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rna
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l J
o
urna
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Appl
ied P
o
wer
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I
J
AP
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)
Vo
l.
1
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,
No
.
3
,
Sep
tem
b
er
20
2
6
,
p
p
.
1
3
6
6
~
1
374
I
SS
N:
2252
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8
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:
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1
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1
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i
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1
3
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4
1366
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//
ija
p
e.
ia
esco
r
e.
co
m/
Electric
vehicle
c
ha
rg
ing
statio
ns lo
ca
tion o
ptimiza
t
io
n in
distribut
io
n sy
ste
ms
using
meerkat
optimiza
tion a
lg
o
rithm
M
a
dh
u
ba
bu
T
hiruv
ee
d
ula
,
Sa
nd
ee
p Dha
ra
v
a
t
h,
J
a
rpula
G
a
nes
h Na
ik
,
Ro
y
y
a
la
Vis
hn
u De
v
,
G
o
g
ika
r
Yo
g
endh
a
r,
Ag
ull
a
Ra
hu
l
D
e
p
a
r
t
me
n
t
o
f
El
e
c
t
r
i
c
a
l
a
n
d
El
e
c
t
r
o
n
i
c
s
En
g
i
n
e
e
r
i
n
g
,
T
e
e
g
a
l
a
K
r
i
sh
n
a
R
e
d
d
y
E
n
g
i
n
e
e
r
i
n
g
C
o
l
l
e
g
e
,
H
y
d
e
r
a
b
a
d
,
I
n
d
i
a
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
No
v
2
9
,
2
0
2
5
R
ev
is
ed
J
u
l 9
,
2
0
2
6
Acc
ep
ted
Au
g
1
5
,
2
0
2
6
Th
e
m
e
e
rk
a
t
o
p
ti
m
iza
ti
o
n
a
l
g
o
rit
h
m
(M
OA
)
is
u
se
d
i
n
t
h
is
stu
d
y
to
su
g
g
e
s
t
a
n
e
ffe
c
ti
v
e
m
u
lt
i
-
o
b
jec
ti
v
e
o
p
ti
m
iza
ti
o
n
fra
m
e
wo
rk
fo
r
th
e
b
e
st l
o
c
a
ti
o
n
a
n
d
d
ime
n
sio
n
s
o
f
e
lec
tri
c
v
e
h
icle
c
h
a
rg
in
g
sta
ti
o
n
s
(EVCS
s)
in
ra
d
ial
d
i
strib
u
ti
o
n
sy
ste
m
s
(RDS).
Th
e
p
e
rfo
rm
a
n
c
e
o
f
t
h
e
sy
ste
m
i
n
term
s
o
f
p
o
w
e
r
lo
ss
a
n
d
v
o
lt
a
g
e
sta
b
il
it
y
is
si
g
n
ifi
c
a
n
t
ly
a
f
fe
c
ted
th
e
g
ro
win
g
p
re
v
a
le
n
c
e
o
f
EV
lo
a
d
s.
To
re
d
u
c
e
th
e
re
a
l
p
o
we
r
lo
ss
e
s
a
n
d
a
v
e
ra
g
e
v
o
lt
a
g
e
d
e
v
iatio
n
i
n
d
e
x
(AV
DI)
wh
il
e
imp
r
o
v
i
n
g
th
e
v
o
lt
a
g
e
sta
b
i
li
ty
in
d
e
x
(VSI)
,
a
m
u
l
ti
-
o
b
jec
ti
v
e
fu
n
c
ti
o
n
wa
s
d
e
v
e
lo
p
e
d
.
Th
e
IEE
E
6
9
-
b
u
s
sy
ste
m
is
su
b
jec
ted
t
o
v
a
rio
u
s
l
o
a
d
in
g
c
o
n
d
i
ti
o
n
s
u
sin
g
th
e
re
c
o
m
m
e
n
d
e
d
M
OA
,
wh
ich
is
d
isti
n
g
u
ish
e
d
b
y
it
s
b
a
lan
c
e
d
e
x
p
lo
ra
ti
o
n
-
e
x
p
l
o
it
a
ti
o
n
p
ro
c
e
ss
a
n
d
p
a
ra
m
e
ter
-
fre
e
stru
c
tu
re
.
I
n
c
o
m
p
a
riso
n
with
th
e
b
a
sic
a
n
d
c
u
rre
n
t
m
e
th
o
d
o
l
o
g
ies
,
sim
u
latio
n
fin
d
in
g
s
sh
o
w
t
h
a
t
t
h
e
re
c
o
m
m
e
n
d
e
d
a
p
p
r
o
a
c
h
imp
r
o
v
e
s
th
e
v
o
lt
a
g
e
p
ro
fi
le,
d
e
c
re
a
se
s
p
o
we
r
lo
ss
e
s,
a
n
d
e
n
h
a
n
c
e
s th
e
VSI.
Th
e
a
d
v
a
n
tag
e
s o
f
th
e
M
OA
in
term
s o
f
c
o
n
v
e
rg
e
n
c
e
ti
m
e
,
so
lu
t
io
n
q
u
a
l
it
y
,
a
n
d
re
sili
e
n
c
e
we
re
c
o
n
fir
m
e
d
b
y
a
c
o
m
p
a
riso
n
wit
h
t
h
e
HBA
,
TL
B
O,
ALO,
a
n
d
F
P
A.
Th
e
re
su
lt
s
c
o
n
firm
t
h
a
t
th
e
su
g
g
e
ste
d
a
p
p
ro
a
c
h
is
e
ffe
c
t
iv
e
fo
r
m
o
d
e
rn
EV
-
in
teg
ra
te
d
d
i
strib
u
ti
o
n
n
e
two
rk
s.
K
ey
w
o
r
d
s
:
Av
er
ag
e
v
o
ltag
e
d
ev
iatio
n
in
d
ex
C
h
ar
g
in
g
s
tatio
n
s
E
lectr
ic
v
eh
icles
Me
er
k
at
o
p
tim
izatio
n
al
g
o
r
ith
m
R
ad
ial
d
is
tr
ib
u
tio
n
s
y
s
tem
s
Vo
ltag
e
s
tab
ilit
y
in
d
ex
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Ma
d
h
u
b
a
b
u
T
h
i
r
u
v
ee
d
u
la
Dep
ar
tm
en
t o
f
E
lectr
ical
an
d
E
lectr
o
n
ics E
n
g
in
ee
r
i
n
g
,
T
ee
g
ala
Kr
is
h
n
a
R
ed
d
y
E
n
g
in
ee
r
in
g
C
o
lleg
e
Me
er
p
et,
Me
d
b
o
wli,
Hy
d
er
ab
ad
,
T
elan
g
a
n
a
5
0
0
0
9
7
,
I
n
d
ia
E
m
ail:
m
ad
h
u
m
k
4
4
8
@
g
m
ail.
co
m
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
r
a
p
id
a
d
o
p
tio
n
o
f
elec
tr
i
c
v
eh
icles
(
E
Vs)
h
as
b
r
o
u
g
h
t
b
o
th
ch
allen
g
es
a
n
d
o
p
p
o
r
t
u
n
ities
to
co
n
tem
p
o
r
ar
y
p
o
wer
d
is
tr
ib
u
t
io
n
n
etwo
r
k
s
.
