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ar
e
co
m
p
ar
ed
w
it
h
v
ar
io
u
s
alg
o
r
it
h
m
s
to
ch
ec
k
its
s
u
p
r
e
m
ac
y
.
2.
O
B
J
E
CT
I
V
E
F
UNC
T
I
O
N
T
h
e
o
b
j
ec
tiv
e
f
u
n
ct
io
n
o
f
ca
p
ac
ito
r
allo
ca
tio
n
p
r
o
b
lem
is
t
o
m
in
i
m
ize
th
e
to
tal
co
s
t
d
u
e
to
en
er
g
y
lo
s
s
an
d
r
ea
ctiv
e
p
o
w
er
co
m
p
en
s
atio
n
u
n
d
er
ce
r
tain
o
p
er
atin
g
co
n
s
tr
ai
n
ts
.
Ma
th
e
m
atica
ll
y
t
h
e
p
r
o
b
lem
c
an
b
e
w
r
itte
n
as:
Min
.
f
=
E
n
er
g
y
lo
s
s
co
s
t +
R
e
ac
tiv
e
p
o
w
er
co
m
p
e
n
s
atio
n
co
s
t
Min
.
f
=
K
p
*P
loss
*
t+
K
i
*
C
B
+ K
C
*
∑
(
1
)
w
h
er
e
th
e
co
n
s
ta
n
ts
ar
e
tak
e
n
as [
1
9
]
.
T
h
e
o
p
e
r
atin
g
co
n
s
tr
ain
ts
ar
e:
1.
T
h
e
v
o
ltag
e
o
f
ea
ch
b
u
s
m
u
s
t
b
e
m
ai
n
tai
n
ed
b
et
w
ee
n
s
p
ec
if
i
ed
li
m
its
.
V
m
in
≤
V≤
V
max
2.
T
h
e
to
tal
r
ea
ctiv
e
p
o
w
er
in
j
ec
ted
is
n
o
t
to
ex
ce
ed
t
h
e
to
tal
r
ea
ctiv
e
p
o
w
er
d
e
m
an
d
i
n
r
ad
ial
d
is
tr
ib
u
tio
n
s
y
s
te
m
.
3.
T
h
e
r
ea
ctiv
e
p
o
w
er
in
j
ec
tio
n
at
ea
ch
ca
n
d
id
ate
b
u
s
is
g
i
v
en
b
y
i
ts
m
i
n
i
m
u
m
a
n
d
m
ax
i
m
u
m
co
m
p
e
n
s
at
io
n
li
m
it.
3.
P
RO
P
O
SE
D
M
E
T
H
O
DO
L
O
G
Y
An
an
al
y
tical
ap
p
r
o
ac
h
h
as
b
ee
n
p
r
esen
ted
f
o
r
ca
p
ac
ito
r
p
l
ac
e
m
en
t
p
r
o
b
lem
.
T
h
e
Po
w
er
Vo
ltag
e
Sen
s
iti
v
it
y
C
o
n
s
tan
t
(
P
VSC
)
i
s
p
r
o
p
o
s
ed
to
d
eter
m
in
e
t
h
e
s
i
ze
an
d
lo
ca
tio
n
o
f
ca
p
ac
ito
r
u
n
its
.
T
h
is
co
n
s
ta
n
t
tak
es
ac
ti
v
e
p
o
w
er
lo
s
s
an
d
v
o
ltag
e
li
m
i
ts
o
f
in
d
i
v
id
u
al
b
u
s
es
in
ac
co
u
n
t
a
n
d
s
u
g
g
e
s
t
th
e
o
p
tim
a
l
lo
ca
tio
n
o
f
th
e
ca
p
ac
ito
r
.
(
2
)
w
h
er
e,
P
realloss
: b
ase
ca
s
e
r
ea
l p
o
w
er
l
o
s
s
.
P
caploss
: a
ctiv
e
p
o
w
er
lo
s
s
a
f
ter
ca
p
ac
ito
r
p
lace
m
en
t a
t i
th
b
u
s
.
