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s
ed
m
et
h
o
d
r
ed
u
ce
d
th
e
co
m
p
u
ta
t
io
n
al
e
f
f
o
r
ts
o
f
th
e
o
p
tim
izatio
n
p
r
o
ce
s
s
s
i
g
n
if
ica
n
tl
y
.
S
i
m
u
lta
n
eo
u
s
DG
an
d
ca
p
ac
ito
r
p
lace
m
en
t
i
s
d
o
n
e
b
y
m
ea
n
s
o
f
a
m
u
lt
i
o
b
j
ec
tiv
e
f
u
n
c
tio
n
c
o
n
s
is
t
in
g
o
f
lo
s
s
r
ed
u
ctio
n
,
v
o
lta
g
e
i
m
p
r
o
v
e
m
en
t
a
n
d
av
ailab
le
tr
a
n
s
f
er
ca
p
ac
it
y
u
s
in
g
g
en
et
ic
alg
o
r
it
h
m
in
[
1
7
]
.
E
v
o
lu
tio
n
ar
y
p
ar
ticle
s
w
ar
m
o
p
tim
izatio
n
(
E
P
SO
)
is
u
s
ed
[
1
8
]
to
o
p
tim
ize
t
h
e
D
G
ca
p
ac
it
y
co
n
s
id
er
i
n
g
p
o
w
er
lo
s
s
an
d
v
o
ltag
e
p
r
o
f
ile
i
m
p
r
o
v
e
m
en
t
.
A
m
u
lti
-
o
b
j
ec
tiv
e
h
ar
m
o
n
y
s
ea
r
ch
alg
o
r
it
h
m
[
1
9
]
to
ev
al
u
ate
t
h
e
i
m
p
ac
t
o
f
DG
p
lac
e
m
en
t
f
o
r
o
p
tim
a
l
p
lan
n
i
n
g
is
p
r
ese
n
te
d
.
T
h
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
s
co
n
s
id
er
ed
ar
e
p
o
w
er
lo
s
s
a
n
d
v
o
lta
g
e
p
r
o
f
ile
i
m
p
r
o
v
e
m
en
t.
A
m
u
lt
i
-
o
b
j
ec
tiv
e
p
ar
ticle
s
w
ar
m
o
p
ti
m
izat
io
n
[
2
0
]
is
p
r
o
p
o
s
ed
to
d
eter
m
i
n
e
th
e
o
p
ti
m
al
D
G
lo
ca
tio
n
,
s
ize,
a
n
d
g
e
n
er
ated
p
o
w
er
co
n
tr
ac
t
p
r
ice.
T
h
e
o
b
j
ec
tiv
e
o
f
t
h
is
o
p
ti
m
iza
tio
n
is
to
m
i
n
i
m
ize
th
e
d
is
tr
ib
u
tio
n
co
m
p
a
n
y
’
s
co
s
t
an
d
m
ax
i
m
ize
th
e
DG
o
w
n
er
’
s
b
en
ef
it
s
i
m
u
lta
n
eo
u
s
l
y
.
T
h
e
o
p
tim
a
l
p
lace
m
en
t
p
r
o
b
lem
is
f
o
r
m
u
lated
a
s
a
m
i
x
ed
in
te
g
er
p
r
o
g
r
a
m
m
i
n
g
[
2
1
]
co
n
s
id
er
in
g
t
h
e
p
r
o
b
ab
il
is
tic
n
atu
r
e
o
f
DG
o
u
tp
u
ts
an
d
lo
ad
co
n
s
u
m
p
t
i
o
n
,
w
h
er
ei
n
t
h
e
co
s
ts
ar
e
m
in
i
m
ized
a
n
d
p
r
o
f
its
ar
e
m
a
x
i
m
ized
.
Fro
m
th
e
liter
atu
r
e
ca
r
r
ied
o
u
t
it
is
cl
ea
r
th
at
ar
tific
ial
i
m
m
u
n
e
s
y
s
te
m
(
A
I
S)
is
n
o
t
u
s
ed
w
i
d
ely
to
s
o
lv
e
th
i
s
o
p
tim
izatio
n
p
r
o
b
le
m
.
I
n
th
i
s
p
ap
er
,
th
e
f
ea
s
ib
ilit
y
o
f
A
I
S
tec
h
n
iq
u
e
f
o
r
th
e
DG
o
p
ti
m
al
p
lace
m
en
t
p
r
o
b
le
m
i
s
ev
alu
a
t
ed
an
d
its
p
er
f
o
r
m
an
ce
is
co
m
p
a
r
ed
w
it
h
t
h
at
Ge
n
etic
a
lg
o
r
it
h
m
(
G
A
)
a
n
d
P
ar
ticle
S
w
ar
m
Op
ti
m
izatio
n
(
P
SO)
alg
o
r
ith
m
r
es
u
lts
.
