Int
ern
at
i
onal
Journ
al of Inf
orm
at
ic
s
and
Co
m
munic
at
i
on
Tec
hn
olog
y (IJ
-
I
CT)
Vo
l.
8
,
No.
3
,
D
ecembe
r
201
9
, pp.
111
~
116
IS
S
N:
22
52
-
8776
, DO
I: 10
.11
591/ij
ic
t.v8
i
3.p
p
111
-
116
111
Journ
al h
om
e
page
:
http:
//
ia
escore.c
om/j
ourn
als/i
ndex.
ph
p/IJI
C
T
Powe
r loss reduct
ion by a
rctic w
olf optim
iza
tion alg
orithm
Ka
n
agasab
ai
Le
nin
Depa
rt
m
ent
o
f
E
EE
,
Prasad
V
.
Potluri
Siddhart
h
a Instit
ute of Te
ch
nology
,
Ind
ia
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
J
ul
19
, 2
01
9
Re
vised
N
ov
1
2,
201
9
Accepte
d Nov
27
, 201
9
Thi
s
p
ape
r
prop
oses
Arctic
Wolf
opt
im
i
za
t
ion
(
AWO)
al
go
rit
h
m
to
solv
e
the
opti
mal
re
active
power
proble
m
.
Dee
ds
of
the
Ar
ct
i
c
wolf
hav
e
b
ee
n
i
mi
t
at
ed
to
formulat
e
th
e
proposed
al
gor
ithm.
Arc
ti
c
wolf
al
so
identif
ie
d
a
s
the
whit
e
wolf
or
pol
ar
wolf
is
a
bre
ed
of
gra
y
wolf
inha
bi
ta
nt
from
Me
lvi
l
le
Island
t
o
El
le
sm
ere
Isl
an
d.
I
t
is
ave
r
age
size
,
v
ery
sm
al
l
er
when
com
par
ed
to
nor
th
weste
rn
wolf
,
i
t
poss
ess
whiter
col
or
at
ion
,
n
a
rrower
bra
in
ca
s
e
and
big
ca
rna
ss
ials.
Particle
sw
arm
opt
i
m
iz
a
ti
on,
Gen
et
i
c
al
gorit
h
m
has
b
e
en
used
to
im
prove
th
e
Exp
lora
ti
on
&
Expl
o
it
ation
abi
l
it
y
of
t
he
al
gori
thm
by
uti
lizes
fla
g
vec
tor
&
posi
t
ion,
vel
o
city
u
pdat
e
prope
rtie
s.
Propos
ed
A
rct
i
c
Wol
f
opti
mization
(A
WO)
al
gor
it
hm
has
bee
n
te
st
ed
i
n
standa
rd
I
EEE
30
bus
te
st
sys
te
m
and
simu
la
ti
on
r
esult
s
sh
ow
the
proj
ec
t
ed
al
go
rit
h
ms
red
u
ce
d
the
r
ea
l
power
loss c
onsi
der
abl
y
.
Ke
yw
or
d
s
:
Ar
ct
ic
wo
lf
opt
imi
zat
ion
Op
ti
mal
r
eact
ive
p
owe
r
Transmi
ssio
n
l
os
s
Copyright
©
201
9
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
:
Kan
a
gasa
bai L
enin
,
Dep
a
rtme
nt of
EEE
,
Pr
asa
d V.
Potl
uri
Sid
dhartha
Insti
tute o
f
Tec
hnolog
y
,
Chala
sani
Nagar, Ka
nuru,
Vija
yaw
a
da, A
nd
hr
a
Pr
a
des
h 5
2000
7,
I
nd
ia
.
Emai
l:
gk
le
nin@g
mail
.co
m
1.
INTROD
U
CTION
Re
act
ive
powe
r
prob
le
m
play
s
an
imp
ort
ant
ro
le
i
n
sec
ure
a
nd
eco
nomic
operati
ons
of
power
syst
em
.
