T
E
L
KO
M
N
I
KA
T
e
lec
om
m
u
n
icat
ion
,
Com
p
u
t
i
n
g,
E
lec
t
r
on
ics
an
d
Cont
r
ol
Vol.
18
,
No.
1
,
F
e
br
ua
r
y
2020
,
pp.
376
~
384
I
S
S
N:
1693
-
6930,
a
c
c
r
e
dit
e
d
F
ir
s
t
G
r
a
de
by
Ke
me
nr
is
tekdikti
,
De
c
r
e
e
No:
21/E
/KP
T
/2018
DO
I
:
10.
12928/
T
E
L
KO
M
NI
KA
.
v18i1.
13379
376
Jou
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h
omepage
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tp:
//
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id/
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owe
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R
e
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hunt
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C
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u
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or
:
He
r
lamba
ng
S
e
ti
a
di,
De
pa
r
tm
e
nt
of
E
nginee
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ing,
F
a
c
ult
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ti
ona
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S
tudi
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E
mail:
he
r
lamba
ng
.
s
e
ti
a
di@vokas
i.
una
ir
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a
c
.
id
1.
I
NT
RODU
C
T
I
ON
I
n
e
lec
tr
ic
powe
r
s
ys
tems
,
tr
a
ns
mi
s
s
ion
li
ne
s
play
a
ke
y
r
ole
to
dis
tr
ibut
e
e
lec
tr
ica
l
e
ne
r
gy
f
r
om
powe
r
plants
to
c
ons
umer
s
.
E
lec
tr
ica
l
e
ne
r
gy
dis
tr
ibut
e
d
by
tr
a
ns
mi
s
s
ion
li
ne
s
c
on
s
is
ts
of
a
c
ti
ve
a
nd
r
e
a
c
ti
ve
powe
r
s
.
I
n
f
a
c
t,
the
plac
e
o
f
e
lec
tr
ic
powe
r
p
lants
i
s
s
pa
ti
a
ll
y
is
olate
d
f
r
om
the
c
ons
umer
.
T
his
c
a
us
e
s
a
n
e
nor
mous
c
ha
ll
e
nge
in
e
lec
tr
icity
tr
a
ns
por
tati
on
ove
r
a
long
dis
tanc
e
whic
h
c
ould
a
f
f
e
c
t
the
leve
l
of
pe
r
f
or
manc
e
a
nd
s
e
c
ur
it
y
of
the
s
ys
tem.
R
e
a
c
ti
ve
powe
r
is
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ne
r
a
ted
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im
pe
da
n
c
e
o
f
a
lar
ge
powe
r
s
ys
tem
ne
twor
k
but
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ls
o
pr
oduc
e
d
by
e
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tr
ica
l
de
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s
s
uc
h
a
s
mo
tor
,
t
r
a
ns
f
or
mer
a
nd
o
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powe
r
e
lec
tr
onic
c
omponents
.
He
nc
e
,
thi
s
powe
r
may
ha
v
e
a
gr
e
a
t
im
pa
c
t
on
the
s
ys
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pe
r
f
or
manc
e
.
R
e
a
c
ti
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load
s
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s
uppli
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by
ge
ne
r
a
ti
on
unit
s
whe
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e
a
r
e
no
s
our
c
e
s
of
r
e
a
c
ti
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powe
r
on
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lec
tr
ica
l
load
f
r
o
m
the
t
r
a
ns
mi
s
s
ion
li
ne
s
ys
te
m.
T
he
c
ur
r
e
nt
f
lowing
in
the
tr
a
ns
mi
s
s
ion
li
ne
s
incr
e
a
s
e
s
due
to
r
e
a
c
ti
ve
powe
r
on
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lec
tr
ica
l
load
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e
a
s
e
s
whic
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ini
ti
a
tes
l
a
r
ge
r
e
a
c
ti
ve
c
ur
r
e
nt
f
l
owing
in
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
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NI
KA
T
e
lec
omm
un
C
omput
E
l
C
ontr
o
l
I
mpr
ov
e
me
nt
of
v
olt
age
pr
ofi
le
for
lar
ge
s
c
ale
pow
e
r
s
y
s
t
e
m
us
ing
s
oft
c
omputing…
(
M
uhamm
ad
A
bd
il
lah
)
377
the
tr
a
ns
mi
s
s
ion
li
ne
s
.
A
la
r
ge
a
mount
o
f
r
e
a
c
ti
ve
c
ur
r
e
nts
f
lowing
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tr
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ns
mi
s
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ion
li
ne
c
a
us
e
s
de
c
r
e
a
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ing
in
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powe
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f
a
c
tor
,
incr
e
a
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ing
ne
twor
k
los
s
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nd
volt
a
ge
dr
op.
T
he
r
e
f
or
e
,
the
de
s
ir
e
d
volt
a
ge
p
r
of
il
e
on
the
c
ons
umer
s
ide
be
c
omes
inappr
opr
iate
.
T
o
ove
r
c
ome
thi
s
pr
oblem,
the
s
hunt
c
a
pa
c
it
or
is
a
n
im
po
r
ta
nt
de
vice
to
ins
tall
in
the
tr
a
ns
mi
s
s
ion
li
ne
a
s
r
e
a
c
ti
ve
powe
r
c
ompens
a
ti
on
[
1]
.
An
a
ppr
opr
iate
planning
meth
odology
s
hould
be
c
onduc
ted
f
or
mer
ging
s
hunt
c
a
pa
c
it
or
s
a
s
r
e
a
c
ti
ve
powe
r
c
ompens
a
ti
on
int
o
a
powe
r
s
ys
tem
ne
twor
k
in
or
de
r
to
ge
t
it
s
be
ne
f
it
.
T
he
ins
tallation
of
thes
e
c
ompens
a
ti
ng
de
vice
s
a
t
non
-
a
ppr
opr
iate
a
r
e
a
s
with
incor
r
e
c
t
s
izing
lea
ds
to
ne
ga
ti
ve
c
ons
e
que
nc
e
s
s
uc
h
a
s
a
n
incr
e
a
s
e
in
powe
r
los
s
a
nd
volt
a
ge
ins
tabili
ty.
T
h
e
r
e
we
r
e
c
las
s
ica
l
a
ppr
oa
c
h
e
s
f
or
s
olvi
ng
r
e
a
c
ti
ve
powe
r
pr
oblems
s
uc
h
a
s
mi
xe
d
-
int
e
ge
r
pr
ogr
a
mi
ng,
n
on
-
li
ne
a
r
pr
ogr
a
mi
ng,
li
ne
a
r
pr
ogr
a
mi
ng
a
nd
qua
dr
a
ti
c
pr
o
gr
a
mi
ng
[2
-
4]
.
