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s
ta.
d
z
1.
I
NT
RO
D
UCT
I
O
N
Af
ter
th
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r
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id
in
cr
ea
s
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in
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tr
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n
d
,
th
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b
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d
elec
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p
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s
.
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o
d
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with
th
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a
co
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tio
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g
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tr
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n
s
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es
[
1
]
.
As
th
e
wo
r
ld
h
ea
d
s
to
war
d
g
r
o
win
g
its
r
elian
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,
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m
b
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DGs
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k
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to
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t
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d
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b
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t
w
o
r
k
(
E
DN
)
h
as
r
is
en
r
ap
i
d
ly
[
2
]
.
I
n
o
r
d
er
to
c
o
p
e
with
t
h
is
h
ig
h
p
en
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n
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DGs
in
to
th
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E
DN,
it is
cr
iti
ca
l th
at
DGs a
r
e
p
o
s
itio
n
ed
at
th
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o
p
ti
m
u
m
lo
ca
tio
n
with
th
e
o
p
tim
u
m
p
r
o
d
u
ctio
n
s
ize.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
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J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
Op
tima
l in
teg
r
a
tio
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f p
h
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to
v
o
lta
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d
is
tr
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ted
g
en
era
tio
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i
n
elec
tr
ica
l…
(
N
a
s
r
ed
d
in
e
B
elb
a
ch
ir
)
51
R
ec
en
tly
,
v
ar
io
u
s
r
esear
c
h
er
s
h
av
e
s
u
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n
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f
PV
-
DG
in
to
E
DN
b
ased
th
r
e
e
ca
teg
o
r
ies:
an
aly
tical,
o
p
ti
m
izatio
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an
d
h
y
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r
id
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o
r
ith
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s
.
I
n
th
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is
s
u
e,
th
e
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im
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ted
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ith
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s
id
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:
ap
p
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in
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b
ased
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p
tim
izatio
n
(
T
L
B
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to
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p
ti
m
ize
s
im
u
ltan
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s
ly
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ac
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p
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wer
lo
s
s
es
(
APL)
an
d
v
o
ltag
e
s
tab
ilit
y
in
d
ex
(
VSI
)
[
3
]
,
p
ar
ticle
s
war
m
o
p
tim
izatio
n
(
PS
O)
alg
o
r
ith
m
f
o
r
two
o
b
jectiv
e
f
u
n
ctio
n
s
,
th
e
APL
r
ed
u
ctio
n
a
n
d
VS
I
im
p
r
o
v
em
e
n
ts
b
y
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
DG
[
4
]
,
T
h
e
in
v
asiv
e
wee
d
o
p
tim
izatio
n
(
I
W
O)
alg
o
r
ith
m
test
ed
f
o
r
d
if
f
e
r
en
t
lo
ad
m
o
d
els
with
th
e
o
b
jectiv
e
f
u
n
ct
io
n
to
r
e
d
u
cin
g
APL
an
d
o
p
er
atin
g
co
s
t
wh
ile
en
h
an
cin
g
th
e
VSI
[
5
]
.
Ap
p
lied
cu
ck
o
o
s
ea
r
ch
o
p
tim
izati
on
(
C
SO)
alg
o
r
ith
m
f
o
r
th
e
s
izin
g
o
f
lar
g
e
-
s
ca
le
g
r
id
-
co
n
n
ec
ted
p
h
o
to
v
o
ltaic
s
y
s
tem
[
6
]
,
ad
ap
tiv
e
g
e
n
etic
al
g
o
r
ith
m
(
AGA)
with
o
n
-
lo
a
d
tap
s
ch
an
g
er
to
t
h
e
o
b
jectiv
e
o
f
m
in
im
izin
g
APL
an
d
m
a
x
im
u
m
b
u
s
v
o
ltag
e
[
7
]
,
an
d
s
y
m
b
io
tic
o
r
g
an
is
m
s
ea
r
ch
(
SOS)
alg
o
r
ith
m
with
lo
s
s
s
en
s
it
iv
ity
f
ac
to
r
to
m
in
im
ize
th
e
APL
o
f
th
e
E
DN
[
8
]
.
I
n
2
0
1
8
,
ap
p
lied
b
in
ar
y
p
ar
ticle
s
war
m
o
p
tim
izatio
n
(
B
PS
O)
to
m
in
im
izin
g
th
e
APL
f
o
r
5
9
-
b
u
s
C
air
o
E
DN
[
9
]
,
n
o
v
el
cu
c
k
o
o
s
ea
r
ch
(
C
S)
alg
o
r
ith
m
with
g
en
etica
lly
r
e
p
lace
d
n
ests
in
o
r
d
e
r
to
m
i
n
im
is
e
APL,
VSI
,
an
d
v
o
ltag
e
p
r
o
f
il
e
[
1
0
]
,
s
em
id
e
f
in
ite
o
p
tim
izat
io
n
alg
o
r
ith
m
(
SOA)
with
th
e
f
o
r
m
u
late
p
r
o
b
lem
b
ased
o
n
m
in
im
izin
g
th
e
AP
L
an
d
t
h
e
s
ize
o
f
DGs
[
1
1
]
,
a
n
d
p
o
p
u
latio
n
-
b
ased
i
n
cr
em
en
tal
lear
n
in
g
(
PB
I
L
)
alg
o
r
ith
m
to
r
ed
u
ce
th
e
APL
an
d
th
e
s
q
u
ar
e
er
r
o
r
in
th
e
v
o
l
tag
e
p
r
o
f
iles
o
f
th
e
E
DN
[
1
2
]
.
