I
nd
o
ne
s
ia
n J
o
urna
l o
f
E
lect
rica
l En
g
ineering
a
nd
Co
m
pu
t
er
Science
Vo
l.
3
7
,
No
.
2
,
Feb
r
u
ar
y
20
2
5
,
p
p
.
730
~
739
I
SS
N:
2
502
-
4
7
52
,
DOI
: 1
0
.
1
1
5
9
1
/ijee
cs
.v
3
7
.
i
2
.
pp
730
-
7
3
9
730
J
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na
l ho
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ep
a
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e
:
h
ttp
:
//ij
ee
cs
.
ia
esco
r
e.
co
m
Two
RC
mo
del
a
nd
pa
ra
meter
esti
ma
tion
of
l
ithi
um
-
i
on
b
a
tt
e
ry
G
iris
ha
J
o
s
hi
1
,
L
a
k
s
hm
i
Na
ra
y
a
na
Va
llu
ru
2
,
Am
o
l
P
r
a
ka
s
h
K
ha
de
2
1
D
e
p
a
r
t
me
n
t
of
El
e
c
t
r
i
c
a
l
a
n
d
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e
c
t
r
o
n
i
c
s
E
n
g
i
n
e
e
r
i
n
g
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N
M
A
M
I
n
st
i
t
u
t
e
of
Te
c
h
n
o
l
o
g
y
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N
i
t
t
e
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D
e
e
me
d
to
be
U
n
i
v
e
r
si
t
y
)
,
N
i
t
t
e
,
K
a
r
n
a
t
a
k
a
,
I
n
d
i
a
2
L&T
T
e
c
h
n
o
l
o
g
y
S
e
r
v
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c
e
s
,
B
a
n
g
a
l
u
r
u
,
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
J
ul
2
,
2
0
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4
R
ev
is
ed
Sep
17
,
2
0
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4
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ted
Sep
30
,
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0
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e
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v
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h
icle
s
a
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tren
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h
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e
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a
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e
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re
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u
e
n
t
h
ig
h
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p
o
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re
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u
irem
e
n
ts
o
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lec
tri
c
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e
h
icle
s,
m
a
k
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th
e
b
a
tt
e
ries
d
isc
h
a
rg
e
a
t
h
i
g
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e
r
C
ra
te.
Disc
h
a
rg
in
g
a
t
a
h
ig
h
e
r
C
ra
te
will
lea
d
to
h
ig
h
e
r
h
e
a
t
p
ro
d
u
c
ti
o
n
lea
d
in
g
t
o
d
e
stru
c
ti
o
n
a
n
d
e
x
p
l
o
si
o
n
o
f
t
h
e
b
a
tt
e
ry
.
T
o
o
p
ti
m
ize
th
e
c
h
a
rg
in
g
a
n
d
d
isc
h
a
rg
i
n
g
C
ra
tes
c
o
n
si
d
e
rin
g
b
o
th
sa
fe
ty
a
n
d
p
e
rfo
rm
a
n
c
e
fa
c
to
rs,
b
a
tt
e
ry
m
a
n
a
g
e
m
e
n
t
sy
ste
m
(B
M
S
)
is
u
se
d
a
s
a
n
e
ter
n
a
l
c
o
m
p
o
n
e
n
t
o
f
p
o
we
r
so
u
rc
e
.
T
o
e
stim
a
te
th
e
sta
te
o
f
c
h
a
rg
e
(S
OC),
wh
ich
is
a
n
e
ss
e
n
ti
a
l
c
o
m
p
o
n
e
n
t
o
f
BM
S
,
a
c
c
u
ra
te
b
a
t
tery
m
o
d
e
ll
in
g
is
re
q
u
ired
.
T
wo
RC
m
o
d
e
l
is
o
n
e
o
f
t
h
e
m
o
st
u
se
d
li
t
h
iu
m
-
i
o
n
b
a
tt
e
ry
m
o
d
e
l,
d
u
e
t
o
it
s
sim
p
li
c
it
y
a
n
d
a
c
c
u
ra
c
y
.
Th
e
e
q
u
i
v
a
len
t
c
ircu
i
t
p
a
ra
m
e
ters
,
re
sista
n
c
e
s
a
n
d
c
a
p
a
c
it
a
n
c
e
d
o
c
h
a
n
g
e
wit
h
S
OC
a
n
d
tem
p
e
ra
t
u
re
s.
Th
is
p
a
p
e
r
fo
c
u
se
s
o
n
e
sti
m
a
ti
o
n
o
f
e
q
u
iv
a
len
t
c
ircu
it
p
a
ra
m
e
ters
fo
r
a
wid
e
ra
n
g
e
o
f
tem
p
e
ra
tu
re
s
a
n
d
S
OCs
ra
n
g
in
g
fro
m
-
2
0
d
e
g
re
e
c
e
lsiu
s
to
+
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5
d
e
g
re
e
c
e
lsiu
s
a
n
d
1
0
0
to
0
re
sp
e
c
ti
v
e
ly
.
We
h
a
v
e
d
e
v
e
lo
p
e
d
two
RC
m
o
d
e
l
f
o
r
P
a
n
a
so
n
ic
1
8
6
5
0
P
F
a
n
d
e
stim
a
ted
th
e
p
a
ra
m
e
ters
o
f
th
e
m
o
d
e
l
u
sin
g
h
y
b
rid
p
u
ls
e
p
o
we
r
c
h
a
r
a
c
teriz
a
ti
o
n
(HPP
C)
d
a
ta.
M
ATLAB
b
a
se
d
p
a
ra
m
e
ter
e
stim
a
t
o
r
is
u
se
d
in
d
e
term
in
i
n
g
th
e
e
q
u
i
v
a
len
t
c
irc
u
it
p
a
ra
m
e
ters
.
K
ey
w
o
r
d
s
:
B
atter
y
m
an
ag
em
en
t
s
y
s
tem
C
r
ate
E
lectr
ic
v
eh
icles
Hy
b
r
id
p
u
ls
e
p
o
wer
ch
ar
ac
ter
izatio
n
test
MA
T
L
AB
State
of
ch
ar
g
e
T
h
is
is
an
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r
th
e
CC
BY
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Gir
is
h
a
J
o
s
h
i
Dep
ar
tm
en
t
of
E
lectr
ical
an
d
E
lectr
o
n
ics
E
n
g
in
ee
r
i
n
g
,
NM
AM
I
n
s
titu
te
of
T
ec
h
n
o
lo
gy
Nitte
(
Dee
m
ed
to
be
Un
iv
e
r
s
ity
)
Nitte,
Kar
n
atak
a
-
5
7
4
1
1
0
,
I
n
d
i
a
E
m
ail:
g
ir
is
h
jo
s
h
i8
5
@
n
itte.e
d
u
.
in
1.
I
NT
RO
D
UCT
I
O
N
On
e
of
th
e
ch
allen
g
es
in
ac
h
iev
in
g
th
e
tr
an
s
itio
n
f
r
o
m
IC
en
g
in
e
-
b
ased
tec
h
n
o
lo
g
y
to
elec
tr
ic
v
eh
icles
(
E
V)
is
b
atter
ie
s
.
T
h
e
co
n
v
en
tio
n
al
lead
-
ac
id
b
a
tter
ies
u
s
ed
as
an
au
x
iliar
y
p
o
wer
s
o
u
r
ce
in
IC
en
g
in
e
-
b
ased
v
eh
icles
ar
e
n
o
t
s
u
itab
le
f
o
r
elec
tr
ic
v
e
h
icles.
T
h
is
is
due
to
th
eir
l
o
w
p
o
wer
to
weig
h
t
an
d
p
o
wer
to
s
ize
r
atio
[
1
]
,
[
2
]
.
D
u
e
to
th
e
ad
v
a
n
tag
es
s
u
ch
as
h
ig
h
en
er
g
y
d
en
s
ity
,
lo
n
g
life
s
p
an
,
lig
h
t
in
weig
h
t,
lo
wer
s
elf
-
d
is
ch
ar
g
e
an
d
less
ch
ar
g
in
g
tim
e,
lith
i
u
m
-
io
n
b
atter
ies
h
av
e
b
ec
o
m
e
th
e
f
ir
s
t
ch
o
ice
f
o
r
elec
tr
ic
v
eh
icle
p
o
wer
s
o
u
r
ce
[
3
]
,
[
4
]
.
Hig
h
ch
ar
g
i
n
g
an
d
d
is
ch
ar
g
in
g
C
r
ates
ca
u
s
e
th
er
m
al
r
u
n
awa
y
in
th
ese
b
atter
ies.
T
h
is
h
as
r
ai
s
ed
m
ajo
r
co
n
ce
r
n
s
with
r
esp
ec
t
to
t
h
e
s
af
ety
of
th
e
p
ass
en
g
er
s
an
d
elec
tr
ic
v
eh
icles.
T
h
er
e
a
r
e
two
ap
p
r
o
ac
h
es
in
m
o
d
elin
g
of
lith
iu
m
-
i
o
n
b
atter
ies
n
am
ely
p
h
y
s
ics
b
a
s
ed
m
o
d
ellin
g
an
d
eq
u
iv
alen
t
cir
cu
it
m
o
d
el.
