I
nd
o
ne
s
ia
n J
o
urna
l o
f
E
lect
rica
l En
g
ineering
a
nd
Co
m
pu
t
er
Science
Vo
l.
25
,
No
.
2
,
Feb
r
u
ar
y
2
0
2
2
,
p
p
.
610
~
625
I
SS
N:
2
5
0
2
-
4
7
5
2
,
DOI
: 1
0
.
1
1
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9
1
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25
.i
2
.
p
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6
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610
J
o
ur
na
l ho
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:
h
ttp
:
//ij
ee
cs.ia
esco
r
e.
co
m
Energ
y
ha
rv
estin
g
ma
x
imiza
tion b
y
int
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ra
tion o
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stribute
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.
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P
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g
i
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e
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I
n
st
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t
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t
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o
f
A
v
i
a
t
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o
n
En
g
i
n
e
e
r
i
n
g
a
n
d
T
e
c
h
n
o
l
o
g
y
(
I
.
A
.
E.
T)
,
G
i
z
a
,
Eg
y
p
t
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
J
an
27
,
2
0
2
1
R
ev
is
ed
Dec
19
,
2
0
2
1
Acc
ep
ted
Dec
27
,
2
0
2
1
Th
e
p
u
r
p
o
se
o
f
d
istri
b
u
ted
g
e
n
e
ra
ti
o
n
sy
ste
m
s
(DG
S
)
is
to
e
n
h
a
n
c
e
th
e
d
istri
b
u
ti
o
n
sy
ste
m
(DS)
p
e
rfo
rm
a
n
c
e
to
b
e
b
e
tt
e
r
k
n
o
w
n
with
it
s
b
e
n
e
fit
s
in
th
e
p
o
we
r
se
c
to
r
a
s
i
n
sta
ll
in
g
d
is
tri
b
u
te
d
g
e
n
e
ra
ti
o
n
(DG
)
u
n
it
s
in
to
t
h
e
DS
c
a
n
in
tr
o
d
u
c
e
e
c
o
n
o
m
ic,
e
n
v
ir
o
n
m
e
n
tal
a
n
d
tec
h
n
ica
l
b
e
n
e
fi
ts.
Th
o
se
b
e
n
e
fit
s
c
a
n
b
e
o
b
tain
e
d
if
t
h
e
D
G
u
n
it
s'
site
a
n
d
siz
e
is p
ro
p
e
rly
d
e
term
in
e
d
.
Th
e
a
im
o
f
t
h
is
p
a
p
e
r
is
st
u
d
y
in
g
a
n
d
re
v
iew
in
g
t
h
e
e
ffe
c
t
o
f
c
o
n
n
e
c
ti
n
g
DG
u
n
it
s
in
th
e
D
S
o
n
tran
sm
issio
n
e
fficie
n
c
y
,
re
a
c
ti
v
e
p
o
we
r
l
o
ss
a
n
d
v
o
lt
a
g
e
d
e
v
iatio
n
i
n
a
d
d
it
io
n
t
o
t
h
e
e
c
o
n
o
m
ica
l
p
o
i
n
t
o
f
v
iew
a
n
d
c
o
n
si
d
e
rin
g
t
h
e
in
tere
st
a
n
d
in
f
latio
n
ra
te.
W
h
a
le
o
p
ti
m
iza
ti
o
n
a
lg
o
rit
h
m
(W
OA
)
is
in
tro
d
u
c
e
d
to
f
in
d
th
e
b
e
st
so
l
u
ti
o
n
t
o
t
h
e
d
istr
ib
u
ted
g
e
n
e
ra
ti
o
n
p
e
n
e
tratio
n
p
ro
b
lem
in
t
h
e
DS.
T
h
e
re
su
lt
o
f
WOA
is
c
o
m
p
a
re
d
with
t
h
e
g
e
n
e
ti
c
al
g
o
rit
h
m
(G
A),
p
a
rti
c
le sw
a
r
m
o
p
ti
m
iza
ti
o
n
(
P
S
O),
a
n
d
g
re
y
w
o
lf
o
p
ti
m
ize
r
(G
WO).
Th
e
p
ro
p
o
se
d
so
l
u
ti
o
n
s
m
e
th
o
d
o
lo
g
ies
h
a
v
e
b
e
e
n
tes
ted
u
sin
g
M
ATLAB
so
ftwa
re
o
n
IEE
E
3
3
s
tan
d
a
rd
b
u
s s
y
ste
m
.
K
ey
w
o
r
d
s
:
Dis
tr
ib
u
ted
g
en
er
atio
n
Gen
etic
alg
o
r
ith
m
Gr
ey
wo
lf
o
p
ti
m
izer
Par
ticle
s
war
m
o
p
tim
izatio
n
W
h
ale
o
p
tim
izatio
n
alg
o
r
ith
m
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
T
ar
ek
A
.
B
o
g
h
d
ad
y
Dep
ar
tm
en
t o
f
E
lectr
ical
Po
wer
E
n
g
in
ee
r
in
g
,
Facu
lty
o
f
E
n
g
in
ee
r
in
g
,
C
air
o
Un
iv
er
s
ity
E
l G
am
m
a
Stre
et,
Giza
,
E
g
y
p
t
E
m
ail: E
n
g
tar
ek
8
2
@
g
m
ail.
co
m
1.
I
NT
RO
D
UCT
I
O
N
I
n
th
e
last
f
ew
y
ea
r
s
,
s
o
ciet
y
an
d
elec
tr
ic
p
o
wer
s
y
s
tem
u
tili
ties
h
av
e
m
et
n
u
m
er
o
u
s
ec
o
n
o
m
ic
,
en
v
ir
o
n
m
en
tal
an
d
tech
n
ical
p
o
wer
q
u
ality
p
r
o
b
lem
s
ass
o
ciate
d
with
p
o
wer
s
y
s
tem
s
.
So
,
with
b
etter
en
er
g
y
p
lan
n
in
g
an
d
th
e
u
s
e
o
f
em
er
g
in
g
s
m
ar
t
tech
n
o
lo
g
y
,
r
esear
ch
is
n
o
w
m
ak
in
g
a
g
r
ea
t
ef
f
o
r
t
to
p
ay
atten
tio
n
to
th
e
ex
is
tin
g
in
f
r
astru
ctu
r
e.
O
n
e
o
f
th
e
m
o
s
t
ap
p
licab
le
s
o
lu
tio
n
s
f
o
r
im
p
r
o
v
i
n
g
DS
p
er
f
o
r
m
an
ce
is
th
e
o
p
tim
u
m
allo
ca
tio
n
o
f
d
is
tr
i
b
u
ted
g
en
er
atio
n
(
DG)
in
th
e
d
is
tr
ib
u
tio
n
s
y
s
tem
(
DS)
.
A
s
th
e
n
o
n
-
o
p
tim
al
allo
ca
tio
n
o
f
DG
m
ay
co
n
s
eq
u
en
ce
i
n
an
in
cr
ea
s
e
in
en
e
r
g
y
l
o
s
s
,
lo
wer
v
o
ltag
e
p
r
o
f
i
le
th
an
ac
c
e
p
tab
le
b
o
u
n
d
ar
ies
in
ad
d
itio
n
to
h
ig
h
ex
p
en
d
s
[
1
]
.
I
f
r
ea
l
ac
tiv
e
p
o
wer
lo
s
s
es
ar
e
f
ar
h
ig
h
er
th
a
n
th
e
n
o
r
m
al
v
alu
es,
DS
co
m
p
an
ies
in
E
g
y
p
t
ar
e
ec
o
n
o
m
ically
p
en
alize
d
.
Or
,
o
n
th
e
o
th
er
h
an
d
,
t
h
ey
g
ain
a
g
o
o
d
p
r
o
f
it
[
2
].
Als
o
,
h
ig
h
r
ea
l
ac
tiv
e
p
o
wer
l
o
s
s
es
d
ec
r
ea
s
e
th
e
tr
an
s
m
is
s
io
n
ef
f
icien
cy
to
th
e
e
n
d
u
s
er
;
th
er
ef
o
r
e,
its
d
ec
r
ea
s
e
attr
ac
ted
m
u
ch
m
o
r
e
atten
tio
n
f
r
o
m
d
is
tr
ib
u
tio
n
co
m
p
an
ies
[
3
]
.
L
i
k
ewise,
d
ec
r
ea
s
in
g
t
h
e
r
ea
ctiv
e
p
o
wer
lo
s
s
is
also
o
b
jectiv
e
t
h
at
s
h
o
u
ld
b
e
tak
en
in
to
co
n
s
id
er
atio
n
d
u
r
in
g
DG
p
lan
n
in
g
.
T
h
u
s
,
r
e
d
u
cin
g
th
e
r
ea
ctiv
e
p
o
wer
co
n
s
u
m
p
tio
n
,
d
im
in
is
h
in
g
v
o
ltag
e
d
r
o
p
s
an
d
em
p
o
wer
in
g
s
y
s
tem
lo
ad
ab
ilit
y
a
r
e
o
n
e
o
f
th
e
m
o
s
t
co
m
m
o
n
o
b
jectiv
es
[
4
]
.
M
o
r
e
o
v
er
,
it
aid
s
ac
tiv
e
p
o
wer
f
lo
w
th
r
o
u
g
h
tr
an
s
m
is
s
io
n
an
d
d
is
tr
ib
u
tio
n
(
T
&
D)
lin
es to
th
e
en
d
u
s
er
[
3
]
.
T
h
e
o
p
tim
al
DG
s
ize
a
n
d
s
ite
s
u
p
p
o
r
ts
in
d
ec
r
ea
s
in
g
t
h
e
r
esi
s
tan
ce
l
o
s
s
es
(
2
)
,
th
e
r
ea
ctan
ce
lo
s
s
e
s
(
2
)
an
d
co
n
s
eq
u
en
tly
th
e
v
o
lta
g
e
d
r
o
p
i
n
th
e
two
co
m
p
o
n
en
ts
(
I
R
an
d
I
X)
in
th
e
DS
[
2
]
.
Ma
n
y
r
esear
ch
o
b
jectiv
es
in
DG
p
lan
n
in
g
b
ased
o
n
th
e
s
in
g
le
o
b
jectiv
e
in
d
ex
(
SOI
)
alm
o
s
t
as
if
it
wer
e
r
ea
l
p
o
wer
o
r
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
E
n
erg
y
h
a
r
ve
s
tin
g
ma
ximiza
tio
n
b
y
i
n
teg
r
a
tio
n
o
f
d
is
tr
ib
u
ted
g
en
era
tio
n
…
(
Ta
r
ek
A
.
