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lect
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a
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m
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o
d
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o
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k
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ro
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ip
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d
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it
h
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g
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:
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h
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u
y
en
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f
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lectr
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n
g
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T
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n
d
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s
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n
i
v
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s
it
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C
h
i M
in
h
C
it
y
,
No
.
1
2
Ng
u
y
e
n
Van
B
ao
,
W
ar
d
4
,
Go
Va
p
Dis
tr
ict,
Ho
C
h
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Min
h
C
it
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Viet
Na
m
.
E
m
ail:
n
g
u
y
en
th
a
n
h
th
u
a
n
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iu
h
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u
.
v
n
1.
I
NT
RO
D
UCT
I
O
N
E
lectr
ic
d
is
tr
ib
u
tio
n
s
y
s
te
m
(
E
DS)
h
as
m
es
h
to
p
o
lo
g
y
b
u
t
it
is
u
s
u
a
ll
y
o
p
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ated
in
r
ad
ial
to
p
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d
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e
s
o
m
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ta
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s
s
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c
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ed
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r
t
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cir
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it
c
u
r
r
en
t
an
d
in
s
tallatio
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o
f
p
r
o
tect
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ev
ices.
Ho
w
e
v
er
,
r
ad
ial
o
p
e
r
atio
n
tak
es
m
o
r
e
p
o
w
er
lo
s
s
co
m
p
ar
ed
w
it
h
m
es
h
o
p
er
atio
n
.
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h
er
ef
o
r
e,
r
e
d
u
ctio
n
o
f
p
o
w
er
lo
s
s
i
n
E
DS
tak
e
s
a
h
ig
h
r
o
le
in
o
p
er
atin
g
E
DS.
I
n
a
m
o
n
g
m
et
h
o
d
s
o
f
r
ed
u
ctio
n
p
o
w
er
lo
s
s
,
n
et
wo
r
k
r
ec
o
n
f
i
g
u
r
atio
n
(
NR
)
is
t
h
e
m
o
s
t e
f
f
icie
n
t te
c
h
n
iq
u
e
b
ec
a
u
s
e
o
f
n
o
co
s
t
s
.
I
t is
p
er
f
o
r
m
ed
b
y
ch
a
n
g
i
n
g
th
e
s
t
atu
s
o
f
o
p
en
ed
an
d
clo
s
ed
s
w
itch
e
s
in
E
D
S.
T
h
e
NR
p
r
o
b
lem
is
f
ir
s
t
p
r
o
p
o
s
ed
in
[
1
]
.
I
n
th
i
s
s
tu
d
y
,
th
e
NR
p
r
o
b
le
m
is
f
o
r
m
u
la
ted
b
y
a
m
i
x
ed
i
n
te
g
er
n
o
n
-
li
n
ea
r
p
r
o
b
lem
an
d
s
o
lv
ed
b
y
a
d
is
cr
ete
b
r
an
ch
-
an
d
-
b
o
u
n
d
tech
n
iq
u
e.
T
h
en
,
C
iv
a
n
lar
et
al.
,
[
2
]
s
o
lv
ed
th
e
N
R
p
r
o
b
lem
b
ase
d
o
n
ex
ch
a
n
g
i
n
g
s
w
i
tch
e
s
to
r
ed
u
ce
p
o
w
er
l
o
s
s
.
Af
ter
al
m
o
s
t
f
o
u
r
d
ec
ad
es,
th
e
N
R
p
r
o
b
le
m
h
as
s
o
lv
ed
b
y
m
an
y
m
o
d
er
n
m
et
h
o
d
s
s
ti
m
u
lated
f
r
o
m
p
h
e
n
o
m
en
a
o
f
n
at
u
r
e
o
r
s
o
ciet
y
s
u
ch
as
g
en
e
tic
alg
o
r
it
h
m
(
G
A
)
,
p
ar
ticle
s
w
ar
m
o
p
ti
m
izatio
n
(
P
SO)
,
f
ir
e
w
o
r
k
s
al
g
o
r
ith
m
(
FW
A
)
an
d
cu
c
k
o
o
s
ea
r
ch
al
g
o
r
ith
m
(
C
S
A
)
,
b
io
g
e
o
g
r
ap
h
y
b
ased
o
p
ti
m
izatio
n
(
B
B
O)
,
g
r
ey
w
o
l
f
o
p
ti
m
izatio
n
(
GW
O)
.
I
n
[3
-
5]
,
GA
h
as
b
ee
n
u
s
ed
to
s
o
lv
e
th
e
NR
p
r
o
b
lem
f
o
r
m
i
n
i
m
izi
n
g
p
o
w
er
lo
s
s
.
I
n
[6
-
8]
,
P
SO
is
p
r
o
p
o
s
ed
f
o
r
s
o
lv
in
g
th
e
N
R
p
r
o
b
le
m
to
r
ed
u
ce
p
o
w
er
lo
s
s
.
I
n
[
9
,
10]
FW
A
is
p
r
o
p
o
s
ed
f
o
r
th
e
N
R
p
r
o
b
le
m
t
o
r
ed
u
ce
p
o
w
er
lo
s
s
an
d
i
m
p
r
o
v
e
t
h
e
n
o
d
e
v
o
lta
g
e.
I
n
[
1
1
-
13]
,
C
S
A
h
as
b
ee
n
s
u
cc
e
s
s
f
u
l
s
o
l
v
ed
t
h
e
N
R
p
r
o
b
le
m
f
o
r
r
ed
u
ci
n
g
p
o
w
er
lo
s
s
an
d
i
m
p
r
o
v
i
n
g
n
o
d
e
v
o
ltag
e.
I
n
[
1
4
]
mo
d
if
ied
B
B
O
is
s
u
cc
ess
f
u
l
ap
p
lied
f
o
r
f
in
d
i
n
g
t
h
e
o
p
ti
m
a
l
co
n
f
i
g
u
r
atio
n
f
o
r
p
o
w
er
lo
s
s
r
ed
u
ctio
n
.
T
h
e
GW
O
is
also
s
u
cc
e
s
s
f
u
l
ap
p
lied
f
o
r
th
e
NR
p
r
o
b
lem
to
r
ed
u
ce
p
o
w
er
lo
s
s
[
1
5
,
1
6
]
.