E
Vs
h
av
e
th
e
p
o
ten
tial
to
s
ig
n
if
ica
n
tly
r
e
d
u
ce
g
r
ee
n
h
o
u
s
e
g
as
em
is
s
io
n
s
an
d
f
o
s
s
il
f
u
el
r
elian
ce
wh
en
co
m
b
in
e
d
with
lo
w
-
ca
r
b
o
n
s
o
u
r
ce
s
o
f
elec
tr
icity
.
Ho
wev
er
,
wid
esp
r
ea
d
E
V
ch
ar
g
in
g
in
tr
o
d
u
ce
s
ad
d
itio
n
al
tim
e
-
v
ar
y
i
n
g
lo
ad
s
o
n
d
i
s
tr
ib
u
tio
n
f
ee
d
er
s
,
wh
ich
in
c
r
ea
s
e
p
ea
k
d
em
an
d
,
v
o
ltag
e
d
ev
iatio
n
,
lin
e
lo
s
s
es,
a
n
d
ca
n
ca
u
s
e
co
o
r
d
in
atio
n
p
r
o
b
lem
s
in
p
r
o
tectin
g
eq
u
ip
m
en
t,
esp
ec
ially
in
r
ad
ial
d
is
tr
ib
u
tio
n
s
y
s
tem
s
,
wh
ich
ar
e
co
m
m
o
n
in
r
esid
en
tial
s
er
v
ices
an
d
r
u
r
al
s
ettin
g
s
.
T
h
er
ef
o
r
e,
th
e
s
tr
ateg
ic
lo
ca
tio
n
s
an
d
s
ize
o
f
E
V
ch
a
r
g
er
s
h
av
e
b
ec
o
m
e
a
m
ajo
r
c
h
allen
g
e
in
p
lan
n
i
n
g
,
wh
ich
d
ir
ec
tly
ef
f
ec
ts
th
e
p
er
f
o
r
m
an
ce
o
f
p
o
wer
s
y
s
tem
s
,
ac
ce
s
s
ib
ilit
y
,
an
d
ec
o
n
o
m
ic
f
ea
s
ib
ilit
y
o
f
elec
tr
if
ied
tr
an
s
p
o
r
tatio
n
.
T
h
is
s
tu
d
y
ad
d
r
ess
es
th
ese
c
h
allen
g
es
b
y
p
r
o
p
o
s
in
g
a
m
e
tah
eu
r
is
tic
o
p
tim
izatio
n
ap
p
r
o
ac
h
f
o
r
s
izin
g
an
d
lo
ca
tin
g
E
V
ch
ar
g
in
g
s
tatio
n
(
E
VC
S
)
in
r
ad
ial
d
is
tr
ib
u
tio
n
s
y
s
tem
s
(
R
DS
)
.
B
o
th
class
ical
alg
o
r
ith
m
s
an
d
s
o
f
t
-
co
m
p
u
ti
n
g
s
tr
ateg
ies
h
a
v
e
b
ee
n
e
x
am
in
ed
in
cu
r
r
e
n
t
r
esear
ch
to
o
p
tim
ize
th
e
lo
ca
tio
n
o
f
E
VC
S
in
r
ad
ial
d
is
tr
ib
u
tio
n
s
y
s
tem
s
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R
DS)
.
T
o
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s
e
co
n
g
esti
o
n
,
r
ed
u
ce
ch
ar
g
in
g
co
s
ts
,
an
d
m
in
im
ize
n
etwo
r
k
l
o
s
s
es,
[
1
]
em
p
l
o
y
ed
p
ar
ti
cle
s
war
m
o
p
tim
izatio
n
(
PS
O)
.
Vo
ltag
e
s
tab
ilit
y
is
s
ig
n
if
ican
tly
en
h
a
n
ce
d
wh
e
n
p
h
o
to
v
o
ltaic
(
PV)
g
e
n
er
atio
n
is
in
teg
r
ated
in
to
m
etr
o
p
o
litan
s
y
s
tem
s
.
T
o
lo
wer
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
E
lectric v
eh
icle
ch
a
r
g
in
g
s
ta
tio
n
s
lo
ca
tio
n
o
p
timiz
a
tio
n
in
d
is
tr
ib
u
tio
n
…
(
Ma
d
h
u
b
a
b
u
Th
i
r
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ve
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)
1367
en
er
g
y
lo
s
s
es
an
d
ca
p
ital
ex
p
en
s
es,
r
esu
lt
in
[
2
]
,
[
3
]
s
u
g
g
e
s
ted
a
s
itin
g
s
tr
ateg
y
f
o
r
f
ast
ch
ar
g
in
g
s
tatio
n
s
.
A
b
i
-
lev
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m
ix
ed
-
in
te
g
er
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r
o
g
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am
m
in
g
m
o
d
el
was p
r
esen
ted
in
[
4
]
f
o
r
E
VC
S si
tin
g
an
d
o
p
er
atio
n
al
co
n
tr
o
l in
tr
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s
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o
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t
n
etwo
r
k
s
.
Me
an
wh
il
e,
PS
O
was
u
s
ed
b
y
[
5
]
t
o
p
r
ec
i
s
ely
lo
ca
te
f
u
el
ce
ll
s
tatio
n
s
an
d
allo
ca
te
ca
p
ac
ities
am
o
n
g
in
tr
a
-
city
d
is
tr
ib
u
tio
n
lin
es
.
Ah
m
a
d
et
a
l
.
[
6
]
u
s
ed
a
h
y
b
r
id
GA
-
SAA
to
s
tr
ateg
ically
d
eter
m
in
e
th
e
id
ea
l
PEVCS
lo
ca
tio
n
s
to
s
o
lv
e
th
e
in
teg
r
atio
n
ch
allen
g
e.
I
n
a
d
d
itio
n
,
Hash
em
ian
et
a
l
.
[
7
]
d
em
o
n
s
tr
ated
th
at
in
teg
r
atin
g
E
V
f
ast
-
ch
a
r
g
in
g
p
o
in
ts
in
to
a
d
y
n
am
ic
b
u
s
s
er
v
ice
in
L
u
x
em
b
o
u
r
g
ca
n
b
e
ac
h
iev
ed
u
s
in
g
a
s
u
r
r
o
g
ate
-
ass
is
ted
o
p
tim
al
tech
n
iq
u
e.
Giv
en
its
im
p
ac
t
o
n
s
y
s
tem
r
eliab
ilit
y
,
ex
p
en
s
es,
an
d
s
u
s
tain
ab
ilit
y
f
o
o
tp
r
i
n
ts
,
th
e
c
o
n
tin
u
o
u
s
in
te
g
r
atio
n
o
f
E
V
ch
a
r
g
in
g
s
tatio
n
(
E
VC
S)
in
f
r
astru
ctu
r
e
in
t
o
d
is
tr
ib
u
tio
n
n
etwo
r
k
s
co
n
tin
u
es
to
p
iq
u
e
in
ter
est
[
8
]
.