Ph
y
s
ics
b
ased
m
o
d
ellin
g
is
a
co
m
p
lex
an
d
in
v
o
lv
ed
m
eth
o
d
.
T
h
is
ap
p
r
o
ac
h
em
p
l
o
y
s
m
ath
em
atica
l
f
o
r
m
u
las
b
ased
on
c
h
em
ical
a
n
d
p
h
y
s
ical
p
r
in
cip
les
to
d
escr
ib
e
th
e
ev
e
n
ts
th
at
tak
e
p
lace
in
s
id
e
th
e
b
atter
y
.
C
o
m
p
a
r
ed
to
th
is
eq
u
iv
ale
n
t
cir
cu
it
m
o
d
els
ar
e
s
im
p
le
an
d
r
o
b
u
s
t
[
5
]
−
[
7
]
.
Mo
s
t
of
th
e
b
atter
y
m
an
ag
em
en
t
s
y
s
tem
s
(
B
MS)
u
s
e
an
eq
u
iv
ale
n
t
cir
cu
it
m
o
d
el
of
th
e
b
atter
y
[
8
]
−
[
1
0
]
.
E
v
en
th
o
u
g
h
th
e
eq
u
iv
alen
t
cir
cu
it
m
o
d
el
is
less
ac
cu
r
ate
an
d
do
not
h
av
e
a
ll
th
e
f
ea
tu
r
es
of
p
h
y
s
ics
-
b
ased
m
o
d
els
th
ey
ar
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2
5
0
2
-
4
7
52
Tw
o
R
C
mo
d
el
a
n
d
p
a
r
a
mete
r
esti
ma
tio
n
o
f
lith
iu
m
-
io
n
b
a
tt
ery
(
Gir
is
h
a
Jo
s
h
i
)
731
p
r
ef
er
r
e
d
in
b
atter
y
m
an
ag
em
en
t
s
y
s
tem
s
of
m
ajo
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ity
of
th
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b
atter
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b
ec
a
u
s
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of
th
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im
p
licity
an
d
ad
eq
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ate
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o
d
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ac
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In
eq
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alen
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it
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h
e
n
o
m
e
n
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im
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of
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atter
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d
o
n
e
u
s
in
g
th
e
elec
tr
ical
co
m
p
o
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en
ts
[
1
1
]
.
T
h
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eq
u
iv
alen
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cir
cu
it
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ar
am
et
er
s
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ap
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atter
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ar
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f
o
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R1
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e
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t
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ch
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o
ce
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th
e
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atter
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B
u
t
u
s
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e
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o
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e
will
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a
b
le
to
m
o
d
el
th
e
c
o
m
p
lete
b
e
h
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io
r
of
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e
g
iv
en
lith
iu
m
-
io
n
b
atter
y
at
d
if
f
er
en
t
tem
p
er
atu
r
es
an
d
s
tate
of
ch
ar
g
e.
E
q
u
iv
alen
t
cir
cu
it
m
o
d
els
u
s
e
b
asic
elec
tr
ical
cir
cu
it
co
m
p
o
n
en
ts
in
s
u
ch
a
way
th
at
it
wil
l
be
ab
le
to
r
ep
r
esen
t
b
atter
y
v
o
ltag
e
f
o
r
d
i
f
f
er
en
t
cu
r
r
en
t
s
tim
u
li
ap
p
lied
to
th
e
b
atter
y
ce
ll.
Du
e
to
n
o
n
lin
ea
r
r
elatio
n
s
h
ip
b
etwe
en
v
o
ltag
e
a
n
d
SOC
of
lith
iu
m
-
io
n
b
atter
ies,
v
o
ltag
e
alo
n
e
ca
n
n
o
t
be
u
s
ed
to
ca
lcu
late
th
e
SOC
.
To
r
ed
u
ce
th
e
am
b
ig
u
ity
ab
o
u
t
th
e
d
is
tan
ce
th
at
co
u
ld
be
tr
av
elle
d
with
av
ailab
le
ch
ar
g
e
in
b
atter
ies
co
r
r
ec
t
esti
m
atio
n
of
s
tate
of
ch
ar
g
e
(
SOC
)
is
n
ee
d
ed
.
To
esti
m
ate
SOC
,
h
av
in
g
th
e
p
ar
am
eter
s
of
th
e
eq
u
i
v
alen
t
cir
cu
it
is
v
er
y
m
u
ch
ess
en
tial.
W
h
en
SOC
is
esti
m
ated
in
r
ea
l
tim
e
by
B
MS
at
an
y
g
iv
en
d
r
iv
e
cy
cl
e,
v
alu
es
of
th
e
cir
cu
it
p
a
r
am
eter
s
is
n
ee
d
ed
.
T
h
e
cir
cu
it
p
ar
am
eter
s
do
ch
a
n
g
e
with
tem
p
er
atu
r
e
an
d
s
tate
of
ch
ar
g
e
of
th
e
b
atter
y
wh
ic
h
m
ak
es
th
e
m
o
d
el
co
m
p
lex
.
Un
d
er
s
tan
d
in
g
th
e
c
h
ar
ac
ter
is
tics
of
th
e
b
atter
y
w
ith
r
esp
ec
t
to
ch
a
n
g
e
in
SOC
an
d
tem
p
er
atu
r
e
is
ess
en
tial
f
ac
to
r
f
o
r
th
e
s
u
cc
es
s
of
B
MS
[
1
2
]
.
Ver
y
f
ew
r
esear
ch
er
s
h
a
v
e
p
u
b
lis
h
ed
th
ei
r
wo
r
k
in
th
is
lin
e
a
n
d
r
ep
o
r
ted
t
h
e
p
ar
am
eter
esti
m
atio
n
at
d
if
f
er
e
n
t
SOC
an
d
tem
p
er
atu
r
es
[
1
3
]
.
Z
h
an
g
et
a
l.
[
1
4
]
esti
m
ated
SOC
co
n
s
id
er
in
g
o
n
ly
th
e
d
ata
f
o
r
th
r
ee
tem
p
er
atu
r
es.
W
o
r
k
ca
r
r
ied
by
Kh
an
u
m
et
a
l.
[
1
5
]
esti
m
ates
v
alu
es
of
in
ter
n
al
r
esis
tan
ce
R0
f
o
r
d
i
f
f
er
en
t
tem
p
er
at
u
r
es
an
d
SOC
.
In
th
e
wo
r
k
ca
r
r
ied
out
by
J
u
n
g
an
d
T
u
llu
[
1
6
]
d
ev
elo
p
e
d
ex
p
r
ess
io
n
s
f
o
r
T
h
ev
en
in
eq
u
iv
alen
t
cir
c
u
it
m
o
d
el
as
a
f
u
n
ctio
n
of
SOC
but
ef
f
ec
t
of
tem
p
er
atu
r
e
on
eq
u
iv
alen
t
cir
c
u
it
p
ar
am
eter
s
is
not
an
aly
ze
d
.
Sin
ce
th
e
b
atter
y
tem
p
er
at
u
r
e
d
e
p
en
d
s
on
am
b
ie
n
t
tem
p
er
atu
r
e
an
d
C
-
r
ate
at
wh
ich
it
is
d
is
ch
ar
g
ed
,
p
ar
am
eter
s
n
ee
d
to
be
esti
m
ated
f
o
r
wid
e
r
an
g
e
of
tem
p
er
atu
r
es.
W
o
r
k
r
elate
d
t
o
,
im
p
ac
t
of
tem
p
er
atu
r
e
an
d
SOC
on
th
e
e
q
u
iv
alen
t
cir
cu
it
p
ar
am
eter
s
is
not
s
ig
n
if
ican
tly
r
ep
o
r
ted
in
th
e
l
iter
atu
r
e.
Pre
s
en
t
wo
r
k
ad
d
r
e
s
s
es
th
i
s
is
s
u
e
an
d
esti
m
ates
th
e
p
ar
am
eter
s
f
o
r
tem
p
er
atu
r
es
r
an
g
i
n
g
f
r
o
m
-
20
to
+2
5
-
d
e
g
r
ee
C
elsi
u
s
f
o
r
SOC
ch
an
g
in
g
f
r
o
m
ze
r
o
to
o
n
e.
T
h
is
wo
r
k
is
s
ig
n
if
ican
t
co
n
s
id
er
in
g
th
e
f
ac
t
th
at
d
u
r
i
n
g
t
h
e
o
p
er
atio
n
of
t
h
e
b
atter
y
,
b
o
t
h
d
u
r
in
g
ch
ar
g
i
n
g
an
d
d
is
ch
ar
g
in
g
,
tem
p
er
atu
r
e
do
ch
an
g
e
an
d
f
o
r
ac
cu
r
ate
SOC
esti
m
atio
n
,
h
av
in
g
eq
u
i
v
alen
t
cir
cu
it
p
ar
a
m
eter
s
f
o
r
th
e
en
tire
r
an
g
e
of
o
p
er
atin
g
tem
p
er
atu
r
e
is
v
er
y
im
p
o
r
tan
t.
2.
M
E
T
H
O
D
In
th
is
s
ec
tio
n
in
f
o
r
m
atio
n
ab
o
u
t
d
if
f
er
e
n
t
s
tate
of
th
e
ar
t
eq
u
iv
alen
t
cir
cu
its
an
d
th
e
p
r
o
ce
s
s
in
Fig
u
r
e
1
of
p
ar
am
eter
esti
m
atio
n
is
ex
p
lain
ed
.