I
n
co
m
p
ar
is
o
n
w
it
h
th
e
h
eu
r
i
s
tic
m
et
h
o
d
s
w
h
ic
h
ar
e
b
ased
o
n
th
e
k
n
o
w
led
g
e
o
f
elec
tr
ic
p
o
w
er
s
y
s
te
m
s
u
c
h
a
s
[1
,
2]
,
th
e
m
o
d
er
n
m
et
h
o
d
s
h
av
e
m
o
r
e
ad
v
an
tag
e
s
.
W
h
ile
t
h
e
h
e
u
r
is
tic
m
e
th
o
d
s
ar
e
o
n
l
y
u
s
u
a
ll
y
to
o
p
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m
ize
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r
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p
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f
o
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r
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,
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e
m
o
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er
n
m
et
h
o
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s
ca
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m
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r
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u
te
m
o
r
e
e
f
f
ec
t
iv
e
m
et
h
o
d
s
f
o
r
th
e
NR
p
r
o
b
le
m
.
R
u
n
n
er
r
o
o
t
alg
o
r
ith
m
(
R
R
A
)
is
a
r
ec
en
t
m
eta
-
h
eu
r
i
s
tic
m
e
th
o
d
in
s
p
ir
ed
f
r
o
m
r
u
n
n
er
s
an
d
r
o
o
ts
o
f
p
lan
ts
to
s
ea
r
ch
w
ater
an
d
m
i
n
er
als
[
1
7
]
.
T
o
ex
p
lo
r
e
th
e
s
ea
r
ch
s
p
ac
e,
R
R
A
u
s
e
s
r
an
d
o
m
j
u
m
p
s
tech
n
iq
u
e
w
it
h
h
ig
h
s
tep
s
to
g
e
n
er
ate
th
e
n
e
w
s
o
lu
tio
n
s
f
a
r
f
r
o
m
cu
r
r
en
t
s
o
lu
tio
n
s
a
n
d
th
e
r
e
-
i
n
itial
izatio
n
tech
n
iq
u
e
to
r
estar
t
th
e
c
u
r
r
en
t
p
o
p
u
latio
n
.
T
o
ex
p
lo
it
th
e
s
ea
r
c
h
s
p
ac
e,
R
R
A
u
s
es
r
an
d
o
m
j
u
m
p
s
te
ch
n
iq
u
e
w
i
th
s
m
all
s
tep
s
to
g
en
er
ate
n
e
w
s
o
l
u
tio
n
s
ar
o
u
n
d
t
h
e
cu
r
r
en
t
b
est
s
o
lu
tio
n
a
n
d
th
e
el
ite
s
elec
tio
n
tech
n
iq
u
e
to
s
av
e
th
e
cu
r
r
en
t
b
est
s
o
l
u
tio
n
f
o
r
n
ex
t
g
e
n
er
atio
n
.
Fo
r
s
o
lv
i
n
g
t
w
en
t
y
-
f
iv
e
b
en
c
h
m
ar
k
f
u
n
ctio
n
s
,
R
R
A
h
as
d
em
o
n
s
tr
ated
ad
v
a
n
tag
e
s
co
m
p
ar
ed
to
o
th
er
s
m
et
h
o
d
s
[
1
7
]
.
Fo
r
ap
p
lica
tio
n
o
f
R
R
A
f
o
r
th
e
p
r
o
b
lem
s
o
f
th
e
p
o
w
er
s
y
s
te
m
,
R
R
A
h
a
v
e
b
ee
n
s
u
cc
e
s
s
f
u
l
ap
p
lied
f
o
r
th
e
NR
p
r
o
b
lem
w
it
h
m
u
lti
-
o
b
j
ec
tiv
e
f
u
n
ctio
n
[
1
8
]
an
d
th
e
p
lace
m
e
n
t
o
f
DG
in
t
h
e
E
DS
[
1
9
]
.
I
n
th
is
p
ap
er
,
R
R
A
is
ad
ap
ted
to
s
o
lv
e
th
e
N
R
p
r
o
b
lem
f
o
r
p
o
w
er
lo
s
s
r
ed
u
ctio
n
.
T
h
e
p
er
f
o
r
m
an
ce
o
f
R
R
A
i
s
test
ed
in
d
i
f
f
er
en
t
E
DS
an
d
co
m
p
ar
ed
w
ith
t
h
e
w
ell
-
k
n
o
w
n
P
SO
th
at
h
as
b
ee
n
s
u
cc
e
s
s
f
u
l
ap
p
lied
f
o
r
th
e
NR
p
r
o
b
le
m
[8
,
2
0
]
.
I
n
ad
d
itio
n
,
th
e
ca
lcu
lated
r
esu
lt
s
o
b
tain
ed
b
y
R
R
A
ar
e
also
co
m
p
ar
ed
to
o
th
er
m
e
th
o
d
s
i
n
liter
at
u
r
e.
T
h
e
h
ig
h
lig
h
t
s
o
f
t
h
e
p
ap
er
is
s
u
m
m
ar
ized
as f
o
llo
w
s
:
-
R
R
A
i
s
ad
ap
ted
f
o
r
s
o
lv
e
th
e
NR
p
r
o
b
lem
f
o
r
p
o
w
er
lo
s
s
r
e
d
u
ctio
n
;
-
R
R
A
o
u
tp
er
f
o
r
m
s
P
SO
a
n
d
o
th
er
m
et
h
o
d
s
i
n
l
iter
atu
r
e
in
t
er
m
s
o
f
s
u
c
ce
s
s
f
u
l
r
ate
an
d
t
h
e
q
u
a
lit
y
o
f
th
e
o
b
tain
ed
o
p
ti
m
al
s
o
l
u
tio
n
.
I
n
th
e
b
ello
w
i
n
g
s
ec
t
io
n
,
t
h
e
p
r
o
b
lem
f
o
r
m
u
latio
n
is
p
r
ese
n
ted
.
T
h
e
ap
p
licatio
n
o
f
R
R
A
f
o
r
th
e
NR
p
r
o
b
lem
is
p
r
ese
n
ted
in
s
ec
tio
n
3
.
Sectio
n
4
s
h
o
w
s
t
h
e
r
es
u
l
ts
an
d
an
a
l
y
s
is
a
n
d
f
i
n
all
y
co
n
clu
s
io
n
s
ar
e
lis
ted
in
s
ec
tio
n
5
.
2.
P
RO
B
L
E
M
F
O
R
M
UL
AT
I
O
N
T
h
e
p
u
r
p
o
s
e
o
f
th
e
N
R
is
tr
an
s
f
er
r
i
n
g
a
p
ar
t
o
f
lo
ad
s
f
r
o
m
t
h
e
h
ea
v
y
b
r
an
c
h
es
to
li
g
h
t
b
r
an
ch
e
s
b
y
ch
an
g
i
n
g
t
h
e
o
p
en
ed
/clo
s
ed
s
tatu
s
o
f
s
w
itc
h
es
lo
ca
ted
o
n
e
ac
h
b
r
an
ch
.