A
s
tu
d
y
in
[
9
]
u
s
ed
tr
af
f
ic
f
l
o
w
d
ata
an
d
a
m
ix
ed
-
i
n
teg
er
l
in
ea
r
p
r
o
g
r
am
m
in
g
m
o
d
el
t
o
f
i
n
e
-
tu
n
e
f
ast
-
ch
ar
g
in
g
s
tatio
n
s
itin
g
v
ia
GAM
S,
an
d
a
s
tu
d
y
in
[
1
0
]
u
s
ed
a
g
en
etic
a
lg
o
r
ith
m
to
r
ed
u
ce
p
o
wer
lo
s
s
es
th
r
o
u
g
h
th
e
g
r
id
.
Me
an
wh
ile,
f
o
r
th
e
I
E
E
E
3
3
test
s
y
s
tem
,
th
e
p
r
o
b
ab
ilis
tic
c
o
n
tr
o
l
ar
ch
itectu
r
e
p
r
o
v
id
e
d
in
[
1
1
]
in
teg
r
ates v
o
l
tag
e
s
tab
ilit
y
m
ea
s
u
r
em
en
ts
an
d
lo
ad
v
ar
iab
ilit
y
co
n
s
id
er
ati
o
n
s
.
An
ar
ith
m
etic
o
p
tim
izatio
n
al
g
o
r
ith
m
was
p
r
o
p
o
s
ed
in
[
1
2
]
to
en
h
a
n
ce
th
e
p
lace
m
e
n
t
o
f
E
VC
Ss
co
n
n
ec
ted
t
o
p
o
wer
p
lan
ts
.
T
h
is
m
eth
o
d
was
s
u
p
er
io
r
to
b
o
th
PS
O
an
d
HHO.
Dis
tr
ib
u
tio
n
-
lev
el
E
SS
in
s
tallatio
n
in
cr
ea
s
es
v
o
ltag
e
co
n
tr
o
l
m
o
r
e
ef
f
ec
tiv
ely
th
an
ce
n
tr
al
ized
s
y
s
tem
s
,
f
u
lf
illi
n
g
th
e
v
o
ltag
e
co
m
p
lian
ce
lim
itatio
n
s
estab
lis
h
ed
b
y
g
r
id
co
d
es.
T
h
e
s
tu
d
y
in
[
1
3
]
ass
ess
es
d
is
tr
ib
u
ted
E
SS
in
teg
r
atio
n
o
n
p
o
wer
q
u
alit
y
u
s
in
g
NE
PLAN
.
T
h
e
s
tu
d
y
in
[
1
4
]
u
s
es
th
e
I
E
E
E
6
9
b
u
s
s
tan
d
ar
d
an
d
th
e
B
FOA
-
PS
O
alg
o
r
ith
m
,
wh
er
ea
s
[
1
5
]
u
s
es
a
n
o
d
e
-
s
elec
tio
n
h
ier
ar
c
h
y
to
h
asten
th
e
co
m
m
er
cial
p
e
n
etr
atio
n
o
f
E
Vs.
T
o
s
u
p
p
o
r
t
v
o
ltag
e
s
tab
ilit
y
,
a
s
tu
d
y
in
[
1
6
]
in
teg
r
ated
d
is
tr
ib
u
ted
g
en
er
at
o
r
s
in
to
th
e
d
is
tr
ib
u
tio
n
s
y
s
tem
(
UR
DS)
,
an
d
a
s
t
u
d
y
in
[
1
7
]
p
r
o
v
i
d
ed
a
f
r
am
ewo
r
k
th
at
co
m
b
in
ed
th
e
d
ep
lo
y
m
en
t
o
f
E
VC
S
with
tr
an
s
m
is
s
io
n
n
etwo
r
k
(
T
N)
an
d
d
is
tr
ib
u
tio
n
n
etwo
r
k
(
PDN)
d
esig
n
s
.
T
o
p
er
f
o
r
m
a
n
im
p
ac
t
an
aly
s
is
,
th
e
s
tu
d
ies
in
[
1
8
]
,
[
1
9
]
u
s
ed
s
tab
ilit
y
in
d
ices
in
co
n
ju
n
ctio
n
with
2
4
-
h
o
u
r
lo
a
d
p
r
o
f
iles
.
Alth
o
u
g
h
m
an
y
s
tu
d
ies
h
av
e
b
ee
n
co
n
d
u
cte
d
o
n
E
VC
S
allo
ca
tio
n
u
tili
zin
g
m
etah
eu
r
is
tic
tech
n
iq
u
es,
cu
r
r
en
t
m
eth
o
d
s
f
r
e
q
u
en
tly
h
av
e
lim
ited
ex
p
l
o
r
atio
n
ca
p
ab
ilit
ies,
p
r
em
atu
r
e
co
n
v
er
g
en
ce
,
an
d
d
if
f
ic
u
lt
p
ar
am
eter
twea
k
in
g
.
T
h
ese
r
estrictio
n
s
ar
e
ad
d
r
ess
ed
b
y
th
e
r
ec
o
m
m
en
d
e
d
m
ee
r
k
at
o
p
tim
izatio
n
alg
o
r
ith
m
(
MO
A)
,
wh
ich
u
s
es
a
two
-
p
h
ase
ad
ap
tiv
e
s
ea
r
ch
m
ec
h
an
is
m
th
at
g
u
ar
a
n
tees
ef
f
icien
t
lo
ca
l
ex
p
lo
itatio
n
an
d
g
lo
b
al
ex
p
lo
r
atio
n
with
o
u
t th
e
n
ee
d
f
o
r
alg
o
r
ith
m
-
s
p
ec
if
ic
p
ar
am
eter
twea
k
in
g
.
T
h
e
k
ey
co
n
tr
i
b
u
tio
n
s
m
a
d
e
b
y
th
is
wo
r
k
ar
e:
i)
Dev
elo
p
m
en
t
o
f
an
E
VC
S
allo
ca
tio
n
m
o
d
el
with
s
ev
er
al
o
b
jectiv
es
t
h
at
co
n
s
id
e
r
s
p
o
wer
lo
s
s
es,
VSI
,
an
d
AV
DI
;
ii)
T
h
e
u
s
e
o
f
th
e
MO
A
f
o
r
E
VC
S
p
lace
m
en
t
in
R
DS
h
as
n
o
t
b
ee
n
th
o
r
o
u
g
h
ly
in
v
esti
g
ated
in
th
e
liter
atu
r
e
;
iii)
T
h
e
p
er
f
o
r
m
an
c
e
o
f
th
e
MO
A
was
b
en
ch
m
ar
k
ed
b
y
a
th
o
r
o
u
g
h
c
o
m
p
ar
is
o
n
with
HB
A,
T
L
B
O,
FP
A,
an
d
AL
O
;
an
d
iv
)
Vali
d
atio
n
o
f
t
h
e
I
E
E
E
69
-
b
u
s
s
y
s
tem
u
n
d
er
v
ar
io
u
s
E
V
p
en
etr
atio
n
s
ce
n
a
r
io
s
.