Fig
u
r
e
1
(
a
)
s
h
o
ws
th
e
f
lo
w
ch
ar
t
of
p
ar
am
eter
esti
m
atio
n
.
Fig
u
r
e
1
(
b
)
s
h
o
ws
th
e
p
ar
a
m
eter
esti
m
atio
n
win
d
o
w
of
MA
T
L
AB
u
s
ed
in
th
e
wo
r
k
,
f
o
r
esti
m
atio
n
of
p
ar
am
eter
s
.
L
ith
iu
m
-
io
n
b
atter
y
is
m
o
d
ele
d
u
s
in
g
2
RC
eq
u
iv
alen
t
cir
cu
it.
T
h
e
eq
u
i
v
alen
t
cir
cu
it
is
d
e
v
elo
p
ed
in
MA
T
L
AB
Simu
lin
k
p
latf
o
r
m
.
Par
am
eter
esti
m
ato
r
ap
p
li
ca
tio
n
of
MA
T
L
AB
is
u
s
ed
in
th
is
wo
r
k
.
Data
g
en
er
ated
f
r
o
m
h
y
b
r
id
p
u
ls
e
p
o
wer
ch
ar
ac
ter
izatio
n
(
HPPC
)
test
s
p
er
f
o
r
m
ed
at
th
e
Un
iv
er
s
ity
of
W
is
co
n
s
in
-
Ma
d
is
o
n
by
Ko
llm
ey
er
[
1
7
]
h
as
b
ee
n
u
s
ed
in
our
wo
r
k
.
HPPC
test
d
ata
co
n
s
is
ts
of
in
f
o
r
m
atio
n
of
v
o
ltag
e,
cu
r
r
en
t,
tim
e,
b
atter
y
tem
p
er
atu
r
e,
Am
p
er
e
h
o
u
r
,
W
att
hour
an
d
p
o
wer
.
T
h
e
b
r
ief
p
r
o
ce
s
s
f
o
llo
wed
in
MA
T
L
AB
p
ar
am
eter
esti
m
ati
o
n
is
as
f
o
llo
ws.
E
q
u
iv
alen
t
ci
r
cu
it
p
ar
am
eter
s
ar
e
g
iv
en
s
o
m
e
in
itial
v
alu
e.
Fo
r
a
g
iv
en
cu
r
r
en
t
im
p
u
ls
e
d
ata
f
r
o
m
HPPC
test
,
th
e
m
o
d
el
ter
m
in
al
v
o
ltag
e
is
co
m
p
a
r
ed
wit
h
HPPC
ex
p
er
im
en
t
ter
m
in
al
v
o
ltag
e
d
ata.
T
h
e
p
a
r
am
eter
s
ar
e
ad
ju
s
ted
till
R
MSE
v
alu
e
of
th
is
ter
m
i
n
al
v
o
lta
g
e
er
r
o
r
r
e
d
u
ce
s
to
th
e
ac
ce
p
tab
le
lev
el
s
et
in
th
e
ap
p
licatio
n
.
T
h
e
p
r
o
ce
s
s
is
ex
p
lain
ed
in
d
etail
in
f
o
llo
win
g
s
u
b
s
ec
tio
n
s
.
2
.
1
.
Dev
el
o
pm
ent
of
equiv
a
lent
circ
uit
m
o
del
of
lithium
-
i
o
n
ba
t
t
er
y
First
E
lem
en
t
of
eq
u
iv
alen
t
cir
cu
it
m
o
d
el
is
s
elec
ted
s
u
c
h
th
at
th
e
p
r
ed
o
m
in
an
t
b
eh
a
v
io
r
of
th
e
b
atter
y
ce
ll
m
u
s
t
be
r
ep
r
esen
ted
.
An
y
d
i
f
f
er
en
ce
in
ch
ar
ac
t
er
is
tics
b
etwe
en
ce
ll
m
o
d
el
a
n
d
ac
tu
al
ce
ll
is
th
e
m
o
d
ellin
g
e
r
r
o
r
.
T
h
e
eq
u
iv
al
en
t
cir
cu
it
m
o
d
el
is
im
p
r
o
v
e
d
by
ad
d
in
g
one
more
elem
en
t
s
u
ch
th
at
th
e
m
o
d
ellin
g
er
r
o
r
r
ed
u
ce
s
s
ig
n
if
ican
tly
.
Ad
d
i
n
g
th
e
elem
e
n
ts
to
eq
u
iv
alen
t
ci
r
cu
it
m
o
d
el
co
n
tin
u
es
till
th
e
e
r
r
o
r
r
ed
u
ce
s
s
ig
n
if
ican
tly
an
d
th
e
co
r
r
esp
o
n
d
in
g
b
atter
y
ce
ll
m
o
d
el
is
ca
lled
as
“g
o
o
d
en
o
u
g
h
”
m
o
d
el
of
th
e
b
atter
y
ce
ll
[
1
8
]
.
T
h
e
f
u
n
d
a
m
en
tal
o
b
s
er
v
ed
b
eh
av
io
r
of
th
e
b
atter
y
ce
ll
is
v
o
ltag
e
at
th
e
ter
m
in
als
of
th
e
b
atter
y
ce
ll.
To
s
tar
t
with
,
a
b
atter
y
ce
ll
is
r
ep
r
esen
ted
by
an
id
ea
l
v
o
ltag
e
s
o
u
r
ce
.
Fig
u
r
e
2
to
Fig
u
r
e
6
s
h
o
ws
v
ar
io
u
s
s
tag
es
of
2
RC
eq
u
i
v
alen
t
cir
cu
it
m
o
d
el
d
ev
elo
p
m
en
t.
Fig
u
r
e
2
s
h
o
ws
th
e
r
ep
r
esen
tatio
n
of
th
e
b
atter
y
ce
ll
u
s
in
g
id
ea
l
v
o
ltag
e
s
o
u
r
ce
.
T
h
e
r
e
p
r
esen
tatio
n
s
h
o
wn
in
Fig
u
r
e
2,
is
v
ali
d
o
n
ly
d
u
r
in
g
t
h
e
in
itial
p
h
ase
wh
er
e
th
e
b
atter
y
is
ju
s
t
co
n
n
ec
te
d
to
th
e
l
o
ad
.
T
h
e
i
d
ea
l
v
o
ltag
e
s
o
u
r
ce
alo
n
e
is
n
o
t
ab
le
to
r
e
p
r
esen
t
th
e
b
eh
av
io
r
of
b
atter
y
as
b
atter
y
ter
m
in
al
v
o
ltag
e
is
d
ep
en
d
en
t
on
th
e
lo
ad
c
u
r
r
e
n
t.
Af
ter
th
e
in
itial
p
h
ase
th
e
ter
m
in
al
v
o
ltag
e
d
ep
en
d
s
on
th
e
am
o
u
n
t
of
cu
r
r
en
t
d
r
awn
f
r
o
m
th
e
b
atter
y
,
r
ec
en
t
u
s
a
g
e,
an
d
m
an
y
o
th
er
asp
ec
ts
of
th
e
b
atter
y
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
52
In
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
3
7
,
No
.
2
,
Feb
r
u
a
r
y
20
2
5
:
7
3
0
-
7
3
9
732
(
a)
(
b
)
Fig
u
r
e
1
.
Par
am
eter
esti
m
atio
n
(
a)
Flo
w
ch
a
r
t o
f
p
ar
am
eter
esti
m
atio
n
an
d
(
b
)
MA
T
L
AB
p
ar
am
eter
esti
m
atio
n
W
in
d
o
w
F
i
g
u
r
e
2
.
C
o
n
s
t
a
n
t
o
u
t
p
u
t
v
o
l
tag
e
c
e
l
l
m
o
d
e
l
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2
5
0
2
-
4
7
52
Tw
o
R
C
mo
d
el
a
n
d
p
a
r
a
mete
r
esti
ma
tio
n
o
f
lith
iu
m
-
io
n
b
a
tt
ery
(
Gir
is
h
a
Jo
s
h
i
)
733
An
in
d
ep
en
d
e
n
t
s
o
u
r
ce
v
o
ltag
e
r
ep
r
esen
tatio
n
of
th
e
b
atter
y
ce
ll
alo
n
e
is
in
co
m
p
lete.
B
at
te
r
y
v
o
ltag
e
will
be
g
r
ea
ter
in
f
u
lly
c
h
ar
g
ed
ce
lls
co
m
p
ar
ed
to
a
d
is
ch
ar
g
ed
ce
ll.
T
h
is
f
ac
t
in
s
p
ir
es
ch
an
g
e
in
th
e
o
p
en
cir
cu
it
v
o
ltag
e
(
OC
V
)
r
ep
r
esen
tatio
n
f
r
o
m
in
d
e
p
en
d
e
n
t
v
o
lt
ag
e
s
o
u
r
ce
to
d
ep
en
d
en
t
v
o
ltag
e
s
o
u
r
ce
of
s
tate
of
ch
ar
g
e.
