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1.
I
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RO
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Gen
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all
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,
t
h
e
elec
tr
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d
is
t
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n
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w
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k
(
DN)
is
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f
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ta
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elec
tr
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d
th
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w
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lo
s
s
es
d
u
e
to
h
i
g
h
(
R
/X)
r
atio
[
1
]
.
T
o
o
v
er
co
m
e
th
is
p
r
o
b
lem
m
a
n
y
r
esear
ch
e
s
ar
e
p
er
f
o
r
m
ed
o
n
t
h
e
i
n
te
g
r
at
io
n
o
f
d
is
tr
ib
u
ted
g
e
n
er
ato
r
s
(
DGs)
in
DN
[
2
]
.
DG
s
k
n
o
wn
as
a
s
m
al
l
s
ca
l
e
elec
tr
ical
g
e
n
er
atio
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u
n
it
(
t
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y
1
kW
-
50
MW
)
it
is
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ted
n
ea
r
to
lo
ad
s
id
e.
D
Gs
m
a
y
d
ep
en
d
o
n
co
n
v
e
n
tio
n
al
an
d
/o
r
n
o
n
-
co
n
v
en
t
io
n
al
s
o
u
r
ce
s
.
R
e
n
e
w
ab
le
en
er
g
y
p
o
w
er
g
e
n
er
atio
n
is
in
cr
ea
s
i
n
g
r
ap
id
l
y
.
So
lar
an
d
w
i
n
d
r
eso
u
r
ce
s
ar
e
th
e
m
o
s
t
r
ea
d
il
y
a
v
ai
lab
le
s
o
u
r
ce
s
.
A
l
s
o
,
DGs
p
la
y
s
s
ig
n
i
f
ica
n
t
r
o
le
i
n
d
ec
r
ea
s
in
g
p
o
w
er
lo
s
s
e
s
,
e
n
h
a
n
cin
g
v
o
lta
g
e
s
tab
ilit
y
a
n
d
v
o
l
tag
e
p
r
o
f
ile
o
f
all
b
u
s
s
es
[
3
]
.
I
n
o
r
d
er
T
o
b
en
ef
it
f
r
o
m
in
s
tallatio
n
DG
s
i
n
DN;
p
lace
m
e
n
t
a
n
d
s
ize
o
f
DGs
m
u
s
t
b
e
o
p
ti
m
ized
C
o
n
s
id
er
in
g
DG
s
ca
p
a
cit
y
a
n
d
v
o
ltag
e
li
m
it.
T
h
e
in
ap
p
r
o
p
r
ia
te
s
itin
g
an
d
s
izi
n
g
o
f
DG
u
n
its
in
t
h
e
R
DS
w
il
l
ad
v
er
s
el
y
af
f
ec
t
t
h
e
s
y
s
te
m
,
w
h
ic
h
is
i
n
cr
ea
s
ed
p
o
w
er
lo
s
s
an
d
v
o
lta
g
e
in
s
tab
ilit
y
[
4
]
.
T
h
u
s
,
s
e
v
er
al
r
esear
c
h
h
a
s
b
ee
n
d
o
n
e
to
ev
alu
ate
th
e
ad
v
an
ta
g
es
o
f
i
n
teg
r
atio
n
R
D
Gs
o
n
DN
b
y
o
p
ti
m
al
l
y
s
iz
in
g
an
d
p
lacin
g
f
o
r
th
ese
u
n
ites
th
r
o
u
g
h
s
o
lv
i
n
g
a
s
in
g
le
o
r
s
ev
er
al
o
b
j
ec
tiv
es
p
r
o
b
lem
s
.
Ma
n
y
al
g
o
r
ith
m
s
ar
e
u
s
ed
to
s
o
lv
e
th
i
s
p
r
o
b
le
m
to
e
n
h
an
ce
th
e
p
er
f
o
r
m
a
n
ce
o
f
elec
tr
ical
D
N.
