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K
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Dis
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en
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Ph
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to
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ltaic
Plu
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-
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R
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W
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FO
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A
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:
A
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Ma
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Dep
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Osma
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1.
I
NT
RO
D
UCT
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N
T
h
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d
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elec
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d
is
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Acc
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[
1
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,
tr
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s
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s
s
till
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o
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th
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y
in
d
u
s
tr
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.
So
lar
p
h
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to
v
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ltaic
(
PV)
u
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its
an
d
win
d
tu
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b
in
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m
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m
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tech
n
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[
2]
th
at
m
a
y
g
en
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ate
elec
tr
icity
f
r
o
m
lo
w
-
ca
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b
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.
Am
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last
1
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s
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tp
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all
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s
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A
n
o
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2
4
%
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in
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2
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liter
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e
d
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m
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th
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p
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f
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allo
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(
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DGs
)
with
in
th
e
d
is
tr
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u
tio
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s
y
s
te
m
[
3
]
,
in
clu
d
in
g
m
in
im
izin
g
o
f
en
er
g
y
lo
s
s
[
4
]
,
en
h
an
ce
m
e
n
t
o
f
th
e
v
o
ltag
e
p
r
o
f
ile
[
5
]
,
m
ax
im
izatio
n
o
f
l
o
ad
ab
ilit
y
[
6
]
,
an
d
a
u
g
m
en
ta
tio
n
o
f
th
e
v
o
ltag
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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E
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I
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N:
2252
-
8
7
9
2
Op
tima
l a
llo
ca
tio
n
o
f P
V
u
n
its
u
s
in
g
mu
ltio
b
jective
meta
h
eu
r
is
tic
o
p
timi
z
a
tio
n
a
p
p
r
o
a
c
h
…
(
A
.
Ma
n
ju
la
)
283
s
tab
ilit
y
lim
it
[
7
]
.
Ho
wev
er
,
th
e
o
p
tim
al
allo
ca
tio
n
o
f
D
Gs
p
r
esen
ts
a
lar
g
e
-
s
ca
le,
n
o
n
lin
ea
r
,
an
d
m
u
lti
-
o
b
jectiv
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p
tim
izatio
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p
r
o
b
le
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,
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f
ten
p
o
s
in
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s
ig
n
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ican
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c
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allen
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in
f
in
d
i
n
g
n
ea
r
-
o
p
t
im
al
s
o
lu
tio
n
s
[
8
]
.
C
o
n
s
eq
u
en
tly
,
n
at
u
r
e
-
in
s
p
ir
e
d
m
etah
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r
is
tic
alg
o
r
ith
m
s
h
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ain
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p
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m
in
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ce
as
ef
f
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ap
p
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o
ac
h
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f
o
r
ad
d
r
ess
in
g
th
is
in
tr
icate
o
p
ti
m
izatio
n
p
r
o
b
lem
[
9]
.
E
lectr
i
c
v
eh
icles
(
E
Vs)
ar
e
b
ec
o
m
in
g
m
o
r
e
c
o
m
m
o
n
an
d
ar
e
ex
p
ec
ted
t
o
p
lay
a
b
ig
p
ar
t
in
r
ed
u
ci
n
g
ca
r
b
o
n
em
is
s
io
n
s
f
r
o
m
r
o
ad
tr
av
el,
in
ad
d
i
tio
n
to
PV
s
y
s
tem
in
teg
r
atio
n
[
1
0]
.
No
n
et
h
eless
,
th
e
in
clu
s
io
n
o
f
p
lu
g
-
i
n
elec
t
r
ic
v
eh
icle
(
PEV
)
c
h
ar
g
i
n
g
lo
ad
s
r
em
ain
s
lar
g
ely
u
n
ad
d
r
ess
ed
in
th
e
liter
atu
r
e
c
o
n
ce
r
n
in
g
DG
allo
ca
tio
n
[
1
1
]
.
Var
io
u
s
s
tu
d
ies
h
av
e
in
co
r
p
o
r
ated
d
if
f
er
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t
PEV
ch
ar
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in
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p
r
o
f
iles
to
ev
alu
ate
t
h
e
im
p
ac
t o
f
PEV
lo
ad
s
[
1
2
]
.
I
n
[
1
3
]
,
th
e
a
p
p
licatio
n
o
f
a
n
o
v
el
lig
h
tn
in
g
s
ea
r
c
h
ca
lcu
latio
n
is
p
r
o
p
o
s
ed
to
ad
d
r
ess
th
e
DG
ass
ig
n
m
en
t
is
s
u
e.
Nev
er
th
eless
,
th
e
s
tu
d
y
[
1
4
]
o
v
er
lo
o
k
s
a
cr
u
cial
o
b
jectiv
e,
n
a
m
ely
,
t
h
e
v
o
ltag
e
s
tab
ilit
y
in
d
ex
(
VSI
)
,
d
u
r
in
g
DG
allo
ca
tio
n
a
n
d
co
n
f
i
n
es
its
in
v
esti
g
atio
n
to
d
is
p
atch
ab
le
DGs
ex
clu
s
iv
el
y
.
I
n
co
n
tr
ast,
San
k
ar
an
d
C
h
atter
jee
[
1
5
]
d
eter
m
in
e
t
h
e
p
lace
m
en
t
an
d
d
im
en
s
io
n
s
o
f
DGs b
y
u
s
e
o
f
t
h
e
g
o
r
illa tr
o
o
p
s
o
p
tim
izatio
n
tech
n
iq
u
e.