T
h
is
m
o
d
if
icatio
n
is
ju
s
tifie
d
b
ec
au
s
e
te
r
m
in
al
v
o
ltag
e
of
f
u
lly
ch
ar
g
ed
ce
lls
is
d
if
f
er
e
n
t
f
r
o
m
p
ar
tially
d
is
ch
ar
g
e
d
ce
lls
.
SOC
is
m
ea
s
u
r
e
of
am
o
u
n
t
of
c
h
ar
g
e
av
ailab
le
in
th
e
b
atter
y
at
a
g
iv
en
in
s
tan
t
co
m
p
ar
ed
to
to
tal
ch
ar
g
e
h
o
ld
in
g
ca
p
ac
ity
of
th
e
b
atter
y
.
SOC
,
wh
ich
is
a
u
n
itles
s
p
ar
am
eter
,
v
ar
ies
f
r
o
m
ze
r
o
to
o
n
e.
T
h
e
s
y
m
b
o
l
u
s
ed
f
o
r
SOC
is
“z”
W
h
en
th
e
b
atter
y
is
f
u
lly
d
is
ch
ar
g
ed
,
th
e
SOC
v
alu
e
is
ze
r
o
an
d
wh
en
th
e
b
atter
y
is
f
u
lly
c
h
ar
g
ed
,
c
o
r
r
esp
o
n
d
in
g
SOC
v
alu
e
is
o
n
e.
T
o
tal
ch
ar
g
e
h
o
ld
in
g
ca
p
ac
ity
or
to
tal
ca
p
ac
ity
co
u
ld
be
d
ef
i
n
ed
as
to
tal
am
o
u
n
t
of
ch
a
r
g
e
r
em
o
v
e
d
f
r
o
m
th
e
b
atter
y
wh
e
n
s
tate
of
ch
ar
g
e
is
v
ar
ied
f
r
o
m
o
n
e
to
ze
r
o
.
It
is
m
ea
s
u
r
e
d
in
eith
er
am
p
er
e
-
h
o
u
r
s
or
m
i
lli
am
p
er
e
h
o
u
r
s
d
ep
en
d
in
g
on
th
e
b
atter
y
r
atin
g
.
It
is
r
ep
r
esen
ted
by
th
e
s
y
m
b
o
l
Q.
T
h
e
to
tal
ca
p
ac
ity
is
a
p
ar
am
eter
of
eq
u
iv
ale
n
t
cir
cu
it
m
o
d
el,
wh
ic
h
d
o
es
not
ch
a
n
g
e
with
cu
r
r
en
t
a
n
d
te
m
p
er
atu
r
e.
T
h
is
m
a
y
ch
a
n
g
e
f
r
o
m
ce
ll
to
ce
ll.
H
o
wev
er
,
th
e
v
alu
e
of
Q
r
ed
u
ce
s
g
r
ad
u
ally
with
a
g
ein
g
of
th
e
b
atter
y
.
T
h
e
(
1
)
p
r
o
v
i
d
es
th
e
m
o
d
el
of
SOC
.
̇
(
)
=
−
(
)
(
)
(
1
)
Sig
n
of
th
e
cu
r
r
en
t
is
p
o
s
itiv
e
wh
ile
d
is
ch
ar
g
in
g
an
d
n
eg
ati
v
e
d
u
r
in
g
ch
ar
g
in
g
.
T
h
e
s
y
m
b
o
l
η
u
s
ed
in
(
1
)
is
co
u
lo
m
b
ic
ef
f
icien
cy
wh
ich
is
d
ef
in
ed
as
th
e
r
atio
of
ch
ar
g
e
out
to
ch
ar
g
e
in
an
d
th
e
S
O
C
v
alu
e
is
r
etain
ed
to
th
e
v
alu
e
b
ef
o
r
e
d
is
ch
ar
g
in
g
a
n
d
ch
ar
g
in
g
c
y
cle.
T
h
e
v
alu
e
of
η
is
one
d
u
r
i
n
g
d
is
ch
ar
g
in
g
an
d
it
is
less
th
an
one
d
u
r
in
g
c
h
ar
g
in
g
.
Du
e
to
h
ig
h
er
co
u
lo
m
b
ic
e
f
f
icien
cies
of
lith
iu
m
-
io
n
b
atter
y
,
t
h
e
a
p
p
r
o
x
im
atio
n
of
η
to
one
d
u
r
in
g
b
o
th
c
h
ar
g
in
g
an
d
d
is
ch
ar
g
in
g
p
h
ases
lead
s
to
r
el
iab
le
m
o
d
el
r
e
p
r
esen
tatio
n
.
By
in
teg
r
atin
g
(
1
)
we
can
h
av
e
e
x
p
r
ess
io
n
f
o
r
th
e
s
t
ate
of
ch
ar
g
e.
T
h
e
(
2
)
r
ep
r
esen
ts
th
e
co
n
tin
u
o
u
s
tim
e
m
o
d
el.
(
)
=
(
0
)
−
1
∫
(
)
(
)
(
)
0
(
2
)
T
h
e
d
is
cr
ete
tim
e
s
tate
of
ch
ar
g
e
ex
p
r
ess
io
n
is
r
ep
r
esen
ted
in
th
e
(
3
)
.
[
+
1
]
=
[
]
−
Δ
[
]
[
]
(
3
)
I
m
p
r
o
v
ed
cir
c
u
it
m
o
d
el
wh
e
r
e
OC
V
is
a
f
u
n
ctio
n
of
s
tate
of
ch
ar
g
e
is
s
h
o
wn
in
F
ig
u
r
e
3
.
Mo
d
els
r
ep
r
esen
ted
in
F
ig
u
r
e
s
2
an
d
3
d
escr
ib
es
th
e
s
tatic
m
o
d
els
an
d
d
o
es
not
i
n
co
r
p
o
r
ate
th
e
ef
f
ec
ts
of
c
h
ar
g
in
g
a
n
d
d
is
ch
ar
g
in
g
on
th
e
ter
m
in
al
v
o
ltag
e.
In
an
y
b
atter
y
,
it
is
o
b
s
er
v
ed
f
ac
t
t
h
at
ter
m
in
al
v
o
ltag
e
is
less
th
an
th
e
o
p
en
cir
cu
it
v
o
ltag
e
d
u
r
in
g
d
is
ch
a
r
g
in
g
an
d
ter
m
in
al
v
o
ltag
e
is
g
r
ea
ter
th
an
o
p
en
cir
cu
it
v
o
ltag
e
d
u
r
in
g
d
is
ch
a
r
g
in
g
.
T
h
is
ch
ar
ac
ter
is
tic
can
be
em
b
e
d
d
ed
in
th
e
m
o
d
el
by
co
n
n
ec
tin
g
a
r
esis
tan
ce
in
s
er
ies
with
th
e
co
n
tr
o
lled
v
o
ltag
e
s
o
u
r
ce
.
T
h
e
r
e
s
is
tan
ce
is
n
am
ed
as
eq
u
iv
alen
t
cir
cu
it
r
esis
tan
ce
(
E
SR
)
.
T
h
e
im
p
r
o
v
ed
m
o
d
el
is
r
ep
r
esen
ted
in
F
ig
u
r
e
4
.
Fig
u
r
e
3
.
SOC
d
ep
en
d
en
t
v
o
ltag
e
s
o
u
r
ce
C
ell
m
o
d
el
Fig
u
r
e
4.
E
q
u
iv
alen
t
cir
c
u
it
r
e
s
is
tan
ce
m
o
d
el
Ma
th
em
atica
l
eq
u
atio
n
s
g
o
v
e
r
n
in
g
th
e
m
o
d
el
s
h
o
wn
in
F
ig
u
r
e
4
ar
e
as
f
o
llo
ws.
Fo
r
co
n
tin
u
o
u
s
tim
e
d
o
m
ain
,
e
q
u
atio
n
f
o
r
s
tate
of
c
h
ar
g
e
is
s
am
e
as
(
2
)
.
T
er
m
in
al
v
o
ltag
e
is
ex
p
r
ess
ed
as,
(
)
=
(
(
)
)
−
(
)
0
(
4
)
(
)
>
(
(
)
)
(
)
<
0
.
ℎ
(
)
<
(
(
)
)
(
)
>
0
i.e
d
u
r
in
g
d
is
ch
ar
g
in
g
Fo
r
d
is
cr
ete
tim
e
d
o
m
ain
.
E
q
u
atio
n
f
o
r
S
O
C
is
s
am
e
as
(
3
)
,
B
atter
y
ter
m
in
al
v
o
ltag
e
is
ex
p
r
ess
ed
as,
(
)
=
(
(
)
)
−
(
)
0
(5
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
52
In
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
3
7
,
No
.
2
,
Feb
r
u
a
r
y
20
2
5
:
7
3
0
-
7
3
9
734
An
y
ch
an
g
e
in
th
e
ter
m
in
al
v
o
ltag
e
with
r
esp
ec
t
to
o
p
en
cir
cu
it
v
o
ltag
e
due
to
cu
r
r
en
t
f
lo
w
in
g
in
th
e
b
atter
y
ce
ll
is
ter
m
e
d
as
p
o
lar
iz
atio
n
[
1
8
]
.