I
n
[
5
]
,
p
er
f
o
r
m
an
ce
i
m
p
r
o
v
e
m
e
n
t
o
f
d
is
tr
ib
u
tio
n
s
y
s
t
e
m
s
is
p
r
o
p
o
s
ed
b
y
s
o
lv
i
n
g
m
u
l
ti
-
o
b
j
ec
tiv
e
f
u
n
cti
o
n
s
u
s
i
n
g
t
h
e
g
e
n
etic
a
lg
o
r
it
h
m
(
G
A
)
.
I
n
[
6
]
,
an
ap
p
r
o
ac
h
i
s
p
r
ese
n
ted
f
o
r
o
p
tim
u
m
DGs
s
it
in
g
to
en
h
a
n
ce
v
o
ltag
e
s
tab
il
it
y
f
o
r
al
l
b
u
s
es
o
f
n
et
w
o
r
k
a
n
d
les
s
p
o
w
er
lo
s
s
es.
I
n
[
7
]
,
g
en
et
ic
an
d
p
ar
ticle
s
w
a
r
m
o
p
ti
m
izatio
n
ar
e
i
m
p
le
m
e
n
ted
to
f
in
d
t
h
e
o
p
ti
m
u
m
s
ize
a
n
d
lo
ca
tio
n
o
f
DG
s
to
r
ed
u
ce
p
o
w
er
lo
s
s
es
a
n
d
to
e
n
h
a
n
ce
v
o
ltag
e
r
e
g
u
la
tio
n
a
n
d
v
o
ltag
e
s
tab
ilit
y
o
f
DN.
I
n
[
8
]
,
m
u
lti
-
o
b
j
ec
tiv
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
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0
8
8
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8708
I
n
t J
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&
C
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p
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n
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,
Vo
l.
11
,
No
.
2
,
A
p
r
il 2
0
2
1
:
9
7
5
-
983
976
o
p
tim
izatio
n
i
s
p
r
o
p
o
s
ed
t
o
f
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n
d
o
p
tim
a
l
s
izi
n
g
a
n
d
p
lace
m
en
t
o
f
DGs
u
s
i
n
g
P
ar
eto
f
r
o
n
tier
d
if
f
er
en
tial
ev
o
lu
tio
n
alg
o
r
it
h
m
.
I
n
[
9
]
a
s
tr
ateg
y
f
o
r
p
r
o
g
r
am
m
i
n
g
g
o
als
u
s
i
n
g
G
A
w
a
s
p
r
o
p
o
s
ed
f
o
r
s
o
lv
in
g
a
m
u
lti
-
o
b
j
ec
tiv
e
DGs
p
lan
n
in
g
in
d
is
tr
ib
u
tio
n
p
o
w
er
s
y
s
te
m
.
I
n
[
1
0
]
,
f
ir
ef
l
y
alg
o
r
it
h
m
i
s
i
m
p
le
m
en
ted
to
o
b
tain
an
o
p
tim
a
l
s
i
ti
n
g
o
f
m
u
ltip
le
DG
s
in
t
h
e
DN.
So
m
e
r
esear
ch
e
s
tak
e
i
n
to
ac
co
u
n
t
t
h
e
ec
o
n
o
m
i
ca
l
p
er
s
p
ec
tiv
es
o
f
DGs
allo
ca
tio
n
p
r
o
b
lem
s
s
u
c
h
as
in
[
1
1
]
th
at
p
r
esen
ted
o
p
ti
m
al
s
iz
in
g
an
d
p
lace
m
e
n
t
o
f
DGs
f
o
r
r
ed
u
cin
g
p
o
w
er
lo
s
s
es
a
n
d
to
tal
i
n
v
est
m
en
t
co
s
t
u
s
i
n
g
p
r
o
b
ab
ilis
tic
m
u
lti
-
o
b
j
ec
tiv
e
o
p
ti
m
izatio
n
alg
o
r
ith
m
.
I
n
[
1
2
]
,
R
DGs
ar
e
in
teg
r
ated
i
n
to
a
d
is
tr
ib
u
tio
n
s
y
s
te
m
f
o
r
p
o
w
er
lo
s
s
es
r
ed
u
ctio
n
u
s
in
g
a
h
o
n
e
y
b
ee
m
ati
n
g
o
p
tim
izatio
n
al
g
o
r
ith
m
.
