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Vo
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10
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Dec
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m
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s v
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ro
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w
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s
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Dis
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ib
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Dis
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lt
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.
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DS
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d
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te
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s
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r
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t
d
is
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in
f
r
astru
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ai
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d
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ter
est
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tec
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t
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av
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c
u
l
m
i
n
ated
in
t
h
e
u
s
e
o
f
d
is
tr
ib
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ted
g
e
n
er
atio
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(
DG)
.
T
h
er
e
is
o
th
er
ter
m
i
n
o
lo
g
y
an
d
m
ea
n
i
n
g
s
u
s
ed
to
d
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DG,
an
d
th
is
p
r
o
d
u
ce
s
v
ar
io
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s
v
ie
w
p
o
i
n
ts
[
1
]
:
T
h
e
E
lectr
ic
P
o
w
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R
esear
c
h
I
n
s
tit
u
te
(
E
P
R
I
)
class
if
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DG
as
g
en
er
atio
n
f
r
o
m
a
f
e
w
k
ilo
w
att
s
u
p
to
50
MW
.
I
n
ter
n
atio
n
al
en
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g
y
ag
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n
c
y
(
I
E
A
)
id
en
tifie
s
DG
as
g
e
n
e
r
atin
g
p
lan
t
s
u
p
p
l
y
in
g
a
cu
s
t
o
m
er
o
n
-
s
i
t
e
o
r
s
u
p
p
o
r
tin
g
to
a
d
is
tr
ib
u
tio
n
n
e
t
w
o
r
k
co
n
n
ec
ted
to
th
e
g
r
id
.
T
h
e
I
n
ter
n
atio
n
a
l
C
o
n
f
er
e
n
ce
o
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lar
g
e
Hig
h
Vo
lta
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E
lectr
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c
S
y
s
te
m
s
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C
I
GR
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cla
s
s
i
f
ies
DG
as
s
m
alle
r
th
an
5
0
-
1
0
0
MW
.
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
.
6
,
Dec
em
b
er
2
0
2
0
:
6
1
5
3
-
6
1
6
3
6154
DG
ca
n
b
e
d
ef
i
n
ed
as
s
m
all
-
s
ca
le
p
o
w
er
g
e
n
er
atio
n
to
r
ed
u
ce
cu
s
to
m
er
d
e
m
a
n
d
n
ea
r
to
l
o
ad
ce
n
ter
.
Dis
tr
ib
u
ted
g
e
n
er
atio
n
m
a
y
co
m
e
f
r
o
m
s
ev
er
al
t
ec
h
n
o
lo
g
ie
s
an
d
s
o
u
r
ce
s
.
T
h
e
p
r
in
cip
al
ex
p
lan
atio
n
s
f
o
r
DG
'
s
g
r
o
w
i
n
g
u
s
e
ca
n
b
e
o
u
tli
n
ed
as b
elo
w
[
2
]
:
Hig
h
ly
e
f
f
icie
n
t
m
o
d
er
n
tec
h
n
o
lo
g
y
.
C
o
s
t
o
f
T
r
an
s
m
is
s
io
n
an
d
D
is
tr
ib
u
tio
n
s
y
s
te
m
s
ca
n
b
e
r
e
d
u
ce
d
b
ec
au
s
e
o
f
th
e
DG
u
n
its
ar
e
n
ea
r
to
co
n
s
u
m
er
s
.
I
ts
p
o
s
it
io
n
s
ca
n
b
e
lo
ca
ted
b
e
tter
d
u
e
to
s
m
all
ca
p
ac
it
y
.
T
h
e
in
s
tallatio
n
p
er
io
d
o
f
th
e
DG
p
lan
ts
i
s
s
h
o
r
ter
,
an
d
th
e
i
n
v
e
s
t
m
en
t r
is
k
i
s
n
't v
er
y
h
i
g
h
.
Si
m
p
lici
t
y
o
f
th
e
e
n
er
g
y
m
a
n
a
g
e
m
e
n
t b
y
tr
ac
k
i
n
g
t
h
e
lo
ad
s
d
u
e
to
its
s
m
all
ca
p
ac
it
y
.
P
r
o
v
id
es a
f
lex
ib
le
w
a
y
to
s
ele
ct
a
w
id
e
v
ar
iet
y
o
f
co
s
t
in
g
an
d
r
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l
e
co
m
b
in
atio
n
s
.
DG
tech
n
o
lo
g
ies
ar
e
b
r
o
ad
ly
ca
teg
o
r
ized
in
to
t
w
o
t
y
p
e
s
:
r
en
e
w
ab
le
tech
n
o
lo
g
ies
(
P
V,
W
T
)
an
d
n
o
n
-
r
en
e
w
ab
le
tec
h
n
o
lo
g
ies
(
f
u
el
ce
lls
)
.
I
t
is
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m
p
o
r
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t
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m
i
n
e
th
e
o
p
ti
m
a
l
lo
ca
tio
n
an
d
s
ize
o
f
D
Gs
to
ac
h
iev
e
t
h
e
d
esire
d
p
er
f
o
r
m
a
n
ce
,
g
r
id
r
ei
n
f
o
r
ce
m
e
n
t
,
m
in
i
m
izi
n
g
p
o
w
er
lo
s
s
a
n
d
o
n
-
p
e
ak
o
p
er
atin
g
co
s
t
s
,
i
m
p
r
o
v
e
t
h
e
v
o
lta
g
e
p
r
o
f
ile
an
d
lo
ad
in
g
f
ac
to
r
s
,
r
ep
r
iev
e
o
r
ca
n
ce
lin
g
t
h
e
s
y
s
te
m
u
p
g
r
ad
es,
i
m
p
r
o
v
i
n
g
th
e
s
y
s
te
m
s
ec
u
r
it
y
,
in
cr
ea
s
in
g
r
eliab
ilit
y
a
n
d
ef
f
icie
n
c
y
,
a
n
d
i
m
p
r
o
v
i
n
g
t
h
e
p
o
w
er
q
u
al
it
y
o
f
t
h
e
elec
tr
ica
l
g
r
id
.
Dif
f
er
en
t a
p
p
r
o
ac
h
es h
a
v
e
b
ee
n
s
u
g
g
e
s
ted
f
o
r
d
eter
m
i
n
i
n
g
t
h
e
o
p
ti
m
al
s
ite
a
n
d
s
ize
o
f
DGs in
t
h
e
DN.
Gan
d
o
m
k
ar
et
al.
,
p
r
o
v
id
ed
a
n
e
w
ap
p
r
o
ac
h
b
ased
o
n
a
co
m
b
in
atio
n
o
f
g
en
e
tic
alg
o
r
i
t
h
m
(
GA
)
an
d
S
A
alg
o
r
ith
m
s
f
o
r
o
p
ti
m
al
all
o
ca
tio
n
o
f
DGs
in
d
is
tr
ib
u
tio
n
n
et
w
o
r
k
s
to
i
m
p
r
o
v
e
th
e
o
p
ti
m
izat
io
n
g
o
al
[
3
]
.
Su
tt
h
ib
u
n
a
n
d
B
h
a
s
ap
u
tr
a
ap
p
lied
SA
f
o
r
o
p
ti
m
al
lo
ca
tio
n
o
f
DG
o
n
t
h
e
I
E
E
E
3
0
b
u
s
test
s
y
s
te
m
[
4
].
Kef
a
y
at
et
al.
,
p
r
esen
ted
a
h
y
b
r
id
o
f
an
t
co
lo
n
y
o
p
ti
m
iza
tio
n
an
d
ar
tif
icial
b
ee
co
lo
n
y
o
p
ti
m
izatio
n
f
o
r
o
p
tim
a
l
s
it
in
g
a
n
d
s
izi
n
g
o
f
DG
[
5
]
.