T
h
e
liter
atu
r
e
r
e
v
iew
u
n
d
er
s
co
r
es
th
e
n
ec
ess
ity
o
f
co
n
s
i
d
er
in
g
p
lu
g
-
i
n
elec
tr
ic
v
e
h
icles
(
PEVs
)
ch
ar
g
in
g
d
em
an
d
wh
en
allo
c
atin
g
PV
u
n
its
with
in
th
e
co
n
tex
t
o
f
co
n
tem
p
o
r
ar
y
r
esear
ch
.
I
n
th
is
v
ein
,
we
em
p
lo
y
th
e
weig
h
ted
m
u
ltio
b
j
ec
tiv
e
elec
tr
ic
ee
l
f
o
r
ag
in
g
o
p
t
im
izatio
n
(
E
E
FO)
alg
o
r
ith
m
t
o
s
o
lv
e
th
e
PV
u
n
it
allo
ca
tio
n
p
r
o
b
lem
.
T
h
e
E
E
F
O
alg
o
r
ith
m
as
d
etailed
b
y
[
1
6
]
,
e
m
u
lates
th
e
f
o
r
a
g
in
g
b
e
h
av
io
r
o
f
elec
tr
ic
ee
ls
an
d
h
as
b
ee
n
r
ig
o
r
o
u
s
ly
test
ed
an
d
co
m
p
ar
ed
with
v
a
r
io
u
s
r
e
n
o
wn
ed
alg
o
r
ith
m
s
.
T
h
is
s
tu
d
y
co
n
tr
ib
u
tes
to
th
e
ex
is
tin
g
s
tate
-
of
-
th
e
-
ar
t in
th
e
f
o
llo
win
g
asp
ec
ts
:
-
I
n
co
r
p
o
r
atin
g
PEVs
ch
ar
g
i
n
g
d
em
an
d
in
t
h
e
allo
ca
tio
n
o
f
PV
u
n
its
.
C
o
n
s
id
er
in
g
th
e
s
to
ch
asti
c
m
o
d
e
l
in
g
o
f
th
e
u
n
ce
r
tain
n
atu
r
e
o
f
PV
g
en
er
atio
n
.
-
C
o
m
p
r
eh
en
s
iv
e
ass
ess
m
en
t
o
f
PEVs
d
em
an
d
c
o
m
p
r
is
in
g
o
f
f
-
p
ea
k
c
h
ar
g
in
g
s
ce
n
ar
i
o
(
OPC
S
)
,
p
ea
k
ch
ar
g
in
g
s
ce
n
ar
io
(
PC
S
)
,
an
d
s
to
ch
asti
c
ch
ar
g
in
g
s
ce
n
ar
i
o
(
SC
S
)
s
ce
n
ar
io
s
o
n
th
e
d
is
tr
i
b
u
tio
n
n
etwo
r
k
.
Dis
tr
ib
u
tin
g
PV u
n
its
wh
ile
k
e
ep
in
g
in
m
in
d
a
n
u
m
b
e
r
o
f
im
p
o
r
tan
t o
b
jectiv
es su
ch
as p
o
wer
lo
s
s
,
v
o
ltag
e
d
ev
iatio
n
,
a
n
d
s
tab
ilit
y
in
d
e
x
.
-
I
n
tr
o
d
u
cin
g
a
n
o
v
el
ap
p
lica
tio
n
o
f
t
h
e
weig
h
ted
m
u
lti
o
b
jectiv
e
elec
tr
ic
ee
l
f
o
r
ag
i
n
g
o
p
tim
izatio
n
(
W
MO
E
E
FO
)
alg
o
r
ith
m
t
o
a
d
d
r
ess
th
e
c
o
m
p
lex
PV
allo
ca
ti
o
n
p
r
o
b
lem
a
n
d
co
m
p
a
r
in
g
W
MO
E
E
FO
with
th
e
weig
h
ted
m
u
ltio
b
jectiv
e
g
r
ey
wo
lf
o
p
tim
izatio
n
(
W
MO
GW
O
)
[
1
7
]
an
d
weig
h
te
d
m
u
ltio
b
jectiv
e
d
if
f
er
en
tial e
v
o
lu
tio
n
ar
y
(
W
MO
DE
)
[
1
8
]
.
-
Simu
latin
g
n
u
m
er
o
u
s
s
tu
d
y
s
ce
n
ar
io
s
to
ass
es
s
th
e
im
p
ac
t
o
f
th
e
n
u
m
b
er
o
f
PV
u
n
its
in
s
talled
,
an
d
co
n
s
id
er
in
g
test
ca
s
es
to
q
u
an
t
itativ
ely
ev
alu
ate
th
e
o
b
jectiv
e
s
in
ea
ch
s
ce
n
ar
io
.
T
h
e
f
o
llo
win
g
is
a
n
o
v
er
v
iew
o
f
th
e
p
ap
er
:
i)
S
ec
tio
n
2
d
e
s
cr
ib
es
th
e
PV
m
o
d
elin
g
;
ii)
T
h
e
m
u
ltio
b
jectiv
e
p
r
o
b
lem
f
o
r
m
u
latio
n
is
m
ad
e
in
s
ec
tio
n
3
;
iii)
I
n
s
ec
tio
n
4
,
th
e
E
E
FO
alg
o
r
ith
m
is
d
escr
ib
ed
in
g
r
ea
t
len
g
th
;
iv
)
Sectio
n
5
d
elv
es th
e
r
esu
lts
an
d
d
is
cu
s
s
io
n
s
; a
n
d
v
)
I
n
s
ec
tio
n
6
th
e
f
in
al
co
n
cl
u
s
io
n
is
s
u
m
m
ar
ized
.