2.
P
RO
B
L
E
M
F
O
R
M
U
L
AT
I
O
N
T
h
is
s
tu
d
y
ex
a
m
in
es th
e
im
p
a
ct
o
f
E
V
i
n
teg
r
atio
n
o
n
R
DS.
E
Vs ac
t a
s
ad
d
itio
n
al
lo
a
d
s
o
n
th
e
s
y
s
tem
an
d
th
u
s
r
ed
u
ce
th
e
v
o
ltag
e
p
r
o
f
ile
an
d
VSI
,
r
ea
ctiv
e
an
d
r
e
al
p
o
wer
lo
s
s
es,
an
d
in
tr
o
d
u
ce
v
o
ltag
e
v
ar
iatio
n
s
.
T
h
ese
is
s
u
es
ca
n
b
e
r
eso
lv
e
d
b
y
d
ef
in
i
n
g
th
e
p
r
o
b
lem
as
th
e
o
p
tim
izatio
n
o
f
a
lar
g
e
n
u
m
b
e
r
o
f
g
o
als,
wh
ich
ar
e
th
e
r
ed
u
ctio
n
o
f
th
e
p
o
wer
lo
s
s
an
d
v
o
ltag
e
v
ar
iatio
n
l
o
s
s
an
d
im
p
r
o
v
ed
v
o
ltag
e
p
r
o
f
ile
o
f
th
e
s
y
s
tem
co
u
p
led
with
th
e
VSI
.
A
r
ad
ial
d
is
tr
ib
u
tio
n
s
y
s
tem
'
s
(
R
DS)
lo
ad
f
lo
w
is
s
o
lv
ed
u
s
in
g
th
e
B
W
/FW
L
F a
p
p
r
o
ac
h
[
2
0
]
.
2
.
1
.
M
ulti
-
o
bje
ct
iv
e
f
un
ct
io
n
Her
e
is
a
m
ath
em
atica
l d
escr
ip
tio
n
o
f
th
e
s
u
g
g
ested
m
u
lti
-
o
b
jectiv
e
o
p
tim
izatio
n
f
u
n
ctio
n
.
=
(
1
1
+
2
2
+
3
(
1
3
)
)
(
1
)
T
h
e
(
2
)
d
ef
in
es
th
e
R
DS's
r
ea
l
p
o
wer
lo
s
s
es,
wh
ich
ar
e
b
as
ed
o
n
th
e
p
r
o
p
o
s
ed
test
s
y
s
tem
'
s
r
ea
ctiv
e
an
d
r
ea
l
p
o
wer
f
lo
w.
1
=
=
∑
(
2
+
2
)
2
=
1
(
2
)
T
h
e
s
ec
o
n
d
g
o
al,
wh
ic
h
is
ex
p
r
ess
ed
m
ath
em
atica
lly
in
(
3
)
,
i
s
to
lo
wer
th
e
AVDI
.
2
=
=
1
∑
|
1
−
|
=
1
(
3
)
E
n
h
an
cin
g
th
e
p
r
o
p
o
s
ed
test
s
y
s
tem
's VSI
is
th
e
th
ir
d
g
o
al,
wh
ich
is
d
escr
ib
ed
as
(
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
5
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
1
3
6
6
-
1
3
7
4
1368
3
=
=
[
|
|
4
−
4
(
−
)
−
4
(
+
)
|
|
2
]
(
4
)
W
h
er
e
is
th
e
r
esi
s
tan
ce
o
f
th
e
b
r
an
ch
"ij",
is
th
e
"ij"
b
r
an
ch
r
ea
ctan
ce
,
is
th
e
i
th
b
u
s
v
o
ltag
e,
is
th
e
o
v
er
all
r
ea
l
p
o
wer
r
eq
u
ir
em
e
n
t
at
th
e
j
th
b
u
s
,
an
d
is
th
e
o
v
er
all
d
em
an
d
f
o
r
r
ea
ctiv
e
p
o
wer
at
th
e
j
th
b
u
s
.
W
eig
h
ted
ag
g
r
eg
atio
n
is
u
s
ed
to
co
n
v
e
r
t
th
e
m
u
lti
-
o
b
jec
tiv
e
f
u
n
ctio
n
in
to
a
s
in
g
le
-
o
b
jectiv
e
f
o
r
m
.
T
h
e
n
o
r
m
alize
d
o
b
jectiv
e
v
al
u
es a
n
d
s
y
s
tem
p
er
f
o
r
m
an
ce
p
r
io
r
ities
ar
e
u
s
ed
to
s
elec
t th
e
weig
h
tin
g
f
ac
to
r
s
.
2
.
2
.
Sy
s
t
e
m
co
ns
t
ra
ints
T
h
e
r
ec
o
m
m
en
d
e
d
m
u
lti
-
o
b
je
ctiv
e
f
u
n
ctio
n
,
as
s
tated
in
(
4
)
,
is
lo
wer
ed
wh
ile
co
n
s
id
er
in
g
o
p
er
atio
n
al
r
estrictio
n
s
o
n
b
r
an
c
h
p
o
wer
f
lo
ws
(
|
Si
|
)
an
d
n
o
d
e
v
o
ltag
es
(
Vi)
,
as
well
as
d
es
ig
n
r
estrictio
n
s
o
n
ch
ar
g
i
n
g
s
tatio
n
s
(
C
Ss
)
,
s
u
ch
as
th
e
q
u
an
tity
o
f
ch
ar
g
i
n
g
s
tatio
n
s
(
C
Ss
)
an
d
ch
ar
g
in
g
p
o
in
ts
(
C
Ps
)
,
as
s
p
ec
if
ied
in
(
5
)
-
(
8
)
.
B
r
an
c
h
cu
r
r
en
t
lim
its
ar
e
in
d
ir
ec
tly
e
n
f
o
r
ce
d
th
r
o
u
g
h
ap
p
a
r
en
t
p
o
wer
co
n
s
tr
ain
ts
an
d
v
o
ltag
e
lim
its
to
en
s
u
r
e
s
af
e
s
y
s
tem
o
p
er
atio
n
.
-
C
o
n
s
tr
ain
ts
o
n
v
o
ltag
e
lim
it
≤
≤
i=1
,
2
,
…n
b
(
5
)
-
C
o
n
s
tr
ain
ts
o
n
to
tal
p
o
wer
lim
it
|
|
≤
|
,
|
l=1
,
2
….
n
b
l
(
6
)
-
L
im
itatio
n
s
o
n
ch
ar
g
in
g
p
o
in
t
s
≤
≤
(
7
)
-
C
h
ar
g
in
g
s
tatio
n
s
lim
it c
o
n
s
tr
ain
ts
≤
≤
(
8
)
3.