A
li
n
ez
h
ad
et
a
l.,
p
r
o
p
o
s
ed
th
r
ee
alg
o
r
ith
m
s
,
P
SO,
GS
A
a
n
d
G
A
f
o
r
o
p
tim
a
l
lo
ca
tio
n
o
f
D
G
i
n
d
i
s
tr
ib
u
tio
n
s
y
s
te
m
[
6
]
.
J
o
r
d
eh
i
p
r
o
p
o
s
ed
v
ar
io
u
s
ap
p
r
o
ac
h
es
f
o
r
d
eter
m
i
n
atio
n
th
e
b
est
s
i
tti
n
g
a
n
d
s
izi
n
g
o
f
DGs
i
n
elec
tr
ic
p
o
w
er
s
y
s
te
m
s
[
7
]
.
Pra
k
ash
a
n
d
Kh
ato
d
p
r
esen
ted
a
r
ev
ie
w
f
o
r
m
i
n
i
m
izi
n
g
t
h
e
s
y
s
te
m
lo
s
s
e
s
,
i
m
p
r
o
v
in
g
t
h
e
v
o
ltag
e
p
r
o
f
i
l
e,
en
h
a
n
ci
n
g
th
e
s
y
s
te
m
r
elia
b
ilit
y
,
s
tab
il
it
y
a
n
d
lo
ad
ab
ilit
y
b
y
o
p
ti
m
al
s
iz
in
g
a
n
d
s
iti
n
g
tech
n
iq
u
es
f
o
r
DG
[
8
]
.
V
ij
a
y
e
t
al.
,
ap
p
l
y
in
g
b
at
m
o
tiv
a
ted
o
p
tim
izatio
n
al
g
o
r
ith
m
(
B
MO
A
)
f
o
r
o
p
tim
a
l
p
lace
m
e
n
t
a
n
d
s
izi
n
g
o
f
d
i
s
tr
ib
u
ted
p
o
w
e
r
s
o
u
r
ce
s
to
r
ed
u
ce
th
e
ac
ti
v
e
p
o
w
er
lo
s
s
i
n
3
3
-
b
u
s
te
s
t
s
y
s
te
m
[
9
].
Sin
g
h
a
n
d
Sh
ar
m
a,
il
lu
s
tr
ated
a
r
ev
ie
w
o
n
DG
p
lan
n
in
g
i
n
th
e
d
is
tr
ib
u
tio
n
s
y
s
te
m
p
er
f
o
r
m
an
ce
s
s
u
c
h
as r
ea
l a
n
d
r
ea
cti
v
e
p
o
w
er
lo
s
s
,
p
o
w
er
s
y
s
te
m
l
o
ad
ab
ilit
y
,
s
tab
ilit
y
,
r
eliab
ilit
y
,
s
ec
u
r
it
y
,
av
ai
lab
le
p
o
w
er
tr
an
s
f
er
ca
p
ac
it
y
[
10
].
B
an
h
t
h
asit
et
al.
,
s
u
g
g
e
s
t
an
o
p
tim
a
l
g
e
n
er
atio
n
s
ch
ed
u
lin
g
m
e
th
o
d
f
o
r
in
te
g
r
ated
o
f
r
en
e
w
ab
le
en
er
g
y
-
b
ase
d
DG
s
an
d
en
er
g
y
s
to
r
a
g
e
s
y
s
te
m
s
w
it
h
elec
tr
ical
p
o
w
er
s
y
s
te
m
[
1
1
]
.
Ush
a
R
ed
d
y
e
t
al.
,
p
r
o
p
o
s
ed
L
SF
&
D
E
to
d
eter
m
in
e
th
e
o
p
ti
m
al
s
i
ze
an
d
lo
ca
tio
n
o
f
ca
p
ac
ito
r
s
f
o
r
m
i
n
i
m
izi
n
g
th
e
p
o
w
er
lo
s
s
e
s
an
d
i
m
p
r
o
v
i
n
g
t
h
e
v
o
lta
g
e
p
r
o
f
ile
in
R
DN
[
1
2
]
.
L
in
et
al.
,
p
r
esen
ted
a
h
y
b
r
id
ap
p
r
o
ac
h
o
f
an
al
y
tical
m
eth
o
d
(
L
S
F)
f
o
r
s
izin
g
DGs
a
n
d
m
eta
-
h
e
u
r
is
t
ic
m
e
th
o
d
(
P
SO)
f
o
r
s
itti
n
g
D
Gs
b
ased
o
n
o
p
ti
m
al
r
ea
ctiv
e
p
o
w
er
d
is
p
atch
f
o
r
d
ec
r
ea
s
in
g
t
h
e
r
ea
l
p
o
w
er
lo
s
s
[
1
3
].
E
L
-
Sa
y
ed
,
d
eter
m
in
e
t
h
e
o
p
ti
m
al
lo
ca
ti
o
n
,
s
ize
an
d
n
u
m
b
er
s
o
f
D
Gs
to
r
ed
u
ce
p
o
w
er
lo
s
s
a
n
d
im
p
r
o
v
e
v
o
lta
g
e
p
r
o
f
ile
[
1
4
]
.
M.
H.
Mo
r
ad
i
an
d
M.
A
b
ed
in
i,
p
r
esen
ted
a
h
y
b
r
id
ap
p
r
o
ac
h
o
f
g
en
et
ic
al
g
o
r
ith
m
an
d
p
ar
ticle
s
w
ar
m
o
p
ti
m
izatio
n
f
o
r
o
p
tim
al
D
G
lo
ca
tio
n
a
n
d
s
izin
g
in
d
is
tr
ib
u
tio
n
s
y
s
te
m
[
1
5
]
.
J
ith
e
n
d
r
an
at
h
et
al.
,
illu
s
tr
ated
a
co
m
b
in
at
io
n
ap
p
r
o
ac
h
b
ased
o
n
P
SO
an
d
GS
A
to
s
o
l
v
e
t
h
e
o
p
ti
m
al
r
ea
cti
v
e
p
o
w
er
d
is
p
atc
h
p
r
o
b
lem
i
n
p
o
w
er
s
y
s
te
m
[
1
6
]
.
Ver
m
a
a
n
d
L
ak
h
w
a
n
i,
p
r
esen
t
s
tr
o
n
g
r
u
les
d
is
co
v
er
ed
in
d
atab
ases
u
s
in
g
h
y
b
r
id
alg
o
r
ith
m
o
f
G
A
a
n
d
P
SO
[
1
7
]
.
I
n
th
is
p
ap
er
,
L
S
I
,
S
A
,
P
SO
,
L
SI
S
A
,
L
S
I
P
SO
an
d
SA
P
SO
o
p
tim
izatio
n
al
g
o
r
ith
m
s
ar
e
u
s
ed
f
o
r
p
o
s
itio
n
in
g
an
d
s
izin
g
o
f
DGs.
T
h
ese
alg
o
r
it
h
m
s
h
av
e
b
ee
n
test
ed
o
n
I
E
E
E
3
3
-
b
u
s
r
ad
ial
d
is
tr
ib
u
tio
n
s
y
s
te
m
.
2.
P
RO
B
L
E
M
F
O
R
M
UL
AT
I
O
N
T
h
e
h
ig
h
er
lo
s
s
es,
h
i
g
h
er
v
o
lt
ag
e
d
r
o
p
an
d
t
h
er
m
al
li
m
itat
i
o
n
ar
e
v
er
y
m
o
s
t
s
i
g
n
i
f
ican
t
p
r
o
b
lem
i
n
th
e
d
is
tr
ib
u
tio
n
s
y
s
te
m
.