B
o
g
h
d
a
d
y
)
611
m
in
im
izin
g
th
e
en
er
g
y
lo
s
s
o
f
th
e
DS
an
d
n
o
t
tak
in
g
n
o
te
o
f
th
e
m
er
its
o
f
t
h
e
s
u
m
o
f
t
h
e
weig
h
ted
m
u
lti
-
o
b
jectiv
es
in
d
ex
(
MO
I
)
,
s
u
c
h
as
en
er
g
y
lo
s
s
m
in
im
izatio
n
,
v
o
ltag
e
p
r
o
f
ile
en
h
an
ce
m
en
t
an
d
to
tal
co
s
t
r
ed
u
ctio
n
o
f
t
h
e
DS.
A
n
ew
p
r
o
p
o
s
ed
o
p
tim
izatio
n
tech
n
iq
u
e
is
p
r
o
p
o
s
ed
f
o
r
lo
ca
tio
n
a
n
d
h
o
w
to
s
ize
th
e
DG
in
DS
with
a
ch
a
n
g
ed
lo
ad
in
g
co
n
d
itio
n
s
f
o
r
m
in
im
izatio
n
o
f
r
ea
l
p
o
wer
lo
s
s
o
f
th
e
s
y
s
tem
,
is
p
r
o
p
o
s
ed
in
[
5
]
-
[
7
]
.
T
h
e
MO
I
o
f
p
er
f
o
r
m
an
ce
f
o
r
DS
with
DG,
wh
ich
in
clu
d
es
a
wid
e
r
an
g
e
o
f
elec
tr
ic
tech
n
ical
p
r
o
b
lem
s
,
is
p
r
o
p
o
s
ed
in
[
8
]
.
T
h
e
o
p
tim
al
MO
I
s
izin
g
a
n
d
lo
ca
tio
n
o
f
m
u
ltip
le
DGS
in
ad
d
itio
n
to
s
h
u
n
t
ca
p
ac
ito
r
b
a
n
k
s
all
to
g
eth
e
r
in
v
iew
o
f
lo
ad
u
n
ce
r
tain
ty
b
y
ad
ju
s
ted
p
ar
ticl
e
s
war
m
o
p
tim
izatio
n
(
PSO
)
ap
p
r
o
ac
h
f
r
o
m
d
is
s
im
ilar
p
o
w
er
s
y
s
tem
p
er
f
o
r
m
an
ce
s
v
iews,
is
p
r
esen
ted
in
[
9
]
.
A
tech
n
iq
u
e
o
n
em
p
o
wer
in
g
th
e
p
o
wer
s
y
s
tem
p
ar
am
eter
s
s
y
s
tem
s
b
y
s
e
lectin
g
th
e
o
p
tim
ally
lo
ca
ted
DG
in
DS
is
p
r
o
p
o
s
ed
in
[
1
0
]
.
S
tates
th
at
th
e
ef
f
ec
t
th
at
was
elev
ated
b
ec
au
s
e
o
f
th
e
jo
in
in
g
o
f
DG
in
to
th
e
p
r
esen
t
n
etwo
r
k
f
r
o
m
d
if
f
er
en
t
p
o
wer
s
y
s
tem
p
er
f
o
r
m
an
ce
s
v
iewp
o
in
ts
[
1
1
]
.
T
h
e
o
b
jectiv
e
f
u
n
ctio
n
co
n
tain
s
v
o
ltag
e
p
r
o
f
ile
en
h
an
ce
m
en
t
an
d
p
o
wer
lo
s
s
es
m
in
im
izatio
n
u
s
in
g
an
t
co
l
o
n
y
alg
o
r
ith
m
,
th
e
s
u
g
g
ested
m
eth
o
d
was
co
n
f
ir
m
ed
o
n
I
E
E
E
3
3
-
b
u
s
test
s
y
s
tem
,
th
e
r
esu
lts
d
is
p
lay
a
s
ig
n
if
ican
t
less
en
in
g
in
th
e
to
tal
p
o
wer
l
o
s
s
an
d
en
h
a
n
ce
d
v
o
ltag
e
p
r
o
f
iles
o
f
all
th
e
b
u
s
es.
C
o
r
r
esp
o
n
d
in
g
ly
,
allo
ca
tin
g
o
f
DGS
an
d
o
p
tim
al
p
e
n
etr
atio
n
o
f
s
o
lid
s
tate
f
au
lt
c
u
r
r
e
n
t
lim
iter
s
(
SS
FC
L
s
)
h
av
e
b
ee
n
a
p
p
lied
[
1
2
]
-
[
1
3
]
.
I
t
was
als
o
d
is
co
v
er
ed
th
at
ad
d
in
g
DG
u
n
its
to
th
e
DS
d
ec
r
ea
s
es
th
e
r
ea
ctiv
e
an
d
ac
tiv
e
p
o
we
r
lo
s
s
an
d
en
h
a
n
ce
th
e
s
tab
ilit
y
o
f
v
o
ltag
e
o
f
th
e
s
y
s
tem
.
PS
O
h
as
b
ee
n
p
r
esen
ted
in
[
1
4
]
f
o
r
p
e
n
etr
atio
n
o
f
DGS
f
o
r
lo
s
s
m
in
im
izatio
n
.
Sev
e
r
al
r
esear
c
h
es
m
o
tiv
ated
in
d
ec
r
ea
s
in
g
t
h
e
s
y
s
tem
lo
s
s
es
n
eg
lectin
g
t
h
e
co
s
ts
o
f
lo
s
s
es,
DGS
u
n
its
'
co
n
n
ec
tio
n
an
d
its
m
ain
ten
an
ce
.
Alth
o
u
g
h
p
ar
ti
cu
lar
p
ap
er
s
[
1
5
]
-
[
1
8
]
th
ey
to
o
k
th
ese
co
s
ts
in
to
ac
co
u
n
t,
b
u
t
o
n
ly
co
n
ce
n
tr
ate
d
o
n
im
p
r
o
v
in
g
v
o
ltag
e
s
tab
ilit
y
with
o
u
t
r
ed
u
ci
n
g
s
y
s
tem
l
o
s
s
es.
T
h
is
p
ap
er
is
p
r
o
v
id
i
n
g
a
co
m
p
lete
r
ev
iew
o
n
th
e
ef
f
ec
t
o
f
co
n
n
ec
tin
g
D
G
u
n
its
in
th
e
DS.
C
o
m
p
r
eh
e
n
s
iv
e
m
eth
o
d
o
l
o
g
y
u
s
in
g
g
en
etic
alg
o
r
ith
m
is
p
r
o
p
o
s
ed
an
d
o
th
er
m
eth
o
d
s
to
d
e
ter
m
in
e
:
−
Op
tim
u
m
s
ize
DGs a
n
d
m
ax
i
m
izatio
n
SOI
o
f
tr
a
n
s
m
is
s
io
n
ef
f
icien
cy
.
−
Op
tim
u
m
s
ite
DGs a
n
d
m
ax
im
izatio
n
SOI
o
f
tr
an
s
m
is
s
io
n
ef
f
icien
cy
.
−
Allo
ca
tio
n
o
f
DGs a
n
d
m
a
x
im
izatio
n
SOI
o
f
tr
an
s
m
is
s
io
n
ef
f
icien
cy
.
−
Allo
ca
tio
n
o
f
DGs
an
d
m
in
im
izatio
n
MO
I
o
f
r
ea
ctiv
e
p
o
wer
lo
s
s
(
Qlo
s
s
)
,
v
o
ltag
e
d
ev
i
atio
n
(
VD)
an
d
m
ax
im
izatio
n
o
f
tr
an
s
m
is
s
io
n
ef
f
icien
cy
.
−
Allo
ca
tio
n
o
f
DGs a
n
d
m
i
n
im
i
za
tio
n
SOI
o
f
to
tal
c
o
s
t
an
d
m
ax
im
izatio
n
o
f
t
r
an
s
m
is
s
io
n
ef
f
icien
cy
.
T
h
e
p
r
o
p
o
s
ed
3
3
-
b
u
s
I
E
E
E
D
S
r
ad
ial
alg
o
r
ith
m
s
wer
e
a
p
p
l
ied
an
d
th
e
r
esu
lts
wer
e
co
m
p
ar
ed
with
o
th
er
tec
h
n
iq
u
es.
T
h
e
b
ac
k
wa
r
d
/f
o
r
war
d
s
wee
p
(
B
FS
)
m
eth
o
d
is
u
s
ed
h
e
r
e
f
o
r
later
al
r
ad
ial
DS
p
o
wer
f
lo
w
an
aly
s
is
b
ec
au
s
e
it
is
s
im
p
le
to
im
p
lem
en
t,
f
lex
ib
le,
f
ast
,
an
d
h
as
ex
tr
e
m
e
ac
cu
r
ac
y
[
1
9
]
-
[
2
0
]
.
T
h
e
r
est
o
f
th
is
p
ap
er
is
ar
r
an
g
ed
as
f
o
llo
w
s
.
Sectio
n
2
d
is
cu
s
s
es
th
e
p
r
o
b
lem
f
o
r
m
u
latio
n
,
wh
ile
s
ec
tio
n
s
3
p
r
esen
t
m
eth
o
d
o
l
o
g
y
a
n
d
4
p
r
esen
t si
m
u
latio
n
r
esu
lts
,
f
in
ally
th
e
p
a
p
er
co
n
cl
u
s
io
n
s
ex
p
lain
ed
in
s
ec
tio
n
5
.
2.
P
RO
B
L
E
M
F
O
R
M
U
L
AT
I
O
N
2
.
1
.
P
o
wer
f
lo
w
f
o
rm
ula
t
i
o
n
T
h
e
B
FS
alg
o
r
ith
m
f
o
r
Fig
u
r
e
1
m
ea
s
u
r
es
th
e
p
o
wer
f
l
o
w
esti
m
ates.
Sh
o
ws
th
e
DS
s
eg
m
en
t,
p
r
o
v
id
e
d
th
at
th
e
N
lin
e
is
li
n
k
ed
b
etwe
en
th
e
two
‘
i
’
a
n
d
‘
j
’
b
u
s
es
g
iv
e
n
.
T
h
r
ee
m
ea
s
u
r
es
b
ased
o
n
th
e
cu
r
r
en
ts
an
d
v
o
ltag
e
law
o
f
th
e
Kir
ch
h
o
f
f
ar
e
u
s
ed
to
ev
al
u
ate
th
e
B
FS
tech
n
iq
u
e
Kir
c
h
h
o
f
f
'
s
cu
r
r
e
n
t
law
(
KC
L
)
an
d
Kir
c
h
h
o
f
f
'
s
v
o
ltag
e
law
(
KVL
)
,
c
o
r
r
esp
o
n
d
in
g
ly
.
