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a
lo
w
r
ip
p
le
ch
ar
g
in
g
cu
r
r
en
t
(
less
th
an
1
%)
[
1
2
]
.
T
h
e
o
f
f
-
b
o
ar
d
ch
ar
g
in
g
to
p
o
lo
g
y
u
s
es th
e
co
m
m
o
n
AC
/D
C
lin
k
[
1
3
]
.
T
h
e
d
ev
elo
p
m
en
t
o
f
E
V
ch
ar
g
in
g
tech
n
o
lo
g
y
h
as
r
esu
lted
in
v
ar
io
u
s
in
n
o
v
atio
n
s
in
co
n
v
er
ter
s
y
s
tem
s
.
Dir
ec
t
cu
r
r
en
t
f
ast
ch
ar
g
in
g
(
DC
FC
)
s
tatio
n
s
o
f
f
er
a
s
h
o
r
t
c
h
ar
g
i
n
g
s
o
l
u
tio
n
d
esp
ite
r
e
q
u
ir
in
g
co
m
p
lex
elec
tr
ical
cir
cu
its
.
T
h
is
s
y
s
tem
u
s
es
two
s
tag
es
o
f
co
n
v
er
s
io
n
,
n
am
el
y
AC
-
DC
co
n
v
er
ter
to
co
n
v
er
t
alter
n
atin
g
c
u
r
r
en
t
(
AC
)
v
o
lta
g
e
to
d
ir
ec
t
cu
r
r
en
t
(
DC
)
,
f
u
r
t
h
er
with
a
DC
-
DC
co
n
v
er
ter
t
o
ad
ju
s
t
th
e
v
o
ltag
e
r
eq
u
ir
ed
b
y
th
e
b
atter
y
[
4
]
,
[
1
4
]
,
a
s
in
g
le
ac
tiv
e
b
r
id
g
e
(
S
AB
)
ap
p
r
o
ac
h
th
at
p
r
o
v
id
es
h
ig
h
ef
f
icien
cy
an
d
DAB
th
at
ef
f
ec
tiv
ely
r
ed
u
ce
i
n
r
u
s
h
c
u
r
r
e
n
t
[
1
5
]
.
T
h
e
latest
tech
n
o
l
o
g
ical
b
r
ea
k
th
r
o
u
g
h
s
h
av
e
im
p
r
o
v
ed
th
e
ef
f
icien
cy
o
f
th
e
c
h
ar
g
in
g
s
y
s
tem
.
T
h
e
d
ev
elo
p
m
en
t
o
f
a
m
o
d
u
lar
o
n
-
b
o
ar
d
ch
a
r
g
er
(
OB
C
)
b
ased
o
n
SEPI
C
co
n
tr
o
l
(
MSOBC
)
th
at
ac
h
iev
es
p
o
wer
co
n
v
er
s
io
n
ef
f
icien
c
y
o
f
u
p
to
9
7
%
at
f
u
ll
lo
ad
an
d
a
1
0
0
V
<
b
atter
y
[
1
6
]
.
I
n
th
e
h
ig
h
-
v
o
ltag
e
s
y
s
t
em
asp
ec
t,
th
e
8
0
0
V
s
y
s
tem
allo
ws
ch
ar
g
in
g
o
f
u
p
to
4
0
0
k
W
with
a
DC
ch
ar
g
in
g
ca
b
le
th
at
is
6
0
%
s
m
aller
,
wh
ile
th
e
4
0
0
V
s
y
s
tem
,
alth
o
u
g
h
it
lim
its
ch
ar
g
in
g
t
o
2
0
0
k
W
,
r
esu
lts
in
th
e
o
p
tim
u
m
ef
f
icien
cy
o
f
its
in
v
er
ter
[
1
7
]
.
Fo
r
s
tan
d
ar
d
izati
o
n
,
th
e
ch
a
r
g
in
g
p
o
wer
lev
el
h
as b
ee
n
s
et
in
th
r
ee
lev
els:
lev
el
1
to
1
.
9
k
W
; le
v
el
2
u
p
t
o
1
9
.
2
k
W
; a
n
d
lev
el
3
ab
o
v
e
5
0
k
W
[
8
]
,
[
1
8
]
.
I
n
h
ig
h
ch
ar
g
in
g
a
p
p
licatio
n
s
ab
o
v
e
5
0
k
W
,
it
is
p
o
s
s
ib
le
to
u
s
e
th
e
co
n
s
tan
t
cu
r
r
en
t
(
C
C
)
-
co
n
s
tan
t
v
o
ltag
e
(
C
V)
co
n
tr
o
l
m
o
d
el
with
a
two
-
s
tag
e
ap
p
r
o
ac
h
:
c
o
n
s
tan
t
cu
r
r
e
n
t
ch
ar
g
in
g
u
n
til
it
r
ea
ch
es
a
ce
r
tain
v
o
ltag
e,
f
o
llo
wed
b
y
th
e
co
n
s
tan
t
v
o
ltag
e
m
ain
ten
an
ce
s
tag
e
u
s
in
g
th
e
DC
-
DC
H
-
b
r
id
g
e
co
n
v
er
ter
to
p
o
lo
g
y
[
1
9
]
-
[
2
3
]
.
T
h
is
ch
a
r
g
in
g
m
ee
t
s
th
e
lev
el
3
ch
a
r
g
in
g
s
tan
d
ar
d
,
wh
er
e
t
h
e
ch
ar
g
in
g
s
tatio
n
ca
n
b
e
p
lace
d
in
t
h
e
r
est
ar
ea
.
R
esear
ch
to
m
ain
tain
co
n
s
tan
t
v
o
ltag
e,
with
th
e
u
s
e
o
f
g
r
id
-
tied
7
-
lev
el
3
-
ce
ll
H
-
B
r
id
g
e
ca
s
ca
d
e
co
n
v
er
ter
s
(
C
HB
)
[
2
1
]
.
