h
e
o
pt
i
m
a
l
rati
ng
of
T
CS
C
a
n
d
bes
t
s
iz
in
g
o
f
S
TA
TCO
M
i
s
o
p
t
im
iz
ed
b
y
us
i
n
g
t
h
e
G
enetic
a
l
g
o
r
it
hm.
The
ob
j
ecti
v
e
fu
nc
ti
o
n
is to r
educe
se
ve
ri
t
y
o
f t
h
e
sys
t
e
m
l
oad
i
ngs
a
nd e
n
han
ce
me
n
t
o
f
vol
tage
s
tab
i
l
ity
o
f th
e
s
y
st
e
m
.
In
[
47]
2
0
0
9
,
P
a
r
i
z
a
d
a
n
d
K
h
az
al
i
pro
p
o
se
d
heur
ist
i
c
m
e
th
o
d
s
a
n
d
se
nsi
t
i
v
it
y
i
nde
x
for
op
t
i
m
a
l
place
me
nt
o
f
F
A
CTS
dev
i
ce
s.
H
S
A
a
nd
G
A
have
u
se
d
t
o
d
ete
r
mine
o
pti
m
al
l
o
cat
i
o
n
of
T
CPAR,
U
P
FC
a
nd
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
A rev
i
e
w
o
n
o
p
tim
al
p
l
ac
em
e
n
t
an
d sizi
ng
of
cus
t
om
p
o
we
r dev
i
ce
s/
FA
CT
S .
.
. (V.
T
e
jaswin
i)
90
5
SVC
dev
i
ce
s.
F
o
r
s
yste
m
a
n
a
l
y
s
is,
T
h
r
ee
d
i
ffere
n
t
c
ases
a
r
e
c
o
n
s
i
d
e
r
e
d
:
1
)
T
C
P
A
R
,
U
P
F
C
,
S
V
C
a
r
e
p
l
a
c
e
d
in
div
i
dua
l
l
y
2
)
an
y
tw
o
de
vi
ce
s
p
l
ac
e
d
r
a
n
doml
y
3
)
thre
e
de
vice
s
a
r
e
pla
c
e
d
s
imu
l
ta
ne
ous
l
y
.
I
n
a
l
l
t
hre
e
ca
se
s
v
o
l
t
a
g
e
i
n
d
i
c
e
s
a
n
d
los
s
es
s
ho
ul
d
be
calc
u
la
t
e
d
t
o
s
e
l
ect
t
h
e
b
ett
e
r
p
l
ace
s
fo
r
th
e
d
e
vi
c
e
s
.
Th
e
ma
i
n
ob
jec
t
i
v
e
fu
nc
tio
n
is
t
o
impr
ove
v
o
l
t
a
ge
p
rofi
le,
reduc
e
p
o
w
e
r
l
o
sses,
i
nc
rea
s
ing
pow
er
t
r
a
nsfe
r
ca
pacit
y
,
ma
ximum
loa
d
in
g a
n
d vo
l
t
a
g
e stab
il
i
t
y
ma
rgi
n
.
b)
A
l
g
o
ri
thms for
D
istrib
u
tio
n
Sys
t
em
In
[
4
8
]
N
ov
2
0
1
8
,
S
e
lva
Ra
j
,
R
a
j
an
ga
m
i
n
tr
od
uc
e
d
m
ul
ti
o
bj
e
c
t
iv
e
mo
di
fi
ed
f
l
o
wer
p
o
ll
in
at
i
o
n
alg
o
ri
t
h
m
(Mo
-
MF
P
A
)
for
p
o
w
e
r
lo
ss
r
ed
uc
t
i
on,
m
i
n
im
um
l
oad
b
a
la
n
c
in
g
i
nde
x
a
n
d
ma
x
i
m
u
m
v
o
l
t
a
g
e
profi
l
e
in
r
a
d
ia
l
dis
t
ri
but
i
on.
P
V
array
use
d
a
s
d
i
str
i
b
u
t
e
d
g
e
nera
tor
(
D
G
)
,
pre
ide
n
t
i
fy
t
he
m
o
s
t
c
a
n
d
i
date
bus
se
s
f
o
r
pla
c
in
g
P
V
a
nd
D
S
TA
TCO
M
by
us
i
n
g
v
o
lta
ge
s
ta
bil
i
t
y
i
n
d
ex.
The
n
t
he
M
O
-
MF
P
A
i
s
use
d
t
o
reduc
e
t
h
e
s
i
z
e
an
d
loc
a
t
i
ons
o
f
P
V
a
rra
ys
a
nd
D
S
T
A
T
CO
M
from
t
h
e
s
e
l
e
c
t
e
d
b
u
s
s
e
s
.
I
n
[
4
9
]
V
S
I
i
s
u
s
e
d
t
o
fi
n
d
t
he
p
la
ce
m
e
nt
o
f
D
-
S
T
A
T
CO
M
dev
i
c
e
s
and
op
t
i
ma
l
siz
e
o
f
D
-
S
TA
TCO
M
i
s
de
term
ine
d
b
y
us
in
g
b
a
t
sw
arm
opt
i
m
iz
ati
o
n
a
l
g
o
ri
th
m
.
I
n
[5
0]
2
016,
S
a
f
ari
a
n
d
A
h
m
a
d
us
e
d
d
i
s
c
r
ete
im
peri
ali
s
t
i
c
c
o
mpe
titi
o
n
&
nel
d
er
-me
a
d
al
gor
it
hm
t
o
s
o
l
v
e
D
-
S
T
A
T
CO
M
p
l
ace
me
n
t
p
rob
l
em
i
n
d
i
s
tri
b
u
t
ion
s
y
s
t
e
m
s,
w
hile
D
G
’
s
are
prev
io
us
ly
i
ns
t
a
lle
d
i
n
i
t
.
V
o
l
t
a
ge
s
t
a
b
i
l
i
t
y
i
nde
x
(V
S
I)
is
a
p
p
l
ied
t
o
i
d
e
n
tif
y
the
w
e
a
k
b
us
e
s
i
n
t
h
e
ne
t
w
o
r
k.
O
b
jec
t
i
v
e
f
u
nc
tio
n
is
m
i
n
i
m
i
z
in
g
the
s
u
m
o
f
n
orm
a
lize
d
a
cti
v
e
p
ow
e
r
l
o
sses
an
d
D
-
S
T
A
T
CO
M
ins
t
a
l
l
a
ti
on
cos
t
.
C
oord
i
na
tio
n
of
D
G
’
s
a
n
d
D
-
S
T
A
T
CO
M’s
w
i
l
l
g
iv
e
be
tter
res
u
l
t
s
c
o
m
par
e
t
o
D
-
S
T
A
T
CO
M’s
w
i
t
hou
t
D
G
’
s
i
n
d
istr
ibu
t
io
n
fe
e
d
er
.
N
e
w
D
I
CA
-N
M
h
y
b
r
i
d
a
l
gor
it
hm
i
s
pr
ov
i
d
e
mor
e
a
cc
urac
y
c
o
m
p
ar
e
to
evo
l
ut
iona
r
y
meth
o
d
s su
ch
a
s GA,
P
S
O
, AC
O
e
tc.