T
h
e
th
r
ee
s
tag
es
ar
e:
(
a)
b
ac
k
war
d
s
wee
p
,
(
b
)
f
o
r
war
d
s
wee
p
,
an
d
(
c)
n
o
d
a
l
cu
r
r
en
t
a
n
aly
s
is
.
Su
ch
m
ea
s
u
r
es
d
ep
en
d
o
n
c
o
n
co
u
r
s
e
a
ch
iev
em
en
ts
if
th
e
m
ax
im
u
m
m
is
m
atch
b
etwe
en
v
o
ltag
es is
less
th
an
th
e
ep
s
ilo
n
ac
ce
p
tan
ce
p
r
o
v
i
d
ed
.
Fig
u
r
e
1
.
A
s
ec
tio
n
o
f
DS
I
t
is
ea
s
y
to
esti
m
ate
th
e
ac
ti
v
e
an
d
r
ea
ctiv
e
p
o
wer
lo
s
s
es
f
o
r
th
e
r
ad
ial
DS
a
f
ter
t
h
e
c
o
n
co
u
r
s
e.
T
h
e
B
FS
p
o
wer
f
lo
w
ev
alu
atio
n
s
ar
e
p
r
esen
ted
as:
t
h
e
f
lo
w
o
f
ac
tiv
e
(
P_
ij)
an
d
r
ea
ctiv
e
(
Q_
ij)
p
o
wer
s
f
r
o
m
n
o
d
e
‘
i
’
to
n
o
d
e
‘
j
’
v
ia
b
r
an
ch
‘
N
’
ca
n
b
e
o
b
tain
e
d
f
r
o
m
th
e
l
atest n
o
d
e
in
(
a)
b
ac
k
war
d
s
s
wee
p
p
ath
as
:
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.
25
,
No
.
2
,
Feb
r
u
a
r
y
20
22
:
6
1
0
-
6
2
5
612
=
′
+
(
′
2
+
′
2
)
2
(
1
)
=
′
+
(
′
2
+
′
2
)
2
(
2
)
w
h
er
e
,
`
=
+
an
d
`
=
+
.
an
d
ar
e
lo
ad
s
th
at
ar
e
attac
h
ed
at
n
o
d
e
‘
j
’
.
ar
e
th
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
f
lo
win
g
f
r
o
m
n
o
d
e
‘
j
’
.
T
h
e
m
ag
n
itu
d
e
an
d
a
n
g
le
o
f
v
o
ltag
e
at
ea
ch
n
o
d
e
ar
e
co
n
s
i
d
er
ed
in
(
b
)
f
o
r
war
d
d
i
r
ec
tio
n
.
tak
e
in
to
ac
co
u
n
t
a
v
o
ltag
e
∠
i
at
n
o
d
e
‘
i
’
an
d
∠
at
n
o
d
e
‘
j
’
,
th
en
t
h
e
(
c)
th
e
cu
r
r
en
t f
lo
win
g
th
r
o
u
g
h
th
e
b
r
an
ch
‘
N
’
h
av
in
g
an
im
p
ed
an
ce
,
=
+
lin
k
ed
b
etwe
en
‘
I
’
an
d
‘
j
’
a
r
e
g
iv
e
n
as
:
=
(
∠
−
∠
)
+
(
3
)
=
(
−
)
∠
−
(
4
)
h
en
ce
f
r
o
m
(
3
)
an
d
(
4
)
th
e
b
u
s
v
o
ltag
e
at
‘
j
’
ca
n
b
e
ca
lcu
lated
as:
=
[
2
−
2
∗
(
+
)
+
(
2
+
2
)
∗
2
+
2
2
]
0
.
5
(
5
)
t
he
m
ag
n
itu
d
e
an
d
p
h
ase
an
g
le
eq
u
atio
n
s
ca
n
b
e
s
u
g
g
ested
co
r
r
esp
o
n
d
in
g
ly
in
(
b
)
th
e
f
o
r
war
d
d
ir
ec
tio
n
to
f
in
d
th
e
v
o
ltag
e
an
d
an
g
le
o
f
a
ll
r
ad
ial
DS
n
o
d
es.
I
t
is
p
o
s
s
ib
le
to
p
r
esen
t
th
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
lo
s
s
es
o
f
lin
e
‘
N
’
b
etwe
en
b
u
s
es
‘
i
’
an
d
‘
j
’
as
:
(
)
=
(
2
+
2
)
2
(
6
)
(
)
=
(
2
+
2
)
2
(
7
)
t
h
e
to
tal
ac
tiv
e
p
o
wer
lo
s
s
o
f
r
ad
ial
DS c
an
b
e
co
n
s
id
er
ed
as
:
=
∑
(
)
=
1
(
8
)
w
h
er
e
‘
N
’
is
th
e
n
u
m
b
er
o
f
b
r
an
ch
es,
i=1
: n
a
n
d
‘
n
’
is
th
e
n
u
m
b
er
o
f
b
u
s
es.
2
.
2
.
P
o
wer
lo
s
s
estim
a
t
io
n i
n c
a
s
e
o
f
ex
is
t
ing
DG
S uni
t
s
T
h
en
th
e
p
o
wer
lo
s
s
es with
in
a
lin
e
s
ec
to
r
in
Fig
u
r
e
1
wh
en
p
u
ttin
g
DG
u
n
its
in
th
e
DS.
I
t
is
:
,
(
)
=
(
(
)
2
+
(
)
2
)
2
(
9
)
,
=
∑
,
(
)
=
1
(
1
0
)
w
h
er
e,
,
(
)
an
d
,
(
)
is
th
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
lo
s
s
wh
en
lo
ca
t
in
g
DGS
b
etwe
en
b
u
s
es
‘
i
’
an
d
‘
j
’
,
,
is
th
e
to
tal
p
o
wer
lo
s
s
with
lo
ca
tin
g
DGS.
2
.
3
.
I
nd
ex
o
f
po
wer
l
o
s
s
es
T
h
e
to
tal
p
o
wer
lo
s
s
in
d
ex
is
ca
lcu
lated
as
th
e
d
iv
is
io
n
o
f
to
tal
p
o
wer
lo
s
s
with
co
n
n
ec
ti
n
g
DGS
b
y
th
e
to
tal
p
o
wer
lo
s
s
with
o
u
t c
o
n
n
ec
tin
g
DGS
an
d
it is
p
r
esen
ted
as:
∆
=
,
(
1
1
)
b
y
m
in
im
izin
g
,
th
e
to
tal
p
o
we
r
lo
s
s
in
th
e
s
y
s
tem
r
ed
u
ce
d
b
y
in
teg
r
atio
n
DGS.
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
E
n
erg
y
h
a
r
ve
s
tin
g
ma
ximiza
tio
n
b
y
i
n
teg
r
a
tio
n
o
f
d
is
tr
ib
u
ted
g
en
era
tio
n
…
(
Ta
r
ek
A
.
B
o
g
h
d
a
d
y
)
613
2
.
4
.
V
o
l
t
a
g
e
dev
i
a
t
io
n
i
nd
ex
(
VDI)
T
h
e
V
DI
ca
n
b
e
p
r
esen
ted
as
(
1
2
)
.
=
ma
x
(
1
−
1
)
,
∀
=
1
,
2
,
…
…
…
.
,
(
1
2
)
2
.
5
.
DG
S c
o
s
t
e
v
a
lua
t
io
n
DS
co
m
p
an
ies
ar
e
m
ain
ly
r
esp
o
n
s
ib
le
f
o
r
p
r
o
v
i
d
in
g
th
e
d
e
m
an
d
o
f
e
n
d
u
s
er
.
So
th
at,
b
e
n
ef
its
an
d
co
s
ts
o
f
DGs si
te
an
d
s
ize
in
a
u
tili
ty
n
etwo
r
k
m
a
y
b
e
p
r
o
p
o
s
ed
as sh
o
wn
:
−
C
o
s
t o
f
in
v
estme
n
t
I
n
v
estme
n
t
co
s
t
in
clu
d
es
DG
u
n
its
co
s
t,
in
v
esti
g
atio
n
f
ee
,
DG
u
n
its
in
s
tallatio
n
,
p
r
ep
ar
at
io
n
o
f
lo
ca
tio
n
.
I
t c
an
b
e
p
r
esen
ted
as:
1
=
∑
=
1
∗
(
1
3
)
w
h
er
e,
i=1
,
2
,
3
…
NDG,
n
o
.
o
f
DGS
th
at
s
h
o
u
ld
b
e
lo
ca
ted
.
K_
DGi
I
s
t
h
e
MW
ca
p
ac
ity
o
f
i
DG.
I
C
_
i
is
th
e
in
itial c
o
s
t o
f
i D
G
in
$
/
MW
.
−
C
o
s
t o
f
o
p
er
atio
n
DG
o
p
er
atin
g
c
o
s
t
is
m
ain
ly
d
ep
en
d
i
n
g
o
n
DGs
o
p
er
atio
n
to
p
r
o
d
u
ce
p
o
wer
f
o
r
e
n
d
u
s
er
s
ca
n
b
e
p
r
esen
ted
as:
2
=
∑
[
=
1
∗
]
∗
∆
(
1
4
)
w
h
ile,
OC
i
is
th
e
co
s
t
o
f
o
p
er
atio
n
o
f
i
DG
in
$
/MWh
o
f
i
DG
,
∆
T
is
th
e
o
p
er
atin
g
h
o
u
r
s
d
u
r
in
g
a
y
ea
r
.
A
n
d
if
th
e
in
f
latio
n
r
ate
(
I
F)
an
d
th
e
in
ter
est
r
ate
(
I
R
)
,
s
o
t
h
at
th
e
p
r
esen
t
wo
r
th
v
alu
e
(
PW
V)
ca
n
b
e
s
ig
n
if
ied
as:
=
∑
=
1
(
1
+
1
+
)
(
1
5
)
w
h
er
e,
is
PW
V,
n
is
th
e
p
lan
n
in
g
p
er
io
d
in
y
ea
r
s
.
PW
V
o
f
o
p
e
r
atin
g
c
o
s
t
in
p
lan
n
in
g
y
ea
r
ca
n
b
e
co
n
s
id
er
ed
as:
(
2
)
=
∑
[
=
1
∗
]
∗
∆
∗
(
1
6
)
−
Ma
in
ten
an
ce
co
s
t
MC
D
G
i
C
an
b
e
ca
lcu
lated
as (
p
e
r
ce
n
t
ag
e%
o
f
in
itial c
o
s
t p
er
y
ea
r
.
