Int
ern
at
i
onal
Journ
al of Ele
ctrical
an
d
Co
mput
er
En
gin
eeri
ng
(IJ
E
C
E)
Vo
l.
8
, No
.
6
,
Decem
ber
201
8
, p
p.
4079
~
4088
IS
S
N: 20
88
-
8708
,
DOI: 10
.11
591/
ijece
.
v8
i
6
.
pp4079
-
40
88
4079
Journ
al h
om
e
page
:
http:
//
ia
es
core
.c
om/
journa
ls
/i
ndex.
ph
p/IJECE
Co
or
din
ated
Pla
ce
m
ent a
nd
Setting of FACTS
in
Electri
cal
Network
b
ased on
Ka
l
ai
-
s
morodi
nsky Bargain
ing
S
olution
and
V
oltage
D
evi
atio
n
I
nd
ex
Az
i
z
Ouk
enn
ou
1
,
A
bdelh
alim Sa
nd
ali
2
,
S
amira
El
moum
en
3
1,2
Advanc
ed
Con
t
rol
of
Elec
tri
c
al
S
y
stems
Team
-
LE
SE,
ENSEM, H
assan
II
Unive
rsit
y
,
Moroc
co
3
LIMSA
D,
Mathe
m
at
ic
s
and
C
o
m
puti
ng
Depa
rt
m
ent
,
Ain
Choc
k
Scie
n
ce
s Fa
cult
y
,
Moroc
co
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
A
pr
30
, 201
8
Re
vised
Ju
l
11
,
201
8
Accepte
d
Aug
2
, 2
01
8
To
ai
d
the
d
ec
isi
on
m
ake
r,
the
o
pti
m
al
place
m
en
t
of
FA
CTS
in
t
he
el
e
ct
ri
cal
net
work
is
per
f
orm
ed
through
ver
y
spe
ci
fi
c
cr
i
te
ri
a.
In
thi
s
pa
per
,
a
useful
appr
oac
h
is
foll
owed;
i
t
is
base
d
par
ticul
a
rl
y
on
th
e
use
of
Kala
i
-
Sm
orodinsky
ba
rga
ini
ng
soluti
o
n
for
choosing
t
he
best
comprom
ise
bet
wee
n
the
diff
ere
nt
ob
j
ec
t
ive
s
comm
onl
y
posed
to
the
n
et
work
m
ana
ger
such
as
the
cost
of
produc
tion,
tot
a
l
tra
nsm
ission
losses
(Tl
oss
),
and
volt
a
ge
stabil
i
t
y
inde
x
(L
inde
x)
.
In
the
c
ase
of
m
an
y
poss
ibl
e
soluti
ons,
Volt
age
Profil
e
Quali
t
y
is
adde
d
to
sel
ec
t
the
b
es
t
one.
Thi
s
appr
oac
h
h
as
offe
red
a
ba
la
nc
ed
soluti
on
and
h
as
prove
n
it
s
eff
e
ct
iv
ene
ss
in
find
ing
the
b
est
pl
a
ce
m
ent
and
sett
ing
of
two
t
y
pes
of
FA
CTS
namel
y
St
at
i
c
Var
Com
p
ensa
t
or
(SV
C)
and
Th
y
r
istor
Contr
oll
ed
Seri
es
Com
pensa
tor
(TCSC)
in
the
power
s
y
stem.
Th
e
te
st
ca
s
e
under
inve
stigation
i
s
IEE
E
-
14
bus
s
y
stem
which
has
bee
n
sim
ula
te
d
in
MA
TL
AB E
nv
iron
m
ent
.
Ke
yw
or
d:
Diff
e
re
ntial
e
voluti
on
FA
CTS
Kalai
S
m
or
odinsk
y
ba
r
gaini
ng
so
luti
on
Mult
iobject
ive
o
ptim
iz
ation
Op
ti
m
al
p
ow
e
r
f
low
Pareto
f
ront
SV
C
TCSC
Vo
lt
age
s
ta
bili
ty
i
nd
e
x
Copyright
©
201
8
Instit
ut
e
o
f Ad
vanc
ed
Engi
n
ee
r
ing
and
S
cienc
e
.
Al
l
rights re
serv
ed
.
Corres
pond
in
g
Aut
h
or
:
Aziz O
uken
no
u,
Dep
a
rtm
ent o
f
Ind
us
tria
l En
gi
neer
i
ng,
Nati
on
al
Scho
ol of
A
pp
li
ed
S
ci
ences,
63, Sa
fi, Mor
occo.
Em
a
il
:
a.o
uk
e
nnou
@u
ca
.m
a
1.
INTROD
U
CTION
W
it
h
the
gro
wth
of
the
de
m
and
an
d
m
a
ny
vo
lt
a
ge
col
la
ps
e
incide
nts
reco
r
de
d
rece
ntly
aro
un
d
the
w
orl
d
[
1],
The
i
ns
ta
ll
at
ion
of
Fle
xib
le
AC
Tra
ns
m
iss
ion
Syst
em
s
(F
ACTS
)
i
n
the
netw
ork
is
re
qu
i
red.
Ba
sed
on
po
w
er
el
ect
ronics
,
these
new
de
vi
ces
offe
r
an
opportu
nity
to
en
han
ce
c
ontr
ollabil
it
y,
sta
bili
t
y,
and
trans
fer
ca
pa
bi
li
ty
of
the
i
nter
connecte
d
po
w
er
syst
em
s
[2
]
,
[3
]
.
T
he
in
ves
t
m
ent
cost
of
FA
CTS
is
sti
ll
ve
ry
exp
e
ns
i
ve,
but
f
ocu
si
ng
on
their
im
po
rta
nc
e,
TCSC
has
t
he
pr
im
ary
functi
on
to
inc
re
ase
po
wer
tra
ns
fe
rs
sign
ific
a
ntly
and
en
ha
nce
sta
bili
ty
.