2.
SO
L
AR
P
V
UNC
E
R
T
AI
NT
Y
M
O
DE
L
L
I
NG
A
b
eta
p
r
o
b
ab
ilit
y
d
en
s
ity
f
u
n
ctio
n
(
PDF
)
was
u
ti
lized
to
d
ep
ict
th
e
ar
b
itra
r
y
b
eh
a
v
in
g
o
f
s
u
n
-
b
ased
illu
m
in
atio
n
[
1
9
]
.
W
ith
in
a
d
e
s
ig
n
ated
tim
e
f
r
am
e
t
,
th
e
b
et
a
PDF
(
)
s
u
p
p
o
r
ted
b
y
h
is
to
r
ica
l
d
ata
u
s
ed
f
o
r
ass
es
s
in
g
th
e
p
r
o
b
ab
ilit
y
o
f
s
o
lar
ir
r
ad
iatio
n
is
ex
p
r
ess
ed
as
(
1
)
[
2
0
]
.
(
)
=
{
(
+
)
(
)
(
)
(
−
1
)
,
0
≤
≤
1
,
≥
0
,
≥
0
0
,
ℎ
(
1
)
W
h
er
e
s
ig
n
if
ies
th
e
s
o
lar
ir
r
ad
ian
ce
,
an
d
d
ef
in
e
th
e
p
ar
a
m
eter
s
th
at
d
elin
ea
te
th
e
co
n
f
ig
u
r
atio
n
o
f
th
e
PDF.
Po
ten
tial v
alu
es o
f
th
e
s
o
lar
ir
r
ad
ian
ce
s
tate
(
z)
at
an
y
g
iv
en
h
o
u
r
m
ay
b
e
ex
p
r
ess
ed
as
(
2
)
[
2
1
]
.
(
)
=
∫
(
)
.
2
1
(
2
)
PV m
o
d
u
le
o
u
t
p
u
t p
o
wer
m
ay
b
e
ex
p
r
ess
ed
as
(
3
)
.
0
(
)
=
∗
∗
∗
(
3
)
W
h
er
e
is
th
e
f
ill
f
ac
to
r
o
f
PV
m
o
d
u
le
,
is
n
o
o
f
m
o
d
u
les
,
is
th
e
v
o
ltag
e
o
f
t
h
e
PV
m
o
d
u
le
,
an
d
is
th
e
cu
r
r
en
t
o
f
t
h
e
PV
m
o
d
u
le.
Un
d
er
v
ar
y
in
g
s
o
lar
ir
r
ad
ian
ce
c
o
n
d
itio
n
s
,
t
h
e
s
p
ec
if
ic
p
er
f
o
r
m
an
ce
ch
ar
ac
ter
is
tics
o
f
PV p
an
els o
u
tp
u
t p
o
wer
ar
e
ca
lcu
lated
as
(
4
)
[
2
2
]
.
(
)
=
(
)
∗
0
(
)
(
4
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
4
,
No
.
2
,
J
u
n
e
20
2
5
:
28
2
-
29
0
284
3.
M
UL
T
I
O
B
J
E
C
T
I
VE
F
UNC
T
I
O
N
F
O
RM
UL
A
T
I
O
N
I
n
th
is
i
n
v
esti
g
atio
n
,
th
r
ee
p
i
v
o
tal
b
o
u
n
d
ar
ies
o
f
th
e
d
is
tr
i
b
u
tio
n
s
y
s
tem
h
av
e
b
ee
n
m
e
ticu
lo
u
s
ly
ex
am
in
ed
to
f
o
r
m
u
late
th
e
o
b
jectiv
e
f
u
n
ctio
n
.
T
h
ese
p
ar
a
m
e
ter
s
en
co
m
p
ass
en
er
g
y
lo
s
s
(
)
,
to
tal
v
o
ltag
e
d
ev
iatio
n
(
T
VD
)
,
an
d
VSI
.
T
h
e
o
b
jectiv
e
f
u
n
ctio
n
(
OF
)
is
ca
lcu
lated
as
(5
)
[
1
5
]
.
=
1
∗
(
1
)
(
1
)
ℎ
+
2
∗
(
2
)
(
2
)
ℎ
+
3
∗
1
(
3
)
(
3
)
ℎ
(
5
)
W
h
er
e
1
,
2
,
an
d
3
d
en
o
te
th
e
p
r
ef
er
en
ce
weig
h
ts
g
iv
en
to
th
e
o
b
jectiv
es f
o
llo
win
g
∑
3
=
1
=
1
an
d
f
o
r
a
g
iv
en
o
b
jectiv
e
is
d
ec
id
ed
b
ased
o
n
th
e
p
r
ef
er
e
n
ce
g
iv
e
n
to
th
at
o
b
jectiv
e
a
n
d
∈
[
0
,
1
]
.
(
)
a
n
d
(
)
ℎ
d
en
o
te
th
e
v
al
u
e
o
f
th
e
p
ar
a
m
eter
b
ef
o
r
e
a
n
d
af
te
r
th
e
i
n
s
tallatio
n
o
f
th
e
DG.
Her
e
is
th
e
o
v
er
all
o
b
jectiv
e
f
u
n
ctio
n
to
b
e
m
in
im
ized
.
I
n
th
is
wo
r
k
,
1
,
2
,
an
d
3
ar
e
ass
ig
n
ed
t
o
0
.