Ne
ve
r
thele
s
s
,
thes
e
a
ppr
oa
c
he
s
ha
ve
s
ome
is
s
ue
s
in
s
olvi
ng
the
objec
ti
ve
f
unc
ti
ons
that
we
r
e
tr
a
ppe
d
in
loca
l
mi
nim
a
.
T
o
tac
kle
the
inher
e
nt
li
mi
tations
of
thes
e
s
olut
ion
methods
,
s
ome
s
im
pli
f
ica
ti
on
h
a
s
be
e
n
us
e
d
to
a
ll
thes
e
pr
a
c
ti
c
e
s
.
Dive
r
ge
nc
e
a
nd
loca
l
mi
nim
um
c
ould
e
mer
ge
due
the
s
im
pli
f
ica
ti
on
o
f
the
pr
obl
e
ms
.
Additi
ona
ll
y,
the
c
onve
nti
ona
l
m
e
thod
is
c
ons
umi
ng
c
omput
a
ti
on
bur
de
n
ti
me
f
o
r
f
indi
ng
th
e
s
olut
ion.
Now
a
da
ys
,
many
ne
w
s
of
t
c
ompu
ti
ng
methods
ha
v
e
be
e
n
us
e
d
f
or
s
olvi
ng
opti
mi
z
a
ti
on
pr
ob
l
e
ms
a
nd
wide
ly
e
mpl
oye
d
to
ha
ndle
va
r
ious
pr
oblems
in
e
nginee
r
ing
f
ields
.
S
mar
t
c
omput
a
ti
on
c
a
n
be
divi
de
d
int
o
thr
e
e
c
a
tegor
ies
:
f
ir
s
t
c
a
tegor
ies
is
biol
ogica
ll
y
in
s
pir
e
d
a
ppr
oa
c
he
s
s
uc
h
a
s
gr
e
y
wolf
opti
mi
z
a
ti
on,
f
r
uit
f
ly
a
lgor
it
hm
a
nd
s
oc
ial
s
pider
a
lgor
i
thm
.
S
e
c
ond
c
a
t
e
gor
ies
is
phys
ica
ll
y
ins
pir
e
d
s
uc
h
a
s
s
im
ulate
d
a
nne
a
li
ng
a
lgor
it
hm,
a
nd
las
tl
y
s
oc
ial
ins
pir
e
d
s
uc
h
a
s
im
pe
r
ialis
t
c
ompetit
ive
a
lgor
it
hm
,
a
nd
tabu
s
e
a
r
c
h
a
lgor
it
hm
[
5]
.
T
he
r
e
a
r
e
a
numbe
r
of
r
e
s
e
a
r
c
he
s
that
uti
li
z
ing
s
of
t
c
omput
ing
ba
s
e
d
on
biol
ogica
l
ins
pir
e
d
a
ppr
oa
c
he
s
to
s
olve
opti
mi
z
a
ti
on
pr
oblems
s
uc
h
a
s
ge
ne
ti
c
a
lgor
it
hm
(
G
A)
to
de
ter
m
ine
the
opti
mal
ge
ne
r
a
tor
ou
tput
[
6
]
,
a
n
t
c
olony
opti
mi
z
a
ti
on
(
AC
O)
f
or
r
e
a
c
ti
ve
powe
r
mana
ge
ment
[
7]
,
di
f
f
e
r
e
nti
a
l
e
volut
ion
(
DE
)
a
lgo
r
it
hm
to
s
olve
non
-
c
onve
x
a
nd
high
non
-
li
ne
a
r
pr
oblems
[
8
,
9]
,
pa
r
ti
c
le
s
wa
r
m
opti
mi
z
a
ti
on
(
P
S
O)
f
o
r
r
e
a
c
ti
v
e
powe
r
dis
pa
tch
[
10]
,
biogeogr
a
phy
ba
s
e
d
opti
mi
z
a
ti
on
(
B
B
O)
f
or
opti
mal
VA
R
c
ontr
ol
[
11
]
,
ha
r
mon
y
s
e
a
r
c
h
a
lgor
it
hm
(
HSA)
f
or
r
e
a
c
ti
ve
dis
pa
tch
[
12
]
,
hyb
r
id
tabu
s
e
a
r
c
h
a
lgor
it
hm
(
T
S
)
a
nd
s
im
u
late
d
a
nne
a
li
ng
a
lgor
it
hm
(
S
A)
f
o
r
op
ti
mal
r
e
a
c
ti
ve
powe
r
pr
obl
e
m
[
13]
,
tea
c
hing
lea
r
ning
ba
s
e
d
opti
mi
z
a
ti
on
a
l
gor
it
hm
(
T
L
B
O)
f
or
r
e
a
c
ti
ve
powe
r
planning
[
14]
,
gr
o
up
s
e
a
r
c
h
opti
mi
z
a
ti
on
(
G
S
O)
f
or
powe
r
a
nd
e
mi
s
s
ion
dis
pa
tch
[
15]
,
hone
y
be
e
mating
opti
mi
z
a
ti
on
(
HB
M
O)
f
or
powe
r
los
s
mi
nim
iza
ti
on
[
16
]
,
gr
a
vit
a
ti
on
a
l
s
e
a
r
c
h
a
lgor
it
hm
(
GSA
)
to
de
ter
mi
ne
the
opti
mal
F
AC
T
S
f
o
r
r
e
a
c
ti
ve
powe
r
planning
[
17]
,
a
r
ti
f
icia
l
b
e
e
c
olony
a
lgor
it
hm
(
AB
C
)
f
o
r
r
e
a
c
ti
ve
powe
r
f
low
[
18
]
,
c
uc
koo
opti
mi
z
a
ti
on
a
lgor
it
hm
(
C
OA
)
[
19]
a
nd
a
r
ti
f
icia
l
im
mune
s
ys
tem
(
AI
S
)
[
20
]
f
o
r
dis
tr
ibu
ti
on
ne
twor
k
r
e
c
onf
igur
a
ti
on
pr
oblem
.
M
or
e
ove
r
,
the
a
ppli
c
a
ti
on
o
f
s
of
t
c
omput
ing
in
o
pti
mi
z
ing
the
s
ize
of
the
s
hunt
c
a
pa
c
it
or
ha
s
be
e
n
inves
ti
ga
ted
by
many
r
e
s
e
a
r
c
he
s
a
s
r
e
a
c
ti
ve
pow
e
r
c
ompens
a
ti
on
a
s
r
e
por
ted
in
[
21]
.
I
n
[
21
]
the
ba
c
ter
ial
f
or
a
ging
a
lgor
it
hm
is
us
e
d
to
loca
te
a
s
we
ll
a
s
s
i
z
ing
the
c
a
pa
c
it
y
of
the
c
a
pa
c
it
or
in
the
r
a
dial
dis
tr
ibut
ion
s
ys
tem.