On
the
oth
e
r
ha
nd,
S
VC
is
qual
ifie
d
as
t
he
prefe
r
red
FA
CT
S
to
pro
vid
e
r
eact
ive
powe
r
at
key
points
of
the
powe
r
s
yst
e
m
.
It
al
so
pr
ese
nts
t
he
l
owest
pr
ic
e
a
s
i
t
has
no
m
ov
i
ng
or
ro
ta
ti
ng
m
a
in
com
po
ne
nts
an
d
presents
c
he
ap
m
ai
ntenan
ce
costs
[4
]
,
[
5]
.
Give
n
the
hi
gh
pr
ic
e
of
F
ACTS,
nu
m
erous
st
udie
s
ha
ve
at
te
m
pted
t
o
ide
ntify
the
best
placem
ent
and
siz
e
of
these
e
quip
m
ents
in
order
to
ta
ke
adv
a
ntage
of t
heir
c
ontrib
ution i
n
a
n o
ptim
al
w
ay
w
it
h l
es
s in
vestm
ent.
Var
i
ou
s
te
ch
ni
qu
e
s
dep
e
ndin
g
on
the
te
ch
nical
or
eco
nom
i
cal
ta
rg
et
fixe
d
by
t
he
op
e
rato
r
wer
e
us
e
d
and
we
re
ve
r
y
us
ef
ul.
It
s
ta
rted
f
ro
m
fixing
sin
gle
-
obj
ect
ive
s
uch
a
s
sta
bili
ty
i
mp
r
ovem
ent
[6
]
,
los
s
m
ini
m
iz
at
ion
[7
]
,
powe
r
qu
al
i
ty
i
m
pr
ov
em
ent
[8
]
…et
c.
In
this
case,
the
de
ci
sion
is
m
ade
qu
ic
kly
bu
t
ha
s
the
disad
va
ntage
of
the
im
pr
ov
e
m
ent
of
the
chosen
c
rite
rion
t
o
the
detr
im
ent
of
the
oth
er
pe
rform
ances
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8708
In
t J
Elec
&
C
om
p
En
g,
V
ol.
8
, N
o.
6
,
Dece
m
ber
2018
:
407
9
-
4088
4080
Conver
sel
y,
in
the
case
of
m
ulti
ple
obj
ect
ives
wh
ic
h
are
ve
r
y
fr
eq
ue
nt
[
9]
-
[11],
the
proce
ssing
bec
om
es
m
or
e
com
plex.
So
m
e
m
et
ho
ds
c
on
sist
of
s
umm
i
ng
al
l
the
obje
ct
ives
by
assi
gn
i
ng
a
weig
ht
coef
fici
e
nt
th
at
the
decisi
on
-
ma
ker
ha
s
to
at
tri
bute
to
eac
h
one
[
12]
,
[
13]
.
The
order
of
m
agn
it
ud
e
m
us
t
al
so
be
kn
own
in
adv
a
nce.
Mo
re
ov
e
r,
t
he
re
su
lt
of
the
op
ti
m
izati
on
is
no
t
uniqu
e
but
the
re
a
re
ot
her
possib
le
so
luti
ons
t
ha
t
can
be prese
nted
as
Par
et
o
F
ront
(
PF)
[
14
]
,
[
15
]
.
The
c
om
pu
ti
ng
of
this
set
of
s
olu
ti
ons
ta
ke
s
en
ough
ti
m
e
as
it
require
s
a
la
r
ge
num
ber
of
m
ono
-
obj
ect
ive
funct
ion
s
optim
iz
ati
on.
It
is
al
so
di
ff
ic
ult
to
qu
al
ify
con
c
retel
y
on
e
of
these
s
olu
ti
ons
as
t
he
best
on
e
.
In
this
c
onte
st,
oth
e
r
m
et
hods
ha
ve
be
en
us
e
d
to
se
le
ct
the
best
c
om
pr
om
ise
.
We
quote
f
or
ex
a
m
ple
NSGA II
[
16]
,
[17]
and
NPS
O
[
18
]
w
hich
a
re
m
or
e p
opula
r
an
d
c
on
si
der
e
d
as one of the best m
e
tho
ds u
sed
to
so
lve
t
he
pro
ble
m
of
F
ACTS
optim
al
placem
ent.
For
th
e
s
e
m
e
tho
d
s
,
t
he
de
gr
ee
of
c
om
plexit
y
see
m
s
to
be
in
creasin
gly
im
po
rtant
giv
e
n
the
tim
e
require
d
f
or
r
unni
ng
a
nd
the
nee
d
to
trace
the
Pareto
F
r
on
t
to
finall
y
sel
ect
the m
os
t
dom
inant so
lu
ti
on
call
ed
the
best c
om
pr
om
i
se.
The
Kalai
-
Sm
or
odins
ky
(
KS)
,
sug
gested
by
Eh
ud
Kalai
and
Me
ir
Sm
oro
din
s
ky
[1
9
]
,
[
20
]
,
is
a
so
luti
on
to
t
he
Ba
rg
ai
ning
prob
le
m
wh
e
re
pl
ay
ers
m
ake
decisi
on
s
i
n
ord
er
to
op
ti
m
iz
e
their
ow
n
util
it
y.
I
n
eng
i
neer
i
ng
pr
ob
le
m
s,
play
er
s
are
re
placed
by
the
ob
j
ect
iv
e
f
un
ct
io
ns
tha
t
the
op
e
rato
rs
ha
ve
t
o
optim
iz
e
at
the
sam
e
tim
e.
The
m
ai
n
adv
anta
ge
of
KS
so
luti
on
is
t
hat
it
prov
i
des
a
c
on
c
r
et
e
crit
eri
on
to
sel
ect
only
an
d
on
ly
on
e
uniq
ue
point alo
ng t
he
Pa
reto
Fro
nt
.