4
,
0
.
3
,
an
d
0
.
3
,
r
esp
ec
tiv
ely
.
T
h
e
in
d
iv
id
u
al
o
b
jectiv
es a
r
e
ca
lcu
lated
as g
iv
en
in
(
6
)
-
(
9
)
.
1
=
=
∑
∑
,
2
−
1
=
1
24
=
1
(
6
)
2
=
=
∑
∑
(
|
1
−
,
|
)
2
=
1
24
=
1
(
7
)
3
=
=
∑
min
(
,
)
=
2
…
…
24
=
1
(
8
)
,
=
|
,
|
4
−
4
[
,
−
,
]
2
−
4
[
,
+
,
]
|
,
|
2
(
9
)
W
h
er
e
,
,
,
an
d
r
esp
ec
tiv
ely
in
d
icate
th
e
th
b
r
a
n
ch
c
u
r
r
e
n
t,
r
esis
tan
ce
o
f
th
e
b
r
an
c
h
,
an
d
t
h
e
to
tal
b
u
s
es
in
th
e
n
etwo
r
k
.
Fo
r
a
g
iv
en
b
u
s
,
,
,
,
,
,
,
,
a
n
d
r
ep
r
esen
t
th
e
b
u
s
v
o
ltag
e,
in
jecte
d
r
ea
l
p
o
wer
,
th
e
r
ea
cta
n
ce
o
f
th
e
lin
e
b
etwe
en
m
an
d
n
b
u
s
es,
th
e
i
n
jecte
d
r
ea
cti
v
e
p
o
wer
in
jecte
d
,
an
d
th
e
r
esis
tan
ce
o
f
th
e
lin
e
b
etwe
en
m
an
d
n
b
u
s
es.
T
h
e
o
b
jectiv
e
f
u
n
ctio
n
f
r
am
e
d
in
(
5
)
is
b
o
u
n
d
to
th
e
b
elo
w
co
n
s
tr
ain
ts
:
|
|
≤
|
,
|
≤
|
|
(
1
0
)
,
+
,
=
,
+
,
+
,
(
1
1
)
,
≤
≤
,
(
1
2
)
W
h
er
e
an
d
r
esp
ec
tiv
ely
d
ef
in
e
th
e
m
in
im
u
m
a
n
d
m
a
x
im
u
m
v
alu
es
o
f
th
e
b
u
s
v
o
ltag
e
.
,
,
,
,
,
,
,
,
an
d
,
r
esp
ec
tiv
ely
d
en
o
te
s
u
b
s
tatio
n
p
o
wer
,
p
o
wer
in
jecte
d
b
y
th
e
DG,
p
o
wer
d
em
a
n
d
o
f
th
e
n
etwo
r
k
,
p
o
we
r
lo
s
s
es
in
th
e
n
etwo
r
k
,
an
d
d
em
an
d
d
u
e
to
PEVs
.
,
an
d
,
in
d
icate
th
e
m
in
im
u
m
an
d
m
ax
im
u
m
s
izes o
f
th
e
DG
r
atin
g
.
4.
E
L
E
C
T
RIC
E
E
L
F
O
RAG
I
NG
O
P
T
I
M
I
Z
A
T
I
O
N
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a
tu
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o
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t
h
e
E
E
FO
[
1
6
]
t
a
k
es
i
ts
c
u
es
f
r
o
m
t
h
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f
o
r
a
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ai
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t
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e
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ate
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k
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y
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ag
in
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v
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s
:
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n
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r
a
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n
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i
d
l
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lo
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r
t
.
4
.
1
.
I
nte
ra
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T
h
is
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eh
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io
r
,
also
ter
m
e
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ch
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r
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r
s
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o
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g
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ch
a
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y
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v
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a
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o
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ir
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ch
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r
e
p
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tio
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.
T
h
e
in
ter
ac
tin
g
p
h
ase
ca
n
b
e
m
o
d
eled
as
(
1
3
)
[
1
6
]
.
[
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(
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3
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I
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g
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SS
N:
2252
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8
7
9
2
Op
tima
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A
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285
W
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1
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2
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ests
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ter
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in
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in
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y
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itra
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p
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n
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s
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h
e
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will m
o
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y
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eir
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o
s
itio
n
f
o
r
id
lin
g
,
w
h
ich
is
m
o
d
eled
as (
1
4
)
[
1
6
]
.
(
+
1
)
=
(
+
1
)
+
×
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(
+
1
)
(
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×
(
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;
~
(
0
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1
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(
1
4
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Fig
u
r
e
1
.
E
E
FO a
lg
o
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ith
m
f
l
o
wch
ar
t
4
.
3
.
H
un
t
ing
Du
r
in
g
p
r
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h
u
n
tin
g
,
elec
tr
ic
ee
ls
cr
ea
te
an
elec
tr
ic
co
m
m
u
n
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cir
cle
a
r
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u
n
d
th
e
ta
r
g
et.
T
h
e
y
en
cir
cle
th
e
p
r
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a
n
d
c
o
m
m
u
n
icate
with
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ch
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th
er
t
h
r
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u
g
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tr
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at
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o
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in
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m
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ich
is
r
ep
r
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ed
as (
1
5
)
[
1
6
]
,
wh
er
e
d
en
o
te
cu
r
lin
g
p
a
r
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eter
.
(
+
1
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(
1
5
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4
.
4
.