I
n
te
r
m
s
o
f
v
alid
atio
n
a
n
d
o
p
tim
izatio
n
,
v
ar
i
o
u
s
test
s
h
av
e
b
ee
n
ca
r
r
ied
o
u
t
o
n
v
ar
io
u
s
ty
p
es
o
f
lith
iu
m
-
io
n
(
L
i
-
i
o
n
)
b
atter
ies,
s
h
o
win
g
in
cr
ea
s
ed
ch
ar
g
in
g
ef
f
icien
cy
u
s
in
g
th
e
C
C
-
C
V
m
eth
o
d
[
2
4
]
.
T
h
e
o
b
tain
ed
r
esu
lts
s
h
o
w
th
at
th
e
L
i
-
io
n
b
atter
y
ca
n
b
e
s
u
c
ce
s
s
f
u
lly
ch
ar
g
ed
with
o
u
t
r
ed
u
cin
g
its
life
cy
cle.
T
h
e
s
y
s
tem
u
s
es
a
b
atter
y
c
o
n
f
ig
u
r
atio
n
with
2
2
p
ar
allel
ar
r
ay
s
,
wh
er
e
ea
c
h
m
o
d
u
le
h
as
1
0
0
ce
lls
ar
r
a
n
g
ed
i
n
s
er
ies
[
1
9
]
.
I
n
th
e
co
n
tr
o
l
m
eth
o
d
,
th
e
ab
il
ity
to
co
n
tr
o
l
th
e
DC
-
DC
b
o
o
s
t
co
n
v
er
ter
is
also
h
ig
h
ly
d
eter
m
in
ed
b
y
th
e
ch
o
ice
o
f
c
o
n
tr
o
ller
.
I
n
s
o
m
e
s
tu
d
ies,
th
e
u
s
e
o
f
in
teg
r
al
p
r
o
p
o
r
tio
n
al
(
PI)
c
o
n
tr
o
l
,
th
e
v
o
ltag
e
is
s
tab
le
at
th
e
r
ef
er
en
ce
7
5
0
V
b
y
Awa
l
et
a
l
.
[
2
5
]
.
T
h
e
r
esu
lts
o
f
Mo
ei
n
i
an
d
W
an
g
[
2
1
]
r
esear
ch
in
teg
r
ated
p
h
o
to
v
o
ltaic
(
PV)
p
a
n
els
an
d
g
r
id
s
to
p
r
o
d
u
ce
a
v
o
ltag
e
o
f
4
1
5
V,
a
n
d
Hasy
im
et
a
l
.
[
2
6
]
s
u
cc
ee
d
ed
i
n
r
ed
u
cin
g
r
eso
n
an
ce
an
d
im
p
r
o
v
in
g
s
y
s
tem
s
tab
ilit
y
in
b
att
er
y
c
u
r
r
en
t
r
eg
u
latio
n
.
E
f
f
ec
t
iv
en
ess
o
f
co
n
tr
o
l
s
y
s
tem
with
p
r
o
p
o
r
tio
n
al
in
t
eg
r
al
d
er
iv
ativ
e
(
PID
)
with
PV
m
o
d
u
le
in
p
u
t
v
o
ltag
e
3
W
1
2
V
an
d
o
u
tp
u
t
v
o
ltag
e
1
0
0
W
1
2
V
[
2
7
]
.
On
th
e
g
ain
s
ch
ed
u
lin
g
co
n
tr
o
l,
PI
(
PI
-
GS)
p
r
o
d
u
ce
s
an
o
u
tp
u
t
v
o
ltag
e
o
f
1
2
V
with
th
e
in
p
u
t
v
o
ltag
e
f
lu
ctu
at
in
g
b
etwe
en
9
to
2
2
V
[
2
8
]
.
R
esear
ch
o
n
th
e
d
ev
elo
p
m
en
t
o
f
PI
co
n
tr
o
l
with
a
co
m
b
in
atio
n
o
f
co
n
tr
o
l
d
ev
el
o
p
m
en
t
o
n
f
u
zz
y
-
PI
co
n
tr
o
ller
s
,
im
p
r
o
v
in
g
s
y
s
tem
ef
f
icien
cy
an
d
p
er
f
o
r
m
a
n
ce
[
6
]
,
[
2
9
]
.
I
m
p
lem
en
tatio
n
o
f
PI
co
n
tr
o
l
o
n
m
ax
im
u
m
p
o
w
er
p
o
i
n
t
tr
ac
k
in
g
(
MPPT)
[
3
0
]
.
An
in
ter
leav
e
d
p
ar
tial
p
o
wer
co
n
v
er
ter
(
PP
C
)
is
u
s
ed
at
th
e
DC
-
DC
co
n
v
er
s
io
n
s
tag
e,
p
r
o
ce
s
s
in
g
ap
p
r
o
x
i
m
ately
3
6
%
o
f
t
h
e
p
o
wer
o
u
tp
u
t
r
a
n
g
e
with
an
i
n
cr
ea
s
e
in
co
n
v
er
s
io
n
ef
f
icien
cy
f
r
o
m
9
5
.
1
%
to
9
8
.
3
%
[
3
1
]
.
I
n
ad
d
itio
n
,
th
e
im
p
lem
en
tatio
n
o
f
p
ar
ac
o
n
s
is
ten
t
lo
g
ic
-
b
ased
PI
co
n
tr
o
l
(
PL
-
PI)
h
as
r
esu
lted
i
n
s
u
p
er
io
r
d
y
n
am
ic
p
er
f
o
r
m
an
ce
with
s
m
aller
ca
p
ac
ito
r
r
eq
u
ir
em
en
ts
[
3
2
]
.
I
n
th
e
co
n
tr
o
l
asp
ec
t,
th
e
i
n
er
t
ial
v
ir
tu
al
co
n
tr
o
l
s
tr
ateg
y
b
ased
o
n
th
e
f
r
ac
tio
n
al
o
r
d
er
im
p
ed
a
n
ce
m
o
d
el
(
F
OPI
D)
h
as
d
em
o
n
s
tr
ated
t
h
e
ab
ilit
y
to
p
r
o
v
id
e
a
tim
e
r
esp
o
n
s
e
o
f
0
.
0
2
5
s
with
a
m
ax
im
u
m
DC
v
o
ltag
e
d
e
v
ia
tio
n
o
f
5
%
[
3
3
]
.