The
ob
j
ect
ive
of
this
w
ork
is
to
ap
ply
the
Kalai
-
Sm
or
odinsk
y
te
c
hn
i
qu
e
in
the
opti
m
a
l
placem
ent
and
set
ti
ng
of
coor
din
at
ed
F
ACTS
in
pow
er
syst
e
m
s
by
consi
der
i
ng
t
hree
obj
ect
ives
nam
el
y
Cost
functi
on,
Total
Tra
ns
m
i
ssion
losse
s
a
nd
Li
nd
e
x
as
pl
ay
ers.
In
the
c
ase
of
m
ulti
ple
KS
S
olu
ti
on
s,
Vo
lt
age
De
viati
on
Inde
x
is
ad
de
d
as
ne
w
crit
eria t
o
im
pr
ov
e Volt
age
Pro
file
Qual
it
y.
The
pro
pose
d
m
et
ho
d
he
lps
to
c
hoos
e
o
nly
on
e
uniq
ue sol
ution
with
out e
xp
l
or
i
ng the
w
ho
le
Paret
o
F
r
on
t
w
hich save
s co
m
pu
ta
ti
on
a
l t
i
m
e con
side
r
ably
.
The
rest
of
the
pap
er
is
orga
ni
zed
as
fo
ll
ows
.
Sect
ion
2
pre
sents
a
rev
ie
w
of
the
opti
m
a
l
powe
r
flo
w
pro
blem
.
Op
tim
iz
at
ion
too
l
is
descr
i
bed
in
sect
ion
3.
Ca
se
stud
y,
the
m
od
el
of
S
VC,
TCSC
,
an
d
obje
ct
ives
functi
ons
a
re
pr
ese
nted
in
S
ect
ion
s
4.
T
he
res
ults
of
sim
ulati
on
an
d
dis
cussion
a
re
pr
esented
in
sect
ion
5.
The
c
oncl
us
i
on is the s
ubj
ect
of sect
ion 6
.
2.
OPTIM
AL P
OWER
FLO
W P
ROBLE
M
The
opti
m
a
l
po
we
r
flo
w
(
OPF)
pro
blem
is
t
he
bac
kbone
too
l
f
or
powe
r
syst
e
m
op
erati
on.
The
ai
m
of
the
O
PF
pro
blem
is
to
determ
ine
the
op
ti
m
al
op
erati
ng
sta
te
of
a
pow
er
syst
e
m
by
o
pti
m
iz
ing
a
part
ic
ular
obj
ect
ive
i
n
powe
r
syst
em
s
wh
il
e
sat
isfyi
ng
certai
n
oper
at
ing
c
on
st
rain
ts
[
21
].
Ma
the
m
at
ic
a
l
ly
,
the
OPF
pro
blem
can
be
for
m
ulate
d
a
s foll
ow
:
m
in
(
,
)
(
1)
Subj
ect
t
o
g
(
,
)
=
0
(2)
h
(
,
)
≤
0
(3)
F
obj
can ta
ke va
rio
us
functi
ons
d
e
pendin
g o
n t
he
ta
r
get f
i
xed b
y t
he
ope
rato
r.
In the
OPF, t
he
e
qu
al
it
ie
s a
nd
ineq
ualit
ie
s ar
e
as
f
ollo
ws:
a.
Eq
ualit
y con
str
ai
nts:
(
,
)
−
+
=
0
(
4)
(
,
)
−
+
=
0
(5)
And
l
oad b
al
a
nc
e eq
uatio
n:
∑
=
∑
+
=
1
=
1
(
6)
b.
In
e
qual
it
y con
s
trai
nts:
The
ineq
ualit
y
con
strai
nts
re
pr
ese
nt
the
lim
it
s
on
al
l
var
ia
bles
su
c
h
as
t
he
gen
erat
or
vo
l
ta
ge,
act
ive
and reacti
ve
po
wer
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Elec
&
C
om
p
En
g
IS
S
N: 20
88
-
8708
Coo
r
dinated
P
laceme
nt an
d S
et
ti
ng
o
f
FACT
S
in
Elec
tri
cal
Ne
tw
or
k
... (
Az
iz Ouke
nn
ou
)
4081
≤
≤
i=
1
,
…
.
,
(7)
≤
≤
i=
1
,
…
.
,
(8)
≤
≤
i
=
1
,
…
.
,
(9)
The
m
axi
m
u
m
an
d m
ini
m
u
m
l
i
m
i
ts
of
ta
p
set
ti
ng
s
reg
a
r
ding
the tra
nsfo
rm
e
r
a
nd which
takes
discrete
va
lues
is give
n by,
≤
≤
=
1
,
…
,
(10)
3.
KALAI
-
S
M
O
RODIN
SK
Y SOLUTI
ON AND
DIFFE
R
ENTIAL E
V
OLUTIO
N
3.1.
Ka
lai
-
Sm
orod
insky bar
gaini
ng
So
lu
tion
In
th
e
m
ulti
-
ob
j
ect
iv
e
opti
m
i
zat
ion
pr
ob
le
m
,
w
hen
m
any
obj
ect
ive
funct
ion
s
a
re
co
nfl
ic
ti
ng
,
the
re
are
m
any
po
s
s
ible
so
l
ution
s
.
It
is
im
po
ssible
to
m
ake
any
prefe
ren
ce
cri
te
rion
bette
r
of
f
wit
hout
m
aking
at
le
ast
o
ne
prefe
ren
ce crit
eri
on
worst off.
T
he a
dv
a
ntage of K
S S
olu
ti
on is that i
t sat
isfie
s
m
on
oto
nicit
y so
each
obj
ect
ive
ca
n
be
i
m
pr
oved
we
akly
bette
r.
Ma
them
a
ti
cal
l
y,
it
is
the
intersect
ion
po
i
nt
of
t
he
segm
ent
Ut
(p
oi
nt
of
best
util
it
ie
s
)
an
d
the
point
of
disa
greem
e
nt
D
with
th
e
edg
e
of
t
he
feas
ible
s
et
(P
areto
Fr
ont)
as
s
hown
i
n
F
igure
1.
To
be
near
f
r
om
Ut,
go
al
pr
ogra
m
m
ing
op
ti
m
i
zat
ion
te
ch
nique
will
be
de
pl
oyed
to
ac
hieve
this
ta
rg
et
in
e
quat
ion 1
1
.