P
o
w
er
lo
s
s
o
f
E
DS
is
ca
lc
u
lated
b
y
s
u
m
o
f
p
o
w
er
lo
s
s
o
f
ea
ch
b
r
an
ch
o
f
t
h
e
s
y
s
te
m
.
Ho
w
e
v
er
,
th
er
e
ar
e
clo
s
ed
b
r
an
ch
es
ca
r
r
y
i
n
g
cu
r
r
en
t
a
n
d
o
p
en
ed
b
r
an
ch
es
n
o
t
ca
r
r
y
in
g
cu
r
r
e
n
t
i
n
th
e
E
D
S.
T
h
er
ef
o
r
e
p
o
w
er
l
o
s
s
o
f
th
e
E
D
S
is
ca
lc
u
lated
b
y
as f
o
llo
w
s
:
∆
=
∑
2
+
2
2
=
1
(
1
)
I
n
w
h
ic
h
,
is
a
n
u
m
b
er
o
f
b
r
an
ch
e
s
o
f
E
DS
,
is
th
e
ith
b
r
an
ch
’
s
r
esis
ta
n
ce
.
P
i
an
d
Q
i
ar
e
t
h
e
ac
tiv
e
a
n
d
r
ea
ctiv
e
p
o
w
er
f
lo
w
o
n
th
e
it
h
b
r
an
ch
.
s
tan
d
s
f
o
r
th
e
s
tatu
s
o
f
th
e
b
r
an
ch
ith
in
th
e
E
DS
wh
ich
is
eq
u
al
to
1
f
o
r
clo
s
ed
s
tatu
s
an
d
0
f
o
r
v
ice
v
er
s
a.
T
h
e
r
esu
lts
o
f
N
R
p
r
o
b
lem
i
s
a
r
a
d
ial
to
p
o
l
o
g
y
o
f
E
DS t
h
at
s
atis
f
y
f
o
llo
w
i
n
g
co
n
s
tr
ai
n
ts
:
-
R
ad
ial
to
p
o
lo
g
y
co
n
s
tr
ain
t:
T
o
s
atis
f
y
t
h
i
s
co
n
s
tr
ai
n
t,
th
e
e
m
p
ir
ical
f
o
r
m
u
la
[
2
1
]
is
p
r
o
p
o
s
ed
to
ch
ec
k
ca
n
d
id
ate
s
o
lu
tio
n
s
.
(
)
=
{
−
1
1
,
0
,
(
2
)
I
n
w
h
ic
h
,
d
et(
A
)
i
s
d
eter
m
i
n
a
n
t o
f
m
atr
ix
A
.
A
i
s
th
e
b
r
an
c
h
b
y
n
o
d
e
m
atr
ix
b
u
ilt b
y
co
n
n
e
ctio
n
o
f
E
DS.
-
N
o
d
e
v
o
ltag
e
co
n
s
tr
ai
n
t:
n
o
d
e
v
o
ltag
e
m
ag
n
it
u
d
e
m
u
s
t
lie
i
n
p
er
m
is
s
ib
le
r
an
g
e
s
[
,
]
.
T
h
e
y
ar
e
r
esp
ec
tiv
el
y
s
et
eq
u
al
to
[
0
.
9
5
,
1
]
in
p
er
u
n
it.
≤
≤
ℎ
=
1
,
2
,
.
.
(
3
)
w
h
er
e
is
t
h
e
n
u
m
b
er
o
f
n
o
d
es in
th
e
E
D
S.
-
B
r
an
ch
cu
r
r
en
t
co
n
s
tr
ai
n
t:
Fo
r
av
o
i
d
in
g
o
v
er
lo
ad
,
th
e
b
r
an
ch
e
s
’
cu
r
r
en
t
m
a
g
n
i
tu
d
e
m
u
s
t
lie
in
t
h
eir
p
er
m
i
s
s
ib
le
r
an
g
e.
≤
,
ℎ
=
1
,
2
,
.
.
(
4
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
10
,
No
.
5
,
Octo
b
e
r
2
0
2
0
:
5
0
1
6
-
5024
5018
3.
RRA
F
O
R
T
H
E
NR
P
RO
B
L
E
M
WI
T
H
P
O
WE
R
L
O
SS
RE
DUC
T
I
O
N
R
R
A
i
s
in
s
p
ir
ed
f
r
o
m
t
h
e
p
lan
ts
p
r
o
p
ag
ated
th
r
o
u
g
h
r
u
n
n
er
s
a
n
d
r
o
o
ts
.
T
o
ap
p
ly
th
is
as
a
n
o
p
tim
izatio
n
to
o
l,
Me
r
r
ik
h
-
B
a
y
at
u
s
ed
th
r
ee
id
ea
lized
r
u
les
[
1
7
]
:
-
T
h
e
m
o
t
h
er
p
lan
t is
g
e
n
er
ated
th
e
d
au
g
h
ter
p
la
n
t th
r
o
u
g
h
its
r
u
n
n
er
f
o
r
ex
p
lo
r
in
g
r
eso
u
r
ce
s
.
-
T
h
e
p
lan
ts
p
r
o
d
u
ce
r
o
o
ts
an
d
r
o
o
t h
air
s
to
ex
p
lo
it r
eso
u
r
ce
s
a
r
o
u
n
d
its
p
o
s
itio
n
.
-
T
h
e
d
au
g
h
ter
p
lan
t
s
w
ill
g
r
o
w
f
ast
er
a
n
d
b
ec
o
m
e
t
h
e
m
o
t
h
er
p
lan
t
at
n
e
w
p
o
s
it
io
n
w
it
h
r
ich
r
eso
u
r
ce
s
.
Oth
er
w
i
s
e,
th
e
y
w
ill b
e
d
ie
at
n
e
w
p
o
s
itio
n
w
i
th
p
o
o
r
r
eso
u
r
ce
s
.
I
n
th
i
s
s
t
u
d
y
,
t
h
e
i
m
p
le
m
e
n
tati
o
n
o
f
R
R
A
f
o
r
th
e
N
R
p
r
o
b
lem
is
s
u
m
m
ar
ized
as f
o
llo
w
s
:
-
Step
1
: I
n
itializatio
n
F
o
r
s
o
lv
i
n
g
th
e
N
R
p
r
o
b
l
em
,
e
a
c
h
m
o
th
e
r
p
l
an
t
is
c
o
n
s
i
d
e
r
e
d
a
s
r
a
d
i
a
l
t
o
p
o
l
o
g
y
o
f
th
e
d
i
s
t
r
i
b
u
ti
o
n
s
y
s
tem
.