I
n
2
0
1
9
,
ap
p
lie
d
s
p
id
er
m
o
n
k
e
y
o
p
tim
izatio
n
(
SMO)
alg
o
r
ith
m
f
o
r
r
ed
u
ce
d
o
f
v
o
ltag
e
d
e
v
iatio
n
p
r
o
b
lem
[
1
3
]
,
win
d
d
r
iv
en
o
p
tim
iz
atio
n
(
W
DO)
alg
o
r
ith
m
co
n
s
id
er
m
ax
im
izin
g
th
e
V
SI
[
1
4
]
,
m
o
d
if
ied
cr
o
w
s
ea
r
ch
alg
o
r
ith
m
(
MCS
A)
alg
o
r
ith
m
f
o
r
m
in
im
izin
g
A
PL
an
d
o
v
er
all
v
o
ltag
e
d
e
v
iatio
n
[
1
5
]
,
m
o
th
f
lam
e
o
p
tim
izatio
n
(
MFO)
alg
o
r
ith
m
,
is
im
p
lem
en
ted
to
o
p
tim
al
allo
ca
tio
n
o
f
th
e
PV
-
DG
to
m
in
im
ize
th
e
APL
o
f
th
e
d
is
tr
ib
u
tio
n
s
y
s
tem
[
1
6
]
,
an
d
also
u
s
ed
th
e
g
en
etic
alg
o
r
ith
m
(
G
A)
with
th
e
aim
o
f
APL
an
d
v
o
ltag
e
r
eg
u
latio
n
[
1
7
]
,
an
d
ap
p
licatio
n
o
f
ad
a
p
tiv
e
d
is
s
ip
ativ
e
PS
O
(
ADPSO)
alg
o
r
ith
m
with
an
o
b
jectiv
e
o
f
m
i
n
im
izin
g
th
e
APL
[
1
8
]
.
I
n
2
0
2
0
,
u
s
ed
v
ir
u
s
c
o
lo
n
y
s
ea
r
ch
(
VC
S)
alg
o
r
ith
m
f
o
r
r
ed
u
ce
d
th
e
n
o
t
s
u
p
p
lied
e
n
er
g
y
(
NSE)
[
1
9
]
,
co
m
p
r
eh
e
n
s
iv
e
lear
n
in
g
PS
O
(
C
L
PS
O)
alg
o
r
ith
m
with
an
o
b
jectiv
e
o
f
m
in
im
izin
g
th
e
APL
[
2
0
]
,
ap
p
lied
v
ar
io
u
s
ad
ap
ti
v
e
ac
ce
ler
atio
n
co
ef
f
icien
ts
PS
O
alg
o
r
ith
m
s
o
n
m
ax
im
izin
g
th
e
APL
l
ev
el
[
2
1
]
,
v
ar
i
o
u
s
ad
ap
tiv
e
PS
O
alg
o
r
ith
m
s
f
o
r
m
in
im
izin
g
th
e
th
r
ee
te
c
h
n
ica
l
p
ar
am
eter
s
[
2
2
]
,
an
d
h
y
b
r
id
ch
ao
tic
m
ap
s
an
d
ad
ap
tiv
e
ac
ce
ler
atio
n
co
e
f
f
icien
ts
PS
O
alg
o
r
ith
m
to
m
u
lti
-
o
b
jectiv
e
f
u
n
ctio
n
s
[
2
3
]
.
R
ec
en
tly
,
ap
p
lied
f
in
e
-
tu
n
ed
p
ar
ticle
s
war
m
o
p
tim
iz
atio
n
(
FP
SO)
alg
o
r
ith
m
f
o
r
A
PL
with
E
DN
r
ec
o
n
f
i
g
u
r
atio
n
[
2
4
]
,
ch
ao
ti
c
g
r
e
y
wo
lf
o
p
tim
izer
(
C
GW
O)
to
m
in
im
ize
a
m
u
lti
-
o
b
jectiv
e
f
u
n
c
tio
n
co
n
s
id
er
in
g
o
v
er
cu
r
r
en
t
r
elay
s
in
d
ices
[
2
5
]
,
an
d
ad
a
p
tiv
e
q
u
a
n
tu
m
in
s
p
ir
ed
ev
o
lu
tio
n
ar
y
al
g
o
r
ith
m
(
AQiE
A)
to
m
in
im
izatio
n
o
f
APL
in
ad
d
itio
n
to
v
o
ltag
e
d
ep
en
d
en
t
lo
ad
m
o
d
els
[
2
6
]
.
T
h
e
au
th
o
r
s
in
th
is
p
ap
er
h
av
e
p
r
o
p
o
s
ed
v
ar
io
u
s
h
y
b
r
id
PS
O
a
lg
o
r
ith
m
s
b
ased
o
n
ch
a
o
tic
m
ap
s
a
n
d
a
d
ap
tiv
e
ac
ce
ler
atio
n
co
e
f
f
icie
n
ts
f
o
r
th
e
o
p
tim
al
lo
ca
tio
n
a
n
d
s
izin
g
o
f
PV
-
DG
s
o
u
r
ce
s
in
I
E
E
E
3
3
-
b
u
s
an
d
6
9
-
b
u
s
E
DNs
to
m
in
im
ize
s
im
u
ltan
io
u
s
ely
th
r
ee
tech
n
ical
p
ar
am
eter
s
r
ep
r
esen
ted
b
y
th
e
m
u
lti
-
o
b
jec
tiv
e
f
u
n
ctio
n
(
MO
F)
.
2.
P
RO
B
L
E
M
F
O
R
M
U
L
AT
I
O
N
2
.
1
.