2
.
6
.
DG
S benef
it
s
ev
a
lua
t
io
n
−
R
ea
l p
o
wer
d
em
an
d
d
ec
r
ea
s
es f
r
o
m
DS n
etwo
r
k
I
n
an
e
n
er
g
y
ef
f
icien
t
p
o
wer
s
y
s
tem
,
tr
an
s
m
is
s
io
n
g
r
id
s
o
l
d
its
p
o
wer
to
DS
c
o
m
p
an
y
t
o
ac
h
iev
e
t
h
e
en
er
g
y
r
eq
u
est
o
f
en
d
u
s
er
s
.
DS
c
o
r
p
o
r
atio
n
ca
n
r
eso
u
r
ce
d
em
an
d
o
f
p
o
wer
with
e
x
is
tin
g
o
f
DGS,
th
e
n
o
b
tain
lo
wer
elec
tr
ical
p
o
wer
f
r
o
m
tr
a
n
s
m
is
s
io
n
g
r
id
.
DS
c
o
m
p
an
y
ca
n
cr
ea
te
a
m
a
r
k
et
an
d
s
ell
th
e
en
er
g
y
t
o
th
e
g
r
id
as p
er
ag
r
ee
d
co
n
tr
ac
t a
s
s
h
o
wn
:
1
=
∑
=
1
∗
∗
∆
(
1
7
)
w
h
ile,
EP
G
is
th
e
p
r
ice
o
f
elec
tr
icit
y
in
(
$
/KW
h
)
,
an
d
∆
T
is
tim
e
s
eg
m
en
t
in
wh
ich
en
er
g
y
is
s
o
ld
t
o
g
r
id
.
PW
V
o
f
th
e
g
en
er
ated
elec
tr
ic
ity
f
r
o
m
DG
b
y
th
e
DS
c
o
m
p
a
n
y
ca
n
b
e
co
n
s
id
er
ed
as sh
o
w
n
:
(
1
)
=
∑
=
1
∗
∗
∆
∗
(
1
8
)
−
L
o
s
s
r
ed
u
ctio
n
r
e
v
en
u
e
E
co
n
o
m
ic
b
e
n
ef
it
is
th
e
m
ain
tar
g
et
o
f
DS
c
o
m
p
an
y
f
o
r
m
ax
im
izin
g
th
e
p
r
o
f
it.
So
,
th
e
r
ev
en
u
e
ca
m
e
f
r
o
m
th
e
lo
s
s
r
ed
u
ctio
n
i
n
th
e
ex
is
ten
ce
o
f
DGs e
s
tim
ated
as:
2
=
∑
∆
=
1
∗
∗
∆
(
1
9
)
∆
L
OS
S
ij
I
s
th
e
ac
tiv
e
p
o
wer
lo
s
s
r
e
d
u
ctio
n
,
wh
en
DGs
is
s
ited
in
th
e
n
etwo
r
k
an
d
EP
G
is
th
e
elec
tr
icity
p
r
ice
in
th
e
g
r
id
in
$
/k
W
h
.
T
h
e
PW
V
o
f
lo
s
s
r
ed
u
ctio
n
r
ev
e
n
u
e
in
a
p
lan
n
e
d
zo
n
e
ca
n
b
e
c
alcu
lated
as:
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.
25
,
No
.
2
,
Feb
r
u
a
r
y
20
22
:
6
1
0
-
6
2
5
614
(
2
)
=
∑
∆
=
1
∗
∗
∆
∗
(2
0)
3.
M
E
T
H
O
DO
L
G
Y
I
t
is
co
m
m
o
n
ly
k
n
o
wn
th
at
th
e
MO
F
is
m
ath
em
atica
lly
m
o
d
eled
in
o
r
d
er
t
o
o
p
tim
ize
th
e
o
b
tain
e
d
b
en
ef
its
o
f
th
e
DG
in
teg
r
atio
n
in
to
th
e
DS
in
ter
m
s
o
f
d
if
f
er
en
t
in
d
ices.
T
h
ese
in
d
ices
im
p
o
r
tan
ce
ap
p
ea
r
s
wh
en
p
lan
n
in
g
an
d
o
p
er
atio
n
o
f
DG
b
ec
au
s
e
o
f
th
eir
s
ig
n
if
ican
t
im
p
ac
t
o
n
th
e
in
co
m
e
o
f
u
tili
ties
'
,
p
o
wer
q
u
ality
,
s
ec
u
r
ity
,
en
v
i
r
o
n
m
e
n
t
al
ef
f
ec
t
an
d
s
y
s
tem
s
tab
ilit
y
[
4
]
.
I
n
o
u
r
r
e
v
iew
we
h
av
e
two
p
h
ases
,
th
e
f
ir
s
t
o
n
e
was
m
ax
i
m
izin
g
tr
a
n
s
m
is
s
io
n
ef
f
icien
cy
,
m
in
im
izin
g
v
o
ltag
e
d
e
v
iatio
n
a
n
d
r
ea
ctiv
e
p
o
wer
lo
s
s
.
T
h
e
s
ec
o
n
d
p
h
ase
was
a
s
in
g
le
o
b
j
ec
tiv
e
f
u
n
ctio
n
(
SOI
)
to
m
i
n
i
m
ize
th
e
to
tal
c
o
s
t.
T
h
e
MO
F
ca
n
b
e
s
tated
as
th
e
weig
h
ted
s
u
m
o
f
th
e
tr
an
s
m
is
s
io
n
ef
f
icien
cy
(
T
E
I
)
an
d
th
e
v
o
ltag
e
d
ev
iatio
n
in
d
e
x
(
VDI
)
an
d
r
ea
ctiv
e
p
o
wer
lo
s
s
r
ed
u
ctio
n
in
d
e
x
(
QL
I
)
.
T
h
e
weig
h
ted
s
u
m
m
atio
n
m
eth
o
d
is
ef
f
icien
t,
th
e
d
ev
elo
p
m
e
n
t
o
f
a
s
tr
o
n
g
ly
n
o
n
-
d
o
m
in
ated
s
o
lu
tio
n
th
at
ca
n
b
e
u
s
ed
as
th
e
in
itial
s
o
lu
tio
n
f
o
r
o
th
er
a
p
p
r
o
ac
h
es
is
s
im
p
le
an
d
f
ea
s
ib
le
[
2
1
]
.
MO
F m
in
im
izatio
n
ca
n
b
e
s
tat
ed
f
r
o
m
(
2
1
)
:
(
)
=
[
+
+
]
(
2
1
)
+
+
=
1
(
2
2
)
t
h
e
r
ea
ctiv
e
p
o
we
r
lo
s
s
r
ed
u
ctio
n
(
W
QL
)
,
v
o
ltag
e
d
ev
iatio
n
(
W
VD
)
.
T
h
e
t
r
an
s
m
is
s
io
n
e
f
f
icien
cy
ar
e
ea
ch
ass
ig
n
ed
with
d
if
f
er
en
t w
eig
h
t
in
g
f
ac
to
r
s
ac
co
r
d
in
g
to
th
eir
i
m
p
o
r
tan
ce
.
3
.
1
.
Rea
c
t
iv
e
a
nd
re
a
l po
we
r
lo
s
s
ind
ice
s
(
,
P
L
I
)
I
n
th
is
ap
p
r
o
ac
h
,
t
h
e
b
en
e
f
its
ca
n
b
e
ac
h
iev
ed
wh
e
n
lo
wer
in
g
th
e
in
d
ices
v
alu
es.
T
h
e
r
e
ac
tiv
e
an
d
r
ea
l p
o
wer
lo
s
s
in
d
ic
es a
r
e
we
ll
-
d
ef
in
ed
as
;
=
(
2
3
)
=
(
2
4
)
w
h
er
e,
QL
DG
an
d
PL
DG
ar
e
th
e
to
tal
r
ea
ctiv
e
an
d
r
ea
l
p
o
wer
l
o
s
s
es
o
f
th
e
DS
af
ter
p
r
esen
ce
o
f
DG.
QL
an
d
PL
ar
e
th
e
to
tal
r
ea
ctiv
e
a
n
d
r
e
al
lo
s
s
es with
o
u
t e
x
is
tin
g
DG
in
th
e
DS.
3
.
2
.
Vo
l
t
a
g
e
dev
i
a
t
io
n
i
nd
ex
(
)
I
n
th
is
ap
p
r
o
ac
h
,
th
e
b
etter
n
etwo
r
k
p
er
f
o
r
m
an
ce
ca
n
b
e
a
ch
iev
ed
wh
en
th
is
in
d
ex
is
m
u
ch
lo
wer
.
Selectin
g
th
e
p
r
o
p
er
lo
ca
tio
n
o
f
DG
im
p
r
o
v
es
th
e
v
o
ltag
e
p
r
o
f
ile.
T
h
is
in
d
ex
m
ay
b
e
is
u
s
ed
f
o
r
f
in
d
i
n
g
th
e
DG
lo
ca
tio
n
s
tak
in
g
i
n
to
co
n
s
id
er
atio
n
th
e
p
r
e
-
estab
lis
h
ed
v
o
ltag
e
d
e
v
iatio
n
lim
it,
a
n
d
al
s
o
f
o
r
e
n
s
u
r
in
g
th
e
r
ated
v
o
ltag
e
c
o
n
ce
r
n
ed
f
o
r
ea
ch
b
u
s
with
in
th
e
allo
wab
le
lim
its
.
W
h
er
e,
V1
is
th
e
r
ated
v
o
ltag
e
(
n
o
r
m
ally
V
1
=1
0
0
%),
‘
n
’
is
th
e
n
o
d
es n
u
m
b
er
an
d
Vi
is
t
h
e
b
u
s
I
v
o
ltag
e.
T
h
e
VDI
ca
n
b
e
esti
m
ated
:
=
(
1
−
1
)
,
∀
=
1
,
2
,
…
…
…
.
,
(
2
5
)
3
.
3
.