In
[
51]
2
01
5,
l
oss
se
ns
iti
v
ity
f
ac
tor
(LS
I)
and
ba
c
t
eria
l
for
a
g
in
g
o
p
t
i
m
i
z
a
tio
n
a
l
gori
t
hm
h
a
v
e
be
en
hy
bri
d
i
z
ed
f
or
D
-S
TA
TCO
M
’s
a
nd
D
G
’
s
place
me
n
t
i
n
d
i
stri
bu
t
i
on
s
yst
e
m.
I
t
i
s
u
se
d
to
r
e
d
u
ce
p
o
w
e
r
loss
and
impr
oves
the
vo
ltage
p
rofi
le
o
f
t
h
e
sys
t
e
m
.
The
fi
ve
l
oss
s
e
n
s
iti
v
ity
f
ac
tor
v
a
lue
s
w
e
r
e
so
rte
d
i
n
desce
n
d
i
ng
order,
t
he
t
r
i
a
l
a
nd
e
rror
me
tho
d
i
s
use
d
t
o
de
ter
m
i
ne
o
p
t
im
al
l
oca
t
i
o
n
be
tw
e
e
n
five
b
us
es.
The
bus
w
h
i
c
h
i
s
h
a
vi
n
g
l
eas
t
am
ou
n
t
o
f
pow
e
r
l
o
s
s,
t
ha
t
bu
s
i
s
s
e
l
ecte
d
a
s
c
a
nd
i
d
ate
bus
f
or
p
lac
e
m
e
n
t
o
f
D
G
’
s
or D
-S
TA
T
C
OM’s.
M
e
t
a
-h
eu
ri
st
i
c
o
pti
m
i
z
a
t
ion
t
ech
niq
u
e
s
a
r
e
si
mp
l
e
a
nd
e
a
si
er
t
o
f
ind
o
p
ti
mal
so
lu
ti
o
n
t
o
t
h
e
pro
b
lem
s
.
Co
m
p
ar
e
to
a
na
l
y
tic
a
l
m
e
t
ho
ds
a
n
d
A
rti
f
icia
l
N
e
ur
al
n
et
wo
rk
b
a
s
ed
m
e
t
h
o
d
s
,
M
e
t
a
-h
e
u
ri
st
ic
me
tho
d
s
are
e
a
s
y
to
d
e
f
i
n
e
a
nd
use
d
f
or
m
ul
ti
obje
c
tive
func
tio
n
by
c
ons
id
e
r
i
n
g
many
c
o
n
st
ra
int
s
.
But
thi
s
tech
n
i
q
u
e
i
s
s
uffer
e
d
from
pre
ma
tu
r
e
c
on
verge
n
ce
an
d
l
a
c
k
of ac
cura
cy
[
5
2
-5
7].
S
e
nsi
t
i
v
i
t
y
a
p
p
r
oa
ches
a
re
s
i
m
pl
e
a
n
d
m
o
s
t
s
u
i
tab
l
e
for
t
h
e
pl
a
ce
me
nt
p
ro
blem
,
b
u
t
i
t
i
s
c
o
nsi
d
e
r
on
ly
one
o
b
j
e
c
ti
ve
p
ro
blem
[
58-
6
1
].
A
n
y
s
e
n
s
i
t
i
vit
y
a
p
p
r
oac
h
i
s
d
e
s
i
g
ned
to
f
i
n
d
th
e
crit
i
c
al
l
oca
tio
n
o
f
cus
t
om
pow
e
r
d
e
v
ice
s
/F
A
C
TS
d
ev
ices
f
r
o
m
a
spe
c
i
f
ic
p
oi
nt
o
f
v
i
e
w
,
a
n
d
i
t
i
s
d
i
f
f
i
c
u
l
t
t
o
c
o
n
s
i
d
e
r
m
a
n
y
c
o
nst
r
a
i
nt
s
fo
r
t
h
e
p
r
obl
em.
Th
e
co
mb
in
at
i
o
n
o
f
s
en
si
ti
v
i
ty
a
pp
roac
h
e
s
an
d
me
ta-h
eur
i
s
tic
m
et
ho
ds
a
r
e
m
o
s
t
l
y
u
s
e
d
t
o
s
o
l
v
e
t
h
e
p
r
o
b
l
e
m
s
.
S
e
n
s
i
t
i
v
i
t
y
a
p
p
r
o
a
c
h
e
s
a
r
e
u
sed
for
fi
nd
ing
m
o
st
c
ri
tica
l
n
ode
s,
t
o
ma
ke
the
pro
b
le
m
s
m
aller.
O
ptimi
z
atio
n
t
e
c
h
ni
q
u
es
c
an
b
e
ap
p
lie
d
to
no
des,
t
o
det
e
r
m
ine
the
fe
w
spec
i
f
ic
n
o
d
es
for
t
h
e
bes
t
s
i
ze
of
c
u
s
t
o
m
power/F
AC
TS
d
e
v
i
c
es.
Usin
g
t
h
is
p
ro
ce
s
s
,
the
r
e
ex
is
t
b
a
lanc
e
be
twee
n
t
h
e
ac
cura
cy
a
n
d
s
pee
d
, an
d it i
s
possi
b
l
e to use
mult
i
o
bjec
t
i
v
e
f
unc
t
i
o
n
s
a
n
d
cons
ider m
any
c
onstra
i
nt
s.
R
evie
w
of
d
iffere
n
t
re
s
e
a
rc
h w
o
r
k
s
on
cust
o
m
pow
er
de
v
ic
es
/F
A
C
T
S
d
evic
es
a
l
l
oc
ati
o
n as
s
ho
w
n
i
n Ta
ble
2.
Tab
l
e
2.
R
e
v
i
e
w
of D
iffe
ren
t
R
e
s
e
a
rc
h W
o
r
k
s on
Cus
t
om
P
ow
er D
e
v
ic
es
/FA
C
TS
D
evice
s
A
lloca
t
i
o
n
.
S.
no
Obj
e
c
tiv
e
s
D
e
v
i
c
e
s
A
l
gor
it
hm
R
e
m
a
r
ks
1
Pow
e
r
loss
re
du
c
t
i
on,
G
ood
d
a
m
ping
ch
a
r
act
er
i
s
t
i
c
s
STA
T
C
O
M
&
PS
S
Ge
n
e
t
i
c
R
un tim
e, Re
quire l
ong re
vis
iting o
f
o
pt
im
al
soluti
ons.
2
Re
ac
tive
powe
r
d
ispa
t
c
h
problem
,
m
i
nim
u
m
tra
n
s
m
iss
i
on
losses
a
nd
volt
a
ge
d
e
v
i
a
tion
STA
T
C
O
M
Ch
emi
c
a
l
Re
ac
tion
Its
loc
a
l
s
e
a
r
c
h
a
bi
lit
y
of
i
s
wea
k
,
I
t
i
s
ofte
n
tra
p
s
i
n
to
l
oca
l
opti
m
a
3
Ove
r
a
ll
volta
g
e
p
r
o
file
i
m
p
r
ude
nt,
s
yste
m
loa
d
a
bility.