M
ulti
-
o
bje
ct
iv
e
f
un
ct
io
n
T
h
e
p
r
o
p
o
s
ed
MO
F
is
co
n
s
id
er
ed
to
o
p
tim
ally
allo
ca
te
th
e
PV
-
DGs
b
y
m
in
im
izin
g
s
im
u
ltan
eo
u
s
ly
th
e
th
r
ee
p
a
r
am
eter
s
:
t
o
t
a
l
a
c
t
i
v
e
p
o
w
e
r
l
o
s
s
(
T
APL
)
,
T
VD,
a
n
d
T
OT
,
as f
o
llo
ws:
,
1
2
1
b
u
s
b
u
s
R
NN
N
i
j
j
i
i
j
i
M
O
F
M
in
im
ize
TA
P
L
TV
D
TO
T
=
=
=
=
+
+
(
1
)
Firstl
y
,
th
e
T
APL
,
ex
p
r
ess
ed
a
s
[
1
6
]
,
[
2
5
]
:
,,
12
b
u
s
b
u
s
N
N
i
j
i
j
ij
T
A
P
L
A
P
L
==
=
(
2
)
(
)
(
)
,
i
j
ij
i
j
i
j
ij
i
j
i
j
A
P
L
P
P
Q
Q
Q
P
P
Q
=
+
+
+
(
3
)
(
)
c
o
s
ij
i
j
i
j
ij
R
VV
=−
,
(
)
s
in
ij
i
j
i
j
ij
R
VV
=+
(
4
)
W
h
er
e,
N
bus
is
th
e
b
u
s
n
u
m
b
e
r
,
R
ij
is
t
h
e
lin
e
r
esis
tan
ce
,
V
i
,
V
j
a
n
d
δ
i
,
δ
j
ar
e
th
e
v
o
ltag
es
an
d
an
g
les
at
th
e
b
u
s
es.
P
i
, P
j
an
d
Q
i
, Q
j
r
ep
r
esen
t p
o
wer
s
at
b
u
s
es.
Seco
n
d
ly
,
th
e
T
VD
,
wh
ich
is
ex
p
r
ess
es b
y
[
2
2
]
,
[
2
3
]
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci,
Vo
l.
24
,
No
.
1
,
Octo
b
er
2
0
2
1
:
50
-
60
52
2
1
bus
N
jj
j
T
V
D
V
=
=−
(
5
)
Fin
ally
,
th
e
o
v
er
c
u
r
r
e
n
t
r
elay
’
s
T
OT
,
o
f
th
e
ty
p
e
b
ased
tim
e
-
cu
r
r
en
t
-
v
o
ltag
e
tr
ip
p
i
n
g
ch
a
r
ac
ter
is
tic
(
NS
-
OC
R
)
[
2
7
]
,
wich
is
d
ef
in
ed
as f
o
llo
w:
1
R
N
ii
i
T
O
T
T
=
=
(
6
)
(
)
1
1
1
FM
K
ii
B
V
i
A
T
TD
S
M
e
−
=
−
,
F
i
P
I
M
I
=
(
7
)
W
h
er
e,
T
i
is
th
e
r
elay
’
s
o
p
er
at
io
n
tim
e,
TDS
i
is
th
e
tim
e
d
ial
s
ettin
g
,
A
,
B
an
d
K
ar
e
co
n
s
ta
n
ts
s
et
to
0
.
1
4
,
0
.
0
2
an
d
1
.
5
r
esp
ec
tiv
ely
,
V
FM
is
t
h
e
f
a
u
lt
v
o
ltag
e
m
a
g
n
itu
d
e
an
d
N
R
is
th
e
o
v
e
r
cu
r
r
e
n
t
r
elay
s
n
u
m
b
er
.
M
i
is
th
e
m
u
ltip
le
o
f
p
ic
k
u
p
c
u
r
r
e
n
t,
I
F
an
d
I
P
ar
e
th
e
f
a
u
lt c
u
r
r
e
n
t a
n
d
th
e
p
ick
u
p
cu
r
r
en
t,
r
esp
ec
tiv
e
ly
.
2
.
2
.
E
qu
a
lity
co
ns
t
ra
ints
E
q
u
ality
co
n
s
tr
ain
ts
ca
n
b
e
ex
p
r
ess
ed
b
y
th
e
f
o
llo
win
g
e
q
u
at
io
n
s
o
f
p
o
wer
b
alan
ce
:
G
P
V
D
G
D
L
o
s
s
P
P
P
P
−
+
=
+
(
8
)
G
D
Lo
s
s
Q
Q
Q
=+
(
9
)
2
.
3
.
Dis
t
ributio
n
lin
e
co
ns
t
ra
ints
T
h
e
d
is
tr
ib
u
tio
n
lin
e
in
eq
u
ality
co
n
s
tr
ain
ts
ca
n
b
e
g
iv
en
as:
m
in
m
a
x
i
V
V
V
(
1
0
)
m
a
x
1
j
VV
−
(
1
1
)
m
a
x
ij
SS
(
1
2
)
2
.
4
.
PV
-
DG
un
it
s
co
ns
t
ra
ints
T
h
e
PV
-
DG
u
n
it lim
its
in
eq
u
a
lity
co
n
s
tr
ain
ts
ca
n
b
e
ex
p
r
ess
ed
as:
m
i
n
m
a
x
P
V
D
G
P
V
D
G
P
V
D
G
PPP
−−−
(
1
3
)
(
)
(
)
11
P
V
D
G
b
u
s
NN
D
ii
P
V
D
G
i
P
i
−
==
−
(
1
4
)
2
P
o
s
i
t
i
o
n
b
u
s
P
V
D
G
N
−
(
1
5
)
.
m
a
x
P
V
D
G
P
V
D
G
NN
−−
(
1
6
)
,
/1
P
V
D
G
i
n
L
o
c
a
t
i
o
n
−
(
1
7
)
3.
O
VE
RVI
E
W
O
F
H
YB
RID
P
SO
AL
G
O
RI
T
H
M
3
.
1
.