T
he
a
ppli
c
a
ti
on
o
f
f
uz
z
y
logi
c
f
or
plac
e
ment
of
the
c
a
pa
c
it
or
in
the
r
a
dial
d
is
tr
ibut
ion
s
ys
tem
is
r
e
por
ted
in
[
22]
.
M
or
e
ove
r
,
the
a
ppli
c
a
ti
on
of
a
wha
le
opt
i
mi
z
a
ti
on
a
lgor
it
hm
f
or
the
s
it
ing
o
f
c
a
pa
c
it
or
s
in
t
he
r
a
dial
dis
tr
ibut
ion
ne
twor
k
is
r
e
por
ted
in
[
23]
.
I
n
thi
s
pa
pe
r
,
thr
e
e
c
omput
ing
methods
i.
e
GA
,
P
S
O
a
nd
AB
C
a
r
e
e
mpl
oye
d
to
f
ind
the
opti
m
a
l
s
ize
of
the
s
hunt
c
a
p
a
c
it
or
a
s
r
e
a
c
ti
ve
powe
r
c
ompens
a
ti
on.
T
he
GA
,
P
S
O,
a
nd
AB
C
a
r
e
us
e
d
in
thi
s
s
tudy
be
c
a
us
e
they
ha
ve
be
e
n
popular
in
a
c
a
de
mi
a
a
nd
indus
tr
y
be
c
a
us
e
of
it
s
a
bil
it
y
to
e
f
f
e
c
ti
ve
ly
s
olve
highl
y
non
-
li
ne
a
r
pr
oblems
.
S
ome
be
ne
f
it
s
of
GA
a
r
e
de
f
ined
a
s
f
oll
ow:
a
)
i
t
ha
s
the
a
pti
tude
to
e
lude
be
ing
t
r
a
ppe
d
in
loca
l
opti
mal
due
to
GA
s
e
a
r
c
h
pa
r
a
ll
e
l
f
r
om
a
population
of
poin
ts
unli
ke
tr
a
dit
ional
a
nd
other
opti
mi
z
a
ti
on
methods
,
whic
h
s
e
a
r
c
h
f
r
om
a
s
ingl
e
point
a
nd
a
f
f
e
c
t
the
methods
t
o
tr
a
ppe
d
on
loca
l
opti
ma
,
b)
i
t
us
e
s
pr
oba
bil
is
ti
c
pr
e
f
e
r
e
nc
e
r
ules
r
a
ther
than
de
ter
mi
nis
ti
c
one
s
,
c
)
t
he
po
tential
s
olut
ion
pa
r
a
mete
r
s
a
r
e
e
nc
ode
d
to
c
hr
omos
ome
r
a
ther
tha
n
the
pa
r
a
mete
r
s
thems
e
lves
,
d)
t
he
f
it
ne
s
s
s
c
or
e
obtaine
d
f
r
om
ob
jec
ti
ve
f
unc
ti
ons
is
uti
li
z
e
d
without
o
ther
de
r
ivative
or
a
uxil
iar
y
inf
o
r
mation.
M
e
a
nwhile,
th
e
GA
ha
s
dr
a
wba
c
ks
due
to
it
ha
s
many
pa
r
a
mete
r
s
that
s
hould
be
s
e
t
a
pp
r
opr
iate
ly
a
nd
ha
s
e
xpe
ns
ive
c
omp
utational
c
os
t.
F
ur
ther
mor
e
,
the
P
S
O
method
ha
s
a
tt
r
a
c
ted
m
uc
h
a
tt
e
nti
on
f
r
om
r
e
s
e
a
r
c
he
r
c
omm
unit
ies
due
to
it
ha
s
f
e
w
pa
r
a
mete
r
s
to
a
djus
t,
it
c
a
n
be
s
im
ple
to
im
p
leme
nt,
it
c
a
n
c
onve
r
ge
f
a
s
t,
it
doe
s
n’
t
ne
e
d
a
c
r
os
s
ove
r
a
nd
mut
a
te,
it
ha
s
higher
p
r
oba
bil
it
y
a
nd
e
f
f
icie
nc
y
in
f
indi
ng
global
opti
ma,
a
nd
it
ha
s
s
hor
t
c
omput
a
ti
ona
l
ti
m
e
.
T
hos
e
a
r
e
the
a
dva
ntage
s
of
P
S
O
c
ompar
e
d
to
GA
.
W
hil
e
the
us
a
ge
of
AB
C
due
to
AB
C
ha
s
the
s
a
me
e
f
f
e
c
ti
ve
ne
s
s
(
f
indi
ng
the
t
r
ue
global
opti
mal
s
olut
ion)
a
s
the
P
S
O.
B
oth
P
S
O
a
nd
AB
C
a
r
e
ha
ving
s
igni
f
ica
nt
ly
be
tt
e
r
c
omput
a
ti
ona
l
e
f
f
icie
nc
y
(
f
e
we
r
f
unc
ti
on
e
v
a
luatio
ns
)
than
GA
.
2.
RE
S
E
AR
CH
M
E
T
HO
D
T
he
objec
ti
ve
f
unc
ti
on
is
to
mi
nim
ize
the
a
c
ti
ve
powe
r
los
s
(
P
l
o
s
s
)
of
the
tr
a
ns
mi
s
s
ion
li
ne
.
R
e
a
c
ti
ve
powe
r
c
ompens
a
ti
on
is
obtaine
d
by
ins
t
a
ll
ing
the
s
hunt
c
a
pa
c
it
or
on
J
a
va
-
M
a
dur
a
-
B
a
li
(
J
AM
AL
I
)
500
kV
powe
r
s
ys
tem
g
r
id
to
r
e
duc
e
the
l
os
s
e
s
of
P
l
o
s
s
.
T
he
a
c
ti
ve
powe
r
los
s
(
P
l
o
s
s
)
c
a
n
be
c
a
lcula
ted
us
ing
(
1)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
1693
-
6930
T
E
L
KO
M
NI
KA
T
e
lec
omm
un
C
omput
E
l
C
ontr
o
l
,
Vol.
18
,
No
.
1
,
F
e
br
ua
r
y
2020
:
376
-
384
378
22
1
[
(
)
2
c
os
]
Nl
loss
k
k
i
j
k
i
j
ij
k
P
g
t
V
V
t
V
V
=
=
+
−
(
1)
I
n
(
1
)
,
N
1
is
the
numbe
r
of
tr
a
ns
mi
s
s
ion
li
ne
s
,
g
k
is
c
onduc
tanc
e
of
br
a
nc
h
k
be
twe
e
n
i
a
nd
j
,
t
k
is
the
tap
r
a
ti
o
of
tr
a
ns
f
or
mer
k
,
V
i
is
the
volt
a
ge
magnitude
a
t
bus
i
,
a
nd
θ
ij
is
the
d
if
f
e
r
e
nc
e
o
f
vol
tage
a
ngle
be
twe
e
n
bus
e
s
i
a
nd
j
,
r
e
s
pe
c
ti
ve
ly.