I
n
th
e
f
i
r
s
t
s
t
e
p
,
th
e
p
o
p
u
l
a
ti
o
n
o
f
th
e
p
r
o
b
l
em
is
g
e
n
e
r
at
e
d
a
s
(
5
)
.
I
n
w
h
i
ch
,
e
a
ch
r
a
d
i
a
l
t
o
p
o
l
o
g
y
is
p
r
e
s
en
t
e
d
as
(
6
)
a
n
d
e
ac
h
v
a
r
i
ab
l
e
o
f
c
an
d
i
d
at
e
s
o
l
u
t
i
o
n
w
h
i
ch
i
s
an
o
p
en
s
w
i
t
ch
is
g
en
e
r
a
te
d
r
a
n
d
o
m
ly
a
s
(
7
)
.
=
{
ℎ
,
1
ℎ
,
2
…
ℎ
,
(
5
)
ℎ
(
)
=
[
1
,
2
,
…
,
,
…
,
]
(
6
)
(
)
=
[
,
+
×
(
ℎ
ℎ
,
−
,
)
]
(
7
)
w
h
er
e
,
k
=
1
,
2
,
…,
N
an
d
d
=
1
,
2
,
…,
d
im
w
it
h
N
an
d
d
im
ar
e
r
esp
ec
ti
v
el
y
p
o
p
u
latio
n
s
ize
an
d
th
e
n
u
m
b
er
o
f
v
ar
iab
les.
,
an
d
ℎ
ℎ
,
ar
e
r
esp
ec
tiv
el
y
lo
w
a
n
d
h
i
g
h
li
m
it
o
f
tie
-
s
w
itc
h
Xd
.
B
ased
o
n
th
e
in
i
tia
lized
p
o
p
u
latio
n
o
f
th
e
m
o
t
h
er
p
lan
ts
,
e
ac
h
m
o
th
er
p
lan
is
ev
a
l
u
ated
b
y
t
h
e
f
it
n
e
s
s
f
u
n
ctio
n
an
d
th
e
p
lan
t
w
i
th
th
e
b
est
f
i
tn
e
s
s
f
u
n
c
tio
n
i
s
s
a
v
ed
to
th
e
b
est
d
a
u
g
h
ter
p
la
n
t
ℎ
,
.
No
ted
th
at,
to
ca
lc
u
late
th
e
f
i
tn
es
s
f
u
n
ctio
n
v
al
u
e,
t
h
e
p
o
w
er
f
lo
w
i
s
p
er
f
o
r
m
ed
an
d
th
e
v
al
u
e
o
f
th
e
(
1
)
is
o
b
tain
ed
.
-
Step
2
: G
lo
b
al
s
ea
r
ch
w
it
h
g
e
n
er
atio
n
o
f
d
au
g
h
ter
p
lan
t
s
T
o
ex
p
lo
r
e
s
ea
r
ch
s
p
ac
e,
a
n
e
w
p
o
p
u
la
tio
n
o
f
d
au
g
h
ter
p
la
n
ts
i
s
g
en
er
ated
to
r
ep
lace
t
h
e
p
o
p
u
latio
n
o
f
m
o
t
h
er
p
lan
ts
.
ℎ
(
)
=
{
ℎ
,
,
,
=
1
[
ℎ
,
(
)
+
×
]
,
=
2
,
…
,
(
8
)
w
h
e
r
e
,
th
e
c
o
n
s
t
an
t
p
a
r
am
et
e
r
d
runner
is
a
l
a
r
g
e
d
i
s
ta
n
c
e
b
e
t
w
ee
n
th
e
m
o
th
e
r
an
d
d
au
g
h
t
e
r
p
lan
t
.
T
h
e
n
,
th
e
f
i
tn
es
s
f
u
n
c
t
i
o
n
o
f
e
a
ch
d
au
g
h
t
e
r
p
l
an
t
i
s
ev
a
lu
at
e
d
an
d
a
b
e
s
t
d
a
u
g
h
te
r
p
l
a
n
t
(
ℎ
,
)
i
s
u
p
d
at
e
d
.
-
Step
3
: L
o
ca
l sear
ch
w
it
h
lar
g
e
an
d
s
m
al
l d
is
tan
ce
s
T
o
ex
p
lo
it
s
ea
r
ch
s
p
ac
e,
th
is
s
tep
is
p
er
f
o
r
m
ed
as
th
e
v
a
lu
e
o
f
th
e
b
est
d
au
g
h
ter
p
lan
t
in
t
w
o
g
en
er
atio
n
s
i
s
n
o
t i
m
p
r
o
v
ed
co
n
s
id
er
ab
l
y
.
T
h
e
b
est d
au
g
h
te
r
p
lan
t
w
ill
g
e
n
er
ate
d
i
m
n
e
w
p
lan
ts
b
y
m
o
d
i
f
y
in
g
o
n
e
b
y
o
n
e
ele
m
en
t
in
th
e
b
est
d
au
g
h
ter
p
lan
t.
T
h
e
f
ir
s
t
d
i
m
n
e
w
p
l
an
ts
ar
e
g
en
er
ate
d
ar
o
u
n
d
th
e
b
es
t
d
au
g
h
ter
p
lan
t
w
it
h
lar
g
e
d
i
s
ta
n
ce
s
as
f
o
llo
w
s
:
,
=
[
{
1
,
1
…
,
1
,
1
,
1
+
×
,
1
,
…
,
1
}
×
ℎ
,
(
)
]
(
9
)
w
h
er
e
{
1
,
1
…
,
1
,
1
,
1
+
×
,
1
,
…
,
1
}
is
a
v
ec
to
r
w
it
h
all
e
le
m
e
n
ts
ar
e
eq
u
a
l
to
1
ex
ce
p
t
f
o
r
th
e
d
-
t
h
o
n
e,
w
h
ic
h
i
s
eq
u
al
t
o
1
+
×
.
T
h
e
s
ec
o
n
d
d
i
m
n
e
w
p
la
n
t
s
ar
e
g
e
n
er
ated
b
y
r
ep
laci
n
g
w
it
h
,
w
h
ic
h
is
m
u
c
h
s
m
a
lle
r
th
an
.