B
a
s
ic
P
SO
a
lg
o
rit
hm
T
h
e
PS
O
alg
o
r
ith
m
was
in
tr
o
d
u
ce
d
in
1
9
9
5
to
d
ev
el
o
p
an
o
p
tim
al
s
o
lu
tio
n
to
a
p
r
o
b
lem
,
wh
ich
is
in
s
p
ir
ed
f
r
o
m
th
e
s
o
cial
b
eh
av
io
r
o
f
an
im
als
e
v
o
lv
in
g
in
s
war
m
s
.
E
ac
h
in
d
iv
id
u
al
o
f
its
p
o
p
u
latio
n
is
ca
lled
a
p
ar
ticle,
th
at
illu
s
tr
ates
a
s
o
lu
t
io
n
,
h
en
ce
th
is
p
ar
ticle
is
m
o
v
in
g
ac
c
o
r
d
in
g
to
th
e
f
o
ll
o
win
g
eq
u
atio
n
s
at
ea
c
h
iter
atio
n
k
[
2
8
]
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
Op
tima
l in
teg
r
a
tio
n
o
f p
h
o
to
v
o
lta
ic
d
is
tr
ib
u
ted
g
en
era
tio
n
i
n
elec
tr
ica
l…
(
N
a
s
r
ed
d
in
e
B
elb
a
ch
ir
)
53
1
1
1
2
2
.
k
k
k
k
k
k
i
i
be
st
i
be
st
i
V
V
c
r
P
X
c
r
G
X
+
=
+
−
+
−
(
1
8
)
11
k
k
k
i
i
i
X
X
V
++
=+
(
1
9
)
(
)
m
a
x
m
a
x
m
in
m
a
x
k
k
=
−
−
(
2
0
)
W
h
er
e,
ω
is
t
h
e
in
e
r
tia
weig
h
t
,
V
i
is
t
h
e
v
el
o
city
o
f
p
ar
ticle,
X
i
is
th
e
p
o
s
itio
n
o
f
p
ar
ticle,
G
best
a
n
d
P
best
a
r
e
th
e
s
war
m
o
v
er
all
b
est
an
d
p
r
e
v
io
u
s
p
er
s
o
n
al
b
est
o
f
th
e
p
ar
ticle,
r
esp
ec
tiv
ely
.
k
an
d
k
max
ar
e
iter
atio
n
an
d
m
ax
im
u
m
iter
atio
n
s
n
u
m
b
er
s
,
c
1
,
c
2
ar
e
th
e
ac
ce
ler
atio
n
co
ef
f
icien
ts
,
an
d
r
is
a
r
an
d
o
m
n
u
m
b
er
.
R
esear
ch
er
s
h
av
e
p
r
o
p
o
s
ed
m
an
y
PS
O
al
g
o
r
ith
m
s
b
y
ed
itin
g
t
h
e
p
ar
a
m
eter
s
o
f
(
ω
,
c
1
,
c
2
an
d
r
)
to
r
ea
ch
its
o
p
tim
u
m
p
er
f
o
r
m
an
ce
s
an
d
f
u
n
ctio
n
.
T
h
er
ef
o
r
it
is
ch
o
s
en
in
th
is
p
a
p
er
an
im
p
r
o
v
ed
PS
O
a
lg
o
r
ith
m
s
wh
ich
b
ased
o
n
ch
ao
tic
m
ap
s
an
d
ad
ap
tiv
e
ac
c
eler
atio
n
co
ef
f
icie
n
ts
.
3
.
2
.
Cha
o
t
ic
P
SO
a
lg
o
rit
hm
T
h
e
ch
ao
tic
m
ap
s
ar
e
im
p
o
r
ta
n
t
f
u
n
ctio
n
s
u
s
ed
f
o
r
s
o
l
v
in
g
p
r
o
b
lem
s
in
o
p
tim
izatio
n
m
eth
o
d
s
,
wh
er
e
g
en
er
ally
u
tili
ze
d
as
g
en
e
r
at
o
r
s
o
f
r
an
d
o
m
n
u
m
b
e
r
s
.
T
h
e
u
s
ed
o
n
es
in
th
is
p
ap
er
ar
e
d
escr
ib
ed
b
y
th
eir
v
is
u
aliza
tio
n
in
Fig
u
r
e
1
an
d
th
eir
m
ath
em
atica
l f
o
r
m
s
as [
2
9
]
:
-
C
h
ao
tic
lo
g
is
tic
PS
O
(
C
L
-
P
S
O)
:
(
)
1
1
k
k
k
x
x
x
+
=−
(
2
1
)
-
C
h
ao
tic
iter
ativ
e
PS
O
(
C
I
-
PS
O)
:
1
sin
k
k
x
x
+
=
(
2
2
)
-
C
h
ao
tic
cir
cle
PS
O
(
C
C
-
PS
O)
:
1
2
m
o
d
s
i
n
,
1
2
kk
k
xx
x
+
=
+
−
(
2
3
)
Fig
u
r
e
1
.
Vis
u
aliza
tio
n
o
f
ch
a
o
tic
m
ap
s
3
.
3
.
Ada
ptiv
e
a
cc
eler
a
t
i
o
n c
o
ef
f
icient
s
T
h
e
ap
p
lied
PS
O
alg
o
r
ith
m
s
in
th
is
p
r
o
b
lem
b
ased
o
n
a
d
a
p
tiv
e
ac
ce
ler
atio
n
c
o
ef
f
icien
ts
c
1
,
c
2
a
r
e
r
ep
r
esen
ted
in
t
h
e
f
o
llo
win
g
eq
u
atio
n
s
,
also
b
y
t
h
e
co
e
f
f
icien
ts
’
v
ar
iatio
n
in
Fig
u
r
e
2
.