Fre
itas
et
a
l
.
[
3
4
]
an
d
Gaji
ć
et
a
l
.
[
3
5
]
ar
g
u
e
th
at
p
ar
ticle
s
war
m
o
p
tim
izatio
n
(
PS
O)
s
ig
n
if
ican
tly
im
p
r
o
v
es
th
e
p
er
f
o
r
m
a
n
ce
o
f
th
e
alg
o
r
ith
m
o
n
m
o
s
t
o
f
th
e
f
u
n
ctio
n
s
test
e
d
,
in
ter
m
s
o
f
im
p
r
o
v
in
g
its
ef
f
ec
tiv
en
ess
an
d
ef
f
icien
c
y
.
St
u
d
y
in
teg
r
ates
d
ee
p
d
eter
m
in
is
tic
p
o
licy
g
r
a
d
ien
t
(
DDPG)
with
PS
O,
o
p
tim
izin
g
DDPG
ac
to
r
n
etwo
r
k
p
ar
a
m
eter
s
,
p
r
o
v
id
in
g
a
r
o
b
u
s
t
in
itial
p
o
licy
.
DDPG
th
en
r
ef
in
es
th
ese
p
ar
am
eter
s
b
y
in
ter
ac
tin
g
with
th
e
en
e
r
g
y
s
y
s
tem
,
m
ak
in
g
d
ec
is
io
n
s
ab
o
u
t b
atter
y
s
ch
ed
u
lin
g
an
d
g
r
id
u
s
ag
e
to
m
a
x
im
ize
co
s
t r
ewa
r
d
s
[
3
6
]
.
I
n
th
is
r
esear
ch
,
th
er
e
ar
e
th
r
ee
m
ain
p
r
o
b
lem
s
.
First,
h
o
w
to
m
in
im
ize
th
e
ch
ar
g
i
n
g
cir
cu
it
o
n
an
E
V,
s
o
th
at
th
e
cir
cu
it
is
n
o
t
m
o
r
e
co
m
p
licated
.
Seco
n
d
,
h
o
w
d
o
es
th
e
b
atter
y
ar
r
an
g
em
e
n
t
wo
r
k
to
d
eter
m
in
e
th
e
ch
ar
g
in
g
o
u
tp
u
t
v
o
ltag
e
o
f
8
0
0
to
1
,
1
0
0
V.
T
h
ir
d
,
h
o
w
to
s
et
th
e
PI
co
n
tr
o
l
o
n
th
e
DC
-
DC
b
o
o
s
t
co
n
v
er
ter
,
s
o
th
at
th
e
o
u
tp
u
t
f
r
o
m
c
h
ar
g
i
n
g
is
s
tab
le
with
i
n
th
e
v
o
ltag
e
v
alu
e
r
an
g
e
o
f
8
0
0
t
o
1
,
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First,
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ch
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tp
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t
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T
h
ir
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,
u
s
in
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PI
c
o
n
tr
o
l
with
ex
p
er
im
en
tal
tu
n
i
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g
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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8
6
9
4
Desig
n
a
n
d
s
imu
la
tio
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o
f
a
n
e
lectric v
eh
icle
ch
a
r
g
in
g
s
ystem
w
ith
b
a
tter
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a
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r
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g
eme
n
t …
(
N
u
r
mia
ti P
a
s
r
a
)
2523
m
eth
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d
tu
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o
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ith
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with
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atio
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ig
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ican
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Fr
o
m
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tech
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ical
d
ep
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asp
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t,
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m
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im
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o
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al
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Y
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∆
tr
an
s
f
o
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m
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t
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o
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n
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M
with
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L
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atter
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ate
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ig
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im
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tem
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s
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an
s
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en
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ter
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m
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o
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s
e
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o
wer
lo
s
s
.
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h
e
r
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in
n
o
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s
in
cl
u
d
e
th
e
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im
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lific
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o
f
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ics
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ctio
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m
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co
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p
o
n
e
n
ts
u
s
ed
an
d
co
n
tr
o
l
s
y
s
tem
s
.
T
h
is
d
esig
n
im
p
r
o
v
es
m
ai
n
ten
an
c
e
an
d
o
f
f
e
r
s
b
etter
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lex
ib
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d
p
o
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ilit
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.
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h
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s
,
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s
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en
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m
o
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d
ec
o
n
o
m
ical
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V
ch
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g
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n
g
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r
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ctu
r
e,
esp
ec
ially
f
o
r
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lace
m
e
n
t
in
v
eh
icle
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est
ar
ea
s
th
at
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en
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ate
a
n
o
v
elty
.
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h
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esear
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lted
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a
n
ew
m
eth
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o
r
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o
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o
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ilin
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atter
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m
o
d
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in
E
Vs.
T
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m
eth
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s
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ically
d
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f
o
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atter
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with
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atter
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o
ltag
e
in
th
e
v
o
ltag
e
r
an
g
e
o
f
8
0
0
to
1
,
1
0
0
V.
T
h
is
in
n
o
v
atio
n
is
f
u
r
th
er
n
am
ed
“
E
V
b
atter
y
ar
r
a
n
g
em
en
t
p
atter
n
m
o
d
el
m
eth
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d
with
m
in
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m
c
o
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p
o
n
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ts
in
th
e
E
V
c
h
ar
g
in
g
cir
cu
it
”
.
2.
M
E
T
H
O
D
T
h
e
c
h
a
r
g
i
n
g
c
i
r
c
u
it
w
as
d
es
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g
n
e
d
i
n
a
t
h
r
e
e
-
p
h
as
e
ci
r
c
u
i
t
u
s
in
g
P
S
I
M
2
2
s
o
f
t
wa
r
e
i
n
s
i
m
u
la
t
i
o
n
w
it
h
a
n
i
s
o
l
at
e
d
m
o
d
e
l
.