So
,
i
n
ten
s
i
v
e
at
ten
tio
n
to
t
h
e
DG
s
t
ec
h
n
o
lo
g
y
h
as
b
ec
o
m
e
a
v
ital
is
s
u
e
t
h
at
m
u
s
t
b
e
tak
en
in
to
co
n
s
id
er
atio
n
f
o
r
its
i
m
p
ac
t
o
n
t
h
e
d
is
tr
ib
u
tio
n
s
y
s
te
m
.
T
o
s
o
lv
e
th
i
s
p
r
o
b
lem
,
i
t
b
ec
a
m
e
n
ec
es
s
ar
y
to
d
eter
m
i
n
e
t
h
e
o
p
ti
m
al
lo
c
atio
n
an
d
s
ize
o
f
DGs
a
s
it
r
ep
r
esen
ted
th
e
m
ai
n
p
r
o
b
le
m
u
n
d
er
n
e
t
w
o
r
k
r
estrictio
n
s
i
n
cl
u
d
in
g
lo
ad
f
lo
w
i
n
o
r
d
er
to
in
cr
ea
s
e
th
e
o
v
er
all
ef
f
icie
n
c
y
o
f
s
y
s
te
m
p
er
f
o
r
m
an
ce
.
2
.
1
.
L
o
a
d F
lo
w
I
t
is
an
i
m
p
o
r
tan
t
to
o
l
f
o
r
p
o
w
er
s
y
s
te
m
p
la
n
n
in
g
,
o
p
er
atio
n
,
o
p
ti
m
izatio
n
a
n
d
co
n
tr
o
l
to
en
s
u
r
e
s
tab
ilit
y
,
r
eliab
il
it
y
a
n
d
ec
o
n
o
m
y
f
o
r
th
e
elec
tr
ical
s
y
s
te
m
.
T
r
a
d
itio
n
al
m
et
h
o
d
s
f
o
r
lo
ad
f
lo
w
a
n
al
y
s
is
s
u
ch
a
s
N
e
w
t
o
n
R
a
p
h
s
o
n
(
N
R
)
,
G
a
u
s
s
S
e
i
d
e
l
(
G
S
)
m
ay
b
e
u
n
s
u
i
t
a
b
l
e
f
o
r
t
h
e
d
i
s
t
r
i
b
u
t
i
o
n
n
e
t
w
o
r
k
a
n
d
d
i
v
e
r
g
e
d
u
e
t
o
[
1
8
]
:
R
ad
ial
o
r
w
ea
k
l
y
m
es
h
n
et
w
o
r
k
.
Hig
h
R
/X
r
atio
.
Un
b
alan
ce
d
o
p
er
atio
n
.
Dis
tr
ib
u
ted
g
e
n
er
atio
n
.
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
Op
tima
l p
la
n
n
in
g
o
f R
DGs in
elec
tr
ica
l d
is
tr
ib
u
tio
n
n
etw
o
r
ks
…
(
Mo
h
a
mme
d
Ha
mo
u
d
a
)
6155
B
ac
k
w
ar
d
/Fo
r
w
ar
d
S
w
ee
p
(
B
FS
)
alg
o
r
it
h
m
i
s
p
r
ef
er
r
ed
f
o
r
co
r
r
ec
t
p
lan
n
in
g
d
u
e
to
:
T
h
e
ill
-
s
tate
n
at
u
r
e
o
f
R
D
S.
A
cc
u
r
ate
r
esu
lts
o
f
p
o
w
er
f
lo
w
d
ep
en
d
o
n
co
n
v
er
g
e
n
ce
,
i
m
p
le
m
en
ta
tio
n
ti
m
e
a
n
d
iter
atio
n
s
n
u
m
b
er
.
T
h
is
ap
p
r
o
ac
h
is
i
m
p
le
m
e
n
ted
in
t
w
o
s
tep
s
:
t
h
e
b
ac
k
w
ar
d
an
d
f
o
r
w
ar
d
s
w
ee
p
u
s
i
n
g
th
e
lo
a
d
an
d
lin
e
d
ata.
I
n
t
h
e
b
ac
k
w
ar
d
s
w
ee
p
,
v
o
ltag
e
s
a
n
d
cu
r
r
e
n
ts
ar
e
ca
lcu
la
ted
u
s
i
n
g
KV
L
a
n
d
KC
L
s
tar
tin
g
f
r
o
m
th
e
f
ar
t
h
est
n
o
d
e.
I
n
f
o
r
w
ar
d
s
w
ee
p
,
th
e
d
o
w
n
s
tr
ea
m
v
o
lt
ag
e
is
ca
lcu
lated
s
tar
ti
n
g
f
r
o
m
th
e
s
o
u
r
ce
n
o
d
e.
T
h
e
s
tep
s
o
f
B
FS
alg
o
r
it
h
m
ar
e
m
en
t
io
n
ed
b
elo
w
:
I
n
itialize
t
h
e
in
j
ec
ted
cu
r
r
en
t (
=
0
)
I
n
itialize
all
b
u
s
es
v
o
ltag
e
(
=
1
p
u
)
C
alcu
late
th
e
n
o
d
e
cu
r
r
en
t (
=
∗
∗
)
C
alcu
late
th
e
li
n
e
c
u
r
r
en
t (
b
ac
k
w
ar
d
s
w
ee
p
)
(
,
+
1
)
=
+
1
+
∑
(
ℎ
′
+
1
)
Up
d
ate
th
e
b
u
s
es
v
o
ltag
e
(
=
+
1
+
(
(
,
+
1
)
∗
(
,
+
1
)
)
)
Un
til
s
to
p
p
in
g
cr
iter
io
n
.
2
.
2
.
O
bje
c
t
iv
e
f
un
ct
io
n (
O
F
)
T
h
e
m
ai
n
o
b
j
ec
tiv
e
p
r
o
b
lem
is
to
r
ed
u
ce
th
e
to
tal
p
o
w
er
lo
s
s
es a
n
d
b
o
o
s
t th
e
s
y
s
te
m
's
v
o
lta
g
e
p
r
o
f
ile
th
r
o
u
g
h
d
eter
m
in
e
t
h
e
o
p
ti
m
al
ca
p
ac
ity
a
n
d
p
o
s
itio
n
i
n
g
o
f
th
e
DGs u
s
in
g
t
h
e
v
ar
io
u
s
p
r
o
p
o
s
ed
m
et
h
o
d
s
.
=
(
)
=
∑
(
2
+
2
−
2
c
os
(
−
)
)
=
1
(
1
)
2
.
3
.
Sy
s
t
em
co
n
s
t
r
a
ins
T
h
er
e
ar
e
tw
o
t
y
p
es o
f
co
n
s
tr
a
in
ts
w
h
ic
h
co
n
tr
o
l th
e
m
i
n
i
m
iz
atio
n
o
f
o
b
j
ec
tiv
e
f
u
n
ctio
n
:
E
q
u
alit
y
co
n
s
tr
ai
n
ts
:
T
h
ese
c
o
n
s
tr
ain
ts
f
o
r
m
u
lated
th
e
ac
ti
v
e
an
d
r
ea
ctiv
e
p
o
w
er
b
alan
c
e
b
y
p
o
w
er
f
lo
w
eq
u
atio
n
s
.
−
−
=
0
(
2
)
−
−
=
0
(
3
)
I
n
eq
u
alit
y
co
n
s
tr
ain
t
s
: T
h
ese
c
o
n
s
tr
ain
ts
d
eter
m
i
n
e
t
h
e
tech
n
ical
o
p
er
atio
n
li
m
it
s
o
f
p
o
w
er
s
y
s
te
m
.
B
u
s
v
o
lta
g
e
≤
≤
(
4
)
DG
ca
p
ac
it
y
≤
≤
,
≤
≤
(
5
)
DG
lo
ca
tio
n
2
≤
≤
(
6
)
3.
