I
nte
rna
t
io
na
l J
o
urna
l o
f
P
o
wer
E
lect
ro
nics
a
nd
Driv
e
S
y
s
t
em
s
(
I
J
P
E
DS
)
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2
0
2
1
,
p
p
.
2
5
5
7
~
25
69
I
SS
N:
2088
-
8
6
9
4
,
DOI
: 1
0
.
1
1
5
9
1
/
ijp
ed
s
.
v
1
2
.
i
4
.
p
p
2
5
5
7
-
25
69
2557
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
p
e
d
s
.
ia
esco
r
e.
co
m
O
ptima
l si
zing
an
d sitt
ing
o
f
elec
tri
c vehicle
cha
rg
ing
statio
n by
using
Archime
des
o
ptimiza
tion a
lg
o
rithm
techni
que
M
o
ha
m
ed
A
bd
elha
m
ed
Z
a
k
i
1
,
T
a
re
k
M
a
hm
o
ud
2
, M
o
ha
m
ed
At
ia
3
,
E
l
S
a
id
A
bd
E
l
A
ziz
O
s
m
a
n
4
1,
3
De
p
a
rtme
n
t
o
f
El
e
c
tri
c
a
l
P
o
we
r
a
n
d
M
a
c
h
in
e
s E
n
g
i
n
e
e
rin
g
,
th
e
Hig
h
e
r
In
st
it
u
te
o
f
E
n
g
in
e
e
rin
g
,
E
lsh
o
ro
u
k
Cit
y
,
E
g
y
p
t
2,
4
De
p
a
rtme
n
t
o
f
El
e
c
tri
c
a
l
En
g
in
e
e
rin
g
,
Al
-
Az
h
a
r
Un
iv
e
rsity
,
Ca
ir
o
,
E
g
y
p
t
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
May
6
,
2
0
21
R
ev
is
ed
Sep
17
,
2
0
21
Acc
ep
ted
Sep
24
,
2
0
21
In
c
re
a
sin
g
p
e
n
e
tratio
n
o
f
e
lec
tri
c
v
e
h
icle
(
EV
)
l
o
a
d
in
t
o
t
h
e
e
lec
tri
c
it
y
se
c
to
r
will
re
su
lt
in
g
e
n
e
ra
ti
o
n
imb
a
lan
c
e
,
a
n
i
n
c
re
a
se
in
re
a
l
p
o
we
r
l
o
ss
,
a
l
o
w
v
o
lt
a
g
e
p
ro
fil
e
a
n
d
c
o
n
se
q
u
e
n
tl
y
a
d
e
c
re
a
se
in
th
e
m
a
rg
in
o
f
sta
b
il
it
y
o
f
v
o
lt
a
g
e
.
It
is n
e
c
e
ss
a
ry
fo
r
t
h
e
c
o
o
rd
i
n
a
ti
o
n
o
f
c
h
a
r
g
in
g
sta
ti
o
n
s (CS
s)
fo
r
EV
a
t
th
e
re
lev
a
n
t
lo
c
a
ti
o
n
s
t
o
m
in
imiz
e
th
e
e
ffe
c
t
o
f
in
c
re
a
se
d
EV
lo
a
d
p
e
n
e
tratio
n
in
ra
d
ial
sy
ste
m
s.
In
th
is
p
a
p
e
r,
a
n
e
w
o
p
t
imiz
a
ti
o
n
m
e
th
o
d
n
a
m
e
d
Arc
h
ime
d
e
s
o
p
ti
m
iza
ti
o
n
a
lg
o
rit
h
m
(AO
A)
is
p
ro
p
o
se
d
;
it
d
e
term
in
e
d
th
e
o
p
ti
m
a
l
lo
c
a
ti
o
n
a
n
d
siz
e
f
o
r
EV
-
CS
f
o
r
re
d
u
c
in
g
p
o
we
r
lo
ss
e
s
a
n
d
imp
ro
v
e
d
v
o
l
tag
e
p
ro
fi
le.
I
n
t
h
is
w
o
rk
we
u
se
d
th
e
p
h
o
t
o
v
o
lt
a
ic
(P
V)
re
n
e
wa
b
le
so
u
rc
e
a
s
a
m
a
in
fe
e
d
e
r
fo
r
th
e
CS
s.
M
a
n
y
o
f
Artifi
c
ial
In
telli
g
e
n
c
e
tec
h
n
iq
u
e
a
re
a
p
p
li
e
d
to
d
e
term
in
e
th
e
o
p
ti
m
a
l
siz
in
g
a
n
d
sitt
i
n
g
o
f
EV
-
CS
s
c
o
n
sid
e
ri
n
g
th
e
o
b
je
c
ti
v
e
o
f
m
i
n
imiz
a
ti
o
n
o
f
re
a
l
p
o
we
r
lo
ss
.
IEE
E
3
3
-
b
u
s
tes
ti
n
g
n
e
two
r
k
c
o
n
d
u
c
ts
sim
u
latio
n
tes
ts.
T
h
e
re
su
lt
s
h
ig
h
li
g
h
ted
th
e
n
e
e
d
t
o
re
fin
e
th
e
EV
-
CS
a
ll
o
c
a
ti
o
n
t
o
im
p
ro
v
e
th
e
p
e
rfo
rm
a
n
c
e
.
Th
e
a
b
il
it
y
to
so
l
v
e
c
o
m
p
lex
,
n
o
n
-
li
n
e
a
r
o
b
jec
ti
v
e
o
p
ti
m
iza
ti
o
n
issu
e
s
u
sin
g
AO
A
a
n
d
t
o
c
o
m
p
a
r
e
th
e
re
su
lt
s
wit
h
o
t
h
e
r
a
l
g
o
rit
h
m
s,
n
a
m
e
ly
p
a
rti
c
le
sw
a
rm
o
p
t
imiz
a
ti
o
n
(P
S
O),
c
u
c
k
o
o
se
a
rc
h
a
lg
o
r
it
h
m
(C
S
A),
sh
o
ws
it
s e
ffe
c
ti
v
e
n
e
ss
in
m
in
imiz
in
g
th
e
p
o
we
r
lo
ss
a
s req
u
ired
.
K
ey
w
o
r
d
s
:
E
lectr
ic
v
eh
ic
les
O
p
tim
a
l sizin
g
an
d
s
itti
n
g
o
f
EV
-
C
Ss
P
ar
t
icle
s
war
m
o
p
tim
izatio
n
C
uc
k
o
o
s
ea
r
ch
alg
o
r
ith
m
Ar
ch
im
ed
es o
p
tim
izatio
n
alg
o
r
ith
m
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Mo
h
am
ed
A
b
d
elh
am
ed
Z
ak
i
Dep
ar
tm
en
t o
f
E
lectr
ical
Po
wer
an
d
Ma
c
h
in
es E
n
g
in
ee
r
in
g
T
h
e
Hig
h
er
I
n
s
titu
te
o
f
E
n
g
in
e
er
in
g
E
ls
h
o
r
o
u
k
C
ity
,
C
air
o
,
E
g
y
p
t
E
m
ail:
m
.
za
k
y
@
s
h
a.
ed
u
.
eg
1.
I
NT
RO
D
UCT
I
O
N
T
o
d
ay
,
t
h
e
wo
r
ld
'
s
d
em
an
d
f
o
r
f
o
s
s
il
f
u
els
is
in
cr
ea
s
in
g
r
ap
id
ly
in
b
o
th
th
e
tr
an
s
p
o
r
t
an
d
p
o
wer
g
en
er
atio
n
s
ec
to
r
s
.
No
t
o
n
ly
d
o
es
th
e
u
s
e
o
f
th
ese
to
o
ls
co
n
t
r
ib
u
te
to
h
ig
h
p
r
ices,
b
u
t
also
to
g
r
ee
n
h
o
u
s
e
g
as
em
is
s
io
n
s
an
d
en
v
ir
o
n
m
e
n
tal
p
o
llu
tio
n
.
[
1
]
.
Acc
o
r
d
in
g
to
s
tu
d
ies
p
r
esen
ted
in
[
2
]
,
Pro
d
u
ctio
n
will
r
is
e
b
y
5
4
%
in
th
e
tr
an
s
p
o
r
t
in
d
u
s
tr
y
b
y
2
0
3
5
,
wh
ich
will
in
cr
ea
s
e
p
r
ices
an
d
air
p
o
llu
tio
n
b
y
s
ig
n
if
ican
t
d
em
an
d
.
T
h
er
ef
o
r
e,
m
a
n
y
n
atio
n
s
ar
e
s
ee
k
in
g
to
r
ep
lace
g
r
ee
n
v
eh
icles
in
s
tead
o
f
in
ter
n
al
c
o
m
b
u
s
t
io
n
ca
r
s
[
3
]
.
E
lectr
ic
v
eh
icles
(
E
Vs)
h
av
e
s
h
o
wn
ad
d
itio
n
al
b
en
ef
its
co
m
p
ar
ed
with
th
ei
r
f
o
s
s
il
f
u
el
v
eh
iclec
o
u
n
ter
p
ar
ts
.
T
h
ey
p
r
o
d
u
ce
f
ewe
r
e
m
is
s
i
o
n
s
ev
en
w
h
en
c
o
n
s
id
er
in
g
th
eir
wh
o
le
p
r
o
ce
s
s
o
f
e
n
er
g
y
p
r
o
d
u
c
tio
n
,
in
d
ep
en
d
en
tly
o
f
th
eir
en
er
g
y
s
o
u
r
ce
[
4
]
.
E
lectr
ic
v
eh
icle
(
EV
)
is
an
u
p
-
an
d
-
co
m
in
g
s
o
lu
ti
o
n
f
o
r
th
e
p
r
o
b
lem
o
f
tr
an
s
p
o
r
tatio
n
an
d
p
o
llu
tio
n
[
5
]
.
T
h
e
f
ir
s
t
tech
n
o
lo
g
y
in
tr
o
d
u
ce
d
will
tak
e
p
lace
v
ia
v
e
h
icle
-
to
-
g
r
id
i
n
1
9
7
7
[
6
]
.
T
h
is
p
r
o
m
is
in
g
f
r
a
m
ewo
r
k
h
as
b
ee
n
f
ir
s
t
u
s
ed
b
y
th
e
p
r
o
v
is
io
n
o
f
a
r
ev
en
u
e
an
d
ex
p
en
d
itu
r
e
m
o
d
el
f
o
r
r
eg
u
lato
r
y
an
d
au
x
iliar
y
s
er
v
ices [
7
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
25
57
–
25
69
2558
Pen
etr
atio
n
s
o
f
elec
tr
ical
v
eh
i
cles
(
E
Vs)
in
th
e
g
r
id
f
ac
e
c
h
a
llen
g
es
in
clu
d
in
g
th
er
m
al
lim
i
t
b
r
ea
ch
es
in
ce
r
tai
n
s
en
s
itiv
e
n
etwo
r
k
b
u
s
es
o
f
tr
an
s
m
is
s
io
n
lin
es
b
ec
au
s
e
o
f
o
v
er
lo
a
d
o
r
v
o
ltag
e
d
r
o
p
an
d
d
em
a
n
d
u
n
ce
r
tain
ty
[
8
]
,
[
9
]
.
