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[
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Sci,
Vo
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21
,
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2
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Feb
r
u
ar
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2
0
2
1
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3
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r
id
d
eter
m
in
e
s
th
e
h
o
u
r
l
y
o
p
er
atio
n
ti
m
etab
le
o
f
t
h
e
co
m
m
itted
DGs,
in
cl
u
d
i
n
g
co
n
v
e
n
tio
n
al
g
en
er
atin
g
u
n
i
ts
a
n
d
R
E
S,
to
s
ati
s
f
y
t
h
e
h
o
u
r
l
y
lo
ad
d
em
a
n
d
w
it
h
th
e
lo
w
e
s
t
o
p
er
atio
n
co
s
t
o
v
er
a
2
4
-
h
o
u
r
ti
m
e
s
p
an
[
1
7
]
.
T
o
co
n
s
id
er
th
e
u
n
ce
r
tain
t
y
o
f
R
E
S
in
p
o
w
er
s
y
s
te
m
p
r
o
b
le
m
s
,
s
to
ch
ast
ic
o
p
ti
m
izat
io
n
tec
h
n
i
q
u
es
ar
e
u
s
ed
;
s
u
ch
as
f
u
ll
s
to
c
h
asti
c
p
r
o
g
r
a
m
m
in
g
,
c
h
an
ce
-
co
n
s
tr
ai
n
ed
p
r
o
g
r
a
m
m
i
n
g
an
d
r
o
b
u
s
t
o
p
tim
izatio
n
[
1
8
]
.
T
h
e
tr
ad
itio
n
al,
an
d
w
id
el
y
u
s
ed
,
m
et
h
o
d
to
r
ep
r
esen
t
th
e
u
n
ce
r
tain
t
y
i
s
s
ce
n
ar
io
g
e
n
er
atio
n
in
f
u
ll
s
to
c
h
ast
ic
p
r
o
g
r
am
m
i
n
g
[
1
9
]
.
Ho
w
e
v
er
,
s
ce
n
ar
io
g
e
n
er
atio
n
tec
h
n
iq
u
e
s
ar
e
co
m
p
u
tatio
n
a
ll
y
i
n
e
f
f
icie
n
t [
1
8
]
.
I
n
th
is
p
ap
er
,
a
m
o
d
el
is
p
r
o
p
o
s
ed
to
d
is
p
atch
a
m
i
n
ig
r
id
th
at
co
n
s
is
t
s
o
f
s
m
all
co
n
v
e
n
tio
n
al
g
en
er
ato
r
s
a
n
d
a
lar
g
e
p
en
etr
a
tio
n
le
v
e
l
o
f
s
o
lar
P
V
en
er
g
y
s
o
u
r
ce
s
,
as
w
ell
as
a
r
es
id
en
tial
lo
ad
d
em
an
d
.
T
h
e
s
o
lar
ir
r
ad
ian
ce
o
f
t
h
e
s
o
lar
P
V
is
m
o
d
eled
as
a
r
an
d
o
m
v
a
r
iab
le
u
s
i
n
g
a
p
r
o
b
ab
ilit
y
d
en
s
it
y
f
u
n
ctio
n
(
P
DF)
ca
lled
B
eta
d
is
tr
ib
u
tio
n
to
r
e
p
r
esen
t
its
u
n
ce
r
tai
n
t
y
in
t
h
e
s
to
ch
asti
c
o
p
ti
m
izatio
n
ap
p
r
o
ac
h
.
T
h
e
r
esu
ltin
g
n
o
n
li
n
ea
r
s
to
ch
a
s
tic
s
c
h
ed
u
li
n
g
p
r
o
b
lem
is
ap
p
r
o
x
i
m
ated
in
t
o
a
lin
ea
r
eq
u
iv
alen
t
to
b
e
s
o
lv
ed
b
y
t
h
e
ef
f
icie
n
t
m
i
x
ed
in
teg
er
li
n
ea
r
p
r
o
g
r
a
m
m
i
n
g
(
MI
L
P
)
tech
n
iq
u
e.
T
h
e
latter
,
MI
L
P
,
is
w
id
el
y
ad
o
p
ted
b
y
t
h
e
u
ti
lit
y
in
d
u
s
tr
y
d
u
e
to
its
ac
cu
r
ac
y
i
n
ac
h
iev
i
n
g
o
p
ti
m
al
s
o
lu
tio
n
s
i
n
lar
g
e
-
s
ca
le
p
r
o
b
le
m
s
[
2
0
]
.
