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1.
I
NT
RO
D
UCT
I
O
N
W
ith
th
e
d
is
co
v
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y
o
f
elec
tr
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,
o
u
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life
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as
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af
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tead
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wh
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lam
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ab
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ce
t
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e
in
tr
o
d
u
ctio
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icity
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p
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o
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ea
g
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to
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ar
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ar
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an
g
in
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lig
h
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to
elec
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r
s
in
o
r
d
er
to
m
ak
e
th
eir
liv
es
co
n
v
en
ien
t
[
1
]
,
[
2
]
.
I
t
h
elp
s
in
th
e
d
ev
elo
p
m
e
n
t
o
f
a
n
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tan
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s
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icity
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th
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f
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atio
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h
u
m
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g
r
o
wth
a
n
d
ad
v
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ce
m
e
n
t [
3
]
,
[
4
]
.
Ho
wev
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,
th
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s
till
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ajo
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ch
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m
itti
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ate
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s
m
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[
5
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,
[
6
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.
C
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b
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ar
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also
d
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[
7
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,
[
8
]
.
Fu
r
th
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r
co
s
t r
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u
ctio
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is
ex
p
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ted
an
d
co
n
s
eq
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t c
lim
ate
ch
a
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g
e
m
itig
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.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
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2
5
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I
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d
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J
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&
C
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p
Sci,
Vo
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24
,
No
.
3
,
Dec
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b
er
2
0
2
1
:
1
2
6
9
-
1
2
7
7
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T
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9
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1
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n
d
s
o
n
u
t
i
l
i
t
y
g
r
i
d
.
T
h
i
s
i
s
s
u
e
c
a
n
b
e
o
v
e
r
c
o
m
e
b
y
t
h
e
m
u
t
u
a
l
c
o
m
b
i
n
a
t
i
o
n
o
f
s
o
l
a
r
a
n
d
w
i
n
d
c
h
a
r
a
c
t
e
r
i
s
t
i
c
s
b
y
t
a
k
i
n
g
i
n
t
o
a
c
c
o
u
n
t
t
h
e
c
o
m
p
l
e
m
e
n
t
a
r
y
c
h
a
r
a
c
t
e
r
i
s
t
i
c
s
o
f
s
o
l
a
r
a
n
d
w
i
n
d
e
n
e
r
g
y
[
1
2
]
,
[
1
3
]
.
A
n
a
p
p
r
o
p
r
i
a
t
e
s
o
l
a
r
,
b
a
t
t
e
r
y
a
n
d
w
i
n
d
e
n
e
r
g
y
s
y
s
t
e
m
c
a
n
m
a
x
i
m
i
z
e
t
h
e
r
e
l
i
a
b
i
l
i
t
y
o
f
p
o
w
e
r
s
u
p
p
l
y
a
n
d
r
e
d
u
c
e
s
t
h
e
c
o
s
t
o
f
t
h
e
s
y
s
t
e
m
[
1
4
]
.
I
n
a
g
r
i
d
c
o
n
n
e
c
t
e
d
h
y
b
r
i
d
s
y
s
t
e
m
,
g
r
i
d
i
s
k
e
p
t
a
s
a
b
a
c
k
-
u
p
p
o
w
e
r
s
y
s
t
e
m
f
o
r
f
u
l
f
i
l
l
i
n
g
t
h
e
r
e
q
u
i
r
e
d
l
o
a
d
d
e
m
a
n
d
[
1
5
]
-
[
1
8
]
.
I
n
t
h
i
s
p
a
p
e
r
,
a
s
t
u
d
y
w
a
s
c
o
n
d
u
c
t
e
d
b
e
t
w
e
e
n
t
w
o
t
e
c
h
n
i
q
u
e
s
u
s
i
n
g
H
O
M
E
R
a
n
d
b
a
c
k
t
r
a
c
k
s
e
a
r
c
h
a
l
g
o
r
i
t
h
m
(
B
S
A
)
f
i
n
m
a
t
r
i
x
l
a
b
o
r
a
t
o
r
y
(
M
A
T
L
A
B
)
e
n
v
i
r
o
n
m
e
n
t
(
R
2
0
1
8
a
v
e
r
s
i
o
n
,
4
0
8
3
2
9
0
0
)
t
o
f
i
n
d
t
h
e
b
e
s
t
r
e
s
u
l
t
a
n
d
r
e
d
u
c
e
d
c
o
s
t
i
s
s
u
g
g
e
s
t
e
d
f
o
r
h
y
b
r
i
d
r
e
n
e
w
a
b
l
e
e
n
e
r
g
y
s
y
s
t
e
m
f
o
r
p
o
w
e
r
i
n
g
t
h
e
N
a
t
i
o
n
a
l
I
n
s
t
i
t
u
t
e
o
f
T
e
c
h
n
o
l
o
g
y
M
a
n
i
p
u
r
a
n
d
S
h
i
j
a
H
o
s
p
i
t
a
l
s
,
M
a
n
i
p
u
r
.
Fig
u
r
e
1
.
Sch
em
atic
lay
o
u
t o
f
th
e
h
y
b
r
id
s
y
s
tem
2.
M
E
T
H
O
DO
L
O
G
Y
AND
N
UM
E
RICA
L
F
O
RM
UL
A
T
I
O
N
T
h
e
p
r
o
ce
s
s
o
f
o
p
tim
izatio
n
is
im
p
lem
en
ted
u
s
in
g
a
n
alg
o
r
it
h
m
k
n
o
wn
as
a
m
o
d
if
ied
B
SA.
B
SA
is
a
n
ewly
d
ev
elo
p
ed
p
r
o
g
r
ess
iv
e
alg
o
r
ith
m
an
d
it
h
as
a
p
ar
t
icu
lar
m
ec
h
an
is
m
to
g
en
e
r
at
e
tr
ial
in
d
iv
id
u
als
en
ab
lin
g
it
to
p
er
f
o
r
m
ca
lcu
l
atio
n
o
f
n
u
m
e
r
ical
o
p
tim
izatio
n
p
r
o
b
lem
s
v
er
y
f
ast
[
1
9
]
-
[
2
2
]
.