M
E
E
RK
A
T
O
P
T
I
M
I
Z
A
T
I
O
N
AL
G
O
RIT
H
M
T
h
e
m
ee
r
k
at
o
p
tim
izatio
n
alg
o
r
ith
m
(
MO
A)
[
2
1
]
is
a
r
ec
en
tl
y
d
e
v
elo
p
ed
m
etah
e
u
r
is
tic
tech
n
iq
u
e
th
at
was
p
r
o
p
o
s
ed
as
a
m
eth
o
d
f
o
r
id
en
tify
in
g
th
e
lo
ca
tio
n
o
f
E
VC
Ss
in
a
R
DS.
T
h
e
I
E
E
E
6
9
-
b
u
s
test
s
y
s
tem
wa
s
ch
o
s
en
as
th
e
s
tu
d
y
n
etwo
r
k
b
ec
au
s
e
o
f
its
ap
p
r
o
p
r
iaten
e
s
s
f
o
r
s
tu
d
y
in
g
th
e
m
ed
iu
m
-
v
o
ltag
e
d
i
s
tr
ib
u
tio
n
p
er
f
o
r
m
an
ce
u
n
d
e
r
d
i
f
f
er
en
t
l
o
ad
co
n
d
itio
n
s
.
T
h
e
al
g
o
r
ith
m
m
o
d
els
th
e
lo
o
k
o
u
t
an
d
co
o
p
er
ativ
e
b
eh
a
v
io
r
o
f
m
ee
r
k
ats
to
p
er
f
o
r
m
o
p
tim
izatio
n
,
wh
er
e
th
ey
u
s
e
v
ig
ilan
ce
an
d
co
o
r
d
in
ated
g
r
o
u
p
b
eh
a
v
io
r
th
at
f
o
cu
s
es
o
n
th
e
p
r
ey
.
T
h
e
o
p
tim
izatio
n
p
r
o
ce
s
s
is
b
ased
o
n
th
ese
s
tr
ateg
ies.
˗
Step
1
:
T
h
e
I
E
E
E
6
9
-
b
u
s
s
y
s
tem
n
etwo
r
k
an
d
lo
a
d
d
ata
wer
e
g
ath
er
ed
alo
n
g
with
th
e
lin
e
p
ar
am
eter
s
,
b
ase
lo
ad
s
,
an
d
o
p
e
r
atin
g
lim
its
.
T
h
e
p
r
o
f
iles
o
f
t
h
e
r
e
p
r
esen
tativ
e
E
V
ch
a
r
g
in
g
d
em
a
n
d
s
wer
e
f
o
r
m
e
d
u
n
d
er
lo
w
-
,
m
ed
iu
m
-
,
an
d
h
ig
h
-
p
e
n
etr
atio
n
co
n
d
itio
n
s
.
T
h
e
v
o
ltag
e
an
d
lo
s
s
b
eh
av
i
o
u
r
we
r
e
an
aly
s
ed
b
y
m
o
d
ellin
g
th
e
s
y
s
tem
in
a
MA
T
L
AB
en
v
ir
o
n
m
e
n
t u
s
in
g
s
u
it
ab
le
p
o
wer
f
lo
w
an
aly
s
is
r
o
u
ti
n
es.
˗
Step
2
:
T
h
e
p
ar
am
eter
s
o
f
th
e
p
r
o
b
lem
wer
e
s
tated
b
y
d
eter
m
in
in
g
th
e
f
ea
s
ib
le
b
u
s
es
o
n
w
h
ich
th
e
c
h
ar
g
in
g
s
tatio
n
s
wer
e
to
b
e
in
s
talled
an
d
th
e
m
a
x
im
u
m
lim
its
th
r
o
u
g
h
wh
ich
th
e
c
h
ar
g
i
n
g
s
tatio
n
s
wo
u
ld
b
e
d
eter
m
in
ed
.
T
h
e
an
aly
s
is
was
p
er
f
o
r
m
ed
o
n
b
o
th
p
lace
m
en
t
-
o
n
ly
a
n
d
p
lace
m
en
t
-
with
-
s
iz
in
g
ca
s
es
b
ased
o
n
th
e
cir
c
u
m
s
tan
ce
s
in
v
o
lv
e
d
.
˗
Step
3
:
T
h
e
aim
o
f
th
e
o
p
tim
iz
atio
n
was
to
d
ec
r
ea
s
e
v
o
ltag
e
v
ar
iatio
n
s
an
d
ac
tiv
e
p
o
we
r
lo
s
s
an
d
m
ee
t
o
th
e
r
o
p
er
atio
n
al
r
eq
u
ir
e
m
en
ts
,
in
cl
u
d
in
g
v
o
ltag
e
co
n
s
tr
ain
ts
,
lin
e
lo
ad
in
g
,
an
d
in
v
estme
n
t
ca
p
ac
ity
.
T
h
e
p
r
o
b
lem
was c
o
d
ed
in
to
a
d
ec
is
io
n
v
ec
t
o
r
,
wh
ich
is
th
e
p
o
s
s
ib
le
s
tatio
n
ar
ea
s
an
d
s
ites
.
˗
Step
4
:
T
h
e
m
ee
r
k
at
o
p
tim
izatio
n
alg
o
r
ith
m
was
in
itiated
with
s
ev
er
al
r
an
d
o
m
ca
n
d
id
at
e
s
o
lu
tio
n
s
in
its
p
o
p
u
latio
n
.
T
h
e
ca
n
d
i
d
ates a
r
e
p
o
ten
tial a
r
r
an
g
em
e
n
ts
o
f
E
V
ch
ar
g
in
g
s
tatio
n
s
in
th
e
n
etwo
r
k
.
Fit
n
ess
was
ass
es
s
ed
b
y
r
u
n
n
in
g
p
o
wer
-
f
lo
w
an
aly
s
es o
f
all
ca
n
d
id
ates a
n
d
ca
lcu
latin
g
t
h
eir
p
er
f
o
r
m
a
n
ce
in
d
ices.
˗
Step
5
:
T
h
e
MO
A
s
ea
r
ch
ac
ti
v
ity
s
witch
es
b
etwe
en
ex
p
lo
r
atio
n
an
d
ex
p
lo
itatio
n
s
tag
es.
New
ca
n
d
id
ate
s
o
lu
tio
n
s
wer
e
p
r
o
d
u
ce
d
d
u
r
i
n
g
ex
p
lo
r
atio
n
b
y
m
a
k
in
g
r
a
n
d
o
m
alter
atio
n
s
to
en
s
u
r
e
th
at
a
wid
e
r
an
g
e
o
f
s
o
lu
tio
n
s
wer
e
s
ea
r
c
h
ed
.
I
n
ex
p
lo
itatio
n
,
t
h
e
s
o
lu
tio
n
s
th
at
p
er
f
o
r
m
e
d
well
wer
e
twea
k
e
d
t
o
im
p
r
o
v
e
th
eir
p
er
f
o
r
m
an
ce
.