Numer
ous
ty
pe
s
of
meth
ods
[1
-
6]
ha
ve
bee
n
util
iz
ed
to
s
ol
ve
the
opti
mal
reacti
ve
po
we
r
pro
blem.
H
oweve
r
man
y
sci
entifi
c
d
iffic
ulti
es are f
ound
wh
il
e s
olv
in
g pro
blem
d
ue
t
o
an
ass
ort
ment
of
c
onstrai
nts.
E
voluti
on
a
r
y
te
chn
iq
ues
[
7
-
16]
a
re
a
pp
li
e
d
to
so
l
ve
th
e
reacti
ve
po
wer
pro
blem.
This
pa
per
pro
poses
Ar
ct
ic
W
olf
op
ti
miza
ti
on
(
AWO)
al
gorith
m
to
so
l
ve t
he
op
ti
mal
reacti
ve
power
pro
blem. A
rcti
c
wo
l
f a
lso
identifie
d
as
the
wh
it
e
w
olf
or
po
la
r
w
olf
is
a
bree
d
of
gray
w
olf
in
ha
bitant
from
M
el
vil
le
Isla
nd
to
El
le
smere
Isla
nd.
It
is
aver
a
ge
siz
e,
very
s
mall
er
wh
e
n
co
mp
a
re
d
t
o
north
we
ste
rn
w
olf,
it
po
s
sess
w
hiter
col
or
at
io
n,
na
rrow
e
r
br
ai
ncase and
b
ig
car
nassial
s.
A
rcti
c w
ol
f
is
f
ai
rly
una
fr
ai
d
of p
eo
ple,
an
d ca
n
be
e
ntice
to
a
ppr
oac
h
pe
ople
in
sever
al
areas
.
Very
par
ti
c
ular
ly
the
y
do
no
t
f
ear
human
s
&
appr
oach
cauti
ou
sl
y,
cu
rio
us
l
y a
nd
cl
ose
ly.
Duri
ng
winterti
me
wh
en
t
her
e
is a
bsolute
dark
ness
Ar
ct
ic
wo
l
f wil
l make
the
m
oveme
nt at te
m
per
at
ur
e
w
as
a
s lo
w
as
-
53
°C
(
-
63
°F
)
an
d
mai
nly
t
hey
prey
mainl
y
on
the
musk
ox
e
n.
Mus
koxe
n
are
ce
rtai
nl
y
their
mo
st
i
mporta
nt
pr
e
y
because
Ar
ct
ic
w
olf
presence
a
nd
re
p
rod
uction
see
m
to
be
s
up
e
rior
w
hen
musk
ox
e
n
a
re
m
or
e
avai
la
ble
than
normal
a
vaila
bili
ty.
Pa
r
ti
cl
e
swar
m
opti
miza
ti
on
,
G
eneti
c
al
gorith
m
has
bee
n
use
d
to
i
mpro
ve
the
Ex
plo
rati
on
&
Ex
pl
oitat
ion
abili
ty
of
the
al
gorithm
by
util
iz
es
flag
ve
ct
or
&
posit
ion,
vel
ocity
update
pro
per
ti
es.
P
r
o
po
s
e
d
A
rcti
c
Wo
l
f
op
ti
miza
ti
on
(
AWO)
al
gorith
m
has
be
e
n
t
e
s
t
e
d
i
n
s
t
a
n
da
r
d
I
E
E
E
57
bu
s
t
e
s
t
s
ys
t
e
m
a
nd
s
i
m
ul
a
t
i
on
r
e
s
ul
t
s
s
ho
w
t
he
p
r
oj
e
c
t
e
d
a
l
go
r
i
t
hm
r
e
du
c
e
d
t
he
r
e
a
l
po
w
e
r
l
os
s
c
o
ns
i
de
r
a
bl
y.
2.
PROBLE
M
F
ORMUL
ATI
ON
O
bj
e
c
t
i
ve
of
t
h
e
pr
o
bl
e
m
i
s
t
o
r
e
du
c
e
t
he
t
r
ue
po
w
e
r
l
os
s
:
F
=
P
L
=
∑
g
k
k
∈
Nbr
(
V
i
2
+
V
j
2
−
2
V
i
V
j
cos
θ
ij
)
(1)
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2252
-
8776
In
t J
Inf & C
ommu
n Tec
hn
ol
,
V
ol.