T
h
e
p
r
o
b
le
m
is
s
o
l
v
ed
u
s
i
n
g
a
m
u
l
ti
-
o
b
jectiv
e
in
d
e
x
co
n
s
id
er
i
n
g
r
ea
l
an
d
r
ea
ctiv
e
p
o
w
er
lo
s
s
es,
v
o
ltag
e
s
tab
ilit
y
a
n
d
v
o
ltag
e
r
e
g
u
l
atio
n
.
T
h
e
p
r
o
b
le
m
is
s
o
lv
ed
u
s
i
n
g
clo
n
al
s
e
lectio
n
b
ased
A
I
S
alg
o
r
ith
m
alo
n
g
w
it
h
o
p
ti
m
al
p
o
w
er
f
lo
w
.
T
h
e
DG
s
o
u
r
ce
s
u
s
u
all
y
h
a
v
e
a
p
r
ed
eter
m
i
n
e
d
ca
p
ac
it
y
an
d
it
i
s
i
m
p
r
ac
tical
to
alter
it
s
o
u
tp
u
t
ac
co
r
d
in
g
to
th
e
v
ar
iatio
n
s
i
n
t
h
e
lo
ad
th
r
o
u
g
h
o
u
t
a
d
a
y
.
Hen
ce
in
t
h
is
p
ap
er
th
e
DG
s
izes
ar
e
ch
o
s
e
n
f
r
o
m
a
g
iv
en
s
et
o
f
d
is
cr
ete
DG
s
izes
an
d
p
ea
k
lo
ad
lev
el
is
co
n
s
id
e
r
ed
th
r
o
u
g
h
o
u
t
t
h
e
an
al
y
s
is
.
T
h
e
o
p
ti
m
al
s
iti
n
g
p
r
o
b
lem
i
s
s
o
l
v
ed
f
o
r
in
s
ta
lli
n
g
t
h
r
ee
DG
s
o
u
r
ce
s
i
n
t
h
e
d
is
tr
ib
u
tio
n
n
et
w
o
r
k
.
T
h
e
alg
o
r
ith
m
is
te
s
ted
o
n
an
I
E
E
E
3
3
b
u
s
s
y
s
te
m
.
2.
M
UL
T
I
-
O
B
J
E
CT
I
V
E
T
E
C
H
NICAL
I
ND
E
X
F
O
RM
UL
AT
I
O
N
T
h
e
m
u
l
ti
-
o
b
j
ec
tiv
e
tec
h
n
ical
in
d
ex
e
lu
cid
ate
s
t
h
e
d
if
f
er
e
n
t
i
m
p
ac
t
s
o
f
i
n
te
g
r
atio
n
o
f
D
G
s
o
u
r
ce
s
f
r
o
m
a
tec
h
n
ical
p
er
s
p
ec
tiv
e.
MO
T
I
is
f
o
r
m
u
la
ted
w
it
h
f
o
u
r
d
if
f
er
e
n
t
o
b
j
ec
tiv
e
f
u
n
ctio
n
s
an
d
it
is
s
o
lv
ed
as
a
m
ax
i
m
izatio
n
p
r
o
b
le
m
u
s
i
n
g
w
ei
g
h
ted
s
u
m
m
e
th
o
d
.
T
h
e
f
o
u
r
o
b
j
ec
tiv
es
ar
e
to
m
i
n
i
m
ize
t
h
e
r
ea
l
an
d
r
ea
cti
v
e
p
o
w
er
lo
s
s
,
i
m
p
r
o
v
e
t
h
e
v
o
l
tag
e
r
eg
u
latio
n
a
n
d
v
o
lta
g
e
s
tab
ilit
y
.
T
h
e
lo
ca
tio
n
o
f
D
G
w
h
ic
h
g
i
v
es
t
h
e
m
i
n
i
m
u
m
r
ea
l
p
o
w
e
r
lo
s
s
m
a
y
n
o
t
b
e
th
e
o
n
e
w
it
h
th
e
b
est
v
o
ltag
e
p
r
o
f
ile.
Hen
ce
it
is
im
p
o
r
ta
n
t
to
co
n
s
id
er
all
th
ese
o
b
j
ec
tiv
es s
i
m
u
lta
n
eo
u
s
l
y
.
T
h
e
v
ar
io
u
s
i
n
d
ices
u
s
ed
f
o
r
MO
T
I
a
r
e
ex
p
lain
ed
b
elo
w
.
2
.
1
.
Rea
l
P
o
w
er
L
o
s
s
I
nd
e
x
(
RP
L
I
)
T
h
e
r
ea
l
p
o
w
er
lo
s
s
i
s
o
b
tain
e
d
f
r
o
m
l
o
ad
f
lo
w
an
a
l
y
s
is
.
T
h
e
n
o
d
e
w
h
ic
h
g
i
v
es
th
e
m
i
n
i
m
u
m
ac
tiv
e
p
o
w
er
lo
s
s
i
s
p
r
ef
er
r
ed
f
o
r
D
G
p
lace
m
e
n
t.