Reset
t
le
m
ent
R
esettlem
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t
is
a
m
ig
r
ato
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eh
av
io
r
o
b
s
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n
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f
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e
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n
e.
T
h
e
(
1
6
)
d
elin
ea
te
th
e
r
esett
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t tr
ait
in
E
E
FO
[
1
3
]
.
(
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1
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=
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×
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+
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2
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1
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−
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(
1
6
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W
h
er
e
d
en
o
tes
an
y
p
o
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itio
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with
in
th
e
h
u
n
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g
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e,
1
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d
2
r
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t
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o
m
ly
s
elec
ted
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es
with
in
th
e
in
ter
v
al
(
0
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1
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.
st
a
r
t
R
e
a
d
test syst
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d
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ta
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c
ti
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r
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i
t
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P
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S
t
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p
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R
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n
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est
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d
NO
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S
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
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2
2
5
2
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8
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9
2
I
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2
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J
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2
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28
2
-
29
0
286
5.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
Usi
n
g
th
e
I
E
E
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3
3
-
b
u
s
r
ad
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al
d
is
tr
ib
u
tio
n
s
y
s
tem
s
(
R
DS
)
,
a
s
tan
d
ar
d
test
s
y
s
tem
,
th
is
r
esear
ch
v
alid
ates
th
e
ap
p
r
o
p
r
iate
d
ep
l
o
y
m
en
t
o
f
PV
u
n
its
in
a
d
is
tr
i
b
u
tio
n
s
y
s
tem
th
at
s
u
p
p
o
r
ts
PEVs.
R
ef
er
en
ce
[
2
3
]
is
u
s
ed
to
g
et
d
ata
o
f
b
u
s
an
d
lin
e
in
f
o
r
m
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th
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3
3
-
b
u
s
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y
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tem
.
Fig
u
r
e
2
s
h
o
ws
a
3
3
-
b
u
s
R
DS
with
a
b
ase
v
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ltag
e
o
f
1
2
.
6
6
KV
an
d
a
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ase
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f
1
0
0
MV
A;
th
e
p
ea
k
v
alu
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r
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o
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em
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d
o
f
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.
7
1
5
MW
,
an
d
r
ea
ctiv
e
p
o
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d
e
m
an
d
a
r
e
2
.
3
0
0
MV
AR
.
T
h
e
test
s
y
s
te
m
s
'
h
o
u
r
ly
p
o
wer
n
ee
d
s
f
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ch
b
u
s
ar
e
d
er
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ed
f
r
o
m
th
e
n
o
r
m
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d
aily
lo
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p
a
tter
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[
2
4
]
s
h
o
wn
in
F
ig
u
r
e
3
.
A
PV
u
n
it
w
ith
a
m
ax
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m
ca
p
ac
ity
o
f
3
2
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d
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m
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m
ca
p
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f
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k
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n
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id
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ed
[
2
5
]
.
A
t
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tal
o
f
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e
tak
en
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to
ac
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u
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t
f
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all
alg
o
r
ith
m
s
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th
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r
esear
c
h
,
with
a
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s
ize
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f
2
0
0
.
T
h
e
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am
eter
-
f
r
ee
o
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t
im
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m
eth
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d
s
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d
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r
ates
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cr
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s
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et
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.
7
.
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e
o
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tim
al
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ted
af
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o
r
ith
m
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u
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s
.
T
h
e
MA
T
L
AB
s
im
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latio
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s
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e
p
er
f
o
r
m
ed
o
n
a
co
m
p
u
ter
wit
h
8
GB
o
f
R
AM
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d
an
I
n
te
l(
R
)
C
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r
e
(
T
M)
i5
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7
2
0
0
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2
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5
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GHz
C
PU.
T
h
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r
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'
s
p
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f
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r
m
an
ce
in
e
ac
h
o
f
th
e
f
o
llo
win
g
s
ce
n
ar
io
s
:
-
S
ce
n
ar
io
0
:
with
o
u
t PV
u
n
its
an
d
with
o
u
t
PEVs lo
ad
d
em
an
d
,
o
n
ly
c
o
n
v
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n
tio
n
al
lo
a
d
d
em
a
n
d
in
R
DS.
-
S
ce
n
ar
io
1
:
w
ith
o
u
t PV
u
n
its
an
d
w
ith
PEVs
,
lo
ad
d
em
a
n
d
a
n
d
co
n
v
en
tio
n
al
lo
ad
in
R
DS.
-
S
c
e
n
a
r
i
o
2
:
o
p
t
i
m
a
l
d
e
p
l
o
y
m
e
n
t
o
f
o
n
e
P
V
u
n
i
t
i
n
R
DS
h
o
s
ti
n
g
P
E
V
s
'
l
o
a
d
d
e
m
a
n
d
a
n
d
c
o
n
v
e
n
t
i
o
n
a
l
l
o
a
d
.
-
S
c
e
n
a
r
i
o
3
:
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p
t
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m
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l
d
e
p
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e
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t
o
f
t
w
o
P
V
u
n
it
s
i
n
R
D
S
h
o
s
t
in
g
P
E
V
s
'
l
o
a
d
d
e
m
a
n
d
a
n
d
c
o
n
v
e
n
t
i
o
n
a
l
l
o
a
d
.
-
S
c
e
n
a
r
i
o
4
:
o
p
t
i
m
a
l
d
e
p
l
o
y
m
e
n
t
o
f
t
h
r
e
e
P
V
u
n
i
t
s
i
n
R
D
S
h
o
s
t
i
n
g
P
E
V
s
'
l
o
a
d
d
e
m
a
n
d
a
n
d
c
o
n
v
e
n
t
i
o
n
a
l
l
o
a
d
.