T
h
e
p
r
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p
o
s
e
d
c
h
a
r
g
i
n
g
a
r
r
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y
d
e
s
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g
n
c
o
n
s
is
ts
o
f
a
t
h
r
e
e
-
p
h
a
s
e
n
et
w
o
r
k
,
t
r
a
n
s
f
o
r
m
e
r
s
,
AC
-
DC
c
o
n
v
e
r
t
e
r
s
,
DC
-
DC
b
o
o
s
t
c
o
n
v
e
r
t
e
r
s
,
b
at
t
e
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i
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a
n
d
P
I
c
o
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t
r
o
ls
.
A
ls
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h
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v
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e
.
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e
ct
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V
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s
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e
f
f
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c
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(
9
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t
o
9
5
%
)
w
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t
h
m
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n
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m
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m
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.
T
h
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s
w
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p
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p
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w
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t
h
m
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d
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l
a
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n
(
P
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)
w
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P
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O
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9
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l
e
ct
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f
t
h
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I
c
o
n
t
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l
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s
b
a
s
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o
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s
t
a
b
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a
l
y
s
is
a
n
d
d
y
n
a
m
i
c
r
e
s
p
o
n
s
e
,
w
h
e
r
e
t
h
e
P
I
c
o
n
t
r
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ll
e
r
p
r
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v
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m
al
o
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h
o
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t
(
<
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%
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th
a
f
a
s
t
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t
tl
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n
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m
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(
<
0
.
1
s
)
.
2
.
1
.
Sy
s
t
e
m
re
s
ea
rc
h a
nd
des
ig
n pro
ce
s
s
T
h
e
u
s
e
o
f
PS
I
M
s
o
f
twar
e
v
er
s
io
n
2
2
,
wh
er
e
PS
I
M
allo
ws
s
im
u
latio
n
s
to
b
e
ca
r
r
ied
o
u
t
f
aster
an
d
s
im
p
ly
in
d
r
awin
g
an
d
s
im
u
latio
n
.
Use o
f
q
u
a
n
titativ
e
d
ata
o
b
tain
ed
f
r
o
m
th
e
s
im
u
latio
n
r
e
s
u
lts
.
T
h
e
co
m
p
u
te
s
etu
p
in
clu
d
es
a
co
m
p
r
e
h
en
s
iv
e
s
im
u
latio
n
p
latf
o
r
m
an
d
o
p
tim
izatio
n
p
ar
am
eter
s
.
P
SIM
2
2
s
im
u
latio
n
p
latf
o
r
m
with
v
ar
ia
b
le
-
s
tep
s
o
lv
er
with
er
r
o
r
to
le
r
an
ce
o
f
1
e
-
6
an
d
m
a
x
im
u
m
s
tep
s
ize
o
f
1
e
-
5
s
to
en
s
u
r
e
h
i
g
h
s
im
u
latio
n
ac
cu
r
ac
y
.
T
h
e
co
n
v
er
g
e
n
ce
cr
iter
ia
f
o
r
th
e
PS
O
alg
o
r
ith
m
ar
e
s
et
with
a
m
ax
im
u
m
o
f
1
0
0
iter
atio
n
s
,
an
er
r
o
r
to
ler
a
n
ce
o
f
1
e
-
4
,
a
n
d
a
p
ar
ticle
p
o
p
u
latio
n
o
f
5
0
to
en
s
u
r
e
o
p
tim
al
co
n
v
e
r
g
en
ce
.
Simu
latio
n
p
ar
am
eter
s
in
clu
d
e
a
2
0
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4
I
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16
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4
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Dec
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20
25
:
2521
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2524
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.
1
0
]
(
7
)
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:
2088
-
8
6
9
4
Desig
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a
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tio
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lectric v
eh
icle
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ith
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a
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a
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cr
ete
eq
u
atio
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y
d
ef
in
in
g
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e
eq
u
atio
n
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ter
m
s
o
f
tim
e
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o
th
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t
h
e
tim
e
it
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t
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o
ller
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t
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ter
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ed
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m
all
(
d
t
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.
T
h
e
eq
u
atio
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is
s
tated
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(
8)
:
=
(
)
+
.
(
)
(
8
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T
h
e
in
ter
v
al
(
d
t
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ex
p
r
ess
ed
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ter
m
s
o
f
th
e
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p
lin
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e
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s
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o
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at
th
e
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u
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t
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ize
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d
er
r
o
r
in
th
e
f
o
r
m
o
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ch
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g
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ea
c
h
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p
lin
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r
o
ce
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s
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ca
n
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e
k
n
o
w
n
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T
h
e
eq
u
at
io
n
is
s
tated
as
(
9
)
:
∆
=
∆
+
.
(
9
)
wh
er
e
:
u
(
t)
=
co
n
tr
o
l
s
ig
n
al,
e(
t)
=
er
r
o
r
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ig
n
al,
K
p
=
p
r
o
p
o
r
tio
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ain
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K
i
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teg
r
al
g
ain
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K
p
/T
i
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,
an
d
T
i
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in
teg
r
al
tim
e
co
n
s
tan
t.
I
n
(
7
)
is
u
s
ed
to
d
esig
n
a
m
o
d
el
o
f
th
e
PI
o
p
e
r
ato
r
.
2
.
4
.
P
a
rt
icle
s
wa
rm
o
ptim
iz
a
t
io
n a
lg
o
ri
t
hm
PS
O
i
s
an
alg
o
r
ith
m
th
at
is
in
d
ep
en
d
e
n
t
o
f
th
e
p
r
o
b
lem
;
it
ca
n
b
e
u
s
ed
in
a
v
ar
iety
o
f
ap
p
licatio
n
s
,
wh
ich
in
th
is
alg
o
r
ith
m
,
is
an
ev
alu
atio
n
o
f
th
e
f
itn
ess
o
f
ea
ch
s
o
lu
tio
n
ca
n
d
id
ate
(
an
d
p
o
s
s
ib
ly
also
a
s
et
o
f
co
n
s
tr
ain
ts
o
f
th
e
p
r
o
b
lem
)
[
3
4
]
.
On
e
o
f
th
e
s
war
m
-
b
ased
o
p
tim
izatio
n
tech
n
iq
u
es
in
s
p
ir
ed
b
y
n
atu
r
e,
it
is
f
lex
ib
le
an
d
ea
s
y
to
im
p
lem
en
t
[
3
8
]
.