T
h
e
v
al
u
e
o
f
f
o
r
th
e
k
th
d
is
tr
ib
u
tio
n
n
et
w
o
r
k
co
n
f
i
g
u
r
atio
n
is
o
b
tain
ed
f
r
o
m
(
1
)
,
w
h
er
e
th
e
r
ea
l
p
o
w
er
lo
s
s
f
o
r
ea
ch
s
ec
tio
n
o
f
t
h
e
d
is
tr
ib
u
tio
n
n
et
w
o
r
k
an
d
it
i
s
ev
alu
a
ted
u
s
i
n
g
(
2
)
.
[
∑
∑
]
(
1
)
*
+
(
2
)
w
h
er
e
is
t
h
e
r
ea
l
p
o
w
er
lo
s
s
b
et
w
ee
n
b
u
s
es
i
a
n
d
i+1
,
an
d
ar
e
th
e
r
ea
l
an
d
r
ea
cti
v
e
p
o
w
er
f
lo
w
f
r
o
m
b
u
s
i to
b
u
s
i+1
,
is
th
e
r
e
s
is
ta
n
ce
o
f
t
h
e
li
n
e
co
n
n
ec
t
in
g
b
u
s
i a
n
d
b
u
s
i+1
.
2
.2
.
Rea
c
t
iv
e
P
o
w
er
L
o
s
s
I
nd
ex
(
Q
P
L
I
)
T
h
e
v
alu
e
o
f
QP
L
I
is
ca
lcu
lated
u
s
i
n
g
(
3
)
an
d
th
e
r
ea
c
tiv
e
p
o
w
er
lo
s
s
f
o
r
ea
ch
s
e
ctio
n
i
n
a
d
is
tr
ib
u
tio
n
n
et
w
o
r
k
,
is
g
i
v
en
b
y
(
4
)
.
[
∑
∑
]
(
3
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
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8708
I
J
E
C
E
Vo
l.
7
,
No
.
2
,
A
p
r
il 2
0
1
7
:
6
4
1
–
649
643
*
+
(
4
)
w
h
er
e
th
e
r
ea
cta
n
ce
o
f
t
h
e
lin
e
co
n
n
ec
ti
n
g
b
u
s
es i
a
n
d
i+1
.
2.
3
.
Vo
lt
a
g
e
Reg
ula
t
i
o
n In
de
x
(
VRI)
I
n
a
d
is
tr
ib
u
tio
n
n
et
w
o
r
k
,
w
h
e
n
DG
s
o
u
r
ce
s
ar
e
in
s
talled
,
th
e
n
et
w
o
r
k
v
o
lta
g
es
te
n
d
to
v
ar
y
.
I
n
o
r
d
er
to
u
n
d
er
s
ta
n
d
th
i
s
ef
f
ec
t,
es
p
ec
iall
y
f
o
r
a
cr
itical
o
p
er
atin
g
ca
s
e
li
k
e
m
in
i
m
u
m
d
e
m
an
d
an
d
m
a
x
i
m
u
m
g
en
er
atio
n
,
th
e
v
o
lta
g
e
r
eg
u
la
tio
n
in
d
ex
i
s
ca
lcu
lated
.
T
h
e
m
i
n
i
m
u
m
lo
ad
co
n
d
itio
n
is
co
n
s
id
er
ed
as
1
0
%
o
f
th
e
p
ea
k
lo
ad
.
Fo
r
th
e
b
est
l
o
ca
tio
n
,
th
e
v
o
lta
g
e
r
eg
u
latio
n
v
alu
e
s
h
o
u
ld
b
e
t
h
e
leas
t
o
r
th
e
V
R
I
v
a
lu
e
a
s
ca
lcu
lated
f
r
o
m
(
5
)
s
h
o
u
ld
b
e
clo
s
er
to
u
n
it
y
.
[
∑
(
)
]
(
5
)
w
h
er
e
is
th
e
v
o
lta
g
e
at
n
o
d
e
‘
i
’
w
h
en
t
h
e
lo
ad
is
m
i
n
i
m
u
m
an
d
is
t
h
e
v
o
ltag
e
a
t
n
o
d
e
‘
i’
w
h
e
n
th
e
lo
ad
is
m
a
x
i
m
u
m
,
i.e
.
p
ea
k
lo
ad
f
o
r
th
e
k
th
d
is
tr
ib
u
tio
n
n
e
t
w
o
r
k
co
n
f
ig
u
r
atio
n
.
2.
4
.
Vo
lt
a
g
e
Sta
bil
it
y
I
nd
ex
(
VSI
)
T
h
e
v
o
ltag
e
s
tab
ili
t
y
i
n
d
ex
is
ev
alu
a
ted
u
s
i
n
g
(
6
)
.
T
h
e
n
o
d
e
w
it
h
th
e
m
i
n
i
m
u
m
v
al
u
e
o
f
V
SI
is
p
r
o
n
e
to
v
o
ltag
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[
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2
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MO
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as g
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as g
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(
8
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.
(
8)
T
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m
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th
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g
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n
s
tr
ain
ts
.
1
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Po
w
er
f
lo
w
co
n
s
tr
ain
t
s
[
2
3
]
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(
9
)
)
(
1
0
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)
)
(
)
(
1
1
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w
h
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th
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ac
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p
o
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j
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ted
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i+1
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s
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.