V
m
ax
i
s
m
ax
i
m
u
m
b
u
s
v
o
ltag
e
in
p
u
a
f
ter
ca
p
ac
ito
r
p
lace
m
e
n
t a
t i
th
b
u
s
.
V
m
in
i
s
m
in
i
m
u
m
b
u
s
v
o
lta
g
e
i
n
p
u
af
ter
ca
p
ac
ito
r
p
lace
m
e
n
t
at
i
th
b
u
s
.
Fo
r
o
p
tim
al
p
lace
m
en
t o
f
ca
p
ac
ito
r
b
an
k
th
e
v
al
u
e
o
f
P
VSC
s
h
o
u
ld
b
e
m
in
i
m
u
m
.
C
o
m
p
u
tatio
n
al
p
r
o
ce
s
s
f
o
r
p
r
o
p
o
s
ed
an
al
y
tical
tec
h
n
iq
u
e
is
e
x
p
lain
ed
b
elo
w
:
S
tep
1
:
R
u
n
t
h
e
b
a
s
e
ca
s
e
lo
a
d
flo
w
p
r
o
g
r
a
m
a
n
d
c
a
lcu
la
te
r
ea
l p
o
w
er lo
s
s
P
realloss
.
S
tep
2
:
S
et
a
n
y
s
iz
e
o
f c
a
p
a
cit
o
r
u
n
it a
n
d
r
u
n
lo
a
d
flo
w
p
r
o
g
r
a
m.
S
tep
3
:
C
a
lcu
l
a
te
th
e
r
ea
l p
o
w
er lo
s
s
o
f th
e
s
ystem
a
n
d
“PV
S
C
” v
a
lu
es fo
r
ea
ch
b
u
s
u
s
in
g
eq
.
2
.
S
tep
4
:
N
o
w
va
r
y
th
e
s
iz
e
o
f
ca
p
a
cito
r
in
min
u
te
s
tep
(
1
0
kV
A
R
)
a
n
d
co
mp
u
te
r
ea
l
p
o
w
er
lo
s
s
b
y
r
u
n
n
in
g
lo
a
d
flo
w
p
r
o
g
r
a
m.
S
tep
5
:
S
to
r
e
th
e
s
iz
e
o
f c
a
p
a
c
ito
r
w
h
ich
g
ives le
a
s
t a
mo
u
n
t
o
f rea
l p
o
w
er lo
s
s
.
S
tep
6
:
Th
e
b
u
s
,
w
h
ich
h
a
s
lea
s
t “P
V
S
C
” v
a
lu
e,
w
ill b
e
th
e
o
p
tima
l lo
ca
tio
n
o
f c
a
p
a
cito
r
u
n
it.
S
tep
7
:
R
ep
ea
t
S
tep
s
4
to
6
to
f
in
d
mo
r
e
lo
ca
tio
n
o
f c
a
p
a
cito
r
s
.
4.
T
E
ST
R
E
SU
L
T
S AN
D
D
I
S
CUSS
I
O
N
I
n
p
r
o
p
o
s
ed
an
al
y
tica
l
ap
p
r
o
ac
h
,
ca
p
ac
ito
r
u
n
it
s
ar
e
p
lac
ed
to
m
i
n
i
m
ize
r
ea
l
p
o
w
er
l
o
s
s
a
n
d
to
en
h
a
n
ce
v
o
ltag
e
p
r
o
f
ile.
A
s
tan
d
ar
d
s
y
s
te
m
o
f
6
9
b
u
s
an
d
a
r
ea
l
1
3
0
b
u
s
d
is
tr
ib
u
tio
n
s
y
s
te
m
o
f
J
am
w
ar
a
m
g
ar
h
,
J
aip
u
r
ar
e
e
m
p
lo
y
ed
to
i
m
p
le
m
e
n
t
t
h
e
p
r
o
p
o
s
ed
tech
n
iq
u
e.