S
T
ATCO
M
C
u
c
koo
sea
r
c
h
D
i
ff
ic
ult
to
S
olve
m
ult
i
objec
tive
pr
oble
m
s
4
M
i
ni
m
i
z
a
t
ion
of
pow
e
r
f
low
proble
m
s
S
V
C
&
TC
S
C
B
F +
NMA
D
e
la
y
i
n
rea
c
h
ing
t
h
e
globa
l
sol
u
tion
5
Pow
e
r
loss
re
du
c
t
i
on
&
b
e
t
t
e
r
volta
g
e
sta
b
i
lit
y
ma
r
g
i
n
U
P
F
C
&
I
PFC
P
S
O
+
GS
A
S
l
o
w c
onve
rge
n
c
e
,
g
e
t
ting
tr
a
ppe
d
in loca
l
a
r
eas
6
Vol
t
a
g
e
pr
ofile
e
n
h
a
n
ce
m
e
nt
,
s
y
s
tem
la
ud
a
b
ilit
y im
pr
ove
ment
STA
T
C
O
M
I
C
A
R
e
q
u
i
red
to
d
eter
min
e
to
t
al p
o
w
e
r
.
Re
quire
d m
o
r
e
s
e
t
t
i
ng
ti
m
e
.
7
Pow
e
r
loss
re
du
c
t
i
on
&
volta
g
e
p
rof
i
le
i
m
provem
e
nt
S
T
ATCO
M
PS
O
Sl
ow c
onve
rge
n
c
e
, c
a
n
’t
w
ork
out
t
he
pro
b
lem
of
s
ca
tt
e
r
ing
&
opti
m
i
z
a
t
i
o
n
.
8
Ha
r
m
oni
c
dist
or
ti
on
&
v
o
l
t
a
g
e
d
e
vi
a
t
ion
r
e
duc
ti
on
D
-
ST
A
T
C
O
M
Fire
fly
D
e
la
y
in
r
ea
c
h
ing
t
h
e
globa
l
sol
u
tion
9
Pow
e
r
loss
re
du
c
t
i
on,
volta
ge
p
rof
i
l
e
i
m
provem
e
nt
D
-
ST
A
T
C
O
M
I
m
m
u
n
e
R
e
quire
m
ore C
o
m
p
u
t
ing
tim
e
10
M
ini
m
u
m
t
ota
l
pow
e
r
l
oss
e
s
D
-
ST
A
T
C
O
M
Ha
r
m
on
y
Eac
h
objec
tive
f
unc
tion
h
a
s
b
e
e
n
h
a
n
dle
d
se
p
a
rat
e
ly a
s
a
single
obj
ec
tiv
e
opti
m
i
z
a
t
i
o
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
Pow
El
ec &
D
ri
S
yst
,
Vol
.
10,
N
o.
2
, June 2019: 900
–
90
8
90
6
3.
CONCL
U
S
ION
Thi
s
p
ap
er
h
as
p
res
e
n
t
e
d
M
e
t
a
h
e
u
r
i
s
t
i
c
m
e
t
hod
s,
s
en
si
ti
v
e
i
nd
e
x
m
e
tho
d
s
a
n
d
t
h
e
i
r
hy
br
i
d
c
o
mb
in
a
t
i
o
n
fo
r
d
e
t
e
rmin
i
ng
t
h
e
op
ti
ma
l
l
o
ca
t
i
on
a
nd
s
i
z
in
g
o
f
c
u
st
om
power
d
e
v
i
c
es/F
ACTS
d
evice
s
.
An
exte
ns
i
v
e
a
n
d
com
p
rehe
n
s
i
v
e
sur
v
ey
o
f
p
u
b
l
i
s
h
e
d
l
ite
ratur
e
s
on
th
is
f
iel
d
i
s
prese
n
t
e
d.
F
rom
the
ana
l
ys
is
o
f
com
p
aris
on,
i
t
is
i
n
f
e
rre
d
th
at
o
n
l
y
a
few
e
r
rese
a
r
c
h
w
or
k
is
d
o
n
e
o
n
d
istr
ib
u
tio
n
sys
t
e
m
c
om
par
e
d
t
o
transm
i
s
s
i
on
s
ys
tem
.
There
i
s
ve
ry
s
l
i
ght im
p
rove
me
n
t
in
o
p
t
i
m
i
za
tio
n t
e
chn
i
q
u
e
s
tha
t a
r
e used
for p
la
cem
ent
and
s
i
z
i
n
g
o
f
c
u
s
t
om
p
ower
d
e
v
ic
es
/FAC
TS
d
evic
e
s
.
A
com
p
ar
ative
s
t
udy
o
n
t
h
e
app
l
i
cati
o
n
of
d
if
f
e
ren
t
op
tim
iza
t
i
o
n
t
e
c
h
n
i
que
s
a
r
e
do
ne
i
n
ter
m
s
of
ac
cura
c
y
a
n
d
s
pe
e
d
.
It
i
s
als
o
c
onc
l
u
ded
th
a
t
f
or
p
ow
e
r
l
o
s
s
minim
i
z
a
t
i
on
i
n
pow
e
r
s
ys
te
m
s
,
most
o
f
th
e
re
se
arc
h
h
a
s
c
onc
e
n
t
rate
d
o
n
l
y
o
n
si
ng
le d
evice
p
l
ac
em
e
n
t
ra
t
h
e
r
tha
n
p
lac
e
m
e
n
t
o
f
m
u
lti
de
v
i
c
e
s.
A
fter
r
e
v
iew
of
d
iffere
n
t
t
yp
e
s
of
m
et
a-he
urist
i
c
al
g
o
ri
thms
&
s
e
n
siti
v
i
t
y
in
de
x
m
e
t
h
o
d
s,
s
till
t
h
ere
is
a
s
c
ope
f
or
i
m
p
lem
e
n
t
at
i
o
n
of
d
if
fe
ren
t
t
ype
s
o
f
n
ew
h
ybr
id
a
lgor
i
t
h
m
s
for
op
tim
al p
la
ce
m
e
nt a
nd s
i
zi
n
g
of
cus
t
om
p
o
w
er
d
evice
s
/F
AC
TS
de
v
i
ces i
n
po
wer s
y
st
ems.
REFERE
NC
E
S
[1]
R
a
hu
l
Ag
r
a
w
a
l,
S
.
K
.
B
h
a
r
a
d
w
a
j
,
D
.
P
.
K
o
th
a
r
i,
“
P
o
p
u
l
a
ti
o
n
b
a
s
e
d
ev
ol
uti
onary
o
p
t
i
m
i
zati
o
n
t
echni
qu
es
f
o
r
o
p
t
i
m
a
l
allocat
io
n
and
si
zin
g
o
f
Thy
r
isto
r
Co
ntro
ll
ed
S
eri
e
s
Ca
paci
tor”,
Jou
r
n
a
l
o
f
Elect
r
i
c
a
l
S
y
stem
s
an
d
Informa
tio
n Te
c
h
no
lo
gy
,
7
F
e
b
ru
ary
20
18
[2]
A
.
R
ezaee
J
ord
e
hi,
“O
p
t
im
al
a
llo
catio
n
o
f
F
A
C
TS
d
ev
ices
f
o
r
s
ta
tic
s
ecu
rit
y
e
nh
ancem
ent
in
p
ow
er
s
ys
tems
v
ia
i
m
peri
alisti
c co
m
p
eti
t
i
v
e al
gorith
m
(ICA)”,
Appl
i
e
d Soft
Compu
ting
,
v
o
l
.