2
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Vo
ltag
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co
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s
tr
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(
1
2
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w
h
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ar
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m
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m
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d
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li
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in
p
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r
u
n
it.
3
)
DG
ca
p
ac
ity
co
n
s
tr
ain
ts
(
1
3
)
Evaluation Warning : The document was created with Spire.PDF for Python.
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m
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d
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m
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ter
m
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as
s
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m
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y
p
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m
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.
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h
e
n
e
w
l
y
p
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d
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to
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s
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m
u
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p
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f
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ti
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B
c
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[
2
4
]
.
T
h
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ad
ap
tiv
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n
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r
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o
f
t
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m
m
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s
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m
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h
e
clo
n
al
s
elec
tio
n
b
ased
A
I
S a
l
g
o
r
ith
m
[
2
5
]
.
3
.
1
.
Clo
na
l Sele
ct
io
n
B
a
s
ed
AIS
Alg
o
rit
h
m
I
n
th
is
al
g
o
r
ith
m
,
in
i
tiall
y
a
r
an
d
o
m
p
o
p
u
latio
n
o
f
an
tib
o
d
i
es
is
g
en
er
ated
.
T
h
ese
ar
e
th
e
ca
n
d
id
ate
s
o
lu
tio
n
s
f
o
r
th
e
o
p
ti
m
izatio
n
p
r
o
b
lem
.
T
h
en
af
f
i
n
it
y
i
s
ca
lc
u
lated
f
o
r
ea
ch
o
f
t
h
ese
an
tib
o
d
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A
m
e
m
o
r
y
s
et
is
f
o
r
m
ed
w
ith
th
e
s
e
i
n
d
iv
i
d
u
als.
I
n
m
a
x
i
m
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n
p
r
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b
le
m
,
t
h
e
s
o
l
u
tio
n
s
h
a
v
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n
g
h
i
g
h
er
v
al
u
es
o
f
th
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o
b
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v
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t
er
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f
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it
y
.
T
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a
n
tib
o
d
ies
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n
d
er
g
o
clo
n
al
p
r
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lif
er
at
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n
p
r
o
p
o
r
tio
n
al
to
th
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a
f
f
i
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it
y
.
T
h
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s
m
o
r
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ar
e
g
e
n
er
ated
f
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r
an
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ig
h
er
f
itn
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s
s
f
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tio
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v
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s
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en
h
y
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m
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tatio
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i
s
p
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f
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m
ed
to
th
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s
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clo
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at
a
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ate
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v
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s
el
y
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r
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p
o
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to
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f
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it
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in
f
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r
an
tib
o
d
ies
u
n
d
er
g
o
m
u
tatio
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w
it
h
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h
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g
h
er
m
u
tatio
n
r
ate.
Ag
ai
n
a
f
f
in
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t
y
i
s
ev
al
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ated
f
o
r
th
e
m
u
tate
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in
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id
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T
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s
co
m
p
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t
h
e
f
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s
t
iter
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n
.
T
h
e
p
r
o
ce
s
s
is
r
ep
ea
ted
u
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til
th
e
s
to
p
p
in
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cr
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is
s
atis
f
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d
an
d
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ch
ti
m
e
t
h
e
m
e
m
o
r
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s
et
h
as to
b
e
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p
d
ated
b
y
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ep
laci
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g
t
h
e
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n
f
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r
an
tib
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d
ies
w
it
h
t
h
e
n
e
w
i
m
p
r
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v
ed
in
d
iv
id
u
als.
3
.
2
.
I
m
ple
m
ent
a
t
io
n o
f
AIS
Alg
o
rit
h
m
f
o
r
O
pti
m
a
l Sit
in
g
o
f
DG
So
urce
s
T
h
e
s
tep
s
in
v
o
l
v
ed
in
t
h
e
A
I
S
alg
o
r
ith
m
f
o
r
o
p
ti
m
al
s
iti
n
g
o
f
DG
s
o
u
r
ce
s
i
n
a
d
is
tr
ib
u
t
io
n
n
et
w
o
r
k
ar
e
as f
o
llo
w
s
.
1.
I
n
p
u
t
t
h
e
lin
e
a
n
d
lo
ad
d
ata
o
f
th
e
d
i
s
tr
ib
u
tio
n
n
et
w
o
r
k
,
th
e
r
atin
g
s
o
f
t
h
e
DG
s
o
u
r
ce
s
a
n
d
th
e
v
o
ltag
e
li
m
it
s
.
P
er
f
o
r
m
th
e
lo
ad
f
lo
w
a
n
al
y
s
i
s
f
o
r
th
e
te
s
t s
y
s
te
m
w
it
h
o
u
t D
G
s
o
u
r
ce
s
.
2.
Gen
er
ate
a
r
an
d
o
m
p
o
p
u
latio
n
o
f
in
d
i
v
id
u
al
s
o
r
an
tib
o
d
ie
s
.