T
h
is
p
ap
er
in
tr
o
d
u
ce
ap
p
licati
o
n
o
f
n
e
w
e
f
f
ec
tiv
e
al
g
o
r
ith
m
ca
lled
“
co
y
o
te
o
p
ti
m
izatio
n
alg
o
r
ith
m
(
C
O
A
)
”
to
f
i
n
d
th
e
o
p
ti
m
al
s
ize
an
d
lo
ca
tio
n
o
f
DG
s
b
ase
d
r
en
e
w
ab
le
en
er
g
y
b
y
s
o
l
v
i
n
g
m
u
l
ti
-
o
b
j
ec
tiv
e
f
u
n
ctio
n
.
T
h
e
o
b
j
ec
tiv
es
ar
e
m
i
n
i
m
izi
n
g
p
o
w
er
lo
s
s
e
s
,
en
h
an
ce
m
e
n
t
o
f
VSI
f
o
r
all
b
u
s
es
o
f
n
et
w
o
r
k
,
an
d
d
ec
r
ea
s
in
g
t
h
e
to
tal
o
p
er
atio
n
co
s
t
at
co
n
s
tan
t
lo
ad
p
o
w
er
.
B
y
s
o
l
v
i
n
g
t
h
ese
o
b
j
ec
tiv
es,
t
h
e
p
er
f
o
r
m
an
ce
o
f
elec
tr
ical
n
et
w
o
r
k
s
w
ill
b
e
im
p
r
o
v
ed
.
T
w
o
t
y
p
es
o
f
D
Gs
ar
e
u
s
ed
;
t
y
p
e
I
d
eliv
er
ac
tiv
e
p
o
w
er
o
n
l
y
lik
e
p
h
o
to
v
o
ltaic
an
d
t
y
p
e
I
I
d
eliv
er
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
w
er
at
d
if
f
er
e
n
t
p
o
w
er
f
ac
to
r
s
0
.
9
5
an
d
0
.
8
5
s
u
ch
as
w
i
n
d
t
u
r
b
in
e.
T
h
e
p
r
o
p
o
s
ed
C
O
A
al
g
o
r
it
h
m
is
i
m
p
le
m
e
n
t
ed
o
n
t
h
e
I
E
E
E
R
DS
i
n
cl
u
d
i
n
g
I
E
E
E
3
3
b
u
s
a
n
d
I
E
E
E
6
9
b
u
s
.
C
O
A
al
g
o
r
ith
m
g
iv
e
s
b
etter
r
esu
lt
s
co
m
p
ar
ed
to
o
th
er
alg
o
r
ith
m
s
.
2.
P
RO
B
L
E
M
F
O
R
M
UL
AT
I
O
N
2
.
1
.
P
o
w
er
f
lo
w
a
na
ly
s
is
I
n
R
D
S
P
o
w
er
f
lo
w
an
d
v
o
ltag
e
co
r
r
esp
o
n
d
in
g
to
ea
ch
b
u
s
ca
n
b
e
ca
lcu
la
ted
u
s
in
g
f
o
r
w
ar
d
-
b
ac
k
w
ar
d
s
w
ee
p
al
g
o
r
ith
m
[
1
3
]
,
a
s
in
g
le
li
n
e
d
iag
r
a
m
o
f
t
h
e
s
a
m
p
le
R
DS is
s
h
o
w
n
in
Fig
u
r
e
1
.
Fig
u
r
e
1
.