M
E
T
H
O
DO
L
O
G
I
E
S
DG’
s
p
r
o
b
lem
i
s
ev
a
lu
at
in
g
th
e
o
p
ti
m
al
s
ize
a
n
d
lo
ca
tio
n
to
o
p
ti
m
ize
t
h
e
r
eq
u
ir
ed
o
b
j
ec
tiv
e
f
u
n
ctio
n
.
M
aj
o
r
m
et
h
o
d
o
lo
g
ical
tech
n
iq
u
es
f
o
r
s
izi
n
g
a
n
d
s
it
tin
g
o
f
DG
s
ar
e
s
u
m
m
ar
ized
as b
elo
w
[
1
9
]
:
An
al
y
tical
tec
h
n
iq
u
e.
C
o
n
v
en
t
io
n
al
tec
h
n
iq
u
e.
Me
ta
-
h
eu
r
i
s
tic
o
p
ti
m
iza
tio
n
te
ch
n
iq
u
e.
H
y
b
r
id
tech
n
iq
u
e.
A
r
ti
f
icial
i
n
tel
lig
e
n
ce
tec
h
n
iq
u
e.
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
.
6
,
Dec
em
b
er
2
0
2
0
:
6
1
5
3
-
6
1
6
3
6156
4.
M
AT
H
E
M
AT
I
CL
E
M
O
DE
L
O
F
O
P
T
I
M
I
Z
AT
I
O
N
T
E
CH
NIQU
E
S
4
.
1
.
L
o
s
s
s
ens
it
iv
it
y
f
a
ct
o
r
(
L
SF)
L
S
F
is
h
elp
f
u
l
to
o
b
tain
th
e
cr
itical
b
u
s
es
in
t
h
e
n
et
w
o
r
k
.
I
t
ca
n
esti
m
ate
w
h
ich
b
u
s
w
ill
h
av
e
th
e
g
r
ea
test
lo
s
s
r
ed
u
ctio
n
w
h
en
a
DG
is
p
lace
d
.
T
h
e
s
ea
r
ch
s
p
ac
e
o
f
th
e
o
p
tim
izatio
n
p
r
o
b
le
m
is
r
ed
u
ce
d
d
u
e
to
th
e
esti
m
a
tio
n
o
f
t
h
ese
ca
n
d
id
ate
b
u
s
es
[
1
2
,
2
0
,
2
1
]
.
Fig
u
r
e
1
illu
s
tr
ates
a
d
is
tr
ib
u
t
io
n
lin
e
"
"
w
it
h
an
i
m
p
ed
an
ce
+
an
d
a
lo
ad
o
f
+
co
n
n
ec
ted
b
et
w
ee
n
‘
’
an
d
‘
’
b
u
s
e
s
.
Fig
u
r
e
1
.
A
r
ad
ial
d
is
tr
ib
u
tio
n
f
ee
d
er
T
h
e
r
ea
l p
o
w
er
lo
s
s
(
2
)
at
ea
ch
n
o
d
e
in
r
ad
ial
d
is
tr
ib
u
tio
n
n
et
w
o
r
k
(
R
DN
)
ca
n
b
e
ca
lcu
lated
as:
(
)
=
(
2
(
)
+
2
(
)
)
(
(
)
)
2
∗
(
)
(
7
)
A
l
s
o
,
th
e
r
ea
ctiv
e
p
o
w
er
lo
s
s
(
2
)
at
ea
ch
n
o
d
e
in
R
DN
ca
n
b
e
g
iv
e
n
as
:
(
)
=
(
2
(
)
+
2
(
)
)
(
(
)
)
2
∗
(
)
(
8
)
w
h
er
e:
(
)
=
T
o
tal
r
ea
l p
o
w
er
s
u
p
p
lied
b
e
y
o
n
d
th
e
b
u
s
"
".
(
)
=
T
o
tal
r
ea
ctiv
e
p
o
w
er
s
u
p
p
li
ed
b
ey
o
n
d
th
e
b
u
s
"
".
No
w
,
t
h
e
L
SF
ca
n
b
e
ex
p
r
es
s
e
d
as:
=
2
∗
(
)
∗
(
)
(
(
)
)
2
(
9
)
=
2
∗
(
)
∗
(
)
(
(
)
)
2
(
1
0
)
T
h
e
s
tep
s
o
f
L
S
F to
f
i
n
d
th
e
s
elec
ted
b
u
s
f
o
r
DG
p
lace
m
e
n
t
ca
n
b
e
s
u
m
m
ar
ized
as b
elo
w
:
L
S
F
h
a
s
b
ee
n
ca
lcu
lated
as
g
i
v
en
i
n
(
9
)
f
r
o
m
t
h
e
b
ase
ca
s
e
lo
ad
f
lo
w
.
T
h
e
v
al
u
es
o
f
L
S
F
h
av
e
b
ee
n
s
o
r
ted
d
escen
d
in
g
a
n
d
its
b
u
s
in
d
ex
i
n
b
u
s
p
o
s
itio
n
s
“
b
p
o
s
(
i)
”,
w
h
ich
d
eter
m
in
e
t
h
e
s
eq
u
en
ce
f
o
r
m
iti
g
atio
n
.
Vo
ltag
e
s
en
s
iti
v
it
y
f
ac
to
r
s
(
VSF)
ar
e
ca
lc
u
lated
a
s
g
i
v
e
n
i
n
(
1
1
)
b
y
co
n
s
id
er
in
g
th
e
m
i
n
i
m
u
m
v
o
l
tag
e
m
ag
n
it
u
d
e
is
0
.
9
5
pu
as b
elo
w
:
(
)
=
(
)
0
.
95
(
1
1
)
w
h
er
e
(
)
is
th
e
b
u
s
v
o
lta
g
e
.
T
h
e
v
alu
e
s
o
f
w
h
ic
h
les
s
t
h
an
1
.
0
1
ca
n
b
e
s
o
r
ted
ascen
d
in
g
a
n
d
its
b
u
s
in
d
ex
in
t
h
e
ca
n
d
id
ate
b
u
s
es
“b
ca
n
(
i)
”.
T
h
e
s
elec
ted
b
u
s
f
o
r
DG
p
lace
m
e
n
t
ca
n
b
e
d
eter
m
in
e
d
b
y
co
m
p
ar
i
n
g
th
e
b
u
s
p
o
s
itio
n
s
a
n
d
th
e
ca
n
d
id
ate
b
u
s
es a
n
d
c
h
o
o
s
in
g
t
h
e
f
ir
s
t c
o
m
m
o
n
b
u
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
Op
tima
l p
la
n
n
in
g
o
f R
DGs in
elec
tr
ica
l d
is
tr
ib
u
tio
n
n
etw
o
r
ks
…
(
Mo
h
a
mme
d
Ha
mo
u
d
a
)
6157
4
.
2
.
Si
m
ula
t
e
d
a
nn
e
a
lin
g
(
S
A)
SA
i
s
a
s
i
m
p
le
f
o
r
m
lo
ca
l
s
e
ar
ch
alg
o
r
it
h
m
(
a
d
esce
n
t
alg
o
r
ith
m
)
,
w
h
ich
p
r
ef
er
r
ed
w
h
e
n
p
r
o
b
le
m
s
ize
is
lar
g
e.
I
t
is
a
m
eta
-
h
eu
r
is
tic
tec
h
n
iq
u
e
t
h
at
h
as
b
ee
n
u
s
ed
e
x
ten
s
i
v
el
y
to
s
o
lv
e
a
co
m
p
licated
o
p
tim
izatio
n
p
r
o
b
le
m
.
T
h
e
w
o
r
d
an
n
ea
lin
g
r
ef
er
s
to
th
e
c
o
o
lin
g
p
r
o
ce
s
s
a
f
ter
h
ea
ti
n
g
o
f
th
e
m
ater
ial
to
b
ec
o
m
e
h
o
m
o
g
e
n
eo
u
s
an
d
m
o
r
e
h
ar
d
en
[
1
4
]
.