R
ea
l
co
d
in
g
i
s
u
s
ed
f
o
r
r
ep
r
esen
tin
g
t
h
e
an
tib
o
d
ies.
T
h
e
an
t
ib
o
d
ies
th
a
t
v
io
late
th
e
co
n
s
tr
ain
t
s
ar
e
r
e
m
o
v
ed
f
r
o
m
th
e
p
o
p
u
latio
n
.
T
h
e
an
tib
o
d
ies
g
iv
e
th
e
lo
ca
tio
n
s
f
o
r
i
n
s
ta
lli
n
g
th
e
DG
s
o
u
r
ce
s
a
n
d
ca
n
b
e
r
ep
r
esen
ted
as
Ab
i
=
{
L
1……
……
L
N
},
i=1
,
2
,
3
…….
n
,
w
h
er
e
n
i
s
t
h
e
n
u
m
b
er
o
f
in
d
i
v
id
u
al
s
i
n
t
h
e
p
o
p
u
latio
n
an
d
N
is
t
h
e
to
tal
n
u
m
b
er
o
f
DG
s
o
u
r
ce
s
w
h
o
s
e
p
o
s
itio
n
,
L
h
a
s
to
b
e
o
p
ti
m
ized
.
3.
C
alcu
late
t
h
e
a
f
f
in
i
t
y
f
o
r
ea
ch
s
et
o
f
th
e
ca
n
d
id
ate
s
o
lu
tio
n
s
.
T
h
e
af
f
in
i
t
y
is
b
ased
o
n
t
h
e
f
i
tn
es
s
f
u
n
ctio
n
o
r
th
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
.
As
t
h
e
o
b
j
ec
tiv
e
is
to
m
a
x
i
m
ize
t
h
e
v
alu
e
o
f
MO
T
I
,
af
f
i
n
it
y
ca
n
b
e
ca
lcu
lated
d
ir
ec
tl
y
f
r
o
m
(
7
)
.
T
h
e
an
tib
o
d
ies
h
a
v
i
n
g
h
ig
h
er
v
al
u
e
s
o
f
th
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
ar
e
s
to
r
ed
in
th
e
m
e
m
o
r
y
s
et
an
d
th
e
y
w
il
l h
a
v
e
h
i
g
h
er
af
f
in
i
t
y
.
4.
C
lo
n
al
p
r
o
lif
er
atio
n
is
d
o
n
e
f
o
r
an
tib
o
d
ies
w
it
h
a
f
f
i
n
it
y
g
r
ea
ter
th
a
n
0
.
5
5
.
T
h
e
an
tib
o
d
ies
h
a
v
i
n
g
h
i
g
h
er
v
alu
e
s
o
f
th
e
tech
n
ical
i
n
d
ex
w
il
l
h
a
v
e
h
i
g
h
er
a
f
f
i
n
it
y
an
d
h
en
ce
th
e
y
w
il
l
p
r
o
lif
er
ate
m
o
r
e.
T
h
e
n
u
m
b
er
o
f
clo
n
es p
r
o
d
u
ce
d
f
o
r
an
an
ti
b
o
d
y
v
ar
ie
s
b
et
w
ee
n
2
to
5
d
e
p
en
d
in
g
u
p
o
n
it
s
af
f
i
n
it
y
.
5.
T
h
e
m
at
u
r
atio
n
p
r
o
ce
s
s
o
f
th
e
s
e
clo
n
e
s
i
s
ac
h
iev
ed
th
r
o
u
g
h
h
y
p
er
m
u
tatio
n
an
d
th
e
r
ate
o
f
it
i
s
i
n
v
er
s
el
y
p
r
o
p
o
r
tio
n
al
to
th
e
a
f
f
i
n
it
y
.
I
n
t
h
is
p
ap
er
b
o
th
b
in
ar
y
a
n
d
r
ea
l
m
u
tatio
n
s
ar
e
d
o
n
e
an
d
t
w
o
m
u
tated
in
d
iv
id
u
als ar
e
g
e
n
er
ated
f
o
r
a
s
in
g
le
clo
n
e.
B
in
ar
y
m
u
tatio
n
is
ac
h
ie
v
ed
th
r
o
u
g
h
b
it
f
lip
m
u
tatio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8708
I
J
E
C
E
Vo
l.
7
,
No
.
2
,
A
p
r
il 2
0
1
7
:
6
4
1
–
649
645
6.
T
o
u
r
n
am
e
n
t
s
elec
tio
n
is
u
s
ed
to
ch
o
o
s
e
th
e
s
a
m
e
f
ix
ed
n
u
m
b
er
o
f
an
tib
o
d
ies
as
i
n
t
h
e
i
n
it
ial
p
o
p
u
latio
n
.
T
h
e
in
f
er
io
r
an
tib
o
d
ies
i
n
th
e
m
e
m
o
r
y
s
et
ar
e
r
ep
lace
d
w
it
h
n
e
w
i
m
p
r
o
v
ed
in
d
i
v
id
u
als
a
n
d
t
h
u
s
t
h
e
m
e
m
o
r
y
s
et
i
s
u
p
d
ated
.