8
,
No.
3,
Dec
201
9
:
111
–
116
112
vo
l
t
a
ge
de
vi
a
t
i
on
gi
ve
n
a
s
f
ol
l
ow
s
:
F
=
P
L
+
ω
v
×
Volt
ag
e
D
ev
iat
ion
(2)
vo
l
t
a
ge
de
vi
a
t
i
on
gi
ve
n
by
:
Volt
ag
e
D
ev
iat
ion
=
∑
|
V
i
−
1
|
Npq
i
=
1
(3)
const
raint
(
E
qual
it
y)
P
G
=
P
D
+
P
L
(4)
const
raints
(
I
ne
qu
al
it
y)
P
g
slac
k
min
≤
P
g
slac
k
≤
P
g
slac
k
max
(5)
Q
gi
min
≤
Q
gi
≤
Q
gi
max
,
i
∈
N
g
(6)
V
i
min
≤
V
i
≤
V
i
ma
x
,
i
∈
N
(7)
T
i
min
≤
T
i
≤
T
i
max
,
i
∈
N
T
(8)
Q
c
min
≤
Q
c
≤
Q
C
max
,
i
∈
N
C
(9)
3.
ARCTI
C
W
O
LF OPT
I
MIZ
ATIO
N
Ar
ct
ic
W
olf
op
ti
miza
ti
on
(AWO)
mimi
cs
t
he
de
eds
of
A
r
ct
ic
Wo
lf
i
n
na
ture.
The
dee
ds
of
t
he
ar
ct
ic
wo
l
f ha
ve bee
n
imi
ta
t
ed t
o fo
r
mu
la
te
the
al
gorith
m.
D
uri
ng
winterti
me
w
he
n t
her
e
is
a
bsolute
da
rkness
Ar
ct
ic
wo
l
f
will
mak
e
the
m
ov
e
me
n
t
at
te
mp
e
ratu
re
was
a
s
lo
w
as
-
53
°C
(
-
63
°F)
a
nd
mainl
y
they
pr
e
y
m
ai
nly
on
the
m
uskoxe
n.
M
usk
ox
e
n
a
re
certai
nly
t
heir
mo
st
im
portant
prey
because
Ar
ct
i
c
w
olf
presen
ce
an
d
reprod
uction
s
eem
to
be
s
uperi
or
w
he
n
mu
s
koxe
n
are
m
or
e
a
vaila
bl
e
than
norma
l
avail
abili
ty.
Huntin
g
proce
dure
of
t
he
arcti
c
w
olf
i
s
desig
ne
d
to
f
ormulat
e
th
e
al
gorithm
.
T
her
e
are
thr
ee
fitt
est
cand
id
at
e
so
l
utions
(Arcti
c
W
olf)
embe
dd
e
d
as
,
and
to
le
a
d
th
e
popula
ti
on
t
owar
d
ca
pab
le
r
egio
ns
of
t
he
e
xp
l
or
at
io
n
s
pa
ce
in
each
it
erati
on o
f
A
rcti
c
W
ol
f
opti
miza
ti
on.
is
name
d
for
the
rest of A
rct
ic
Wo
l
f
a
n
d
it
will
assist
,
an
d
to
encircle
,
hu
nt,
an
d
at
ta
ck
pr
e
y
;
to
fin
d
imp
rove
d
so
l
ution
s
.
I
n
order
to
te
ch
nical
ly
imi
ta
te
the
encircli
ng
deeds
of
A
rcti
c wolves
, th
e
fo
ll
ow
in
g
e
qu
at
i
on
s
are
pr
oject
ed:
⃗
⃗
=
|
.
⃗
⃗
⃗
(
)
−
(
)
|
,
(10)
(
+
1
)
=
⃗
⃗
⃗
(
)
−
.