T
h
e
s
tr
u
ct
u
r
e
o
f
th
i
s
p
ap
er
is
as
f
o
llo
w
s
.
P
r
o
b
le
m
f
o
r
m
u
latio
n
is
o
u
tli
n
ed
i
n
Sectio
n
2
.
Sectio
n
3
d
esc
r
ib
es
th
e
n
u
m
er
ical
s
i
m
u
lat
io
n
s
i
n
d
etail.
C
o
n
clu
s
i
o
n
s
ar
e
p
r
esen
ted
in
Sect
io
n
4
.
2.
P
RO
B
L
E
M
F
O
R
M
UL
AT
I
O
N
Min
i
m
izi
n
g
th
e
to
tal
o
p
er
atio
n
co
s
t
is
th
e
m
ai
n
o
b
j
ec
tiv
e
o
f
th
e
p
r
o
p
o
s
ed
m
i
n
i
g
r
id
s
ch
ed
u
lin
g
ap
p
r
o
ac
h
,
tak
in
g
i
n
to
ac
co
u
n
t
th
e
tech
n
ical
a
n
d
o
p
er
atio
n
al
co
n
s
tr
ain
ts
o
f
co
n
v
e
n
tio
n
al
g
e
n
er
atio
n
as
w
ell
as
s
o
lar
en
er
g
y
p
e
n
et
r
atio
n
lev
el.
T
h
e
to
tal
o
p
er
atio
n
co
s
t
r
eq
u
i
r
ed
f
o
r
m
i
n
i
g
r
id
d
is
p
atch
co
n
s
is
ts
o
f
t
h
r
ee
p
ar
ts
:
f
u
e
l
co
s
t,
s
tar
tu
p
co
s
t,
an
d
s
h
u
td
o
w
n
co
s
t.
So
lar
en
er
g
y
’
s
o
p
er
atio
n
co
s
t
is
n
eg
li
g
ib
le,
an
d
is
m
o
d
eled
as
a
n
eg
at
iv
e
lo
ad
as d
escr
ib
ed
in
t
h
e
f
o
llo
w
i
n
g
.
2
.
1
.
O
bje
c
t
iv
e
f
un
ct
io
n
T
h
e
g
en
er
ic
o
b
j
ec
tiv
e
f
u
n
ctio
n
is
g
i
v
en
:
∑
(
1
)
w
h
er
e
is
th
e
f
u
el
co
s
t
f
u
n
ctio
n
o
f
co
n
v
en
tio
n
al
g
en
er
ati
n
g
u
n
i
ts
.
is
th
e
s
tar
t
u
p
co
s
t
f
u
n
c
tio
n
w
h
ic
h
is
ex
p
o
n
e
n
tiall
y
i
n
cr
ea
s
in
g
,
an
d
is
th
e
s
h
u
td
o
w
n
co
s
t
f
u
n
ct
io
n
.
T
h
e
n
o
n
li
n
ea
r
ities
ass
o
ciate
d
w
it
h
th
e
q
u
ad
r
atic
f
u
el
co
s
t
f
u
n
ct
io
n
a
n
d
t
h
e
e
x
p
o
n
e
n
tial
i
n
cr
ea
s
i
n
g
f
u
n
ctio
n
o
f
th
e
s
tar
t
u
p
co
s
t
in
cr
ea
s
e
t
h
e
co
m
p
u
tatio
n
al
b
u
r
d
en
o
f
t
h
e
d
is
p
atch
p
r
o
b
le
m
.
T
h
er
ef
o
r
e,
all
n
o
n
lin
ea
r
it
ies
ar
e
ap
p
r
o
x
im
ated
i
n
to
a
lin
ea
r
f
o
r
m
an
d
f
o
r
m
u
lated
to
f
it
th
e
MI
L
P
s
tr
u
ctu
r
e,
f
o
llo
w
i
n
g
th
e
m
o
d
el
p
r
esen
ted
in
[
2
1
]
.