T
h
e
u
s
e
o
f
c
o
n
s
tr
ain
t
h
an
d
lin
g
s
tr
ateg
ies
en
s
u
r
ed
th
e
m
ain
te
n
an
ce
o
f
f
ea
s
ib
ilit
y
th
r
o
u
g
h
th
e
r
ep
air
o
f
in
f
ea
s
ib
le
s
o
lu
tio
n
s
o
r
p
en
aliza
tio
n
.
˗
Step
6
:
T
h
is
was
r
ep
ea
ted
u
n
til
co
n
v
er
g
en
ce
was
r
ea
ch
ed
o
r
u
n
til
th
e
m
a
x
im
u
m
lim
it
o
f
iter
atio
n
s
was
r
ea
ch
ed
.
T
h
e
o
b
tain
ed
o
p
tim
al
s
o
lu
tio
n
was
d
is
cu
s
s
ed
with
r
e
g
ar
d
t
o
b
u
s
p
o
s
itio
n
s
,
s
tatio
n
c
ap
ac
ity
,
v
o
ltag
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
E
lectric v
eh
icle
ch
a
r
g
in
g
s
ta
tio
n
s
lo
ca
tio
n
o
p
timiz
a
tio
n
in
d
is
tr
ib
u
tio
n
…
(
Ma
d
h
u
b
a
b
u
Th
i
r
u
ve
ed
u
la
)
1369
p
r
o
f
ile
elev
atio
n
,
an
d
m
i
n
im
izatio
n
o
f
lo
s
s
es.
A
b
ase
ca
s
e
w
as u
s
ed
to
p
er
f
o
r
m
a
co
m
p
a
r
at
iv
e
an
aly
s
is
an
d
p
r
o
v
e
t
h
e
ef
f
ec
tiv
e
n
ess
o
f
th
e
s
u
g
g
ested
ap
p
r
o
ac
h
.
3
.
1
.
Addr
ess
i
ng
t
he
E
VC
Ss
a
llo
ca
t
io
n pr
o
blem wit
h t
he
M
O
A
t
ec
hn
i
qu
e
˗
I
n
itializatio
n
:
I
n
p
u
t
n
etwo
r
k
d
ata
an
d
s
y
s
tem
p
ar
am
eter
s
.
T
h
e
I
E
E
E
6
9
-
b
u
s
s
y
s
tem
co
n
f
i
g
u
r
atio
n
an
d
b
u
s
lo
ad
d
ata
ar
e
u
s
ed
as th
e
b
ase
f
o
r
o
p
tim
izatio
n
.
˗
C
an
d
id
ate
s
o
lu
tio
n
g
e
n
er
atio
n
:
T
h
e
m
ee
r
k
at
o
p
tim
izatio
n
alg
o
r
ith
m
g
en
er
ates
r
a
n
d
o
m
s
o
lu
tio
n
s
b
y
s
u
g
g
esti
n
g
d
if
f
er
en
t
p
o
s
s
ib
le
p
lace
m
en
ts
f
o
r
E
V
ch
ar
g
in
g
s
tatio
n
s
.
˗
Fit
n
ess
ev
alu
atio
n
:
E
ac
h
ca
n
d
id
ate
s
o
lu
tio
n
is
ev
alu
ate
d
u
s
in
g
p
o
wer
f
lo
w
an
aly
s
is
(
u
s
u
ally
b
ac
k
war
d
-
f
o
r
war
d
s
wee
p
s
f
o
r
r
ad
ial
n
et
wo
r
k
s
)
,
tar
g
etin
g
th
e
r
ed
u
ctio
n
o
f
p
o
we
r
lo
s
s
es
an
d
i
n
cr
e
m
en
t
o
f
v
o
lta
g
e
p
r
o
f
iles
.
˗
Me
er
k
at
alg
o
r
ith
m
cy
cles
:
T
h
e
alg
o
r
ith
m
p
er
f
o
r
m
s
ex
p
l
o
r
atio
n
(
s
ea
r
ch
in
g
b
r
o
ad
l
y
ac
r
o
s
s
th
e
s
o
lu
tio
n
s
p
ac
e)
an
d
e
x
p
lo
itatio
n
(
f
o
c
u
s
in
g
th
e
s
ea
r
ch
ar
o
u
n
d
p
r
o
m
is
in
g
s
o
lu
tio
n
s
)
,
u
p
d
atin
g
th
e
p
o
p
u
latio
n
iter
ativ
ely
.
˗
C
o
n
v
er
g
en
ce
ch
ec
k
:
T
h
e
alg
o
r
ith
m
ch
ec
k
s
if
th
e
o
b
jectiv
e
f
u
n
ctio
n
m
ee
ts
th
e
co
n
v
er
g
en
ce
cr
iter
ia
o
r
m
ax
im
u
m
iter
atio
n
s
ar
e
r
ea
ch
ed
.
I
f
n
o
t,
s
o
lu
tio
n
u
p
d
atin
g
c
o
n
tin
u
es.
˗
Ou
tp
u
t:
T
h
e
lo
ca
tio
n
s
(
b
u
s
n
u
m
b
er
s
)
o
f
th
e
p
r
o
p
o
s
ed
o
p
tim
al
E
V
ch
ar
g
in
g
s
tatio
n
s
ar
e
s
e
lecte
d
,
en
ab
lin
g
p
r
ac
tical
d
ep
lo
y
m
en
t in
t
h
e
I
E
E
E
6
9
-
b
u
s
s
y
s
tem
.
3
.
2
.
Co
m
pu
t
a
t
io
na
l c
o
m
plex
it
y
In
ad
d
itio
n
to
s
o
lu
tio
n
q
u
ali
ty
,
co
m
p
u
tatio
n
al
ef
f
icien
c
y
is
an
im
p
o
r
tan
t
f
ac
to
r
wh
en
ass
ess
in
g
o
p
tim
izatio
n
alg
o
r
ith
m
s
f
o
r
r
e
al
-
wo
r
ld
p
o
wer
s
y
s
tem
ap
p
licatio
n
s
.
T
h
e
p
o
p
u
latio
n
(
N)
,
n
u
m
b
er
o
f
iter
atio
n
s
(
T
)
,
a
n
d
lo
a
d
f
l
o
w
ca
lcu
latio
n
s
af
f
ec
t
th
e
c
o
m
p
u
tatio
n
a
l
co
m
p
lex
ity
o
f
th
e
MO
A.
T
h
e
o
v
er
all
co
m
p
lex
ity
ca
n
b
e
ap
p
r
o
x
im
ated
as
O
(
N
×
T
×
L
F),
w
h
er
e
L
F
r
ep
r
esen
ts
th
e
co
m
p
le
x
ity
o
f
lo
ad
f
lo
w
ca
lcu
latio
n
s
.