In
t
h
e
m
o
d
el
d
is
cu
s
s
ed
ab
o
v
e
as
s
h
o
wn
in
F
ig
u
r
e
4
,
p
o
lar
izatio
n
ef
f
ec
t
is
m
o
d
elled
as
v
o
ltag
e
d
r
o
p
tak
in
g
p
lace
ac
r
o
s
s
th
e
e
q
u
iv
alen
t
cir
c
u
it
r
esis
to
r
R
o
.
In
a
b
atter
y
ce
ll
th
e
p
o
lar
izatio
n
ef
f
ec
t
is
d
if
f
er
en
t
f
r
o
m
th
is
.
T
h
is
d
ev
elo
p
s
s
lo
wly
with
tim
e
wh
en
cu
r
r
en
t
is
d
em
an
d
ed
f
r
o
m
th
e
b
atter
y
ce
ll.
T
h
e
p
o
lar
izatio
n
v
o
ltag
e
d
ec
ay
s
wh
en
th
e
b
atte
r
y
is
at
r
est.
T
h
i
s
s
lo
wly
ch
an
g
in
g
v
o
ltag
e
d
u
e
to
p
o
lar
izatio
n
ef
f
ec
t
is
ca
lled
d
i
f
f
u
s
io
n
v
o
ltag
e.
T
h
e
d
if
f
u
s
io
n
v
o
ltag
e
is
m
o
d
elled
by
co
n
n
ec
tin
g
one
or
more
r
esis
to
r
ca
p
ac
ito
r
p
ar
allel
s
u
b
cir
cu
its
in
s
er
ies
with
th
e
eq
u
iv
alen
t
s
er
ies
r
esis
to
r
.
Fig
u
r
e
5
s
h
o
ws
th
e
eq
u
iv
alen
t
cir
c
u
it
in
clu
d
in
g
th
e
ef
f
ec
t
of
d
if
f
u
s
io
n
v
o
ltag
e.
T
h
e
s
tate
of
ch
ar
g
e
eq
u
atio
n
is
s
am
e
as
r
ep
r
esen
ted
in
(
2
)
an
d
(
3
)
.
T
h
e
ter
m
in
al
v
o
ltag
e
eq
u
atio
n
s
f
o
r
c
o
n
tin
u
o
u
s
an
d
d
is
c
r
ete
d
o
m
ain
ar
e
as
ex
p
r
ess
ed
in
(
6
)
an
d
(
7
)
.
(
)
=
(
(
)
)
−
1
1
(
)
−
0
(
)
(
6
)
(
)
=
(
(
)
)
−
1
1
(
)
−
0
(
)
(
7
)
To
r
e
p
r
esen
t
th
e
d
if
f
u
s
io
n
v
o
ltag
e
more
ac
cu
r
ately
th
e
n
u
m
b
er
of
p
ar
allel
RC
b
r
a
n
ch
es
co
u
ld
be
in
cr
ea
s
ed
[
1
9
]
.
As
th
e
n
u
m
b
er
of
RC
b
r
an
c
h
es
in
cr
ea
s
es,
th
e
m
o
d
el
b
ec
o
m
es
co
m
p
le
x
.
C
o
n
s
id
er
in
g
t
h
ese
two
co
n
tr
ad
icto
r
y
f
ac
to
r
s
an
o
p
tim
al
n
u
m
b
er
of
RC
b
r
an
ch
es
ar
e
s
elec
ted
.
In
m
o
s
t
of
th
e
ap
p
licatio
n
s
2
RC
eq
u
iv
alen
t
cir
cu
it
is
u
s
ed
.
Fig
u
r
e
6
s
h
o
ws
th
e
eq
u
i
v
alen
t
cir
cu
it,
r
ep
r
esen
tin
g
th
e
d
if
f
u
s
io
n
v
o
ltag
e
more
ef
f
ec
tiv
ely
by
two
p
ar
allel
RC
b
r
an
ch
es
[
2
0
]
.
Fig
u
r
e
5
.
On
e
RC
eq
u
iv
alen
t
c
ir
cu
it
Fig
u
r
e
6
.
T
wo
RC
eq
u
iv
alen
t
cir
cu
it
2
.
2
.
D
et
er
m
ina
t
io
n
of
equiv
a
lent
circ
uit
pa
ra
m
et
er
s
of
lithium
-
io
n
ba
t
t
er
y
We
ar
e
m
ak
in
g
u
s
e
of
two
RC
eq
u
iv
alen
t
cir
cu
it
to
m
o
d
el
b
atter
y
b
eh
av
io
r
.
It
m
ain
ly
co
n
s
is
ts
of
SOC
d
ep
en
d
en
t
v
o
ltag
e
s
o
u
r
c
e
n
am
ed
as
OC
V,
eq
u
iv
alen
t
s
er
ies
r
esi
s
tan
ce
(
R
0
)
,
two
p
ar
allel
r
esis
to
r
s
an
d
ca
p
ac
ito
r
b
lo
ck
s
to
r
ep
r
esen
t
d
if
f
u
s
io
n
v
o
ltag
e.
T
wo
RC
eq
u
iv
alen
t
cir
cu
it
m
o
d
el
is
im
p
lem
en
ted
in
MA
T
L
AB
Simu
lin
k
.
I
n
p
u
t
to
th
e
b
atter
y
m
o
d
el
is
a
cu
r
r
en
t
co
n
tr
o
lled
cu
r
r
en
t
s
o
u
r
ce
an
d
o
u
tp
u
ts
ar
e
ter
m
in
al
v
o
ltag
es
an
d
s
tate
of
c
h
ar
g
e
v
alu
es.
As
th
e
eq
u
iv
alen
t
cir
cu
it
p
ar
am
eter
s
ar
e
f
u
n
ctio
n
s
of
s
tate
of
ch
ar
g
e
[
2
1
]
−
[
2
4
]
th
e
r
an
g
e
of
th
e
SO
C
an
d
eq
u
iv
ale
n
t
cir
cu
it
p
ar
am
eter
s
n
ee
d
to
be
b
r
o
k
en
d
o
wn
d
ep
en
d
i
n
g
on
th
e
n
u
m
b
er
of
ch
ar
g
in
g
a
n
d
d
is
ch
ar
g
in
g
cy
cles
p
er
f
o
r
m
ed
in
HPP
C
te
s
t
[
2
1
]
.
To
esti
m
ate
th
e
p
ar
am
eter
s
of
a
L
ith
iu
m
-
io
n
b
atter
y
,
it
is
ess
en
tial
th
at
a
HPPC
tes
t
is
co
n
d
u
cte
d
on
th
e
s
am
e
b
atter
y
at
d
if
f
er
e
n
t
ch
ar
g
in
g
an
d
d
is
ch
ar
g
in
g
r
ates.
Af
ter
ev
er
y
ch
ar
g
in
g
or
d
is
ch
ar
g
in
g
p
u
ls
e
in
HPP
C
te
s
t,
r
elax
atio
n
is
p
r
o
v
id
ed
so
th
at
ter
m
in
al
v
o
ltag
e
at
th
e
en
d
of
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2
5
0
2
-
4
7
52
Tw
o
R
C
mo
d
el
a
n
d
p
a
r
a
mete
r
esti
ma
tio
n
o
f
lith
iu
m
-
io
n
b
a
tt
ery
(
Gir
is
h
a
Jo
s
h
i
)
735
r
elax
atio
n
p
er
io
d
is
co
n
s
id
er
e
d
as
OC
V
[
2
5
]
−
[
2
7
]
.
In
o
th
er
s
tan
d
ar
d
d
r
iv
e
cy
cles
lik
e
L
A
9
2
,
HW
FET
,
UDD
S
etc.
,
th
e
in
f
o
r
m
atio
n
of
OC
V
ca
n
n
o
t
be
d
er
iv
ed
s
in
ce
we
ca
n
n
o
t
h
av
e
r
e
g
u
lar
r
elax
atio
n
s
wh
en
th
e
b
atter
y
s
u
p
p
ly
in
g
to
lo
ad
.
Hen
ce
,
we
h
av
e
u
s
ed
HPPC
test
d
ata
f
o
r
p
ar
am
eter
esti
m
atio
n
.
A
HPP
C
te
s
t
was
co
n
d
u
cted
on
a
b
r
an
d
-
n
ew
Pan
aso
n
ic
b
atter
y
,
1
8
6
5
0
PF
with
a
r
atin
g
of
2
.
9
Ah
an
d
4
.
2
V
by
Ko
llm
ey
e
r
at
t
h
e
Un
iv
er
s
ity
of
W
is
co
n
s
in
-
Ma
d
is
o
n
an
d
th
is
d
ata
is
av
ailab
le
o
p
en
s
o
u
r
ce
[
1
7
]
.
T
h
e
f
iv
e
-
p
u
ls
e
d
is
ch
ar
g
e
HPPC
test
was
co
n
d
u
cted
at
d
if
f
er
en
t
d
is
ch
ar
g
e
C
-
r
ates
s
u
ch
as
0
.
5
C
,
1
C
,
2
C
,
4C
an
d
6C
f
o
r
d
if
f
er
e
n
t
s
tate
of
ch
ar
g
e
lev
els.