B
y
obtaining
the
mi
n
im
um
objec
ti
ve
f
unc
ti
on,
the
de
ter
mi
na
ti
on
of
th
e
s
ize
of
the
s
hunt
c
a
pa
c
it
or
a
s
r
e
a
c
ti
ve
powe
r
c
ompens
a
ti
on
is
e
s
s
e
nti
a
l.
F
ur
ther
mor
e
,
the
e
qua
li
ty
c
ons
tr
a
int
i
n
opti
mal
powe
r
f
low
c
a
n
be
de
s
c
r
ibed
in
(
2)
a
nd
(
3
)
.
1
(
c
o
s
s
i
n
)
0
bus
ii
N
g
d
i
j
i
j
i
j
i
j
i
j
j
P
P
V
V
G
B
=
−
−
+
=
,
f
o
r
i
=
1
,
…,
N
pv
+
N
pq
(
2)
1
(
s
i
n
c
o
s
)
0
bus
i
i
i
N
g
d
c
i
j
i
j
i
j
i
j
i
j
j
Q
Q
Q
V
V
G
B
=
−
+
−
+
=
,
f
o
r
i
=
1
,
…,
N
pq
(
3)
whe
r
e
N
pv
a
nd
N
pq
a
r
e
the
number
of
ge
ne
r
a
to
r
s
a
nd
load
bus
e
s
,
r
e
s
pe
c
ti
ve
ly.
W
hil
e
the
inequa
li
ty
c
ons
tr
a
int
of
powe
r
f
low
c
a
n
be
c
a
lcula
ted
us
ing
(
4
)
,
(
5)
,
(
6
)
a
nd
(
7)
.
m
i
n
m
a
x
,
,
,
g
s
l
a
c
k
g
e
n
s
l
a
c
k
g
s
l
a
c
k
P
P
P
(
4)
m
in
m
a
x
i
i
i
L
L
L
V
V
V
,
f
o
r
i=1
,
…,
Npq
(5
)
m
in
m
a
x
i
i
i
g
g
g
Q
Q
Q
,
f
o
r
i
=
1
,
…,
N
g
e
n
(6
)
m
a
x
l
i
n
e
l
i
n
e
SS
,
f
o
r
i
=
1
,
…,
N
l
i
n
e
(7
)
T
he
inequa
li
ty
c
ons
tr
a
int
a
s
the
c
ontr
ol
va
r
iable
c
a
n
be
de
s
c
r
ibed
in
(
8
)
,
(
9
)
,
a
nd
(
10
)
:
m
in
m
a
x
i
i
i
g
e
n
g
e
n
g
e
n
V
V
V
,
f
o
r
i
=
1
,
…,
N
pv
(8
)
m
i
n
m
a
x
i
i
i
k
k
k
t
t
t
,
f
o
r
i
=
1
,
…,
N
tf
(9
)
m
i
n
m
a
x
i
i
i
c
c
c
Q
Q
Q
,
f
o
r
i
=
1
,
…,
N
c
o
m
p
(
10
)
whe
r
e
N
tf
a
nd
N
c
o
m
p
a
r
e
the
numbe
r
o
f
tap
tr
a
ns
f
or
mer
a
nd
r
e
a
c
ti
ve
c
ompens
a
ti
ng
de
vice
s
,
r
e
s
pe
c
ti
ve
ly.
3.
T
HE
P
ROP
OS
E
D
AL
GO
RI
T
HM
3.
1.
Genet
ic
a
lgorit
h
m
(
GA)
T
he
g
e
ne
ti
c
a
lgor
it
hm
(
GA
)
is
a
s
of
t
c
omput
ing
method
ins
pir
e
d
by
the
theor
y
of
ge
n
in
biol
ogica
l
s
c
ienc
e
s
[
6]
whe
r
e
int
r
oduc
e
d
by
J
ohn
Holland
in
1970.
C
hr
omos
ome
va
r
iation
will
a
f
f
e
c
t
the
r
e
pr
oduc
ti
on
r
a
te
a
nd
leve
l
of
a
bil
it
y
o
f
the
or
ga
nis
m
to
s
ur
vive
.
T
he
c
ontr
ol
pa
r
a
mete
r
s
o
f
GA
c
ons
is
t
of
popu
lation
s
ize
,
c
r
os
s
ove
r
,
a
nd
mut
a
ti
on.
B
a
s
ica
ll
y,
ther
e
a
r
e
f
ou
r
c
ondit
ions
that
a
f
f
e
c
t
the
e
va
luation
p
r
oc
e
s
s
of
GA
:
-
Or
ga
nis
m's
a
bil
it
y
to
r
e
pr
oduc
e
.
-
T
he
e
xis
tenc
e
of
populations
o
f
or
ga
nis
ms
that
c
a
n
pe
r
f
or
m
r
e
pr
oduc
ti
on
.
-
T
he
diver
s
it
y
o
f
or
ga
nis
ms
withi
n
a
population
.
-
Dif
f
e
r
e
nt
inabil
it
y
to
s
ur
vive.
S
tr
onge
r
indi
viduals
would
ha
ve
the
leve
l
of
s
ur
vival
a
nd
r
e
pr
oduc
ti
on
r
a
tes
a
r
e
higher
whe
n
c
ompar
e
d
to
a
n
indi
vidual
who
is
not
s
t
r
ong
.
At
a
c
e
r
tain
ti
me
(
ge
ne
r
a
ti
on
)
,
the
ove
r
a
ll
popu
lat
ion
will
c
ontain
mor
e
f
it
or
ga
n
-
is
ms
.
P
r
oc
e
s
s
ing
s
teps
of
Ge
ne
ti
c
A
lgor
it
hm
a
r
e
de
f
ined
a
s
f
oll
ow:
-
E
nc
oding
pr
oblem
s
olut
ion
int
o
a
s
e
t
of
c
hr
omos
o
me
s
tr
uc
tur
e
s
-
GA
ini
ti
a
li
z
e
d
to
a
population
wi
th
a
f
e
w
N
c
hr
om
os
omes
-
E
a
c
h
c
hr
omos
ome
will
be
e
nc
ode
d
int
o
a
n
indi
vid
ua
l
with
a
s
pe
c
if
ic
f
it
ne
s
s
va
lue.