=
(
1
−
1
)
2
+
(
2
−
2
)
2
(1
1
)
F
i
gu
r
e
1
.
S
ol
ut
i
on
o
f
K
a
l
a
i
S
m
or
od
i
ns
ky
(
K
S
)
be
t
w
e
e
n
t
w
o
f
un
c
t
i
on
s
f
1
a
nd
f
2
3.2.
Diff
ere
nt
i
al Evo
lu
tio
n
Algo
ri
th
m
Diff
e
re
ntial
Ev
olu
ti
on
(D
E
)
[
22
]
is
one
of
t
he
m
os
t
powe
r
fu
l
al
gorithm
s
for
re
al
num
ber
f
unct
ion
op
ti
m
iz
ation
pro
blem
s.
The
pote
ntial
of
this
te
chn
iq
ue
w
as
dem
on
strat
ed
in
li
te
ratur
e
an
d
was
com
pared
to
oth
e
r
te
ch
niqu
es
su
c
h
as
Ge
netic
Algo
rith
m
(G
A)
a
nd
Partic
le
Sw
a
r
m
Op
tim
iz
at
ion
(
PS
O)
espec
ia
ll
y
to
reso
l
ve
the
O
PF
prob
le
m
[
23
]
an
d
pro
ved
superi
or
it
y
in
te
rm
s
of
so
l
ut
ion
qu
al
it
y.
T
he
fl
ow
c
ha
rt
of
this
al
gorithm
is sh
own
i
n
F
i
gure
2.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8708
In
t J
Elec
&
C
om
p
En
g,
V
ol.
8
, N
o.
6
,
Dece
m
ber
2018
:
407
9
-
4088
4082
F
i
gu
r
e
2
.
F
l
o
w
c
ha
r
t
of
D
E
a
l
g
or
i
t
hm
4.
C
A
SE ST
UDY
,
MO
DELIN
G OF
FACTS
,
A
N
D
OB
JE
CTIVE
FU
N
CTIO
NS
4.1.
Ca
se
S
tu
d
y
Our
stu
dy
is
do
ne
on
the
sta
ndar
d
IE
E
E
14
-
bu
s
te
st
syst
e
m
sh
own
i
n
F
ig
ure
3.
It
re
pr
ese
nts
a
si
m
ple
appr
ox
im
at
ion
of
the
Am
eri
can
Ele
ct
ric
Power
syst
em
;
it
has
14
buses,
20
inter
connecte
d
br
a
nch
e
s,
5 gen
e
rato
rs
a
nd
9
loa
d b
usbar
s.
F
i
gu
r
e
3
.
O
ne
-
l
i
ne
di
a
gr
a
m
of
I
E
E
E
1
4
-
b
us
T
e
s
t
s
y
s
te
m
t
a
ke
n
f
r
om
[
24
]
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Elec
&
C
om
p
En
g
IS
S
N: 20
88
-
8708
Coo
r
dinated
P
laceme
nt an
d S
et
ti
ng
o
f
FACT
S
in
Elec
tri
cal
Ne
tw
or
k
... (
Az
iz Ouke
nn
ou
)
4083
4.2.
Model
of
SVC
an
d
TCS
C
4.2.1.
SVC
The
Stat
ic
V
ar
Com
pen
sat
or
(SVC)
eq
uip
m
ent
is
com
po
sed
of
capaci
tors
,
t
hy
ristors,
an
d
inducta
nces
.
I
n
this
pa
pe
r,
it
is
co
ns
ide
re
d
as
a
n
ideal
re
act
ive
po
wer
c
on
t
ro
ll
er,
w
hic
h
in
j
ect
s
or
a
bsor
bs
reacti
ve
power
in
the
net
work.
The
bus
w
here
the
S
VC
is
placed
is
c
onside
red
a
s
a
P
V
bu
s
w
her
e
the
volt
ag
e
is
con
tr
olled
a
nd
e
qual
to
th
e
un
it
y.
A
negat
ive
value
in
di
cat
es
that
the
SV
C
ge
ne
rates
reacti
ve
powe
r
a
nd
inj
ect
s
it
into
the
net
work
(c
apacit
ive
sta
te
)
an
d
a
posit
ive
value
i
nd
ic
at
es
that
the
S
VC
ab
sorb
s
re
act
ive
powe
r
f
r
om
the n
et
w
ork
(
in
duct
ive stat
e)
.
4.2.2.
TCSC
The
TCSC
is
a
series
com
pensat
ion
de
vice
that
can
m
od
i
fy
and
a
dj
us
t
t
he
tra
nsm
issi
on
li
ne
reacta
nce
a
s
s
how
n
i
n
F
i
gure
4
.
By
t
his
way
,
the
powe
r
tra
ns
fe
r
a
bili
ty
is
i
m
pr
oved
in
st
eady
-
sta
te
.
T
he
ne
w
value o
f
rea
ct
ance
of the li
ne
wh
e
re TC
SC is
instal
le
d
is
give
n by:
=
(
1
+
)
(12)
F
i
gu
r
e
4
.
T
he
b
a
s
i
c
s
t
r
uc
t
ur
e
o
f
T
C
S
C
(
a
)
a
n
d
m
od
e
l
(
b)
The
range
of
com
pen
sat
io
n
(k%)
of
the
TCSC
is
ta
ke
n
betwee
n
20%
in
duct
ive
an
d
80%
ca
pacit
ive
(
-
0.8≤k≤
0.2
)
[
25
]
.
4.3.
Obj
ec
tive fu
n
ctions
Thr
ee
obj
ect
i
ve
functi
ons
wi
ll
be
con
si
der
e
d
The
first
in
ve
sti
gated
one
i
s
the
ge
ner
at
io
n
f
uel
cost
m
ini
m
iz
at
ion
; i
t i
s expr
esse
d
a
s:
=
∑
(
2
+
+
)
=
1
(
$/h)
(13)
,
and
are
the
cost
coe
ff
ic
ie
nt
s
of
t
he
it
h
ge
ner
at
or
.