T
h
e
m
o
s
t
p
o
p
u
lar
v
eh
icles
in
th
e
p
ar
k
in
g
m
o
d
e
a
r
e
alm
o
s
t
9
5
%
o
f
t
h
e
d
ay
,
ac
co
r
d
in
g
to
p
r
ev
io
u
s
s
tu
d
ies.
As
a
co
n
s
eq
u
en
ce
,
ca
n
b
e
u
s
ed
th
is
ca
p
ac
ity
f
o
r
f
r
eq
u
en
cy
an
d
v
o
ltag
e
r
eg
u
latio
n
th
r
o
u
g
h
V2
G
[
1
0
]
.
Veh
icle
p
ar
ticip
ati
o
n
in
V2
G
g
en
er
ates
m
o
n
e
y
f
o
r
o
wn
er
s
o
f
ca
r
s
.
I
t
ca
n
also
b
e
u
s
ed
to
m
in
im
ize
n
etwo
r
k
c
h
allen
g
es
b
y
u
s
in
g
E
V
an
d
PHEV
ch
a
r
g
in
g
s
tatio
n
ca
p
ab
ilit
ies
[
1
1
]
,
[
1
2
]
.
Veh
icles
will
r
ef
ill
b
atter
ies
at
th
ese
s
tatio
n
s
an
d
s
ell
ex
ce
s
s
s
to
r
ed
en
e
r
g
y
t
o
g
r
id
an
d
p
r
o
f
it
f
r
o
m
it.
I
n
th
is
s
itu
atio
n
,
it
is
p
o
s
s
ib
le
to
h
an
d
le
th
e
ch
ar
g
i
n
g
an
d
d
is
ch
ar
g
in
g
o
f
v
e
h
icles
u
s
in
g
v
ar
io
u
s
ap
p
r
o
ac
h
es,
s
u
ch
as
ad
ju
s
tin
g
en
er
g
y
ta
r
if
f
s
at
d
if
f
e
r
en
t tim
e
s
lo
ts
.
R
en
ewa
b
le
s
o
u
r
ce
s
h
av
e
b
ee
n
wid
ely
r
eg
ar
d
ed
in
r
ec
en
t
y
e
ar
s
as
an
alter
n
ativ
e
to
f
o
s
s
il
-
f
u
el
p
o
wer
p
lan
ts
.
Sin
ce
th
ese
to
o
ls
ca
n
b
e
m
o
u
n
ted
n
ea
r
th
e
lo
ad
,
lo
s
s
es a
n
d
v
o
ltag
e
f
lu
ctu
atio
n
s
ca
n
b
e
m
in
im
ized
[
1
3
]
,
B
ec
au
s
e
o
f
th
e
r
an
d
o
m
n
atu
r
e
o
f
th
eir
o
u
tp
u
t,
th
e
wid
esp
r
ea
d
p
en
etr
atio
n
o
f
th
ese
r
eso
u
r
c
es
in
to
th
e
g
r
id
m
ay
cr
ea
te
ch
allen
g
es.
C
o
n
s
eq
u
e
n
t
ly
,
h
ig
h
-
ca
p
ac
ity
e
n
er
g
y
s
to
r
a
g
e
d
ev
ices
ca
n
b
e
u
s
ed
to
s
u
s
t
ain
th
e
n
etwo
r
k
.
I
n
th
is
s
en
s
e,
ch
ar
g
in
g
s
tatio
n
s
ca
n
b
e
in
teg
r
ated
in
to
th
e
n
e
two
r
k
as
E
SS
v
ia
V
2
G.
C
h
ar
g
in
g
s
tatio
n
s
s
to
r
e
ex
ce
s
s
p
o
wer
g
en
er
ate
d
b
y
R
E
S
an
d
in
jects
it
in
to
th
e
elec
tr
icity
g
r
id
in
d
u
e
co
u
r
s
e,
d
is
tr
ib
u
tin
g
th
e
en
er
g
y
an
d
r
ed
u
ci
n
g
th
e
b
u
r
d
en
o
n
th
e
d
is
tr
ib
u
tio
n
n
etwo
r
k
.
E
m
is
s
io
n
r
ates
ar
e
m
in
im
ized
in
a
s
m
ar
t
g
r
id
with
an
o
p
tim
u
m
m
ix
o
f
R
E
S
an
d
PHEV
ch
ar
g
in
g
s
tatio
n
s
an
d
m
a
n
y
tech
n
o
l
o
g
ical
an
d
ec
o
n
o
m
ic
p
r
o
b
lem
s
c
an
b
e
s
o
lv
ed
ef
f
ec
tiv
ely
[
1
4
]
.
L
iter
atu
r
e
r
ev
iews
m
a
n
y
r
esear
ch
er
s
h
a
v
e
in
v
esti
g
ated
th
e
d
esig
n
an
d
o
p
e
r
atio
n
o
f
E
V
C
Ss
an
d
PV
r
en
ewa
b
le
s
o
u
r
ce
o
n
th
e
d
i
s
tr
ib
u
tio
n
s
y
s
tem
s
an
d
litt
le
r
esear
ch
er
u
s
ed
th
e
Ar
ch
i
m
ed
es
o
p
tim
izatio
n
alg
o
r
ith
m
(
AOA
)
.
Li
et
a
l.
[
1
5
]
,
th
e
AOA
to
ch
o
o
s
e
th
e
o
p
tim
u
m
lo
ca
tio
n
a
n
d
ca
p
ac
ity
o
f
DG
an
d
u
s
ed
th
e
p
o
wer
lo
s
s
es o
b
jectiv
e
an
d
co
m
p
ar
e
b
etwe
en
th
e
r
esu
lts
b
y
u
s
in
g
AOA,
I
GA
an
d
p
ar
ticle
s
war
m
o
p
tim
iza
tio
n
(
PSO
)
.
Ali
et
a
l.
[
1
6
]
p
r
esen
t
ed
an
o
b
jectiv
e
o
p
tim
izatio
n
ap
p
r
o
ac
h
is
f
o
r
m
u
lated
to
o
p
t
im
ally
s
ize
m
u
ltip
le
DGs
an
d
SOPs
p
lace
m
en
ts
v
ia
AOA
an
d
NR
f
r
o
m
t
h
e
p
lan
n
in
g
a
n
d
o
p
er
atio
n
al
v
iewp
o
i
n
ts
,
C
ase
s
tu
d
ies
ar
e
co
n
d
u
cte
d
o
n
th
e
r
ea
l d
is
tr
ib
u
t
io
n
n
etwo
r
k
s
,
in
clu
d
in
g
th
e
5
9
-
n
o
d
e
d
is
tr
ib
u
tio
n
n
etwo
r
k
i
n
C
air
o
an
d
th
e
1
3
5
-
n
o
d
e
d
is
tr
ib
u
tio
n
n
etwo
r
k
in
B
r
az
il,
to
s
tep
o
n
th
e
e
f
f
e
ctiv
en
ess
o
f
SOPs
in
s
er
tio
n
in
en
h
an
ci
n
g
DGs
p
en
etr
atio
n
.
Var
io
u
s
EV
-
PV
c
h
ar
g
er
a
r
ch
itectu
r
es
wer
e
test
ed
an
d
a
n
aly
s
es.
Mo
u
li
et
a
l.
[
1
7
]
,
th
e
ch
a
r
g
er
o
f
EV
-
PV
was
p
r
esen
ted
with
two
o
p
tim
al
d
esig
n
s
.
G
o
li
a
n
d
S
h
iree
n
[
1
8
]
,
d
esig
n
o
f
s
m
ar
t
ch
ar
g
in
g
s
tatio
n
was
im
p
lem
en
ted
in
wh
ich
t
h
e
ch
ar
g
in
g
o
f
t
h
e
PHEV
s
was
co
n
tr
o
lled
to
m
i
n
im
ize
th
e
e
f
f
ec
t
o
f
ch
a
r
g
in
g
d
u
r
in
g
th
e
p
ea
k
l
o
ad
p
e
r
io
d
o
n
th
e
g
r
id
.
T
h
e
PHEV
s
wer
e
p
aid
i
n
t
h
at
s
ch
em
e
v
ia
th
e
PV
o
f
g
r
id
-
co
n
n
ec
ted
s
y
s
tem
an
d
/o
r
t
h
e
u
tili
ty
a
s
p
ec
ial
co
n
tr
o
ller
h
as
b
ee
n
d
ev
el
o
p
ed
t
o
allo
w
ef
f
ec
tiv
e
en
er
g
y
tr
a
n
s
f
e
r
wh
ile
at
th
e
s
am
e
tim
e
r
ed
u
cin
g
th
e
c
o
n
v
e
r
s
io
n
s
tag
e
b
etwe
en
s
o
u
r
ce
a
n
d
l
o
a
d
.
[
1
9
]
.
T
h
e
s
y
s
tem
co
n
s
is
ts
o
f
m
o
d
u
les
d
esig
n
ed
to
en
h
an
ce
f
lex
ib
ilit
y
an
d
en
c
o
u
r
ag
e
d
e
v
elo
p
m
e
n
t.
I
n
an
u
n
r
eg
u
lated
ch
a
r
g
e
m
eth
o
d
,
th
e
in
teg
r
atio
n
o
f
PV
an
d
E
Vs
was
s
tu
d
ied
[
2
0
]
.
I
n
ad
d
itio
n
,
we
e
x
p
lo
r
e
d
th
e
i
m
p
lem
en
tatio
n
o
f
in
tellig
en
t
ch
ar
g
in
g
a
n
d
V2
G
s
tr
ateg
ies.
T
h
e
p
ap
er
h
as
s
h
o
wn
th
at
th
e
g
r
id
s
tr
ateg
y
v
eh
i
cles
ca
n
b
e
u
s
ed
to
r
u
b
th
e
p
ea
k
s
o
f
th
e
class
ical
lo
ad
cu
r
v
e
u
s
in
g
t
h
e
PV o
u
tp
u
t.