⃗
⃗
(11)
in
or
der
t
o
sci
e
ntific
al
ly imit
at
e the hu
ntin
g deed
s
of
A
rcti
c wolf,
the
fo
ll
owin
g
e
qu
at
io
ns are
project
ed
,
⃗
⃗
⃗
⃗
⃗
=
|
1
⃗
⃗
,
⃗
⃗
⃗
−
|
⃗
⃗
⃗
⃗
⃗
=
|
2
⃗
⃗
⃗
,
⃗
⃗
⃗
−
|
(12)
⃗
⃗
⃗
⃗
=
|
3
⃗
⃗
⃗
,
⃗
⃗
⃗
−
|
1
⃗
⃗
=
⃗
⃗
⃗
−
1
⃗
⃗
⃗
⃗
.
⃗
⃗
⃗
⃗
⃗
2
⃗
⃗
⃗
=
⃗
⃗
⃗
−
2
⃗
⃗
⃗
.
⃗
⃗
⃗
⃗
⃗
(13)
3
⃗
⃗
⃗
=
⃗
⃗
⃗
−
3
⃗
⃗
⃗
⃗
.
⃗
⃗
⃗
⃗
(
+
1
)
=
1
⃗
⃗
⃗
⃗
+
2
⃗
⃗
⃗
⃗
+
3
⃗
⃗
⃗
⃗
3
(14)
The
posit
ion
of
a
n
Ar
ct
ic
w
olf
is
mode
rn
iz
e
d
a
nd
th
en
the
fo
ll
owin
g
e
qua
ti
on
is
us
e
d
to
discrete
t
he
po
sit
io
n of t
he wo
l
f;
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Inf & C
ommu
n Tec
hn
ol
IS
S
N:
22
52
-
8776
Power l
os
s re
duct
ion by
arct
ic
wolf o
ptimiza
ti
on
algorit
hm
(
Ka
nagas
abai
Lenin
)
113
,
=
{
1
,
>
0
.
475
0
ℎ
(15)
wh
e
re
i
,
in
dica
te
s the jth
po
sit
ion o
f
t
he
it
h A
rcti
c wolf,
,
is f
eat
ur
es
of t
he Arcti
c
wo
l
f.
T
he
i
nteracti
ons
of the
Ar
ct
ic
w
olf
a
mon
g
the
m is inc
rease
d by,
=
+
(
−
)
+
(
−
)
(16)
The
c
onfine
d d
ensity
of
the
A
rcti
c wolf is
de
no
te
d by,
=
∑
−
(
)
2
∈
/
{
}
(17)
Ar
ct
ic
wo
lf
is
le
ss
than
“
dc
”
w
hen
the
t
he
Ar
ct
ic
wo
lf
’s
distance
from
the
j
i
,
the
great
er
tha
n
t
he
confi
ne
d
den
si
ty
of
the
Ar
ct
ic
wo
l
f.
d
ij
sy
m
boli
ze
the
Eu
cl
idean
distance
betwee
n
the
j
i
,
j
j
of
Ar
ct
ic
w
ol
f,
φ
id
i
s a arbit
rary
num
ber in
[0,
1],
φ
id
is a arb
it
ra
ry
numb
e
r
i
n
[
-
1,1]
“2
m”
Ar
ct
ic
Wo
l
f
with
t
he
le
ading
c
onfi
ne
d
thick
ness
is
cho
se
n
&
wel
l
-
orga
nized
by
den
sit
y
[
17]
from
big
to
li
tt
le
in
set
“R
”.
Af
te
r
wa
rd
s
,
“2
m”
Ar
ct
ic
W
ol
f’
s
,
a
r
e
sel
ect
ed
to
a
dju
st
to
t
he
m
os
t
aw
fu
l
Ar
ct
ic
Wo
l
f
’s
a
nd it
ha
s
been
placed
in set
“Y
”
with
r
e
fer
e
nce
to
th
e fitnes
s
values
from
ve
ry sma
ll
to
la
r
ge. “
X”
and
“Y” inte
rsecti
on
of sets i
s s
ymb
olize
d b
y
“
E”:
=
∩
(18)
=
{
;
∈
,
∈
,
=
1
,
2
,
.