Sin
g
le
li
n
e
d
iag
r
a
m
o
f
th
e
s
a
m
p
le
R
DS
Fro
m
Fi
g
u
r
e
1,
th
e
i
n
j
e
cted
cu
r
r
en
t a
t n
o
d
e
m
is
ca
lc
u
lated
f
r
o
m
:
I
m
=
(
P
m
+
jQ
m
V
m
)
∗
(
1
)
T
h
e
v
o
ltag
e
at
b
u
s
m
+1
ca
n
b
e
d
eter
m
i
n
e
as i
n
(
2
)
:
V
m
+
1
=
V
m
−
I
m
,
m
+
1
∗
(
R
mm
+
1
+
jX
m
,
m
+
1
)
(
2
)
T
h
e
b
r
an
ch
cu
r
r
en
t b
et
w
ee
n
b
u
s
m
an
d
b
u
s
m
+1
is
d
eter
m
in
ed
as f
o
llo
w
:
I
m
,
m
+
1
=
I
m
+
1
+
I
m
+
2
(
3
)
P
o
w
er
lo
s
s
i
n
li
n
e
s
ec
tio
n
b
etw
ee
n
b
u
s
e
s
m
a
n
d
m
+1
is
d
ete
r
m
in
ed
as
f
o
llo
w
:
,
+
1
=
,
+
1
∗
(
,
+
1
2
+
,
+
1
2
2
)
(
4
)
T
h
e
n
e
tw
o
r
k
t
o
t
a
l
p
o
w
e
r
l
o
s
s
e
s
c
a
n
b
e
c
a
l
c
u
l
a
t
e
d
t
h
r
o
u
g
h
s
u
m
m
i
n
g
l
o
s
s
e
s
i
n
a
l
l
b
r
a
n
c
h
e
s
o
f
t
h
e
n
e
t
w
o
r
k
w
h
ic
h
is
g
iv
e
n
as:
=
∑
,
+
1
=
1
(
5
)
w
h
er
e
b
is
to
tal
n
u
m
b
er
o
f
b
r
an
ch
e
s
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
C
o
y
o
te
mu
lti
-
o
b
jective
o
p
timiz
a
tio
n
a
lg
o
r
ith
m
fo
r
o
p
tima
l lo
ca
tio
n
…
(
E
.
M.
A
b
d
a
lla
h
)
977
2
.
2
.
P
o
w
er
l
o
s
s
m
ini
m
iza
t
io
n
Af
ter
DGs
i
n
s
ta
llatio
n
at
an
o
p
tim
a
l
lo
ca
tio
n
,
th
e
p
o
w
er
lo
s
s
es
w
ill
b
e
d
ec
r
ee
s
an
d
th
e
v
o
lta
g
e
s
tab
ilit
y
i
n
d
ex
w
i
ll
b
e
en
h
a
n
ce
d
.
T
h
e
p
o
w
er
lo
s
s
e
s
f
o
r
th
e
lin
e
s
ec
tio
n
b
et
w
ee
n
b
u
s
e
s
m
an
d
m
+1
ca
n
b
e
d
eter
m
in
e
as
w
r
i
tten
i
n
(
6
)
[
1
4
]
.
(
,
+
1
)
=
,
+
1
∗
(
,
+
1
2
+
,
+
1
2
2
)
(
6
)
Af
ter
DGs i
n
s
tallatio
n
,
th
e
to
t
al
p
o
w
er
lo
s
s
is
d
eter
m
in
ed
as
f
o
llo
w
s
:
=
∑
,
+
1
=
1
(
7
)
P
o
w
er
lo
s
s
i
n
d
ex
(
P
L
I
)
ca
n
b
e
d
eter
m
i
n
ed
as g
iv
e
n
i
n
[
1
5
]
:
1
=
=
(
8
)
w
h
er
e:
i
s
to
tal
p
o
w
er
lo
s
s
if
t
h
er
e
is
DGs.
i
s
to
t
al
p
o
w
er
lo
s
s
i
n
ab
s
en
ce
o
f
DGs.
B
y
i
n
s
tallatio
n
D
Gs i
n
R
D
S th
e
p
o
w
er
lo
s
s
es c
a
n
b
e
m
i
n
i
m
iz
e,
s
o
P
L
I
w
ill b
e
m
i
n
i
m
ized
.
2
.
3
.
Vo
lt
a
g
e
s
t
a
bil
it
y
ind
ex
(
VSI
)
i
m
pro
v
e
m
e
nt
I
t
is
ex
tr
e
m
el
y
n
ec
e
s
s
ar
y
to
m
ain
tai
n
t
h
e
DN
i
n
s
tab
le
o
p
er
atio
n
u
n
d
er
h
ea
v
y
lo
ad
co
n
d
itio
n
s
,
s
o
it
i
s
i
m
p
o
r
tan
t to
ca
lcu
la
te
VSI
as
s
h
o
w
n
in
(
9
)
[
1
6
]
.