T
h
e
f
u
el
co
s
t
eq
u
at
io
n
is
r
ep
r
esen
ted
as:
(
2
)
w
h
er
e
ar
e
th
e
f
u
el
co
s
t
co
n
s
t
an
ts
an
d
is
th
e
o
u
tp
u
t
p
o
w
er
o
f
u
n
i
t
i
.
T
h
e
f
u
el
co
s
t
f
u
n
c
ti
o
n
is
q
u
ad
r
atic.
I
t is ap
p
r
o
x
im
ated
i
n
to
a
lin
ea
r
eq
u
i
v
ale
n
t a
s
[
2
1
]
:
∑
(
3
)
w
h
er
e
,
is
th
e
s
tat
u
s
o
f
t
h
e
g
e
n
er
atin
g
u
n
it
i
at
t
i
m
e
t
,
is
th
e
s
lo
p
e
o
f
th
e
s
tep
w
is
e
k
an
d
u
n
it
i
a
n
d
is
t
h
e
o
u
tp
u
t p
o
w
er
o
f
u
n
it
i
at
ti
m
e
t
an
d
b
lo
ck
n
u
m
b
er
k
.
(
4
)
(
5
)
∑
(
6
)
(
7
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esia
n
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4752
On
th
e
d
is
p
a
tch
o
f m
in
ig
r
id
s
w
ith
la
r
g
e
p
en
etra
tio
n
leve
ls
o
f v
a
r
ia
b
le
r
en
ewa
b
le
en
erg
y
(
A
n
a
n
A
.
Dw
ee
ka
t)
675
w
h
er
e
is
th
e
o
u
tp
u
t
p
o
w
er
at
th
e
s
tar
ti
n
g
p
o
in
t
o
f
b
lo
ck
k
,
/
ar
e
th
e
m
a
x
i
m
u
m
a
n
d
m
i
n
i
m
u
m
o
u
tp
u
t p
o
w
er
o
f
u
n
it
i
r
esp
ec
ti
v
el
y
a
n
d
n
is
th
e
n
u
m
b
er
o
f
b
l
o
ck
s
.
T
h
e
s
tair
w
i
s
e
ap
p
r
o
x
i
m
atio
n
o
f
th
e
s
tar
tu
p
co
s
t
f
u
n
ctio
n
is
:
[
∑
(
)
]
(
8
)
w
h
er
e
is
u
n
it
i
s
tar
tu
p
co
s
t a
n
d
is
th
e
u
n
it st
a
tu
s
at
ti
m
e
t
.
T
h
e
s
h
u
td
o
w
n
co
s
t e
q
u
atio
n
i
s
ex
p
r
ess
ed
as:
(
)
(
9
)
w
h
er
e
is
t
h
e
s
h
u
td
o
w
n
co
s
t o
f
th
e
g
e
n
er
ati
n
g
u
n
it
i
.
2
.
2
.
O
pera
t
io
na
l a
nd
t
ec
hn
ica
l c
o
ns
t
ra
ints
C
o
n
v
en
t
io
n
al
g
en
er
atio
n
h
a
v
e
tech
n
ical
an
d
o
p
er
atio
n
al
co
n
s
tr
ain
t
s
.
T
h
ese
ar
e
d
escr
ib
ed
a
s
f
o
llo
w
s
:
R
a
mp
u
p
/d
o
w
n
c
o
n
s
tr
a
in
t
:
th
e
ca
p
ab
ilit
y
o
f
a
g
en
er
ati
n
g
u
n
i
t
to
in
cr
ea
s
e
its
g
en
er
atio
n
,
w
i
th
o
u
t
ex
ce
ed
i
n
g
a
m
ax
i
m
u
m
li
m
it
o
f
in
cr
e
m
e
n
t,
is
ca
lled
th
e
r
a
m
p
u
p
.
Si
m
ila
r
l
y
,
th
e
ac
tio
n
o
f
a
u
n
i
t
to
d
ec
r
ea
s
e
its
g
e
n
er
ated
o
u
tp
u
t p
o
w
er
to
a
lo
w
er
v
alu
e
is
ca
lled
r
a
m
p
d
o
w
n
.