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
M
NI
KA
T
e
lec
omm
un
C
omput
E
l
C
ontr
o
l
I
mpr
ov
e
me
nt
of
v
olt
age
pr
ofi
le
for
lar
ge
s
c
ale
pow
e
r
s
y
s
t
e
m
us
ing
s
oft
c
omputing…
(
M
uhamm
ad
A
bd
il
lah
)
379
-
S
e
lec
ti
ng
indi
viduals
with
the
be
s
t
f
it
ne
s
s
va
lue.
T
he
method
us
e
d
is
dif
f
e
r
e
nt,
f
or
e
xa
mpl
e
by
us
ing
the
method
r
oulette
whe
e
l.
-
T
o
ge
ne
r
a
te
a
ne
w
population,
it
is
ne
c
e
s
s
a
r
y
to
us
e
the
ge
ne
ti
c
a.
Cr
os
s
Ove
r
:
ge
ne
r
a
te
ne
w
of
f
s
pr
ing
by
r
e
plac
ing
s
o
me
of
the
inf
o
r
mation
f
r
om
the
pa
r
e
nt
c
hr
omos
omes
that
a
r
e
c
r
os
s
e
d
by.
b.
M
utation:
c
r
e
a
te
ne
w
indi
viduals
by
modi
f
ying
on
e
or
mo
r
e
ge
ne
s
in
the
c
hr
omos
ome.
3.
2.
P
ar
t
icle
s
war
m
op
t
im
izat
io
n
T
he
s
e
c
ond
opti
mi
z
a
ti
on
a
ppr
oa
c
h
e
mpl
oye
d
in
thi
s
pa
pe
r
is
pa
r
ti
c
le
s
wa
r
m
opti
mi
z
a
ti
on
(
P
S
O)
pr
opos
e
d
by
Ke
nne
dy
a
nd
E
be
r
ha
r
t
in
1995
[
10]
whe
r
e
thi
s
a
lgor
it
hm
mi
mi
c
s
the
be
ha
vior
of
bir
d
f
locking.
T
his
a
lgor
it
hm
is
a
population
-
ba
s
e
d
s
e
a
r
c
h
a
ppr
oa
c
h
whe
r
e
e
a
c
h
indi
vidual
in
a
population
is
pr
e
s
e
nted
a
s
a
pa
r
ti
c
le.
E
a
c
h
pa
r
ti
c
le
in
a
s
wa
r
m
f
li
e
s
a
r
ound
in
a
mul
ti
-
dim
e
ns
ional
s
e
a
r
c
h
s
pa
c
e
by
memor
izing
it
s
own
e
xpe
r
ienc
e
a
nd
the
e
xpe
r
ienc
e
of
ne
ighbor
ing
pa
r
ti
c
les
[
10]
.
F
ur
the
r
mor
e
,
the
f
lowc
ha
r
t
o
f
P
S
O
is
de
picte
d
in
F
igur
e
1.
F
igur
e
1.
F
lowc
ha
r
t
of
P
S
O
T
he
ve
locity
of
a
pa
r
t
icle
to
move
c
a
n
be
e
va
luate
d
us
ing
inf
or
mat
ion
f
r
om
:
(
i)
the
pr
e
s
e
nt
ve
locity,
(
ii
)
the
dis
tanc
e
be
twe
e
n
the
s
tar
ti
ng
pos
it
ion
with
the
be
s
t
pos
it
ion
that
ha
s
be
e
n
f
ound
.
B
a
s
e
d
on
the
c
onc
e
pt
of
P
S
O,
the
mathe
matica
l
r
e
pr
e
s
e
ntation
of
pa
r
ti
c
l
e
ve
locity
a
nd
pa
r
ti
c
le
pos
it
ion
c
a
n
be
e
xpr
e
s
s
e
d
u
s
ing
(
1
1
)
a
nd
(
1
2
)
,
1
1
1
2
2
(
)
(
)
i
k
k
k
i
i
b
e
s
t
i
b
e
s
t
i
v
v
c
r
P
x
c
r
G
x
+
=
+
−
+
−
(
11)
11
kk
i
i
i
x
x
v
++
=+
(
12)
i
n
(
11
)
a
nd
(
1
2
)
,
w
is
iner
ti
a
we
ight
,
c
is
the
s
pe
e
d
c
ons
tant,
the
r
and
is
a
uni
f
or
m
r
a
ndom
va
lue
in
t
he
r
a
nge
[
0,
1
]
,
P
b
e
s
t
is
the
be
s
t
pos
it
ion
o
f
the
i
-
th
pa
r
ti
c
le
a
nd
G
b
e
s
t
is
the
be
s
t
pos
it
ion
o
f
a
ll
P
b
e
s
t
.
S
T
A
R
T
I
n
i
s
i
a
l
i
s
a
t
i
o
n
o
f
C
u
r
r
e
n
t
P
o
s
i
t
i
o
n
a
n
d
V
e
l
o
c
i
t
y
O
b
j
e
c
t
i
v
e
F
u
n
c
t
i
o
n
P
o
s
i
t
i
o
n
U
p
d
a
t
e
I
n
d
i
v
i
d
u
a
l
B
e
s
t
U
p
d
a
t
e
V
e
l
o
c
i
t
y
U
p
d
a
t
e
G
l
o
b
a
l
B
e
s
t
U
p
d
a
t
e
M
a
x
I
t
e
r
S
T
O
P
Y
e
s
N
o
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
1693
-
6930
T
E
L
KO
M
NI
KA
T
e
lec
omm
un
C
omput
E
l
C
ontr
o
l
,
Vol.
18
,
No
.
1
,
F
e
br
ua
r
y
2020
:
376
-
384
380
3.
3
.
Ar
t
i
f
icial
b
e
e
c
olo
n
y
T
he
thi
r
d
opti
mi
z
a
ti
on
method
ut
il
ize
d
in
thi
s
s
tudy
is
a
n
a
r
ti
f
icia
l
be
e
c
olony
a
lgor
it
hm
int
r
oduc
e
d
by
Ka
r
a
boga
[
18]
whe
r
e
thi
s
a
lgor
it
hm
mi
m
ics
th
e
be
ha
vior
of
be
e
s
in
s
e
a
r
c
hing
f
or
the
f
ood
.
I
n
t
he
AB
C
a
lgor
it
hm,
the
c
oloni
e
s
o
f
a
r
ti
f
icia
l
be
e
s
a
r
e
c
las
s
if
ied
int
o
thr
e
e
c
a
tegor
ies
of
be
e
s
i.
e
the
e
mpl
oy
e
d
be
e
s
,
the
onlooker
be
e
s
,
a
nd
the
s
c
out
be
e
s
.