T
h
e
n
e
w
d
a
u
g
h
ter
p
lan
ts
ar
e
ev
alu
a
ted
th
e
f
it
n
es
s
f
u
n
ctio
n
an
d
t
h
e
b
est d
au
g
h
ter
p
lan
t is u
p
d
ated
ag
ai
n
.
-
Step
4
: G
en
er
atio
n
o
f
n
e
w
m
o
th
er
p
lan
ts
a
n
d
escap
in
g
t
h
e
lo
ca
l o
p
tim
a
l
A
t
t
h
e
f
i
n
al
s
ta
g
e
o
f
ea
ch
iter
atio
n
,
b
ased
o
n
th
e
f
itn
e
s
s
o
f
th
e
d
au
g
h
ter
p
lan
ts
,
th
e
r
o
u
l
ette
w
h
ee
l
s
elec
tio
n
m
et
h
o
d
[
2
2
]
is
u
s
ed
to
s
elec
tio
n
t
h
e
d
au
g
h
ter
p
lan
ts
a
s
t
h
e
m
o
t
h
er
p
lan
t
s
f
o
r
th
e
n
e
x
t
g
e
n
er
atio
n
.
No
ted
th
at
th
e
b
est
d
au
g
h
ter
p
lan
t
w
i
ll
h
as
lar
g
e
p
r
o
b
ab
ilit
y
s
elec
ted
f
o
r
t
h
e
n
ex
t
g
en
er
atio
n
.
I
n
ad
d
itio
n
,
to
escap
e
lo
ca
l
o
p
tim
al
s
o
lu
ti
o
n
,
a
r
e
-
in
itializat
io
n
s
tr
ate
g
y
is
u
s
ed
to
r
estar
t
th
e
alg
o
r
ith
m
.
I
f
af
ter
Stall
m
ax
g
en
er
atio
n
s
th
at
t
h
e
v
a
lu
e
o
f
th
e
b
est
d
au
g
h
ter
p
lan
t
s
till
n
o
co
n
s
id
er
ab
le
i
m
p
r
o
v
e
m
e
n
t,
th
e
p
o
p
u
lat
io
n
o
f
m
o
th
er
p
lan
t
s
w
ill
b
e
r
an
d
o
m
l
y
g
e
n
er
ated
s
i
m
ilar
to
s
tep
1
.
T
h
e
p
s
eu
d
o
co
d
e
o
f
th
e
R
R
A
f
o
r
th
e
NR
to
m
i
n
i
m
ize
p
o
w
er
is
g
i
v
en
i
n
Fi
g
u
r
e
1
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
E
lectric d
is
tr
ib
u
tio
n
n
etw
o
r
k
r
ec
o
n
fig
u
r
a
tio
n
f
o
r
p
o
w
er lo
s
s
r
ed
u
ctio
n
…
(
Th
u
a
n
Th
a
n
h
N
g
u
ye
n
)
5019
Fig
u
r
e
1
.
P
s
eu
d
o
co
d
e
o
f
th
e
R
R
A
f
o
r
th
e
N
R
p
r
o
b
lem
f
o
r
p
o
w
er
lo
s
s
r
ed
u
ctio
n
4.
RE
SU
L
T
S
A
ND
AN
AL
Y
SI
S
T
o
s
h
o
w
th
e
e
f
f
icie
n
t
o
f
R
R
A
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t
h
e
ap
p
licatio
n
o
f
R
R
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f
o
r
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e
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p
r
o
b
le
m
is
i
m
p
le
m
en
ted
i
n
p
latf
o
r
m
Ma
t
lab
2
0
1
6
a,
ex
ec
u
ted
o
n
a
p
er
s
o
n
al
co
m
p
u
ter
I
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tel(
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r
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h
e
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er
f
o
r
m
a
n
ce
o
f
R
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is
e
v
alu
ated
in
t
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co
n
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ti
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f
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n
o
d
e
an
d
6
9
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n
o
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y
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te
m
.
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n
ad
d
itio
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,
th
e
ap
p
licatio
n
o
f
P
SO
f
o
r
th
e
NR
p
r
o
b
le
m
is
also
i
m
p
le
m
en
ted
an
d
r
u
n
o
n
th
e
s
a
m
e
co
m
p
u
ter
f
o
r
co
m
p
ar
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n
g
w
i
th
R
R
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b
e
s
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d
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o
m
p
ar
i
n
g
R
R
A
w
it
h
o
th
e
r
m
e
th
o
d
s
i
n
liter
at
u
r
e.
4
.
1
.
T
he
1
6
-
no
de
s
y
s
t
em
T
h
e
2
3
k
V
1
6
-
n
o
d
e
test
s
y
s
te
m
s
h
o
w
n
in
F
ig
u
r
e
2
co
n
tain
s
3
f
ee
d
er
s
an
d
1
3
lo
a
d
n
o
d
es.
T
h
e
d
ata
o
f
th
e
s
y
s
te
m
i
s
r
e
f
er
en
ce
d
f
r
o
m
[
3
]
.
T
h
e
th
r
ee
in
i
tiall
y
-
o
p
en
s
w
itc
h
e
s
ar
e
{
S1
4
,
S1
5
an
d
S1
6
}.
T
h
e
to
tal
lo
ad
o
f
th
e
s
y
s
te
m
i
s
2
8
.
7
MW
,
w
h
il
e
th
e
in
itial
to
tal
p
o
w
er
lo
s
s
i
s
5
1
1
.
4
3
5
6
k
W
.
T
h
e
m
i
n
i
m
al
v
o
ltag
e
a
m
p
lit
u
d
e
(V
m
in
)
o
f
t
h
e
s
y
s
te
m
is
0
.
9
6
9
3
p
.
u
.
T
h
e
ca
lcu
lated
ti
m
e
o
f
th
e
alg
o
r
ith
m
u
s
u
al
l
y
d
ep
en
d
s
o
n
th
e
m
ec
h
an
is
m
o
f
o
p
er
atio
n
o
f
th
e
alg
o
r
ith
m
.
W
h
ile
s
o
m
e
al
g
o
r
ith
m
s
cr
ea
t
e
n
e
w
s
o
lu
tio
n
s
u
s
i
n
g
s
i
m
p
le
p
r
o
ce
d
u
r
es,
o
th
er
s
p
r
o
d
u
ce
n
e
w
s
o
lu
tio
n
s
u
s
i
n
g
m
o
r
e
co
m
p
le
x
a
n
d
ti
m
e
-
co
n
s
u
m
i
n
g
p
r
o
c
ed
u
r
es.