Owin
g
to
its
ad
ap
tiv
e
s
ea
r
ch
p
r
o
ce
d
u
r
e
,
th
e
MO
A
ex
h
ib
its
f
aster
co
n
v
er
g
en
ce
d
esp
ite
iter
ativ
e
e
v
alu
atio
n
.
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
e
ap
p
licab
ilit
y
o
f
th
e
p
r
o
p
o
s
ed
MO
A
wa
s
ev
alu
ated
o
n
th
e
I
E
E
E
6
9
-
n
o
d
e
test
s
y
s
tem
,
an
d
th
e
d
ata
r
elate
d
to
th
e
lin
es
an
d
b
u
s
es
o
f
th
e
test
s
y
s
tem
wer
e
ac
q
u
ir
ed
f
r
o
m
[
2
2
]
.
T
h
e
s
im
u
latio
n
s
wer
e
p
er
f
o
r
m
ed
in
MA
T
L
AB
1
4
.
0
an
d
r
u
n
o
n
a
PC
with
th
e
f
o
llo
win
g
s
p
ec
i
f
ica
tio
n
s
:
I
n
tel
C
o
r
e
i5
-
4
2
1
0
U
C
PU
(
m
ax
im
u
m
o
f
2
.
5
GHz
)
an
d
8
GB
R
AM
.
T
h
e
s
tu
d
y
c
o
n
s
id
er
s
b
atter
y
elec
tr
ic
v
e
h
icles
(
B
E
Vs)
an
d
p
lu
g
-
i
n
h
y
b
r
id
elec
tr
ic
v
eh
icles
(
PHEV
s
)
an
d
th
e
d
esig
n
o
f
ap
p
r
o
p
r
iate
ch
ar
g
i
n
g
p
o
i
n
ts
(
C
Ps
)
to
s
er
v
e
b
o
th
.
T
ab
le
1
lis
ts
th
e
d
esig
n
f
ea
tu
r
es
o
f
th
e
E
V
-
C
Ss
.
T
ab
le
1
p
r
esen
ts
th
e
ch
ar
ac
ter
is
tics
o
f
E
Vs,
in
c
lu
d
in
g
th
eir
p
o
wer
r
atin
g
s
a
n
d
ch
ar
g
in
g
s
tatio
n
s
s
p
ec
if
icatio
n
s
.
T
ab
le
1
s
h
o
ws
th
at
th
e
C
S
s
h
av
e
a
p
o
wer
r
atin
g
o
f
a
m
in
im
u
m
o
f
9
7
5
k
W
an
d
a
m
ax
im
u
m
o
f
1
6
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T
h
e
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u
g
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ested
MO
A
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ed
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o
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er
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ce
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d
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ased
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e
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a
r
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o
m
[
2
3
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.
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h
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etwo
r
k
h
as a
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.
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6
KV
r
atin
g
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d
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o
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e
r
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ad
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0
1
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4
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W
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tiv
e
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r
r
en
t)
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d
2
6
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3
.
6
k
V
Ar
(
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ctiv
e
cu
r
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e
n
t)
.
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h
e
p
a
r
am
eter
s
u
s
ed
in
th
e
MO
A
wer
e
s
ev
en
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ar
iab
les,
2
0
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atio
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s
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5
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d
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a
ls
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u
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ize.
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h
e
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o
p
o
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ed
s
y
s
tem
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test
ed
in
f
iv
e
s
ce
n
ar
io
s
.
C
ase
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1
c
o
n
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id
er
s
th
e
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ase
d
is
tr
ib
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tio
n
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ad
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w
.
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ase
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2
p
o
s
ed
a
g
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ea
te
r
d
e
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d
th
an
C
ase
-
3
with
th
e
m
i
n
im
u
m
n
u
m
b
er
o
f
C
Ps
in
th
e
lo
w
est
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atin
g
o
f
C
S
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d
th
e
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ig
h
est
n
u
m
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er
o
f
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Ps
in
th
e
f
u
ll
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atin
g
o
f
C
S,
r
es
p
ec
tiv
ely
.
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ase
-
4
id
en
tifie
s
th
e
b
est
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S
p
lace
m
en
t
b
ased
o
n
th
e
MO
A
with
th
e
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n
u
m
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er
o
f
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Ps
,
an
d
C
ase
-
5
id
e
n
tifie
s
th
e
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est
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p
lace
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en
t
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ased
o
n
th
e
h
ig
h
est n
u
m
b
er
o
f
C
Ps
at
th
e
m
ax
im
u
m
r
atin
g
.
C
ase
-
1
was
a
d
i
s
tr
ib
u
tio
n
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ad
f
lo
w
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aly
s
is
to
d
eter
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in
e
th
e
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o
wer
lo
s
s
,
m
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im
u
m
v
o
ltag
e
,
VSI
,
b
u
s
v
o
ltag
es,
an
d
A
VDI
.
I
n
C
ase
-
2
,
th
e
s
y
s
tem
lo
a
d
in
c
r
ea
s
es,
an
d
th
e
th
r
ee
E
V
-
C
Ss
(
o
n
e
p
er
s
u
b
-
f
ee
d
er
)
with
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
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:
2
2
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p
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l.
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er
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ase
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ase
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ich
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ch
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e
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wer
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s
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es
in
cr
ea
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o
m
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ig
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w
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o
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o
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ed
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e
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ea
s
ed
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1
4
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o
p
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o
s
ed
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n
d
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u
.
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ed
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9
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.
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.
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en
th
e
m
ax
im
u
m
n
u
m
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er
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Ss
(
th
r
ee
)
is
u
s
ed
in
C
a
s
e
-
3
,
th
e
s
y
s
tem
lo
ad
in
g
in
cr
ea
s
es
to
8
8
2
4
.
9
k
W
(
in
s
tead
o
f
3
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0
1
.
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W
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,
w
h
ich
is
2
.
3
2
1
5
tim
es
h
ig
h
er
t
h
an
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ase
-
1
.
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o
n
s
eq
u
e
n
tly
,
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e
ac
tu
al
l
o
s
s
es in
cr
ea
s
ed
f
r
o
m
2
2
4
.
8
8
0
7
to
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1
0
8
.
6
k
W
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9
2
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9
7
m
o
r
e
th
an
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ase
-
1
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d
1
7
2
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o
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e
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an
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ase
-
2
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u
t
th
e
A
VDI
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cr
ea
s
ed
f
r
o
m
0
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0
0
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4
to
0
.
0
0
7
2
.
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h
e
VSI
d
ec
r
ea
s
es
to
0
.
3
9
4
9
0
o
f
t
h
e
p
r
e
v
io
u
s
0
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6
8
2
3
0
,
an
d
th
e
m
in
im
u
m
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o
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e
at
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u
s
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ec
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ea
s
es
to
0
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9
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.
u
.
o
f
0
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9
0
9
2
0
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.
u
.
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h
e
r
ec
o
m
m
e
n
d
ed
MO
A
was
ap
p
lied
to
C
ases
3
an
d
2
t
o
d
eter
m
in
e
th
e
b
est
allo
ca
tio
n
o
f
C
S,
as
in
C
ases
5
an
d
4
.