T
he
e
mpl
oye
d
be
e
s
s
e
e
k
the
ne
w
f
ood
s
our
c
e
that
ne
ve
r
pr
ior
to
be
ing
vi
s
it
e
d,
while
the
onlooker
be
e
s
that
a
r
e
wa
it
ing
i
n
the
da
nc
e
a
r
e
a
a
r
e
to
make
de
c
is
ions
in
the
pr
e
f
e
r
e
nc
e
of
f
ood
s
our
c
e
s
s
it
e
.
T
he
thi
r
d
be
e
s
a
r
e
the
s
c
out
be
e
s
that
a
r
e
doing
r
a
ndom
s
e
a
r
c
hing
f
or
the
f
ood
s
our
c
e
s
.
Note
d
that
only
one
e
mpl
oye
d
be
e
e
xis
ts
f
o
r
e
a
c
h
f
ood
s
our
c
e
.
T
hus
,
it
c
ould
be
e
mphas
ize
d
that
the
number
of
f
ood
s
our
c
e
s
a
r
ound
the
ne
s
t
e
qua
ls
the
s
e
t
of
e
mpl
oye
d
be
e
s
in
the
c
olony.
W
he
n
the
e
mpl
oye
d
be
e
s
r
un
out
of
their
f
ood
s
our
c
e
s
,
then,
they
be
c
ome
the
s
c
out
be
e
s
[
18]
.
T
he
loca
ti
on
of
a
f
ood
s
our
c
e
de
notes
a
potential
s
olut
ion
to
the
opti
mi
z
a
ti
on
is
s
ue
.
T
he
number
o
f
f
ood
s
our
c
e
s
c
a
ll
e
d
the
ne
c
tar
c
or
r
e
s
ponds
to
the
qua
l
it
y
(
f
it
ne
s
s
)
of
the
a
s
s
oc
iate
d
s
olut
ion.
F
ur
ther
mo
r
e
,
the
main
s
tep
s
of
AB
C
a
r
e
de
s
c
r
ibed
be
low
:
-
I
nit
iali
z
e
the
loca
ti
on
f
or
f
ood
s
our
c
e
.
-
De
volve
the
e
mpl
oye
d
be
e
s
onto
their
f
ood
s
our
c
e
s
a
nd
s
pe
c
if
y
the
number
of
their
ne
c
tar
s
.
A
ne
w
f
ood
s
our
c
e
of
e
a
c
h
e
mpl
oye
d
be
e
i
s
de
s
c
r
ibed
a
s
(
13)
.
T
he
ne
w
s
olut
ion
is
c
ompar
e
d
to
the
s
olut
ion
x
ij
a
f
ter
the
r
e
s
ult
in
v
i
j
a
nd
the
e
mpl
oye
d
be
e
e
xploi
ts
the
be
tt
e
r
s
our
c
e
.
()
i
j
i
j
i
j
i
j
k
j
v
x
x
x
=
+
−
(
13)
-
De
volve
the
onlooker
be
e
s
towa
r
ds
the
f
ood
s
our
c
e
s
a
nd
s
pe
c
if
y
the
nu
mber
o
f
their
ne
c
tar
s
.
I
n
thi
s
s
tep,
the
pr
oba
bil
it
y
is
e
mpl
oye
d
by
a
n
onlooker
be
e
to
p
ick
a
f
ood
s
our
c
e
a
nd
yields
a
ne
w
s
our
c
e
in
the
loc
a
ti
on
of
the
c
hos
e
n
f
ood
s
our
c
e
.
W
hil
e
f
or
the
e
mpl
oye
d
be
e
,
the
pr
e
f
e
r
r
e
d
f
ood
s
our
c
e
is
de
f
ined
to
be
e
xpl
oit
e
d
by
(
1
4
).
1
i
i
SN
i
i
fit
P
fit
=
=
(
14)
-
De
ter
mi
ne
the
f
ood
s
our
c
e
to
be
f
o
r
s
a
ke
n
a
nd
a
ll
oc
a
te
it
s
e
mpl
oye
d
be
e
a
s
a
s
c
out
f
or
f
indi
ng
the
ne
w
f
ood
s
our
c
e
s
ba
s
e
d
on
a
r
a
ndom
s
e
a
r
c
h
by
(
1
5
).
m
a
x
m
i
n
m
i
n
[
0
,1
]
(
)
jj
jj
i
x
x
r
a
n
d
x
x
=
+
−
(1
5
)
-
M
e
mor
ize
the
be
s
t
f
ood
s
our
c
e
f
ound
s
o
f
a
r
.
-
Go
s
teps
2
-
unti
l
the
ter
mi
na
ti
on
c
r
it
e
r
ia
a
r
e
s
a
ti
s
f
ied.
4.
NU
M
E
RI
C
AL
RE
S
UL
T
S
I
n
thi
s
pa
pe
r
,
the
tes
t
s
ys
tem
is
J
a
va
-
M
a
dur
a
-
B
a
li
(
J
AM
AL
I
)
500kV
powe
r
gr
id
a
s
de
picte
d
in
F
igur
e
2
.
T
he
da
ta
of
the
J
AM
AL
I
500kV
powe
r
gr
id
is
take
n
f
r
o
m
[
24]
.
S
im
ulation
is
c
onduc
ted
b
y
us
ing
a
MA
T
L
AB
s
of
twa
r
e
e
nvir
onment.
F
ur
ther
mor
e
,
the
a
ppr
opr
iate
c
ontr
ol
pa
r
a
mete
r
p
lays
ke
y
r
ole
in
the
c
omput
a
ti
on
tec
hniques
a
nd
is
ve
r
y
s
e
ns
it
ive
pr
oblem
o
f
f
indi
ng
a
good
s
olut
ion
f
o
r
the
s
of
t
c
o
mput
ing
tec
hnique.
T
he
pa
r
a
mete
r
s
of
s
of
t
c
omput
ing
a
ppr
o
a
c
he
s
us
e
d
f
or
the
s
im
ulations
a
r
e
de
f
ined
a
s
f
oll
o
w
:
GA
par
ame
ter
s
:
N
G
e
n
=
Dimens
ion
of
p
r
oblem;
C
r
os
s
ove
r
pr
oba
bil
i
t
y
=
0.
8;
P
opulation
s
iz
=
50;
M
utation
pr
oba
bil
it
y
=
0.
05;
M
a
xim
um
ge
ne
r
a
ti
on
s
=
150
P
SO
par
ame
ter
s
:
N
V
a
r
i
a
b
e
l
=
Dimens
ion
of
pr
oblem;
S
oc
ial
pa
r
a
mete
r
(
C
2)
=
0.
9;
W
e
ight
(
w
)
=
0.
9
;
C
ognit
ive
pa
r
a
mete
r
(
C
1)
=
1.