=
|
|
4
−
4
∗
[
(
)
+
(
)
]
|
|
2
−
4
∗
|
(
)
+
(
)
|
2
(
9
)
w
h
er
e
,
is
lo
ad
ac
tiv
e
p
o
w
er
at
b
u
s
,
an
d
is
lo
ad
r
ea
ctiv
e
p
o
w
er
b
u
s
,
an
d
ar
e
th
e
r
es
is
ta
n
ce
an
d
r
ea
ctan
ce
o
f
b
r
an
ch
.
T
h
e
b
u
s
w
h
ich
h
a
s
a
m
i
n
i
m
u
m
v
al
u
e
o
f
VSI
is
th
e
m
o
s
t
s
en
s
eti
v
it
y
b
u
s
to
v
o
lta
g
e
co
ll
ap
s
e
u
n
d
er
in
cr
ea
s
i
n
g
lo
ad
th
e
s
e
lead
to
i
n
s
tab
ili
t
y
o
f
t
h
e
v
o
ltag
e.
T
o
m
ain
tai
n
t
h
e
s
y
s
te
m
o
p
er
atio
n
i
n
a
s
tab
le
li
m
it,
it
is
r
e
q
u
i
r
e
d
t
o
m
a
i
n
t
a
i
n
V
S
I
a
t
a
h
i
g
h
e
r
v
a
l
u
e
.
A
s
s
h
o
w
n
i
n
(
1
0
)
s
h
o
w
s
t
h
e
o
b
j
e
c
t
i
v
e
f
u
n
c
t
i
o
n
f
o
r
i
m
p
r
o
v
i
n
g
V
S
I
:
2
=
1
⁄
(
1
0
)
2
.
4
.
O
pera
t
io
n c
o
s
t
m
ini
m
iza
t
io
n
On
e
o
f
th
e
b
e
n
ef
its
o
f
o
p
ti
m
u
m
allo
ca
tio
n
a
n
d
s
izi
n
g
o
f
DGs
i
n
t
h
e
DN
i
s
m
i
n
i
m
izi
n
g
o
v
er
al
l
o
p
er
atin
g
co
s
t
s
.
T
h
e
to
tal
o
p
er
atio
n
co
s
t
(
T
OC
)
co
m
p
r
i
s
es
t
w
o
ele
m
e
n
t
;
t
h
e
f
ir
s
t
ele
m
en
t
is
co
s
t
o
f
t
h
e
r
ea
l
ac
tiv
e
p
o
w
er
d
r
a
w
n
f
r
o
m
elec
tr
ical
s
u
b
s
ta
tio
n
t
h
at
r
ed
u
ce
d
b
y
r
ed
u
ci
n
g
t
h
e
to
tal
p
o
w
er
lo
s
s
es
a
n
d
th
e
s
ec
o
n
d
ele
m
e
n
t is co
s
t o
f
ac
tiv
e
p
o
w
e
r
d
r
o
w
n
f
r
o
m
t
h
e
DG
s
w
h
ich
c
an
b
e
m
i
n
i
m
ized
b
y
m
i
n
i
m
izi
n
g
DGS
s
ize
[
1
7
]
:
TOC
=
(
1
)
+
(
2
)
(
1
1
)
w
h
er
e
1
an
d
2
ar
e
ac
tiv
e
p
o
w
er
c
o
s
t c
o
ef
f
ic
ien
t i
n
$
/KW
s
u
p
p
li
ed
f
r
o
m
s
u
b
s
tatio
n
a
n
d
DGs.
T
h
e
n
et
o
p
er
atio
n
co
s
t c
an
b
e
ca
lcu
lated
as:
3
=
∆
=
2
(
1
2
)
T
h
e
T
OC
w
il
l
b
e
m
i
n
i
m
ized
b
y
m
i
n
i
m
izi
n
g
n
et
o
p
er
atio
n
co
s
ts
.
2
.
5
.