48
,
p
p
.
3
1
7-32
8,
N
ov
em
b
e
r
2
0
1
6
.
[3]
A
.
R
ezaee
J
o
rd
e
h
i,
“
Brainsto
rm
optimis
atio
n
algo
rit
h
m
(BS
OA):
A
n
effici
e
n
t
algor
i
t
h
m
f
o
r
findi
n
g
opt
i
m
a
l
l
o
cat
io
n
and
set
t
in
g
o
f
F
ACTS
d
evi
c
es
i
n
electric
po
wer
sy
st
ems
”,
Int
e
rnational
Journal of Elect
rical
P
o
wer
&
E
n
er
gy S
y
st
em
s
,
v
o
l.
6
9,
p
p.
48
-
5
7
, Ju
l
y
20
15
.
[4]
A
t
m
a
R
am
G
u
p
t
a
a
n
d
Ash
wani
K
u
m
a
r
,
"Op
t
i
m
al
p
lacem
en
t
o
f
D
-STATC
OM
u
s
i
n
g
s
ens
i
tiv
it
y
app
r
oaches
i
n
m
e
s
h
d
istri
bution
sys
t
em
wit
h
t
i
m
e
v
arian
t
l
oad
m
o
d
e
ls
und
er l
o
ad gro
wth
"
,
Ain
Sh
ams Eng
i
n
e
e
r
in
g J
o
urna
l
,
J
u
n
e
20
16
.
[5]
A
c
ha
E
,
F
u
erte-E
sq
u
i
vel
CR,
Am
briz-P
erez
H,
e
t
al
.
FACTS
:
m
od
el
lin
g
an
d
s
im
ul
a
t
i
on
i
n
p
ower
n
etwo
rks
.
J
ohn
W
i
l
e
y
& S
o
ns;
200
4.
[6]
A
z
iz
O
uk
enn
ou,
A
b
d
el
halim
S
and
a
li
,
Sa
m
i
ra
E
lmou
me
n”
C
o
o
r
d
ina
t
e
d
P
lacem
ent
and
S
e
ttin
g
of
F
A
C
TS
i
n
E
l
ect
rical
N
etwork
b
ased
o
n
Kal
a
i-s
m
o
r
odin
s
ky
B
argain
in
g
S
olut
ion
and
V
o
l
t
a
g
e
D
e
vi
atio
n
Index”
V
ol.
8,
N
o.
6, De
c
2
0
1
8
,
p
p
.
40
79
~4
08
8 IS
S
N
:
2
0
8
8
-
87
08
, D
OI: 10
.11
5
9
1
/i
je
c
e
.v
8i6.p
p
.4
07
9-
4
0
8
8
.
[7]
Reza
si
rjan
i,
A
h
m
ad
r
ezae
e
Jord
ehi
,
“
Optim
a
l
placem
en
t
and
s
i
zi
ng
o
f
d
i
stri
buti
o
n
s
t
atic
c
om
pan
s
at
er
i
n
el
e
c
t
r
ic
d
i
stri
butio
n
network
s
:
a
revi
ew” Rn
ewabl
e
a
nd
s
ust
a
in
ab
l
e
e
nerg
y
revi
ews
,
V
ol.
77
p
p
68
8-6
9
4
,
a
pri
l
201
7.
[8]
P
.
L
o
k
e
n
d
e
r
R
e
d
d
y
,
G
.
Y
e
s
u
r
a
t
n
a
m
“
A
m
o
d
i
f
i
e
d
b
a
c
t
e
r
i
a
l
f
o
r
a
g
i
n
g
a
lgo
r
it
h
m
b
ased
opt
im
al
r
eactiv
e
po
wer
disp
at
ch
” Vo
l. 1
3, No
. 1
,
Jan
u
ary
20
19
, pp
.
3
61
~
3
67
ISS
N:
25
0
2
-
4
752
, DOI: 10
.1
1
5
9
1
/ijeecs
.v1
3
.i
1.p
p
3
6
1
-
367.
[9]
G
h
as
san
Abd
u
llah
S
alm
a
n,
M
o
h
am
m
e
d
Hasan
Al
i
,
A
li
Najim
A
bdullah
“
Implem
en
tati
on
O
ptimal
L
o
cati
on
an
d
S
i
zin
g
o
f
UP
F
C
o
n
Iraqi
P
ow
er
S
y
s
t
e
m
Gri
d
(
132
kV)
Us
in
g
Ge
net
i
c
Al
gorith
m”
V
ol.
9
,
N
o
.
4
,
D
ecemb
e
r
2
0
1
8
,
pp.
1607~1615
I
SSN: 2088-8694,
DOI:
10.
11591/ijpeds.
v9n4
.
p
p1
607
-1
61
5.
[10]
Si
ro
t
e
K
hunkit
t
i
,
A
pira
t
Si
ri
t
a
rati
w
a
t
“A
H
ybr
i
d
DA-PSO
O
p
t
i
m
i
z
atio
n
Al
gorith
m
f
o
r
M
ulti
ob
ject
ive
Op
ti
m
a
l
P
o
wer
Fl
ow
P
ro
b
l
em
s” E
nerg
ies
20
18,
11,
2
270;
d
o
i:1
0
.
339
0/
en110
9
2
2
7
0
.www
.
m
dp
i.c
o
m
/
jo
urn
a
l/e
n
e
r
gie
s
.
[11]
S
.
M
.
A
b
d
-Elazim
an
d
E.S.
A
li
,
"Op
t
i
m
al
l
o
cation
of
S
TATCOM
i
n
m
u
l
tim
achin
e
po
wer
s
y
s
t
em
f
o
r
i
n
c
reas
in
g
l
o
ad
abi
l
ity
b
y
Cu
cko
o
S
earch
a
l
g
o
r
it
h
m
",
I
nt
ern
a
ti
on
al
J
ou
rnal
of
E
l
ectri
cal
P
o
w
er
&
E
n
e
rgy
S
y
st
ems,
v
o
l
.
80
,
p
p
.
240
-25
1
,
S
e
p
tem
b
er
2
0
16.
[12]
S
a
i
Ram
In
ko
llu,
V
enk
a
ta
R
ed
dy
K
ot
a
,
“
Optim
a
l
settin
g
of
F
A
C
TS
d
e
vi
ces
f
o
r
v
ol
tage
s
t
a
bilit
y
i
m
p
rove
m
e
n
t
usin
g
PSO
a
d
a
pt
iv
e
GS
A
h
y
b
r
id
a
lg
ori
t
h
m
”
,
Engin
eeri
n
g
Sci
e
nce
an
d T
ech
no
log
y
,
an
Int
e
rn
a
t
ion
a
l
Jo
ur
na
l
,
v
o
l
.
1
9
,
no
.
3,
p
p
.
1
1
6
6-11
76
,
S
eptem
b
er
2
01
6.
[13]
S
.
M
.
A
bd
-Elazi
m
an
d
E.S.
A
li,
"
Im
peria
l
is
t
com
p
et
itiv
e
al
g
o
rith
m
for
op
ti
ma
l
ST
ATC
O
M
d
e
sign
i
n
a
m
u
ltim
achi
n
e
po
wer
s
y
s
t
em
",
In
ter
n
a
tio
nal
Jou
r
n
a
l
of
Elect
r
i
ca
l Po
wer
&
En
ergy S
y
stem
s
,
vo
l.