T
h
e
co
n
ce
p
t
o
f
s
o
l
u
tio
n
b
ased
o
n
co
o
l
d
o
w
n
t
h
e
p
o
s
s
ib
le
s
ta
te
o
f
a
th
er
m
o
d
y
n
a
m
ic
s
y
s
te
m
f
r
o
m
th
e
p
r
eli
m
in
ar
y
h
i
g
h
te
m
p
er
atu
r
e.
T
h
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
o
r
co
s
t
of
a
s
o
lu
tio
n
i
s
co
r
r
esp
o
n
d
in
g
to
th
e
e
n
er
g
y
o
f
t
h
e
p
h
y
s
ica
l
s
ta
te.
All
s
o
l
u
tio
n
s
of
t
h
e
o
p
ti
m
i
za
tio
n
p
r
o
b
le
m
ar
e
ac
ce
p
ted
at
h
ig
h
te
m
p
er
atu
r
e
,
b
u
t
at
lo
w
te
m
p
er
atu
r
e
o
n
l
y
th
e
m
i
n
i
m
al
co
s
t
s
o
lu
t
io
n
s
ar
e
ac
ce
p
ted
.
A
lt
h
o
u
g
h
s
i
m
p
lic
it
y
a
n
d
q
u
ick
ex
ec
u
t
io
n
o
f
S
A
alg
o
r
it
h
m
,
t
h
e
d
r
a
w
b
ac
k
o
f
th
is
ap
p
r
o
ac
h
is
th
at
th
e
lo
ca
l
m
i
n
i
m
u
m
f
o
u
n
d
m
a
y
b
e
f
ar
f
r
o
m
t
h
e
g
lo
b
al
m
i
n
i
m
u
m
[
3
]
.
T
o
av
o
id
th
i
s
d
ef
ec
t,
it i
s
n
ec
es
s
ar
y
to
in
cr
ea
s
e
t
h
e
n
u
m
b
er
o
f
iter
atio
n
s
co
m
b
i
n
ed
w
ith
a
n
in
cr
ea
s
ed
n
u
m
b
er
o
f
s
ea
r
c
h
es
at
ea
ch
iter
atio
n
.
T
h
e
in
itial
s
o
lu
tio
n
o
f
S
A
is
r
an
d
o
m
th
e
n
n
e
w
o
n
es a
r
e
p
r
o
p
o
s
ed
th
r
o
u
g
h
lo
ca
l c
h
a
n
g
e
s
a
n
d
ac
ce
p
ted
d
ep
en
d
o
n
th
e
co
n
tr
o
lled
p
r
o
b
ab
ilit
y
.
T
h
e
m
aj
o
r
s
tep
s
o
f
S
A
al
g
o
r
ith
m
ca
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Set a
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ep
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er
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C
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∆
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I
f
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-
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k
=
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n
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n
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n
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iter
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4
.
3
.
P
a
rt
icle
s
wa
r
m
o
pti
m
iz
a
t
io
n
(
P
SO
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Th
is
alg
o
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it
h
m
i
s
d
ep
en
d
i
n
g
o
n
t
h
e
p
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ce
p
tio
n
o
f
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at
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a
n
d
s
w
ar
m
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ee
n
i
n
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ir
d
s
o
r
f
i
s
h
.
P
SO
is
u
s
e
d
w
h
e
n
t
h
e
o
p
t
i
m
i
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t
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n
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e
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a
l
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i
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I
n
t
h
i
s
a
l
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t
h
m
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s
m
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en
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o
cial
ex
p
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ie
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ce
o
f
th
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s
w
ar
m
[
2
2
-
26
]
.
T
h
e
v
alu
e
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f
t
h
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t
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v
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p
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ated
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F
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g
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r
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2
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u
r
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2
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P
ar
ticle
m
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t i
n
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lg
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m
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1
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,
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2
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−
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1
2
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1
3
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W
h
er
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is
th
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n
u
m
b
er
o
f
p
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cles,
is
th
e
d
i
m
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n
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io
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o
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le
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&
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e
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ar
t
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an
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o
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itio
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esp
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er
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est
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w
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g
o
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d
p
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itio
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f
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r
N
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ar
ticles (
&
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
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0
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8708
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n
t J
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lec
&
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p
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,
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l.
10
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6
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2
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1
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3
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4
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4
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y
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o
r
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s
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a.
T
o
r
e
d
u
ce
th
e
co
m
p
lex
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f
c
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m
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u
tatio
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al,
s
ea
r
c
h
s
p
ac
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th
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d
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m
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n
s
io
n
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f
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h
e
o
p
ti
m
iza
ti
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n
p
r
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b
lem
an
d
in
cr
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s
e
t
h
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ac
c
u
r
ac
y
,
a
co
m
b
in
atio
n
o
f
an
al
y
tical
tec
h
n
iq
u
e
(
L
S
F)
an
d
h
e
u
r
is
tic
al
g
o
r
ith
m
s
(
S
A
,
P
SO)
is
u
s
ed
in
t
w
o
s
tep
s
f
o
r
s
o
lv
i
n
g
th
e
p
r
o
b
lem
.
T
h
e
f
ir
s
t
s
tep
to
d
eter
m
in
e
t
h
e
o
p
ti
m
al
lo
ca
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n
b
y
u
s
in
g
L
SF
an
d
S
A
o
r
P
SO in
s
ec
o
n
d
s
tep
f
o
r
o
p
tim
al
s
ize
as d
e
m
o
n
s
tr
a
ted
in
F
ig
u
r
e
3
.
Fig
u
r
e
3
.
L
SIS
A
&
L
SIP
SO a
l
g
o
r
ith
m
s
b.
T
o
av
o
id
th
e
d
r
a
w
b
ac
k
o
f
h
e
u
r
is
tic
al
g
o
r
ith
m
(
S
A
&
P
S
O)
,
th
is
p
ap
er
s
u
g
g
e
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ted
a
n
e
w
ap
p
r
o
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as
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r
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F
i
g
u
r
e
4
,
its
co
n
ce
p
t b
ased
o
n
co
m
b
in
a
tio
n
o
f
S
A
a
n
d
P
SO b
y
t
w
o
s
tr
ateg
ie
s
:
T
h
e
f
ir
s
t
s
tr
ate
g
y
is
av
o
id
i
n
g
th
e
d
ef
ec
t
o
f
S
A
,
w
h
ic
h
i
s
u
p
d
atin
g
th
e
s
o
lu
tio
n
r
a
n
d
o
m
l
y
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n
til
s
to
p
p
in
g
cr
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io
n
b
y
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s
y
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te
m
at
ic
ap
p
r
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t
h
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o
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ti
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al
s
o
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t
f
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i
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g
th
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s
a
m
e
m
a
n
n
er
in
P
SO.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
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g
I
SS
N:
2
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f
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SO
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t
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h
ig
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g
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e
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ted
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tr
ateg
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o
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b
u
t
w
it
h
d
ec
r
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s
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te
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r
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it
ca
n
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n
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g
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al
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ti
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al
v
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u
e
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ased
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r
o
b
a
b
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w
h
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a.
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a)
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b
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u
r
e
4
.
SA
P
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g
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r
ith
m
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a
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First s
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ateg
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S
A
P
SO1
,
(
b
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Seco
n
d
s
tr
ateg
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S
A
P
SO2
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
:
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0
8
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6
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Dec
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2
0
2
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[
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w
h
ile
af
t
er
ad
d
in
g
DG
a
s
i
g
n
i
f
ican
t
i
m
p
r
o
v
e
m
e
n
t
o
f
v
o
lta
g
e
p
r
o
f
ile
w
i
th
in
li
m
it
s
(
ac
ce
p
ted
)
.