T
h
e
alg
o
r
ith
m
is
in
s
p
ir
ed
b
y
th
e
s
o
cial
an
d
b
io
l
o
g
ica
l
b
eh
av
i
o
r
o
f
f
lo
ck
s
o
f
b
ir
d
s
lo
o
k
in
g
f
o
r
f
o
o
d
s
o
u
r
ce
s
.
I
n
d
iv
i
d
u
als
ar
e
r
ef
e
r
r
e
d
to
as
p
ar
ticles
an
d
f
ly
ac
r
o
s
s
s
ea
r
ch
s
p
ac
es
in
s
ea
r
ch
o
f
th
e
b
est g
lo
b
al
p
o
s
itio
n
s
th
at
m
in
im
ize
(
o
r
m
ax
i
m
ize)
th
e
g
iv
e
n
p
r
o
b
lem
[
3
4
]
.
I
n
th
is
alg
o
r
ith
m
,
s
p
ee
d
r
eg
u
l
atio
n
is
co
n
s
id
er
ed
a
k
e
y
f
ea
t
u
r
e,
as
it
is
th
e
m
ai
n
m
ec
h
a
n
i
s
m
u
s
ed
to
m
o
v
e
th
e
p
o
s
itio
n
o
f
p
ar
ticles
in
s
ea
r
ch
o
f
o
p
tim
al
s
o
lu
tio
n
s
in
th
e
s
ea
r
ch
s
p
ac
e.
E
b
er
h
ar
t
u
s
es
th
e
m
ax
im
u
m
v
alu
e
o
f
s
p
ee
d
an
d
d
is
cu
s
s
es
th
e
r
esu
lts
f
o
r
d
if
f
er
en
t
v
elo
city
v
alu
es.
T
h
e
s
p
ee
d
o
f
th
e
k
p
ar
ticles
in
th
e
s
war
m
in
iter
atio
n
(
i
+
1
)
,
ac
c
o
r
d
in
g
to
(
1
0
)
[
3
4
]
,
[
3
8
]
.
(
+
1
)
=
(
)
+
1
1
(
,
−
(
)
)
+
2
2
(
,
−
(
)
)
(
1
0
)
T
h
e
p
o
s
itio
n
o
f
ea
ch
k
p
ar
ticle
,
at
ea
ch
iter
atio
n
(
i
+
1
)
,
v
ar
ie
s
ac
co
r
d
in
g
t
o
(
1
1
)
:
(
+
1
)
=
(
)
+
(
+
1
)
(
1
1
)
wh
er
e:
V
k
(
i
+
1
)
=
th
e
s
p
ee
d
o
f
th
e
k
p
a
r
ticle
in
th
e
iter
atio
n
(
i
+
1
)
,
X
k
(
i
)
=
th
e
p
o
s
itio
n
o
f
th
e
k
p
ar
ticle
in
iter
atio
n
to
-
i
,
,
=
T
h
e
b
est
p
o
s
i
tio
n
o
f
th
e
in
d
iv
i
d
u
al
o
f
th
e
k
p
ar
ticle
in
iter
atio
n
to
-
i
,
g
best,
i
=
th
e
g
lo
b
al
b
est
p
o
s
itio
n
o
f
a
n
y
p
ar
ticle
i
n
iter
atio
n
to
-
i
,
c
1
an
d
c
2
=
T
h
e
r
ea
l
ac
ce
ler
atio
n
co
ef
f
icien
t
th
at
co
n
tr
o
ls
h
o
w
m
u
ch
th
e
g
lo
b
al
b
est
p
o
s
itio
n
an
d
in
d
iv
id
u
al
s
h
o
u
ld
af
f
e
ct
th
e
p
ar
ticle
v
elo
city
as
well
as
r
1
an
d
r
2
=
A
r
an
d
o
m
n
u
m
b
er
th
at
is
u
n
if
o
r
m
ly
d
is
tr
ib
u
ted
in
a
r
an
g
e
[
0
,
1
]
an
d
X
k
(
i
+
1
)
is
th
e
p
o
s
itio
n
o
f
th
e
k
p
ar
ticle
in
th
e
iter
atio
n
(
i
+
1
)
.
T
h
e
DC
-
DC
b
o
o
s
t
co
n
v
er
ter
with
o
p
tim
ized
PI
co
n
tr
o
l
u
s
i
n
g
PS
O
ac
ts
as
a
p
o
wer
co
n
d
itio
n
in
g
u
n
it
th
at
r
eg
u
lates
th
e
f
l
o
w
o
f
e
n
er
g
y
f
r
o
m
th
e
p
o
wer
g
r
id
t
o
th
e
E
V
b
atter
y
.
T
h
is
co
n
v
er
ter
c
an
b
e
im
p
lem
e
n
ted
as
an
o
f
f
-
b
o
a
r
d
ch
ar
g
er
as
well
as
a
tr
ac
tio
n
s
y
s
tem
in
ter
f
ac
e
to
s
u
p
p
o
r
t
th
e
p
er
f
o
r
m
a
n
ce
o
f
th
e
d
r
iv
e
m
o
to
r
.
T
h
e
o
u
tp
u
t
v
o
ltag
e
is
in
th
e
r
a
n
g
e
o
f
8
0
0
to
1
,
1
0
0
V,
s
o
it
c
an
b
e
u
s
ed
d
ir
ec
tly
to
d
r
iv
e
in
d
u
ctio
n
m
o
to
r
s
an
d
s
y
n
ch
r
o
n
o
u
s
m
o
t
o
r
s
in
E
Vs.
Du
ty
cy
cle
r
eg
u
latio
n
b
y
PI
co
n
tr
o
l k
ee
p
s
v
o
ltag
e
r
e
g
u
latio
n
s
tab
le
with
m
in
im
al
o
v
er
s
h
o
o
t,
s
o
th
at
th
e
q
u
ality
o
f
s
u
p
p
ly
to
th
e
b
atter
y
an
d
tr
ac
tio
n
in
v
er
ter
is
m
ain
tain
ed
.