76,
p
p
.
1
36
-146
,
M
a
rch
20
16
.
[14]
S
u
san
t
a
D
u
tta,
Prov
a
s
K
um
ar
R
oy
an
d
Debas
h
i
s
N
and
i
,
"
O
p
t
im
al
l
o
cati
on
o
f
S
TA
T
C
OM
u
s
i
ng
c
hem
i
cal
r
eact
ion
o
p
t
i
mi
zatio
n
f
o
r
reacti
v
e
po
wer
d
i
s
p
atch
p
ro
bl
e
m
",
Ain
Sh
ams
En
gi
neeri
n
g
Journ
a
l
,
vo
l.
7
,
n
o
.
1
,
p
p.
2
33
-247
,
M
a
rch
20
16
.
[15]
A
.
R
ezaee
J
o
rd
e
h
i,
“
Brainsto
rm
optimis
atio
n
algo
rit
h
m
(BS
OA):
A
n
effici
e
n
t
algor
i
t
h
m
f
o
r
findi
n
g
opt
i
m
a
l
l
o
cat
io
n
and
set
t
in
g
o
f
F
ACTS
d
evi
c
es
i
n
electric
po
wer
sy
st
ems
”,
Int
e
rnational
Journal of Elect
rical
P
o
wer
&
E
n
er
gy S
y
st
em
s
,
v
o
l.
6
9,
p
p.
48
-
5
7
, Ju
l
y
20
15
.
[16]
T
h
an
hL
ong
D
u
o
n
g
,
Y
a
o
J
i
an
Gang
,
V
i
etA
n
h
Tru
o
n
g
,
“
A
pplicatio
n
o
f
m
i
n
c
u
t
a
l
go
r
i
th
m
for
o
p
t
i
m
a
l
l
o
c
a
t
io
n
o
f
F
A
CTS
d
e
vi
ces
c
o
n
s
i
deri
ng
s
y
s
t
e
m
l
o
adab
il
it
y
an
d
cost
o
f
inst
al
la
t
i
on
”
,
I
n
te
r
n
a
t
io
na
l J
o
ur
na
l o
f
E
l
e
c
t
r
i
c
a
l
Po
w
e
r &
E
n
e
r
gy
S
y
ste
m
s
, v
o
l
. 6
3
, p
p. 97
9
-98
7
, D
ecem
ber 2
0
1
4
.
[17]
J.
B
e
l
win
E
d
w
a
r
d
,
N.
R
a
j
a
s
e
k
a
r
,
K.
S
a
t
hiy
a
se
k
a
r
,
N
.
Se
n
t
h
i
ln
a
t
h
an
,
R.
S
arjila,
“A
n
enh
a
nced
b
a
c
teri
al
f
orag
in
g
al
go
rit
h
m
app
r
o
ach
f
o
r
o
p
tim
al
p
o
w
er
f
l
o
w
p
r
o
b
lem
i
n
clu
d
i
n
g
F
A
C
TS
d
evi
c
e
s
c
on
si
derin
g
s
y
s
tem
lo
adab
ilit
y
”,
ISA Tr
ansact
ion
s
, vo
l
. 5
2
, no
.
5
, p
p
.
6
22
-62
8
, Se
p
t
e
mber 2
01
3.
[18]
Sa
fa
ri
A
,
Ahm
a
d
i
a
n
A
a
n
d
G
olka
r
MAA,
"
Co
ntro
lle
r
d
e
s
ig
n
of
S
T
A
T
C
O
M
f
o
r
power
system
s
tabi
lity
i
m
pro
v
e
m
ent
u
s
in
g
h
o
n
e
y
b
ee
m
a
ti
ng
optim
i
zati
o
n
"
,
J
Ap
p
l
Res
Techn
o
l
,
vo
.
11,
no.
1
,
p
p
.
1
4
4
–55
, 2
01
3.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
A rev
i
e
w
o
n
o
p
tim
al
p
l
ac
em
e
n
t
an
d sizi
ng
of
cus
t
om
p
o
we
r dev
i
ce
s/
FA
CT
S .
.
. (V.
T
e
jaswin
i)
90
7
[19]
A
l
i
ES
a
n
d
A
bd
-El
azim
S
M
,
"Coo
rd
in
ated
d
esig
n
of
P
SS
s
an
d
TCS
C
via
bact
erial
sw
arm
o
p
tim
i
zatio
n
algo
rit
h
m
i
n
a
m
u
l
tim
ach
in
e po
wer s
y
s
t
em
"
,
In
t
J
El
ectr
Power E
n
er
gy S
y
s
t
,
v
o
l
.
3
6,
n
o
.
1
,
pp.84
–9
2,
2
01
2.
[20]
J
.
P
.
S
r
id
har,
R
.
P
r
ak
ash
“
M
u
l
ti-o
bj
ecti
v
e
w
h
ale
op
tim
izati
o
n
b
ased
m
inimizat
io
n
of
l
oss,
m
aximi
zati
on
o
f
v
o
l
t
ag
e
st
a
b
ilit
y
c
o
n
s
i
deri
ng
c
ost
o
f
DG
f
o
r
o
p
tim
a
l
si
z
i
ng
a
nd
p
l
acemen
t
o
f
DG”,
Inter
nati
o
n
a
l
Jour
na
l of
E
l
ect
r
i
cal
a
n
d
Co
mp
ut
er En
gi
ne
eri
n
g
(
I
J
E
CE),
V
ol
.
9
,
N
o
.
2
,
Ap
ril
2
0
1
9
,
p
p
.
835
~8
39
I
S
S
N:
208
8-87
08
,
DO
I:
1
0
.
115
91
/i
jece.v9i2
.
p
p
.8
35
-839
.
[21]
M
.
L
ax
m
i
devi
R
aman
aiah
,
M
.
D
am
od
ar
R
edd
y
“
M
o
th
F
lam
e
O
ptimizati
o
n
M
et
ho
d
f
o
r
U
n
ifi
e
d
Po
wer
Q
u
alit
y
Conditioner
A
l
l
o
cation”,
Inter
n
a
t
i
onal Jo
ur
nal
o
f
Electrica
l
a
n
d
Comp
ut
er E
ngineer
in
g (
I
JECE)
V
o
l
.
8
,
N
o
.
1
,
F
e
b
r
uary
2
0
18,
pp
.
5
30~
5
37
IS
SN:
20
88-8
7
0
8
,
D
OI:
1
0
.
1
15
91
/
i
j
e
ce
.
v
8
i
1
.
pp
53
0-5
3
7.
[22]
M
.
Laks
h
m
i
Dev
i
,
dam
o
d
a
r Redd
y “
o
p
t
im
al
u
n
i
fie
d
p
ower
qual
i
t
y
c
o
nditioner
alloca
t
i
on
i
n D
i
s
t
rnition
sy
stems
f
o
r
l
o
s
s
m
in
imi
z
a
t
ion
us
in
g
Gray
w
o
l
f
o
p
tim
azati
on”.
In
t.
Jou
r
n
a
l
of En
gi
neeri
n
g
R
e
sea
r
ch a
nd Ap
pl
ica
tio
n,
Vo
l.
7
,
Is
su
e
11
,
(P
art
-3)
p
p
.