B
u
t
o
v
er
all,
in
cr
ea
s
i
n
g
th
e
p
o
p
u
latio
n
s
ize
(
N)
th
e
m
ax
i
m
u
m
n
u
m
b
er
o
f
iter
atio
n
s
(
iter
m
ax
)
an
d
t
h
e
m
a
x
i
m
u
m
n
u
m
b
er
o
f
f
it
n
e
s
s
Input: Line and load data of the EDS.
Output: Optimal configuration with minimum power loss
Step 1:
Generate randomly initial population of N mother plants
ℎ
(
)
=
[
1
,
2
,
…
,
,
…
,
]
with
k
= 1, 2…
N
.
Check radially condition of each plant by Equation (2)
If
ℎ
(
)
is radial configuration
then
Calculate the fitness function of
ℎ
(
)
to find the best plant
ℎ
,
Else
Fitness function of
ℎ
(
)
= inf
End if
While
(Maximum evaluation fitness function not reach
or
current iteration (i) < maximum
iteration
)
do
Step 2:
Global search with generation of daughter plants
Generate the new population of daughter plants from the population of mother
plants by Equation (8)
Check radially condition of each plant by Equation (2)
If
ℎ
(
)
is radial configuration
then
Evaluate fitness function and update the best plant
Else
Fitness function of
ℎ
(
)
= inf
End if
Step 3:
Local search with large and small distances
Generate the number of dim new plants
,
by modifying the best plant through
Equation (9) and dim new plants based on replacing
by
Check radially condition of each plant by Equation (2)
If
the each new plant is radial configuration
then
Evaluate fitness function
Else
Fitness function of Xi = inf
End if
If
fitness (
,
) < fitness (
ℎ
,
)
then
ℎ
,
=
,
End if
Save the fitness of
ℎ
,
called the best fitness for
current iteration
Step 4:
Generation of new mother plants and escaping the local optimal
Selection daughter plants to become the next mother plants based on the roulette
wheel selection
If
the best fitness (i) = the best fitness (i
-
1)
then
Counter =
Counter + 1
Else
Counter = 0
End if
If
Counter =
Stall
max
then
Generate randomly population of mother plants similar to Step 1.
End if
End While
Post process result:
best fitness
value and the plant
ℎ
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
10
,
No
.
5
,
Octo
b
e
r
2
0
2
0
:
5
0
1
6
-
5024
5020
ev
alu
a
tio
n
(
MFE
)
to
h
ig
h
v
al
u
es
ca
n
h
e
lp
th
e
alg
o
r
ith
m
s
t
o
p
r
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d
u
ce
th
e
h
ig
h
er
n
u
m
b
er
o
f
n
e
w
s
o
lu
t
io
n
s
i
n
th
e
s
ea
r
ch
i
n
g
s
p
ac
e
b
u
t
i
t
w
i
ll
tak
e
a
lo
n
g
ti
m
e
f
o
r
s
ea
r
ch
i
n
g
o
p
tim
a
l
s
o
l
u
tio
n
s
.
T
h
er
ef
o
r
e,
i
n
t
h
is
s
t
u
d
y
b
ased
o
n
th
e
s
ca
le
an
d
co
m
p
le
x
it
y
o
f
th
e
test
s
y
s
te
m
,
t
h
e
co
n
tr
o
l
p
ar
am
eter
s
o
f
R
R
A
a
n
d
P
SO
co
n
s
is
ti
n
g
o
f
N,
iter
m
ax
an
d
M
FE
ar
e
e
x
p
er
im
en
ted
s
e
v
er
al
ti
m
es
an
d
c
h
o
s
en
to
1
0
,
5
0
an
d
5
0
0
r
esp
ec
tiv
el
y
.
Fo
r
R
R
A
,
th
e
d
runner
a
n
d
d
root
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e
s
et
to
4
an
d
2
r
esp
ec
tiv
e
l
y
[
1
8
]
.
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r
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t
w
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ta
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s
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1
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tain
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ith
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.
REFEREN
CES
[1
]
A
.
M
e
rli
n
a
n
d
H.
Ba
c
k
,
“
S
e
a
rc
h
f
o
r
a
m
in
i
m
a
l
lo
ss
o
p
e
ra
t
in
g
sp
a
n
n
in
g
tree
c
o
n
f
ig
u
ra
ti
o
n
in
a
n
u
rb
a
n
p
o
w
e
r
d
istri
b
u
ti
o
n
sy
ste
m
,
”
Pro
c
e
e
d
in
g
in
5
t
h
p
o
we
r
sy
ste
m
c
o
mp
u
ta
ti
o
n
c
o
n
f
(
PS
CC),
Ca
mb
ri
d
g
e
,
UK
,
v
o
l.
1
,
p
p
.
1
-
1
8
,
1
9
7
5
.
[2
]
S
.
C
iv
a
n
lar,
J.
J.
G
ra
in
g
e
r,
H.
Yi
n
,
a
n
d
S
.
S
.
H.
L
e
e
,
“
Distrib
u
ti
o
n
f
e
e
d
e
r
re
c
o
n
f
i
g
u
ra
ti
o
n
f
o
r
lo
ss
re
d
u
c
ti
o
n
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r De
li
v
e
ry
,
v
o
l.
3
,
n
o
.
3
,
p
p
.
1
2
1
7
-
1
2
2
3
,
1
9
8
8
.
[3
]
J.
Z.
Zh
u
,
“
Op
ti
m
a
l
re
c
o
n
f
ig
u
ra
ti
o
n
o
f
e
lec
tri
c
a
l
d
istri
b
u
ti
o
n
n
e
tw
o
rk
u
sin
g
th
e
re
f
in
e
d
g
e
n
e
ti
c
a
lg
o
rit
h
m
,
”
El
e
c
tric
Po
we
r S
y
ste
ms
Res
e
a
rc
h
,
v
o
l.
6
2
,
n
o
.
1
,
p
p
.
3
7
-
4
2
,
2
0
0
2
,
d
o
i
:
1
0
.
1
0
1
6
/S
0
3
7
8
-
7
7
9
6
(
0
2
)
0
0
0
4
1
-
X.
[4
]
R.
T
.