T
h
is
in
teg
r
atio
n
im
p
r
o
v
es
th
e
ef
f
icien
cy
o
f
p
o
wer
d
eliv
er
y
an
d
d
y
n
am
ic
r
es
p
o
n
s
e
o
f
th
e
s
y
s
tem
,
an
d
is
co
m
p
atib
le
with
th
e
is
o
lated
th
r
ee
-
p
h
ase
ar
c
h
itectu
r
e
u
s
ed
.
2
.
5
.
T
he
pro
ce
s
s
o
f
det
er
m
i
nin
g
t
he
wind
i
ng
s
o
n t
he
t
ra
ns
f
o
rm
er
Dete
r
m
in
atio
n
o
f
th
e
ty
p
e
o
f
tr
an
s
f
o
r
m
er
m
o
d
el
Y
-
∆
with
a
th
r
ee
-
p
h
ase
p
o
wer
g
r
id
v
o
ltag
e
s
o
u
r
ce
o
f
3
8
0
/4
0
0
V
as
th
e
p
r
im
ar
y
v
o
l
tag
e
(
V
p
)
an
d
r
aisi
n
g
th
e
v
o
lt
ag
e
to
6
0
0
V
as
th
e
s
ec
o
n
d
ar
y
v
o
ltag
e
(
V
s
)
.
T
h
e
u
s
e
o
f
Y
-
∆
tr
an
s
f
o
r
m
er
s
as
v
o
ltag
e
[
1
0
]
.
T
h
e
d
eter
m
in
atio
n
o
f
th
e
tr
an
s
f
o
r
m
e
r
p
ar
am
ete
r
v
alu
e
is
b
ased
o
n
th
e
tr
an
s
f
o
r
m
er
p
ar
am
ete
r
s
f
r
o
m
th
e
tr
an
s
f
o
r
m
er
'
s
PS
I
M
d
ata
s
h
ee
t.
T
h
ese
v
alu
es
ar
e:
p
r
i
m
ar
y
r
esis
tan
ce
(
R
p
)
0
.
0
0
1
o
h
m
,
s
ec
o
n
d
ar
y
r
esis
tan
ce
(
R
s
)
0
.
0
0
1
o
h
m
,
p
r
im
ar
y
in
d
u
ctan
ce
(
L
p
)
0
.
0
0
0
0
1
H,
s
ec
o
n
d
ar
y
in
d
u
ctan
ce
(L
s
)
0
.
0
0
0
0
1
H,
an
d
m
a
g
n
eti
c
in
d
u
ctan
ce
(
L
m
)
0
.
5
H.
C
o
m
p
ar
is
o
n
o
f
p
r
im
a
r
y
win
d
i
n
g
(
N
p
)
an
d
s
ec
o
n
d
ar
y
win
d
in
g
(
N
s
)
,
u
s
in
g
(
1
2
)
.
=
(1
2
)
Fo
r
th
e
v
alu
e
o
f
V
p
=
3
9
0
V
an
d
th
e
v
alu
e
o
f
V
s
=
6
0
0
V,
ass
u
m
in
g
th
e
v
alu
e
o
f
N
p
=
1
,
0
0
0
win
d
in
g
s
,
th
e
n
th
e
v
alu
e
o
f
N
s
is
o
b
tain
ed
b
ased
o
n
(
1
2
)
,
f
o
llo
win
g
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
4
,
Dec
em
b
er
20
25
:
2521
-
2
5
3
7
2526
=
.
=
600
3
9
0
.
1000
=
1
,
538
win
d
in
g
s
B
y
u
s
in
g
th
ese
ca
lcu
latio
n
s
,
th
e
win
d
in
g
r
atio
is
N
p
: N
s
=
1
: 1
.
5
4
.
T
h
e
s
elec
tio
n
o
f
Y
-
Δ
tr
an
s
f
o
r
m
er
s
is
b
ased
o
n
th
e
an
aly
s
is
o
f
th
e
ef
f
icien
cy
a
n
d
ca
p
ac
ities
o
f
g
alv
an
ic
in
s
u
latio
n
.
T
h
e
Y
-
Δ
tr
an
s
f
o
r
m
er
p
r
o
v
id
es
9
5
-
9
8
%
ef
f
icien
cy
with
g
o
o
d
i
n
s
u
latio
n
ca
p
ab
ilit
y
an
d
ev
en
lo
ad
d
is
tr
ib
u
tio
n
in
all
th
r
ee
p
h
ases
[
1
0
]
,
[
2
1
]
.
T
h
e
r
o
le
o
f
p
o
wer
elec
tr
o
n
ics
in
th
is
s
tu
d
y
in
clu
d
es
m
o
d
elin
g
,
n
am
ely
,
m
o
d
elin
g
co
n
v
er
ter
d
y
n
a
m
ics
u
s
in
g
s
tate
-
s
p
ac
e
eq
u
atio
n
s
f
o
r
DC
-
DC
b
o
o
s
t
co
n
v
er
ter
s
d
er
iv
ed
f
r
o
m
th
e
a
n
aly
s
is
o
f
t
h
e
o
p
e
r
atin
g
m
o
d
es
o
f
th
e
ON
an
d
OFF
s
witch
es,
allo
win
g
f
o
r
ac
cu
r
ate
s
tab
ilit
y
an
d
tr
an
s
ien
t r
esp
o
n
s
e
an
aly
s
is
.
T
h
e
u
s
e
o
f
a
co
n
tr
o
l a
lg
o
r
ith
m
u
s
es a
PI
co
n
tr
o
ller
with
p
ar
am
eter
s
o
p
tim
ized
u
s
in
g
PS
O,
wh
er
e
t
h
is
co
n
tr
o
l
r
eg
u
lates
th
e
PW
M
d
u
t
y
cy
cle
b
ased
o
n
v
o
ltag
e
er
r
o
r
to
r
ea
ch
t
h
e
d
esire
d
s
etp
o
in
t w
ith
o
p
tim
al
s
tab
ilit
y
.