Scen
ar
io
0
in
v
o
lv
es
a
d
is
tr
ib
u
t
io
n
s
y
s
tem
s
u
b
jecte
d
to
a
lo
ad
f
lo
w
alg
o
r
ith
m
with
o
u
t
PV
u
n
its
to
g
et
a
h
ig
h
-
lev
el
p
ict
u
r
e
o
f
t
h
e
s
y
s
tem
'
s
tech
n
ical
p
ar
am
eter
s
.
I
n
s
ce
n
ar
io
1
,
t
h
e
lo
a
d
f
l
o
w
alg
o
r
ith
m
is
u
tili
ze
d
to
d
is
s
ec
t
th
e
in
f
lu
e
n
ce
o
n
s
y
s
tem
tech
n
ical
m
etr
ics
ca
u
s
ed
b
y
th
e
a
d
d
itio
n
o
f
PEVs
to
th
e
tr
ad
itio
n
al
lo
a
d
d
em
an
d
.
Fo
r
s
ce
n
a
r
io
s
2
,
3
,
a
n
d
4
,
th
e
b
est
way
t
o
m
ee
t
t
h
e
lo
ad
d
em
an
d
o
f
PEVs
is
to
u
s
e
o
n
e,
two
,
o
r
th
r
ee
PV u
n
its
in
an
R
DS.
T
h
is
will
r
ed
u
ce
th
e
n
etwo
r
k
,
T
VD
,
an
d
im
p
r
o
v
e
th
e
s
y
s
tem
VSI
.
Fig
u
r
e
2
.
I
E
E
E
3
3
-
b
u
s
s
y
s
tem
s
in
g
le
lin
e
d
iag
r
am
Fig
u
r
e
3
.
L
o
ad
c
u
r
v
e
in
p
.
u
.
T
h
e
r
esu
lts
p
r
o
d
u
ce
d
b
y
W
MO
E
E
FO
f
o
r
s
ce
n
ar
io
s
2
-
4
,
ar
e
s
u
m
m
ar
ized
in
T
ab
le
1
,
ar
e
a
s
f
o
llo
ws.
A
to
tal
o
f
2
6
7
7
k
W
o
f
,
1
.
6
9
3
1
p
.
u
.
o
f
T
VD,
an
d
0
.
7
5
7
p
.
u
.
o
f
VSI
wer
e
r
ec
o
r
d
e
d
i
n
s
ce
n
ar
io
0
lo
a
d
f
lo
w
r
esu
lts
.
Scen
ar
io
1
co
n
s
id
er
s
a
3
3
-
b
u
s
s
y
s
tem
with
a
to
tal
lo
ad
o
f
2
8
8
PEVs,
PEVs
o
f
9
p
er
b
u
s
as
s
h
o
wn
in
Fig
u
r
e
2
,
t
o
co
n
ce
n
tr
ate
o
n
t
h
e
in
ter
est
o
n
th
e
elec
tr
ic
cir
cu
latio
n
f
r
a
m
ewo
r
k
b
r
o
u
g
h
t
ab
o
u
t
b
y
PEVs.
I
t
i
s
as
s
u
m
ed
th
at
th
e
s
tate
o
f
ch
ar
g
e
(
SOC
)
o
f
PEVs
is
5
0
%,
an
d
all
PEVs
u
s
e
2
5
k
W
h
b
atter
ies
[
1
5
]
.
T
h
e
d
aily
ch
ar
g
in
g
o
f
2
8
8
PE
Vs
r
eq
u
ir
es
a
to
tal
o
f
3
6
0
0
k
W
o
f
elec
tr
ical
p
o
we
r
,
ca
lcu
l
ated
as
2
8
8
*
2
5
*
0
.
5
.
T
h
r
ee
d
if
f
e
r
en
t
s
ce
n
ar
io
s
f
o
r
ch
ar
g
in
g
PEVs
ar
e
s
h
o
wn
in
Fig
u
r
e
4
:
PC
S,
OP
C
S,
an
d
SC
S.
T
h
is
r
esear
ch
co
n
s
id
er
s
th
at
PEVs
ch
ar
g
e
eq
u
ally
u
n
d
er
PC
S,
OPC
S,
an
d
SC
S.
Scen
ar
io
s
PC
S,
OP
C
S,
a
n
d
SC
S
ar
e
u
s
ed
to
ca
lcu
late
th
e
elec
tr
ic
p
o
we
r
n
ee
d
ed
to
c
h
ar
g
e
PEVs
in
a
d
a
y
.
Scen
ar
io
2
in
v
o
lv
es
th
e
ex
ec
u
tio
n
o
f
th
e
l
o
ad
f
lo
w
alg
o
r
ith
m
.
Fig
u
r
e
5
d
is
p
lay
s
th
e
h
o
u
r
ly
v
ar
iatio
n
o
f
s
u
b
s
tatio
n
p
o
wer
in
s
ce
n
ar
io
s
0
an
d
1
,
in
d
icatin
g
th
at
th
e
s
y
s
tem
's
lo
ad
d
em
an
d
f
r
o
m
PEVs
ca
u
s
es
an
in
cr
ea
s
e
in
s
u
b
s
tatio
n
p
o
wer
.
T
h
r
ee
tech
n
ical
m
ea
s
u
r
es
h
av
e
d
eter
io
r
ated
s
u
b
s
eq
u
en
tl
y
:
o
f
s
y
s
tem
h
as
d
eter
i
o
r
ate
d
to
2
9
1
3
k
W
,
wh
ich
ac
co
u
n
ts
f
o
r
an
8
.