M
a
x
i
m
izing
p
ro
f
it
(
)
I
n
a
f
ew
wo
r
d
s
,
th
e
v
iew
p
o
in
t
o
f
b
en
e
f
it
an
d
c
o
s
t
th
at
h
av
e
b
ee
n
s
h
o
wn
i
n
th
e
p
r
ev
io
u
s
s
e
ctio
n
s
ar
e
wo
r
k
ed
i
n
a
o
n
e
s
in
g
le
o
b
jec
tiv
e
f
u
n
ctio
n
(
SOF)
th
at
is
e
x
p
r
ess
ed
b
elo
w
f
o
r
m
ax
im
izi
n
g
th
e
d
is
tr
ib
u
tio
n
c
o
m
p
an
y
p
r
o
f
it tak
in
g
in
to
co
n
s
id
er
atio
n
th
e
c
o
n
s
tr
ain
ts
.
ma
x
pr
ofi
t
=
−
Inve
s
tme
n
ts
(
2
6
)
M
in
c
ost
=
∑
K
D
G
i
N
D
G
i
=
1
∗
EP
G
∗
∆
T
∗
β
t
+
∑
∆
l
oss
s
∗
EP
G
N
D
G
i
=
1
−
∑
K
D
G
i
N
D
G
i
=
1
∗
OCi
∆
T
∗
β
t
−
∑
[
K
D
G
i
N
D
G
i
=
1
∗
IC
i
∗
{
1M
C
DG
∗
β
t
}]
(
2
7
)
3
.
4
.
So
lutio
n
m
et
ho
do
lo
g
y
f
o
r
m
ultiple
DG
co
nn
ec
t
ing
T
h
e
m
eth
o
d
o
lo
g
y
o
f
co
n
n
ec
tin
g
f
o
r
m
u
lti
DG
ca
n
b
e
ex
p
r
ess
ed
in
th
r
ee
s
tag
es.
T
h
e
f
ir
s
t
s
tag
e
i
s
id
en
ti
f
y
in
g
th
e
o
p
tim
al
DG
lo
ca
tio
n
,
t
h
en
th
e
o
p
tim
al
D
G
s
ize
an
d
f
i
n
ally
b
y
o
p
tim
izin
g
th
e
o
p
tim
al
p
lace
m
en
t a
n
d
s
ize.
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
E
n
erg
y
h
a
r
ve
s
tin
g
ma
ximiza
tio
n
b
y
i
n
teg
r
a
tio
n
o
f
d
is
tr
ib
u
ted
g
en
era
tio
n
…
(
Ta
r
ek
A
.
B
o
g
h
d
a
d
y
)
615
3
.
4
.
1
.
I
dentif
y
ing
t
he
o
ptim
a
l D
G
s
o
urce
’
s
lo
ca
t
io
n
T
h
is
p
r
o
ce
d
u
r
e
is
r
e
p
etitiv
e
f
o
r
m
u
ltip
le
DGs
co
n
n
ec
tin
g
.
T
h
e
s
tar
tin
g
b
ase
s
y
s
tem
is
r
e
f
o
r
m
ed
b
y
co
n
s
id
er
in
g
a
f
ix
ed
o
p
tim
al
DG
s
ize
at
th
e
b
est
lo
ca
tio
n
s
in
th
e
DS
co
n
f
ig
u
r
atio
n
(
DSC
)
f
ir
s
tly
b
y
in
jectin
g
a
DG
u
n
it
o
n
e
-
by
-
o
n
e
in
th
e
D
SC
.
T
h
e
o
b
tain
ed
DG
will
b
e
lo
ca
ted
in
th
e
s
y
s
tem
s
o
th
at
d
ev
elo
p
in
g
a
n
ew
s
tar
in
g
b
ase
ca
s
e
with
r
ep
etitiv
e
s
tep
s
o
f
p
lacin
g
s
in
g
le
DG.
T
h
e
b
est s
elec
t o
f
DG
s
izes c
an
n
o
t b
e
t
h
e
o
p
tim
al
o
v
er
all
c
h
o
ices.
I
t
is
r
ea
s
o
n
ab
l
y
illu
s
tr
ated
th
at
th
e
o
p
tim
al
DG
(
s
ize
an
d
p
lace
m
en
t)
is
o
p
tim
u
m
ch
o
ice
at
th
e
tim
e
o
f
a
d
d
in
g
o
f
ea
c
h
DG,
b
u
t
n
o
t
f
o
r
th
e
o
v
e
r
all
co
m
p
lete
s
y
s
tem
.
Ho
wev
er
,
th
e
o
p
ti
m
u
m
o
v
er
all
g
lo
b
al
DG
s
ize
ch
o
ices
ar
e
d
etec
ted
b
y
u
s
in
g
a
lg
o
r
ith
m
s
p
r
o
v
id
e
d
th
at
th
e
p
lace
m
en
t
o
f
DGs
wh
ich
ar
e
s
tr
o
n
g
-
m
in
d
ed
b
y
s
in
g
le
a
lg
o
r
ith
m
s
o
f
p
lacin
g
DGs.
3.
4
.
2.
I
dentif
y
ing
t
he
g
lo
ba
l
o
ptim
a
l D
G
s
o
urce
s
s
izes
T
h
e
co
m
m
o
n
p
r
o
ce
d
u
r
e
f
o
r
o
b
tain
in
g
th
e
o
p
tim
al
s
izin
g
o
f
m
u
lti
-
DG
co
n
n
ec
tin
g
is
as f
o
llo
ws:
1)
I
n
p
u
t
p
r
o
b
ab
le
b
u
s
es
th
at
ar
e
th
e
b
est
o
p
tim
al
DG
lo
ca
tio
n
s
ar
e
g
iv
e
n
b
y
s
in
g
le
p
lace
m
e
n
t
o
f
DG
a
n
d
ap
p
ly
in
g
g
en
etic
alg
o
r
ith
m
a
g
ain
.
2)
I
n
a
r
a
n
d
o
m
way
s
elec
tin
g
th
e
in
itial GA
p
o
p
u
latio
n
.
3)
Ap
p
ly
in
g
th
e
p
o
wer
f
lo
w
f
o
r
t
h
e
DSC
with
th
e
ex
is
tin
g
o
f
th
e
in
jecte
d
DG
at
th
e
b
est o
p
ti
m
al
lo
ca
tio
n
.
4)
Ass
es
s
th
e
n
ee
d
ed
o
b
jectiv
e
f
u
n
ctio
n
b
y
th
e
p
o
wer
f
lo
w
wi
th
th
e
ex
is
tin
g
o
f
t
h
e
in
s
er
ted
DG
f
r
o
m
th
e
GA
s
ea
r
ch
.
5)
R
ep
ea
tin
g
s
tep
s
3
,
4
f
o
r
all
g
r
o
u
p
in
g
s
p
o
p
u
latio
n
s
o
f
GA.
6)
Giv
in
g
v
alu
es to
th
e
o
b
jectiv
e
f
u
n
ctio
n
as a
f
itn
ess
to
GA.
7)
C
h
ec
k
in
g
th
e
cr
iter
ia
o
f
GA
c
o
n
v
er
g
en
ce
if
it'
s
s
atis
f
ied
th
e
n
g
o
es to
s
tep
n
o
9
.
8)
Gen
er
atin
g
o
n
e
a
n
e
w
g
en
er
ati
o
n
an
d
th
en
g
o
to
s
tep
n
o
3
.
9)
Prin
tin
g
th
e
r
esu
lt f
o
r
all
p
r
o
b
ab
le
ca
n
d
id
ate
b
u
s
es.
3
.
4
.
3
.
O
ptim
a
l
s
it
es a
nd
s
izes o
f
DG
us
ing
G
A
T
h
is
p
r
o
ce
s
s
is
r
ep
etitiv
e
f
o
r
m
u
ltip
le
lo
ca
tio
n
s
an
d
s
izes
o
f
DGs.
B
y
u
s
in
g
GA,
s
im
p
ly
we
ca
n
o
b
tain
b
o
th
th
e
o
p
tim
al
s
ite
an
d
s
ize
f
o
r
th
e
f
o
llo
win
g
ca
s
es:
a)
C
o
n
s
id
er
ex
is
tin
g
o
f
1
DG.
b)
C
o
n
s
id
er
ex
is
tin
g
o
f
2
DG.
c)
C
o
n
s
id
er
ex
is
tin
g
o
f
3
DG
.
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
e
test
s
y
s
tem
i
s
th
e
s
tan
d
ar
d
3
3
b
u
s
r
ad
ial
DS
n
etwo
r
k
g
iv
en
in
Fig
u
r
e
2
(
a)
an
d
Fig
u
r
e
2
(
b
)
,
with
n
u
m
b
er
o
f
th
ir
ty
-
two
b
r
a
n
ch
e
s
an
d
th
r
ee
later
als.
T
h
e
r
ea
cti
v
e
an
d
r
ea
l p
o
wer
s
o
f
th
e
co
n
n
ec
ted
lo
ad
s
f
o
r
t
h
is
n
etwo
r
k
a
r
e
2
.
3
MV
AR
an
d
3
.
7
2
MW
r
esp
ec
tiv
ely
.
T
h
e
ac
t
iv
e
an
d
r
ea
ctiv
e
p
o
wer
lo
s
s
es
f
o
r
th
is
r
ad
ial
DS
n
etwo
r
k
with
o
u
t D
Gs ar
e
2
0
1
.
8
9
3
k
W
an
d
1
3
4
.
6
4
1
k
VAR r
e
s
p
ec
tiv
ely
.
(
a)
(
b
)
Fig
u
r
e
2
.
T
h
e
test
s
y
s
tem
is
th
e
s
tan
d
ar
d
3
3
b
u
s
r
a
d
ial
DS n
e
two
r
k
:
(
a)
s
in
g
le
lin
e
d
iag
r
am
o
f
s
tan
d
ar
d
I
E
E
E
3
3
b
u
s
DS
an
d
(
b
)
m
ag
n
itu
d
e
o
f
th
e
n
o
d
e
v
o
ltag
e
o
f
b
ase
ca
s
e
o
f
3
3
-
b
u
s
test
DS
4
.
1
.
Usi
ng
s
ing
le
o
bje
ct
iv
e
f
un
ct
io
n
o
f
t
ra
ns
m
is
s
io
n e
f
f
iciency
4
.
1
.
1
.
O
ptim
um
s
ize
DG
s
Ass
u
m
in
g
DG
lo
ca
tio
n
as f
o
ll
o
ws:
a)
E
x
is
tin
g
o
n
e
DG
at
b
u
s
6
as it is
th
e
lo
n
g
est b
r
an
c
h
an
d
n
ea
r
to
lo
ad
ce
n
ter
.
b)
T
h
e
r
esu
lts
as
s
h
o
wn
in
T
ab
le
1
ar
e
ap
p
r
o
x
im
ately
eq
u
al
b
etwe
en
o
p
tim
izatio
n
tech
n
i
q
u
es
an
d
t
h
e
o
p
tim
al
s
ize
is
2
5
8
8
k
w
at
b
u
s
6
.
c)
E
x
is
tin
g
two
DG
at
b
u
s
6
a
n
d
1
8
as it is n
ea
r
to
lo
a
d
ce
n
ter
a
n
d
th
e
e
n
d
n
o
d
e
o
f
t
h
e
lo
n
g
est
b
r
an
ch
.
d)
T
h
e
r
esu
lts
as
s
h
o
w
n
in
T
ab
le
1
s
h
o
w
th
e
o
p
tim
al
s
ize
to
ac
h
iev
e
m
a
x
im
u
m
tr
an
s
m
is
s
io
n
is
2
0
7
9
k
w
at
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.