W
ith
m
o
d
elin
g
f
r
o
m
g
r
id
in
p
u
t (
3
8
0
/4
0
0
V)
th
r
o
u
g
h
Y
-
Δ
tr
an
s
f
o
r
m
er
(
6
0
0
V)
,
AC
-
DC
co
n
v
er
ter
,
DC
-
DC
b
o
o
s
t c
o
n
v
er
ter
,
to
b
atter
y
o
u
t
p
u
t (
8
0
0
t
o
1
,
1
0
0
V)
.
2
.
6
.
B
a
t
t
er
y
m
o
delin
g
pro
ce
s
s
Li
-
io
n
b
atter
ies
ar
e
u
s
ed
in
s
im
u
latio
n
s
p
r
o
v
i
d
ed
b
y
PS
I
M.
Dete
r
m
in
atio
n
o
f
th
e
b
atter
y
a
r
r
ay
m
o
d
el
is
n
ee
d
ed
to
d
eter
m
in
e
th
e
t
o
tal
v
o
ltag
e
o
f
th
e
b
atter
y
an
d
t
h
e
p
o
wer
to
b
e
g
en
e
r
ated
.
T
h
e
d
eter
m
in
atio
n
o
f
th
e
n
u
m
b
e
r
o
f
b
atter
ies
to
b
e
u
s
ed
is
ca
r
r
ied
o
u
t
b
y
p
er
f
o
r
m
in
g
a
s
er
ies
ar
r
an
g
em
en
t
p
atte
r
n
,
s
tar
tin
g
f
r
o
m
1
0
b
atter
ies
to
2
4
0
b
atter
ies.
T
h
e
r
esu
lts
o
b
tain
ed
ar
e
in
t
h
e
f
o
r
m
o
f
b
atter
y
v
o
ltag
e
as
lo
ad
v
o
ltag
e
an
d
b
atter
y
cu
r
r
en
t
as
lo
ad
cu
r
r
e
n
t.
T
h
e
in
cr
ea
s
in
g
n
u
m
b
e
r
o
f
b
atter
ies
r
esu
lts
in
g
r
ea
ter
v
o
ltag
e
an
d
s
m
aller
cu
r
r
en
t.
So
,
it
is
n
ec
e
s
s
ar
y
to
u
s
e
a
p
ar
allel
ar
r
an
g
em
en
t
p
atter
n
to
in
cr
ea
s
e
th
e
cu
r
r
en
t.
T
h
e
b
a
tter
y
ar
r
an
g
em
e
n
ts
p
r
o
p
o
s
ed
in
p
atter
n
I
a
r
e
S4
0
,
S8
0
,
an
d
S1
0
0
,
wh
er
e
S
is
a
s
er
ial
ar
r
ay
,
S4
0
is
4
0
b
atter
ies
ar
r
an
g
ed
i
n
s
er
ies,
S8
0
is
8
0
b
atter
ies
ar
r
an
g
ed
in
s
er
ies,
an
d
S1
0
0
is
1
0
0
b
atter
ies
ar
r
an
g
ed
in
s
er
ies.
Fu
r
t
h
er
m
o
r
e
,
p
atter
n
I
I
with
th
e
ar
r
an
g
em
en
t o
f
S4
0
-
P2
,
S8
0
-
P2
,
a
n
d
S1
0
0
-
P2
,
w
h
er
e
P
is
p
ar
allel,
S4
0
-
P2
is
th
e
ar
r
an
g
e
m
en
t
o
f
S4
0
ar
r
an
g
e
d
in
2
p
ar
allels,
S8
0
-
P
2
is
ar
r
a
n
g
ed
in
2
p
ar
allels,
a
n
d
S1
0
0
-
P2
is
ar
r
a
n
g
ed
in
2
p
ar
allels.
B
y
s
ettin
g
th
e
n
u
m
b
er
o
f
b
atter
ies in
th
e
b
atter
y
p
ar
a
m
eter
s
in
PS
I
M.
T
h
e
s
ettin
g
s
in
th
e
n
o
o
f
ce
lls
in
s
er
ies
an
d
n
o
o
f
ce
lls
in
p
ar
allel
s
ec
tio
n
s
,
ac
co
r
d
in
g
to
t
h
e
b
atter
y
p
atter
n
m
o
d
el.
T
h
e
b
atter
y
v
o
l
tag
e
f
o
r
f
u
ll
b
atter
y
v
o
ltag
e
co
n
d
itio
n
s
is
4
.
2
V,
an
d
th
e
n
o
m
in
al
v
o
ltag
e
is
3
.
6
V,
as
well
as
o
th
er
p
ar
am
eter
s
,
ac
co
r
d
in
g
to
t
h
e
b
atter
y
p
ar
am
eter
s
in
PS
I
M.
T
h
e
d
ata
in
T
ab
le
1
s
h
o
ws
th
e
s
im
u
lated
v
o
ltag
e
(
V
sim
)
,
s
im
u
lated
cu
r
r
e
n
t
(
I
sim
)
,
an
d
s
im
u
lated
p
o
wer
(
P
sim
)
with
a
s
im
u
latio
n
tim
e
o
f
2
0
s
ec
o
n
d
s
.
T
h
e
V
sim
v
alu
e
o
n
t
h
e
S4
0
-
P2
is
alm
o
s
t
th
e
s
am
e
as
th
e
V
sim
v
alu
e
o
n
th
e
S4
0
-
P1
,
an
d
th
e
I
sim
v
alu
e
o
n
th
e
S4
0
-
P2
is
alm
o
s
t
d
o
u
b
l
e
th
e
I
sim
v
alu
e
o
n
th
e
S4
0
-
P1
.
T
h
is
is
also
th
e
s
am
e
in
th
e
S
8
0
-
P2
an
d
S1
0
0
-
P2
ar
r
ay
s
,
as
ca
n
b
e
s
ee
n
in
T
ab
le
1
.
T
h
ese
v
alu
es
will
b
e
u
s
ed
t
o
g
en
er
ate
lo
a
d
v
o
ltag
e
(
V
L
)
a
n
d
lo
ad
f
o
r
ce
(
P
L
)
.