G
a
n
e
sh
V
u
las
a
la,
S
iv
a
n
a
g
a
ra
ju
S
iri
g
iri
,
“
F
e
e
d
e
r
R
e
c
o
n
f
ig
u
ra
ti
o
n
f
o
r
L
o
ss
Re
d
u
c
ti
o
n
in
Un
b
a
lan
c
e
d
Distrib
u
ti
o
n
S
y
ste
m
Us
in
g
G
e
n
e
t
ic
A
l
g
o
rit
h
m
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
El
e
c
tro
n
ic
s
En
g
i
n
e
e
rin
g
,
v
o
l.
3
,
n
o
.
1
2
,
p
p
.
7
5
4
-
7
6
2
,
2
0
0
9
.
[5
]
P
.
S
u
b
b
u
ra
j
,
K.
Ra
m
a
r,
L
.
Ga
n
e
s
a
n
,
a
n
d
P
.
V
e
n
k
a
tes
h
,
“
Distrib
u
ti
o
n
S
y
ste
m
Re
c
o
n
f
i
g
u
ra
ti
o
n
f
o
r
Lo
ss
Re
d
u
c
ti
o
n
u
sin
g
G
e
n
e
ti
c
A
l
g
o
rit
h
m
,
”
J
o
u
rn
a
l
o
f
El
e
c
trica
l
S
y
ste
ms
,
v
o
l.
2
,
n
o
.
4
,
p
p
.
1
9
8
-
2
0
7
,
2
0
0
6
.
[6
]
K.
K.
Ku
m
a
r,
N.
V
e
n
k
a
ta,
a
n
d
S
.
Ka
m
a
k
sh
a
iah
,
“
F
DR
p
a
rti
c
l
e
sw
a
r
m
a
lg
o
rit
h
m
f
o
r
n
e
tw
o
rk
re
c
o
n
f
ig
u
ra
ti
o
n
o
f
d
istri
b
u
ti
o
n
sy
ste
m
s,”
J
o
u
rn
a
l
o
f
T
h
e
o
re
ti
c
a
l
a
n
d
Ap
p
li
e
d
In
fo
rm
a
t
io
n
T
e
c
h
n
o
lo
g
y
,
v
o
l.
3
6
,
n
o
.
2
,
p
p
.
1
7
4
-
1
8
1
,
2
0
1
2
.
[7
]
T
.
M
.
Kh
a
li
l
a
n
d
A
.
V
G
o
rp
in
ic
h
,
“
Re
c
o
n
f
ig
u
ra
ti
o
n
f
o
r
L
o
ss
Re
d
u
c
ti
o
n
o
f
Distrib
u
ti
o
n
S
y
ste
m
s
Us
in
g
S
e
lec
ti
v
e
P
a
rti
c
le
S
w
a
r
m
Op
ti
m
iz
a
ti
o
n
,
”
I
n
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
M
u
lt
id
isc
ip
li
n
a
ry
S
c
ien
c
e
s
a
n
d
E
n
g
i
n
e
e
rin
g
,
v
o
l
.
3
,
n
o
.
6
,
p
p
.
1
6
-
2
1
,
2
0
1
2
.
[8
]
A
.
Y.
A
b
d
e
laz
iz,
S
.
F
.
M
e
k
h
a
m
e
r,
F
.
M
.
M
o
h
a
m
m
e
d
,
a
n
d
M
.
a
L
.
Ba
d
r,
“
A
M
o
d
if
ied
P
a
rti
c
le
S
w
a
r
m
T
e
c
h
n
iq
u
e
f
o
r
Distrib
u
ti
o
n
S
y
ste
m
s
Re
c
o
n
f
i
g
u
ra
ti
o
n
,
”
T
h
e
o
n
li
n
e
j
o
u
rn
a
l
o
n
e
lec
tro
n
ics
a
n
d
e
lec
trica
l
e
n
g
in
e
e
rin
g
(
OJ
EE
E)
,
v
o
l.
1
,
n
o
.
1
,
p
p
.
1
2
1
-
1
2
9
,
2
0
0
9
.
[9
]
A
.
M
o
h
a
m
e
d
I
m
ra
n
a
n
d
M
.
Ko
w
sa
l
y
a
,
“
A
n
e
w
p
o
we
r
s
y
ste
m
re
c
o
n
f
ig
u
ra
ti
o
n
sc
h
e
m
e
f
o
r
p
o
w
e
r
lo
ss
m
in
i
m
iza
ti
o
n
a
n
d
v
o
lt
a
g
e
p
ro
f
il
e
e
n
h
a
n
c
e
m
e
n
t
u
sin
g
F
irew
o
rk
s
A
lg
o
rit
h
m
,
”
I
n
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
El
e
c
trica
l
Po
we
r
a
n
d
En
e
rg
y
S
y
ste
ms
,
v
o
l.
6
2
,
p
p
.
3
1
2
-
3
2
2
,
2
0
1
4
,
d
o
i:
1
0
.
1
0
1
6
/
j.
ij
e
p
e
s.
2
0
1
4
.
0
4
.
0
3
4
.
[1
0
]
A
.
M
o
h
a
m
e
d
I
m
ra
n
,
M
.
Ko
w
s
a
l
y
a
,
a
n
d
D.
P
.
K
o
th
a
ri,
“
A
n
o
v
e
l
in
teg
ra
ti
o
n
tec
h
n
iq
u
e
f
o
r
o
p
ti
m
a
l
n
e
tw
o
rk
re
c
o
n
f
ig
u
ra
ti
o
n
a
n
d
d
istri
b
u
ted
g
e
n
e
ra
ti
o
n
p
lac
e
m
e
n
t
in
p
o
w
e
r
d
istri
b
u
ti
o
n
n
e
tw
o
rk
s,”
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
El
e
c
trica
l
Po
we
r a
n
d
En
e
rg
y
S
y
st
e
ms
,
v
o
l.
6
3
,
p
p
.
4
6
1
-
4
7
2
,
2
0
1
4
,
d
o
i:
1
0
.
1
0
1
6
/j
.
ij
e
p
e
s.2
0
1
4
.
0
6
.
0
1
1.
[1
1
]
T
.
T
.
Ng
u
y
e
n
a
n
d
A
.
V
.
T
ru
o
n
g
,
“
Distrib
u
t
io
n
n
e
tw
o
rk
re
c
o
n
f
ig
u
ra
ti
o
n
f
o
r
p
o
w
e
r
lo
ss
m
in
im
iza
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
u
sin
g
c
u
c
k
o
o
se
a
rc
h
a
lg
o
ri
th
m
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
P
o
w
e
r
a
n
d
E
n
e
rg
y
S
y
ste
ms
,
v
o
l.
6
8
,
p
p
.