7.
T
h
e
p
r
o
ce
s
s
is
r
ep
ea
ted
u
n
til
th
e
m
a
x
i
m
u
m
n
u
m
b
er
o
f
iter
atio
n
s
is
r
ea
ch
ed
.
Fro
m
th
e
m
e
m
o
r
y
s
et,
th
e
s
o
lu
tio
n
w
h
ich
g
i
v
es
t
h
e
m
ax
i
m
u
m
v
al
u
e
o
f
f
it
n
e
s
s
f
u
n
ctio
n
is
c
h
o
s
e
n
as
t
h
e
o
p
ti
m
a
l
lo
ca
ti
o
n
f
o
r
D
G
p
lace
m
en
t.
8.
T
h
e
w
h
o
le
p
r
o
ce
s
s
is
r
ep
ea
ted
f
o
r
d
if
f
er
en
t
co
m
b
i
n
atio
n
s
o
f
d
is
cr
ete
DG
s
izes
f
o
r
a
p
ar
ticu
lar
v
al
u
e
o
f
th
e
to
tal
DG
ca
p
ac
it
y
.
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
e
m
u
lti
o
b
j
ec
tiv
e
o
p
ti
m
al
D
G
p
lace
m
en
t
p
r
o
b
le
m
is
s
o
l
v
e
d
u
s
in
g
A
I
S
i
n
M
A
T
L
A
B
en
v
ir
o
n
m
e
n
t.
T
h
e
p
er
s
o
n
al
co
m
p
u
ter
co
n
f
i
g
u
r
atio
n
i
s
I
n
tel(
R
)
co
r
e,
2
.
3
G
Hz,
4
GB
R
A
M.
T
h
e
test
s
y
s
t
e
m
co
n
s
id
er
ed
is
th
e
s
tan
d
ar
d
3
3
b
u
s
r
ad
ial
d
is
tr
ib
u
tio
n
n
et
w
o
r
k
g
i
v
en
i
n
Fi
g
u
r
e
1
,
w
ith
3
2
b
r
an
ch
es
i
n
cl
u
d
in
g
3
later
als.
T
h
e
r
ea
l
an
d
r
ea
ctiv
e
p
o
w
er
o
f
th
e
co
n
n
ec
ted
lo
ad
s
f
o
r
th
is
n
et
w
o
r
k
i
s
3
.
7
2
MW
an
d
2
.
3
MV
A
R
r
esp
ec
tiv
el
y
.
T
h
e
r
ea
l
an
d
r
ea
ctiv
e
p
o
w
er
lo
s
s
es
f
o
r
th
is
r
ad
ial
d
is
tr
ib
u
tio
n
n
et
w
o
r
k
w
i
th
o
u
t
DG
s
o
u
r
ce
s
ar
e
2
1
0
.
9
9
8
k
W
an
d
1
4
3
k
Var
r
esp
ec
tiv
e
l
y
.
T
h
r
ee
d
if
f
e
r
en
t
ca
s
es
ar
e
co
n
s
id
er
ed
w
h
e
r
ein
th
e
to
tal
DG
ca
p
ac
it
y
is
1
MW
,
2
MW
an
d
3
MW
.
Fo
r
ea
ch
o
f
th
ese
ca
s
es,
d
if
f
er
e
n
t
co
m
b
i
n
atio
n
s
o
f
t
h
r
e
e
DG
s
o
u
r
ce
s
o
f
p
r
ed
eter
m
i
n
e
d
d
is
cr
ete
s
izes
ar
e
co
n
s
id
er
ed
.
T
h
e
DG
s
o
u
r
ce
s
ar
e
ch
o
s
en
f
r
o
m
a
u
n
iv
er
s
al
s
et
co
n
s
is
ti
n
g
o
f
DG
s
w
it
h
ca
p
ac
ities
r
an
g
i
n
g
f
r
o
m
0
.
1
2
5
MW
to
2
.
2
5
MW
.
Fig
u
r
e
1.
I
E
E
E
3
3
b
u
s
r
ad
ial
d
is
tr
ib
u
tio
n
n
et
w
o
r
k
T
h
e
o
p
tim
a
l
DG
p
lace
m
e
n
t
p
r
o
b
lem
i
s
s
o
l
v
ed
u
s
i
n
g
ar
ti
f
icial
i
m
m
u
n
e
s
y
s
te
m
.
T
h
e
m
ax
i
m
u
m
n
u
m
b
er
o
f
iter
atio
n
s
i
s
s
et
a
s
1
0
0
an
d
th
e
n
u
m
b
er
o
f
i
n
d
i
v
i
d
u
als
i
n
t
h
e
p
o
p
u
latio
n
i
s
5
0
.
Fo
r
ea
ch
ca
s
e,
t
h
e
o
p
tim
a
l
s
o
l
u
tio
n
is
o
b
tain
ed
af
ter
p
er
f
o
r
m
i
n
g
2
0
tr
ial
r
u
n
s
.