Fro
m
th
is
HPP
C
te
s
t,
we
m
ad
e
u
s
e
of
d
ata
with
r
esp
ec
t
to
in
p
u
t
cu
r
r
en
t
im
p
u
ls
e,
o
u
tp
u
t
ter
m
i
n
al
v
o
lt
ag
e,
tem
p
er
atu
r
e,
Am
p
er
e
-
h
o
u
r
,
tim
e
s
tam
p
in
g
.
HPPC
tes
t
co
n
d
u
cted
f
o
r
a
ch
am
b
er
tem
p
e
r
atu
r
e
of
ze
r
o
d
eg
r
ee
C
elsi
u
s
h
as
54
p
u
ls
es
an
d
SOC
an
d
eq
u
iv
alen
t
cir
cu
it
p
ar
am
eter
s
h
av
e
b
ee
n
d
iv
id
e
d
in
to
55
b
r
ea
k
p
o
i
n
ts
.
T
h
e
r
an
g
e
of
SOC
is
f
r
o
m
ze
r
o
to
o
n
e
.
SOC
an
d
o
th
e
r
cir
cu
it
p
ar
am
eter
s
r
an
g
e
is
d
iv
id
e
d
in
to
54
e
q
u
al
in
ter
v
als.
In
th
is
wo
r
k
an
a
p
p
licatio
n
by
n
am
e
p
ar
am
eter
esti
m
atio
n
,
av
ailab
le
in
MA
T
L
AB
as
s
h
o
wn
in
Fig
u
r
e
1
(
b
)
,
is
u
s
ed
to
esti
m
ate
th
e
eq
u
iv
alen
t
cir
c
u
it
p
ar
am
eter
s
of
th
e
b
atter
y
.
I
n
itial
v
al
u
es
an
d
r
an
g
e
of
t
h
e
p
ar
am
eter
s
to
be
esti
m
ated
ar
e
d
ef
in
ed
.
Du
r
in
g
p
ar
am
eter
es
tim
atio
n
as
in
d
icate
d
in
F
ig
u
r
e
1
(
a
)
,
s
h
o
win
g
th
e
f
lo
wch
ar
t
of
p
ar
a
m
eter
esti
m
atio
n
,
o
u
tp
u
t
of
th
e
two
RC
eq
u
iv
alen
t
cir
cu
it
m
o
d
el
ter
m
in
al
v
o
ltag
e
is
co
m
p
ar
ed
with
th
e
ter
m
i
n
al
v
o
ltag
e
o
b
s
er
v
ed
d
u
r
in
g
th
e
HPPC
test
f
o
r
a
g
iv
en
ch
ar
g
e
or
d
is
ch
ar
g
e
cu
r
r
en
t
p
u
ls
e,
T
er
m
i
n
al
v
o
ltag
e
v
alu
e
f
r
o
m
th
e
s
im
u
latio
n
is
n
o
t
s
a
m
e
as
ter
m
in
al
v
o
ltag
e
of
HP
PC
test
.
T
h
is
is
s
in
ce
th
e
in
itial
v
alu
es
of
th
e
eq
u
iv
alen
t
cir
cu
it
p
ar
am
eter
s
ar
e
not
ac
tu
al
eq
u
i
v
alen
t
cir
cu
it
p
ar
am
eter
s
.
T
h
e
d
if
f
er
en
ce
b
etwe
en
s
im
u
latio
n
ter
m
in
al
v
o
ltag
e
an
d
ter
m
in
al
v
o
ltag
e
f
r
o
m
HPPC
te
s
t
d
ata
is
u
s
ed
to
tu
n
e
th
e
eq
u
iv
alen
t
cir
cu
it
p
ar
am
eter
s
of
th
e
two
RC
m
o
d
els.
C
o
s
t
f
u
n
ctio
n
u
s
ed
is
s
u
m
-
s
q
u
ar
ed
er
r
o
r
.
Af
ter
s
ev
er
al
iter
atio
n
s
of
u
p
d
atin
g
t
h
e
eq
u
iv
alen
t
cir
cu
it
p
a
r
am
eter
s
,
t
er
m
in
al
v
o
ltag
e
er
r
o
r
r
e
d
u
ce
s
.
If
th
e
er
r
o
r
c
o
s
t
f
u
n
ctio
n
v
alu
e
c
o
m
es
b
elo
w
th
e
p
er
m
is
s
ib
le
lim
it
s
et
,
th
en
p
ar
am
eter
s
esti
m
atio
n
s
to
p
s
.
Fig
u
r
e
7
s
h
o
ws
eq
u
iv
alen
t
cir
c
u
it
p
ar
am
eter
s
v
s
SOC
at
2
5
d
eg
r
ee
s
C
elsi
u
s
.
Fig
u
r
es
7
(
a)
to
7
(
f
)
s
h
o
w
t
h
e
p
lo
t
of
o
p
en
cir
cu
it
v
o
ltag
e,
R
0
,
R
1
,
R
2
,
τ1
a
n
d
τ2
f
o
r
th
e
SOC
v
ar
y
in
g
f
r
o
m
0
to
1
f
o
r
th
e
ch
a
m
b
er
tem
p
er
at
u
r
es
of
+2
5
d
eg
r
ee
s
C
elsi
u
s
.
W
h
er
e
τ
is
a
m
u
ltip
le
of
r
esis
tan
ce
an
d
ca
p
ac
itan
ce
.
We
h
av
e
esti
m
ated
th
e
p
ar
am
eter
s
of
th
e
Pan
aso
n
ic
1
8
6
5
0
PF
2
.
9
Ah
4
.
2
V
b
atter
y
u
s
in
g
th
e
ab
o
v
e
a
p
p
r
o
ac
h
u
s
in
g
th
e
HPPC
test
r
esu
lts
av
ailab
le
f
o
r
d
if
f
er
en
t
ch
am
b
er
tem
p
er
atu
r
e
s
u
ch
as
-
20
-
d
eg
r
ee
,
-
10
-
d
e
g
r
ee
,
0
-
d
eg
r
ee
,
10
-
d
e
g
r
ee
,
25
-
d
eg
r
ee
s
C
elsi
u
s
[
1
7
]
.
W
h
en
th
e
s
im
u
latio
n
s
to
p
s
eq
u
iv
alen
t
cir
cu
it
p
ar
am
eter
s
,
S
OC
,
R
o
,
R
1
,
R
2
,
τ1
an
d
τ2
ar
e
s
av
ed
in
MA
T
L
AB
wo
r
k
s
p
ac
e.
T
h
e
o
b
jectiv
e
of
th
e
wo
r
k
is
to
u
n
d
er
s
tan
d
th
e
ef
f
ec
t
of
tem
p
er
atu
r
e
on
eq
u
iv
alen
t
cir
cu
it
p
ar
am
eter
s
of
t
h
e
b
atter
y
.
(
a)
(
b
)
(
c)
(
d
)
(
e)
(f)
Fig
u
r
e
7.
E
q
u
iv
alen
t
cir
c
u
it
p
a
r
am
eter
s
vs
SOC
at
25
d
eg
r
ee
s
ce
ls
iu
s
(
a)
no
-
lo
ad
ter
m
in
al
v
o
ltag
e,
(
b
)
ter
m
in
al
r
esis
tan
ce
(
R
0
)
,
(
c)
d
if
f
u
s
io
n
r
esis
tan
ce
(
R
1
)
,
(
d
)
d
if
f
u
s
io
n
r
esis
tan
ce
(
R
2
)
,
(
e)
tim
e
co
n
s
tan
t
(
τ
1
)
,
an
d
(
f
)
tim
e
co
n
s
tan
t
(
τ
2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
52
In
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
3
7
,
No
.
2
,
Feb
r
u
a
r
y
20
2
5
:
7
3
0
-
7
3
9
736
3.
RE
SU
L
T
S
AND
D
I
SCU
SS
I
O
N
As
ex
p
lain
ed
in
th
e
m
eth
o
d
s
e
ctio
n
eq
u
i
v
alen
t
cir
c
u
it
p
ar
am
eter
s
f
o
r
wid
e
tem
p
er
at
u
r
e
r
an
g
in
g
f
r
o
m
-
20
d
eg
r
ee
C
elsi
u
s
to
25
d
eg
r
ee
C
els
iu
s
at
d
if
f
er
en
t
SOC
s
2
0
%,
3
0
%,
4
0
%,
5
0
%,
6
0
%,
7
0
%,
8
0
%,
90%
an
d
100%
ar
e
n
o
te
d
d
o
wn
a
n
d
tab
u
lated
in
T
ab
le
s
1
to
5.
T
ab
le
1
s
h
o
ws
th
e
v
alu
es
of
in
ter
n
al
r
esis
tan
ce
R
0
,
f
o
r
d
if
f
er
en
t
tem
p
er
atu
r
es
a
n
d
SO
C
lev
els.
It
co
u
ld
be
n
o
ticed
t
h
at
f
o
r
a
g
iv
e
n
SOC
lev
el
th
e
r
esis
tan
ce
d
ec
r
ea
s
es
with
an
in
cr
ea
s
e
in
tem
p
er
atu
r
e.
At
1
0
0
%
SOC
Ro
v
alu
e
at
m
in
u
s
20
d
e
g
r
ee
ce
ls
iu
s
is
0
.
0
5
8
9
7
4
4
4
Ω
a
n
d
at
25
d
eg
r
ee
ce
ls
iu
s
its
v
alu
e
is
0
.