2
3
3
-
2
4
2
,
2
0
1
5
,
d
o
i:
1
0
.
1
0
1
6
/
j.
ij
e
p
e
s.
2
0
1
4
.
1
2
.
0
7
5
.
[1
2
]
T
.
T
.
Ng
u
y
e
n
a
n
d
T
.
T
.
Ng
u
y
e
n
,
“
A
n
i
m
p
ro
v
e
d
c
u
c
k
o
o
se
a
rc
h
a
l
g
o
rit
h
m
f
o
r
th
e
p
ro
b
lem
o
f
e
lec
t
ric
d
istri
b
u
ti
o
n
n
e
tw
o
rk
re
c
o
n
f
ig
u
ra
ti
o
n
,
”
Ap
p
li
e
d
S
o
ft
C
o
mp
u
ti
n
g
,
v
o
l.
8
4
,
p
.
1
0
5
7
2
0
,
2
0
1
9
,
d
o
i:
1
0
.
1
0
1
6
/
j.
a
so
c
.
2
0
1
9
.
1
0
5
7
2
0
.
[1
3
]
T
.
T
.
Ng
u
y
e
n
,
A
.
V
.
T
ru
o
n
g
,
a
n
d
T
.
A
.
P
h
u
n
g
,
“
A
n
o
v
e
l
m
e
th
o
d
b
a
se
d
o
n
a
d
a
p
ti
v
e
c
u
c
k
o
o
se
a
rc
h
f
o
r
o
p
ti
m
a
l
n
e
tw
o
rk
re
c
o
n
f
ig
u
ra
ti
o
n
a
n
d
d
ist
rib
u
te
d
g
e
n
e
ra
ti
o
n
a
ll
o
c
a
ti
o
n
i
n
d
istri
b
u
ti
o
n
n
e
tw
o
rk
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
El
e
c
trica
l
Po
we
r a
n
d
En
e
rg
y
S
y
st
e
ms
,
v
o
l.
7
8
,
p
p
.
8
0
1
-
8
1
5
,
2
0
1
6
,
d
o
i:
1
0
.
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0
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6
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.
ij
e
p
e
s.2
0
1
5
.
1
2
.
0
3
0
.
[1
4
]
H.
F
.
Ka
d
o
m
,
A
.
N.
Hu
ss
a
in
,
a
n
d
W
.
K.
S
.
A
l
-
Ju
b
o
ri,
“
Du
a
l
tec
h
n
iq
u
e
o
f
re
c
o
n
f
ig
u
ra
ti
o
n
a
n
d
c
a
p
a
c
it
o
r
p
lac
e
m
e
n
t
f
o
r
d
istri
b
u
ti
o
n
sy
ste
m
,
”
In
ter
n
a
t
io
n
a
l
J
o
u
rn
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d
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y
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ra
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g
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m
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ter
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l
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6
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Yu
,
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[1
7
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8
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[1
9
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0
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lg
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m
,
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tric
Po
we
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Res
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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[2
1
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A
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d
r,
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2
]
I.
J.
Ra
m
irez
-
Ro
sa
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o
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d
J.
L.
Be
rn
a
l
-
Ag
u
stin
,
“
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e
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ti
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rit
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m
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a
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p
li
e
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to
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e
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e
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n
o
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lar
g
e
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r
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b
u
ti
o
n
sy
ste
m
s,”
IEE
E
T
ra
n
sa
c
ti
o
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s
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n
P
o
we
r
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y
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ms
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0
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.
[2
3
]
A
.
F
a
th
y
,
M
.
El
-
A
rin
i,
a
n
d
O.
El
-
Ba
k
sa
wy
,
“
A
n
e
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f
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ti
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u
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o
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tw
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rk
c
o
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b
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v
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ra
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h
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l
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h
m
,
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Ne
u
r
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l
Co
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u
t
in
g
a
n
d
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p
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[2
4
]
H.
-
D.
Ch
ian
g
a
n
d
R.
Je
a
n
-
Ju
m
e
a
u
,
“
Op
ti
m
a
l
n
e
tw
o
rk
re
c
o
n
f
ig
u
ra
ti
o
n
s
i
n
d
istr
ib
u
ti
o
n
sy
ste
m
s:
P
a
rt
2
:
S
o
lu
t
io
n
a
lg
o
rit
h
m
s
a
n
d
n
u
m
e
rica
l
re
su
lt
s
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
P
o
we
r
De
li
v
e
ry
,
v
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l.
5
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.
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,
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p
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,
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.
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0
2
.
[2
5
]
A
.
On
la
m
,
D.
Yo
d
p
h
e
t,
R.
C
h
a
tt
h
a
w
o
rn
,
C.
S
u
ra
w
a
n
it
k
u
n
,
A
.
S
iri
tara
ti
w
a
t,
a
n
d
P
.
Kh
u
n
k
it
t
i,
“
P
o
w
e
r
L
o
ss
M
in
im
iza
ti
o
n
a
n
d
Vo
lt
a
g
e
S
tab
il
it
y
I
m
p
ro
v
e
m
e
n
t
in
El
e
c
tri
c
a
l
Di
str
ib
u
ti
o
n
S
y
ste
m
v
ia
N
e
t
w
o
rk
R
e
c
o
n
f
ig
u
ra
ti
o
n
a
n
d
Distrib
u
ted
G
e
n
e
ra
ti
o
n
P
la
c
e
m
e
n
t
Us
in
g
No
v
e
l
A
d
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p
ti
v
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S
h
u
f
f
led
F
ro
g
s
Lea
p
in
g
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lg
o
rit
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m
,
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e
rg
ies
,
v
o
l.
1
2
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.
3
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5
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.
[2
6
]
R.
S
.
Ra
o
,
K.
Ra
v
in
d
ra
,
K.
S
a
ti
s
h
,
a
n
d
S
.
V
.
L
.
Na
ra
si
m
h
a
m
,
“
P
o
w
e
r
L
o
ss
M
in
i
m
iza
ti
o
n
in
Distrib
u
ti
o
n
S
y
ste
m
Us
in
g
Ne
t
w
o
rk
Re
c
o
n
f
ig
u
ra
ti
o
n
in
th
e
P
re
se
n
c
e
o
f
Distrib
u
te
d
G
e
n
e
ra
ti
o
n
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r
S
y
ste
ms
,
v
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l
.
2
8
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.
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,
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.
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:
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9
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RS
.
2
0
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2
.
2
1
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7
2
2
7
.
Evaluation Warning : The document was created with Spire.PDF for Python.