4
8-5
3
,
N
o
v
e
m
b
er
2
017
,
.
I
S
S
N:
2
24
8-9
622,
[23]
T
Y
u
v
a
raj,
K
R
Dev
a
balaj
i
“
Op
ti
ma
l
placem
en
t
and
si
zin
g
o
f
D
S
T
A
T
COM
us
in
g
ga
rm
on
y
se
a
r
c
h
a
lg
oith
a
m
”
i
n
t
e
rn
a
tion
con
f
ira
n
ce o
n
a
n
ltem
t
ive
energ
y
in
devel
op
in
g co
un
t
r
i
e
s a
n
d
emer
g
i
ng econ
o
mi
ces
vo
l
:
79
,
2
01
5
.
[24]
S
.
D
e
v
i
and
M
.
G
eet
han
j
ali
,
"
O
p
t
i
m
a
l
lo
catio
n
and
s
i
z
i
ng
d
e
term
in
atio
n
of
D
i
s
t
r
ibuted
G
enerati
o
n
an
d
D
S
TA
TCOM
us
i
ng
P
arti
cle
S
w
a
r
m
Opti
mizati
on alg
o
rithm
"
,
Inte
r
n
a
t
i
ona
l Jour
nal o
f
El
ec
t
r
i
c
al
Po
wer
&
Ener
gy
Sy
ste
m
s,
vol.
6
2
,
p
p.
5
62
-570,
N
o
v
em
ber
2
014
.
[25]
S
e
y
e
d
Ab
bas
Taher,
S
ey
ed
A
h
m
ad
reza
Af
sari
,
“
O
ptim
al
l
ocatio
n
an
d
si
zing
o
f
D-S
T
A
T
COM
in
d
istribu
tion
sy
ste
m
s
by
i
m
m
u
ne
a
lg
or
ith
m”
,
Inter
n
a
t
i
o
n
a
l
Jou
r
n
a
l
of
El
ectr
i
cal
P
o
wer
&
Ene
r
gy
Sys
t
ems
,
vol.
60
,
pp.
3
4-4
4
,
S
e
p
t
em
ber
201
4.
[26]
M
a
s
o
u
d
F
arh
o
o
dnea,
A
zah
M
oh
a
m
ed
,
H
u
s
s
a
i
n
S
h
areef
,
H
a
d
i
Z
ayan
deh
aroo
di
“
op
tim
a
l
DST
A
T
C
O
M
p
lacdem
en
t
usi
n
g
firefl
y
alg
o
rit
h
m
f
o
r
powe
r
qualtiy
e
nhancement
”
IEEE 7
th
in
ter
natio
na
l
po
wer
e
ng
ineering and
optimizaion
co
nf
eren
c
e
(
PEO
CON)
,
20
13
.
[27]
S
e
y
e
d
abb
a
s
a
h
er
a
n
d
s
ey
ed
a
h
m
adreza
af
s
a
ri
“
optim
al
l
oact
io
n
a
n
d
s
i
z
in
g
of
U
P
Q
C
in
d
istribut
io
n
ne
tw
ork
s
us
in
g
d
i
f
f
e
r
e
n
t
i
a
l
e
vo
lu
ti
o
n
a
l
g
o
r
it
h
m
”
Hid
a
v
i
p
u
bl
is
hi
ng
c
o
rp
o
r
atio
n math
emati
c
a
l
pro
b
l
e
ms
in
eng
i
n
e
er
in
g
20
12
.
[28]
M
u
teg
i
A
M,
K
ih
a
t
o
C.M
&
S
a
ul
o
M.
J
“
o
p
tim
a
l
p
l
acemen
t
of
F
ACTS
d
evices
u
sing
v
o
l
tage
s
t
a
bility
i
nd
ices.
”
A
n
n
u
a
l
co
nf
eren
ce on suitain
ab
le
r
s
ear
c
h and
i
n
no
vat
i
o
n
20
1
6
[29]
m
.
a
l
ba
t
s
h,
s
h
m
eem
A
h
m
ad
“
opti
m
a
l
p
lacem
en
t
o
f
u
n
i
fied
p
o
w
er
f
l
o
w
c
o
n
t
r
o
l
l
e
r
s
t
o
i
m
p
r
o
v
e
d
y
n
a
m
i
c
v
o
l
t
a
g
e
s
t
bilit
y
u
si
ng
power
s
ystem
vari
abl
e
based voltag
e
s
tabi
lit
y
i
n
d
i
ces
” Ap
ril
20
15.
[30]
Muh
a
mma
d
nu
r
d
in
,
fa
th
in
s
a
i
fur
R
a
hma
n
,
“P
la
c
e
me
nt
o
f
sh
un
t
VAR
co
m
p
ens
a
to
r
based
on
s
en
s
t
i
v
ity
a
n
a
ly
s
i
s”
Ju
ne
2
01
4v
ol
.6.
[31]
Bu
sh
ra
w
eq
ar,
M
o
hd
T
a
u
seef
K
h
a
n
“
O
ptim
a
l
p
l
acemen
t
of
d
istri
b
u
t
ed
g
en
era
t
i
on
and
D
-
STA
T
COM
in
r
adi
a
l
d
i
stri
butio
n
network
”
h
t
t
ps://d
oi.o
rg
/1
0.
1
0
8
0
/
2
3
0
80
47
7.
2
0
1
7
.
1
40
56
25.
[32]
P
e
n
k
i
t
a
M
e
hta,
P
rag
h
n
e
sh
B
hat
t
a
“
O
ptim
a
l
select
io
n
of
d
idtrib
u
t
io
n
g
e
nerat
i
ng
u
ni
ts and
i
t
s
p
lace
m
e
n
t
f
o
r
v
o
l
t
a
ge
s
t
ab
ilit
y
enh
a
ncem
ent
an
d
ener
g
y
l
o
ss
m
i
n
i
mi
z
a
ti
on
”
2
0
9
0
-44
7
9
2
01
5
Ai
n
S
h
am
s
U
n
i
v
ersity.
P
r
odu
cti
o
n
an
d
h
o
s
t
i
n
g
by
El
sevier
B
.V
.
[33]
J
a
in
A
,
G
upta
A,
K
u
m
ar
A
,
An
e
ffi
c
ient
m
etho
d
for
D-S
T
ATCOM
pl
ace
me
n
t
i
n
ra
dia
l
d
is
tribu
tio
n
sy
ste
m
;
20
14
.
p. 1–
6
.
[34]
H
u
s
s
ai
n
S
,
V
is
ali
N.
“
Iden
tifi
ca
ti
on
o
f
w
eak
b
us
es
u
si
ng
Volta
g
e
S
t
ab
ilit
y
I
ndi
cator
a
nd
it
s
v
o
l
t
age
profile
i
m
pro
v
e
m
ent
by
u
s
i
ng
DST
A
TCO
M
i
n
radi
al
d
istri
b
u
t
i
o
n
sy
st
e
m
s”,
IO
S
R
J E
l
ectr
E
l
ectr
o
n
En
g (
I
OS
R
J
EEE)
,
v
o
l
.
2
,
n
o
.
4
;
2012.
p
.
17–
23
.