Haf
ez
an
d
B
h
attac
h
ar
y
a
[
2
1
]
p
r
o
p
o
s
ed
o
p
tim
u
m
co
n
f
ig
u
r
atio
n
,
with
r
e
g
ar
d
to
r
e
n
ewa
b
le
e
n
er
g
y
an
d
d
iesel
g
en
er
atio
n
,
f
o
r
an
elec
tr
ic
v
eh
icle
ch
ar
g
e
s
tatio
n
(
E
VC
S).
T
h
e
g
o
al
was
th
at
th
e
life
cy
cle
co
s
ts
wer
e
r
ed
u
ce
d
w
h
ile
tak
in
g
e
n
v
ir
o
n
m
en
tal
p
o
llu
tio
n
in
to
ac
co
u
n
t.
Mo
u
li
et
a
l.
[
2
2
]
p
r
o
p
o
s
ed
th
e
o
p
tio
n
o
f
ch
a
r
g
in
g
E
V
o
n
s
ite
u
s
in
g
an
o
p
tim
ized
s
to
r
ag
e
p
o
wer
s
y
s
tem
PV
h
as
b
ee
n
in
v
esti
g
ated
.
A
c
o
m
p
ar
i
s
o
n
b
etwe
en
th
ese
p
r
o
f
iles
an
d
a
co
m
p
ar
is
o
n
b
et
wee
n
th
ese
p
r
o
f
iles
wer
e
ca
r
r
ied
o
u
t
to
m
in
im
ize
th
e
r
elian
ce
o
n
g
r
id
s
an
d
to
o
p
tim
ize
th
e
u
s
e
o
f
PV
p
o
wer
to
ch
a
r
g
e
t
h
e
elec
tr
icity
d
ir
ec
tly
.
Kh
a
n
et
a
l.
[
2
3
]
,
t
h
e
p
r
o
p
o
s
ed
r
ap
id
d
e
liv
er
y
n
etwo
r
k
lin
k
ed
E
V
-
C
S
m
o
d
el.
B
y
r
ed
u
cin
g
h
ar
m
o
n
ic
c
u
r
r
en
t,
th
e
p
r
o
p
o
s
ed
m
o
d
el
i
m
p
r
o
v
es
t
h
e
p
o
wer
ef
f
icien
cy
.
I
n
o
r
d
er
to
m
i
n
im
ize
th
e
ef
f
ec
t
o
f
f
ast
ch
ar
g
in
g
o
n
th
e
g
r
id
,
a
PV
p
o
w
er
s
y
s
tem
was
al
s
o
d
ev
elo
p
e
d
with
a
s
tr
ateg
y
f
o
cu
s
ed
o
n
o
p
tim
u
m
p
o
wer
f
lo
w
E
V
-
C
S.
A
g
en
etic
alg
o
r
ith
m
was
u
s
ed
b
y
o
p
tim
izin
g
b
e
n
ef
it
d
eter
m
i
n
e
d
b
y
its
n
et
cu
r
r
en
t
v
alu
e
to
m
ax
im
ize
th
e
in
s
tallatio
n
an
d
ac
tiv
ity
o
f
E
V
f
ast
ch
ar
g
in
g
[
2
4
]
.
I
n
o
r
d
er
to
i
n
cr
ea
s
e
th
e
p
r
o
f
itab
ilit
y
o
f
t
h
e
s
tatio
n
s
an
d
d
e
cr
ea
s
e
th
e
h
ig
h
g
r
id
e
n
er
g
y
r
eq
u
ir
em
e
n
ts
,
win
d
,
p
h
o
to
v
o
ltaic
an
d
s
to
r
ag
e
s
y
s
tem
s
h
av
e
b
ee
n
co
n
n
ec
ted
to
E
V
-
C
S.
T
h
e
m
ain
co
n
tr
i
b
u
tio
n
s
o
f
th
is
wo
r
k
ar
e
illu
s
tr
ated
as
f
o
llo
ws:
1
)
d
is
cu
s
s
es
th
e
im
p
ac
t
o
f
E
V
-
C
Ss
o
n
elec
tr
ic
f
ee
d
er
lo
s
s
es
b
y
f
ee
d
i
n
g
th
e
PV
,
2
)
t
h
e
m
ain
o
b
jecti
v
e
o
f
th
is
p
ap
e
r
is
to
d
etec
t
th
e
o
p
tim
al
allo
ca
tio
n
o
f
C
Ss
f
o
r
lo
s
s
r
ed
u
ctio
n
s
u
b
j
ec
ted
to
s
y
s
tem
c
o
n
s
tr
ain
ts
,
3
)
t
h
e
PS
O,
C
u
ck
o
o
s
ea
r
ch
alg
o
r
ith
m
(
C
SA
)
,
an
d
AOA
tech
n
iq
u
es
ar
e
u
s
ed
to
d
etec
t
th
e
o
p
tim
al
p
lace
m
en
t
f
o
r
th
e
C
Ss
,
4
)
th
e
p
r
o
p
o
s
ed
al
g
o
r
ith
m
is
a
p
p
li
ed
t
o
a
s
tan
d
ar
d
3
3
-
b
u
s
r
ad
ial
d
is
tr
ib
u
tio
n
s
y
s
tem
,
to
d
eter
m
in
e
o
p
tim
u
m
s
ize
an
d
lo
ca
tio
n
o
f
E
V
-
CS
,
an
d
5
)
t
h
e
re
s
u
lts
ar
e
an
aly
s
ed
an
d
c
o
m
p
ar
ed
.
T
h
is
p
ap
er
is
o
r
g
a
n
ized
;
s
ec
tio
n
2
p
r
esen
ts
th
e
m
ath
em
a
tical
f
o
r
m
u
latio
n
o
f
th
e
p
r
o
b
lem
.
T
h
e
d
ef
in
itio
n
an
d
d
escr
ip
tio
n
o
f
th
e
PS
O,
C
SA,
an
d
AOA
m
eth
o
d
s
ar
e
in
tr
o
d
u
ce
d
in
s
ec
tio
n
3
.
Sectio
n
4
p
r
esen
ts
th
e
p
r
o
ce
d
u
r
e
u
s
ed
f
o
r
s
o
lv
in
g
th
e
p
r
o
b
lem
wh
er
ea
s
s
ec
tio
n
5
in
tr
o
d
u
ce
s
n
u
m
er
ic
al
ap
p
licatio
n
s
an
d
ca
s
e
s
tu
d
ies.
T
h
e
r
esu
lts
an
d
d
is
cu
s
s
io
n
ar
e
in
tr
o
d
u
ce
d
in
s
ec
tio
n
6
,
wh
er
ea
s
s
ec
tio
n
s
ev
en
co
n
clu
d
es
th
e
p
ap
er
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2
0
8
8
-
8
694
Op
tima
l siz
in
g
a
n
d
s
itti
n
g
o
f
e
lectric v
eh
icle
ch
a
r
g
i
n
g
s
ta
tio
n
b
y
u
s
in
g
A
r
ch
imed
es …
(
Mo
h
a
med
A
.
Za
ki
)
2559
2.
P
RO
B
L
E
M
F
O
R
M
U
L
AT
I
O
N
T
h
e
p
r
o
b
lem
is
f
o
r
m
u
lated
a
s
an
o
p
tim
izatio
n
f
o
r
g
e
n
er
a
l
C
S
s
p
lace
m
en
t
co
n
s
id
er
in
g
p
r
ac
tical
f
ea
tu
r
es
o
f
C
S,
th
e
o
p
er
atio
n
,
an
d
lo
ad
r
estrictio
n
s
at
d
if
f
er
e
n
t
r
ates
o
f
th
e
lo
ad
.
T
h
e
o
p
tim
izatio
n
p
r
o
b
le
m
is
f
o
r
m
u
lated
with
a
n
o
n
-
d
if
f
er
e
n
tiab
le
o
b
jectiv
e
f
u
n
ctio
n
.
T
h
i
s
p
ap
er
p
r
o
p
o
s
es
a
s
o
lu
tio
n
alg
o
r
ith
m
d
ep
e
n
d
s
o
n
PS
O,
C
SA
an
d
AOA
tech
n
iq
u
es
an
d
aim
s
to
d
etec
t
th
e
lo
ca
t
io
n
s
wh
er
e
C
Ss
ar
e
to
b
e
in
s
talled
.
T
h
e
alg
o
r
ith
m
ca
n
d
etec
t th
e
g
l
o
b
al
o
p
tim
al
s
o
lu
tio
n
f
o
r
s
itti
n
g
th
e
C
Ss
.
2
.
1
.
O
bje
ct
iv
e
f
un
ct
io
n
T
h
e
aim
o
f
th
is
ar
ticle
is
to
f
i
n
d
th
e
b
est
lo
ca
tio
n
s
an
d
s
ize
o
f
ch
a
r
g
e
s
tatio
n
b
y
in
c
r
ea
s
e
t
h
e
s
y
s
tem
lo
s
s
es.
T
h
e
p
r
o
b
lem
o
f
o
p
tim
i
za
tio
n
is
co
n
ce
iv
e
d
as
o
n
e
p
u
r
p
o
s
e
f
u
n
ctio
n
.
T
h
e
ca
lcu
latio
n
o
f
th
e
p
o
wer
lo
s
s
in
th
e
lin
e
s
ec
tio
n
co
n
n
ec
tin
g
b
u
s
es i
an
d
i+1
b
e
f
o
r
e
i
n
teg
r
at
in
g
an
y
ch
ar
g
i
n
g
s
tatio
n
f
o
r
m
u
lated
as
(
1
)
[
2
5
]
:
P
L
o
s
s
(
i
.
i
+
1
)
=
R
i
(
P
i
2
+
Q
i
2
|
V
i
2
|
)
(
1
)
wh
er
e:
R
i
:
th
e
s
ec
tio
n
lin
e
r
esis
tan
ce
,
Ω
P
i
:
ac
tiv
e
p
o
wer
o
f
th
e
i
th
b
u
s
,
W
Q
i
:
r
ea
ctiv
e
p
o
wer
o
f
th
e
i
th
b
u
s
,
V
AR
V
i
:
v
o
ltag
e
o
f
th
e
i
th
b
u
s
,
V
T
h
e
to
tal
n
etwo
r
k
lo
s
s
es a
r
e
ca
lcu
lated
as
(
2
)
:
(
.
+
1
)
=
∑
I
i
2
R
i
=
1
(
2
)
w
h
er
e
n
is
th
e
to
tal
lin
e
s
ec
tio
n
s
in
th
e
s
y
s
tem
.
Netwo
r
k
lo
s
s
es
can
b
e
f
o
r
m
u
l
ated
d
u
e
to
th
e
ad
d
itio
n
o
f
C
Ss
as
(
3
)
[
2
5
]
:
′
(
.