The
te
chn
ic
al
obj
ect
ive
f
unct
ion
is
the
T
otal
Powe
r
losses a
nd is
giv
en
b
y:
=
√
2
+
2
(M
VA)
(14)
w
he
re
Pl
a
nd
Ql
are
the
act
i
ve
an
d
reacti
ve
powe
r
losses
of
t
he
po
wer
syst
e
m
.
The
la
st
obj
ect
ive
functi
on
relat
ed
to
sec
uri
ty
is the volt
age sta
bili
ty
ind
ex (Lin
dex)
[26]
,
[
27
]
.
I
t i
s
gi
ven b
y:
=
{
}
=
1
≤
≤
|
1
−
∑
=
1
|
(1
5
)
are
the
com
plex
volt
age
of
i
th
an
d
j
t
h
ge
ne
rators,
is
t
he
nu
m
ber
of
ge
ne
rator
unit
s
and
is
the
nu
m
ber
of loa
d b
us
.
L
-
i
nd
e
x v
aries in a
r
a
nge
b
et
wee
n 0 (
no Lo
a
d) an
d 1 (
vo
lt
age
co
ll
a
pse
).
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
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8708
In
t J
Elec
&
C
om
p
En
g,
V
ol.
8
, N
o.
6
,
Dece
m
ber
2018
:
407
9
-
4088
4084
5.
S
IM
ULATI
O
N AND
RES
U
LT
S
In
orde
r
t
o
ide
ntify
the
best
c
oor
din
at
ed
pla
ce
m
ent
of
S
V
C
an
d
TCSC
de
vice.
Fi
gure
5
is
res
pecte
d
for
each
pair
of
obj
ect
ive
fun
ct
ion
s
sel
ect
ed
.
Since
FA
CT
S
hav
e
a
n
inter
va
l
wh
ere
th
ey
can
operate,
al
l
buse
s
and li
nes wil
l b
e scan
ne
d
to
h
a
ve
the
b
e
st l
oc
at
ion
a
nd the
val
ue
of
Kalai
S
m
or
od
ins
ky'
s so
luti
on.
F
i
gu
r
e
5
.
F
l
o
w
c
ha
r
t
of
a
l
g
or
i
t
hm
f
or
pl
a
c
em
e
nt
In
t
he
case
of
m
any
KS
s
olu
t
ion
s
,
the
volt
age
prof
il
e
qu
al
it
y
in
equ
at
io
n
16
will
be
c
onside
red
as
a
ddit
ion
al
crit
eria t
o
sel
ec
t t
he
be
st o
ne.
The
i
nd
e
x
is
gi
ven b
y:
=
∑
|
−
1
|
=
1
(16)
w
he
re
N
is t
he t
otal nu
m
ber
of
bu
ses
in
the s
yst
e
m
.
In
al
l
that
f
oll
ow
s
,
the
reacti
ve
po
wer
of
th
e
ge
ner
at
ors
is
consi
de
red
un
restrict
ed
a
nd
on
t
he
oth
e
r
side,
the
vo
lt
a
ges
of
ge
ne
rator
s
a
re
ta
ke
n
c
on
sta
nt
w
hich
is
po
ssi
ble
bec
ause
the
r
eal
syst
e
m
s
po
ssess
m
eans
for
regulat
in
g
the volt
age au
to
m
at
ic
ally (A
VR).
Th
e only
co
nt
ro
l va
riable
s that will
b
e c
on
si
der
e
d
are:
Acti
ve
powe
r
of g
ene
r
at
or
s
a
nd
ta
p
c
hange
rs.
H
owe
ver,
the n
ecess
ary
value
s
of
r
eact
ive
powe
r
of
SV
C,
an
d
ra
ng
e of
com
pen
sat
ion
of TCSC
(k
%
) wil
l be c
om
pu
te
d.
5.1.
Tl
os
s and
C
ost Fu
ncti
o
n
The
obta
ine
d
r
esults
are
as
can
see
in
Figure
6.
Five
non
-
dom
inate
d
location
s
are
ide
ntif
ie
d
for
SV
C
and
TCSC
place
m
ent.
The
s
ol
ution
num
ber
(5)
is
e
xclu
ded
as
it
consi
ders
the
bus
7
for
SV
C
placem
en
t,
or
it
is
a
par
t
of
the thr
ee
-
windin
g
-
trans
form
er.
Us
ing
the volt
ag
e
dev
ia
ti
on
in
de
x
(
VD),
t
he
s
olu
ti
on
(
1)
is
t
he
best
on
e
w
her
e
it
is
equ
al
to
0.59p
u,
the
n
S
VC
is
placed
in
B
us
14
a
nd
TCSC
in
li
ne
1
-
5.
To
evaluate
the
re
su
lt
of
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Elec
&
C
om
p
En
g
IS
S
N: 20
88
-
8708
Coo
r
dinated
P
laceme
nt an
d S
et
ti
ng
o
f
FACT
S
in
Elec
tri
cal
Ne
tw
or
k
... (
Az
iz Ouke
nn
ou
)
4085
this
si
m
ulati
on
,
two
oth
e
rs
D
E
m
on
o
-
ob
j
ect
ive
op
ti
m
iz
a
ti
on
s
were
done
to
find
t
he
be
s
t
Cost
and
the
best
Total
Lo
sses
m
ini
m
iz
at
ion
without
F
ACT
S.
Ta
ble
1
giv
es
t
he
ob
ta
in
ed
resu
lt
s
i
n
com
par
ison
w
it
h
K
S
So
luti
on
with
FA
CTS
.
F
i
gu
r
e
6
.
K
S
S
ol
ut
i
on
s
i
n
c
a
s
e
5.
1
T
a
bl
e
1
.
C
on
t
r
ol
va
r
i
a
bl
e
s
a
n
d
o
bj
e
c
t
i
ve
f
u
n
c
t
i
on
s
i
n
c
a
s
e
5
.