F
o
r
m
ula
t
io
n o
f
m
ulti
-
o
bje
ct
iv
e
f
un
ct
io
n a
nd
co
ns
t
ra
ints
T
h
e
p
r
o
p
o
s
e
d
o
b
j
e
c
t
i
v
e
f
u
n
c
t
i
o
n
s
a
i
m
t
o
m
i
n
i
m
i
z
e
p
o
w
e
r
l
o
s
s
e
s
,
T
O
C
a
n
d
m
a
x
i
m
i
z
e
V
S
I
a
s
s
h
o
w
n
i
n
(
1
3
)
.
min
i
mize
OF
=
min
(
1
1
+
2
2
+
3
3
)
(
1
3
)
w
h
er
e,
1
+
2
+
3
=
1
(
14)
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.
11
,
No
.
2
,
A
p
r
il 2
0
2
1
:
9
7
5
-
983
978
w
h
er
e
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th
e
w
ei
g
h
t
f
ac
to
r
an
d
its
v
a
lu
e
i
s
ch
o
s
e
n
co
r
r
esp
o
n
d
in
g
to
th
e
i
m
p
o
r
tan
ce
o
f
p
o
w
e
r
lo
s
s
es,
v
o
lta
g
e
s
t
a
b
i
l
i
t
y
i
n
d
e
x
,
a
n
d
o
p
e
r
a
t
i
o
n
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o
s
t
.
T
h
e
m
i
n
i
m
i
z
a
t
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o
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o
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o
b
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o
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r
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i
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o
m
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e
t
t
h
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l
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t
r
i
c
a
l
p
o
w
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r
s
y
s
t
e
m
r
e
q
u
i
r
e
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e
n
t
.
T
h
e
s
e
c
o
n
s
t
r
a
i
n
t
s
a
r
e
p
r
e
s
e
n
t
e
d
a
s
f
o
l
l
o
w
s
:
P
o
w
er
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S
[1
]
G
.
Na
m
a
c
h
iv
a
y
a
m
,
e
t
a
l.
,
“
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
o
f
ra
d
ial
d
istri
b
u
ti
o
n
sy
ste
m
s
b
y
m
o
d
i
f
ie
r
f
lo
we
r
p
o
ll
in
a
ti
o
n
a
lg
o
rit
h
m
,
”
El
e
c
trica
l
p
o
we
r c
o
m
p
o
n
e
n
ts
a
n
d
sy
ste
s
,
v
o
l.
4
4
,
n
o
.
1
3
,
p
p
.
1
-
1
1
,
2
0
1
6
.
[2
]
Ak
o
re
d
e
,
M
.
F
.
,
e
t
a
l.
,
“
A
r
e
v
ie
w
o
f
stra
te
g
ies
f
o
r
o
p
ti
m
a
l
p
lac
e
m
e
n
t
o
f
d
istri
b
u
ted
g
e
n
e
ra
ti
o
n
i
n
p
o
w
e
r
d
is
tri
b
u
ti
o
n
s
y
ste
m
s,
”
Res
e
a
rc
h
J
o
u
rn
a
l
o
f
Ap
p
li
e
d
S
c
ien
c
e
s
,
v
o
l.
5
,
n
o
.
2
,
p
p
.
1
3
7
-
1
4
5
,
2
0
1
0
.
[3
]
G
.
R.
P
ru
d
h
v
i
Ku
m
a
r,
D.
S
a
tt
ian
a
d
a
n
,
K.
V
i
jay
a
k
u
m
a
r,
“
A
su
r
v
e
y
o
n
p
o
w
e
r
m
a
n
a
g
e
m
e
n
t
stra
t
e
g
ies
o
f
h
y
b
rid
e
n
e
rg
y
s
y
ste
m
s
in
m
icro
g
rid
,
”
I
n
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
Co
mp
u
ter
En
g
in
e
e
rin
g
(
I
J
ECE
)
,
v
o
l.
1
0
,
n
o
.
2
,
p
p
.
1
6
6
7
-
1
6
7
3
,
2
0
2
0
.
[4
]
M
e
n
d
e
z
,
V.
H.,
e
t
a
l.