Sig
m
o
id
-
b
ased
ac
ce
ler
atio
n
co
ef
f
icien
ts
(
SB
A
C
-
PS
O)
[
3
0
]
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci,
Vo
l.
24
,
No
.
1
,
Octo
b
er
2
0
2
1
:
50
-
60
54
(
)
m
a
x
2
1
1
1
1
21
1
fi
k
m
a
x
k
k
c
c
c
k
e
−
=
+
−
−
+
,
(
)
m
a
x
2
2
1
1
1
1
fi
k
m
a
x
k
k
c
c
c
k
e
−
=
+
−
+
(
2
4
)
W
h
er
e,
λ
=
0
.
0
0
0
1
,
c
1f
=
2
.
5
,
c
1i
=
0
.
5
.
No
n
-
lin
ea
r
d
y
n
am
ic
a
cc
eler
atio
n
co
ef
f
icien
ts
(
NDAC
-
PS
O)
[
3
1
]
:
(
)
2
1
1
1
1
m
a
x
f
i
f
k
c
c
c
c
k
=
−
−
+
,
2
2
1
1
m
a
x
m
a
x
1
if
kk
c
c
c
kk
=
−
+
(
2
5
)
W
h
er
e,
c
1f
=
2
.
5
,
c
1i
=
0
.
5
.
T
i
m
e
-
v
ar
y
i
n
g
ac
ce
ler
atio
n
-
PS
O
(
T
VA
-
PS
O)
[
3
2
]
:
11
11
m
ax
fi
i
cc
c
c
k
k
−
=+
,
22
22
m
a
x
fi
i
cc
c
c
k
k
−
=+
(
2
6
)
W
h
er
e,
c
1f
=
0
.
5
,
c
1i
=
2
.
5
an
d
c
2f
=
2
.
5
,
c
2i
=
0
.
5
Fig
u
r
e
2
.
T
h
e
v
ar
iatio
n
o
f
ac
c
eler
atio
n
co
ef
f
icie
n
ts
f
o
r
v
a
r
io
u
s
PS
O
alg
o
r
ith
m
s
B
ased
o
n
h
y
b
r
id
izatio
n
o
f
t
wo
PS
O
alg
o
r
ith
m
s
wh
ich
d
ep
en
d
o
n
ch
ao
tic
m
ap
s
an
d
ad
ap
tiv
e
ac
ce
ler
atio
n
co
ef
f
icien
ts
as
p
r
ev
io
u
s
ly
m
en
tio
n
e
d
.
T
h
is
p
ap
er
p
r
o
p
o
s
ed
f
ir
s
tly
f
o
r
th
e
ch
ao
tic
lo
g
is
tic
(
C
L
)
alg
o
r
ith
m
:
(
C
L
-
SB
AC
-
P
SO)
,
(
C
L
-
NDAC
-
P
SO)
an
d
(
C
L
-
T
VA
-
PS
O)
,
th
en
f
o
r
th
e
ch
ao
tic
iter
ativ
e
(
C
I
)
alg
o
r
ith
m
:
(
C
I
-
SB
AC
-
PS
O)
,
(
C
I
-
NDAC
-
PS
O)
an
d
(
C
I
-
T
VA
-
PS
O)
.
Fin
ally
,
f
o
r
th
e
c
h
ao
tic
cir
cle
(
C
C
)
alg
o
r
ith
m
: (
C
C
-
SB
AC
-
PS
O)
,
(
C
C
-
NDA
C
-
PS
O)
an
d
(
C
C
-
T
VA
-
PS
O)
.
4.
O
P
T
I
M
AL
R
E
SU
L
T
S
,
D
IS
CUSS
I
O
NS A
ND
CO
M
P
AR
I
SO
N
T
h
e
p
r
o
p
o
s
ed
h
y
b
r
id
PS
O
alg
o
r
ith
m
s
wer
e
ev
alu
ated
an
d
v
alid
ated
o
n
th
e
s
tan
d
ar
d
s
I
E
E
E
3
3
-
b
u
s
,
an
d
6
9
-
b
u
s
,
wh
er
ea
s
illu
s
tr
ate
d
b
y
th
e
s
in
g
le
lin
e
d
iag
r
am
s
i
n
Fig
u
r
es 3
(
a)
a
n
d
3
(
b
)
r
esp
ec
tiv
ely
,
u
n
d
er
a
b
ase
v
o
ltag
e
o
f
1
2
.
6
6
k
V
in
th
e
two
o
f
th
em
[
2
2
]
.
T
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
s
ar
e
im
p
lem
e
n
ted
in
MA
T
L
AB
s
o
f
twar
e
(
v
er
s
io
n
2
0
1
7
.
b
)
in
a
PC
th
at
h
as a
p
r
o
ce
s
s
o
r
I
n
tel
C
o
r
e
i5
with
3
.
4
GHz
a
n
d
8
GB
o
f
R
AM
.
T
h
e
f
ir
s
t
s
y
s
tem
,
th
e
to
tal
ac
ti
v
e
an
d
r
ea
ctiv
e
lo
ad
ar
e
3
7
1
5
.
0
0
k
W
an
d
2
3
0
0
.
0
0
k
Var
,
wh
ile
f
o
r
th
e
s
ec
o
n
d
s
y
s
tem
,
ar
e
3
7
9
0
.
0
0
k
W
an
d
2
6
9
0
.
0
0
k
Var
.
E
v
er
y
b
u
s
o
f
th
e
two
s
y
s
tem
s
i
s
p
r
o
tecte
d
an
d
co
v
er
ed
b
y
a
p
r
im
ar
y
o
v
e
r
cu
r
r
e
n
t
r
elay
(
OC
R
)
,
f
o
llo
wed
b
y
its
b
ac
k
u
p
,
an
d
a
co
o
r
d
in
atio
n
tim
e
in
ter
v
al
(
C
T
I
)
s
et
ab
o
v
e
0
.