An
Am
er
ican
m
ath
em
atician
D.
H.
L
eh
m
a
r
was th
e
f
ir
s
t to
in
tr
o
d
u
ce
th
e
t
er
m
“b
ac
k
tr
ac
k
”
in
th
e
1
9
5
0
s
.
2
.
1
.
M
a
t
hema
t
ica
l
m
o
delin
g
o
f
t
he
re
qu
ired
co
m
po
nents
T
h
e
p
o
wer
o
u
tp
u
t f
o
r
th
e
p
h
o
t
o
v
o
ltaic
ar
r
a
y
s
is
g
iv
en
b
y
,
P
pv
=
f
pv
P
pv
_
r
G
G
S
T
C
[
1
+
α
T
(
T
−
T
S
T
C
)
]
(
1
)
wh
er
e
P
pv
_
r
=
r
ated
p
o
wer
o
u
tp
u
t
o
f
th
e
PV m
o
d
u
le
,
f
pv
=
d
e
-
r
atin
g
f
ac
to
r
(
lo
s
s
an
d
s
h
ad
in
g
co
n
s
id
er
ed
)
G
S
T
C
=
s
ta
n
d
ar
d
s
o
lar
r
ad
iatio
n
o
n
PV
T
S
T
C
=
s
tan
d
ar
d
tem
p
e
r
atu
r
e
o
n
PV
T
an
d
G
=
r
e
al
tim
e
tem
p
er
atu
r
e
an
d
s
o
lar
r
ad
iatio
n
α
T
=
tem
p
er
atu
r
e
co
ef
f
icien
t
S
o
l
a
r
P
V
M
o
d
u
l
e
B
a
t
t
e
r
y
S
t
o
r
a
g
e
W
i
n
d
T
u
r
b
i
n
e
D
C
/
A
C
L
o
a
d
D
C
B
u
s
B
a
r
A
C
B
u
s
B
a
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
Op
timiz
a
tio
n
o
f wi
n
d
s
o
la
r
a
n
d
b
a
tter
y
h
yb
r
id
r
en
ewa
b
le
s
y
s
tem
u
s
in
g
…
(
I
n
g
u
d
a
m
C
h
itr
a
s
en
Meitei
)
1271
T
h
e
cu
r
v
e
f
o
r
th
e
g
e
n
er
ated
w
in
d
p
o
wer
f
r
o
m
th
e
win
d
tu
r
b
i
n
e
ca
n
b
e
r
ep
r
esen
ted
b
y
(
2
)
,
P
wt
=
{
0
v
w
<
V
ci
or
v
w
>
V
co
P
wt
_
r
v
w
−
V
ci
V
r
−
V
ci
V
ci
≤
v
w
≤
V
P
wt
_
r
V
r
≤
v
w
≤
V
co
(
2
)
wh
er
e
P
wt
_
r
=
r
ated
p
o
wer
o
u
tp
u
t o
f
win
d
tu
r
b
in
e
,
v
w
=
win
d
s
p
ee
d
V
r
=
r
ated
win
d
s
p
ee
d
V
ci
=
cu
t
-
in
s
p
ee
d
V
co
=
cu
t
-
o
u
t sp
ee
d
T
h
e
ter
m
in
al
v
o
ltag
e
o
f
th
e
b
a
tter
y
is
g
iv
en
b
y
,
V
bs
=
E
bs
−
I
d
ch
R
0
(
3
)
wh
er
e
E
bs
=
ef
f
ec
tiv
e
in
ter
n
al
v
o
l
tag
e
,
I
d
ch
=
d
is
ch
ar
g
e
cu
r
r
en
t
R
0
=
in
ter
n
al
r
esis
tan
ce
T
h
e
ef
f
ec
tiv
e
in
te
r
n
al
v
o
ltag
e
is
g
iv
en
b
y
,
E
bs
=
E
o
+
AX
+
CX
(
D
−
X
)
⁄
(
4
)
wh
er
e
E
o
=
in
ter
n
al
b
atter
y
v
o
lta
g
e
at
f
u
lly
c
h
ar
g
e
d
/d
is
ch
ar
g
ed
s
tate,
A
=
v
ar
iatio
n
in
in
itial
lin
ea
r
in
t
er
n
al
b
atter
y
v
o
ltag
e
with
c
h
ar
g
in
g
s
tate
D,
C
=
in
cr
ea
s
e/
d
ec
r
ea
s
e
in
b
atter
y
v
o
ltag
e
d
u
r
i
n
g
p
r
o
g
r
ess
iv
e
ch
ar
g
in
g
/d
is
ch
ar
g
in
g
X
=
m
ax
im
u
m
n
o
r
m
alize
d
ca
p
ac
ity
at
s
p
ec
if
ied
cu
r
r
e
n
t
2
.
2
.
St
r
a
t
eg
y
o
f
ener
g
y
ma
na
g
em
ent
C
o
n
s
id
er
in
g
th
e
h
y
b
r
id
p
o
wer
s
y
s
tem
,
wh
en
th
e
to
tal
p
o
wer
g
en
er
ated
b
y
th
e
s
y
s
tem
is
le
s
s
th
an
th
e
lo
ad
d
em
an
d
,
th
e
b
atter
y
will
b
e
d
is
ch
ar
g
ed
a
n
d
is
g
iv
en
b
y
(
5
)
.
An
d
wh
en
th
e
t
o
tal
p
o
wer
g
en
er
ated
is
m
o
r
e
th
an
th
e
lo
a
d
,
th
e
b
a
tter
y
will
b
e
ch
ar
g
e
d
an
d
is
g
iv
en
b
y
(
6
)
.
T
h
e
p
o
wer
f
lo
w
e
x
p
r
ess
io
n
i
s
g
iv
en
b
y
,
(
)
=
(
)
+
(
)
+
_
ℎ
(
)
(
5
)
(
)
=
(
)
+
(
)
−
_
ℎ
(
)
(
6
)
2
.
3
.