T
h
i
s
co
m
p
lete
s
c
h
e
m
e
i
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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C
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T
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it
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h
n
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li
k
e
Dir
e
ct
Sear
ch
A
l
g
o
r
ith
m
[
2
1
]
,
Differ
en
tia
l
E
vo
lu
tio
n
a
lg
o
r
ith
m
[
2
2
]
,
Fl
o
w
er
P
o
llin
atio
n
A
l
g
o
r
ith
m
[
2
3
]
.
T
h
e
co
m
p
ar
ativ
e
an
al
y
s
is
is
s
h
o
w
n
in
T
ab
le
2
.
I
t
is
n
o
ticed
f
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m
tab
le
t
h
at
t
h
e
p
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s
ed
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ax
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m
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m
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s
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ctio
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ize
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f
ca
p
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r
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k
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e
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.
Ja
lali,
K.
Zare
,
Op
ti
m
a
l
a
ll
o
c
a
ti
o
n
o
f
c
a
p
a
c
it
o
rs
in
ra
d
ial/
m
e
sh
d
istri
b
u
ti
o
n
sy
ste
m
s
u
sin
g
m
ix
e
d
in
teg
e
r
n
o
n
li
n
e
a
r
p
ro
g
ra
m
m
in
g
a
p
p
r
o
a
c
h
,
In
t.
J
.
E
lec
tric P
o
we
r S
y
st.
Res
.
1
0
7
(
2
0
1
4
)
1
1
9
–
1
2
4
.
[4
]
S
w
a
ru
p
KS.
Ge
n
e
ti
c
a
lg
o
ri
th
m
f
o
r
o
p
t
ima
l
c
a
p
a
c
it
o
r
a
ll
o
c
a
ti
o
n
i
n
ra
d
i
a
l
d
istrib
u
ti
o
n
sy
ste
ms
.
In
:
P
r
o
c
e
e
d
in
g
s
o
f
th
e
6
t
h
W
S
EA
S
in
tern
a
ti
o
n
a
l
c
o
n
f
e
r
e
n
c
e
o
n
e
v
o
lu
t
io
n
a
ry
,
L
isb
o
n
,
P
o
rtu
g
a
l,
J
u
n
e
1
6
–
1
8
,
2
0
0
5
.
p
.
1
5
2
–
9.
[5
]
H.D.
Ch
ian
g
,
J.C.
W
a
n
g
,
O.
Co
c
k
in
g
s,
H.D.
S
h
in
,
Op
ti
m
a
l
c
a
p
a
c
it
o
r
p
lac
e
m
e
n
ts
in
d
istri
b
u
ti
o
n
sy
ste
m
s:
p
a
rt
1
:
a
n
e
w
f
o
r
m
u
latio
n
a
n
d
th
e
o
v
e
ra
ll
p
ro
b
lem
,
IEE
E
T
ra
n
s.
P
o
we
r De
li
v
.
5
(
2
)
(
1
9
9
0
)
6
3
4
–
6
4
2
.
[6
]
Da
s
P
,
Ba
n
e
rjee
S
.
P
lac
e
m
e
n
t
o
f
c
a
p
a
c
it
o
r
in
a
ra
d
ial
d
istri
b
u
ti
o
n
s
y
ste
m
u
sin
g
lo
ss
se
n
siti
v
it
y
fa
c
to
r
a
n
d
c
u
c
k
o
o
se
a
rc
h
a
lg
o
rit
h
m
.
In
t
J
S
c
i
Res
M
a
n
a
g
e
,
2
0
1
3
;
2:
7
5
1
–
7.
[7
]
Ha
m
o
u
d
a
A
,
S
a
y
a
h
S
.
Op
ti
m
a
l
c
a
p
a
c
it
o
rs
siz
in
g
in
d
istri
b
u
ti
o
n
f
e
e
d
e
rs
u
sin
g
h
e
u
risti
c
s
se
a
rc
h
b
a
se
d
n
o
d
e
sta
b
il
it
y
in
d
ice
s.