1
SVC
T
C
S
C
O
p
t
i
m
a
l
v
a
l
u
e
s
o
f
c
o
n
t
r
o
l
v
ar
ia
b
l
e
s
C
o
s
h
(
$
/
h
)
T
o
t
a
l
L
o
s
s
e
s
(
MV
A)
VD
(
p
u
)
B
e
s
t
l
o
c
.
B
e
s
t
s
e
t
.
B
e
s
t
l
o
c
.
B
e
s
t
s
e
t
.
P
g
1
(
p
u
)
P
g
2
(
p
u
)
P
g
3
(
p
u
)
P
g
6
(
p
u
)
P
g
8
(
p
u
)
T1
T2
T3
W
i
t
h
o
u
t
F
A
C
TS
B
e
s
t
c
o
s
t
-
-
-
-
2
.
1
3
0
.
2
0
0
.
1
5
0
.
1
0
0
.
1
0
1
.
0
1
0
.
9
0
0
.
9
9
8
2
6
.
5
8
4
8
.
0
3
0
.
7
1
B
e
s
t
l
o
s
s
e
s
-
-
-
-
0
.
9
7
0
.
8
0
0
.
5
0
0
.
3
5
0
.
1
0
1
.
1
0
0
.
9
8
1
.
0
3
9
8
3
.
1
2
2
0
.
4
5
0
.
7
0
W
i
t
h
F
A
C
TS
B
e
s
t
K
S
S
o
l
u
t
i
o
n
B
u
s
14
-
0
.
1
3
L
i
n
e
1
-
5
-
0
.
8
0
1
.
5
0
0
.
3
4
0
.
2
8
0
.
3
5
0
.
1
7
1
.
0
0
0
.
9
9
0
.
9
9
8
7
6
.
6
4
2
1
.
1
8
0
.
5
9
W
it
hout
F
AC
TS,
t
he
values
of
obj
ect
ives
functi
ons
a
re
bette
r.
H
ow
e
ve
r,
t
he
values
of
the
oth
e
r
perform
ances
are
w
or
st,
For
Cost
Mi
ni
m
izati
on
,
the
valu
e
of
T
otal
loss
es
is
equ
al
to
48.03MV
A,
a
nd
t
he
value
of
Cost
pro
du
ct
io
n
is
equ
al
t
o
876.6
4$
/
h
in
Total
Loss
es
m
ini
m
i
zat
ion
.
The
t
w
o
values
a
re
m
u
ch
i
m
pr
oved
with
KS
so
l
ution
w
hich
gi
ves
a
ve
ry
good
com
pr
om
ise
.
In
add
it
ion
to
this,
the
vo
lt
age
de
viati
on
is
reduce
d
in
the
pro
po
se
d
a
ppr
oach.
5.2.
Li
ndex
an
d
Cost Func
tio
n
The
su
m
m
ariz
ed
res
ults
of
the
si
m
ulati
on
are
giv
e
n
in
F
igure
7.
F
our
dom
inate
d
KS
so
l
utio
ns
ar
e
ob
ta
ine
d,
the
so
luti
ons
(
3)
and
(
4)
are
re
la
te
d
to
bus
7
w
hich
re
pr
es
ents
in
reali
ty
,
the
three
wind
i
ng
-
trans
form
er
so
they
are
excl
uded
.
In
this
ca
se
only
so
l
utio
n
(1)
a
nd
(
2)
a
re
m
ai
ntained.
Fo
c
us
in
g
on
V
oltage
Dev
ia
ti
on
I
nde
x
of
eac
h
s
olu
t
ion
,
t
he
sec
ond
one
is
bette
r.
SV
C
is
instal
le
d
in
bus
9
a
nd
TCSC
in
li
ne
4
-
9.
Both
of
thes
e
equ
i
pm
ents
op
e
rate
in
ca
pacit
ive
sta
te
.
Table
2
giv
e
s
a
com
par
iso
n
stu
dy
betwe
en
the
op
ti
m
iz
ation
r
esults
of
the
pr
opos
e
d
s
olu
ti
on
an
d
the
tr
adi
ti
on
al
m
on
o
-
obj
ect
if
o
pti
m
izati
on
of
c
os
t
f
un
ct
io
n
or Lin
dex.
As
see
n
in
Ta
ble
2,
t
he
m
on
o
-
obj
ect
ive
optim
iz
ation
of
Cost
f
un
ct
io
n
ha
s
al
lowed
t
o
ha
ve
the
best
op
ti
m
al
cost
(8
26.
59$/
h)
w
hi
ch
m
eans
an
econom
ic
gain.
H
ow
e
ve
r,
the
degree
of
sta
bi
li
t
y
is
red
uce
d
since
the
Lin
de
x
is
hi
gh
.
T
he
sam
e
log
ic
ca
n
be
a
ppli
ed
for
Li
nd
e
x
op
ti
m
iz
a
t
ion
wh
e
re
sta
bili
ty
is
im
pr
ov
e
d
at
the
detrim
ent
of
producti
on
cost.
In
the
case
of
our
ap
proac
h
and
us
in
g
FA
C
TS,
al
l
obj
ect
ive
f
un
ct
io
ns
ar
e
in
the
acce
ptable
ra
nge.
W
e
al
s
o
no
te
that
Lind
ex
and
vo
lt
age
de
viati
on
are
bette
r
wh
ic
h
m
eans
m
or
e
secur
it
y
and
best
vo
lt
age
pr
of
il
e in
the
w
hole
po
wer sy
stem
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8708
In
t J
Elec
&
C
om
p
En
g,
V
ol.
8
, N
o.
6
,
Dece
m
ber
2018
:
407
9
-
4088
4086
F
i
gu
r
e
7
.
K
S
S
ol
ut
i
on
s
i
n
c
a
s
e
5.
2
T
a
bl
e
2
.