0
2
7
0
1
4
Ω
w
h
ich
is
45%
of
it
i
s
v
alu
e
at
m
in
u
s
20
d
eg
r
ee
ce
ls
iu
s
.
T
ab
le
2
s
h
o
ws
Par
allel
b
r
an
ch
-
1
d
if
f
u
s
io
n
r
esis
tan
ce
R1
,
f
o
r
d
if
f
er
en
t
tem
p
er
atu
r
es
an
d
S
OC
lev
els
.
It
co
u
ld
be
n
o
ticed
th
at
f
o
r
a
g
iv
en
SOC
lev
el
th
e
r
esis
tan
ce
d
ec
r
ea
s
es
with
an
in
cr
ea
s
e
in
tem
p
er
atu
r
e.
At
100%
SOC
R1
v
alu
e
at
m
in
u
s
20
d
e
g
r
ee
ce
ls
iu
s
is
0
.
2
5
2
6
4
9
Ω
an
d
at
25
d
eg
r
ee
s
c
elsi
u
s
it
i
s
v
alu
e
is
0
.
0
1
1
9
9
8
Ω
wh
ich
is
4
.
7
%
of
it
i
s
v
alu
e
at
m
in
u
s
20
d
eg
r
ee
ce
ls
iu
s
.
T
ab
le
3
s
h
o
ws
Par
allel
b
r
an
ch
-
2
d
if
f
u
s
io
n
r
esis
tan
ce
R
2
,
f
o
r
d
if
f
er
en
t
tem
p
er
atu
r
es
an
d
S
OC
lev
els
.
It
co
u
ld
be
n
o
ticed
th
at
f
o
r
a
g
iv
en
SOC
lev
el
th
e
r
esis
tan
ce
d
ec
r
ea
s
es
with
an
in
cr
ea
s
e
in
tem
p
er
atu
r
e.
At
100%
SOC
R2
v
alu
e
at
m
in
u
s
20
d
e
g
r
ee
ce
ls
iu
s
is
0
.
4
9
9
0
8
3
Ω
an
d
at
25
d
eg
r
ee
s
c
elsi
u
s
it
i
s
v
alu
e
is
0
.
0
2
2
2
1
3
Ω
wh
ich
is
4
.
4
5
%
of
it
i
s
v
alu
e
at
m
in
u
s
20
d
eg
r
e
e
ce
ls
iu
s
.
T
ab
le
1.
R0
Fo
r
d
if
f
er
e
n
t
tem
p
er
atu
r
e
an
d
SOC
S
O
C
-
20
D
e
g
r
e
e
-
10
D
e
g
r
e
e
0
D
e
g
r
e
e
10
D
e
g
r
e
e
25
D
e
g
r
e
e
1
0
0
0
.
0
5
9
0
0
.
0
4
0
9
0
.
0
4
3
8
0
.
0
4
0
6
0
.
0
2
7
0
90
0
.
0
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atio
n
of
L
ith
iu
m
-
io
n
b
atter
ies
is
f
o
u
n
d
in
th
e
liter
atu
r
e
[
3
]
,
[
1
9
]
,
[
2
0
]
,
[
2
2
]
,
[
2
4
]
−
[
2
7
]
co
m
p
ar
is
o
n
of
b
atter
y
p
ar
a
m
eter
s
f
o
r
a
wid
e
r
an
g
e
of
tem
p
er
atu
r
es
is
not
m
u
ch
f
o
cu
s
ed
.
To
m
ak
e
th
e
p
r
o
d
u
ct
g
lo
b
all
y
a
cc
ep
tab
le,
f
o
r
all
tem
p
er
atu
r
es,
m
an
u
f
ac
tu
r
e
r
s
of
th
e
lith
iu
m
-
io
n
b
atter
y
ar
e
r
eq
u
ir
ed
to
f
u
r
n
is
h
th
e
d
etails
of
th
eir
b
atter
y
eq
u
iv
alen
t
ci
r
cu
it
p
ar
am
eter
s
so
th
at
SO
C
esti
m
atio
n
will
be
ac
cu
r
ate
an
d
m
ak
es
th
e
ap
p
licatio
n
s
p
o
wer
ed
by
th
ese
b
atter
ies
lik
e
elec
tr
ic
v
eh
icles
will
be
r
eliab
le
an
d
s
af
e.
4.
CO
NCLU
SI
O
N
In
th
is
wo
r
k
we
h
a
v
e
esti
m
ated
two
RC
eq
u
iv
alen
t
cir
cu
it
p
ar
am
eter
s
of
Pan
aso
n
ic
1
8
6
5
0
PF
2
.
9
Ah
4
.
2
V
b
atter
y
at
d
if
f
e
r
en
t
tem
p
er
atu
r
es
lik
e
-
2
0
,
-
1
0
,
0,
10
an
d
25
d
e
g
r
ee
s
C
elsi
u
s
.
In
th
e
p
r
o
ce
s
s
,
we
c
o
u
l
d
an
aly
ze
th
e
im
p
ac
t
of
tem
p
er
a
tu
r
e
on
eq
u
i
v
alen
t
cir
cu
it
p
ar
a
m
eter
s
f
o
r
a
g
iv
en
SOC
lev
el.
It
is
o
b
s
er
v
ed
f
r
o
m
th
e
esti
m
ated
p
ar
am
eter
s
th
at
r
esis
tan
ce
s
of
th
e
eq
u
i
v
alen
t
c
ir
cu
it,
R
0
,
R1
,
an
d
R2
d
ec
r
ea
s
e
with
in
cr
ea
s
e
in
tem
p
er
atu
r
e
an
d
ca
p
ac
itan
ce
s
C1
an
d
C2
in
cr
ea
s
e
with
r
is
e
in
th
e
te
m
p
er
atu
r
e.
T
h
is
in
f
o
r
m
atio
n
of
eq
u
iv
alen
t
cir
cu
it
p
ar
am
eter
s
is
v
er
y
c
r
u
cial
in
SOC
est
im
atio
n
of
th
e
b
atter
y
.
T
h
e
o
u
tco
m
e
of
th
e
wo
r
k
will
em
p
h
asis
th
e
n
ee
d
of
e
q
u
iv
alen
t
cir
c
u
it
p
ar
am
eter
s
f
o
r
wid
e
r
a
n
g
e
of
tem
p
er
atu
r
e.
Sin
ce
s
o
m
e
of
th
e
p
ar
am
ete
r
s
as
m
en
tio
n
ed
in
th
e
d
is
cu
s
s
io
n
p
ar
t,
f
o
r
ex
am
p
le
th
e
v
alu
es
of
ca
p
ac
ito
r
s
do
ev
e
n
ch
a
n
g
e
by
th
e
o
r
d
e
r
of
50
tim
es.
No
n
av
ailab
ilit
y
of
th
is
in
f
o
r
m
atio
n
will
m
ak
e
th
e
S
OC
est
im
atio
n
poor
an
d
due
to
its
n
atu
r
e
b
atter
y
b
ec
o
m
es
u
n
s
af
e
an
d
n
o
n
-
r
eliab
le
f
o
r
u
s
e.
On
th
e
o
th
er
h
a
n
d
,
co
m
p
lete
b
atter
y
p
ar
am
et
er
in
f
o
r
m
atio
n
will
m
ak
e
th
e
p
r
o
d
u
ct
g
lo
b
ally
ac
c
ep
tab
le,
r
eliab
le
an
d
s
af
e
.
ACK
NO
WL
E
DG
E
M
E
NT
S
T
h
e
au
th
o
r
s
wo
u
ld
lik
e
to
th
a
n
k
Dr
.
Su
r
y
an
ar
a
y
an
a
K.
,
Pro
f
ess
o
r
an
d
Head
Dep
a
r
tm
en
t
of
E
lectr
ical
an
d
E
lectr
o
n
ics
E
n
g
in
ee
r
in
g
,
NM
AM
I
T
,
Nitte
an
d
Ms.
Sp
o
o
r
th
y
Sh
etty
,
Pr
o
ject
Ma
n
ag
er
,
L
&
T
T
ec
h
n
o
lo
g
y
Ser
v
ices,
B
an
g
alu
r
u
f
o
r
p
r
o
v
i
d
in
g
th
e
o
p
p
o
r
tu
n
ity
to
ca
r
r
y
out
th
e
wo
r
k
in
B
atter
y
Ma
n
a
g
em
en
t
p
r
o
ject
an
d
p
r
o
v
id
i
n
g
tim
ely
a
n
d
v
al
u
ab
le
s
u
g
g
esti
o
n
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
52
In
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
3
7
,
No
.
2
,
Feb
r
u
a
r
y
20
2
5
:
7
3
0
-
7
3
9
738
RE
F
E
R
E
NC
E
S
[
1
]
C
.
N
.
V
a
n
a
n
d
T
.
N
.
V
i
n
h
,
“
S
t
a
t
e
o
f
c
h
a
r
g
e
e
st
i
mat
i
o
n
f
o
r
l
i
t
h
i
u
m
-
i
o
n
b
a
t
t
e
r
i
e
s
c
o
n
n
e
c
t
e
d
i
n
ser
i
e
s u
si
n
g
t
w
o
s
i
g
ma
p
o
i
n
t
K
a
l
ma
n
f
i
l
t
e
r
s,”
I
n
t
e
r
n
a
t
i
o
n
a
l
J
o
u
r
n
a
l
o
f
El
e
c
t
ri
c
a
l
a
n
d
C
o
m
p
u
t
e
r
E
n
g
i
n
e
e
r
i
n
g
(
I
J
EC
E)
,
v
o
l
.