I
n
t
J
El
e
c
tr
P
o
we
r E
n
e
rg
y
S
y
st
2
0
1
3
;
4
6
:
56
–
6
4
.
[8
]
Am
a
n
if
a
r
O,
G
o
lsh
a
n
M
EH.
Op
ti
m
a
l
d
istri
b
u
ted
g
e
n
e
ra
ti
o
n
p
lac
e
m
e
n
t
a
n
d
siz
in
g
f
o
r
lo
ss
a
n
d
TH
D
re
d
u
c
ti
o
n
a
n
d
v
o
lt
a
g
e
p
ro
f
il
e
im
p
ro
v
e
m
e
n
t
in
d
istri
b
u
t
io
n
sy
ste
m
s
u
sin
g
p
a
rti
c
le
sw
a
r
m
o
p
ti
m
i
z
a
ti
o
n
a
n
d
se
n
siti
v
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y
a
n
a
l
y
sis.
In
t
J
T
e
c
h
Ph
y
s P
ro
b
l
E
n
g
,
2
0
1
1
;
3
(2
):
47
–
5
3
.
[9
]
P
ra
k
a
sh
K.
S
y
d
u
lu
M
.
P
a
rti
c
le
s
w
a
r
m
o
p
ti
m
i
z
a
ti
o
n
b
a
se
d
c
a
p
a
c
it
o
r
p
lac
e
m
e
n
t
o
n
ra
d
ial
d
istr
ib
u
ti
o
n
sy
ste
m
s.
IEE
E
p
o
we
r en
g
in
e
e
rin
g
so
c
iety
g
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n
e
ra
l
me
e
ti
n
g
,
2
0
0
7
,
2
4
–
2
8
Ju
n
e
2
0
0
7
.
p
.
1
–
5.
[1
0
]
M
.
M
.
L
e
g
h
a
,
M
.
T
a
v
a
k
o
li
,
F
.
Os
to
v
a
r,
M
.
A
.
Ha
sh
e
m
a
b
a
d
i,
Ca
p
a
c
it
o
r
p
lac
e
m
e
n
t
in
ra
d
ial
d
istri
b
u
ti
o
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sy
ste
m
f
o
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p
ro
v
e
n
e
t
w
o
rk
e
f
f
i
c
ien
c
y
u
sin
g
a
rti
f
icia
l
b
e
e
c
o
lo
n
y
,
In
t.
J
.
En
g
.
Res
.
Ap
p
l
.
3
(6
)
(2
0
1
3
)
2
2
8
–
2
3
3
.
[1
1
]
P
.
Da
s,
S
.
Ba
n
e
rjee
,
Op
ti
m
a
l
si
z
in
g
a
n
d
p
lac
e
m
e
n
t
o
f
c
a
p
a
c
it
o
r
in
a
ra
d
ial
d
istri
b
u
ti
o
n
sy
ste
m
u
sin
g
lo
ss
se
n
siti
v
it
y
f
a
c
to
r
a
n
d
f
iref
l
y
a
lg
o
rit
h
m
,
In
t.
J
.
En
g
.
C
o
mp
u
t.
S
c
i
.
3
(4
)
(2
0
1
4
)
5
3
4
6
–
5
3
5
2
.
[1
2
]
S
.
S
u
lt
a
n
a
,
P
.
K.
Ro
y
,
Op
ti
m
a
l
c
a
p
a
c
it
o
r
p
lac
e
m
e
n
t
in
ra
d
ial
d
ist
rib
u
ti
o
n
sy
ste
m
s
u
sin
g
tea
c
h
in
g
lea
rn
in
g
b
a
se
d
o
p
ti
m
iza
ti
o
n
,
I
n
t.
J
.
El
e
c
tr.
P
o
we
r E
n
e
rg
y
S
y
st
.
5
4
(2
0
1
4
)
3
8
7
–
3
9
8
.
[1
3
]
R.
S
.
Ra
o
,
S
.
V
.
L
.
Na
ra
si
m
h
a
m
,
M
.