+
1
)
=
∑
I
T
2
R
i
=
1
(
3
)
wh
er
e
I
T
is
th
e
cu
r
r
e
n
t to
tal
lin
e
s
ec
tio
n
,
in
clu
d
i
n
g
th
e
c
u
r
r
e
n
t c
h
ar
g
in
g
s
tatio
n
.
T
h
e
PV lo
s
s
es to
th
e
ch
ar
g
e
s
tatio
n
ar
e
r
e
p
r
esen
ted
:
′′
=
∑
(
I
cs
−
I
pv
)
2
R
i
=
1
(
4
)
wh
er
e
I
pv
is
p
h
o
to
v
o
ltaic
cu
r
r
en
t
d
eliv
er
ed
to
t
h
e
C
S o
r
th
e
u
tili
ty
.
Su
b
s
titu
tin
g
(
6
)
it is
p
r
o
p
o
s
ed
o
b
jectiv
e
f
u
n
ctio
n
ca
n
b
e
e
x
p
r
ess
ed
as
(
5
)
:
.
=
∑
(
+
−
)
2
=
1
(
5
)
2
.
2
.
Co
ns
t
ra
ints
V
o
l
t
a
g
e
co
n
s
tr
ain
ts
:
m
a
x
i
m
u
m
a
n
d
m
i
n
i
m
u
m
v
o
l
t
a
g
e
s
l
i
m
i
t
s
a
t
e
a
c
h
b
u
s
b
a
r
t
h
a
t
is
,
±
5
%
o
f
t
h
e
n
o
m
i
n
a
l
v
a
l
u
e
.
0
.
9
5
p
u
≤
V
i
≤
1
.
0
5
p
u
(
6
)
L
in
e
lo
ad
in
g
co
n
s
tr
ain
ts
: m
ax
i
m
u
m
an
d
m
in
im
u
m
ap
p
a
r
en
t
p
o
wer
lim
its
o
f
ea
ch
lin
e
.
_
≤
≤
_
(
7
)
C
h
ar
g
in
g
s
tatio
n
s
’
ca
p
ac
ity
c
o
n
s
tr
ain
ts
: m
ax
im
u
m
an
d
m
in
i
m
u
m
lim
its
o
f
ea
ch
E
V
-
C
S c
ap
ac
ity
.
CCS
k
_
m
i
n
≤
CCS
k
≤
CCS
k
_
m
ax
(
8
)
Activ
e
p
o
wer
b
alan
ce
co
n
s
tr
ai
n
ts
:
th
e
to
tal
g
en
er
ated
ac
tiv
e
p
o
wer
m
u
s
t
eq
u
al
th
e
d
e
m
an
d
ac
tiv
e
p
o
wer
p
lu
s
th
e
lo
s
s
es.
P
i
+
1
=
P
i
−
P
l
o
s
s
.
i
−
P
L
.
i
+
1
(
9
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
25
57
–
25
69
2560
R
ea
ctiv
e
p
o
wer
b
alan
ce
co
n
s
tr
ain
ts
: th
e
to
tal
g
en
er
ated
r
ea
ctiv
e
p
o
wer
m
u
s
t e
q
u
al
th
e
d
em
an
d
r
ea
ctiv
e
p
o
wer
p
lu
s
th
e
lo
s
s
es.
Q
i
+
1
=
Q
i
−
Q
l
o
s
s
.
i
−
Q
L
.
i
+
1
(
1
0
)
T
h
e
(
9
)
an
d
(
1
0
)
ca
n
b
e
m
o
d
elled
th
r
o
u
g
h
th
e
f
o
llo
win
g
m
at
h
em
atica
l r
elatio
n
s
[
25
].
P
i
+
1
=
P
i
−
P
l
o
s
s
.
i
−
P
L
.
i
+
1
=
P
i
−
R
i
|
V
i
2
|
(
P
i
2
+
(
Q
i
+
Y
i
|
V
i
2
|
2
)
2
)
−
P
L
.
i
+
1
(
1
1
)
+
1
=
−
.
−
.
+
1
=
−
|
2
|
(
2
+
(
+
1
|
2
|
2
)
2
)
−
1
|
2
|
−
2
|
+
1
2
|
−
.
+
1
(
1
2
)
|
+
1
2
|
=
|
2
|
+
2
+
2
|
2
|
(
2
+
2
)
−
2
(
+
)
(
1
3
)
w
h
er
e
:
,
:
m
in
im
u
m
an
d
m
ax
im
u
m
b
u
s
v
o
ltag
es,
:
ca
p
ac
ity
o
f
th
e
ℎ
PV c
h
ar
g
in
g
s
tatio
n
,
_
:
m
in
im
u
m
ca
p
ac
ity
o
f
t
h
e
ℎ
PV
ch
ar
g
in
g
s
tatio
n
,
_
:
m
ax
im
u
m
ca
p
ac
ity
o
f
th
e
ℎ
PV c
h
ar
g
in
g
s
tatio
n
,
:
ap
p
ar
en
t
p
o
wer
in
th
e
lin
e
co
n
n
ec
tin
g
b
etwe
en
b
u
s
an
d
b
u
s
,
_
:
m
in
im
u
m
ap
p
ar
en
t
p
o
wer
o
f
t
h
e
lin
e
,
_
:
m
ax
im
u
m
a
p
p
ar
en
t
p
o
wer
o
f
t
h
e
lin
e
,
,
:
r
ea
l a
n
d
r
ea
ctiv
e
p
o
wer
f
lo
w
o
u
t o
f
th
e
ℎ
b
u
s
,
.
+
1
,
+
1
:
lo
ad
r
ea
l a
n
d
r
ea
ctiv
e
p
o
wer
a
t b
u
s
+
1
,
,
:
se
c
ti
on li
ne
re
sis
tanc
e
a
n
d re
a
c
t
a
nc
e
re
spe
c
ti
ve
ly
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
3
.
1
.
P
a
rt
icle
s
wa
rm
o
pti
m
iza
t
io
n
a
lg
o
rit
hm
T
o
d
eter
m
in
e
E
V
-
C
S
lo
ca
tio
n
an
d
s
izin
g
,
PS
O
alg
o
r
ith
m
[
26
]
,
[
27
]
is
ap
p
lied
t
o
o
p
t
im
ize
th
e
co
n
s
tr
ain
ed
o
b
jectiv
e
f
u
n
ctio
n
in
(
1
4
)
f
o
r
th
e
ca
s
e
s
tu
d
y
.
T
h
e
n
u
m
b
er
o
f
v
ar
iab
les
in
th
e
o
p
tim
izatio
n
p
r
o
b
lem
is
2
.
T
h
u
s
,
ea
ch
p
a
r
ticle
o
f
s
war
m
s
ea
r
ch
es
f
o
r
o
p
tim
al
r
esu
lt
in
2
-
d
im
en
s
io
n
al
s
ea
r
ch
s
p
ac
e.
C
an
b
e
r
ep
r
esen
ted
th
e
p
ar
ticle
as:
=
(
,
)
(
1
4
)
w
h
er
e,
is
th
e
E
V
-
C
S lo
ca
tio
n
an
d
is
th
e
E
V
-
C
S si
ze
.
T
h
e
f
lo
wch
ar
t
o
f
o
p
tim
izatio
n
tech
n
iq
u
e
u
s
in
g
PS
O
s
h
o
wn
in
Fig
u
r
e1
.
3
.
2
.
Cuck
o
o
s
ea
rc
h a
lg
o
rit
hm
C
u
ck
o
o
s
ea
r
ch
(
C
S)
is
an
o
p
tim
izatio
n
alg
o
r
ith
m
wh
ich
in
v
en
ted
b
y
Yan
g
an
d
Deb
[
2
8
]
.
C
S
is
d
r
iv
en
b
y
th
e
ag
g
r
ess
iv
e
p
ar
asit
is
m
b
eh
av
io
r
o
f
c
u
ck
o
o
s
p
ec
ies
th
at
lay
th
eir
eg
g
s
with
f
ascin
atin
g
ab
ilit
ies
in
th
e
n
ests
o
f
o
th
er
h
o
s
t
b
ir
d
s
,
s
u
ch
as
th
e
s
elec
tio
n
o
f
n
ewly
s
p
awn
ed
n
ests
an
d
th
e
r
em
o
v
al
o
f
h
o
s
t
b
ir
d
eg
g
s
th
at
in
cr
ea
s
e
th
e
lik
elih
o
o
d
o
f
h
atch
in
g
th
eir
eg
g
s
.
E
g
g
s
ar
e
tak
en
ca
r
e
o
f
b
y
th
e
h
o
s
t
b
ir
d
,
ass
u
m
in
g
th
at
th
e
eg
g
s
ar
e
th
eir
o
wn
.
I
f
a
h
o
s
t
b
ir
d
f
in
d
s
f
o
r
eig
n
eg
g
s
in
its
n
e
s
t,
it
eith
er
leav
es
th
e
n
est
an
d
o
th
er
wis
e
b
u
ild
s
a
n
ew
n
est
o
r
m
er
ely
th
r
o
ws
a
way
th
e
f
o
r
eig
n
eg
g
s
.
T
h
is
m
eth
o
d
is
b
ased
o
n
th
r
ee
b
a
s
ic
r
u
les
[
2
9
]
.
I
n
a
r
an
d
o
m
l
y
s
elec
ted
n
est,
ea
ch
cu
ck
o
o
lay
s
o
n
e
eg
g
(
s
o
lu
tio
n
)
at
a
tim
e;
th
e
b
est
o
p
tio
n
(
n
est)
with
th
e
b
est
q
u
ality
eg
g
s
will
b
e
tr
an
s
p
o
r
te
d
to
th
e
n
ex
t
g
en
er
atio
n
.
T
h
e
n
u
m
b
er
o
f
h
o
s
t
n
ests
av
ailab
le
is
s
e
t,
an
d
th
e
eg
g
laid
b
y
a
c
u
ck
o
o
is
f
o
u
n
d
b
y
t
h
e
h
o
s
t
b
ir
d
with
a
p
r
o
b
a
b
ilit
y
p
a
∈
[
0
,
1
]
o
f
th
e
h
o
s
t
b
ir
d
will
eith
er
th
r
o
w
awa
y
th
e
alien
eg
g
o
r
lea
v
e
th
e
n
est
an
d
estab
lis
h
a
n
ew
n
est.
A
cu
ck
o
o
e
g
g
r
e
p
r
esen
ts
a
n
ew
s
o
l
u
tio
n
to
d
ef
in
e
t
h
is
alg
o
r
ith
m
f
o
r
s
im
p
licity
,
wh
ile
ea
ch
h
o
s
t
b
ir
d
eg
g
in
a
n
est
r
ep
r
esen
ts
a
s
o
lu
tio
n
.