T
a
b
le
2
,
s
h
o
w
s
t
h
e
m
o
s
t
p
r
o
p
er
lo
ca
tio
n
an
d
ca
p
ac
it
y
o
f
D
G
an
d
co
r
r
esp
o
n
d
i
n
g
th
e
to
tal
lo
s
s
e
s
f
o
r
ea
ch
s
ce
n
ar
io
.
A
l
s
o
,
it
is
clea
r
th
e
m
i
n
i
m
u
m
v
o
lta
g
e
b
u
s
a
n
d
it
s
v
a
lu
e.
T
h
is
in
d
icat
es
th
a
t
t
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
s
p
r
ed
ict
t
h
e
o
p
ti
m
al
p
o
s
itio
n
an
d
s
ize
f
o
r
DG
s
w
it
h
h
i
g
h
e
f
f
ic
ien
c
y
a
n
d
ac
cu
r
ac
y
.
T
o
p
r
o
v
e
th
e
e
f
f
ec
tiv
e
n
e
s
s
o
f
t
h
e
n
o
v
el
alg
o
r
ith
m
S
A
P
SO,
t
h
e
r
es
u
lts
ac
h
ie
v
ed
b
y
t
h
is
tech
n
iq
u
e
h
av
e
b
ee
n
co
m
p
ar
ed
w
it
h
th
o
s
e
o
b
tain
ed
b
y
t
h
e
o
t
h
er
alg
o
r
ith
m
s
.
B
y
co
m
p
ar
is
o
n
,
i
t d
e
m
o
n
s
tr
ated
th
e
ab
ilit
y
o
f
S
A
P
SO2
to
r
ed
u
ce
s
y
s
te
m
lo
s
s
es
to
th
e
lo
w
est
p
o
s
s
ib
le
v
al
u
e
6
7
.
8
1
1
3
k
w
an
d
in
cr
ea
s
i
n
g
t
h
e
v
o
lta
g
e
p
r
o
f
ile
to
th
e
h
ig
h
est
v
alu
e
0
.
9
5
8
9
6
p
u
(
w
it
h
i
n
ac
ce
p
ted
li
m
it)
s
i
m
u
lta
n
eo
u
s
l
y
.
I
n
ad
d
itio
n
,
th
e
DG
'
s
ca
p
ac
it
y
is
t
h
e
lo
w
e
s
t,
w
h
ic
h
m
ea
n
s
th
at
t
h
e
m
i
n
i
m
u
m
co
s
t is ac
h
ie
v
ed
.
T
h
e
o
p
ti
m
izatio
n
p
r
o
ce
s
s
to
r
ea
ch
th
e
o
p
ti
m
al
s
o
l
u
tio
n
f
o
r
th
e
co
n
s
tr
ai
n
ed
o
b
j
ec
tiv
e
f
u
n
ct
io
n
ca
n
b
e
i
m
p
le
m
en
ted
iter
ati
v
el
y
.
First
l
y
,
in
i
tialize
t
h
e
s
o
lu
t
io
n
r
an
d
o
m
l
y
t
h
e
n
th
e
s
o
l
u
tio
n
u
p
d
ated
iter
ativ
e
till
it
is
r
ea
ch
ed
to
g
lo
b
al
o
p
ti
m
al
m
i
n
i
m
u
m
r
ea
l
p
o
w
er
lo
s
s
is
o
b
tain
ed
,
w
h
ich
ar
o
u
n
d
6
7
.
8
1
1
3
k
w
.
F
ig
u
r
e
8
illu
s
tr
ates
t
h
e
f
it
n
es
s
f
u
n
ct
i
o
n
co
n
v
er
g
e
n
ce
f
o
r
all
al
g
o
r
ith
m
s
.
S
A
P
SO
a
lg
o
r
it
h
m
h
av
e
d
e
m
o
n
s
tr
ated
th
e
s
u
p
er
io
r
it
y
th
r
o
u
g
h
d
is
co
v
er
y
t
h
e
o
p
ti
m
al
s
o
lu
tio
n
to
ac
h
iev
e
g
lo
b
al
m
in
i
m
u
m
f
i
tn
ess
.
Fi
g
u
r
e
8
s
h
o
w
s
th
e
n
o
v
el
t
y
o
f
t
h
e
S
A
P
SO
alg
o
r
ith
m
,
w
h
ic
h
co
n
v
er
g
es
q
u
ick
l
y
b
e
f
o
r
e
t
h
e
o
t
h
er
al
g
o
r
ith
m
s
to
ac
h
ie
v
e
th
e
o
p
ti
m
a
l
f
itn
e
s
s
f
u
n
c
tio
n
.
W
h
er
e
S
A
P
SO1
,
S
A
P
SO2
,
L
SIP
SO,
L
SIS
A
,
P
SO
a
n
d
S
A
r
ea
ch
a
f
ter
1
0
iter
atio
n
s
,
1
8
iter
atio
n
s
,
3
3
iter
atio
n
s
,
6
3
iter
atio
n
s
,
4
0
iter
atio
n
s
an
d
6
0
iter
atio
n
s
,
r
esp
ec
ti
v
el
y
.
Fig
u
r
e
6
.
L
o
s
s
s
e
n
s
iti
v
it
y
in
d
e
x
Fig
u
r
e
7
.
Vo
ltag
e
p
r
o
f
ile
f
o
r
I
E
E
E
-
3
3
b
u
s
test
s
y
s
te
m
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I
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p
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alg
o
r
ith
m
s
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IEEE
-
3
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test
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te
m
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c
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r
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Fig
u
r
e
8
.
C
o
n
v
er
g
en
ce
c
h
ar
ac
t
er
is
tic
o
f
p
r
o
p
o
s
ed
alg
o
r
ith
m
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
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:
2
0
8
8
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8708
I
n
t J
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&
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n
g
,
Vo
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10
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6
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Dec
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b
er
2
0
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0
:
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1
5
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1
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3
6162
7.
CO
NCLU
SI
O
N
Du
e
to
ill
-
co
n
d
itio
n
ed
n
at
u
r
e
o
f
R
DN
s
,
lo
s
s
es
m
i
n
i
m
izatio
n
an
d
v
o
lta
g
e
p
r
o
f
ile
en
h
an
ce
m
en
t
h
a
v
e
b
ee
n
o
f
g
r
ea
t
co
n
ce
r
n
.
T
h
e
in
te
g
r
atio
n
o
f
o
p
ti
m
al
p
lace
m
en
t
an
d
s
izi
n
g
o
f
R
DGs
i
n
R
DS
m
i
n
i
m
ized
th
e
s
y
s
te
m
lo
s
s
es
a
n
d
en
h
a
n
ce
d
th
e
v
o
lta
g
e
p
r
o
f
ile.
T
h
e
v
o
lt
ag
e
p
r
o
f
ile
i
m
p
r
o
v
e
m
e
n
t
ca
n
b
e
ac
h
iev
ed
w
it
h
i
n
th
e
n
et
w
o
r
k
co
n
s
tr
ai
n
t
s
,
s
in
ce
th
e
DGs
i
s
lo
ca
ted
clo
s
el
y
a
t
lo
ad
s
an
d
ca
n
b
e
p
ar
tially
s
u
p
p
lied
a
r
ea
l
an
d
r
ea
ctiv
e
p
o
w
er
to
th
e
lo
ad
s
.
I
t
ca
n
b
e
co
n
clu
d
ed
th
a
t,
th
e
o
p
ti
m
al
DG
p
lace
m
e
n
t
an
d
s
izi
n
g
g
i
v
es
o
r
ien
tatio
n
f
o
r
th
e
ec
o
n
o
m
ic
p
la
n
n
i
n
g
an
d
o
p
er
atio
n
o
f
p
o
w
er
s
y
s
t
e
m
i
n
t
h
e
m
o
d
er
n
i
n
te
g
r
ate
d
g
r
id
.