25
,
No
.
2
,
Feb
r
u
a
r
y
20
22
:
6
1
0
-
6
2
5
616
b
u
s
6
an
d
4
6
2
k
w
at
b
u
s
1
8
.
e)
E
x
is
tin
g
3
DG
at
b
u
s
6
.
1
8
,
an
d
3
3
n
ea
r
to
lo
a
d
ce
n
ter
,
th
e
en
d
n
o
d
e
o
f
th
e
lo
n
g
est
b
r
a
n
ch
,
an
d
s
ec
o
n
d
f
a
r
en
d
n
o
d
e
at
th
e
s
ec
o
n
d
-
lar
g
est b
r
an
ch
.
f)
T
h
e
r
esu
lts
as
s
h
o
wn
in
T
ab
le
1
ar
e
th
e
o
p
tim
u
m
s
ize,
in
th
is
ca
s
e,
o
b
tain
ed
b
y
GW
O
o
r
W
OA
is
1
3
9
6
k
w
at
b
u
s
6
,
4
5
7
k
w
at
b
u
s
1
8
,
an
d
6
5
8
k
w
at
b
u
s
3
3
.
B
ef
o
r
e
in
s
tallin
g
th
e
DG,
th
e
v
o
ltag
e
p
r
o
f
iles
o
f
s
o
m
e
o
f
th
e
b
u
s
es
in
all
d
is
tr
ib
u
tio
n
s
y
s
tem
s
ex
ce
ed
th
e
r
eq
u
ir
e
d
co
n
s
tr
ain
t
lim
itatio
n
s
.
As
a
r
esu
lt,
af
ter
u
s
in
g
th
e
g
en
etic
alg
o
r
ith
m
to
id
en
tify
th
e
id
ea
l
s
ize
DG
as
th
e
b
ase
tec
h
n
iq
u
e
,
th
e
v
o
ltag
e
p
r
o
f
ile
o
f
all
b
u
s
es
in
all
s
y
s
tem
s
m
o
v
ed
to
th
e
s
u
itab
le
r
an
g
e,
a
s
s
h
o
wn
in
Fig
u
r
e
3
(
a)
.
Af
ter
a
d
d
in
g
DG
s
o
u
r
ce
s
,
th
er
e
is
th
e
in
cr
ea
s
e
in
th
e
s
y
s
tem
's
tr
an
s
m
is
s
io
n
ef
f
icien
cy
.
C
o
m
p
ar
e
d
to
s
in
g
le
DG
p
lace
m
en
t,
th
e
to
tal
DG
ca
p
ac
ity
m
o
u
n
ted
in
th
e
d
ev
ice
is
s
m
aller
f
o
r
m
u
lti
DG
p
o
s
itio
n
in
g
af
ter
p
u
ttin
g
th
e
o
p
tim
al
DG
d
e
ter
m
in
ed
b
y
th
e
g
e
n
etic
alg
o
r
ith
m
as b
ase
tech
n
iq
u
e
as sh
o
wn
in
Fig
u
r
e
3
(
b
)
.
T
ab
le
1
.
Glo
b
al
o
p
tim
u
m
s
ize
o
f
DGs f
o
r
tr
a
n
s
m
is
s
io
n
ef
f
icien
cy
m
ax
im
izatio
n
C
A
S
E
NO.
B
A
S
E
W
/
O
D
G
(
k
w
)
2
0
1
.
8
9
3
Te
c
h
n
i
q
u
e
s
GA
PSO
W
O
A
G
W
O
1
D
G
B
U
S
N
O
.
-
6
6
6
6
DG
S
I
ZE
(
k
w
)
-
2
8
1
8
2
5
8
8
2
5
8
8
2
5
8
8
P
o
w
e
r
L
o
ss (
k
w
)
-
1
0
3
.
0
5
.
0
0
1
0
2
.
0
8
.
0
0
1
0
2
.
0
8
.
0
0
1
0
2
.
0
8
.
0
0
P
LO
S
S
r
e
d
u
c
t
i
o
n
%
-
4
8
%
4
9
%
4
9
%
4
9
%
2
D
G
B
U
S
N
O
.
-
6
18
6
18
6
18
6
18
D
G
S
I
ZE
(
k
w
)
-
2
8
5
6
3
3
8
2
0
7
9
4
6
2
2
0
9
9
4
5
6
2
0
9
9
4
5
6
O
v
e
r
a
l
l
S
i
z
e
(
k
w
)
-
3
1
9
4
2
5
4
1
2
5
5
5
2
5
5
5
P
o
w
e
r
L
o
ss (
k
w
)
-
97
9
0
.
0
8
.
0
0
9
0
.
0
8
.
0
0
9
0
.
0
8
.
0
0
P
LO
S
S
r
e
d
u
c
t
i
o
n
%
-
5
2
%
5
5
%
5
5
.
1
%
5
5
.
1
%
3
D
G
B
U
S
N
O
.
-
6
18
33
6
18
33
6
18
33
6
18
33
D
G
S
I
ZE
(
k
w
)
-
1
8
0
4
2
5
0
6
1
7
1
5
1
0
4
4
2
7
0
8
1
3
8
3
4
5
9
6
6
3
1
3
9
6
4
5
7
6
5
8
O
v
e
r
a
l
l
S
i
z
e
(
k
w
)
-
2
6
7
1
2
6
6
0
2
5
0
5
2
5
1
1
P
o
w
e
r
L
o
ss (
k
w
)
-
8
1
.
0
1
.
0
0
7
8
.
7
1
7
8
.
3
3
.
0
0
7
8
.
3
2
.
0
0
P
LO
S
S
r
e
d
u
c
t
i
o
n
%
-
5
9
.
8
%
6
1
%
6
1
.
2
%
6
1
.
2
%
(
a)
(
b
)
Fig
u
r
e
3
.
O
p
tim
u
m
allo
ca
tio
n
o
f
DGs: (
a)
m
ag
n
itu
d
e
o
f
th
e
n
o
d
e
v
o
ltag
e
an
d
(
b
)
tr
an
s
m
is
s
io
n
ef
f
icien
c
y
4
.
1
.
2
.
O
ptim
um
s
it
e
DG
s
Ass
u
m
in
g
DG
s
ize
f
r
o
m
th
e
r
e
s
u
lts
as f
o
llo
ws in
T
ab
le
1
:
−
E
x
is
tin
g
o
n
e
DG
with
s
ize
2
5
8
8
k
w.
−
T
h
e
r
esu
lts
ar
e
witten
in
T
ab
le
2
ar
e
ap
p
r
o
x
im
ately
e
q
u
al
b
etwe
en
o
p
tim
izatio
n
tech
n
iq
u
es
an
d
th
e
o
p
tim
al
s
ite
is
b
u
s
6
.
T
h
e
lo
s
s
r
ed
u
ctio
n
p
er
ce
n
ta
g
e,
in
th
is
c
ase,
is
4
9
%.
−
E
x
is
tin
g
two
DG
with
s
ize
2
0
7
9
k
w
an
d
4
6
2
k
w
as in
W
OA
.
−
T
h
e
r
esu
lts
ar
e
s
h
o
wn
in
T
ab
le
2
illu
s
tr
ate
th
e
o
p
tim
al
s
ite
to
ac
h
iev
e
m
ax
im
u
m
tr
a
n
s
m
is
s
io
n
at
b
u
s
6
an
d
b
u
s
1
8
.
T
h
e
lo
s
s
r
ed
u
ctio
n
p
er
ce
n
tag
e,
in
th
is
ca
s
e,
is
5
5
.
6
%.
−
E
x
is
tin
g
3
DG
f
o
r
e
x
am
p
le
f
r
o
m
d
if
f
er
e
n
t te
ch
n
iq
u
es with
s
izes 1
5
1
0
,
4
4
2
,
an
d
7
0
8
k
w
as
in
PS
O.
−
T
h
e
r
esu
lts
s
h
o
wn
in
T
ab
le
2
ar
e
t
h
e
o
p
tim
u
m
s
ite
at
b
u
s
2
9
,
b
u
s
1
6
,
a
n
d
b
u
s
2
5
.
T
h
e
l
o
s
s
r
ed
u
ctio
n
p
er
ce
n
tag
e,
i
n
th
is
ca
s
e,
is
6
2
.
4
%.
B
ef
o
r
e
in
s
tallin
g
th
e
DG,
th
e
v
o
ltag
e
p
r
o
f
iles
o
f
s
o
m
e
b
u
s
es
in
th
e
d
is
tr
ib
u
tio
n
s
y
s
tem
ex
ce
ed
th
e
r
eq
u
ir
ed
c
o
n
s
tr
ain
t
lim
itatio
n
s
.
As
a
r
esu
lt,
af
ter
u
s
in
g
th
e
d
if
f
er
en
t
o
p
tim
izatio
n
alg
o
r
ith
m
es
to
id
en
tify
th
e
o
p
tim
u
m
s
ite
DG
f
o
r
th
e
th
r
ee
ca
s
es
(
1
DG,
2
DG,
an
d
3
D
G)
.
T
h
e
v
o
ltag
e
p
r
o
f
ile
o
f
all
b
u
s
es
in
all
s
y
s
tem
s
m
o
v
ed
to
th
e
s
u
itab
le
r
a
n
g
e,
as
s
h
o
wn
in
Fig
u
r
e
4
(
a
)
.
T
h
er
e
is
th
e
in
cr
ea
s
e
in
th
e
s
y
s
tem
's
tr
an
s
m
is
s
io
n
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
E
n
erg
y
h
a
r
ve
s
tin
g
ma
ximiza
tio
n
b
y
i
n
teg
r
a
tio
n
o
f
d
is
tr
ib
u
ted
g
en
era
tio
n
…
(
Ta
r
ek
A
.
B
o
g
h
d
a
d
y
)
617
ef
f
icien
cy
af
ter
ad
d
in
g
DG
s
o
u
r
ce
s
,
wh
en
co
m
p
a
r
ed
to
th
e
b
ase
ca
s
e
with
o
u
t
DG
a
n
d
th
e
s
in
g
le
DG
in
s
tallatio
n
.