T
h
e
g
o
a
l
is
to
s
u
b
s
t
itu
te
th
e
latest
an
d
e
v
en
b
etter
alter
n
ati
v
es
f
o
r
th
e
wo
r
s
t
s
o
lu
tio
n
i
n
t
h
e
n
ests
.
T
h
e
f
lo
wc
h
ar
t
o
f
o
p
t
im
izatio
n
tech
n
iq
u
e
u
s
in
g
CS
s
h
o
wn
in
Fig
u
r
e2
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2
0
8
8
-
8
694
Op
tima
l siz
in
g
a
n
d
s
itti
n
g
o
f
e
lectric v
eh
icle
ch
a
r
g
i
n
g
s
ta
tio
n
b
y
u
s
in
g
A
r
ch
imed
es …
(
Mo
h
a
med
A
.
Za
ki
)
2561
Fig
u
r
e
1
.
Flo
wch
ar
t
o
f
PS
O
alg
o
r
ith
m
Fig
u
r
e
2
.
Flo
wch
ar
t
o
f
C
S a
lg
o
r
ith
m
3
.
3
.
Arc
him
edes
o
ptim
iza
t
io
n a
lg
o
rit
hm
AOA
is
a
p
o
p
u
l
a
t
i
o
n
-
b
a
s
e
d
a
l
g
o
r
i
t
h
m
.
I
n
t
h
e
s
u
g
g
e
s
t
e
d
s
o
l
u
t
io
n
,
t
h
e
s
u
b
m
e
r
g
e
d
o
b
j
e
c
t
s
a
r
e
th
e
c
i
t
i
z
e
n
s
o
f
t
h
e
p
o
p
u
l
a
t
i
o
n
.
A
OA
a
ls
o
b
e
g
i
n
s
t
h
e
s
e
a
r
c
h
p
r
o
c
ess
w
i
t
h
t
h
e
i
n
it
i
al
p
o
p
u
l
a
t
i
o
n
o
f
o
b
j
e
c
ts
(
c
a
n
d
i
d
at
e
s
o
l
u
t
i
o
n
s
)
w
it
h
r
a
n
d
o
m
v
o
l
u
m
e
s
,
d
e
n
s
it
i
es
a
n
d
a
c
c
el
e
r
a
t
i
o
n
s
,
as
o
t
h
e
r
p
o
p
u
l
a
ti
o
n
-
b
a
s
e
d
m
e
t
a
h
e
u
r
is
ti
c
a
l
g
o
r
i
t
h
m
s
.
E
ac
h
o
b
j
e
c
t
i
s
al
s
o
i
n
i
t
i
al
i
z
e
d
at
t
h
is
s
t
a
g
e
b
y
i
ts
r
a
n
d
o
m
f
l
u
i
d
l
o
c
a
t
i
o
n
.
AO
A
f
u
n
c
t
i
o
n
s
i
n
i
t
e
r
a
ti
o
n
s
a
f
t
e
r
a
s
s
es
s
i
n
g
t
h
e
f
it
n
e
s
s
o
f
th
e
o
r
i
g
i
n
a
l
p
o
p
u
l
a
ti
o
n
b
e
f
o
r
e
it
s
at
is
f
i
es
t
h
e
t
e
r
m
i
n
a
ti
o
n
c
r
i
ter
i
o
n
.
A
O
A
c
h
a
n
g
e
s
t
h
e
d
e
n
s
i
t
y
a
n
d
v
o
l
u
m
e
o
f
e
v
e
r
y
o
b
j
e
c
t
i
n
e
v
e
r
y
i
t
e
r
at
i
o
n
.
O
b
je
c
t
a
c
c
el
e
r
a
t
i
o
n
is
m
o
d
i
f
i
e
d
d
ep
e
n
d
i
n
g
o
n
t
h
e
s
t
a
t
e
o
f
i
t
s
c
o
l
li
s
i
o
n
w
i
t
h
s
o
m
e
o
t
h
er
a
d
j
a
c
e
n
t
o
b
j
e
c
t
.
T
h
e
u
p
d
a
t
e
d
d
e
n
s
i
t
y
,
v
o
l
u
m
e
,
a
c
c
el
e
r
a
t
i
o
n
d
e
t
e
r
m
i
n
e
s
t
h
e
n
e
w
p
o
s
i
t
i
o
n
o
f
a
n
o
b
j
e
c
t
.
F
o
ll
o
w
i
n
g
is
t
h
e
d
e
t
a
il
e
d
m
at
h
e
m
a
t
i
c
a
l
e
x
p
r
e
s
s
i
o
n
o
f
A
O
A
s
te
p
s
[
3
0
]
.
T
h
e
A
O
A
a
l
g
o
r
i
t
h
m
is
p
r
o
v
i
d
e
d
i
n
t
h
e
m
a
t
h
e
m
a
t
i
ca
l
f
o
r
m
u
l
at
i
o
n
.
I
n
t
h
e
o
r
y
,
A
O
A
is
a
g
l
o
b
a
l
o
p
tim
i
z
a
t
i
o
n
al
g
o
r
i
t
h
m
,
w
h
i
c
h
i
n
v
o
l
v
es
b
o
t
h
d
i
s
c
o
v
e
r
y
a
n
d
o
p
e
r
a
t
i
n
g
p
r
o
c
ess
e
s
.
Al
g
o
r
i
t
h
m
2
p
r
e
s
e
n
ts
t
h
e
p
s
e
u
d
o
-
c
o
d
e
o
f
t
h
e
p
r
o
p
o
s
ed
a
l
g
o
r
i
t
h
m
;
i
n
c
l
u
d
i
n
g
p
o
p
u
l
a
t
i
o
n
i
n
i
t
ia
l
i
z
at
i
o
n
,
p
o
p
u
l
a
ti
o
n
e
v
al
u
a
t
i
o
n
,
a
n
d
u
p
d
a
ti
n
g
p
a
r
a
m
e
t
er
s
.
M
at
h
e
m
a
t
ic
a
l
l
y
,
s
t
e
p
s
o
f
t
h
e
p
r
o
p
o
s
e
d
A
O
A
a
r
e
d
e
t
a
i
l
e
d
as
:
S
t
e
p
1
:
i
n
it
i
al
i
z
at
i
o
n
,
i
n
i
ti
a
l
iz
e
th
e
p
o
s
i
t
i
o
n
s
o
f
al
l
o
b
j
e
ct
s
u
s
i
n
g
(
1
5
)
.
Q
i
=
lb
i
+
r
a
n
d
∗
(
ub
i
−
lb
i
)
;
i
=
1
,
2
,
3
,
…
,
N
(
1
5
)
wh
er
e
Q
i
is
th
e
ith
o
b
ject
in
a
p
o
p
u
latio
n
o
f
N
o
b
jects.
lb
i
,
an
d
ub
i
ar
e
th
e
lo
wer
an
d
u
p
p
er
b
o
u
n
d
s
o
f
th
e
s
ea
r
ch
-
s
p
ac
e,
r
esp
ec
tiv
ely
.
I
n
i
tialize
v
o
lu
m
e
(
vol
)
an
d
d
en
s
ity
(
de
n
)
f
o
r
ea
c
h
ith
o
b
ject
u
s
in
g
(
1
6
)
:
=
=
(
1
6
)
wh
er
e
r
an
d
is
a
D
d
im
en
s
io
n
al
v
ec
to
r
r
an
d
o
m
ly
g
en
er
ate
s
n
u
m
b
er
b
etwe
en
[
0
,
1
]
.
An
d
f
in
ally
,
i
n
itialize
ac
ce
ler
atio
n
(
a
c
c
)
o
f
ith
o
b
ject
u
s
i
n
g
(
1
7
)
:
=
+
∗
(
−
)
(
1
7
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
25
57
–
25
69
2562
I
n
th
is
s
tep
,
ev
alu
ate
in
itial p
o
p
u
latio
n
an
d
s
elec
t th
e
o
b
ject
with
th
e
b
est f
itn
ess
v
alu
e.
Ass
ig
n
,
,
,
,
.
S
t
e
p
2
:
u
p
d
a
t
e
d
e
n
s
i
t
i
e
s
,
v
o
l
u
m
e
s
t
h
e
d
e
n
s
i
t
y
a
n
d
v
o
l
u
m
e
o
f
o
b
j
e
c
t
f
o
r
t
h
e
i
t
e
r
a
t
i
o
n
+
1
i
s
u
p
d
a
t
e
d
u
s
i
n
g
(
1
8
)
:
+
1
=
+
∗
(
−
+
1
=
+
∗
(
−
)
(
1
8
)
wh
er
e
an
d
ar
e
th
e
v
o
lu
m
e
a
n
d
d
en
s
ity
ass
o
ciate
d
with
th
e
b
est
o
b
ject
f
o
u
n
d
s
o
f
ar
,
a
n
d
r
an
d
is
u
n
if
o
r
m
ly
d
is
tr
ib
u
ted
r
a
n
d
o
m
n
u
m
b
er
.
Step
3
:
t
r
an
s
f
er
o
p
er
ato
r
an
d
d
en
s
ity
f
ac
to
r
in
th
e
b
eg
in
n
in
g
,
co
llis
io
n
b
etwe
en
o
b
jects
o
cc
u
r
s
an
d
af
ter
a
p
er
io
d
o
f
tim
e,
th
e
o
b
je
c
ts
tr
y
to
r
ea
ch
at
eq
u
ilib
r
iu
m
s
tate.
T
h
is
i
s
im
p
lem
en
ted
in
AOA
with
th
e
h
elp
o
f
tr
an
s
f
er
o
p
er
at
o
r
wh
ich
tr
a
n
s
f
o
r
m
s
s
ea
r
ch
f
r
o
m
ex
p
lo
r
ati
o
n
to
e
x
p
lo
itatio
n
,
d
ef
in
ed
u
s
in
g
(
1
9
)
:
=
(
−
)
(
1
9
)
wh
er
e
tr
an
s
f
e
r
in
cr
ea
s
es
g
r
ad
u
ally
with
tim
e
u
n
til
r
ea
ch
i
n
g
1
.
Her
e
an
d
ar
e
iter
atio
n
n
u
m
b
er
a
n
d
m
ax
im
u
m
iter
atio
n
s
,
r
esp
ec
tiv
ely
.
Similar
ly
,
d
en
s
ity
d
ec
r
ea
s
in
g
f
ac
to
r
also
ass
is
ts
AO
A
o
n
g
lo
b
al
to
lo
ca
l
s
ea
r
ch
.