Ra
m
a
k
in
g
a
r
a
ju
,
Op
ti
m
a
l
c
a
p
a
c
it
o
r
p
lac
e
m
e
n
t
in
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ra
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ial
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ist
rib
u
ti
o
n
sy
ste
m
u
sin
g
p
la
n
t
g
ro
w
th
sim
u
latio
n
a
lg
o
rit
h
m
,
In
t.
J
.
El
e
c
tr.
P
o
we
r E
n
e
r
g
y
S
y
st
.
3
3
(
2
0
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1
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1
3
3
–
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1
3
9
.
0
20
40
60
80
100
120
0
.
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8
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s
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o
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t
ca
p
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ci
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o
r
w
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ca
p
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r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
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8708
I
J
E
C
E
Vo
l.
7
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No
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2
,
A
p
r
il 2
0
1
7
:
7
4
8
–
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753
[1
4
]
S
irj
a
n
i
R,
M
o
h
a
m
e
d
A
,
S
h
a
re
e
f
H.
Op
ti
m
a
l
c
a
p
a
c
it
o
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lac
e
m
e
n
t
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ra
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ial
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istri
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u
ti
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sy
ste
m
s
u
sin
g
h
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rm
o
n
y
se
a
rc
h
a
lg
o
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h
m
.
J
Ap
p
l
S
c
i
,
2
0
1
0
;
1
0
(
2
3
):
2
9
9
8
–
3
0
0
6
.
[1
5
]
A
.
A
.
El
-
F
e
rg
a
n
y
,
A
.
Y.
A
b
d
e
laz
iz,
Ca
p
a
c
it
o
r
a
ll
o
c
a
ti
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s
in
ra
d
i
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l
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istri
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ti
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e
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rk
s
u
sin
g
c
u
c
k
o
o
se
a
rc
h
a
lg
o
rit
h
m
,
IET
Ge
n
e
ra
ti
o
n
T
ra
n
s
m.
Distrib
.
8
(
2
)
(2
0
1
4
)
2
2
3
–
2
3
2
.
[1
6
]
C.
F
.
C
h
a
n
g
,
Re
c
o
n
f
ig
u
ra
ti
o
n
a
n
d
c
a
p
a
c
it
o
r
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lac
e
m
e
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t
f
o
r
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ss
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e
d
u
c
ti
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n
o
f
d
istri
b
u
ti
o
n
sy
ste
m
s
b
y
a
n
t
c
o
lo
n
y
se
a
rc
h
a
lg
o
rit
h
m
,
IEE
E
T
ra
n
s
.
Po
we
r
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y
st
.
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3
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)
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0
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7
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7
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1
7
5
5
.
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7
]
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.
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.
T
a
b
a
tab
a
e
i,
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V
a
h
id
i
,
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c
teria
l
f
o
ra
g
in
g
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ti
o
n
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a
se
d
f
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lo
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e
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isio
n
f
o
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p
ti
m
a
l
c
a
p
a
c
it
o
r
a
ll
o
c
a
ti
o
n
in
ra
d
ial
d
istri
b
u
t
io
n
sy
ste
m
,
In
t.
J
.
El
e
c
tric P
o
we
r S
y
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Res
.
8
1
,
1
0
4
5
–
1
0
5
0
,
2
0
1
1
.
[1
8
]
A
.
Y.
A
b
d
e
laz
iz,
E.
S
.
A
li
,
S
.
M
.
A
b
d
El
a
z
im
,
“
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lo
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lg
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m
a
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o
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S
e
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siti
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y
F
a
c
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o
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ti
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a
l
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g
a
n
d
p
lac
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m
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n
t
o
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c
a
p
a
c
it
o
rs
in
ra
d
ial
d
istri
b
u
ti
o
n
sy
ste
m
s
”
,
El
e
c
trica
l
Po
we
r
a
n
d
E
n
e
rg
y
S
y
ste
ms
,
7
8
,
2
0
7
–
2
1
4
,
2
0
1
6
.
Evaluation Warning : The document was created with Spire.PDF for Python.