2
5
s
ec
o
n
d
is
b
etwe
en
t
h
em
.
I
n
g
en
e
r
al,
it
is
ca
lcu
lated
f
o
r
th
e
I
E
E
E
3
3
-
b
u
s
,
3
2
OC
R
s
w
ith
3
1
C
T
I
s
,
wh
ile
f
o
r
th
e
I
E
E
E
6
9
-
b
u
s
,
6
8
OC
R
s
with
6
7
C
T
I
s
.
I
t
is
ch
o
s
en
a
f
ter
th
e
i
n
teg
r
atin
g
o
f
m
u
ltip
l
e
PV
-
DGs
a
ty
p
e
o
f
NS
-
OC
R
f
o
r
all
r
elay
s
in
th
e
two
s
y
s
tem
s
,
wh
er
e
al
s
o
a
d
es
cr
ip
tiv
e
s
u
m
m
ar
y
o
f
th
eir
m
ai
n
ch
ar
ac
ter
is
tics
is
m
en
tio
n
ed
i
n
T
ab
le
1
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
Op
tima
l in
teg
r
a
tio
n
o
f p
h
o
to
v
o
lta
ic
d
is
tr
ib
u
ted
g
en
era
tio
n
i
n
elec
tr
ica
l…
(
N
a
s
r
ed
d
in
e
B
elb
a
ch
ir
)
55
(
a
)
(
b
)
Fig
u
r
e
3
.
Sin
g
le
lin
e
d
iag
r
a
m
o
f
s
tan
d
ar
d
test
s
y
s
tem
s
:
(
a
)
I
E
E
E
3
3
-
bus
an
d
(
b)
I
E
E
E
6
9
-
bus
T
ab
le
1
.
T
h
e
m
ain
c
h
ar
ac
ter
is
tics
o
f
th
e
in
v
esti
g
ated
E
DN
s
y
s
tem
s
C
h
a
r
a
c
t
e
r
i
s
t
i
c
s
B
u
s
e
s
B
r
a
n
c
h
e
s
R
e
l
a
y
s
∑
P
D
(
k
W
)
∑
Q
D
(
k
V
a
r
)
∑
P
L
os
s
(
k
W
)
∑
Q
L
os
s
(
k
V
a
r
)
∑
V
D
(
p
.
u
.
)
∑
T
R
e
l
a
y
(
sec
)
I
EEE
3
3
-
bus
33
32
32
3
7
1
5
.
0
0
2
3
0
0
.
0
0
2
1
0
.
9
8
1
3
5
.
1
4
1
.
8
1
2
0
.
5
7
I
EEE
6
9
-
bus
69
68
68
3
7
9
0
.
0
0
2
6
9
0
.
0
0
2
2
4
.
9
5
1
0
2
.
1
6
1
.
8
7
3
8
.
7
7
Fig
u
r
es
4
(
a)
an
d
4
(
b
)
d
em
o
n
s
tr
ate
th
e
co
n
v
er
g
en
ce
cu
r
v
es
o
f
th
e
MO
F’s
m
in
im
iza
tio
n
wh
en
ap
p
ly
in
g
th
e
v
a
r
io
u
s
p
r
o
p
o
s
ed
h
y
b
r
id
PS
O
alg
o
r
ith
m
s
o
n
b
o
th
s
y
s
tem
s
.
Acc
o
r
d
in
g
to
Fig
u
r
es
4
(
a)
an
d
4
(
b
)
,
th
e
ap
p
licatio
n
o
f
v
a
r
io
u
s
h
y
b
r
id
PS
O
alg
o
r
ith
m
s
o
n
b
o
th
s
y
s
tem
s
wi
th
a
v
alu
e
o
f
k
max
=1
5
0
iter
atio
n
s
,
p
o
p
u
latio
n
s
ize=
1
0
,
s
h
o
ws
f
o
r
th
e
f
ir
s
t
s
y
s
tem
th
at
C
I
-
ND
AC
-
PS
O
alg
o
r
ith
m
co
n
v
er
g
e
d
at
f
ir
s
t
ab
o
u
t
8
5
iter
atio
n
s
an
d
b
etter
th
an
o
th
er
p
r
o
p
o
s
ed
alg
o
r
ith
m
s
.
At
t
h
e
s
am
e
tim
e,
it
m
ay
b
e
s
ee
n
th
at
C
C
-
T
VA
-
PS
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alg
o
r
ith
m
p
r
o
v
id
ed
th
e
b
est
an
d
m
i
n
im
u
m
v
alu
e
o
f
MO
F
am
o
n
g
all
o
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th
e
a
p
p
lied
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ith
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s
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esid
e
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n
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er
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es
late
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o
r
e
th
an
1
4
0
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atio
n
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.
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e
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th
er
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d
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al
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o
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r
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o
r
th
e
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E
E
E
6
9
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b
u
s
,
th
at
th
e
C
C
-
T
VA
-
PS
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alg
o
r
ith
m
p
r
o
v
id
e
d
th
e
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est
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d
m
in
im
u
m
v
al
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e
o
f
MO
F
an
d
c
o
n
v
e
r
g
in
g
b
y
1
2
5
iter
atio
n
s
.
Fig
u
r
es
5
(
a)
a
n
d
5
(
b
)
,
illu
s
tr
a
te
th
e
b
o
x
p
lo
t
o
f
MO
F
r
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lts
af
ter
th
e
ap
p
licatio
n
o
f
th
e
v
ar
io
u
s
h
y
b
r
id
PS
O
alg
o
r
ith
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s
with
2
0
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u
n
s
in
ea
c
h
o
f
two
s
y
s
tem
s
E
DNs.
(
a)
(
b
)
Fig
u
r
e
4
.