1
2
,
n
o
.
2
,
p
p
.
1
3
3
4
–
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3
4
9
,
A
p
r
.
2
0
2
2
,
d
o
i
:
1
0
.
1
1
5
9
1
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j
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c
e
.
v
1
2
i
2
.
p
p
1
3
3
4
-
1
3
4
9
.
[
2
]
A
.
El
M
a
l
i
k
i
,
K
.
A
n
o
u
n
e
,
A
.
B
e
n
l
a
f
k
i
h
,
a
n
d
A
.
H
a
d
j
o
u
d
j
a
,
“
Est
i
ma
t
i
n
g
t
h
e
st
a
t
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o
f
c
h
a
r
g
e
o
f
l
i
t
h
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u
m
-
i
o
n
b
a
t
t
e
r
i
e
s
u
si
n
g
d
i
f
f
e
r
e
n
t
n
o
i
se
i
n
p
u
t
s,”
I
n
t
e
r
n
a
t
i
o
n
a
l
J
o
u
r
n
a
l
o
f
P
o
w
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l
e
c
t
r
o
n
i
c
s
a
n
d
D
r
i
v
e
S
y
st
e
m
s
(
I
J
PED
S
)
,
v
o
l
.
1
5
,
n
o
.
1
,
p
p
.
8
–
1
8
,
M
a
r
.
2
0
2
4
,
d
o
i
:
1
0
.
1
1
5
9
1
/
i
j
p
e
d
s
.
v
1
5
.
i
1
.
p
p
8
-
1
8
.
[
3
]
N
.
K
.
Tr
u
n
g
a
n
d
N
.
T
h
i
D
i
e
p
,
“
O
n
l
i
n
e
p
a
r
a
me
t
e
r
i
d
e
n
t
i
f
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c
a
t
i
o
n
f
o
r
e
q
u
i
v
a
l
e
n
t
c
i
r
c
u
i
t
m
o
d
e
l
o
f
l
i
t
h
i
u
m
-
i
o
n
b
a
t
t
e
r
y
,
”
I
n
d
o
n
e
s
i
a
n
J
o
u
rn
a
l
o
f
El
e
c
t
r
i
c
a
l
E
n
g
i
n
e
e
r
i
n
g
a
n
d
C
o
m
p
u
t
e
r
S
c
i
e
n
c
e
,
v
o
l
.
3
1
,
n
o
.
1
,
p
p
.
1
5
1
–
1
5
9
,
J
u
l
.
2
0
2
3
,
d
o
i
:
1
0
.
1
1
5
9
1
/
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j
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c
s.
v
3
1
.
i
1
.
p
p
1
5
1
-
1
5
9
.
[
4
]
M
.
N
i
z
a
m
a
n
d
M
.
R
.
A
.
P
u
t
r
a
,
“
A
n
a
l
y
s
i
s
o
f
l
i
t
h
i
u
m
-
i
o
n
i
n
d
i
r
e
c
t
l
i
q
u
i
d
c
o
o
l
i
n
g
b
a
t
t
e
r
y
t
h
e
r
mal
ma
n
a
g
e
m
e
n
t
sy
st
e
m
w
i
t
h
h
i
g
h
d
i
s
c
h
a
r
g
e
r
a
t
e
,
”
I
n
t
e
r
n
a
t
i
o
n
a
l
J
o
u
r
n
a
l
o
f
P
o
w
e
r
E
l
e
c
t
ro
n
i
c
s
a
n
d
D
r
i
v
e
S
y
st
e
m
s
(
I
J
P
ED
S
)
,
v
o
l
.
1
4
,
n
o
.
3
,
p
p
.
1
4
1
4
–
1
4
2
0
,
S
e
p
.
2
0
2
3
,
d
o
i
:
1
0
.
1
1
5
9
1
/
i
j
p
e
d
s.
v
1
4
.
i
3
.
p
p
1
4
1
4
-
1
4
2
0
.
[
5
]
I
.
C
h
a
o
u
f
i
,
O
.
A
b
d
e
l
k
h
a
l
e
k
,
a
n
d
B
.
G
a
sb
a
o
u
i
,
“
S
t
a
t
e
o
f
c
h
a
r
g
e
e
s
t
i
m
a
t
i
o
n
o
f
l
i
t
h
i
u
m
-
i
o
n
b
a
t
t
e
r
i
e
s
u
s
i
n
g
a
d
a
p
t
i
v
e
n
e
u
r
o
f
u
z
z
y
i
n
f
e
r
e
n
c
e
s
y
s
t
e
m,
”
I
AE
S
I
n
t
e
rn
a
t
i
o
n
a
l
J
o
u
r
n
a
l
o
f
Art
i
f
i
c
i
a
l
I
n
t
e
l
l
i
g
e
n
c
e
(
I
J
-
AI
)
,
v
o
l
.
1
1
,
n
o
.
2
,
p
p
.
4
7
3
–
4
8
4
,
Ju
n
.
2
0
2
2
,
d
o
i
:
1
0
.
1
1
5
9
1
/
i
j
a
i
.
v
1
1
.
i
2
.
p
p
4
7
3
-
4
8
4
.
[
6
]
J.
K
h
a
l
f
i
,
N
.
B
o
u
ma
a
z
,
A
.
S
o
u
l
ma
n
i
,
a
n
d
E
.
M
.
La
a
d
i
ssi
,
“
A
n
e
l
e
c
t
r
i
c
c
i
r
c
u
i
t
mo
d
e
l
f
o
r
a
l
i
t
h
i
u
m
-
i
o
n
b
a
t
t
e
r
y
c
e
l
l
b
a
se
d
o
n
a
u
t
o
m
o
t
i
v
e
d
r
i
v
e
c
y
c
l
e
s
m
e
a
s
u
r
e
m
e
n
t
s,”
I
n
t
e
r
n
a
t
i
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
t
r
i
c
a
l
a
n
d
C
o
m
p
u
t
e
r
En
g
i
n
e
e
ri
n
g
(
I
J
E
C
E)
,
v
o
l
.
1
1
,
n
o
.
4
,
p
p
.
2
7
9
8
–
2
8
1
0
,
A
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g
.
2
0
2
1
,
d
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:
1
0
.
1
1
5
9
1
/
i
j
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c
e
.
v
1
1
i
4
.
p
p
2
7
9
8
-
2
8
1
0
.
[
7
]
A
.
M
.
A
l
s
a
b
a
r
i
,
M
.
.
H
a
ssa
n
,
A
.
C
S
,
a
n
d
R
.
Za
f
i
r
a
,
“
M
o
d
e
l
i
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g
a
n
d
v
a
l
i
d
a
t
i
o
n
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f
l
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t
h
i
u
m
-
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o
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b
a
t
t
e
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y
w
i
t
h
i
n
i
t
i
a
l
st
a
t
e
o
f
c
h
a
r
g
e
e
st
i
mat
i
o
n
,
”
I
n
d
o
n
e
si
a
n
J
o
u
r
n
a
l
o
f
E
l
e
c
t
r
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c
a
l
En
g
i
n
e
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ri
n
g
a
n
d
C
o
m
p
u
t
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S
c
i
e
n
c
e
,
v
o
l
.
2
1
,
n
o
.
3
,
p
p
.
1
3
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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c
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b
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c
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ste
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s.
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c
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ter
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e
x
p
e
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c
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tri
b
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tes
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n
ifi
c
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n
t
ly
to
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e
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d
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n
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e
m
e
n
t
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rg
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h
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.
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e
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
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a
ll
u
ri
v
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ra
1
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3
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g
m
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il
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c
o
m
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l
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k
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sh
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h
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d
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r
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n
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e
r
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t
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c
h
n
o
l
o
g
y
S
e
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ice
s
.
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b
a
c
k
g
r
o
u
n
d
i
n
Ba
c
h
e
lo
r
o
f
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g
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n
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g
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n
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tro
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n
d
T
e
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o
m
.
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h
a
s
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+
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e
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rs
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e
in
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d
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e
d
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re
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n
d
p
r
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c
t
d
e
v
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lo
p
m
e
n
t.
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h
a
s a
sp
e
c
ializa
ti
o
n
in
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e
c
tri
c
v
e
h
icle
a
rc
h
it
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c
tu
re
a
n
d
d
iffere
n
t
ECU
c
o
m
p
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n
ts
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,
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CU,
a
n
d
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v
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m
a
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m
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t
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g
.
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e
x
p
e
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se
in
a
lg
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ri
th
m
d
e
v
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lo
p
m
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t
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r
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OC,
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tate
o
f
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a
lt
h
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OH
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a
n
d
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m
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d
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n
g
.
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c
a
n
b
e
c
o
n
tac
ted
a
t
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m
a
il
:
a
m
o
lk
h
a
d
e
9
0
9
@
g
m
a
il
.
c
o
m
.
Evaluation Warning : The document was created with Spire.PDF for Python.