T
h
is
p
ap
e
r
in
v
e
s
ti
g
ates
th
e
t
y
p
ical
a
n
al
y
ti
ca
l,
h
eu
r
i
s
tic
a
n
d
h
y
b
r
id
i
n
te
g
r
atin
g
s
c
h
e
m
e
to
ca
lcu
late
th
e
o
p
tim
a
l
p
lace
m
e
n
t
an
d
ca
p
ac
it
y
o
f
DG
s
.
I
n
t
h
is
p
ap
er
,
S
A
a
n
d
P
SO
a
m
o
n
g
h
eu
r
i
s
tic
tech
n
iq
u
e
s
h
av
e
b
ee
n
p
er
f
o
r
m
ed
to
s
o
l
v
e
th
e
DGs
p
r
o
b
lem
.
A
n
e
w
p
o
w
er
f
u
l
ev
alu
atio
n
al
g
o
r
ith
m
L
SIS
A
a
n
d
L
SIP
SO
h
av
e
b
ee
n
p
r
esen
t
ed
in
th
is
r
esear
c
h
.
L
SI
is
a
n
ef
f
icie
n
t
i
n
te
g
r
ated
m
e
t
h
o
d
w
it
h
S
A
a
n
d
P
SO
alg
o
r
ith
m
s
f
o
r
d
eter
m
i
n
in
g
t
h
e
o
p
ti
m
al
lo
ca
tio
n
a
n
d
r
ed
u
ce
d
th
e
ti
m
e
s
i
m
u
latio
n
t
o
r
ea
ch
th
e
o
p
ti
m
al
s
o
l
u
tio
n
t
h
r
o
u
g
h
t
h
e
m
o
s
t
v
o
ltag
e
s
e
n
s
i
tiv
it
y
b
u
s
(
th
e
least
VSF
v
alu
e)
a
n
d
p
o
w
er
lo
s
s
e
s
(
th
e
h
i
g
h
est
L
S
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v
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lu
e)
.
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h
e
s
en
s
iti
v
it
y
f
ac
t
o
r
s
r
ed
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ce
d
t
h
e
s
ea
r
ch
s
p
ac
e
an
d
th
e
d
i
m
e
n
s
io
n
o
f
t
h
e
o
p
ti
m
iz
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n
p
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o
b
lem
b
y
esti
m
ati
n
g
t
h
e
s
elec
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u
s
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r
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s
itti
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g
.
L
SI
ac
cu
r
ac
y
h
a
s
b
ee
n
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er
if
ied
b
y
t
h
e
o
th
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r
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p
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o
r
ith
m
s
f
o
r
f
i
n
d
i
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g
t
h
e
o
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ti
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al
s
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l
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tio
n
.
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n
o
v
el
ap
p
r
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h
p
r
in
cip
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r
o
p
o
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ed
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ased
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n
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d
P
SO
alg
o
r
it
h
m
s
i
n
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e
h
y
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r
id
alg
o
r
ith
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ca
lled
SA
P
SO
al
g
o
r
ith
m
.
T
h
e
n
o
v
elt
y
o
f
t
h
is
a
lg
o
r
it
h
m
b
as
ed
o
n
t
w
o
s
tr
ate
g
ies
:
th
e
f
ir
s
t
s
tr
ateg
y
is
a
v
o
id
in
g
r
an
d
o
m
l
y
g
en
er
at
io
n
an
d
u
p
d
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tin
g
th
e
s
o
l
u
tio
n
in
S
A
b
y
u
s
i
n
g
t
h
e
s
a
m
e
m
a
n
n
er
in
P
SO.
T
h
e
s
ec
o
n
d
s
tr
ateg
y
is
a
v
o
id
in
g
t
h
e
lo
ca
l
m
i
n
i
m
a
p
r
o
b
lem
i
n
P
SO
b
ec
a
u
s
e
its
p
ar
ticles
m
a
y
b
e
f
a
iled
to
co
n
v
er
g
e
d
ep
en
d
o
n
i
ts
in
itial
v
al
u
e,
s
o
it
is
i
n
teg
r
at
ed
w
it
h
S
A
i
n
o
r
d
er
to
b
en
ef
it
f
r
o
m
t
h
e
p
r
o
b
ab
ilit
y
r
ate
t
o
ac
ce
p
t
o
r
d
is
ca
r
d
th
e
s
o
l
u
tio
n
a
n
d
escap
e
f
r
o
m
t
h
e
lo
ca
l
m
i
n
i
m
u
m
.
T
h
e
B
FS
alg
o
r
ith
m
i
s
u
s
ed
f
o
r
p
o
w
er
f
lo
w
ca
lc
u
latio
n
s
.
T
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
s
h
av
e
b
ee
n
tes
ted
o
n
I
E
E
E
3
3
b
u
s
s
y
s
te
m
.
T
h
e
r
es
u
lt
s
p
r
o
v
ed
t
h
e
p
r
o
p
o
s
ed
alg
o
r
it
h
m
s
h
a
v
e
t
h
e
ca
p
ab
ilit
y
to
p
r
o
v
id
e
th
e
o
p
ti
m
al
s
o
lu
tio
n
f
o
r
t
h
e
p
r
o
b
lem
o
p
ti
m
izatio
n
.
F
u
r
th
e
r
m
o
r
e,
th
e
r
e
s
u
l
ts
s
h
o
w
t
h
e
ef
f
icien
c
y
o
f
th
e
s
e
ap
p
r
o
ac
h
es
f
o
r
th
e
v
o
ltag
e
s
a
g
m
it
ig
at
io
n
w
it
h
i
n
li
m
its
an
d
p
o
w
er
lo
s
s
r
ed
u
ctio
n
.
Alth
o
u
g
h
t
h
e
d
is
ti
n
g
u
i
s
h
ed
p
er
f
o
r
m
a
n
ce
o
f
all
tech
n
iq
u
e
s
i
n
ter
m
s
o
f
s
o
l
u
tio
n
a
n
d
co
n
v
er
g
en
ce
p
er
f
o
r
m
a
n
ce
,
S
A
P
SO
al
g
o
r
ith
m
h
av
e
p
r
o
v
ed
th
e
s
u
p
er
io
r
it
y
t
h
r
o
u
g
h
f
i
n
d
i
n
g
th
e
o
p
ti
m
al
s
o
lu
t
i
o
n
r
ap
id
l
y
,
ec
o
n
o
m
icall
y
an
d
ac
cu
r
atel
y
w
h
ic
h
allo
w
i
n
g
its
ap
p
licatio
n
in
t
h
e
lar
g
e
-
s
ca
le
d
is
tr
ib
u
tio
n
s
y
s
te
m
s
.
Fi
n
all
y
,
s
o
m
e
r
ec
o
m
m
e
n
d
atio
n
to
co
n
s
id
er
in
th
e
f
u
tu
r
e
w
o
r
k
in
t
h
is
f
ield
:
(
a)
t
h
e
p
o
w
er
f
ac
to
r
w
h
ile
s
izi
n
g
DGs;
(
b
)
t
h
e
r
eliab
ilit
y
i
n
d
ices
as
a
n
o
b
j
ec
tiv
e
f
u
n
ctio
n
co
m
b
i
n
ed
w
i
th
t
h
e
m
en
ti
o
n
ed
o
b
j
ec
tiv
e
f
u
n
ctio
n
to
h
av
e
a
r
eliab
le
an
d
s
ec
u
r
e
d
is
t
r
ib
u
tio
n
s
y
s
te
m
s
.
RE
F
E
R
E
NC
E
S
[1
]
T
.
Ac
k
e
r
m
a
n
n
,
G
.
A
n
d
e
rss
o
n
,
a
n
d
L
.