C
o
n
v
er
g
e
n
ce
ch
ar
ac
t
er
is
tics
o
f
PS
O
alg
o
r
ith
m
s
:
(
a
)
I
E
E
E
3
3
-
bus
an
d
(
b
)
I
E
E
E
6
9
-
bus
A
b
o
x
p
lo
t
is
p
r
esen
ted
in
Fig
u
r
es
5
(
a)
an
d
5
(
b
)
,
f
o
r
th
e
p
u
r
p
o
s
e
o
f
co
m
p
a
r
is
o
n
im
p
r
o
v
em
e
n
t,
b
esid
e
to
b
etter
ev
al
u
ates
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
s
.
B
y
co
n
s
id
er
in
g
2
0
ex
ec
u
tio
ns
,
it
ca
n
b
e
s
ee
n
f
o
r
all
p
r
o
p
o
s
e
d
h
y
b
r
id
PS
O
alg
o
r
ith
m
s
th
at
th
e
r
esu
lts
ar
e
to
o
n
ea
r
to
th
eir
m
in
im
u
m
an
d
b
est
MO
F
in
th
e
two
s
y
s
tem
s
.
I
t
is
also
clea
r
th
at
C
C
-
T
VA
-
PS
O
alg
o
r
ith
m
p
r
esen
ts
ef
f
icien
cy
i
n
d
eliv
er
in
g
th
e
m
in
im
u
m
v
al
u
e
o
f
MO
F
in
b
o
th
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
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o
m
p
Sci,
Vo
l.
24
,
No
.
1
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Octo
b
er
2
0
2
1
:
50
-
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56
s
y
s
tem
s
with
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e
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e
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s
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9
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s
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p
r
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v
id
e
d
b
y
th
e
C
L
-
T
VA
-
PS
O
alg
o
r
ith
m
.
(
a)
(
b
)
Fig
u
r
e
5
.
B
o
x
p
lo
t o
f
MO
F f
o
r
PS
O
alg
o
r
ith
m
s
ap
p
lied
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o
r
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a
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E
E
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3
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u
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d
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6
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ab
les
2
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d
3
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e
x
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ib
it
th
e
r
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u
lts
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o
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n
d
wh
e
n
ap
p
ly
t
h
e
v
a
r
io
u
s
h
y
b
r
id
PS
O
alg
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r
ith
m
s
o
n
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o
t
h
test
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y
s
tem
s
E
DNs.
B
a
s
ed
o
n
co
m
p
ar
is
o
n
,
it
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n
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e
s
s
ee
n
in
T
ab
les
2
a
n
d
3
,
th
at
all
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r
o
p
o
s
ed
h
y
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r
id
PS
O
alg
o
r
ith
m
s
h
av
e
f
o
u
n
d
g
o
o
d
an
d
clo
s
e
r
esu
lts
to
ea
ch
o
th
er
’
s
.
W
h
ile
th
e
m
in
im
u
m
MO
F
r
esu
lts
wer
e
ac
h
iev
ed
b
y
th
e
C
C
-
T
VA
-
PS
O
alg
o
r
ith
m
f
o
r
b
o
th
s
y
s
tem
s
,
m
o
r
e
o
v
er
,
it
p
r
o
v
id
es
th
e
lo
west
T
OT
v
alu
e
o
f
1
9
.
4
6
9
8
s
ec
o
n
d
s
f
o
r
th
e
I
E
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E
3
3
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u
s
an
d
lo
west T
APL
v
alu
e
o
f
8
7
.
3
5
k
W
f
o
r
t
h
e
I
E
E
E
6
9
-
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u
s
.
T
ab
le
2
.
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o
m
p
a
r
is
o
n
o
f
o
p
tim
izatio
n
r
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lts
f
o
r
I
E
E
E
3
3
-
b
u
s
A
l
g
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r
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t
h
ms
A
p
p
l
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e
d
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u
s
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t
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13
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13
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2
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5
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15
24
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15
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12
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1
8
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16
25
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4
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5
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.
5
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0
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8
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1
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1
3
3
8
1
9
.
4
6
9
8
2
0
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6
7
3
5
T
ab
le
3
.
C
o
m
p
a
r
is
o
n
o
f
o
p
tim
izatio
n
r
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lts
f
o
r
I
E
E
E
6
9
-
b
u
s
A
l
g
o
r
i
t
h
ms
A
p
p
l
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e
d
D
G
B
u
s
L
o
c
a
t
i
o
n
D
G
S
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z
e
-
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DG
(
k
W
)
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P
L
(
k
W
)
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D
(
p
.
u
.
)
TO
T
(
sec
)
M
O
F
DG
1
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2
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3
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1
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2
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3
CL
-
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25
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6
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.
0
4
5
1
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
Op
tima
l in
teg
r
a
tio
n
o
f p
h
o
to
v
o
lta
ic
d
is
tr
ib
u
ted
g
en
era
tio
n
i
n
elec
tr
ica
l…
(
N
a
s
r
ed
d
in
e
B
elb
a
ch
ir
)
57
I
t
m
ay
b
e
n
o
te
d
th
at
th
e
r
est
o
f
th
e
h
y
b
r
id
PS
O
alg
o
r
ith
m
s
a
ls
o
s
h
o
w
a
g
o
o
d
e
f
f
icien
cy
i
n
d
eliv
er
in
g
g
o
o
d
r
esu
lts
.
As
ex
am
p
les,
f
o
r
th
e
f
i
r
s
t
s
y
s
tem
,
th
e
C
L
-
SB
AC
-
PS
O
alg
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RE
F
E
R
E
NC
E
S
[1
]
T.
Ac
k
e
r
m
a
n
n
,
G
.
An
d
e
rso
n
,
a
n
d
L
.