Af
ter
u
s
in
g
th
e
g
e
n
etic
alg
o
r
ith
m
t
o
s
elec
t th
e
o
p
tim
u
m
DG
s
ite,
as sh
o
wn
in
Fig
u
r
e
4
(
b
)
.
(
a)
(
b
)
Fig
u
r
e
4
.
Op
tim
u
m
s
ite
o
f
DG
s
:
(
a)
m
ag
n
itu
d
e
o
f
t
h
e
n
o
d
e
v
o
ltag
e
an
d
(
b
)
t
r
a
n
s
m
is
s
io
n
ef
f
icien
cy
T
ab
le
2
.
Glo
b
al
o
p
tim
u
m
s
ite
o
f
DGs f
o
r
tr
a
n
s
m
is
s
io
n
ef
f
icien
cy
m
ax
im
izatio
n
CA
S
E
N
O
.
BA
S
E
W
/
O
D
G
(k
w
)
2
0
1
.
8
9
3
T
ec
h
n
i
q
u
e
s
GA
PSO
WOA
GWO
ID
G
D
G
S
IZ
E
(k
w
)
-
2
8
1
8
2
5
8
8
2
5
8
8
2
5
8
8
BU
S
N
O
.
-
6
6
6
6
Po
w
er
L
o
s
s
(
k
w
)
-
1
0
3
.
0
5
.
0
0
1
0
2
.
0
8
.
0
0
1
0
2
.
0
8
.
0
0
1
0
2
.
0
8
.
0
0
P
L
O
SS
r
ed
u
c
t
i
o
n
%
-
4
8
%
4
9
%
4
9
%
4
9
%
2
D
G
D
G
S
IZ
E
(k
w
)
-
2
8
5
6
3
3
8
2
0
7
9
4
6
2
2
0
7
9
4
6
2
2
0
7
9
4
6
2
BU
S
N
O
.
-
6
16
26
15
6
15
7
15
O
v
era
l
l
S
i
ze
(
k
w
)
-
3
1
9
4
3
5
4
1
2
5
4
1
2
5
4
1
Po
w
er
L
o
s
s
(k
w
)
-
9
6
.
0
7
.
0
0
8
9
.
0
7
.
0
0
8
9
.
0
6
.
0
0
9
1
.
0
2
.
0
0
P
L
O
SS
r
ed
u
c
t
i
o
n
%
-
5
1
.
9
%
5
5
.
5
%
5
5
.
6
%
5
4
.
8
%
3
D
G
D
G
S
IZ
E
(k
w
)
-
1
8
0
4
2
5
0
6
1
7
1
5
1
0
4
4
2
7
0
8
4
5
9
6
6
3
1
3
8
3
1
3
9
6
4
5
7
6
5
8
BU
S
N
O
.
-
6
17
31
29
16
25
14
25
30
7
15
31
O
v
era
l
l
S
i
ze
(
k
w
)
-
2
6
7
1
2
6
6
0
2
5
0
5
2
5
1
1
Po
w
er
L
o
s
s
(
k
w
)
-
8
0
.
3
4
.
0
0
7
5
.
9
4
7
5
.
3
4
.
0
0
7
6
.
0
5
.
0
0
P
L
O
SS
r
ed
u
c
t
i
o
n
%
-
6
0
.
2
%
6
2
.
4
%
6
2
.
3
%
6
2
%
4
.
1
.
3
.
O
ptim
um
a
llo
ca
t
i
o
n o
f
DG
s
T
h
is
s
ec
tio
n
lo
o
k
s
at
th
e
p
r
o
b
lem
f
o
r
o
n
e
,
two
,
a
n
d
th
r
ee
DGs
ex
is
tin
g
.
T
h
e
d
if
f
er
en
t
tech
n
iq
u
es
d
eter
m
in
e
th
e
ap
p
r
o
p
r
iate
p
o
s
itio
n
o
f
th
e
DG
u
n
it,
in
ad
d
itio
n
to
its
s
ize.
B
u
t
th
e
p
r
ev
io
u
s
s
ec
tio
n
s
d
eter
m
in
e
th
e
s
ize
o
n
l
y
o
r
p
o
s
itio
n
o
f
t
h
e
u
n
its
.
T
h
e
r
esu
lts
o
f
th
is
s
ec
tio
n
ar
e
s
u
m
m
ar
ized
in
T
ab
le
3
.
T
h
e
v
o
lta
g
e
p
r
o
f
ile
o
f
all
b
u
s
es
is
en
h
a
n
ce
d
an
d
is
with
in
th
e
ac
ce
p
t
ab
le
r
an
g
e
in
all
th
r
ee
ca
s
es
(
af
ter
in
s
er
tin
g
th
e
o
p
tim
u
m
lo
ca
tio
n
an
d
ca
p
ac
it
y
o
f
th
e
o
n
e,
two
,
an
d
th
r
ee
D
G
u
n
its
)
as
s
h
o
wn
in
Fig
u
r
e
5
(
a)
.
I
t
illu
s
tr
ates
th
at
th
e
b
etter
v
o
ltag
e
p
r
o
f
ile,
th
e
g
r
ea
ter
th
e
n
u
m
b
er
o
f
DG
u
n
its
.
T
h
e
in
cr
ea
s
in
g
in
th
e
s
y
s
tem
's
tr
an
s
m
is
s
io
n
ef
f
icien
cy
af
ter
ad
d
in
g
DG
s
o
u
r
ce
s
is
s
h
o
wn
in
Fig
u
r
e
5
(
b
)
.
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.
25
,
No
.
2
,
Feb
r
u
a
r
y
20
22
:
6
1
0
-
6
2
5
618
T
ab
le
3
.
Glo
b
al
O
p
tim
u
m
allo
ca
tio
n
o
f
DGs f
o
r
tr
an
s
m
is
s
io
n
ef
f
icien
cy
m
ax
im
izatio
n
CA
S
E
N
O
.
BA
S
E
W
/
O
D
G
(
k
w
)
2
0
1
.
8
9
3
T
ec
h
n
i
q
u
e
s
GA
PSO
WOA
GWO
I
D
G
D
G
S
IZ
E
(k
w
)
-
2
5
8
8
2
4
5
5
2
5
8
8
2
5
8
8
BU
S
N
O
.
-
6
26
6
6
Po
w
er
L
o
s
s
(K
W
)
-
1
0
2
.
0
8
1
0
4
.
0
3
1
0
2
.
0
8
1
0
2
.
0
8
P
L
O
SS
red
u
c
t
i
o
n
%
-
4
9
%
4
8
.
3
%
4
9
%
4
9
%
2
D
G
D
G
S
IZ
E
(k
w
)
-
1
1
9
2
8
5
0
8
5
0
1
1
9
2
8
5
0
1
1
9
2
1
0
0
0
1
1
2
6
BU
S
N
O
.
-
13
30
13
30
14
30
12
30
O
v
era
l
l
S
i
ze
(k
w
)
-
2
0
4
2
2
0
4
2
2
0
4
2
2
1
2
6
Po
w
er
L
o
s
s
(K
W
)
-
8
2
.
0
9
8
2
.
0
9
.
0
0
83
8
3
.
0
2
.
0
0
P
L
O
SS
red
u
c
t
i
o
n
%
-
5
9
%
5
9
%
5
8
.
9
%
5
8
.
8
%
3
D
G
D
G
S
IZ
E
(k
w
)
-
7
2
5
1
0
7
0
1
1
1
9
7
5
9
1
0
7
1
1
1
0
0
7
5
9
1
0
7
1
1
1
0
0
1
3
8
3
1
0
0
0
1
0
0
0
BU
S
N
O
.
-
14
24
30
14
24
30
15
24
31
3
12
30
O
v
era
l
l
S
i
ze
(k
w
)
-
2
9
1
4
2
9
3
0
2
9
3
0
3
3
8
3
Po
w
er
L
o
s
s
(K
W
)
-
6
9
.
0
4
6
9
.
4
7
1
.
0
3
7
6
.
0
6
P
L
O
SS
red
u
c
t
i
o
n
%
-
6
5
.
6
%
5
6
.
6
%
6
4
.
8
%
6
2
%
(
a)
(
b
)
Fig
u
r
e
5
.
Glo
b
al
o
p
tim
u
m
allo
ca
tio
n
o
f
DGs
:
(
a)
m
a
g
n
itu
d
e
o
f
th
e
n
o
d
e
v
o
ltag
e
an
d
(
b
)
tr
an
s
m
is
s
io
n
ef
f
icien
c
y
4
.
2
.
O
pti
m
um
a
llo
ca
t
io
n o
f
DG
s
a
nd
m
ini
m
iza
t
io
n o
f
t
o
t
a
l
c
o
s
t
a
s
SO
I
T
h
e
to
tal
co
s
t
ca
n
b
e
m
in
i
m
ized
b
y
s
elec
tin
g
th
e
o
p
t
im
u
m
allo
ca
tio
n
o
f
DGs
ta
k
in
g
in
to
co
n
s
id
er
atio
n
th
e
in
ter
est
an
d
in
f
latio
n
r
ate,
th
u
s
we
ca
n
ex
tr
ac
t
th
e
m
ax
im
u
m
p
r
o
f
it,
an
d
ce
r
tain
ass
u
m
p
tio
n
s
ar
e
co
n
s
id
er
ed
.
T
h
e
ef
f
ec
t o
f
DG
p
lace
m
en
t a
n
d
ca
p
ac
ity
in
a
3
3
-
b
u
s
test
s
y
s
tem
wa
s
d
em
o
n
s
tr
ated
in
T
ab
le
4
as
a
r
esu
lt
o
f
th
e
s
im
u
latio
n
.
T
h
e
p
r
ice
lis
t
o
f
DG
u
n
its
f
r
o
m
g
en
e
r
ato
r
jo
e
c
o
m
p
an
y
,
t
h
e
co
s
t
o
f
s
er
v
ice
a
n
d
m
ain
ten
an
ce
ar
e
s
h
o
wn
in
T
ab
le
5
,
an
d
th
e
b
en
ef
it
ea
r
n
e
d
d
u
r
i
n
g
th
e
p
lan
n
i
n
g
p
e
r
io
d
.
Fo
r
s
er
v
al
s
tu
d
y
d
u
r
atio
n
,
o
p
tim
u
m
p
o
s
itio
n
in
g
an
d
s
ize
ar
e
ca
r
r
ie
d
o
u
t
with
DG.