,
“
Im
p
a
c
t
o
f
d
istri
b
u
ted
g
e
n
e
ra
ti
o
n
o
n
d
i
stri
b
u
ti
o
n
in
v
e
stm
e
n
t
d
e
f
e
rr
a
l,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
Po
we
r
&
En
e
rg
y
S
y
ste
ms
,
v
o
l.
2
8
,
n
o
.
2
,
p
p
.
2
4
4
-
2
5
2
,
2
0
0
6
.
[5
]
H
a
s
sa
n
,
A
.
A
.
,
e
t
a
l
.
,
“
Hy
b
r
i
d
g
e
n
e
t
i
c
m
u
l
t
i
o
b
j
e
c
t
i
v
e
/f
u
z
z
y
a
lg
o
r
i
t
h
m
f
o
r
o
p
t
im
a
l
s
iz
i
n
g
a
n
d
a
l
l
o
c
a
t
i
o
n
o
f
r
e
n
e
w
a
b
le
DG
sy
s
t
e
m
s
,
”
I
n
t
e
r
n
a
t
i
o
n
a
l
T
r
a
n
s
a
c
t
i
o
n
s
o
n
E
l
e
c
t
r
i
c
a
l
E
n
e
r
g
y
S
y
s
tem
s
,
v
o
l
.
2
6
,
n
o
.
1
2
,
p
p
.
2
5
8
8
-
2
6
1
7
,
2
0
1
6
.
[6
]
M
.
M
.
A
m
a
n
,
e
t
a
l
.
,
“
A
n
e
w
a
p
p
ro
a
c
h
f
o
r
o
p
t
im
u
m
DG
p
l
a
c
e
m
e
n
t
a
n
d
s
i
z
i
n
g
b
a
s
e
d
o
n
v
o
l
t
a
g
e
s
t
a
b
i
l
it
y
m
a
x
im
i
z
a
t
i
o
n
a
n
d
m
i
n
im
iz
a
t
i
o
n
o
f
p
o
w
e
r
l
o
s
s
e
s
,
”
E
n
e
r
g
y
C
o
n
v
e
r
s
i
o
n
a
n
d
M
a
n
a
g
e
m
e
n
t
,
v
o
l
.
7
0
,
p
p
.
2
0
2
-
2
1
0
,
2
0
1
3
.
[7
]
M
.
H.
M
o
ra
d
i.
,
e
t
a
l.
,
“
A
c
o
m
b
in
a
ti
o
n
o
f
g
e
n
e
ti
c
a
lg
o
rit
h
m
a
n
d
p
a
rti
c
le
sw
a
r
m
o
p
ti
m
iza
ti
o
n
f
o
r
o
p
ti
m
a
l
DG
lo
c
a
ti
o
n
a
n
d
siz
i
n
g
in
d
istri
b
u
ti
o
n
sy
ste
m
s,”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
Po
we
r
&
En
e
rg
y
S
y
ste
ms
,
v
o
l.
3
4
,
n
o
.
1
,
p
p
.
6
6
-
7
4
,
2
0
1
2
.
[8
]
M
.
H.
M
o
ra
d
i.
,
e
t
a
l.
,
“
M
u
lt
i
-
o
b
jec
ti
v
e
P
F
DE
a
lg
o
rit
h
m
f
o
r
so
lv
in
g
th
e
o
p
ti
m
a
l
siti
n
g
a
n
d
siz
in
g
p
ro
b
lem
o
f
m
u
lt
ip
le DG
so
u
rc
e
s,”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
E
lec
trica
l
Po
we
r
&
En
e
rg
y
S
y
ste
ms
,
v
o
l.
5
6
,
p
p
.
1
1
7
-
1
2
6
,
2
0
1
4
.
[9
]
K.
Vin
o
th
k
u
m
a
r,
e
t
a
l.
,
“
Distri
b
u
ted
g
e
n
e
ra
ti
o
n
p
la
n
n
i
n
g
:
a
n
e
w
a
p
p
r
o
a
c
h
b
a
se
d
o
n
g
o
a
l
p
r
o
g
ra
m
m
in
g
,
”
El
e
c
tric
Po
we
r Co
mp
o
n
e
n
ts a
n
d
S
y
ste
ms
,
v
o
l.