B
ased
o
n
t
h
e
6
6
4
0
k
W
to
tal
lo
a
d
d
e
m
an
d
in
C
ase
4
,
th
e
MO
A
id
en
tifie
d
t
h
at
b
u
s
es 2
,
2
5
,
an
d
4
wer
e
th
e
b
est
p
lace
s
to
en
s
u
r
e
th
e
least
n
u
m
b
er
o
f
C
Ps
.
T
h
e
lo
s
s
es
d
r
o
p
p
ed
to
2
1
9
.
1
6
4
5
k
W
,
A
VDI
to
0
.
0
0
1
3
6
4
as
co
m
p
ar
e
d
t
o
0
.
0
0
4
0
,
an
d
VSI
to
0
.
6
9
0
8
1
2
as
co
m
p
a
r
e
d
to
0
.
5
1
1
4
,
r
esp
ec
tiv
ely
.
Vm
in
also
im
p
r
o
v
ed
to
0
.
9
0
9
6
p
.
u
.
co
m
p
ar
e
d
to
0
.
8
4
6
2
p
.
u
.
Fig
u
r
es
1
an
d
2
d
e
p
ict
th
e
VSI
an
d
v
o
ltag
e
p
r
o
f
iles
o
f
C
ase
4
an
d
th
e
b
ase
ca
s
e,
r
esp
ec
tiv
ely
.
Fig
u
r
e
1
.
V
o
ltag
e
p
r
o
f
ile
o
f
6
9
-
b
u
s
s
y
s
tem
Fig
u
r
e
2
.
VSI
o
f
6
9
-
b
u
s
s
y
s
tem
In
C
ase
-
5
,
th
e
MO
A
p
r
o
v
id
es
th
e
b
est
C
S
lo
ca
tio
n
s
at
b
u
s
es
2
,
2
5
,
an
d
4
an
d
m
in
im
izes
lo
s
s
es
in
th
e
s
y
s
tem
at
1
1
0
8
.
6
2
6
6
to
2
1
9
.
8
4
2
1
k
W
,
A
VDI
0
.
0
0
1
3
to
0
.
0
0
7
2
,
an
d
VSI
0
.
6
9
0
6
4
2
to
0
.
3
9
4
9
.
T
h
e
lo
west
v
o
ltag
e
was
also
im
p
r
o
v
ed
to
0
.
9
0
9
4
p
.
u
.
,
c
o
m
p
a
r
ed
to
0
.
7
9
3
5
0
p
.
u
.
All
s
ce
n
ar
io
s
r
esu
lted
in
a
s
u
m
m
ar
y
o
f
th
e
o
u
tco
m
es,
wh
ich
a
r
e
s
u
m
m
ar
i
ze
d
in
T
ab
le
2
.
T
h
e
p
o
wer
lo
s
s
es
in
C
ase
s
4
an
d
5
(
2
1
9
.
1
6
4
5
an
d
2
1
9
.
8
4
2
1
k
W
,
r
esp
ec
tiv
ely
)
wer
e
co
n
s
id
er
ab
l
y
r
ed
u
ce
d
co
m
p
ar
ed
with
th
o
s
e
in
C
ases
2
an
d
3
.
Fig
u
r
e
3
s
h
o
ws
th
e
co
n
v
er
g
en
ce
cu
r
v
e
o
f
th
e
6
9
-
b
u
s
s
y
s
tem
.
Fig
u
r
e
4
s
h
o
ws t
h
e
p
o
wer
lo
s
s
co
m
p
ar
is
o
n
o
f
MO
A
with
ex
is
tin
g
m
eth
o
d
s
.
4
.
2
.
Dis
cus
s
io
n
T
h
e
f
in
d
i
n
g
s
u
n
e
q
u
iv
o
ca
lly
s
h
o
w
th
at
in
teg
r
atin
g
E
VC
S with
o
u
t o
p
tim
izatio
n
(
C
ases
2
an
d
3
)
ca
u
s
es
a
s
ig
n
if
ican
t
d
ec
lin
e
in
th
e
s
y
s
tem
p
er
f
o
r
m
an
ce
,
in
clu
d
in
g
h
ig
h
er
p
o
wer
lo
s
s
es
an
d
wo
r
s
e
v
o
ltag
e
s
tab
ilit
y
.
Ho
wev
er
,
th
e
ap
p
licatio
n
o
f
th
e
MO
A
(
C
ases
4
an
d
5
)
s
i
g
n
if
ican
tly
r
esto
r
ed
th
e
s
y
s
tem
p
er
f
o
r
m
a
n
ce
b
y
o
p
tim
ally
lo
ca
tin
g
th
e
E
VC
Ss
.
I
n
C
ase
4
,
th
e
MO
A
ac
h
ie
v
ed
2
.
7
%
less
p
o
wer
lo
s
s
th
an
th
e
b
est
ap
p
r
o
ac
h
cu
r
r
en
tly
in
u
s
e
(
HB
A:
2
2
5
.
1
7
k
W
v
s
.
MO
A:
2
1
9
.
1
6
k
W
)
wh
en
co
m
p
a
r
ed
to
HB
A,
T
L
B
O,
AL
O,
an
d
FP
A.
A
3
5
%
im
p
r
o
v
em
en
t
in
th
e
VSI
f
r
o
m
0
.
5
1
1
4
(
ca
s
e
2
)
to
0
.
6
9
0
8
(
ca
s
e
4
)
d
ir
ec
tly
d
ec
r
eses
th
e
p
r
o
b
ab
ilit
y
o
f
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
E
lectric v
eh
icle
ch
a
r
g
in
g
s
ta
tio
n
s
lo
ca
tio
n
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p
timiz
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in
d
is
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ib
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tio
n
…
(
Ma
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h
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a
b
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Th
i
r
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la
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1371
v
o
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e
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llap
s
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A
m
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r
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n
if
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r
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o
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p
r
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ile
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co
n
f
i
r
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ed
b
y
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r
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r
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m
0
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0
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to
0
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h
e
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d
u
ctio
n
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p
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wer
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s
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d
im
p
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o
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em
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t
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em
o
n
s
tr
ated
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e
ef
f
ec
tiv
en
ess
o
f
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e
r
ec
o
m
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en
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al
g
o
r
ith
m
.
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A
d
em
o
n
s
tr
ated
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Fig
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r
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4
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p
ar
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f
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with
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5.
CO
NCLU
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A
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r
th
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p
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o
f
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s
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.
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h
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as
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o
th
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a
n
d
ex
p
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itatio
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a
n
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p
tim
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o
lu
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with
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s
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u
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al
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T
h
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6
9
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FP
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o
m
p
lex
p
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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1372
in
clu
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ib
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Desp
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it
s
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ea
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tain
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ly
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win
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p
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b
in
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RE
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NC
E
S
[
1
]
M
.
Z.
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e
b
e
t
a
l
.
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[
2
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,
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Evaluation Warning : The document was created with Spire.PDF for Python.