I
t d
ec
r
ea
s
es with
tim
e
u
s
in
g
(
2
0
)
:
d
t
+
1
=
e
xp
(
t
m
ax
−
t
t
m
ax
)
−
(
t
t
m
ax
)
(
2
0
)
wh
er
e
+
1
d
ec
r
ea
s
es
o
v
er
tim
e
an
d
en
a
b
les
co
n
v
er
g
en
ce
i
n
th
e
p
r
o
m
is
in
g
ar
ea
th
a
t
h
as
alr
ea
d
y
b
ee
n
estab
lis
h
ed
.
No
te
th
at
p
r
o
p
e
r
h
an
d
lin
g
o
f
th
is
v
ar
iab
le
will
en
s
u
r
e
b
alan
ce
b
etwe
en
ex
p
lo
r
atio
n
an
d
ex
p
lo
itatio
n
in
AOA.
Step
4
.
1
:
ex
p
lo
r
atio
n
ph
ase
(
co
llis
io
n
b
etwe
en
o
b
jects
o
cc
u
r
s
)
I
f
≤
0
.
5
,
co
llis
io
n
b
etwe
en
o
b
jects o
cc
u
r
s
,
s
elec
t a
r
an
d
o
m
m
ater
ial
(
)
an
d
u
p
d
ate
o
b
jec
t’
s
ac
ce
ler
atio
n
f
o
r
iter
atio
n
+
1
u
s
in
g
(
2
1
)
:
+
1
=
+
∗
+
1
∗
+
1
(
2
1
)
wh
er
e
,
,
an
d
ar
e
d
en
s
ity
,
v
o
lu
m
e,
an
d
ac
ce
le
r
atio
n
o
f
o
b
j
ec
t
.
W
h
er
e
as
,
an
d
ar
e
th
e
ac
ce
ler
atio
n
,
d
en
s
ity
,
an
d
v
o
l
u
m
e
o
f
r
an
d
o
m
m
ate
r
ial.
I
t
is
im
p
o
r
tan
t
to
m
en
tio
n
th
at
≤
0
.
5
en
s
u
r
es
ex
p
lo
r
ati
o
n
d
u
r
in
g
o
n
e
th
ir
d
o
f
iter
atio
n
s
.
Ap
p
ly
in
g
v
alu
e
o
th
e
r
th
an
0
.
5
will
ch
an
g
e
ex
p
l
o
r
atio
n
-
ex
p
lo
itatio
n
b
e
h
av
io
r
.
Step
4
.
2
:
ex
p
lo
itatio
n
p
h
ase
(
n
o
co
llis
io
n
b
etwe
en
o
b
jects).
If
>
0
.
5
,
th
er
e
is
n
o
co
llis
io
n
b
etwe
en
o
b
jects,
u
p
d
ate
o
b
ject
’
s
ac
ce
ler
atio
n
f
o
r
iter
atio
n
+
1
u
s
in
g
(
2
2
)
:
+
1
=
+
∗
+
1
∗
+
1
(
2
2
)
wh
er
e
is
th
e
ac
ce
ler
atio
n
o
f
th
e
b
est o
b
ject.
Step
4
.
3
:
n
o
r
m
alize
ac
ce
ler
ati
o
n
,
n
o
r
m
alize
ac
ce
ler
atio
n
to
ca
lcu
late
th
e
p
er
ce
n
tag
e
o
f
ch
an
g
e
u
s
in
g
(
2
3
)
:
−
+
1
=
∗
+
1
−
m
i
n
(
)
m
ax
(
)
−
m
i
n
(
)
+
(
23
)
wh
er
e
an
d
ar
e
th
e
r
an
g
e
o
f
n
o
r
m
aliza
tio
n
an
d
s
et
to
0
.
9
an
d
0
.
1
,
r
esp
ec
tiv
ely
.
T
h
e
−
+
1
d
eter
m
in
es
th
e
p
er
ce
n
tag
e
o
f
s
tep
th
at
e
ac
h
ag
e
n
t
will
ch
a
n
g
e.
I
f
th
e
o
b
ject
is
f
ar
f
r
o
m
b
ein
g
g
l
o
b
ally
o
p
tim
al,
t
h
e
ac
ce
ler
atio
n
v
alu
e
wo
u
ld
b
e
h
i
g
h
—
m
ea
n
in
g
t
h
at
th
e
o
b
ject
will
b
e
in
th
e
d
is
co
v
er
y
p
r
o
ce
s
s
;
o
th
er
wis
e,
it
wil
l
b
e
in
th
e
ex
p
l
o
itatio
n
p
h
ase.
T
h
is
s
h
o
ws
h
o
w
th
e
h
u
n
t
i
s
s
h
if
tin
g
f
r
o
m
s
ca
n
n
in
g
to
m
an
ip
u
latio
n
.
T
h
e
ac
ce
ler
atio
n
f
ac
to
r
u
s
u
ally
s
tar
ts
with
h
ig
h
v
alu
e
an
d
d
ec
r
ea
s
es with
t
im
e.
T
h
is
h
elp
s
q
u
est
en
g
in
ee
r
s
tr
av
el
to
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2
0
8
8
-
8
694
Op
tima
l siz
in
g
a
n
d
s
itti
n
g
o
f
e
lectric v
eh
icle
ch
a
r
g
i
n
g
s
ta
tio
n
b
y
u
s
in
g
A
r
ch
imed
es …
(
Mo
h
a
med
A
.
Za
ki
)
2563
an
d
f
r
o
m
th
e
r
ig
h
t
g
lo
b
al
s
o
lu
tio
n
T
h
ey
ar
e
tu
r
n
in
g
awa
y
f
r
o
m
lo
ca
l
o
p
tio
n
s
co
n
cu
r
r
en
t
ly
.
Ho
wev
er
,
it
is
wo
r
th
n
o
tin
g
th
at
ce
r
tain
s
ea
r
ch
ag
en
ts
m
ay
r
em
ain
th
at
n
e
ed
m
o
r
e
tim
e
th
an
a
v
er
ag
e
to
r
em
ain
in
a
s
ea
r
ch
p
o
in
t.
AOA
th
en
h
its
th
e
b
alan
ce
.
Step
5
:
u
p
d
ate
p
o
s
itio
n
I
f
T
F
≤
0
.
5
(
ex
p
l
o
r
atio
n
p
h
ase)
,
th
e
ℎ
o
b
ject’
s
p
o
s
itio
n
f
o
r
n
ex
t
i
ter
atio
n
+
1
u
s
in
g
(
2
4
)
+
1
=
+
1
∗
∗
−
+
1
∗
∗
(
−
)
(
2
4
)
wh
er
e
1
is
co
n
s
tan
t
eq
u
als
to
2
.
Oth
er
wis
e,
if
>
0
.
5
(
ex
p
lo
itati
o
n
p
h
ase)
,
th
e
o
b
jects
u
p
d
ate
th
eir
p
o
s
itio
n
s
u
s
in
g
(
2
5
)
.
+
1
=
+
∗
2
∗
∗
−
+
1
∗
∗
(
∗
−
)
(
2
5
)
wh
er
e
2
is
a
co
n
s
tan
t
eq
u
al
to
6
.
in
cr
ea
s
es
with
tim
e
an
d
it
is
d
ir
ec
tly
p
r
o
p
o
r
tio
n
al
to
tr
an
s
f
er
o
p
er
ato
r
an
d
it
is
d
ef
in
ed
u
s
in
g
=
3
×
.
in
cr
ea
s
es
with
tim
e
in
r
an
g
e
[
3
∗
0
.
3
,
1
]
an
d
tak
es
a
ce
r
tain
p
er
ce
n
tag
e
f
r
o
m
th
e
b
est p
o
s
itio
n
,
in
itially
.
I
t b
e
g
in
s
with
a
s
m
all
p
er
ce
n
ta
g
e
as th
ese
lead
to
a
lar
g
e
g
ap
b
etwe
en
th
e
b
est
p
o
s
itio
n
an
d
t
h
e
c
u
r
r
en
t
p
o
s
itio
n
,
s
o
th
e
r
an
d
o
m
walk
s
tep
-
s
ize
wo
u
ld
b
e
h
ig
h
.
T
h
is
p
r
o
p
o
r
tio
n
in
c
r
ea
s
es
p
r
o
g
r
ess
iv
ely
to
r
ed
u
ce
t
h
e
g
a
p
b
etwe
en
th
e
o
p
tim
al
lo
ca
tio
n
an
d
th
e
c
u
r
r
e
n
t
p
o
s
itio
n
as
t
h
e
h
u
n
t
p
r
o
g
r
ess
es.
T
h
is
lead
s
to
ac
h
iev
in
g
an
ap
p
r
o
p
r
iate
b
ala
n
ce
b
etwe
en
ex
p
lo
r
atio
n
an
d
ex
p
lo
itatio
n
.
is
th
e
f
lag
to
ch
an
g
e
th
e
d
ir
ec
tio
n
o
f
m
o
tio
n
u
s
in
g
(
2
6
)
:
=
{
+
1
≤
0
.
5
−
1
>
0
.
5
(
2
6
)
wh
er
e
=
2
×
−
4
.
Step
6
:
ev
alu
atio
n
,
ev
alu
ate
e
ac
h
o
b
ject
u
s
in
g
o
b
jectiv
e
f
u
n
ctio
n
f
an
d
r
em
em
b
e
r
th
e
b
e
s
t
s
o
lu
tio
n
f
o
u
n
d
s
o
f
ar
.
Ass
ig
n
,
,
,
an
d
.
4.
O
P
T
I
M
I
Z
AT
I
O
N
T
E
CH
NI
Q
UE
T
h
e
p
r
o
b
lem
is
s
o
lv
ed
f
o
r
th
e
b
ase
ca
s
e
an
d
th
en
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
i
s
ap
p
lied
to
d
etec
t
th
e
o
p
tim
al
lo
ca
tio
n
a
n
d
s
ize
o
f
t
h
e
E
V
-
C
SS
.
T
h
e
p
r
o
ce
d
u
r
e
f
o
r
s
o
lv
in
g
t
h
e
p
r
o
b
lem
ca
n
b
e
s
u
m
m
ar
ized
as:
Step
1
: e
n
ter
in
p
u
t d
ata:
lin
e
d
ata,
b
u
s
d
ata.
Step
2
:
r
u
n
t
h
e
lo
a
d
f
lo
w
p
r
o
g
r
am
,
f
o
r
th
e
b
ase
ca
s
e,
to
d
e
ter
m
in
e
th
e
b
u
s
v
o
ltag
e
p
r
o
f
ile,
b
r
an
ch
es
cu
r
r
en
t,
an
d
n
etwo
r
k
p
o
wer
lo
s
s
es.
Step
3
: in
itializatio
n
o
f
o
p
tim
izatio
n
alg
o
r
is
m
.