Str
a
t
eg
y
o
f
ener
g
y
ma
na
g
em
ent
T
h
e
r
eliab
ilit
y
o
f
th
e
p
o
wer
s
u
p
p
ly
is
g
iv
en
b
y
(
7
)
,
L
PS
P
=
∑
[
P
L
(
t
i
)
−
(
P
wt
(
t
i
)
+
P
pv
(
t
i
)
N
i
=
1
+
P
bs
_
dc
h
(
t
i
)
)
]
∑
P
L
(
t
i
)
N
i
=
1
(
7
)
wh
er
e
t
i
~
t
N
=
o
p
er
atin
g
tim
e
o
f
t
h
e
s
y
s
tem
.
I
f
th
e
s
co
p
e
f
o
r
l
o
ad
s
atis
f
ac
tio
n
(
L
PS
P
)
is
0
,
th
en
it
in
d
icate
s
th
at
th
e
lo
ad
d
em
an
d
is
alwa
y
s
m
et
b
y
th
e
s
y
s
tem
.
An
d
if
it
is
1
,
th
en
th
e
lo
a
d
is
n
ev
er
s
atis
f
ied
.
T
h
e
r
ate
o
f
r
elativ
e
f
lu
ct
u
atio
n
is
g
iv
en
b
y
,
D
L
=
1
P
̅
L
√
1
N
∑
(
P
wt
(
t
i
)
+
P
pv
(
t
i
)
−
P
L
(
t
i
)
)
2
N
i
=
1
(
8
)
wh
er
e
P
̅
L
=
av
er
a
g
e
p
o
wer
o
f
l
o
a
d
.
A
lo
wer
v
alu
e
o
f
D
L
im
p
lies
th
at
co
m
p
lem
en
tar
y
ch
ar
ac
ter
i
s
tics
o
f
s
o
lar
an
d
win
d
is
u
tili
ze
d
ef
f
icien
tly
.
2
.
4
.
Required
co
ns
t
ra
ints
T
h
e
m
a
x
i
m
u
m
n
u
m
b
e
r
o
f
w
i
n
d
g
e
n
e
r
a
t
o
r
t
u
r
b
i
n
e
s
,
s
o
l
a
r
p
a
n
e
ls
a
n
d
b
a
t
t
e
r
y
r
es
p
e
c
t
i
v
el
y
a
r
e
g
i
v
e
n
b
y
,
N
wt
≤
[
L
(
6
−
10
)
d
+
1
]
.
[
W
(
3
−
5
)
d
+
1
]
(
9
)
wh
er
e
L
an
d
W
=
len
g
th
a
n
d
wid
th
f
o
r
th
e
r
eg
io
n
,
d
=
r
o
to
r
d
iam
eter
N
pv
≤
[
S
2
S
pv
⁄
]
.
α
pv
(
1
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
.
3
,
Dec
em
b
er
2
0
2
1
:
1
2
6
9
-
1
2
7
7
1272
wh
er
e
S2
=
g
iv
e
n
in
s
tallatio
n
ar
ea
f
o
r
s
o
lar
PV p
an
el
,
S
pv
=
ar
ea
o
f
o
n
e
PV u
n
it
α
pv
=
co
ef
f
icien
t f
o
r
p
o
s
s
ib
le
s
h
ad
o
w
ar
ea
N
bs
≤
[
S
3
S
bs
⁄
]
(
1
1
)
wh
er
e
S2
=
g
iv
e
n
in
s
tallatio
n
ar
ea
f
o
r
b
atter
y
,
S
bs
=
ar
ea
o
f
s
in
g
le
b
atter
y
T
h
e
m
in
im
u
m
n
u
m
b
er
o
f
win
d
tu
r
b
in
es,
s
o
lar
p
an
els an
d
b
a
tter
y
r
esp
ec
tiv
ely
ar
e
g
iv
en
b
y
,
N
wt
≥
∫
P
L
(
t
)
dt
tm
3
tm
2
∫
P
wt
(
t
)
dt
tm
3
tm
2
⁄
(
1
2
)
wh
er
e
tm
2
–
tm
3
=
ef
f
ec
tiv
e
o
p
er
atin
g
tim
e
o
f
win
d
tu
r
b
in
e
d
u
r
in
g
n
ig
h
t
,
N
pv
≥
∫
P
L
(
t
)
dt
tm
1
tm
0
∫
P
pv
(
t
)
dt
tm
1
tm
0
⁄
(
1
3
)
wh
er
e
tm
0
–
tm
1
=
ef
f
ec
tiv
e
o
p
er
atin
g
tim
e
o
f
PV d
u
r
in
g
d
ay
,
N
bs
≥
λ
.
W
Ld
η
.
C
bs
.
V
bs
.