Ma
t
h
e
m
atica
ll
y
,
r
a
m
p
i
n
g
eq
u
atio
n
s
ca
n
b
e
ex
p
r
ess
ed
as:
(
)
(
1
0
)
(
1
1
)
(
)
(
1
2
)
w
h
er
e
is
t
h
e
o
u
tp
u
t
p
o
w
er
o
f
th
e
g
en
er
ati
n
g
u
n
i
t
i
a
t
t
ime
t
,
an
d
ar
e
th
e
r
a
m
p
i
n
g
u
p
/d
o
w
n
o
f
th
e
g
en
er
ati
n
g
u
n
it
s
r
esp
ec
tiv
el
y
.
an
d
ar
e
th
e
s
tar
tu
p
r
a
m
p
li
m
it
a
n
d
th
e
s
h
u
td
o
w
n
r
a
m
p
li
m
it
o
f
u
n
it
i
r
esp
ec
tiv
el
y
.
Min
imu
m
u
p
/d
o
w
n
time
co
n
s
tr
a
in
t
:
w
h
e
n
a
co
n
v
e
n
tio
n
al
g
en
er
ati
n
g
u
n
it i
s
t
u
r
n
ed
o
f
f
a
f
ter
b
ein
g
co
m
m
i
tted
,
it
h
as
a
m
in
i
m
u
m
ti
m
e
to
s
ta
y
o
f
f
b
ef
o
r
e
tu
r
n
i
n
g
it
o
n
ag
ai
n
.
T
h
is
ti
m
e
is
c
alled
th
e
m
in
i
m
u
m
d
o
w
n
ti
m
e.
I
f
th
e
u
n
it
w
as
o
f
f
an
d
tu
r
n
ed
o
n
,
it
h
a
s
a
m
i
n
i
m
u
m
o
n
ti
m
e,
ca
lled
u
p
ti
m
e,
b
ef
o
r
e
d
ec
o
m
m
it
tin
g
it
ag
ai
n
.
T
h
e
eq
u
atio
n
s
ar
e
m
o
d
eled
w
i
th
a
s
i
n
g
le
b
in
ar
y
v
ar
iab
le
to
e
n
h
a
n
ce
t
h
e
m
o
d
el
co
m
p
u
tatio
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(
1
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∑
(
1
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1
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1
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2
2
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I
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I
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t
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f
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T
h
is
ca
n
b
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o
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eled
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(
1
8
)
w
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th
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lo
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em
an
d
at
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m
i
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th
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V
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4
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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d
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J
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N:
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On
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u
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u
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ated
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atch
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u
r
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4
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atch
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t
s
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o
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u
r
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4
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atch
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ra
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h
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i
s
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e
.
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t
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er
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n
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1
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d
g
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v
e
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ec
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Fig
u
r
e
5
,
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h
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h
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r
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t
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er
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ad
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d
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as
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ela
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e
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m
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e
n
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g
3
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y
7
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o
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r
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n
Fig
u
r
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5
,
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n
Fig
u
r
e
2
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d
Fi
g
u
r
e
3
.
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th
e
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e
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o
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er
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s
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ts
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h
e
d
o
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n
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ar
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ad
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u
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e
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tu
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e
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h
r
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ato
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g
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en
er
atio
n
w
i
ll
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ee
t
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h
e
l
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ad
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em
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o
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i
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ig
r
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h
is
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e
s
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ter
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r
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ain
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o
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ic
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atch
o
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e
m
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g
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s
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e
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s
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u
r
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5
.
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li
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% P
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el
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esia
n
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4752
On
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d
is
p
a
tch
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f m
in
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679
Sin
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t
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g
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r
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al
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r
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el
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u
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o
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RE
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NC
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S
[1
]
K.
Ra
h
b
a
r,
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.
C.
Ch
a
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a
n
d
R.
Z
h
a
n
g
,
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e
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o
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1
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[2
]
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.
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.
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n
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.
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o
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a
n
d
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.
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R
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h
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m
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t
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R
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a
b
l
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E
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e
r
g
y
S
o
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s
:
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A
p
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t
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t
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,
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v
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5
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.
[3
]
X
.
X
u
e
t
a
l.
,
“
M
a
x
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u
m
L
o
a
d
a
b
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f
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n
d
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M
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rid
s
w
it
h
Re
n
e
wa
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le
En
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rg
y
Ge
n
e
ra
ti
o
n
,
”
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E
T
ra
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ti
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S
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.
[4
]
S
.
R.
S
in
se
l,
R.
L
.