Set th
e
iter
ati
o
n
co
u
n
ter
k
=
0
.
Step
4
: r
u
n
p
o
wer
f
lo
w
to
d
ete
r
m
in
e
th
e
o
b
jectiv
e
f
u
n
ctio
n
.
Step
5
:
co
m
p
u
te
th
e
C
Ss
s
ize
an
d
lo
ca
tio
n
ac
co
r
d
i
n
g
to
iter
a
tiv
e
s
tep
s
.
Step
6
: r
eb
ait
f
o
r
K=
k
+1
a
n
d
g
o
to
s
tep
4
.
Step
7
: c
o
m
p
ar
is
o
n
b
etwe
en
th
e
n
ew
p
o
wer
lo
s
s
an
d
th
e
b
as
e
ca
s
e
lo
s
s
.
I
f
th
e
d
if
f
er
en
ce
is
less
o
r
eq
u
al
to
th
e
to
ler
an
ce
er
r
o
r
.
T
h
en
s
to
p
a
n
d
r
ec
o
r
d
t
h
e
r
esu
lts
.
Oth
er
wis
e,
g
o
to
s
tep
3
5.
CASE
S
T
UD
Y
5
.
1
.
Sy
s
t
em
da
t
a
T
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
s
ar
e
u
s
ed
o
n
a
3
3
-
b
u
s
d
is
tr
ib
u
tio
n
n
etwo
r
k
with
s
u
b
s
tatio
n
v
o
lta
g
e
o
f
1
2
.
6
6
KV,
b
ase
1
0
0
MV
A
an
d
to
ta
l
lo
ad
o
f
3
.
7
MW
an
d
2
.
3
M
VAR
[
31
]
.
An
d
it
h
as
b
ee
n
im
p
lem
en
ted
u
s
in
g
MA
T
L
AB
en
v
ir
o
n
m
en
t
to
r
u
n
th
e
lo
ad
f
l
o
w,
ca
lcu
late
p
o
wer
lo
s
s
es,
v
o
ltag
e
s
tab
ilit
y
i
n
d
ex
an
d
id
en
tif
y
th
e
o
p
tim
al
s
ize
an
d
lo
ca
tio
n
o
f
E
V
-
C
S
u
n
it.
Fig
u
r
e
3
s
h
o
ws
th
e
m
o
d
if
ied
s
y
s
tem
with
d
if
f
er
en
t
lo
a
d
ty
p
es
co
n
n
ec
ted
t
o
ea
ch
b
u
s
.
5
.
2
.
L
o
a
d m
o
delin
g
a
nd
da
ily
lo
a
d c
urv
es
L
o
ad
s
o
f
th
e
d
is
tr
ib
u
tio
n
n
etw
o
r
k
p
r
esen
ts
d
is
tin
ct
b
eh
av
io
r
s
f
o
r
v
ar
iatio
n
s
in
g
r
id
v
o
ltag
e.
Fo
r
e.
g
.
,
th
e
v
o
ltag
e
m
a
g
n
itu
d
e
is
af
f
ec
ted
s
tr
o
n
g
ly
b
y
th
e
r
ea
l a
n
d
r
e
ac
tiv
e
p
o
wer
u
s
ag
e
o
f
f
lu
o
r
esc
en
t la
m
p
s
,
wh
er
ea
s
p
er
s
o
n
al
co
m
p
u
ter
s
ar
e
less
s
u
s
ce
p
tib
le
to
v
o
ltag
e
v
ar
iatio
n
s
[
32
]
.
T
h
e
ac
tu
al
lo
ad
o
f
t
h
e
d
ev
ice
d
o
es
n
o
t
co
n
s
is
t
o
f
co
n
s
tan
t
p
o
wer
,
co
n
s
tan
t
cu
r
r
en
t
o
r
c
o
n
s
tan
t
f
o
r
m
o
f
im
p
ed
a
n
ce
b
u
t
is
f
u
n
d
a
m
en
tally
co
m
p
lex
.
Dif
f
er
en
t
g
r
o
u
p
s
an
d
ty
p
es
o
f
lo
ad
s
co
u
ld
b
e
p
r
esen
t
in
d
el
iv
er
y
s
y
s
tem
s
,
s
u
ch
as
r
esid
e
n
tial
in
d
u
s
tr
ial
an
d
co
m
m
e
r
cial
lo
ad
s
.
I
n
th
is
ar
tic
le,
th
e
s
tu
d
y
tak
es
in
to
ac
co
u
n
t
th
e
s
tatic
lo
ad
m
o
d
el.
C
an
e
x
p
r
ess
th
e
r
ea
l
an
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
25
57
–
25
69
2564
r
ea
ctiv
e
p
o
wer
s
tatic
lo
ad
m
o
d
el
in
p
o
ly
n
o
m
ial
f
o
r
m
.
T
h
e
P
o
ly
n
o
m
ial
L
o
ad
Mo
d
el
C
h
ar
a
cter
is
tic
[
33
]
ca
n
b
e
g
iv
en
as
:
=
0
[
(
0
)
2
+
(
0
)
+
]
(
2
7
)
=
0
[
′
(
0
)
2
+
′
(
0
)
+
′
]
(
2
8
)
w
h
er
e
co
n
s
tan
ts
an
d
′
ar
e
f
r
a
ctio
n
s
;
an
d
th
e
s
u
b
s
cr
ip
ts
,
an
d
s
tan
d
f
o
r
co
n
s
tan
t
im
p
e
d
an
c
e,
co
n
s
tan
t
cu
r
r
en
t,
an
d
co
n
s
tan
t
p
o
wer
co
n
tr
i
b
u
tio
n
s
,
r
esp
ec
tiv
ely
.
+
+
=
1
an
d
′
+
′
+
′
=
1
.
T
h
e
v
alu
es
o
f
th
e
r
ea
l
an
d
r
ea
ctiv
e
co
n
s
tan
ts
u
s
ed
in
th
e
p
r
esen
t
wo
r
k
f
o
r
in
d
u
s
tr
ial,
r
esid
en
ti
al,
an
d
co
m
m
er
cial
lo
ad
s
ar
e
g
iv
en
in
T
ab
le
1
[
34
]
.
A
ty
p
ical
d
aily
lo
ad
cu
r
v
e
s
o
f
in
d
u
s
tr
ial,
r
esid
en
tial,
an
d
co
m
m
er
cial
lo
ad
ty
p
es
ar
e
g
iv
e
n
i
n
Fig
u
r
es
4
,
5
an
d
6
r
esp
ec
tiv
ely
[
35
].
Fig
u
r
e
3
.
T
h
e
m
o
d
if
ied
3
3
b
u
s
r
ad
ial
d
is
tr
ib
u
tio
n
n
etwo
r
k
s
T
ab
le
1
.
T
h
e
co
m
p
o
s
itio
n
v
alu
es o
f
d
if
f
er
e
n
t lo
ad
s
C
o
m
p
o
si
t
i
o
n
A
c
t
i
v
e
P
o
w
e
r
R
e
si
d
e
n
t
i
a
l
0
.
2
4
0
.
6
2
0
.
1
3
C
o
mm
e
r
c
i
a
l
0
.
1
6
0
.
8
0
0
.
0
4
I
n
d
u
st
r
i
a
l
-
0
.
0
7
0
.
2
4
0
.
8
3
R
e
a
c
t
i
v
e
P
o
w
e
r
R
e
si
d
e
n
t
i
a
l
2
.
4
4
-
1
.
9
4
0
.
5
0
C
o
mm
e
r
c
i
a
l
3
.
2
6
-
3
.
1
0
0
.
8
4
I
n
d
u
st
r
i
a
l
1
.
0
0
0
.
0
0
0
.
0
0
Fig
u
r
e
4.
I
n
d
u
s
tr
ial
lo
a
d
cu
r
v
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2
0
8
8
-
8
694
Op
tima
l siz
in
g
a
n
d
s
itti
n
g
o
f
e
lectric v
eh
icle
ch
a
r
g
i
n
g
s
ta
tio
n
b
y
u
s
in
g
A
r
ch
imed
es …
(
Mo
h
a
med
A
.
Za
ki
)
2565
Fig
u
r
e
5.
R
esid
en
tial lo
ad
cu
r
v
e
Fig
u
r
e
6.
C
o
m
m
e
r
cial
lo
ad
cu
r
v
e
5
.
3
.
Da
t
a
o
f
P
V
s
y
s
t
em
T
h
e
f
o
llo
win
g
d
ata
o
f
PV
s
y
s
tem
in
T
a
b
le
2
.
I
t
is
in
clu
d
in
g
t
h
e
ty
p
e
o
f
PV
m
o
d
u
les,
th
e
p
o
wer
,
s
ize
o
f
m
o
d
u
les
.
T
h
e
c
o
s
t f
r
o
m
E
N
FS
OL
A
R
web
s
ite
(
co
s
t ta
k
en
at
5
/2
/2
0
2
1
)
[
36
]
.
T
ab
le
2.
T
y
p
e
o
f
PV
m
o
d
u
les
,
p
r
ice
o
f
item
s
an
d
th
e
s
ize
o
f
PV
m
o
d
u
le
Ty
p
e
P
o
w
e
r
(w)
A
t
I
r
r
.
Le
n
g
t
h
(
mm
)
W
i
d
t
h
(
mm
)
A
r
e
a
(
m
2
)
P
o
w
e
r
(
M
W
)
N
o
.
o
f
M
o
d
u
l
e
s
P
r
i
c
e
(
L.
E/
i
t
e
m)
LE
(
mi
l
l
i
o
n
)
A
r
e
a
(
m
2
)
Le
n
g
t
h
(
mm
)
W
i
d
t
h
(
mm
)
Tr
i
n
a
S
o
l
a
r
TSM
-
P
E
1
5
H
3
4
0
a
t
1
0
0
0
W
/
m
2
2
0
2
4
9
5
9
1
.
9
4
1
0
1
6
2
.
5
7
3
5
3
1
6
3
2
12
1
4
2
7
2
1
5
0
95
P
o
l
y
-
3
2
5
W
,
P
o
l
y
c
r
y
st
a
l
l
i
n
e
3
2
5
a
t
1
0
0
0
W
/
m
2
1
9
5
6
9
9
2
1
.
9
4
0
3
5
2
2
.
5
7
6
9
2
8
9
0
.
5
6
.
8
5
0
1
4
9
3
6
1
5
0
1
0
0
S
e
r
i
e
s
:
G
P
N
E
-
S
1
4
4
/
F
N
H
4
3
5
-
4
6
0
W
,
M
o
n
o
c
r
y
st
a
l
l
i
n
e
4
6
0
a
t
1
0
0
0
W
/
m
2
2
1
0
8
1
0
4
8
2
.