5;
P
opulation
s
ize
=
50;
M
a
xim
um
it
e
r
a
ti
ons
=
150;
ABC
par
ame
ter
s
:
Dimens
ion
(
D)
=
Di
mens
ion
of
p
r
oblem;
F
oodNumbe
r
=
NP/
2;
li
mi
t
=
F
oodNumbe
r
*D;
c
olony
s
ize
(
NP)
=
50;
M
a
xim
um
c
yc
les
=
150;
T
he
dim
e
ns
ion
s
e
a
r
c
h
s
pa
c
e
(
Dim)
of
e
a
c
h
a
lgor
i
th
m
de
pe
nds
on
the
number
of
c
ompens
a
ti
ng
de
vice
s
c
or
r
e
s
ponding
to
the
number
of
bus
s
ys
tems
that
ha
ve
volt
a
ge
va
lue
(
p.
u)
lowe
r
than
vo
lt
a
ge
r
e
f
e
r
e
nc
e
s
tanda
r
d
a
r
ound
-
5%
of
it
s
nomi
na
l
va
lue.
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
M
NI
KA
T
e
lec
omm
un
C
omput
E
l
C
ontr
o
l
I
mpr
ov
e
me
nt
of
v
olt
age
pr
ofi
le
for
lar
ge
s
c
ale
pow
e
r
s
y
s
t
e
m
us
ing
s
oft
c
omputing…
(
M
uhamm
ad
A
bd
il
lah
)
381
F
igur
e
2.
S
ingl
e
li
ne
diagr
a
m
of
J
AM
AL
I
500
kV
t
r
a
ns
mi
s
s
ion
s
ys
tem
[
25]
T
he
e
va
luation
o
f
f
it
ne
s
s
f
or
e
a
c
h
population
o
f
the
GA
,
P
S
O,
a
nd
AB
C
a
lgor
i
thm
s
is
f
r
e
que
ntl
y
c
onduc
ted
in
one
it
e
r
a
ti
on.
T
he
c
onve
r
ge
nc
e
c
ha
r
a
c
ter
is
ti
c
of
thr
e
e
s
of
t
c
omput
ing
tec
hniques
is
c
om
pa
r
e
d
to
the
number
of
f
it
ne
s
s
e
va
luations
due
to
the
f
it
ne
s
s
e
va
luation
is
c
ons
umi
ng
the
opti
mi
z
a
ti
on
pr
oc
e
s
s
ti
me.
T
he
c
onve
r
ge
nc
e
be
ha
vior
of
a
ll
s
of
t
c
omput
ing
a
p
pr
oa
c
he
s
is
de
picte
d
in
F
igur
e
3.
F
igur
e
3
il
lus
tr
a
te
s
that
a
ll
s
of
t
c
omput
ing
a
ppr
oa
c
he
s
obtaine
d
s
a
ti
s
f
a
c
tor
y
pe
r
f
or
manc
e
s
to
r
e
a
c
h
their
c
onve
r
ge
nc
e
va
lues
f
or
th
e
c
hos
e
n
pa
r
a
mete
r
s
.
T
he
c
onve
r
ge
nc
e
c
ha
r
a
c
ter
is
ti
c
s
of
GA
a
r
e
f
a
s
ter
than
AB
C
but
may
not
inves
ti
ga
te
de
e
ply
f
or
potential
c
a
ndidate
s
a
s
f
ound
by
AB
C
.
W
hil
e
P
S
O
towa
r
ds
c
onve
r
ge
nc
e
va
lue
quickly
a
nd
e
xplo
r
e
s
a
good
potential
s
olut
ion
r
a
ther
than
other
s
of
t
c
omput
ing
methods
.
T
a
ble
1
s
hows
the
c
ompar
is
on
of
tot
a
l
los
s
be
f
or
e
a
nd
a
f
ter
the
ins
talli
ng
of
c
a
pa
c
it
or
s
f
r
om
e
a
c
h
of
t
he
s
e
methods
.
T
he
r
e
s
ult
s
obtaine
d
a
r
e
that
the
GA
method
c
a
n
r
e
duc
e
the
tr
a
ns
mi
s
s
ion
li
ne
los
s
e
s
11.
38%
.
A
be
tt
e
r
r
e
s
ult
is
obtaine
d
by
us
ing
P
S
O
a
nd
AB
C
a
lgor
it
hm
P
a
i
t
o
n
G
r
a
t
i
S
u
r
a
b
a
y
a
B
a
r
a
t
G
r
e
s
i
k
T
a
n
j
u
n
g
j
a
t
i
U
n
g
a
r
a
n
K
e
d
i
r
i
P
e
d
a
n
M
a
n
d
i
r
a
c
a
n
S
a
g
u
l
i
n
g
T
a
s
i
k
m
a
l
a
y
a
C
i
r
a
t
a
C
i
b
a
t
u
M
u
a
r
a
t
a
w
a
r
B
e
k
a
s
i
B
a
n
d
u
n
g
D
e
p
o
k
G
a
n
d
u
l
C
i
l
e
g
o
n
S
u
r
a
l
a
y
a
K
e
m
b
a
n
g
a
n
C
a
w
a
n
g
C
i
b
i
n
o
n
g
1
2
3
4
5
6
7
8
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
2
1
2
2
2
3
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
1693
-
6930
T
E
L
KO
M
NI
KA
T
e
lec
omm
un
C
omput
E
l
C
ontr
o
l
,
Vol.
18
,
No
.
1
,
F
e
br
ua
r
y
2020
:
376
-
384
382
with
a
pe
r
c
e
ntage
de
c
r
e
a
s
e
of
11.
63
%
.
W
hil
e
T
a
ble
2
de
picts
the
c
a
pa
c
it
y
of
c
a
pa
c
it
or
s
ins
talled
on
e
a
c
h
of
the
c
r
it
ica
l
bus
e
s
.
T
he
c
ompar
is
on
o
f
the
volt
a
ge
leve
l
on
e
a
c
h
r
e
s
ult
is
de
picte
d
in
F
igur
e
4
.
I
t
i
s
f
ound
t
ha
t
a
f
ter
the
s
ys
tem
is
c
ompens
a
ted,
the
volt
a
ge
dr
ops
de
c
r
e
a
s
e
in
or
de
r
to
obtain
be
tt
e
r
pe
r
f
or
manc
e
of
volt
a
g
e
.
F
igur
e
3.
C
onve
r
ge
nc
e
c
ha
r
a
c
ter
is
ti
c
s
of
a
lgor
i
thm
s
F
igur
e
4
.
C
ompar
is
on
of
volt
a
ge
s
leve
l
T
a
ble
1.