Rie
m
k
e
,
a
n
d
V
.
H.
Ho
ffm
a
n
n
,
“
Ch
a
ll
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e
s
a
n
d
S
o
lu
ti
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T
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ies
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In
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ra
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o
f
Va
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w
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[5
]
P
.
A
.
Os
terg
a
a
rd
,
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ic,
Y.
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ro
ll
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h
i,
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M
ik
u
lcic
,
a
n
d
S
.
Ka
lo
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iro
u
,
“
S
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sta
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a
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le
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v
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t
Us
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,
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1
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p
p
.
2
4
3
0
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4
3
7
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2
0
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0
.
[6
]
J.
O.
P
e
ti
n
ri
n
a
n
d
M
.
S
h
a
a
b
a
n
,
“
Re
n
e
wa
b
le
En
e
rg
y
f
o
r
Co
n
ti
n
u
o
u
s
En
e
rg
y
S
u
sta
in
a
b
il
it
y
in
M
a
la
y
s
ia,”
Ren
e
wa
b
le
a
n
d
S
u
sta
i
n
a
b
le E
n
e
rg
y
Rev
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,
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,
p
p
.
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-
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8
1
,
2
0
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5
.
[7
]
A
.
Za
k
a
ria,
F
.
B.
Ism
a
il
,
M
.
S
.
H.
L
ip
u
,
a
n
d
M
.
A
.
Ha
n
n
a
n
,
“
Un
c
e
rtain
ty
M
o
d
e
ls
f
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S
to
c
h
a
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Op
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m
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Re
n
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wa
b
le E
n
e
rg
y
A
p
p
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c
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ti
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n
s,”
Ren
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wa
b
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En
e
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y
,
v
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.
1
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p
p
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5
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[8
]
T
.
A
.
O.
L
i,
W
.
Hu
,
S
.
M
e
m
b
e
r,
X
.
Xu
,
a
n
d
S
.
M
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m
b
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r,
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Op
ti
m
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Op
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ra
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f
Hy
b
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m
I
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ted
w
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,
P
V
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d
P
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S
Co
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sid
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g
G
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,
”
IEE
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Acc
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[9
]
S
.
R.
S
a
lk
u
ti
,
“
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m
a
l
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ti
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M
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m
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icro
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ri
d
s
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r
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ty
,
”
In
d
o
n
e
sia
n
J
o
u
rn
a
l
o
f
El
e
c
trica
l
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g
a
n
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c
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e
,
v
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1
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1
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0
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H.
D.
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a
n
g
,
“
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y
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ro
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lec
tri
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Da
m
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rsp
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c
ti
v
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,
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l
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l.
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p
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0
2
0
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1
]
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.
D.
F
.
M
o
sc
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rd
in
i
Jú
n
io
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a
n
d
R.
Rü
th
e
r,
“
T
h
e
In
f
lu
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lar
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n
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ra
to
rs,”
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rg
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3
]
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lt
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n
a
les
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lze
is,
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.
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e
o
rg
e
,
a
n
d
T
.
Za
m
a
n
,
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d
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m
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rv
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ro
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a
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p
e
rim
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t
in
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ra
w
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k
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4
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1
9
.
[1
5
]
Y.
K.
W
u
,
G
.
T
.
Ye
,
a
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d
M
.
S
h
a
a
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n
,
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A
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teg
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p
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se
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tu
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in
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iw
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n
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6
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.
R.
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ra
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ro
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lg
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m
,
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d
o
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0
.
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7
]
A
.
J.
W
o
o
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,
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F
.
W
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rg
,
a
n
d
G
.
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h
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lé,
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ra
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.
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.
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8
]
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.
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.
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.
Ka
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ra
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ria
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:
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p
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li
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ti
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n
s
,
a
n
d
F
u
t
u
re
T
re
n
d
s,”
IET
Ge
n
e
ra
ti
o
n
,
T
ra
n
sm
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a
n
d
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.
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2
0
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Evaluation Warning : The document was created with Spire.PDF for Python.
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1
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.
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,
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ro
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lem
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[2
2
]
G
.
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.
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r,
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l,
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ro
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3
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.
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4
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A
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tratio
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5
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R.
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Ro
se
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th
a
l,
“
G
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Us
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.
Evaluation Warning : The document was created with Spire.PDF for Python.