[35]
S
a
p
t
ars
h
i,
s
u
r
esh
“
O
ptim
al
p
lacem
ent
of
T
CS
C
an
d
T
C
P
A
R
us
in
g
s
e
ns
it
iv
it
y
a
n
a
l
ys
i
s
”
h
t
t
p
s
:
//w
ww.
r
es
e
a
rchg
ate.
n
e
t/p
ub
li
catio
n
/
32
41
732
23
.
[36]
V
.
sri
n
i
v
as
a
rao,
r.sri
n
i
v
asa
rao
“
o
p
timal
p
lacem
ent
of
S
TAT
C
OM
u
si
ng
t
wo
s
tage
a
lg
orithm
f
o
r
enh
a
ncin
g
po
wer
syste
m
s
tatic
s
ecurit
y
”
;
PE
C
C
O
N
-
m
a
r
ch
,
2
0
17.
vol:1
17
.
[37]
S.m
a
nika
n
d
a
n
,
p.a
r
u
l
“
op
ti
ma
l
lo
c
a
t
io
n
o
f
m
u
ltip
l
e
F
A
CTS
d
e
vic
e
s
u
s
i
n
g
sens
ti
v
i
ty
m
et
ho
ds
”;
IJE
T
T
-oct,
vo
l.
4,
20
13
.
[38]
F
a
h
a
d
Iqb
a
l,
M
o
h
d
T
a
us
eef
K
h
a
n
“
o
ptim
a
l
p
lacem
ent
of
D
g
&
D
S
TA
T
COM
f
o
r
l
o
ss
redu
ction
an
d
vo
lt
age
p
r
ofi
l
e im
pro
v
em
ent
”
Al
exand
ria E
ngin
eerin
g J
o
ur
na
l,
v
o
l
.
5
7
,
755
–7
65
,
2
0
1
8
.
[39]
A
t
m
a
r
am
g
up
ta,
as
hwan
i
ku
mar
“
P
erf
o
man
c
e
an
aly
s
is
o
f
ra
di
al
d
i
st
ri
buti
on
s
y
s
t
e
m
s
wit
h
U
P
Q
C
an
d
D-
S
T
AT
COM
.
”2016
.
[40]
G
u
p
t
a
AR,
Kum
a
r
A
.
O
ptim
al
p
l
acem
ent
o
f
D
-S
TAT
C
OM
u
si
ng
s
ensiti
v
i
ty
app
r
oa
ches
i
n
mesh
d
istr
ibution
s
y
s
t
e
m
w
it
h time
v
a
riant
l
o
ad
m
odel
s
u
nd
er lo
a
d
g
rowth
.
A
in
S
h
am
s
Eng
J
20
16
[41]
A
t
m
a
r
am
g
u
p
ta,
abh
i
n
a
v
J
a
in
”op
t
im
al
D
-S
T
A
T
C
OM
p
lacem
ent
in
r
ad
ial
di
st
ributi
n
s
ystem
s
b
as
ed
on
po
wer
l
o
s
s
i
n
d
e
x ap
po
arch”
;
ICE
P
E
-
j
un
e
20
1
5
.
[42]
B.
S
ra
va
n
a
K
um
a
r
,
M
.
S
ury
a
ka
la
v
a
th
i
“Th
y
r
i
stor
C
on
tro
lle
d
Se
rie
s
Com
p
en
sa
t
o
r
bas
e
d
Op
tim
al
R
eall
o
cat
ion
o
f
G
e
nerat
o
rs
f
o
r
C
on
ti
ngen
c
y
M
a
n
a
gem
e
nt
”
ECT
I
T
r
a
n
s
a
ct
ion
s
o
n
Ele
c
t
r
ical E
N
G., Electro
ni
cs
,
&
Co
mm
uni
ca
t
i
o
n
s
VOL.16
, NO.
1
February
2
018.
[43]
V
e
nk
ata
p
a
d
m
a
v
at
hi
.
s
,
s
aratkum
ar,”app
l
i
cation
o
f
g
rav
itatio
n
a
l
se
a
r
c
h
a
lg
orit
hm
t
o
i
m
p
r
ov
e
po
we
r
sy
ste
m
s
ecuri
ty
by op
tim
a
l
placem
ent
o
f
F
A
C
TS d
evi
c
e
s
”.
JES
-2
01
5.
[44]
A
.
samim
i
,
m
.
a
.
gol
kar
“
a
nov
el
m
eth
od
f
o
r
o
p
t
i
m
a
l
p
l
acem
ent
of
F
AC
TS
b
a
s
ed
o
n
sensti
v
i
ty
a
nalysis
f
o
r
en
chan
cing
p
ow
er
s
ys
te
m
s
t
atic securi
ty”;
Asia
n jou
r
n
a
l of ap
plie
d
sci
e
nce
-jan.v
ol
.5, 20
1
2
.
[45]
A
.
pari
zad,
a.k
h
azal
i”app
l
i
catio
n
o
f
H
S
A
&
G
A
in
o
ptim
al
p
lace
m
e
nt
o
f
FACTS
d
e
vi
ce
s
con
s
iderin
g
vo
lt
age
s
t
ab
ilit
y
an
d l
o
s
s
es
”
.
worl
d
acad
am
y of sci
e
nce,
en
gi
neer
ing
an
d
tech
nol
og
y
-200
9.
[46]
S
e
l
v
araj
,
Rajan
g
am
“
M
e
ta
H
euristi
c
T
ech
ni
qu
e
for
Net
w
o
r
k
Reco
nf
igurat
ion
in
D
is
t
r
ibu
tion
sy
st
em
w
ith
p
ho
t
o
v
o
l
t
a
i
c and
D-ST
A
T
CO
M
”
h
ttps://i
eeexp
l
ore.
ieee.o
r
g
/
x
p
l/Recent
I
s
s
u
e.
jsp
?
pun
um
b
e
r=408
23
59
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
Pow
El
ec &
D
ri
S
yst
,
Vol
.
10,
N
o.
2
, June 2019: 900
–
90
8
90
8
[47]
D
evabalaj
i
K,
R
avi
K.
“
Op
ti
mal
size
and
si
t
i
n
g
o
f
multiple
D
G
and
D
S
TATCOM
i
n
r
adia
l
distri
bu
ti
on
s
ystem
u
s
i
ng
bact
erial
foragi
ng
o
p
t
im
iza
t
i
on
alg
o
ri
thm
”
.
Ain
Sh
ams
Eng
J.
vol
7
(
3),
pp
.
959–
71
,
2
0
1
6
.
[48]
Bab
a
k
saf
a
ri,
Ahm
a
d
ash
o
u
r
i,
“
op
timal
p
lacem
ent
of
D
-TATCO
M
int
o
t
h
e
radial
d
istr
ibution
n
e
t
w
orks
i
n
t
h
e
p
r
esen
ce of
d
is
tri
but
ed g
enerat
io
n
s
”.
Am
erica
n
j
o
u
r
n
a
l of elect
ri
cal
and el
ec
t
r
o
n
i
c
eng
i
n
e
e
r
in
g
,
.v
o
l
.4
, 20
1
6
.
[49]
G
up
ta
A
R,
K
u
m
ar
A
.
En
ergy
s
a
vin
g
s
u
s
i
n
g
D-S
T
ATCOM
pl
a
cem
ent
in
r
adial
distri
but
ion
sys
t
em.