T
h
e
f
o
u
r
o
b
j
ec
tiv
es
u
s
ed
in
th
e
f
o
r
m
u
latio
n
o
f
MO
T
I
ar
e
g
iv
e
n
eq
u
al
i
m
p
o
r
t
an
ce
b
y
co
n
s
id
er
in
g
t
h
e
v
al
u
e
o
f
ea
c
h
w
e
ig
h
t
a
s
0
.
2
5
.
T
h
e
r
esu
lt
s
o
b
tai
n
ed
ar
e
s
h
o
w
n
i
n
T
ab
le
1
.
T
h
e
s
o
lu
ti
o
n
o
b
tain
ed
f
r
o
m
A
I
S
f
o
r
th
e
co
m
b
in
at
io
n
o
f
D
G
s
ize
s
3
7
5
k
W
,
7
5
0
k
W
an
d
1875
k
W
(
ca
s
e
2
)
ar
e
at
n
o
d
es
1
7
,
3
1
an
d
3
.
T
h
e
r
ea
l
an
d
r
ea
ctiv
e
p
o
w
er
lo
s
s
f
o
r
th
is
o
p
ti
m
al
s
o
lu
tio
n
is
7
6
.
9
2
k
W
an
d
5
5
.
0
2
k
Var
.
I
n
o
r
d
er
to
u
n
d
er
s
tan
d
t
h
e
s
ig
n
i
f
i
ca
n
ce
o
f
o
p
ti
m
al
s
iti
n
g
o
f
DG
s
o
u
r
ce
s
,
t
h
e
s
a
m
e
DGs a
r
e
p
lace
d
at
a
r
an
d
o
m
lo
ca
tio
n
i.e
.
at
n
o
d
es 2
,
1
7
an
d
3
3
.
T
h
e
lo
ad
f
lo
w
a
n
al
y
s
i
s
p
er
f
o
r
m
ed
w
it
h
DG
s
at
th
e
r
an
d
o
m
lo
ca
tio
n
g
i
v
es
i
n
c
r
ea
s
ed
r
ea
l
an
d
r
ea
ctiv
e
p
o
w
e
r
lo
s
s
a
m
o
u
n
ti
n
g
to
1
7
8
.
8
9
k
W
an
d
1
3
8
.
4
8
k
Var
r
esp
ec
tiv
el
y
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
E
I
SS
N:
2
0
8
8
-
8708
Op
tima
l S
itin
g
o
f D
G
in
a
Dis
tr
ib
u
tio
n
N
etw
o
r
k
u
s
in
g
A
r
tifi
c
ia
l I
mmu
n
e
S
ystem
(
Meera
P
.
S
.
)
646
T
ab
le
1
.
Op
tim
al
DG
lo
ca
tio
n
s
o
b
tain
ed
u
s
i
n
g
A
I
S
C
a
se
N
o
.
D
G
si
z
e
s
(
M
W
)
T
o
t
a
l
D
G
si
z
e
(
M
W
)
D
G
l
o
c
a
t
i
o
n
M
O
TI
R
e
a
l
P
o
w
e
r
f
r
o
m
u
t
i
l
i
t
y
(
M
W
)
R
e
a
c
t
i
v
e
p
o
w
e
r
f
r
o
m
u
t
i
l
i
t
y
(
M
W
)
P
l
o
ss
(
M
W
)
Q
l
o
ss
(
M
W
)
V
R
I
V
S
I
1
0
.
7
5
,
0
.
7
5
,
1
.
5
3
3
1
,
1
4
,
3
0
.
7
7
0
4
2
0
.
7
8
8
6
2
2
.
3
5
1
6
9
0
.
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I
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8708
I
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[1
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R.
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1
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,
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T
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ms
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l.
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p
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2
]
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,
IEE
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T
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s
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c
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Po
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2
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p
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[1
3
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Bin
a
y
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k
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n
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rjee
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S
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d
M
.
Isla
m
.
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l.
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,
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p
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8
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1
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[1
4
]
R.
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.
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l
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ri,
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t
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l.
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"
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ti
m
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p
lac
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m
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t
a
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in
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m
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ted
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ra
ti
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n
"
,
IEE
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T
ra
n
sa
c
ti
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s
o
n
Po
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r S
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ms
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l.
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),
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p
.
3
2
6
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3
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4
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2
0
1
3
.
[1
5
]
L
u
is
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.
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h
o
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a
l.
,
"
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v
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lu
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ti
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lt
io
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jec
ti
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te
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ica
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x
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,
IEE
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T
ra
n
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c
ti
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n
s
o
n
Po
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l
ive
ry
,
v
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8
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2
0
0
8
.
[1
6
]
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ter alg
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m
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,
IEE
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ti
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Po
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y
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ms
,
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l.
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4
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3
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p
.
1
3
9
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2
0
0
9
.
[1
7
]
A
.
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h
m
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sh
,
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t
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l.
,
"
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u
ted
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ra
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,
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ter
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lec
trica
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mp
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g
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l.
2
(5
)
,
p
p
.
6
1
5
-
6
2
0
,
2
0
1
2
.
[1
8
]
J.J.