1
%
i
m
p
r
o
v
e
m
e
n
t
;
T
V
D
h
as
d
e
t
e
r
io
r
a
t
e
d
t
o
1
.
8
5
8
1
p
.
u
.
,
a
n
d
V
S
I
h
a
s
f
u
r
t
h
e
r
a
g
g
r
a
v
a
t
e
d
t
o
0
.
7
4
5
p
.
u
.
I
n
s
c
e
n
a
r
i
o
2,
a
s
in
g
le
3
1
9
4
k
W
PV
u
n
it
is
o
p
tim
ally
co
n
n
ec
ted
t
o
th
e
7
th
b
u
s
,
r
ed
u
cin
g
th
e
s
y
s
tem
'
s
to
2
1
0
6
k
W
(
a
2
7
.
7
0
%
d
ec
r
ea
s
e)
,
im
p
r
o
v
in
g
T
VD
to
1
.
0
8
3
7
p
.
u
.
,
an
d
m
ax
im
izin
g
VSI
t
o
0
.
8
2
4
p
.
u
.
S
c
e
n
a
r
i
o
3
'
s
e
f
f
i
c
i
e
n
t
l
i
n
k
i
n
g
o
f
t
w
o
9
3
2
k
W
a
n
d
1
4
2
4
k
W
P
V
u
n
it
s
a
t
t
h
e
1
3
t
h
a
n
d
3
0
t
h
b
u
s
e
s
r
e
d
u
c
e
s
t
h
e
s
y
s
t
em
'
s
t
o
1
8
4
5
k
W
,
wh
ich
is
a
3
6
.
3
6
%
im
p
r
o
v
em
en
t;
it
also
im
p
r
o
v
es
T
VD
to
1
.
0
4
8
1
p
.
u
.
an
d
m
ax
im
i
z
es
VSI
to
0
.
8
3
1
p
.
u
.
As
a
r
esu
lt o
f
co
n
n
ec
tin
g
th
r
ee
PV u
n
its
at
th
e
1
4
th
,
2
4
th
,
an
d
3
0
th
b
u
s
es,
with
a
ca
p
ac
ity
o
f
8
4
4
k
W
,
9
9
2
k
W
,
an
d
1
3
1
3
k
W
,
r
esp
ec
tiv
ely
,
in
s
ce
n
ar
io
4
,
th
e
s
y
s
tem
'
s
is
r
ed
u
c
ed
to
1
7
4
2
k
W
,
ac
c
o
u
n
tin
g
f
o
r
4
0
.
1
9
%
,
t
h
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
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n
g
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2252
-
8
7
9
2
Op
tima
l a
llo
ca
tio
n
o
f P
V
u
n
its
u
s
in
g
mu
ltio
b
jective
meta
h
eu
r
is
tic
o
p
timi
z
a
tio
n
a
p
p
r
o
a
c
h
…
(
A
.
Ma
n
ju
la
)
287
T
VD
is
en
h
an
ce
d
to
1
.
0
4
3
7
p
.
u
,
an
d
th
e
VSI
is
m
ax
im
i
z
ed
to
0
.
8
4
2
p
.
u
.
Fig
u
r
e
6
s
h
o
ws th
e
p
o
wer
p
r
o
d
u
ctio
n
cu
r
v
es f
o
r
th
e
h
o
u
r
ly
PV u
n
its
p
r
o
d
u
ce
d
f
o
r
s
ce
n
ar
i
o
4
o
f
th
e
3
3
-
b
u
s
s
y
s
tem
.
T
ab
le
1
.
Su
m
m
a
r
y
o
f
o
u
tc
o
m
e
s
g
en
er
ated
b
y
W
MO
E
E
FO f
o
r
s
ce
n
ar
io
s
0
-
4
o
f
3
3
-
b
u
s
s
y
s
tem
f
o
r
2
4
h
o
u
r
s
S
.
L.
T
e
c
h
n
i
c
a
l
m
e
t
r
i
c
s
S
c
e
n
a
r
i
o
0
S
c
e
n
a
r
i
o
1
S
c
e
n
a
r
i
o
2
S
c
e
n
a
r
i
o
3
S
c
e
n
a
r
i
o
4
1
P
V
l
o
c
’
s
/
P
V
s
i
z
e
s (k
W
)
-
-
7
/
3
1
9
4
1
3
/
0
9
3
2
3
0
/
1
4
2
4
1
4
/
0
8
4
4
2
4
/
0
9
9
2
3
0
/
1
3
1
3
2
S
u
b
s
t
a
t
i
o
n
p
o
w
e
r
(
k
V
A
)
7
8
3
5
1
8
1
8
1
3
5
3
3
6
5
6
0
2
0
1
5
3
2
5
0
3
O
b
j
e
c
t
i
v
e
f
u
n
c
t
i
o
n
(
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F
)
-
-
0
.
7
3
5
6
0
.
6
9
1
6
0
.
6
7
3
3
4
R
e
a
l
p
o
w
e
r
l
o
ss (
)
i
n
k
W
2
6
7
7
2
9
1
3
2
1
0
6
1
8
4
5
1
7
4
2
5
T
o
t
a
l
v
o
l
t
a
g
e
d
e
v
i
a
t
i
o
n
(
TV
D
)
i
n
p
.
u
.
1
.
6
9
3
1
1
.