Pro
cedi
a
Co
mp
ut Sci
,
vo
l
70
,
p
p
.
5
58
–64
, 2
01
5.
[50]
C
hatt
erjee
A,
R
o
y
K
,
Chatterjee
D.
“
A
G
r
av
i
t
a
t
ion
a
l
S
e
a
r
ch
A
lg
o
r
i
t
h
m
(
G
S
A
)
b
a
s
e
d
P
h
o
t
o
-
V
o
l
t
a
i
c
(
P
V
)
ex
cit
a
ti
on
c
o
n
t
r
ol
s
trat
egy
f
o
r
singl
e
ph
ase
op
erati
on
of
t
h
r
ee
ph
a
s
e
wind
-turb
i
n
e
c
ou
p
l
e
d
i
n
d
u
c
t
io
n
ge
n
e
ra
to
r”
.
En
e
r
g
y
;
vol.
74.
pp
.
7
07–
18
,
2
014.
[51]
K
a
sh
ani
AR,
Gand
om
i
A
H
,
Mous
avi
M
.
“
Im
p
e
ri
ali
s
ti
c
com
p
etiti
v
e
a
lg
orith
m:
a
m
et
a
h
euri
stic
a
l
gori
t
hm
f
or
l
o
cat
in
g
t
h
e cri
t
ical s
li
p
s
u
rf
ace in 2
-dimen
si
on
a
l
s
oil s
l
o
p
es
”.
Geosci Fr
on
t
,
v
o
l
7(1
)
,
p
p.
8
3–
9,
2016.
[52]
L
i
j
uan
W
,
G
u
o
h
u
a
C.
S
easo
n
al
S
VR
w
it
h
F
OA
a
l
go
rit
h
m
f
o
r
si
ngle
-s
tep
and
m
u
lti
-
s
t
e
p
ah
e
a
d
f
o
recasti
ng
i
n
m
o
nt
h
l
y
i
n
b
ound
tou
r
ist fl
ow.
Kn
owl-B
a
s
e
d S
y
st
,
vol.
11
0,
p
p.
157–
66,
2
0
1
6
.
[53]
O
t
hm
an
M
,
El
-Kh
a
ttam
W
,
H
e
g
a
z
y
Y,
e
t
al
.
Op
ti
m
a
l
pl
acem
ent
an
d
siz
i
ng
o
f
vo
lta
g
e
c
on
tro
l
le
d
di
str
i
bu
te
d
g
e
nerat
o
rs
i
n
unbal
a
nced
d
is
tri
b
u
t
i
o
n
net
w
orks
u
si
ng
s
u
p
erv
i
s
e
d
f
i
r
efly algor
i
t
hm.
Int
J
El
ectr Power E
n
er
gy S
y
st
;
82
:1
05
–1
3
, 2
01
6
.
[54]
G
u
o
L,
M
eng
Z,
S
un
Y
,
e
t
al.
P
ara
m
et
er
i
d
e
ntif
i
c
at
io
n
an
d sensi
t
i
vit
y
a
nalysis
of
s
olar
cell
models
w
ith
cat
s
warm
o
p
t
i
m
i
z
a
t
i
o
n
al
go
r
i
t
h
m
.
Ener
gy Co
nver
s
M
ana
g
, Vol
. 10
8
, pp
. 52
0
–
8
, 20
1
6
.
[55]
E
l
s
i
s
i
M
,
S
o
liman
M
,
A
b
o
elel
a
M
,
e
t
al.
“
B
at
i
nsp
i
red
al
go
rith
m
b
as
ed
o
p
t
i
m
a
l
d
es
ig
n
o
f
m
o
d
el
p
redi
ctiv
e
lo
ad
f
r
eq
uen
c
y
co
ntro
l”,
In
t J
El
ectr
Po
wer
E
n
erg
y
Sys
t, Vo
l
.
83
, p
p.
42
6
–3
3, 20
1
6
.
[56]
N
azari-S
h
i
r
ko
uhi
S
,
Ei
vazy
H
,
Gh
od
si
R
,
et
a
l.
“
S
o
lv
ing
th
e
int
e
g
ra
te
d
p
r
od
uc
t
mix-
o
u
t
sou
r
c
i
n
g
p
ro
ble
m
u
sing
t
h
e imperi
a
list
competitive algor
i
t
h
m”.
Exper
t
Syst
Ap
p
l
vol.
3
7
(
1
2
),
p
p
.
7
615
–2
6,
2
0
10.
[57]
S
i
rjan
i
R,
M
o
h
a
m
ed
A
,
S
h
are
e
f
H.
“
Optim
al
a
ll
ocati
o
n
of
s
hu
n
t
V
a
r
c
om
p
e
ns
ators
i
n
p
o
w
er
s
y
s
t
e
ms
u
si
ng
a
no
ve
l glob
a
l
h
a
r
mo
ny
se
a
r
c
h
a
lg
orith
m
”
.
In
t J
Elect
r P
o
wer En
erg
y
Sys
t
,
vo
l. 43
no
.
1
,
pp
. 5
62
–7
2
,
2
01
2.
[58]
K
a
nw
ar
N
,
G
u
p
t
a
N,
S
warnk
a
r
A
,
e
t
a
l
.
“
N
e
w
s
en
siti
vity
b
a
s
ed
a
p
p
r
oach
f
or
o
p
timal
a
l
l
ocati
on
o
f
s
h
unt
capacit
ors in distribut
i
o
n ne
t
w
or
ks
u
sing
P
S
O
”.
En
ergy Pro
cedi
a
;
v
o
l.
7
5,
p
p.
11
5
3
–
8, 20
1
5
.
[59]
L
u
Z
,
L
i
u
J,
Li
u
Y,
et
al.
“T
h
e i
n
ter
v
al
s
ens
i
ti
v
i
t
y
a
nal
y
s
i
s
a
nd
op
t
im
izati
o
n
o
f
t
he
d
i
s
t
r
i
buti
o
n
net
w
ork p
a
ramet
e
rs
co
ns
id
ering
t
h
e lo
ad
u
nce
r
t
a
inty”.
In
t
J
E
l
ectr
P
o
wer E
n
er
gy S
y
st
;
vo
l. 6
4
, pp
.
9
31
–
6
, 20
1
5
.
[60]
E
v
an
gel
opo
ul
os
V
A,
G
eo
rgil
akis
P
S
,
H
a
t
zi
argyri
o
u
N
D
.
“
O
ptim
al
o
perat
i
on
o
f
s
m
art
dist
r
i
bu
tion
networks
:
a
rev
i
ew
o
f
m
o
dels, m
e
t
h
o
d
s
and
fut
u
re res
ea
rch
”
.
E
l
ectr
P
o
wer Sy
st Res,
vo
l
.
14
0,
pp
.
9
5–1
06
,
2
016.
[61]
T
a
rôco
C
G,
T
a
k
ahas
hi
R
H
,
C
a
rran
o
E
G.
M
u
l
tiob
jecti
v
e
pl
annin
g
o
f
p
ower
d
i
s
tribu
tion
networ
ks
w
ith
f
acili
t
y
l
o
cat
ion
f
o
r d
i
s
t
r
i
buted generati
o
n
.
El
ectr Power Syst
Res,
vo
l.
141:5
6
2
–
7
1
,
201
6.
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