D
O
D
m
ax
(
1
4
)
wh
er
e
W
LD
=
en
er
g
y
c
o
n
s
u
m
e
d
ev
er
y
d
ay
b
y
lo
a
d
,
Vb
s
,
Vb
s
=
v
o
ltag
e
an
d
ca
p
ac
i
ty
o
f
s
in
g
le
b
atter
y
η
=
b
atter
y
d
is
ch
ar
g
in
g
e
f
f
icien
cy
T
h
e
r
eser
v
ed
o
p
er
atin
g
ca
p
ac
i
ty
is
g
iv
en
b
y
,
∑
P
DG
≥
(
1
+
μ%
)
P
L
(
1
5
)
wh
er
e
P
DG
=
to
tal
p
o
wer
o
u
t
p
u
t o
f
th
e
d
is
tr
ib
u
ted
g
e
n
er
atio
n
,
μ
=
o
p
er
atin
g
r
eser
v
e
r
atio
(
1
0
%)
T
h
e
ch
ar
g
in
g
a
n
d
d
is
ch
ar
g
in
g
co
n
s
tr
ain
ts
o
f
th
e
b
atter
y
is
g
i
v
en
b
y
,
SOC
m
i
n
≤
SOC
≤
SOC
m
ax
(
1
6
)
r
ch
≤
r
ch
_
R
,
r
d
ch
≤
r
d
ch
_
R
(
1
7
)
wh
er
e
r
ch
,
r
d
ch
=
ch
ar
g
in
g
a
n
d
d
is
ch
ar
g
in
g
r
ate
,
r
ch
_
R
,
r
d
ch
_
R
=
lim
ited
ch
ar
g
in
g
an
d
d
is
ch
ar
g
in
g
r
ate
I
ch
≤
I
chmax
,
I
d
ch
≤
I
d
chma
x
(
1
8
)
wh
er
e
I
ch
,
I
d
ch
=
ch
ar
g
in
g
an
d
d
is
ch
a
r
g
in
g
c
u
r
r
en
t
,
I
chmax
,
I
d
chmax
=
m
ax
im
u
m
c
h
ar
g
in
g
a
n
d
d
is
ch
ar
g
in
g
cu
r
r
e
n
t
0
≤
P
bs
_
ch
≤
P
bs
_
chmax
(
1
9
)
0
≤
P
bs
_
d
ch
≤
P
bs
_
d
chma
x
(
2
0
)
wh
er
e
P
bs
_
ch
,
P
bs
_
d
ch
, =
ch
ar
g
i
n
g
an
d
d
is
ch
ar
g
in
g
p
o
wer
,
P
bs
_
chmax
,
P
bs
_
d
chmax
=
m
ax
im
u
m
ch
ar
g
e
an
d
d
is
ch
ar
g
e
p
o
wer
[
2
3
]
,
[
2
4
]
,
N
C
≤
N
C
m
ax
(
2
1
)
wh
er
e
N
C
,
N
C
m
ax
=
ch
ar
g
in
g
/d
is
ch
ar
g
in
g
cy
cle
o
f
b
atter
y
a
n
d
its
lim
ited
v
alu
e
,
2
.
5
.
T
o
t
a
l c
o
s
t
I
n
itial
co
s
t o
f
th
e
s
y
s
tem
C
i =
(
Np
v
C
p
v
+N
wtC
wt+N
b
s
C
b
s
)
f
cr
(
2
2
)
wh
er
e
C
p
v
,
C
wt,
C
b
s
=
co
s
t o
f
PV p
an
els,
win
d
tu
r
b
in
e
an
d
b
atter
y
,
f
cr
=
ca
p
ital
r
ec
o
v
er
y
f
ac
to
r
Op
er
atin
g
an
d
m
ain
ten
a
n
ce
co
s
t
,
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
timiz
a
tio
n
o
f wi
n
d
s
o
la
r
a
n
d
b
a
tter
y
h
yb
r
id
r
en
ewa
b
le
s
y
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tem
u
s
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g
…
(
I
n
g
u
d
a
m
C
h
itr
a
s
en
Meitei
)
1273
C
OM
=
C
pv
_
OM
t
PV
+
C
wt
_
OM
t
wt
+
C
bs
_
OM
t
bs
(
2
3
)
wh
er
e
C
pv
_
OM
,
C
wt
_
OM
,
C
bs
_
OM
=
o
p
er
atin
g
an
d
m
ain
t
en
an
ce
co
s
t o
f
PV p
an
els,
win
d
tu
r
b
in
e
an
d
b
atter
y
t
PV
,
t
wt
,
t
bs
=
o
p
er
atin
g
tim
e
o
f
PV p
an
e
ls
,
win
d
tu
r
b
in
e
a
n
d
b
atter
y
,
R
ep
lace
m
en
t Co
s
t
C
R
=
C
pv
_
R
+
C
wt
_
R
+
C
bs
_
R
(
2
4
)
wh
er
e
C
pv
_
R
,
C
wt
_
R
,
C
bs
_
R
=
r
ep
lace
m
en
t
co
s
t
o
f
P
V
p
an
els,
win
d
tu
r
b
in
e
an
d
b
at
ter
y
,
2
.
6
.
O
bje
c
t
iv
e
f
un
ct
io
n
R
e
d
u
c
i
n
g
t
h
e
t
o
t
a
l
c
o
s
t
o
f
t
h
e
h
y
b
r
i
d
p
o
w
e
r
s
y
s
t
e
m
i
s
r
e
g
a
r
d
e
d
a
s
t
h
e
o
b
j
e
ct
i
v
e
f
u
n
c
t
i
o
n
.
I
t
i
s
g
i
v
e
n
b
y
,
min
f
=
min
(
C
i
+
C
OM
+
C
R
−
C
gs
+
C
gp
+
C
pc
)
(
2
5
)
wh
er
e
C
gp
,
C
gs
=
C
o
s
t o
f
p
u
r
c
h
asin
g
p
o
wer
f
r
o
m
th
e
g
r
id
a
n
d
s
ellin
g
p
o
wer
t
o
th
e
g
r
id
,
C
pc
=
p
en
alty
co
s
t
.
T
h
e
f
lo
wch
ar
t
o
f
th
e
s
u
g
g
ested
m
eth
o
d
is
s
h
o
wn
in
Fig
u
r
e
2
.
T
h
e
f
lo
wch
ar
t
ex
p
lain
s
th
e
s
tep
-
by
-
s
tep
p
r
o
ce
d
u
r
e
o
f
th
e
o
p
tim
izatio
n
p
r
o
ce
s
s
.
T
h
e
v
a
r
i
o
u
s
d
ata
co
llected
a
r
e
u
s
ed
a
n
d
th
e
f
in
al
n
et
to
tal
co
s
t is f
o
u
n
d
o
u
t.
Fig
u
r
e
2
.
Flo
wch
ar
t
o
f
th
e
p
r
o
p
o
s
ed
m
eth
o
d
S
t
a
r
t
i
=
0
a
n
d
j
=
0
G
e
n
e
r
a
t
i
o
n
p
a
r
a
m
e
t
e
r
D
e
m
a
n
d
l
o
a
d
p
o
w
e
r
Y
e
a
r
l
y
w
e
a
t
h
e
r
d
a
t
a
D
e
f
i
n
e
d
c
o
n
s
t
r
a
i
n
t
s
M
p
o
s
s
i
b
l
e
c
p
m
b
i
n
a
t
i
o
n
s
T
h
e
i
t
h
c
o
m
b
i
n
a
t
i
o
n
C
o
m
p
u
t
e
p
o
w
e
r
o
u
t
p
u
t
C
o
m
p
u
t
e
r
e
l
a
t
i
v
e
f
l
u
c
t
u
a
t
i
o
n
r
a
t
e
(
D
L
)
D
L
≤
Ψ
L
?
i
≥
M
?