S
ö
d
e
r,
"
Distrib
u
ted
g
e
n
e
ra
ti
o
n
:
A
d
e
f
in
it
i
o
n
,"
E
lec
tric
Po
we
r
S
y
ste
ms
Res
e
a
rc
h
,
v
o
l.
5
7
,
p
p
.
1
9
5
-
2
0
4
,
2
0
0
1
.
[2
]
G
.
Ce
ll
i,
F
.
P
il
o
,
“
Op
ti
m
a
l
d
istr
ib
u
te
d
g
e
n
e
ra
ti
o
n
a
ll
o
c
a
ti
o
n
in
M
V
d
istri
b
u
ti
o
n
n
e
tw
o
rk
s
,”
2
2
n
d
In
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
IEE
E
Po
we
r E
n
g
i
n
e
e
rin
g
S
o
c
i
e
ty,
p
p
.
8
1
-
8
6
,
2
0
0
1
.
[3
]
G
a
n
d
o
m
k
a
r
M
,
V
a
k
il
ian
M
,
Eh
s
a
n
M
.
,
"
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
si
m
u
late
d
a
n
n
e
a
li
n
g
f
o
r
o
p
ti
m
a
l
DG
a
ll
o
c
a
ti
o
n
in
d
istri
b
u
t
io
n
n
e
t
w
o
rk
s
,"
Pro
c
e
e
d
in
g
o
f
IEE
E
Ca
n
a
d
ia
n
Co
n
fer
e
n
c
e
o
n
El
e
c
trica
l
a
n
d
C
o
mp
u
ter
En
g
i
n
e
e
rin
g
,
6
4
5
-
6
4
8
,
2
0
0
5
.
[4
]
T
.
S
u
tt
h
ib
u
n
a
n
d
P
.
Bh
a
sa
p
u
tra,
"
M
u
lt
i
-
Ob
jec
ti
v
e
Op
ti
m
a
l
Distr
ib
u
te
d
G
e
n
e
ra
ti
o
n
P
lac
e
m
e
n
t
Us
in
g
S
im
u
late
d
A
n
n
e
a
l
-
in
g
,"
In
ter
n
a
ti
o
n
a
l
Co
n
f
e
re
n
c
e
El
e
c
trica
l
En
g
in
e
e
rin
g
/E
lec
tro
n
ics
Co
mp
u
ter
T
e
le
-
c
o
mm
u
n
ica
ti
o
n
s
a
n
d
In
f
o
rm
a
t
io
n
T
e
c
h
n
o
l
o
g
y
(
ECT
I
-
C
ON),
2
0
1
0
.
[5
]
M
.
Ke
f
a
y
a
t,
A
.
L
a
sh
k
a
r
A
ra
a
n
d
S
.
A
.
Na
b
a
v
i
Nia
k
i,
"
A
h
y
b
rid
o
f
a
n
t
c
o
lo
n
y
o
p
ti
m
iz
a
ti
o
n
a
n
d
a
rti
f
icia
l
b
e
e
c
o
lo
n
y
a
lg
o
rit
h
m
f
o
r
p
ro
b
a
b
il
isti
c
o
p
t
ima
l
p
lac
e
m
e
n
t
a
n
d
siz
in
g
o
f
d
istri
b
u
ted
e
n
e
rg
y
re
so
u
rc
e
s
,"
En
e
rg
y
Co
n
v
e
rs
io
n
a
n
d
M
a
n
a
g
e
me
n
t,
v
o
l.
9
2
,
p
p
.
1
4
9
-
1
6
1
,
2
0
1
5
.
[6
]
A
li
n
e
z
h
a
d
,
P
.
,
Ba
k
h
o
d
a
,
O.
Z.
,
a
n
d
M
e
n
h
a
j,
M
.
B.
"
Op
ti
m
a
l
DG
p
lac
e
m
e
n
t
a
n
d
c
a
p
a
c
it
y
a
ll
o
c
a
ti
o
n
u
s
in
g
in
telli
g
e
n
t
a
lg
o
rit
h
m
s,"
4
th
Ira
n
i
a
n
J
o
i
n
t
Co
n
g
re
ss
o
n
Fu
zz
y
a
n
d
In
telli
g
e
n
t
S
y
ste
ms
(
CFIS
),
p
p
.
1
-
8
,
2
0
1
5
.
[7
]
A
.
R.
Jo
rd
e
h
i,
"
A
ll
o
c
a
ti
o
n
o
f
d
istri
b
u
te
d
g
e
n
e
ra
ti
o
n
u
n
it
s
i
n
e
lec
tri
c
p
o
w
e
r
s
y
st
e
m
s:
A
r
e
v
ie
w
,
"
Ren
e
wa
b
le
a
n
d
S
u
sta
in
a
b
le E
n
e
rg
y
Rev
iews
,
v
o
l.
5
6
,
p
p
.
8
9
3
-
9
0
5
,
2
0
1
6
.
[8
]
P
.
P
ra
k
a
sh
a
n
d
D.
K.
Kh
a
to
d
,
"
Op
ti
m
a
l
siz
in
g
a
n
d
siti
n
g
tec
h
n
iq
u
e
s
f
o
r
d
istri
b
u
te
d
g
e
n
e
ra
ti
o
n
in
d
istri
b
u
ti
o
n
s
y
ste
m
s: A
re
v
ie
w
,"
Ren
e
wa
b
le a
n
d
S
u
st
a
in
a
b
le E
n
e
rg
y
Rev
iews
,
v
o
l.
5
7
,
p
p
.
1
1
1
-
1
3
0
,
2
0
1
6
.
[9
]
V
ij
a
y
R,
J
e
e
v
a
M
,
Ra
v
ich
a
n
d
ra
n
C
.
S
,
"
Op
ti
m
a
l
L
o
c
a
ti
o
n
o
f
Distrib
u
ted
E
n
e
rg
y
Re
so
u
rc
e
s
in
M
icro
g
rid
f
o
r
P
o
w
e
r
L
o
ss
M
in
im
iza
ti
o
n
Us
in
g
Ba
t
I
n
sp
ired
A
lg
o
rit
h
m
,
"
S
S
RG
I
n
ter
n
a
t
i
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
tro
n
ics
a
n
d
Co
mm
u
n
ica
ti
o
n
En
g
i
n
e
e
rin
g
,
p
p
.
1
0
1
-
1
0
6
,
2
0
1
6
.
[1
0
]
B.
S
in
g
h
a
n
d
J
.
S
h
a
rm
a
,
"
A
re
v
ie
w
o
n
d
istri
b
u
ted
g
e
n
e
ra
ti
o
n
p
lan
n
in
g
,
"
Ren
e
wa
b
le
a
n
d
S
u
st
a
in
a
b
le
E
n
e
rg
y
Rev
iews
,
v
o
l.
7
6
,
p
p
.
5
2
9
-
5
4
4
,
2
0
1
7
.
[1
1
]
B
.
Ba
n
h
t
h
a
sit,
C
.
Ja
m
ro
e
n
,
a
n
d
S
.
De
c
h
a
n
u
p
a
p
rit
th
a
,
"
Op
ti
m
a
l
G
e
n
e
ra
ti
o
n
S
c
h
e
d
u
li
n
g
o
f
P
o
w
e
r
S
y
st
e
m
f
o
r
M
a
x
i
m
u
m
Re
n
e
wa
b
le
En
e
rg
y
Ha
rv
e
stin
g
a
n
d
P
o
w
e
r
L
o
ss
e
s
M
in
i
m
iz
a
ti
o
n
,
"
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
Co
mp
u
ter
E
n
g
in
e
e
rin
g
(
IJ
ECE
)
,
v
o
l.
8
,
n
o
.
4
,
p
p
.
1
9
5
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-
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9
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6
,
2
0
1
8
.
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