.
,
}
(19)
Tw
o
maj
or
a
bo
li
ti
on
meth
ods
are im
plement
ed.
Let
“V
”
b
e
the sto
re to st
oc
kp
il
e th
e a
bo
l
ished
in
div
id
ua
ls,
=
{
1
,
>
(
)
2
[
1
;
]
,
ℎ
(20)
Arbit
rary
num
ber
s
are
en
ge
ndere
d
by
the
ra
ndom
f
unct
ion
in
the
i
nter
val
[
0,
1].
T
he
pro
ba
bili
ty
of
the
est
ablishme
nt
of
>
(
)
2
in
the
pri
m
ary
sta
ge
is
big.
Wit
h
the
inc
r
ease
in
it
erati
on
ste
ps
,
the
pro
bab
il
it
y
will
be
re
du
ci
ng
t
o
le
sse
r.
The
a
lgorit
hm
t
o
be
incli
ne
d
t
o
e
xplo
re
globall
y,
an
d
a
fter
ward
s,
the
al
gorithm is
apt
to
ex
plore l
oc
al
mode.
Po
sit
io
ns
a
nd
ve
locit
ie
s
are
m
od
e
r
nized
to
imp
rove
the
pe
r
forma
nce
of
t
he
ex
plorat
io
n
&
e
xp
l
oitat
io
n
in the p
ro
je
ct
e
d
al
go
rithm.
v
t
+
1
i
=
ω
t
.
v
t
i
+
cg
1
.
Rm
1
.
(
m
t
i
−
y
t
i
)
+
cg
2
.
Rm
2
.
(
m
t
g
−
y
t
i
)
(2
1)
y
t
+
1
i
=
y
t
i
+
v
t
+
1
i
(22)
The
pr
e
sent
po
sit
ion
of
par
ti
c
le
is
y
t
i
&
sea
rch
velocit
y
is
v
t
i
.
Global
be
st
-
f
ound
posit
ion
is
.
m
t
g
.
I
n
un
i
for
mly
dist
rib
uted
i
nterva
l
(0
,
1)
Rm
1
&
Rm
2
a
re
ar
bitrar
y
nu
mb
e
rs.
W
her
e
cg
1
an
d
cg
2
are
scal
ing
par
a
mete
rs.
ω
t
is t
he parti
cl
e ine
r
ti
a. Th
e
va
riabl
e
ω
t
is m
od
e
rn
iz
e
d
as
:
ω
t
=
(
ω
max
−
ω
min
)
.
(
t
m
ax
−
t
)
t
m
ax
+
ω
min
(23)
M
a
ximum
a
nd
minim
um
of
ω
t
is
represe
nted
by
ω
max
an
d
ω
min
;
ma
ximum
numb
e
r
of
it
erati
on
s is
gi
ven by
t
ma
x
.
Gen
et
ic
al
go
rithm
(GA)
as
a
n
ada
ptive
opti
miza
ti
on
e
xp
l
orat
ion
meth
od
is
base
d
on
nat
ural
sel
ect
ion
and
ge
netic
s.
I
n
GA,
a
popul
at
ion
is
c
omp
ose
d
of
a
set
of
can
did
at
e
s
ol
utions
cal
le
d
c
hrom
osomes
a
nd
it
include
s
nume
rous
ge
nes
wi
th
bin
a
ry
val
ue
s
0
a
nd
1.
T
he
majo
r
ste
ps
are
of
G
A
a
re
.
(i)
I
niti
al
iz
at
ion
;
Chrom
osomes
are
a
rb
it
ra
rily
ge
ner
at
e
d.
(ii)
Sele
ct
io
n;
to
ch
oose
par
e
nt
ch
romosome
s
a
r
oule
tt
e
ch
oo
si
ng
method
is
us
e
d.