C
on
t
r
ol
V
a
r
i
a
bl
e
s
a
n
d
O
bj
e
c
t
i
ve
F
u
nc
t
i
on
s
i
n
Ca
s
e
5.
2
SVC
T
C
S
C
O
p
t
i
m
a
l
v
a
l
u
e
s
o
f
c
o
n
t
r
o
l
v
ar
ia
b
l
e
s
C
o
s
h
(
$
/
h
)
L
i
n
d
e
x
VD
(
p
u
)
B
e
s
t
l
o
c
.
B
e
s
t
s
e
t
.
B
e
s
t
l
o
c
.
B
e
s
t
s
e
t
.
P
g
1
(
p
u
)
P
g
2
(
p
u
)
P
g
3
(
p
u
)
P
g
6
(
p
u
)
P
g
8
(
p
u
)
T1
T2
T3
W
i
t
h
o
u
t
F
A
C
TS
B
e
s
t
c
o
s
t
-
-
-
-
2
.
1
3
0
.
2
0
0
.
1
5
0
.
1
0
0
.
1
0
1
.
0
1
0
.
9
0
0
.
9
9
8
2
6
.
5
8
0
.
0
7
0
3
0
.
7
1
B
e
s
t
L
.
I
n
d
e
x
-
-
-
-
0
.
9
3
0
.
8
0
0
.
5
0
0
.
1
0
0
.
3
0
0
.
9
0
0
.
9
0
1
.
1
0
9
9
1
.
6
1
0
.
0
6
8
4
0
.
8
6
W
i
t
h
F
A
C
TS
B
e
s
t
KS
S
o
l
u
t
i
o
n
B
u
s
9
-
0
.
7
3
L
i
n
e
4
-
9
-
0
.
8
0
2
.
1
4
0
.
2
0
0
.
1
6
0
.
1
0
0
.
1
0
1
.
0
9
0
.
9
7
1
.
1
0
8
2
9
.
1
0
0
.
0
3
6
8
0
.
4
8
5.3.
Li
ndex
an
d
Tl
os
s
The
res
ult
of
s
i
m
ulati
on
s
is
il
lustrate
d
i
n
F
i
gure
8.
Five
non
-
do
m
inate
d
KS
s
olu
ti
on
s
a
re
ob
ta
ine
d,
so
luti
on 2
is
di
scard
e
d
a
s
it
is l
ink
ed
to
the
t
r
ansfo
rm
er.
If
w
e
lo
ok
at
t
he
vo
lt
age
de
viati
on
in
dex,
t
he
s
olu
ti
on
nu
m
ber
(
3)
see
m
s
to
be
the
be
st
on
e.
I
n
this
case,
SV
C
is
i
ns
ta
ll
ed
in
bus
9
as
well
as
the
TC
SC
in
th
e
li
ne
bu
s
4
-
9.
B
oth
of
them
op
erat
e
in
capaci
ti
ve
sta
te
.
The
Tabl
e
3
show
s
the
corres
pondin
g
resu
lt
s
in
c
om
par
iso
n
with
Lin
dex
o
r
Total
losses
DE
opti
m
iz
at
i
on.
From
T
abl
e
3,
it
is
cl
ear
that
the
best
so
luti
on
is
giv
e
n
by
K
S
so
luti
on,
al
l
obj
ect
iv
e
f
unct
ion
s
we
re
im
prov
e
d
si
gnific
antly
wh
ic
h
de
m
on
strat
es
the
eff
ect
ive
ness
of
t
he
appr
oach in c
om
bin
at
ion
w
it
h
V
oltage
Dev
ia
ti
on
Inde
x
a
nd
the contri
bu
ti
on
of FA
C
TS
i
n t
he powe
r
syst
e
m
.
F
i
gu
r
e
8
.
K
S
S
ol
ut
i
on
s
i
n
c
a
s
e
5.
3
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Elec
&
C
om
p
En
g
IS
S
N: 20
88
-
8708
Coo
r
dinated
P
laceme
nt an
d S
et
ti
ng
o
f
FACT
S
in
Elec
tri
cal
Ne
tw
or
k
... (
Az
iz Ouke
nn
ou
)
4087
T
a
bl
e
3.
C
on
t
r
ol
va
r
i
a
bl
e
s
a
n
d
o
bj
e
c
t
i
ve
f
u
n
c
t
i
on
s
i
n
c
a
s
e
5
.
3
SVC
T
C
S
C
O
p
t
i
m
a
l
v
a
l
u
e
s
o
f
c
o
n
t
r
o
l
v
ar
ia
b
l
e
s
L
i
n
d
e
x
T
o
t
a
l
L
o
s
s
e
s
(
MV
A)
VD
(
p
u
)
B
e
s
t
l
o
c
.
B
e
s
t
s
e
t
.
B
e
s
t
l
o
c
.
B
e
s
t
s
e
t
.
P
g
1
(
p
u
)
P
g
2
(
p
u
)
P
g
3
(
p
u
)
P
g
6
(
p
u
)
P
g
8
(
p
u
)
T1
T2
T3
W
i
t
h
o
u
t
F
A
C
TS
B
e
s
t
L
i
n
d
e
x
-
-
-
-
0
.
9
3
0
.
8
0
0
.
5
0
0
.
1
0
0
.
3
0
0
.
9
0
0
.
9
0
1
.
1
0
0
.
0
6
8
4
3
2
.
1
7
0
.
8
6
B
e
s
t
l
o
s
s
e
s
-
-
-
-
0
.
9
7
0
.
8
0
0
.
5
0
0
.
3
5
0
.
1
0
1
.
1
0
0
.
9
8
1
.
0
3
0
.
0
7
2
1
2
0
.
4
5
0.
70
W
i
t
h
F
A
C
TS
B
e
s
t
K
S
S
o
l
u
t
i
o
n
B
u
s
9
-
0
.
4
8
L
i
n
e
4
-
9
-
0
.
6
5
0
.
6
7
0
.
8
0
0
.
5
0
0
.
3
5
0
.
3
0
1
.
0
0
0
.