Ja
m
ian
,
e
t
a
l.
,
"
I
m
p
le
m
e
n
tati
o
n
o
f
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o
lu
ti
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n
a
ry
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rti
c
le
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iza
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ra
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siz
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,
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ter
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t
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l
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o
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rn
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f
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lec
trica
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n
d
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mp
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ter
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g
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2
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,
p
p
.
1
3
7
-
1
4
6
,
2
0
1
2
.
[1
9
]
Ko
m
a
il
Ne
k
o
o
e
i,
e
t
a
l
.
,
"
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n
im
p
ro
v
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m
u
lt
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o
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jec
ti
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r
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rc
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f
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l
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lac
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m
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n
t
o
f
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Gs
in
d
istri
b
u
ti
o
n
sy
ste
m
s
"
,
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
S
ma
rt
Gr
id
,
v
o
l.
4
(1
),
p
p
.
5
5
7
-
5
6
7
,
2
0
1
3
.
[2
0
]
Am
ir
Am
e
li
,
e
t
a
l.
,
"
A
m
u
lt
io
b
j
e
c
ti
v
e
p
a
rti
c
le
s
w
a
r
m
o
p
ti
m
iza
ti
o
n
f
o
r
siz
in
g
a
n
d
p
lac
e
m
e
n
t
o
f
DG
s
f
ro
m
D
G
o
w
n
e
r’s an
d
d
istri
b
u
ti
o
n
c
o
m
p
a
n
y
’
s v
ie
w
p
o
in
ts
"
,
IEE
E
T
ra
n
sa
c
ti
o
n
s o
n
Po
we
r De
li
v
e
ry
,
v
o
l.
2
9
(
4
),
p
p
.
1
8
3
1
-
1
8
4
0
,
2
0
1
4
.
[2
1
]
Zh
a
o
y
u
W
a
n
g
,
e
t
a
l.
,
"
Ro
b
u
st
o
p
ti
m
iza
ti
o
n
b
a
se
d
o
p
ti
m
a
l
D
G
p
lac
e
m
e
n
t
in
m
icro
g
rid
s
"
,
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
S
ma
rt Grid
,
v
o
l.
5
(
5
),
p
p
.
2
1
7
3
-
2
1
8
2
,
2
0
1
4
.
[2
2
]
M
.
H.
M
o
ra
d
i
a
n
d
M
.
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b
e
d
in
i
,
"
A
c
o
m
b
in
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ti
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o
f
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e
n
e
ti
c
a
lg
o
rit
h
m
a
n
d
p
a
rti
c
le
s
w
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r
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iza
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r
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ti
m
a
l
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lo
c
a
ti
o
n
a
n
d
siz
in
g
in
d
istri
b
u
ti
o
n
sy
ste
m
s
"
,
El
e
c
tric P
o
we
r a
n
d
En
e
rg
y
S
y
ste
ms
,
v
o
l.
34
,
p
p
.
66
-
74
,
2
0
1
2
.
[2
3
]
A
b
u
M
o
u
ti
F
S
a
n
d
El
Ha
w
a
r
y
M
E
,
"
A
n
e
w
a
n
d
fa
st
p
o
we
r
f
lo
w
so
lu
t
io
n
a
lg
o
rith
m
f
o
r
ra
d
ia
l
d
istrib
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ti
o
n
fee
d
e
rs
in
c
lu
d
in
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istri
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ted
g
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n
e
ra
ti
o
n
s
"
,
P
ro
c
e
e
d
in
g
s
o
f
th
e
IEE
E
In
tern
a
ti
o
n
a
l
C
o
n
f
e
re
n
c
e
o
n
S
y
st
e
m
s,
M
a
n
a
n
d
C
y
b
e
rn
e
ti
c
s,
p
p
.
2
6
6
8
-
2
6
7
3
,
2
0
0
7
.
[2
4
]
L
e
a
n
d
ro
N.
d
e
Ca
stro
a
n
d
F
e
rn
a
n
d
o
J.
Vo
n
Z
u
b
e
n
,
"
L
e
a
rn
in
g
a
n
d
o
p
ti
m
iza
ti
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n
u
si
n
g
th
e
c
lo
n
a
l
se
lec
ti
o
n
p
ri
n
c
ip
le
"
,
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Evo
l
u
ti
o
n
a
ry
Co
mp
u
t
a
ti
o
n
,
v
o
l.
6
(3
),
p
p
.
2
3
9
-
2
5
1
,
2
0
0
2
.
[2
5
]
Jo
h
n
E.
Hu
n
t
a
n
d
De
n
ise
E.
Co
o
k
e
,
"
Lea
rn
in
g
u
sin
g
a
n
a
rti
f
i
c
ial
i
m
m
u
n
e
s
y
ste
m
"
,
J
o
u
rn
a
l
o
f
Ne
two
rk
a
n
d
Co
mp
u
ter
A
p
p
li
c
a
ti
o
n
s
,
v
o
l.
19
,
p
p
.
1
8
9
-
2
1
2
,
1
9
9
6
.
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