(iii
)
Cr
os
s
ov
e
r;
to
ge
ne
rate
offs
pr
i
ng
c
hro
m
os
ome
a
si
ng
le
po
i
nt
cr
os
s
ov
e
r
meth
od
is
us
e
d.
(iv
)
M
utati
on;
unva
ry
i
ng
m
utati
on
is
implem
ented
(
v)
Dec
od
e;
Dec
od
e
the
m
utate
d
c
hrom
osomes
a
s
the
pr
el
imi
na
r
y posi
ti
on
s
of po
pula
ti
on
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2252
-
8776
In
t J
Inf & C
ommu
n Tec
hn
ol
,
V
ol.
8
,
No.
3,
Dec
201
9
:
111
–
116
114
Fit
ness funct
io
n wil
l be calc
ulate
d
by,
=
+
−
(24)
Wh
e
re
T
de
fin
e
the
acc
ur
at
e
ness,
G
is
the
le
ng
th
of
c
ho
s
en
el
em
ent
di
vi
sion
,
M
is
the
sum
of
al
l
featur
e
s,
a
nd
an
d
a
re t
he wei
ght o
f
cl
ass
ific
at
ion
a
nd p
i
ckin
g qu
al
it
y,
∈
[
0
,
1
]
=
1
−
In
it
ia
li
zat
ion
of the
p
a
rameter
s
i = 1:
popula
ti
on size;
j =
1:
n
Wh
e
n (i, j)
>
0.4
75
;
(i
)
=
1
;
E
lse
(
j) =
0
;
En
d
if
En
d
f
or
Ca
lc
ulati
on
of
the f
it
nes
s fu
nc
ti
on
s
by;
=
+
−
Pr
imar
y, sec
ondary,
thir
d
m
ax
imum
fitness
of the
Arct
ic
wo
lf is d
e
sig
nated
as “
”, “
”, “
”
Wh
il
e
k
<
ma
xi
mu
m
num
ber
of it
erati
on
Fo
r
i =
1:
p
op
ul
at
ion
size
M
ode
rn
iz
e t
he e
xisti
ng posit
io
n of A
rcti
c wolf
by
(
+
1
)
=
1
⃗
⃗
⃗
⃗
+
2
⃗
⃗
⃗
⃗
+
3
⃗
⃗
⃗
⃗
3
Existi
ng wolf
Ar
ct
ic
locati
on
h
as
b
ee
n revis
ed peri
od
ic
al
ly
En
d
f
or
Fo
r
i =
1:
popu
la
ti
on
size;
F
or i=1:n
I
f (i, j)
>
0.475
; (j) =
1; Else
;
(j)
=
0;
En
d
if
En
d
f
or
At irr
e
gula
r
i
nterv
al
s
re
new th
e p
a
rameter
v
a
lues
Fit
ness
functi
on
will
b
e cal
c
ulate
d
by
;
=
+
−
The
as
sessme
nt
o
f
Arct
ic
Wol
f
"
"
,
"
"
an
d
"
"
has
t
o b
e re
vised
t=
t+
1;
En
d wh
il
e
Re
turn the
best
so
l
ution
”
“
En
d
4.
S
IM
ULATI
O
N
ST
UDY
Pr
op
os
e
d
Ar
ct
i
c
W
olf
opti
miza
ti
on
(AW
O)
a
lgorit
hm
has
be
en
te
ste
d,
i
n
I
EEE
57
B
us
s
ys
te
m
[
18].
Table
1
s
hows
the
co
ns
trai
nts
of
c
on
t
ro
l
var
i
ables,
Ta
ble
2
sh
ows
t
he
li
mit
s
of
reacti
ve
powe
r
ge
ne
rato
r
s
and
com
par
is
on
res
ults
ar
e
pr
e
sen
te
d
i
n
T
able
3.
Fig
ure
1
giv
e
s
the
C
omparis
on
of
real
pow
er
l
os
s
an
d
Fi
gure
2
giv
es
the Re
duct
ion
of r
eal
po
wer l
os
s
(%
) w
it
h
ref
e
re
nce to base
case
valu
e.
Table
1.