C
o
m
p
u
t
e
L
P
S
P
i
=
i
+
1
L
P
S
P
≤
λ
L
?
C
o
m
p
u
t
e
D
g
s
D
g
s
≤
Ψ
g
?
C
o
m
p
u
t
e
t
h
e
t
o
t
a
l
p
r
i
c
e
P
[
j
]
=
C
A
i
j
=
j
+
1
S
e
l
e
c
t
c
o
m
b
i
n
a
t
i
o
n
w
i
t
h
t
h
e
l
o
w
e
s
t
c
o
s
t
P
[
j
]
m
i
n
C
o
m
p
u
t
e
t
h
e
t
o
t
a
l
p
r
i
c
e
E
n
d
i
N
Y
Y
N
Y
N
Y
N
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
.
3
,
Dec
em
b
er
2
0
2
1
:
1
2
6
9
-
1
2
7
7
1274
3.
SI
T
E
UND
E
R
S
T
UDY
A
ND
I
T
S
L
O
AD
E
ST
I
M
A
T
I
O
N
T
h
e
s
u
g
g
ested
m
o
d
el
is
p
r
ese
n
ted
f
o
r
p
o
wer
in
g
th
e
Natio
n
al
I
n
s
titu
te
o
f
T
ec
h
n
o
lo
g
y
M
an
ip
u
r
an
d
Sh
ija
Ho
s
p
itals
,
Ma
n
ip
u
r
.
T
h
ese
two
p
r
em
is
es
ar
e
lo
ca
ted
ad
jace
n
t
t
o
ea
ch
o
th
er
at
th
e
s
am
e
lo
ca
tio
n
in
Ma
n
ip
u
r
.
T
h
e
f
o
r
m
e
r
is
an
ed
u
ca
tio
n
al
in
s
titu
te
o
f
n
atio
n
al
im
p
o
r
tan
ce
an
d
th
e
latter
is
a
r
en
o
wn
ed
h
o
s
p
ital
o
f
th
e
s
tate.
T
h
e
s
elec
ted
s
ite
is
s
itu
ated
at
2
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°5
0
’
3
3
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2
0
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’
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latitu
d
e
an
d
9
3
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5
’
2
8
.
8
2
’
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E
lo
n
g
itu
d
e
[
2
5
]
.
T
h
e
p
o
wer
co
n
s
u
m
ed
b
y
th
e
i
n
s
titu
te
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th
e
h
o
s
p
ital
a
r
e
s
e
g
r
eg
ated
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d
lis
ted
in
th
e
T
ab
le
1
.
T
h
e
to
tal
l
o
ad
d
em
an
d
is
also
n
o
ted
.
T
ab
le
1
.
Deta
ils
o
f
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r
o
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ile
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l
.
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o
Lo
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d
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o
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s
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d
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d
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n
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k
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a
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d
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p
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r
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d
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h
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o
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To
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I
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d
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J
E
lec
E
n
g
&
C
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m
p
Sci
I
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N:
2502
-
4
7
5
2
Op
timiz
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Meitei
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1275
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1
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T
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ad
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Fig
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6
.
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5.
RE
SU
L
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D
D
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SCU
SS
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O
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T
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SA
p
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m
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m
r
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lts
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th
e
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in
al
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.
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f
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HOM
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p
tim
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[
2
5
]
,
[
2
6
]
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p
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3
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To
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s
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f
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if
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tech
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ca
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b
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en
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at
in
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ef
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to
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HOM
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2
7
]
,
[
2
8
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.
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p
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g
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at
ter
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ca
p
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.
6.
CO
NCLU
SI
O
N
An
attem
p
t
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m
a
d
e
t
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p
tim
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m
(
B
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.
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t
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s
h
o
wn
th
at
th
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b
att
er
y
in
v
o
lv
em
e
n
t
is
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
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2
5
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I
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d
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p
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24
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3
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with
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RE
F
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NC
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a
l
o
f
El
e
c
trica
l
a
n
d
Co
m
p
u
ter
En
g
i
n
e
e
rin
g
(
IJ
ECE
)
,
v
o
l.
1
0
.
n
o
.
6
,
p
p
.
6
2
1
4
-
6
2
2
4
,
De
c
.
2
0
2
0
,
d
o
i
:
1
0
.
1
1
5
9
1
/IJECE
.
V1
0
I6
.
P
P
6
2
1
4
-
6
2
2
4
.
[2
]
C.
Ch
o
m
p
o
o
-
I
n
wa
i,
W.
J.
Lee
,
a
n
d
P
.
F
u
a
n
g
f
o
o
,
“
S
y
ste
m
imp
a
c
t
stu
d
y
fo
r
t
h
e
in
terc
o
n
n
e
c
ti
o
n
o
f
win
d
g
e
n
e
ra
ti
o
n
a
n
d
u
ti
li
t
y
sy
ste
m
,
”
IEE
E
T
ra
n
s.
In
d
.
Ap
p
l.
,
v
o
l.
4
1
,
n
o
.
1
,
p
p
.
1
4
5
2
-
1
4
5
8
,
Ja
n
.
2
0
0
5
,
d
o
i:
1
0
.
1
1
0
9
/T
IA.
2
0
0
4
.
8
4
1
0
3
2
.
[3
]
C.
P
h
u
ra
il
a
tp
a
m
,
B
.
S
.
Ra
j
p
u
r
o
h
it
,
a
n
d
L.
Wan
g
,
“
P
lan
n
i
n
g
a
n
d
o
p
t
imiz
a
ti
o
n
o
f
a
u
to
n
o
m
o
u
s
DC
m
ic
ro
g
ri
d
f
o
r
r
u
ra
l
a
n
d
u
rb
a
n
a
p
p
l
ica
ti
o
n
in
In
d
ia
,
”
Ren
e
w.