T
ab
le
4
p
r
esen
ts
th
e
f
in
a
n
cial
an
d
tech
n
ical
b
en
ef
its
an
d
p
r
o
f
its
o
f
DG
s
iz
e
an
d
p
lace
m
e
n
t,
b
ased
o
n
th
e
r
esu
lts
o
f
s
im
u
latio
n
b
y
th
e
p
r
o
p
o
s
ed
GA
as
b
ase
alg
o
r
ith
m
c
o
m
p
ar
e
d
with
o
th
er
te
ch
n
iq
u
es
o
f
al
g
o
r
ith
m
s
,
a
n
d
p
r
esen
ts
th
e
b
est
Glo
b
al
o
p
tim
al
lo
ca
tio
n
a
n
d
s
ize
o
f
DG
s
o
u
r
ce
s
f
o
r
m
in
i
m
izin
g
to
tal
c
o
s
t
in
ca
s
e
o
f
in
ject
in
g
th
r
ee
DGs
with
o
v
er
all
ca
p
ac
ity
6
0
0
k
w
o
n
ly
at
b
u
s
b
ar
(
1
5
,
1
8
,
3
2
)
,
th
e
p
r
o
f
it
1
.
5
5
0
8
*
1
0
^6
$
a
n
d
th
e
lo
s
s
r
ed
u
ctio
n
p
er
ce
n
tag
e
5
2
.
9
%
tak
in
g
in
t
o
co
n
s
id
er
atio
n
i
n
ter
est
an
d
in
f
l
atio
n
r
ates.
I
n
th
e
ca
s
e
o
f
in
j
ec
tin
g
two
DGs
with
an
o
v
e
r
all
ca
p
ac
ity
o
f
4
0
0
KW
o
n
ly
at
th
e
b
u
s
b
ar
(
3
2
,
1
7
)
,
th
e
p
r
o
f
it
0
.
9
2
4
7
1
*
1
0
^
6
$
an
d
th
e
l
o
s
s
r
ed
u
ctio
n
p
er
c
en
tag
e
2
3
%.
I
n
th
e
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
E
n
erg
y
h
a
r
ve
s
tin
g
ma
ximiza
tio
n
b
y
i
n
teg
r
a
tio
n
o
f
d
is
tr
ib
u
ted
g
en
era
tio
n
…
(
Ta
r
ek
A
.
B
o
g
h
d
a
d
y
)
619
ca
s
e
o
f
in
jectin
g
o
n
e
DG
with
an
o
v
er
all
ca
p
ac
ity
o
f
2
0
0
k
w
o
n
ly
at
th
e
b
u
s
b
ar
(
1
7
)
,
th
e
p
r
o
f
it
0
.
8
8
7
1
7
*
1
0
^6
$
an
d
t
h
e
lo
s
s
r
ed
u
ctio
n
p
er
ce
n
tag
e
1
2
.
5
%.
T
h
e
v
o
ltag
e
p
r
o
f
ile
is
s
h
o
wn
i
n
Fig
u
r
e
6
(
a
)
as
an
o
b
tain
e
d
b
y
g
en
etic
alg
o
r
ith
m
an
d
t
h
is
is
th
e
wo
r
s
t
s
o
lu
tio
n
tech
n
iq
u
e
f
o
r
o
p
tim
u
m
allo
ca
tio
n
o
f
DGs
f
o
r
m
in
i
m
izin
g
to
tal
co
s
t
as
SOI
.
T
h
e
v
alu
es
o
f
v
o
ltag
e
p
r
o
f
ile
at
s
o
m
e
b
u
s
es
in
th
e
n
o
n
-
ac
ce
p
tab
le
r
an
g
e.
T
h
e
T
r
an
s
m
is
s
io
n
ef
f
icien
cy
o
f
th
is
ca
s
e
is
s
h
o
wn
in
Fig
u
r
e
6
(
b
)
.
T
h
e
tr
a
n
s
m
is
s
io
n
ef
f
icien
cy
is
n
o
t
s
u
f
f
icien
tly
i
m
p
r
o
v
e
d
lik
e
in
p
r
ev
io
u
s
ca
s
es,
in
ad
d
itio
n
to
th
e
ec
o
n
o
m
ic
p
r
o
f
it wa
s
h
ig
h
er
b
e
ca
u
s
e
th
is
is
f
r
o
m
th
e
ec
o
n
o
m
i
c
p
o
in
t o
f
v
iew.
T
ab
le
4
.
Glo
b
al
o
p
tim
u
m
allo
ca
tio
n
o
f
DGs f
o
r
m
in
im
izin
g
to
tal
co
s
t
CA
S
E
N
O
.
BA
S
E
W
/
O
D
G
(k
w
)
2
0
1
.
8
9
3
T
ec
h
n
i
q
u
e
s
GA
PSO
WOA
GWO
I
D
G
D
G
S
IZ
E
(k
w
)
-
2
0
0
2
0
0
2
0
0
2
0
0
BU
S
N
O
.
-
33
17
17
17
Po
w
er
L
o
s
s
(
K
W
)
-
1
7
8
.
0
7
1
7
6
.
0
6
1
7
6
.
0
6
1
7
6
.
0
6
P
L
O
SS
r
ed
u
c
t
i
o
n
%
-
1
1
.
5
%
1
2
.
5
%
1
2
.
5
%
1
2
.
5
%
Pro
f
i
t
*
1
0
^
6
-
0
,
6
1
3
1
9
4
4
4
4
0
,
6
1
5
9
7
2
2
2
2
0
,
6
1
5
9
7
2
2
2
2
0
,
6
1
5
9
7
2
2
2
2
2
DG
D
G
S
IZ
E
(k
w
)
-
2
0
0
2
0
0
2
0
0
2
0
0
2
0
0
2
0
0
2
0
0
2
0
0
BU
S
N
O
.
-
17
15
17
32
17
33
32
17
Po
w
er
L
o
s
s
(
K
W
)
-
1
6
7
.
0
5
1
5
5
.
0
2
1
5
5
.
0
3
1
5
5
.
0
2
P
L
O
SS
r
ed
u
c
t
i
o
n
%
-
1
7
%
2
3
.
2
%
2
3
.
1
%
2
3
.
2
%
Pro
f
i
t
*
1
0
^
6
0
.
9
0
3
2
4
0
.
9
2
4
7
1
0
.
9
2
4
6
6
0
.
9
2
4
7
1
3
DG
D
G
S
IZ
E
(k
w
)
-
2
0
0
2
0
0
2
0
0
2
0
0
2
0
0
2
0
0
2
0
0
2
0
0
2
0
0
2
0
0
2
0
0
2
0
0
BU
S
N
O
.
-
7
20
29
14
17
32
15
18
32
14
17
32
Po
w
er
L
o
s
s
(
K
W
)
-
1
6
4
.
0
9
1
3
7
.
0
6
9
5
.
0
2
1
3
7
.
0
6
P
L
O
SS
r
ed
u
c
t
i
o
n
%
-
1
8
.
3
%
3
1
.
9
%
5
2
.
9
%
3
1
.
9
%
Pro
f
i
t
*
1
0
^
6
-
1
4
.
2
9
4
1
4
.
7
7
0
1
5
.
5
0
8
1
4
.
7
7
0
(
a)
(
b
)
Fig
u
r
e
6
.
Op
tim
u
m
allo
ca
tio
n
o
f
DGs f
o
r
m
in
im
izin
g
to
tal
c
o
s
t
:
(
a)
m
ag
n
itu
d
e
o
f
th
e
n
o
d
e
v
o
ltag
e
an
d
(
b
)
tr
an
s
m
is
s
io
n
ef
f
ice
n
cy
T
ab
le
5
.
T
h
e
s
am
p
le
o
f
p
r
ice
l
is
t o
f
DG
u
n
its
f
r
o
m
g
en
er
ato
r
jo
e
co
m
p
a
n
y
D
i
e
se
l
g
e
n
e
r
a
t
o
r
s
l
i
st
p
r
i
c
e
o
f
G
e
n
e
r
a
t
o
r
j
o
e
c
o
,
S
e
t
s
6
0
H
Z
2
0
0
K
W
2
1
0
KW
2
5
0
K
W
2
7
5
KW
2
8
0
KW
3
0
0
K
W
3
5
0
K
W
4
0
0
K
W
4
5
0
KW
i
n
v
e
s
t
me
n
t
c
o
s
t
(
$
)
4
6
,
7
0
5
.
6
5
1
,
8
2
3
.
6
5
3
,
6
7
3
.
9
5
7
,
9
0
2
.
5
5
4
,
3
1
0
.
7
6
1
,
7
0
8
.
1
6
5
,
7
9
1
.
3
6
8
,
2
5
3
.
2
7
6
,
9
7
8
.
8
f
u
e
l
c
o
st
5
g
/
h
r
-
1
3
.
4
1
5
.
5
g
/
h
1
8
.
5
g
/
h
1
9
.
5
g
/
h
1
9
.
5
g
/
h
2
3
g
/
h
2
3
g
/
h
2
5
.
8
g
/
h
2
9
.
9
g
/
h
4
0
.
2
$
/
h
4
6
.
5
$
/
h
5
5
.
5
$
/
h
5
8
.
5
$
/
h
5
8
.
5
$
/
h
6
9
$
/
h
6
9
$
/
h
7
7
.
4
$
/
h
8
9
.
7
$
/
h
4
.
2
.
O
ptim
um
a
llo
ca
t
io
n
o
f
DG
s
a
nd
m
ini
m
iza
t
io
n
M
O
I
o
f
re
a
ct
iv
e
po
wer
lo
s
s
(
Q
lo
s
s
)
,
v
o
lt
a
g
e
dev
ia
t
io
n
(
VD)
a
nd
m
a
x
im
iz
a
t
io
n o
f
t
ra
ns
m
is
s
io
n e
f
f
iciency
I
t
is
p
r
esen
ted
as
a
ca
s
e
s
tu
d
y
in
th
e
f
ir
s
t
an
d
th
en
ch
an
g
e
d
th
e
weig
h
ts
,
wh
ich
th
e
r
ea
ctiv
e
p
o
wer
lo
s
s
r
ed
u
ctio
n
,
v
o
ltag
e
d
ev
ia
tio
n
,
an
d
th
e
t
r
an
s
m
is
s
io
n
ef
f
icien
cy
.
E
ac
h
in
d
ex
is
ass
ig
n
ed
with
d
if
f
er
e
n
t
weig
h
tin
g
f
ac
to
r
s
ac
co
r
d
in
g
to
th
eir
im
p
o
r
tan
ce
to
g
et
th
e
b
e
s
t g
lo
b
al
p
er
f
o
r
m
an
ce
in
d
ex
:
Evaluation Warning : The document was created with Spire.PDF for Python.