3
8
,
n
o
.
5
,
p
p
.
2
6
0
-
2
7
4
,
2
0
1
2
.
[1
0
]
S
u
re
sh
k
u
m
a
r
S
.
,
e
t
a
l.
,
“
Op
ti
m
a
l
a
ll
o
c
a
ti
o
n
o
f
m
u
lt
ip
le
d
istri
b
u
te
d
g
e
n
e
ra
to
rs
in
d
istri
b
u
ti
o
n
sy
ste
m
u
sin
g
f
ire
f
l
y
a
lg
o
rit
h
m
,
”
J
o
u
rn
a
l
o
f
El
e
c
trica
l
En
g
i
n
e
e
rin
g
,
v
o
l.
1
7
,
p
p
.
1
-
1
2
,
2
0
1
7
.
[1
1
]
P
a
y
m
a
n
De
h
g
h
a
n
ian
,
e
t
a
l
.
,
“
Op
ti
m
a
l
siti
n
g
o
f
DG
u
n
it
s
in
p
o
w
e
r
s
y
ste
m
s
f
ro
m
a
p
ro
b
a
b
il
isti
c
m
u
lt
i
-
o
b
jec
ti
v
e
o
p
ti
m
iza
ti
o
n
p
e
rsp
e
c
ti
v
e
,”
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
El
e
c
trica
l
P
o
w
e
r
&
En
e
rg
y
S
y
ste
ms
,
v
o
l.
5
1
,
p
p
.
14
-
2
6
,
2
0
1
3
.
[1
2
]
T
a
h
e
r
Nik
n
a
m
,
e
t
a
l.
,
“
A
m
o
d
if
ied
h
o
n
e
y
b
e
e
m
a
ti
n
g
o
p
ti
m
iza
ti
o
n
a
lg
o
ri
th
m
f
o
r
m
u
lt
i
-
o
b
jec
ti
v
e
p
lac
e
m
e
n
t
o
f
re
n
e
wa
b
le en
e
rg
y
re
so
u
rc
e
s
,”
Ap
p
li
e
d
E
n
e
rg
y
,
v
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D.
Da
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a
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m
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th
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d
,”
In
ter
n
a
ti
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a
l
J
o
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rn
a
l
o
f
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e
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trica
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p
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3
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[1
4
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Je
n
-
Ha
o
T
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,
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t
a
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,
“
A
d
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a
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b
u
ti
o
n
sy
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m
lo
a
d
f
lo
w
so
lu
ti
o
n
s
,”
IEE
E
T
r
a
n
sa
c
ti
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P
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li
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3
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p
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3
.
[1
5
]
S
in
g
h
,
D
.
,
“
M
u
lt
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o
b
jec
ti
v
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p
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r
DG
p
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g
w
it
h
l
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m
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ls,
”
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ms
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.
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p
.
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6
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0
0
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Evaluation Warning : The document was created with Spire.PDF for Python.
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983
[1
6
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Ch
a
k
ra
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rt
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,
M
.
,
e
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a
l.
,
“
Vo
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a
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[1
7
]
M
o
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Im
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A
.
,
e
t
a
l.
,
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8
]
M
.
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k
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,
“
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[1
9
]
W
.
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,
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0
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,
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t
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,
"
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iza
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iro
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p
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1
]
M
.
E.
Ba
ra
n
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e
t
a
l.
,
“
Ne
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rk
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c
o
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ra
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2
]
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a
ti
sh
Ku
m
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r
In
jeti,
e
t
a
l.
,
“
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n
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v
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d
ial
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n
sy
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m
s,”
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ter
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J
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r
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l
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3
]
M
.
M
.
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.
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Ja
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M
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.
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4
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S
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lt
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ted
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tri
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ter
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5
]
M
.
E.
Ba
ra
n
,
e
t
a
l.
,
“
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t
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a
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ra
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l
d
istri
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u
ti
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n
sy
ste
m
s
,”
IEE
E
T
ra
n
sa
c
ti
o
n
o
n
Po
we
r De
li
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l.
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o
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.
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H
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RS
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F
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l
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