S
u
sta
in
.
En
e
rg
y
Rev
.
,
v
o
l.
8
2
,
n
o
.
1
,
p
p
.
1
9
8
-
2
0
4
,
F
e
b
.
2
0
1
8
,
d
o
i:
1
0
.
1
0
1
6
/j
.
rse
r.
2
0
1
7
.
0
9
.
0
2
2
.
[4
]
E.
P
lan
a
s,
A.
G
il
-
de
-
M
u
ro
b
,
J.
An
d
re
u
,
I.
K
o
rtab
a
rria
,
a
n
d
I.
M
.
d
e
Ale
g
ría
,
“
G
e
n
e
ra
l
a
sp
e
c
ts,
h
iera
rc
h
ica
l
c
o
n
tro
ls
a
n
d
d
r
o
o
p
m
e
th
o
d
s
i
n
m
icro
g
r
i
d
s:
a
re
v
iew
,
”
Ren
e
w.
S
u
sta
in
En
e
rg
y
Rev
.
,
v
o
l.
1
7
,
p
p
.
1
4
7
-
1
5
9
,
Ja
n
.
2
0
1
3
,
d
o
i:
1
0
.
1
0
1
6
/j
.
rse
r.
2
0
1
2
.
0
9
.
0
3
2
.
[5
]
B.
F
a
ti
m
a
,
C.
M
a
m
a
,
a
n
d
B.
Be
n
a
issa
,
"
De
sig
n
m
e
th
o
d
o
l
o
g
y
o
f
s
m
a
rt
p
h
o
to
v
o
l
taic
p
lan
t,
"
I
n
t
e
r
n
a
t
i
o
n
a
l
J
o
u
r
n
a
l
o
f
E
l
e
c
t
r
ic
a
l
a
n
d
C
o
m
p
u
t
e
r
E
n
g
i
n
e
e
r
i
n
g
(
I
J
E
C
E
)
,
v
o
l.
1
1
,
n
o
.
6
,
p
p
.
4
7
1
8
-
4
7
3
0
,
Ju
n
.
2
0
2
1
,
d
o
i:
1
0
.
1
1
5
9
1
/
ij
e
c
e
.
v
1
1
i6
.
p
p
4
7
1
8
-
4
7
3
0
.
[6
]
A.
Wo
y
te,
V.
Va
n
,
R.
Be
lma
n
s
a
n
d
J.
Nijs,
“
Vo
lt
a
g
e
flu
c
t
u
a
ti
o
n
s
o
n
d
istri
b
u
ti
o
n
le
v
e
l
in
tr
o
d
u
c
e
d
b
y
p
h
o
t
o
v
o
lt
a
ic
sy
ste
m
s,”
IEE
E
T
ra
n
s.
E
n
e
rg
y
C
o
n
v
e
rs
.
,
v
o
l.
2
1
,
n
o
.
1
,
p
p
.
2
0
2
-
2
0
9
,
M
a
r.
2
0
0
6
,
d
o
i:
1
0
.
1
1
0
9
/T
EC
.
2
0
0
5
.
8
4
5
4
5
4
.
[7
]
L
.
O.
Ag
h
e
n
ta
a
n
d
M
.
T
.
Iq
b
a
l
,
“
De
sig
n
a
n
d
Dy
n
a
m
ic
M
o
d
e
ll
i
n
g
o
f
a
Hy
b
rid
P
o
we
r
S
y
ste
m
f
o
r
a
Ho
u
se
in
Nig
e
ria,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
Ph
o
to
e
n
e
rg
y
,
v
o
l.
2
0
1
9
,
p
p
.
1
-
1
3
,
Ju
l.
2
0
1
9
,
d
o
i
:
1
0
.
1
1
5
5
/2
0
1
9
/
6
5
0
1
7
8
5
.
[8
]
J.
B.
F
u
lze
le
a
n
d
S
u
b
ro
t
o
Du
tt
,
“
Op
ti
m
iu
m
P
lan
n
i
n
g
o
f
H
y
b
ri
d
Re
n
e
wa
b
le
En
e
rg
y
S
y
ste
m
Us
in
g
HO
M
ER
,
”
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
tri
c
a
l
a
n
d
Co
m
p
u
ter
E
n
g
i
n
e
e
rin
g
(IJ
ECE
)
,
v
o
l
.
2
,
n
o
.
1
,
p
p
.
6
8
-
7
4
,
Ja
n
.
2
0
1
2
,
d
o
i:
1
0
.
1
1
5
9
1
/
ij
e
c
e
.
v
2
i
1
.
1
5
7
.
[9
]
K.
Ro
u
t
a
n
d
J.
K.
S
a
h
u
,
“
Va
r
io
u
s
o
p
ti
m
iza
ti
o
n
tec
h
n
iq
u
e
s
o
f
h
y
b
rid
re
n
e
wa
b
le
e
n
e
r
g
y
sy
ste
m
s
fo
r
p
o
we
r
g
e
n
e
ra
ti
o
n
:
a
re
v
iew
,
”
In
t.
Res
.
J
.
En
g
.
T
e
c
h
n
o
l.
(IR
J
ET
)
,
v
o
l.
5
,
n
o
.
7
,
J
u
l.
2
0
1
8
.
[1
0
]
A.
M
o
h
a
m
e
d
,
Z.
Ab
d
e
lk
a
d
e
r,
a
n
d
B.
Ab
d
e
l
k
rim,
“
Op
ti
m
a
l
c
o
n
f
ig
u
r
a
ti
o
n
o
f
h
y
b
ri
d
P
V
-
g
e
n
e
ra
to
r(Die
se
l/
G
P
L)
fo
r
a
d
e
c
e
n
tralize
d
p
r
o
d
u
c
ti
o
n
o
f
e
lec
tri
c
it
y
i
n
Alg
e
ria,”
I
n
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
P
o
we
r
El
e
c
tro
n
ics
a
n
d
Dr
ive
S
y
ste
ms
(IJ
PE
DS
)
,
v
o
l.
1
1
,
n
o
.