C
onstrai
nts
of co
ntr
ol
v
aria
bles
Sy
stem
Variables
Minimum
(
P
U)
Maximu
m
(
P
U)
IE
E
E
5
7
Bu
s
Gen
erator
Vo
ltag
e
0
.95
1
.1
Tr
an
sfo
r
m
er
T
ap
0
.9
1
.1
VAR So
u
rce
0
0
.20
Table
2.
C
onstrai
ns
of r
eact
i
ve
pow
e
r ge
ner
a
tors
Sy
stem
Variables
Q M
in
i
m
u
m
(PU
)
Q M
ax
i
m
u
m
(PU
)
IE
E
E
5
7
Bu
s
1
-
140
200
2
-
17
50
3
-
10
60
6
-
8
25
8
-
140
200
9
-
3
9
12
-
150
155
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Inf & C
ommu
n Tec
hn
ol
IS
S
N:
22
52
-
8776
Power l
os
s re
duct
ion by
arct
ic
wolf o
ptimiza
ti
on
algorit
hm
(
Ka
nagas
abai
Lenin
)
115
Table
3.
Simul
at
ion
resu
lt
s
of I
EEE
-
57 syst
em
Co
n
trol v
ariables
Bas
e ca
se
MPSO
[19
]
PSO [
1
9
]
CGA [19
]
AGA
[19
]
AW
O
1
1
.04
0
1
.09
3
1
.08
3
0
.96
8
1
.02
7
1
.00
8
2
1
.01
0
1
.08
6
1
.07
1
1
.04
9
1
.01
1
1
.01
2
3
0
.98
5
1
.05
6
1
.05
5
1
.05
6
1
.03
3
1
.00
4
6
0
.98
0
1
.03
8
1
.03
6
0
.98
7
1
.00
1
1
.02
9
8
1
.00
5
1
.06
6
1
.05
9
1
.02
2
1
.05
1
1
.04
8
9
0
.98
0
1
.05
4
1
.04
8
0
.99
1
1
.05
1
1
.03
9
12
1
.01
5
1
.05
4
1
.04
6
1
.00
4
1
.05
7
1
.02
6
19
0
.97
0
0
.97
5
0
.98
7
0
.92
0
1
.03
0
0
.91
1
20
0
.97
8
0
.98
2
0
.98
3
0
.92
0
1
.02
0
0
.90
9
31
1
.04
3
0
.97
5
0
.98
1
0
.97
0
1
.06
0
0
.90
6
35
1
.00
0
1
.02
5
1
.00
3
NR*
NR*
1
.00
7
36
1
.00
0
1
.00
2
0
.98
5
NR*
NR*
1
.02
1
37
1
.04
3
1
.00
7
1
.00
9
0
.90
0
0
.99
0
1
.03
2
41
0
.96
7
0
.99
4
1
.00
7
0
.91
0
1
.10
0
0
.94
7
46
0
.97
5
1
.01
3
1
.01
8
1
.10
0
0
.98
0
1
.02
8
54
0
.95
5
0
.98
8
0
.98
6
0
.94
0
1
.01
0
0
.93
9
58
0
.95
5
0
.97
9
0
.99
2
0
.95
0
1
.08
0
0
.92
8
59
0
.90
0
0
.98
3
0
.99
0
1
.03
0
0
.94
0
0
.93
8
65
0
.93
0
1
.01
5
0
.99
7
1
.09
0
0
.95
0
1
.02
6
66
0
.89
5
0
.97
5
0
.98
4
0
.90
0
1
.05
0
0
.93
9
71
0
.95
8
1
.02
0
0
.99
0
0
.90
0
0
.95
0
1
.04
2
73
0
.95
8
1
.00
1
0
.98
8
1
.00
0
1
.01
0
1
.01
2
76
0
.98
0
0
.97
9
0
.98
0
0
.96
0
0
.94
0
0
.90
6
80
0
.94
0
1
.00
2
1
.01
7
1
.00
0
1
.00
0
1
.03
0
18
0
.1
0
.17
9
0
.13
1
0
.08
4
0
.01
6
0
.14
0
25
0
.05
9
0
.17
6
0
.14
4
0
.00
8
0
.01
5
0
.13
1
53
0
.06
3
0
.14
1
0
.16
2
0
.05
3
0
.03
8
0
.12
0
(
MW)
1
2
7
8
.6
1
2
7
4
.4
1
2
7
4
.8
1276
1275
1
2
7
2
.6
7
(M
v
a
r)
3
2
1
.08
2
7
2
.27
2
7
6
.58
3
0
9
.1
3
0
4
.4
2
7
2
.38
Red
u
ctio
n
in
PLos
s (%)
0
1
5
.4
1
4
.1
9
.2
1
1
.6
2
7
.43
Total PLos
s (
Mw
)
2
7
.8
2
3
.51
2
3
.86
2
5
.24
2
4
.56
2
0
.17
2
NR*
-
No
t
repo
rte
d
.