9
9
1
.
0
1
0
.
0
3
6
8
1
8
.
0
7
0.
50
1
6.
CONCL
US
I
O
N
This
pap
e
r
pr
e
sents
a
n
ef
fici
ent,
sim
ple
and
fast
ap
proac
h
f
or
t
he
S
VC
a
nd
TCSC
opti
m
al
placem
ent
in
the
netw
ork;
it
was
done
on
IE
EE
14
-
bus
te
st
syst
e
m
by
us
in
g
KA
L
A
I
Sm
or
od
i
ns
ky
s
olu
ti
on
w
hic
h
giv
e
s
a
co
ncr
et
e
s
olu
ti
on.
S
e
ver
al
op
ti
m
iz
ation
te
chn
i
qu
e
s
s
uc
h
as
dif
fer
e
ntial
evo
l
ution
a
nd
goal
pr
ogra
m
m
ing
wer
e
us
e
d
to
achieve
this
t
arg
et
.
Vo
lt
a
ge
Dev
ia
ti
on
I
ndex
was
al
so
us
e
d
in
case
of
m
any
po
ssi
ble
KS
So
luti
ons
.
We
wer
e a
ble t
o
locat
e t
he
be
st place
m
ent o
f
SV
C a
nd TCS
C i
n
the
po
we
r
syst
e
m
w
hich dep
e
nds
on
the
ta
rg
et
s
fi
xe
d
by
the
op
e
rat
or,
an
d
seco
nd
ly
,
the
siz
e
of
FA
CTS
was
c
om
pu
te
d.
T
he
appr
oach
us
e
d
in
this
pap
e
r
can
be
us
e
d
for
ot
her
obj
ect
ives
an
d
oth
e
r
net
work
s
in
orde
r
to
i
m
pr
ove
the
ir
exp
l
oitat
ions
unde
r
op
ti
m
al
co
nd
it
ion
s.
REFERE
NCE
S
[1]
S.
P.
S
ingh
,
“
On
-
li
ne
As
sess
m
e
nt
of
Volta
ge
Stabi
lit
y
using
S
y
nchr
ophasor
Te
c
hnolog
y
,”
Indon
esian
Journal
of
El
e
ct
rica
l
Eng
in
ee
ring a
nd
Computer
Sc
ie
nc
e
,
v
ol
/i
ss
ue:
8
(
1
)
,
p
p
.
1
-
8
,
2017
.
[2]
P.
K
um
ar
,
“
Enh
anc
ement
of
power
qual
ity
b
y
an
appl
icat
ion
FA
CTS
devi
ce
s
,”
Inte
rnat
ional
J
ournal
of
Powe
r
El
e
ct
ronics
and
Dr
iv
e
Syst
ems (
IJP
EDS)
,
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ss
ue:
6
(
1
)
,
p
p
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10
-
17
,
2015
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[3]
Z.
H
amid,
e
t
al
.
,
“
Stabi
lit
y
inde
x
tra
cing
for
deter
m
ini
ng
FA
CTS
devi
c
es
pla
c
eme
nt
loc
a
ti
ons
,”
Po
wer
Engi
ne
ering
and
Optimi
zatio
n
Confe
ren
ce (
PE
DCO
)
Me
lak
a,
Malay
sia
,
2012
I
EEE
Inte
rnat
ion
al
,
p
p
.
17
-
22
,
20
12.
[4]
E.
B
.
M
artine
z
a
nd
C.
Á
.
C
amac
ho,
“
Te
chnica
l
c
om
par
ison
of
F
ACTS
con
trol
le
r
s
in
par
al
lel
con
nec
t
ion
,”
Journa
l
of
App
li
ed
R
ese
a
rch
and
Tec
hnol
ogy
,
vo
l
/i
ss
ue:
15
(
1
)
,
p
p
.
36
-
44
,
2017.
[5]
S.
D
utt
a
,
et
a
l.
,
“
Optimal
al
locat
ion
of
SV
C
and
TCSC
using
quasi
-
oppositi
onal
c
hemica
l
r
eact
ion
opti
m
iz
a
ti
on
fo
r
solvi
ng
m
ult
i
-
ob
je
c
ti
ve
ORP
D probl
em
,”
Journal of
E
le
c
tric
al
Sys
te
ms
and
Inform
ati
on
Te
chnol
og
y
,
2016
.
[6]
K.
V.
R.
R
edd
y
,
et
al
.
,
“
Im
prove
m
ent
of
Volta
g
e
Profile
through
the
Optimal
Pl
acem
en
t
of
FA
CTS
Us
ing
L
-
Inde
x
Method
,”
Int
ernati
onal
Journal
of
el
e
ct
ri
cal
a
nd
Computer
e
ngine
ering
(
IJECE)
,
vol
/i
ss
ue:
4
(
2
)
,
p
p
.
207
-
2
11
,
2014.
[7]
A.
B
aghe
rin
asa
b
,
et
al
.
,
“
Optimal
pla
c
ement
of
D
-
STATCOM
u
sing
h
y
brid
g
en
et
i
c
and
ant
colon
y
a
lgori
thm
t
o
losses re
duction
,”
Int
ernati
onal
J
ournal
of Appl
i
e
d
Powe
r
Engi
n
e
ering
(
IJA
P
E)
,
v
ol
/i
ss
ue:
2
(
2
)
,
p
p
.
53
-
60
,
2013
.
[8]
N.
A.
L
e
,
e
t
al
.
,
“
The
Modeli
n
g
of
SV
C
for
the
Volta
ge
Con
trol
in
Pow
er
Sy
stem
,”
Indon
esi
an
Journal
of
El
e
ct
rica
l
Eng
in
ee
ring a
nd
Computer
Sc
ie
nc
e
,
v
ol
/i
ss
ue:
6
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m
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odifi
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II
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rnat
iona
l
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tric
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ct
rica
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IS
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ul
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ec
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ci
en
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heur
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m
iz
ati
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Evaluation Warning : The document was created with Spire.PDF for Python.