4
,
p
p
.
2
0
3
8
-
2
0
4
5
,
De
c
.
2
0
2
0
,
d
o
i
:
1
0
.
1
1
5
9
1
/i
jp
e
d
s.
v
1
1
.
i
4
.
p
p
2
0
3
8
-
2
0
4
5
.
[1
1
]
D.
E.
Ba
b
a
tu
n
d
e
,
O.
M
.
Ba
b
a
t
u
n
d
e
,
M
.
U.
Eme
z
iri
n
wu
n
e
,
I
.
H.
De
n
wig
we
,
T.
E.
Ok
h
a
re
d
ia
,
a
n
d
O.
J.
Om
o
d
a
ra
,
"
F
e
a
sib
il
it
y
a
n
a
ly
sis
o
f
a
n
o
ff
-
g
ri
d
p
h
o
to
v
o
lt
a
ic
-
b
a
tt
e
ry
e
n
e
rg
y
sy
s
tem
fo
r
a
fa
rm
fa
c
il
it
y
,
"
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
i
n
e
e
rin
g
(IJ
ECE
)
,
v
o
l
.
1
0
,
n
o
.
3
,
p
p
.
2
8
7
4
-
2
8
8
3
,
De
c
.
2
0
1
9
,
d
o
i:
1
0
.
1
1
5
9
1
/
ij
e
c
e
.
v
1
0
i3
.
p
p
2
8
7
4
-
2
8
8
3
.
[1
2
]
C.
Ch
o
m
p
o
o
-
I
n
wa
i,
W.
J.
Lee
a
n
d
P
.
F
u
a
n
g
f
o
o
,
“
S
y
ste
m
imp
a
c
t
stu
d
y
fo
r
t
h
e
in
terc
o
n
n
e
c
ti
o
n
o
f
w
in
d
g
e
n
e
ra
ti
o
n
a
n
d
u
ti
li
t
y
sy
ste
m
,
”
IEE
E
T
ra
n
s.
In
d
.
Ap
p
l.
,
v
o
l.
4
1
,
n
o
.
1
,
p
p
.
1
4
5
2
-
1
4
5
8
,
Ja
n
.
2
0
0
5
,
d
o
i:
1
0
.
1
1
0
9
/T
IA.
2
0
0
4
.
8
4
1
0
3
2
.
[
1
3
]
A
.
W
o
y
t
e
,
V
.
V
a
n
,
R
.
B
e
l
m
a
n
s
,
a
n
d
J
.
N
i
j
s
,
“
V
o
l
t
a
g
e
f
l
u
c
t
u
a
t
i
o
n
s
o
n
d
i
s
t
r
i
b
u
t
i
o
n
l
e
v
e
l
i
n
t
r
o
d
u
c
e
d
b
y
p
h
o
t
o
v
o
l
t
a
i
c
s
y
s
t
e
m
s
,
”
I
E
E
E
T
r
a
n
s
.
E
n
e
r
g
y
C
o
n
v
e
r
s
.
,
v
o
l
.
2
1
,
n
o
.
1
,
p
p
.
2
0
2
-
2
0
9
,
M
a
r
.
2
0
0
6
,
d
o
i
:
1
0
.
1
1
0
9
/
T
E
C
.
2
0
0
5
.
8
4
5
4
5
4
.
[1
4
]
R.
S
riv
a
sta
v
a
a
n
d
V.
K.
G
iri
,
“
Op
ti
m
iza
ti
o
n
o
f
h
y
b
rid
re
n
e
wa
b
le
so
u
rc
e
s
u
sin
g
HO
M
ER
,
”
In
t.
J
.
Ren
e
w.
En
e
rg
y
Res
.
,
v
o
l.
6
,
n
o
.
1
,
Ja
n
.
2
0
1
6
.
[1
5
]
A.
M.
Y
a
s
i
n
a
n
d
M
.
F
.
A
l
s
a
y
e
d
,
"
F
u
z
z
y
lo
g
ic
p
o
we
r
m
a
n
a
g
e
m
e
n
t
fo
r
a
P
V/win
d
m
icro
g
ri
d
wit
h
b
a
c
k
u
p
a
n
d
st
o
ra
g
e
sy
ste
m
s,"
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
Co
m
p
u
ter
En
g
i
n
e
e
rin
g
(IJ
ECE
)
,
v
o
l.
1
1
,
n
o
.
4
,
p
p
.
2
8
7
6
-
2
8
8
8
,
Ja
n
.
2
0
2
1
,
d
o
i:
1
0
.
1
1
5
9
1
/
ij
e
c
e
.
v
1
1
i4
.
p
p
2
8
7
6
-
2
8
8
8
.
[1
6
]
R.
Ch
e
d
id
,
H.
A
k
ik
i
,
a
n
d
S
.
Ra
h
m
a
n
,
“
A
d
e
c
isio
n
su
p
p
o
r
t
tec
h
n
iq
u
e
fo
r
th
e
d
e
sig
n
o
f
h
y
b
rid
s
o
lar
-
win
d
p
o
we
r
sy
ste
m
,
”
IEE
E
T
ra
n
s.
E
n
e
rg
y
Co
n
v
e
rs
.
,
v
o
l
.
1
3
,
n
o
.
1
,
p
p
.
7
6
-
8
3
,
M
a
r.
1
9
9
8
.
[1
7
]
F
.
Ard
a
k
a
n
i,
G
.
Riah
y
,
a
n
d
M
.
Ab
e
d
i,
“
Op
ti
m
a
l
siz
in
g
o
f
a
g
r
id
-
c
o
n
n
e
c
ted
h
y
b
ri
d
sy
st
e
m
f
o
r
n
o
r
th
-
we
st
o
f
Ira
n
-
c
a
se
stu
d
y
,
”
i
n
Pro
c
.
I
EE
E
E
EE
I
C
,
p
p
.
2
9
-
3
2
.
J
u
n
.
2
0
1
0
,
d
o
i
:
1
0
.
1
1
0
9
/E
EE
IC.
2
0
1
0
.
5
4
9
0
0
0
6
.