8
5
8
1
1
.
0
8
3
7
1
.
0
4
8
1
1
.
0
4
3
7
6
V
o
l
t
a
g
e
st
a
b
i
l
i
t
y
i
n
d
e
x
(
V
S
I
)
i
n
p
.
u
.
0
.
7
5
7
0
.
7
4
5
0
.
8
2
4
0
.
8
3
1
0
.
8
4
2
7
%
r
e
d
u
c
t
i
o
n
-
-
2
7
.
7
0
3
6
.
3
6
4
0
.
1
9
Fig
u
r
e
4
.
Dis
tr
ib
u
tio
n
o
f
p
r
o
b
ab
ilit
ies f
o
r
th
e
PEVs in
PC
S,
OP
C
S,
an
d
SC
S scen
ar
io
s
Fig
u
r
e
5
.
Ho
u
r
ly
s
u
b
s
tatio
n
p
o
wer
o
f
3
3
-
b
u
s
s
y
s
tem
with
o
u
t
an
d
with
PEV
s
Fig
u
r
e
6
.
PV u
n
it o
u
tp
u
t c
u
r
v
e
s
f
o
r
s
ce
n
ar
io
4
o
f
t
h
e
33
-
b
u
s
s
y
s
tem
I
n
Fig
u
r
e
7
,
we
ca
n
s
ee
th
e
3
3
-
b
u
s
s
y
s
tem
av
er
a
g
e
v
o
ltag
e
p
r
o
f
ile
f
o
r
s
ce
n
ar
io
s
0
–
4
.
Fig
u
r
e
7
f
u
r
th
er
d
em
o
n
s
tr
ates
th
at,
i
n
s
ce
n
ar
io
1
,
t
h
e
lo
a
d
d
em
an
d
o
f
PEVs
wo
r
s
en
s
th
e
s
y
s
tem
v
o
ltag
e,
wh
ile
th
e
o
p
tim
al
p
o
s
s
ib
le
d
ep
lo
y
m
e
n
t o
f
PV u
n
its
f
u
r
th
er
d
ev
elo
p
s
th
e
v
o
ltag
e
p
r
o
f
ile
o
f
th
e
s
y
s
tem
.
Fig
u
r
e
8
s
h
o
ws th
e
h
o
u
r
ly
lo
s
s
o
f
th
e
s
y
s
tem
f
o
r
s
ce
n
ar
i
o
s
0
–
4
.
I
n
o
r
d
er
to
d
eter
m
in
e
th
e
W
MO
E
E
F
O
alg
o
r
ith
m
'
s
ef
f
ec
tiv
en
ess
u
s
in
g
th
e
W
MO
DE
an
d
W
MO
GW
O
alg
o
r
ith
m
s
to
r
u
n
i
n
s
ce
n
ar
i
o
s
in
v
o
lv
in
g
th
e
f
o
u
r
t
h
s
ce
n
ar
io
o
f
th
e
3
3
-
b
u
s
test
s
y
s
tem
.
T
h
e
s
u
m
m
ar
y
o
f
o
u
t
co
m
es
b
y
co
m
p
ar
i
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ith
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s
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ax
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ased
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ltio
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p
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289
d
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to
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h
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ate
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if
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t
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h
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PC
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S,
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S)
wer
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asis
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n
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f
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Vs
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ad
e
d
th
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tem
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er
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o
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m
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ce
.
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x
im
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ain
s
in
all
th
r
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ar
am
eter
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wer
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h
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b
y
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ateg
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lacin
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th
r
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n
its
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th
e
3
3
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s
d
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tr
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.
R
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l
p
o
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lo
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s
in
3
3
-
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u
s
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ed
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y
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p
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im
ately
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id
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b
s
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o
f
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n
it
p
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r
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r
th
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t
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atch
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th
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ch
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r
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o
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ith
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ith
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ated
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th
e
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tim
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n
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e
n
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d
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F
UNDING
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Au
th
o
r
s
s
tate
n
o
f
u
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.
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R
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s
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ip
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DATA AV
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Der
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d
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[
AM
]
,
o
n
r
eq
u
est.
RE
F
E
R
E
NC
E
S
[
1
]
A
.
Le
b
si
r
a
n
d
T.
B
e
n
a
mi
m
o
u
r
,
“
R
e
n
e
w
a
b
l
e
e
n
e
r
g
i
e
s
i
n
t
h
e
t
w
e
n
t
y
-
f
i
r
s
t
c
e
n
t
u
r
y
:
a
g
l
o
b
a
l
-
v
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e
w
,
”
2
0
2
3
S
e
c
o
n
d
I
n
t
e
rn
a
t
i
o
n
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l
C
o
n
f
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re
n
c
e
o
n
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n
e
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r
a
n
si
t
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a
n
d
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e
c
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ri
t
y
(
I
C
ETS
)
,
2
0
2
3
,
p
p
.
1
-
6
,
d
o
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:
1
0
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0
9
/
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C
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0
9
9
6
.
2
0
2
3
.
1
0
4
1
0
7
5
7
.
[
2
]
P
.
S
i
n
g
h
,
N
.
K
.
M
e
e
n
a
,
J.
Y
a
n
g
,
E.
V
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g
a
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F
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e
n
t
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s,
a
n
d
S
.
K
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i
s
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n
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,
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b
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2
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1
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.
[
3
]
M
.
M
.
S
a
n
k
a
r
a
n
d
K
.
C
h
a
t
t
e
r
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e
,
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p
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m
u
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s,
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v
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