C
ompar
is
on
of
tot
a
l
a
c
ti
ve
powe
r
los
s
B
e
f
or
e
GA
PSO
A
B
C
T
ot
a
l
L
os
s
(
M
W
)
136.539
120.999
120.666
120.666
T
he
di
f
f
e
r
e
nc
e
of
t
ot
a
l
lo
s
s
(
M
W
)
-
15.54
15.873
15.873
%
-
11.38
11.63
11.63
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
M
NI
KA
T
e
lec
omm
un
C
omput
E
l
C
ontr
o
l
I
mpr
ov
e
me
nt
of
v
olt
age
pr
ofi
le
for
lar
ge
s
c
ale
pow
e
r
s
y
s
t
e
m
us
ing
s
oft
c
omputing…
(
M
uhamm
ad
A
bd
il
lah
)
383
T
a
ble
2.
Optim
iza
ti
on
o
f
s
hunt
c
a
pa
c
it
or
’
s
s
ize
U
ni
t
B
us
C
ompe
ns
a
ti
on
C
ompe
ns
a
ti
on
C
ompe
ns
a
ti
on
GA
PSO
A
B
C
(
M
V
A
R
)
(
M
V
A
R
)
(
M
V
A
R
)
1
13
370.451
400
400
2
14
376.878
400
400
3
19
399.272
248.244
248.245
4
20
386.468
400
400
5
21
369.731
400
400
T
ot
a
l
1902.8
1848.244
1848.245
5.
CONC
L
USI
ON
I
n
th
is
pa
pe
r
,
the
us
e
of
th
r
e
e
di
f
f
e
r
e
nt
s
of
t
c
omp
uti
ng
tec
hniques
to
ove
r
c
ome
the
r
e
a
c
ti
ve
powe
r
c
ompens
a
ti
on
is
s
ue
in
the
tr
a
ns
mi
s
s
ion
s
ys
tem
ha
s
be
e
n
inves
ti
ga
ted.
F
r
om
the
s
im
ulation
r
e
s
ult
,
it
i
s
s
hown
that
the
GA
method
to
r
e
a
c
h
c
onve
r
ge
n
c
e
on
the
2
0th
it
e
r
a
ti
on
,
P
S
O
on
the
3r
d
i
ter
a
ti
on
a
nd
AB
C
on
the
23
rd
it
e
r
a
ti
on.
T
he
AB
C
da
n
P
S
O
a
lgor
it
hms
c
a
n
r
e
duc
e
the
tot
a
l
a
c
ti
ve
powe
r
los
s
by
15.
873
M
W
,
f
r
om
136.
539
M
W
to
120.
666
M
W
.
T
he
s
e
r
e
s
ult
s
obtaine
d
a
r
e
be
tt
e
r
than
the
GA
a
ppr
oa
c
h
whe
r
e
i
t
only
c
a
n
r
e
duc
e
by
15.
54
M
W
,
f
r
om
136.
539
M
W
to
120.
999
M
W
.
F
r
om
a
ll
the
s
im
ulation
r
e
s
ult
s
,
the
P
S
O
a
lgor
it
h
m
is
ve
r
y
s
upe
r
ior
r
a
ther
than
the
other
methods
in
the
view
point
of
the
s
e
lec
ted
s
e
t
of
pa
r
a
mete
r
s
to
tac
kle
the
r
e
a
c
ti
ve
powe
r
c
ompens
a
ti
on
is
s
ue
in
the
tr
a
ns
mi
s
s
ion
s
ys
tem.
AC
KNOWL
E
DGE
M
E
NT
S
T
he
a
uthor
s
thank
the
a
nonymous
r
e
view
e
r
s
f
o
r
their
pr
e
c
ious
c
omm
e
nts
a
nd
s
ugge
s
ti
ons
f
or
the
im
pr
ove
ment
o
f
thi
s
pa
pe
r
.
RE
F
E
RE
NC
E
S
[1
]
M.
D
i
x
i
t
,
et
a
l
.
,
"
O
p
t
i
ma
l
In
t
e
g
rat
i
o
n
o
f
Sh
u
n
t
Cap
aci
t
o
r
Ban
k
s
i
n
D
i
s
t
r
i
b
u
t
i
o
n
N
et
w
o
r
k
s
fo
r
A
s
s
e
s
s
me
n
t
o
f
T
ech
n
o
-
E
co
n
o
m
i
c
A
s
s
et
,
"
Co
m
p
u
t
e
r
s
&
E
l
ect
r
i
c
a
l
E
n
g
i
n
eer
i
n
g
,
v
o
l
.
7
1
,
p
p
.
3
3
1
-
3
4
5
,
O
c
t
2
0
1
8
.
[2
]
D.
S.
K
i
r
s
ch
e
n
,
et
a
l
.
,
“MW
/
V
o
l
t
a
g
e
Co
n
t
r
o
l
i
n
L
i
n
ear
Pr
o
g
ramm
i
n
g
Bas
e
d
O
p
t
i
mal
Po
w
er
Fl
o
w
,
”
I
E
E
E
Tr
a
n
s
.
P
o
wer
S
ys
t
.
,
v
o
l
.
3
,
n
o
.
2
,
p
p
.
4
8
1
–
4
8
9
,
May
1
9
8
8
.
[3
]
N
.
G
ru
d
i
n
i
n
,
"
React
i
v
e
p
o
w
er
o
p
t
i
mi
za
t
i
o
n
u
s
i
n
g
s
u
cce
s
s
i
v
e
q
u
ad
ra
t
i
c
p
ro
g
rammi
n
g
met
h
o
d
,
"
i
n
IE
E
E
T
r
a
n
s
a
ct
i
o
n
s
o
n
P
o
wer
S
y
s
t
em
s
,
v
o
l
.
1
3
,
n
o
.
4
,
p
p
.
1
2
1
9
-
1
2
2
5
,
N
o
v
1
9
9
8
.
[4
]
K
.
A
o
k
i
,
M.
Fa
n
an
d
A
.
N
i
s
h
i
k
o
ri
,
"
O
p
t
i
mal
V
A
r
p
l
an
n
i
n
g
b
y
a
p
p
r
o
x
i
mat
i
o
n
me
t
h
o
d
f
o
r
recu
r
s
i
v
e
m
i
x
e
d
-
i
n
t
eg
er
l
i
n
ear
p
ro
g
rammi
n
g
,
"
i
n
I
E
E
E
Tr
a
n
s
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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S
N
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T
E
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KO
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NI
KA
T
e
lec
omm
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C
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E
l
C
ontr
o
l
,
Vol.
18
,
No
.
1
,
F
e
br
ua
r
y
2020
:
376
-
384
384
[1
8
]
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n
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.
)
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m
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p
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ra
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w
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as
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at
PT
.
Pak
o
ak
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n
a,
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ak
ar
t
a,
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d
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s
i
a.
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