S
o
d
e
r
,
"
Distrib
u
ted
g
e
n
e
ra
ti
o
n
:
A
d
e
fin
it
io
n
,
"
El
e
c
tric
Po
we
r
S
y
ste
ms
Res
e
a
rc
h
,
v
o
l.
5
7
,
n
o
.
3
,
p
p
.
1
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5
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0
4
,
2
0
0
1
,
d
o
i:
1
0
.
1
0
1
6
/
S
0
3
7
8
-
7
7
9
6
(0
1
)0
0
1
0
1
-
8
.
[2
]
Y.
Latre
c
h
e
,
H.
R.
E.
H.
Bo
u
c
h
e
k
a
ra
,
F
.
Ke
rro
u
r,
K.
Na
id
u
,
H.
M
o
k
h
li
s,
a
n
d
M
.
S
.
Ja
v
a
id
,
"
C
o
m
p
r
e
h
e
n
siv
e
re
v
iew
o
n
t
h
e
o
p
ti
m
a
l
i
n
teg
ra
ti
o
n
o
f
d
istr
ib
u
te
d
g
e
n
e
ra
ti
o
n
in
d
istri
b
u
ti
o
n
s
y
ste
m
s,
"
J
o
u
r
n
a
l
o
f
Ren
e
wa
b
le
a
n
d
S
u
st
a
in
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b
le
En
e
rg
y
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l.
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0
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5
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0
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3
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1
.
5
0
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0
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0
.
[3
]
S
.
S
u
lt
a
n
a
a
n
d
P
.
K
.
R
o
y
,
"
M
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o
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ti
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q
u
a
si
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p
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b
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iza
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m
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In
ter
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J
o
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[4
]
K.
M
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N
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a
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v
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p
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to
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lt
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rti
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p
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n
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m
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l
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m
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t
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.
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,
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d
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0
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3
3
9
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/en
9
1
2
0
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8
2
.
[5
]
D.
R.
P
ra
b
h
a
a
n
d
T.
Ja
y
a
b
a
ra
th
i
,
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t
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p
lac
e
m
e
n
t
a
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d
siz
in
g
o
f
m
u
lt
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le
d
istri
b
u
ted
g
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ra
ti
n
g
u
n
it
s
i
n
d
istri
b
u
ti
o
n
n
e
two
r
k
s
b
y
in
v
a
siv
e
we
e
d
o
p
ti
m
iza
ti
o
n
a
lg
o
rit
h
m
,
"
A
in
S
h
a
ms
En
g
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n
e
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g
J
o
u
rn
a
l
,
v
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l.
7
,
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o
.
2
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p
p
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9
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,
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0
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6
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6
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.
a
se
j.
2
0
1
5
.
0
5
.
0
1
4
.
[6
]
M
.
Z.
Bin
Ro
ss
e
lan
,
S
.
I.
S
u
laim
a
n
,
a
n
d
I
.
M
u
sirin
,
"
S
izin
g
o
p
t
imiz
a
ti
o
n
o
f
larg
e
-
sc
a
le
g
rid
-
c
o
n
n
e
c
te
d
p
h
o
to
v
o
lt
a
ic
sy
ste
m
u
sin
g
c
u
c
k
o
o
se
a
rc
h
,
"
I
n
d
o
n
e
si
a
n
J
o
u
r
n
a
l
o
f
El
e
c
trica
l
E
n
g
i
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g
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d
C
o
mp
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ter
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c
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e
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l.
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1
,
p
p
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1
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c
s.v
8
.
i
1
.
p
p
1
6
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-
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.
[
7
]
S
.
G
a
n
g
u
l
y
a
n
d
D
.
S
a
m
a
j
p
a
t
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,
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p
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w
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s
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p
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t
i
c
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l
g
o
r
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t
h
m
,
"
A
p
p
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d
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o
f
t
C
o
m
p
u
t
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n
g
,
v
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l
.
5
9
,
p
p
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4
5
-
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2017,
d
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.
a
s
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c
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[8
]
T.
Ng
u
y
e
n
-
P
h
u
o
c
,
D.
V
o
-
Ng
o
c
,
a
n
d
T.
Tran
-
T
h
e
,
"
O
p
ti
m
a
l
n
u
m
b
e
r,
lo
c
a
ti
o
n
,
a
n
d
siz
e
o
f
d
istri
b
u
te
d
g
e
n
e
ra
to
rs
in
d
istri
b
u
ti
o
n
sy
ste
m
s
b
y
sy
m
b
io
ti
c
o
r
g
a
n
ism
se
a
rc
h
-
b
a
se
d
m
e
th
o
d
,
"
Ad
v
a
n
c
e
s
in
El
e
c
trica
l
a
n
d
El
e
c
tro
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En
g
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g
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.
v
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2
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.
[9
]
O.
A.
S
a
l
e
h
,
M
.
El
s
h
a
h
e
d
,
a
n
d
M
.
El
sa
y
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d
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h
a
n
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n
t
o
f
ra
d
ial
d
istri
b
u
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o
n
n
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two
r
k
wi
th
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ib
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ted
g
e
n
e
ra
ti
o
n
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n
d
sy
ste
m
re
c
o
n
fi
g
u
ra
t
io
n
,
"
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o
u
r
n
a
l
o
f
E
lec
trica
l
S
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ste
ms
,
v
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l.
1
4
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o
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3
,
p
p
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[1
0
]
V.
Y.
M
.
De
Oliv
e
ira,
R.
M
.
S
.
De
Oliv
e
ira,
a
n
d
C.
M
.
Affo
n
so
,
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c
k
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3
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.
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8
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H.
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9
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B.
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De
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.
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tt
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0
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E.
Ka
ru
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ra
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,
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P
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su
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leti,
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Ek
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1
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A.
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m
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.
Zellag
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C
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.
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.
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