[1
8
]
M
.
Re
y
a
su
d
i
n
Ba
sir
Kh
a
n
,
J.
P
a
su
p
u
leti,
J.
Al
-
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a
tt
a
h
a
n
d
M
.
Tah
m
a
se
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i,
"
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ti
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ted
P
V
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ste
m
fo
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u
s
m
icro
g
ri
d
,
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I
n
d
o
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sia
n
J
o
u
rn
a
l
o
f
El
e
c
trica
l
En
g
i
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rin
g
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n
d
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mp
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ter
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e
(IJ
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9
]
L
.
Xu
,
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.
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C
.
M
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o
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B
.
Zh
a
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n
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Y
.
Lu
o
,
“
An
Im
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v
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m
a
l
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M
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th
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Wi
n
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Ba
tt
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Hy
b
ri
d
P
o
we
r
S
y
ste
m
,
”
IEE
E
T
ra
n
s.
o
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u
sta
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l
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En
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rg
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l
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2
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5
0
9
.
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
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timiz
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tio
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s
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(
I
n
g
u
d
a
m
C
h
itr
a
s
en
Meitei
)
1277
[2
0
]
P
.
Civ
ici
o
g
l
u
,
“
Ba
c
k
trac
k
in
g
S
e
a
rc
h
Op
ti
m
iza
ti
o
n
Alg
o
rit
h
m
fo
r
n
u
m
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rica
l
p
ti
m
iza
ti
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n
p
ro
b
l
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m
s
,
”
Ap
p
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d
M
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mp
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[2
1
]
D.
M
e
n
n
it
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A.
P
i
n
n
a
re
ll
i
,
a
n
d
N.
S
o
rre
n
ti
n
o
,
“
A
m
e
th
o
d
to
i
m
p
ro
v
e
m
icro
g
rid
re
li
a
b
il
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y
b
y
o
p
ti
m
a
l
siz
in
g
P
V/win
d
p
lan
ts an
d
sto
ra
g
e
s
y
ste
m
s,”
in
Pro
c
.
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,
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9
/cp
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0
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1
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.
[2
2
]
R.
Ch
e
d
i
d
,
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Ak
i
k
i
a
n
d
S
.
Ra
h
m
a
n
,
“
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d
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isio
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p
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rt
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n
o
f
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rid
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l
a
r
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p
o
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ste
m
,
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ra
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rg
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rs
.
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.
[2
3
]
J.
M
a
n
we
ll
a
n
d
J.
M
c
G
o
wa
n
,
“
Lea
d
a
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b
a
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ry
sto
ra
g
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m
o
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fo
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b
r
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r
g
y
sy
ste
m
s,”
S
o
l
a
r
En
e
rg
y
,
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5
0
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9
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0
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-
2
.
[2
4
]
J.
F
.
M
a
n
we
ll
e
t
a
l.
,
“
HYB
RID
2
-
A
h
y
b
rid
sy
ste
m
simu
la
ti
o
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mo
d
e
l
t
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ma
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,
”
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p
.
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n
g
.
,
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.
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a
ss
.
,
Re
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le E
n
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rg
y
Re
se
a
rc
h
Lab
.
,
Ja
n
.
1
9
9
9
.
[2
5
]
I.
C.
M
e
it
e
i,
A.
K.
Ir
u
n
g
b
a
m
,
B
.
A.
S
h
imra
y
,
“
P
e
rfo
rm
a
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v
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f
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ri
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rg
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fo
r
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p
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tri
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it
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o
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n
in
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tu
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d
a
h
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sp
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tal
u
si
n
g
HO
M
ER,
”
In
ter
n
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ti
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l
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fer
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telli
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.
[2
6
]
I.
C.
M
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it
e
i
,
T.
B.
S
i
n
g
h
,
K.
De
n
i
sh
,
H.
H.
M
e
it
e
i
,
a
n
d
N.
A.
S
i
n
g
h
,
“
Op
ti
m
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m
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p
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lt
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sy
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d
ica
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in
stit
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M
ER
,
”
In
ter
n
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ti
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mm
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[2
7
]
I
.
C
.
M
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it
e
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a
n
d
R
.
P
u
d
u
r
,
“
An
a
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a
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d
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p
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m
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f
H
y
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ri
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Re
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En
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s:
A
Ca
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tu
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tan
,
M
a
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r,
”
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o
u
rn
a
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f
Ad
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Res
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.
[2
8
]
A.
G
h
e
iratm
a
n
d
,
R.
Eff
a
tn
e
jad
,
a
n
d
M
.
He
d
a
y
a
ti
,
“
Tec
h
n
ica
l
a
n
d
e
c
o
n
o
m
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l
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rid
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d
/
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v
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a
tt
e
ry
sy
ste
m
s
fo
r
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ff
-
g
rid
a
re
a
s
u
sin
g
HO
M
ER
so
ftwa
re
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Po
we
r
El
e
c
tro
n
ics
a
n
d
Dr
ive
S
y
ste
m
s
(IJ
PE
DS
)
,
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o
l.
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.
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,
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p
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-
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s.v
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.
B
I
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G
RAP
H
I
E
S O
F
AUTH
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RS
Ing
u
d
a
m
Chi
tr
a
se
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c
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p
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d
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in
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tri
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l
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g
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a
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tra
Un
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rsity
(
2
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)
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n
d
M
.
Tec
h
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n
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rsity
(
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)
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sta
rted
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is
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h
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g
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m
2
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.
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is
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rre
n
tl
y
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rk
in
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a
s
a
Lec
tu
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r
in
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d
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p
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g
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h
D.
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p
t
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o
f
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NIT
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n
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c
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ra
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sh
.
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re
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o
f
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tere
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s E
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tri
c
a
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a
c
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s a
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d
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n
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le E
n
e
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d
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(2
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h
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fr
o
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NERIS
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As
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r
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,
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o
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u
a
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ty
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e
s,
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icro
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p
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teg
ra
ti
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n
a
n
d
S
EIG
fo
r
ru
ra
l
a
re
a
s.
Evaluation Warning : The document was created with Spire.PDF for Python.