Nex
t,
it
will
b
e
d
eter
m
in
ed
h
o
w
m
an
y
s
er
ies
o
f
m
ilk
will
b
e
u
s
ed
to
in
cr
ea
s
e
th
e
v
o
ltag
e
v
alu
e.
T
h
is
v
alu
e
will d
eter
m
in
e
h
o
w
m
u
ch
E
V
b
atter
y
v
o
ltag
e
an
d
p
o
wer
will
b
e
u
s
ed
f
o
r
ch
a
r
g
in
g
.
T
ab
le
1
.
B
atter
y
p
atter
n
m
o
d
el
t
=
2
0
s
B
a
t
t
e
r
y
p
a
t
t
e
r
n
m
o
d
e
l
S
4
0
-
P1
S
4
0
-
P2
S
8
0
-
P1
S
8
0
-
P2
S
1
0
0
-
P1
S
1
0
0
-
P2
V
s
i
m
(V)
8
0
3
.
4
6
8
0
4
.
4
8
7
9
9
.
1
8
7
9
9
.
8
2
8
0
0
.
2
1
7
9
9
.
3
3
I
s
i
m
(A)
2
5
3
.
4
8
5
0
8
.
2
1
9
4
.
8
8
1
8
5
.
5
3
6
0
.
2
2
1
2
0
.
1
0
P
s
i
m
(
k
W
)
2
0
3
.
6
6
1
4
0
8
.
8
5
7
4
.
0
0
1
4
8
.
3
9
4
8
.
1
9
9
6
.
0
0
T
h
e
v
o
ltag
e
ca
lc
u
latio
n
in
p
atter
n
I
o
f
th
e
S4
0
b
atter
y
ar
r
ay
f
o
llo
ws:
=
(1
3
)
=
3
.
6
40
=
144
I
n
p
atter
n
I
I
o
f
th
e
S4
0
-
P2
b
atter
y
ar
r
an
g
e
m
en
t,
wh
er
e
th
e
S4
0
is
ar
r
a
n
g
ed
in
2
p
ar
a
llel,
th
e
V
batt
v
alu
e
r
em
ain
s
th
e
s
am
e
in
th
e
S4
0
b
atter
y
ar
r
an
g
em
en
t p
atter
n
.
L
o
ad
p
o
wer
ca
lc
u
latio
n
u
s
in
g
(
1
4
)
.
=
(1
4
)
=
144
508
.
21
=
73
.
18
T
h
is
r
esear
ch
is
p
lan
n
e
d
t
o
p
r
o
d
u
ce
a
lo
a
d
v
o
ltag
e
o
f
ar
o
u
n
d
8
0
0
–
1
,
1
0
0
V
an
d
a
lo
a
d
p
o
wer
o
f
5
0
–
7
5
k
W
.
T
h
e
r
esu
lts
o
f
o
th
er
ar
r
a
n
g
em
en
t
ca
lcu
latio
n
s
ca
n
b
e
s
ee
n
in
T
ab
le
2
,
wh
er
e
th
e
v
o
ltag
e
v
alu
e
at
V
batt
h
as
n
o
t
ap
p
r
o
ac
h
ed
o
r
eq
u
al
to
t
h
e
d
e
s
ir
ed
V
L
v
alu
e,
s
o
it
is
n
ec
ess
ar
y
to
p
er
f
o
r
m
a
th
ir
d
p
atter
n
.
T
h
e
p
atter
n
p
lan
I
I
I
o
f
th
e
b
atter
y
a
r
r
an
g
em
en
t is S4
0
-
P2
-
S6
,
S8
0
-
P2
-
S3
,
an
d
S1
0
0
-
P2
-
S3
,
wh
er
e
S4
0
-
P2
-
S6
is
an
ar
r
an
g
em
en
t
o
f
S4
0
-
P2
ar
r
an
g
ed
in
6
s
er
ies,
S8
0
-
P2
-
S3
is
an
ar
r
an
g
em
en
t
o
f
S8
0
-
P2
ar
r
an
g
ed
in
3
s
er
ies,
an
d
S1
0
0
-
P2
-
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is
an
ar
r
an
g
em
en
t
o
f
S1
0
0
-
P2
ar
r
an
g
ed
i
n
3
s
er
ies.
L
ar
g
e
V
L
=
−
u
s
es
(
1
5
)
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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&
Dr
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s
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N:
2088
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atter
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r
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[
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a
m
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ℎ
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=
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000
800
=
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(1
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T
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len
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(
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s
tim
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ch
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3.
RE
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AND
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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4
I
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t J Po
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Dr
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t
,
Vo
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16
,
No
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4
,
Dec
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b
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20
25
:
2521
-
2
5
3
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o
u
t
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s
b
atter
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p
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ip
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esig
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f
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1
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,
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1
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O
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ba
t
t
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rr
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t
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n
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h
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in
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p
atter
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f
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d
in
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atter
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atter
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o
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atter
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r
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ies
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Fu
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th
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r
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atter
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atter
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atter
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.
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ter
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ely
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r
th
e
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n
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n
th
at
th
e
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e
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th
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n
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at
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atter
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lly
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d
.
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m
es
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is
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atter
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ca
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atter
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n
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e
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lly
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e
d
at
a
V
L
v
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e
o
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ap
p
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x
im
ately
8
0
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I
n
Fig
u
r
es
2
to
4
,
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s
in
g
th
e
p
ar
am
eter
s
C
in
=
8
0
m
F,
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out
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1
3
0
m
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N
p
=
1
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an
d
N
s
=
1
.
5
4
.
Pad
a
Fig
u
r
e
2
o
f
th
e
o
u
tp
u
t
ch
ar
ac
t
er
is
tics
o
f
th
e
ch
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g
in
g
s
y
s
tem
o
n
th
e
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0
-
P2
b
atter
y
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r
a
y
p
atter
n
:
i
)
T
h
e
V
L
p
r
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f
ile
s
h
o
ws
s
tab
ilit
y
at
8
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4
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9
4
V
with
a
m
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im
u
m
o
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o
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e
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L
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s
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g
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ad
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m
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5
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3
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6
4
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wh
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tate
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ch
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So
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a
n
d
iii
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h
e
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le
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u
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e
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atter
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