Figure
1.
Com
par
is
on of
real
powe
r
loss
Fig
ure
2
.
Re
du
ct
ion
of r
eal
po
wer l
os
s
(%
) w
it
h
ref
e
re
nce to base
case
valu
e
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2252
-
8776
In
t J
Inf & C
ommu
n Tec
hn
ol
,
V
ol.
8
,
No.
3,
Dec
201
9
:
111
–
116
116
5.
CONCL
US
I
O
N
In
this
pa
per
Ar
ct
ic
W
olf
opti
miza
ti
on
(
A
WO)
al
gorith
m
s
uccess
fu
ll
y
so
l
ved
the
opti
mal
reacti
ve
powe
r
pro
ble
m
.
(
Ar
ct
ic
W
ol
f)
em
bedde
d
as
,
and
to
le
ad
the
popula
ti
on
t
ow
a
rd
ca
pa
ble
re
gions
of
the
exp
l
or
at
io
n
spa
ce
in
eac
h
it
er
at
ion
of
Ar
ct
ic
W
olf
op
ti
miza
ti
on
.
is
name
d
f
or
the
rest
of
Ar
ct
ic
W
olf
a
nd
it
will
assist
,
an
d
to
enci
rcle, h
unt,
a
nd
at
ta
ck
pr
e
y.
.
P
rop
ose
d
Ar
ct
ic
W
olf
opti
miz
at
ion
(AW
O)
al
gorith
m
has
bee
n
te
ste
d
i
n
sta
ndar
d
I
EEE
57
bus
te
st
sy
ste
m
a
nd
simulat
ion
re
s
ults
s
how
the
project
ed
al
go
rithms
reduce
d
the
r
ea
l powe
r
los
s effi
ci
ently.
REFERE
NCE
S
[1]
K.
Y.
Lee,
"
Fuel
-
cost
mi
ni
mis
at
ion
for
both
rea
l
and
r
ea
c
t
ive
-
power
disp
a
t
che
s,"
P
roce
ed
ings
Gene
ratio
n,
Tr
ansm
i
ss
ion
and
Distributi
on
C
onfe
renc
e
,
vol
.
1
31(3),
pp
.
85
-
93
,
1984
.
[2]
N.
I.
Dee
b
,
"
An
e
ffic
i
ent
t
ec
hn
iqu
e
for
re
ac
t
ive
po
wer
dispat
ch
usi
ng
a
rev
ised
li
n
e
ar
progra
m
mi
ng
appr
oac
h
,
"
Elec
t
ric
Powe
r Sy
st
em
R
ese
arch
,
vol.
15(
2),
pp
.
121
-
134
,
1998.
[3]
M.
R.
Bj
el
ogrl
ic,
M.
S.
C
al
ovi
c,
B.
S.
Bab
ic
, "
Ap
pli
c
at
ion
of
n
ewt
on’s opt
imal
po
wer
flow
in
voltage/
r
eact
iv
e
pow
er
cont
rol
,"
IE
EE Tr
ans P
ower
Syst
em
,
vol
.
5(
4
)
,
pp
.
1447
-
1454
,
19
90.
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