2
0
9
1
8
4
2
.
5
5
4
3
5
1
5
9
1
.
5
8
.
6
4
9
5
2
0
0
6
1
5
0
80
6.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
Acc
o
r
d
in
g
to
l
o
ad
m
o
d
ellin
g
an
d
d
if
f
e
r
en
t
lo
ad
c
u
r
v
es
m
en
tio
n
ed
,
Fig
u
r
e
7
s
h
o
ws
th
e
d
aily
lo
ad
p
r
o
f
ile
o
f
th
e
s
u
b
s
tatio
n
(
at
b
u
s
#
1
)
.
I
t
ca
n
b
e
o
b
s
er
v
ed
f
r
o
m
th
at
th
e
d
aily
lo
ad
is
co
n
tin
u
o
u
s
ly
v
ar
y
in
g
a
n
d
th
e
p
ea
k
lo
ad
is
3
.
2
5
5
MW
at
h
o
u
r
1
8
(
6
PM
).
T
ab
le
3
a
n
d
Fig
u
r
e
8
s
h
o
ws
th
e
b
est
lo
ca
tio
n
an
d
s
ize
f
o
r
2
4
h
o
u
r
s
o
f
th
e
th
r
ee
o
p
tim
izatio
n
tech
n
iq
u
es.
T
a
b
le
3
s
h
o
ws
t
h
e
ef
f
ec
ts
o
f
v
ar
io
u
s
lo
a
d
ty
p
e
s
in
clu
d
e
th
e
ef
f
ec
t
o
f
lo
ad
v
ar
iatio
n
s
th
r
o
u
g
h
o
u
t
a
d
ay
in
th
e
o
p
tim
al
lo
ca
tio
n
an
d
s
ize
o
f
E
V
-
C
S.
I
t
ca
n
b
e
s
ee
n
f
r
o
m
T
ab
le
3
th
at
th
e
r
esu
lts
o
b
tain
ed
b
y
t
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
s
ar
e
c
o
n
cu
r
with
ea
ch
o
th
e
r
an
d
th
at
i
s
s
h
o
w
th
e
v
alid
ity
o
f
th
e
r
esu
lts
.
Fro
m
T
ab
l
e
3
,
it
ca
n
b
e
h
i
g
h
lig
h
ted
th
at
t
h
e
m
ax
im
u
m
s
ize
o
f
E
V
-
C
S
u
n
it
is
2
.
2
7
MW
at
p
ea
k
lo
ad
h
o
u
r
o
f
d
ay
s
o
th
e
d
esig
n
o
f
P
V
s
ize
m
u
s
t b
e
ar
o
u
n
d
t
h
is
s
ize
an
d
lo
ca
ted
at
b
u
s
6
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
25
57
–
25
69
2566
Fig
u
r
e
7
.
Daily
lo
a
d
p
r
o
f
ile
o
f
th
e
s
u
b
s
tatio
n
T
ab
le
3
. EV
-
C
S si
ze
an
d
lo
ca
t
io
n
b
y
t
h
e
p
r
o
p
o
s
ed
al
g
o
r
ith
m
s
f
o
r
all
h
o
u
r
s
o
f
a
d
ay
H
o
u
r
PSO
CS
AOA
H
o
u
r
PSO
CS
AOA
B
u
s
S
i
z
e
B
u
s
S
i
z
e
B
u
s
S
i
z
e
B
u
s
S
i
z
e
B
u
s
S
i
z
e
B
u
s
S
i
z
e
N
o
.
MW
N
o
.
MW
N
o
.
MW
N
o
.
MW
N
o
.
MW
N
o
.
MW
1
6
0
.
8
3
5
3
6
0
.
8
4
8
2
6
0
.
8
1
2
3
13
6
1
.
7
6
6
1
.
6
9
6
6
6
1
.
6
9
9
8
2
6
0
.
7
6
6
8
6
0
.
7
8
9
5
6
0
.
8
0
5
6
14
6
2
.
0
0
8
4
6
2
.
0
1
8
9
6
1
.
9
9
7
3
3
6
0
.
7
1
8
0
6
0
.
7
9
1
0
6
0
.
7
9
3
6
15
6
1
.
9
9
5
4
6
2
.
0
1
3
5
6
2
.
0
2
4
2
4
6
0
.
7
7
1
7
6
0
.
7
8
3
6
6
0
.
7
8
5
2
16
6
2
.
1
3
3
1
6
2
.
0
8
6
4
6
2
.
0
5
1
1
5
6
0
.
8
5
4
9
6
0
.
7
7
0
2
6
0
.
7
8
2
3
17
6
2
.
1
0
7
4
6
2
.
0
9
9
5
6
2
.
0
9
3
8
6
29
0
.
8
2
8
1
29
0
.
8
1
2
8
29
1
.
1
8
4
18
6
2
.
2
7
5
2
6
2
.
1
5
2
5
6
2
.
1
4
5
1
7
30
1
.
0
5
9
5
30
1
.
0
9
1
9
30
1
.
6
2
8
3
19
6
1
.
7
4
8
7
6
1
.
8
5
0
3
6
1
.
8
8
0
4
8
30
1
.
0
1
4
0
30
1
.
0
9
2
3
30
1
.
6
3
3
6
20
7
1
.
7
9
0
6
7
1
.
7
5
9
5
7
1
.
8
4
4
8
9
6
1
.
9
3
2
6
6
1
.
9
3
5
8
6
1
.
9
6
9
6
21
7
1
.
7
9
2
6
7
1
.
7
4
4
6
7
1
.
8
2
7
10
6
2
.
0
8
4
9
6
1
.
9
3
7
9
6
1
.
9
7
4
1
22
7
1
.
5
9
4
3
7
1
.
6
3
0
5
7
1
.
7
0
1
7
11
6
1
.
9
9
1
8
6
1
.
9
5
9
1
6
1
.
9
7
7
8
23
6
0
.
9
4
4
2
6
0
.
9
1
3
6
0
.
9
1
5
6
12
6
1
.
8
2
9
1
6
1
.
7
2
8
2
6
1
.
7
4
5
1
24
7
0
.
7
0
3
1
7
0
.
8
8
0
8
7
0
.
9
0
6
8
Fig
u
r
e
8
.
E
V
-
C
S a
llo
ca
tio
n
b
y
u
s
in
g
AI
tech
n
i
q
u
e
T
a
b
l
e
4
a
n
d
F
i
g
u
r
e
9
,
s
h
o
w
s
t
o
t
a
l
p
o
w
e
r
a
n
d
p
o
w
e
r
l
o
s
s
b
y
t
h
e
p
r
o
p
o
s
e
d
a
l
g
o
r
i
t
h
m
s
f
o
r
a
l
l
h
o
u
r
s
o
f
a
d
a
y
,
i
t
c
a
n
b
e
h
i
g
h
l
i
g
h
t
e
d
t
h
a
t
t
h
e
t
o
t
a
l
p
o
w
e
r
3
.
2
5
M
W
,
a
n
d
m
a
x
i
m
u
m
p
o
w
e
r
l
o
s
s
7
7
.
4
7
k
w
a
t
p
e
a
k
l
o
a
d
h
o
u
r
o
f
d
a
y
.
F
r
o
m
t
h
e
Ta
b
l
e
3
,
i
t
c
a
n
s
e
e
t
h
a
t
t
h
e
t
o
t
a
l
p
o
w
e
r
l
o
s
s
e
s
f
o
r
t
h
e
s
y
s
t
e
m
a
t
w
o
r
s
t
h
o
u
r
(
1
8
:
0
0
)
a
r
e
i
m
p
r
o
v
e
d
t
h
a
n
t
h
e
b
a
s
e
c
a
s
e
(
p
o
w
e
r
l
o
s
s
e
s
i
m
p
r
o
v
e
d
f
r
o
m
1
4
2
.
5
0
9
k
w
t
o
7
7
.
4
7
k
w
,
4
5
.
6
4
%
r
e
d
u
c
t
i
o
n
)
.
I
t
c
a
n
a
l
s
o
s
e
e
t
h
a
t
A
O
A
h
a
s
b
e
s
t
r
e
s
u
l
t
t
h
a
n
C
S
a
n
d
P
S
O
.
T
a
k
i
n
g
h
o
u
r
1
8
a
s
a
n
e
x
a
m
p
l
e
t
h
e
p
o
w
e
r
l
o
s
s
e
s
i
s
7
7
.
2
4
7
5
k
w
i
n
c
a
s
e
o
f
A
O
A
t
e
c
h
n
i
q
u
e
b
e
t
t
e
r
t
h
a
n
t
h
a
t
o
f
P
S
O
w
h
i
c
h
i
s
7
7
.
4
7
3
8
k
w
a
n
d
C
S
w
h
i
c
h
i
s
7
7
.
2
4
8
2
k
w
.
Fig
u
r
e1
0
s
h
o
ws
th
e
v
o
ltag
e
p
r
o
f
ile
f
o
r
all
b
u
s
s
es
in
th
e
s
y
s
tem
at
wo
r
s
t
h
o
u
r
(
1
8
:0
0
)
.
Fro
m
th
e
Fig
u
r
e
1
0
it
ca
n
be
s
ee
n
t
h
at
t
h
e
v
o
ltag
e
p
r
o
f
ile
is
im
p
r
o
v
ed
th
an
th
e
b
ase
ca
s
e
(
m
in
im
u
m
v
o
ltag
e
at
b
u
s
3
3
im
p
r
o
v
e
d
f
r
o
m
0
.
9
2
7
9
p
u
to
0
.
9
5
7
9
p
u
)
.
I
t
ca
n
also
s
ee
th
at
AOA
h
as
b
es
t
r
esu
lt
th
an
C
S
an
d
PS
O.
T
ak
in
g
b
u
s
3
3
as
an
ex
am
p
le
th
e
v
o
lt
ag
e
m
ag
n
itu
ed
is
0
.
9
5
7
9
p
.
u
.
in
ca
s
e
o
f
AOA
tech
n
iq
u
e
b
ett
er
th
an
th
at
o
f
PS
O
wh
ich
is
0
.
9
5
6
2
p
.
u
.
a
n
d
C
S
wh
ich
is
0
.
9
5
6
3
p
.
u
.
T
ab
le
4
s
h
o
wn
th
e
n
u
m
b
er
o
f
m
o
d
u
les
f
o
r
t
h
e
ty
p
e
in
,
th
e
p
r
ice
o
f
item
s
an
d
th
e
s
ize
o
f
m
o
d
u
le.
Evaluation Warning : The document was created with Spire.PDF for Python.