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8
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46
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e
l
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tri
c
v
e
h
icle
s,
e
m
b
e
d
d
e
d
e
lec
tro
n
ics
,
a
n
d
re
n
e
wa
b
le
e
n
e
rg
y
a
p
p
li
c
a
ti
o
n
s,
li
th
iu
m
-
i
o
n
b
a
tt
e
ries
h
a
v
e
b
e
c
o
m
e
a
n
e
ss
e
n
ti
a
l
c
o
m
p
o
n
e
n
t
i
n
m
o
d
e
rn
e
n
e
rg
y
sto
ra
g
e
sy
ste
m
s.
Ac
c
u
ra
t
e
sta
te
o
f
c
h
a
rg
e
(S
OC)
e
stim
a
ti
o
n
is
c
ru
c
i
a
l
fo
r
e
n
su
ri
n
g
b
a
tt
e
ry
re
li
a
b
il
it
y
,
lo
n
g
e
v
it
y
,
a
n
d
sa
fe
ty
,
p
a
rti
c
u
larl
y
u
n
d
e
r
fa
u
l
ty
c
h
a
rg
in
g
c
o
n
d
it
io
n
s
—
a
c
h
a
ll
e
n
g
e
wh
e
re
m
a
n
y
c
o
n
v
e
n
ti
o
n
a
l
e
stim
a
ti
o
n
tec
h
n
i
q
u
e
s
fa
ll
s
h
o
rt
d
u
e
to
m
o
d
e
l
li
m
it
a
ti
o
n
s
o
r
lac
k
o
f
ro
b
u
st
n
e
ss
.
In
th
is
stu
d
y
,
we
p
ro
p
o
se
a
n
a
d
v
a
n
c
e
d
S
OC es
ti
m
a
ti
o
n
a
p
p
ro
a
c
h
b
a
se
d
o
n
a
slid
i
n
g
m
o
d
e
o
b
se
rv
e
r
(S
M
O)
in
teg
ra
ted
wit
h
a
th
ird
-
o
rd
e
r
e
q
u
i
v
a
len
t
c
ircu
it
m
o
d
e
l
(E
CM
).
Un
li
k
e
c
o
n
v
e
n
ti
o
n
a
l
m
e
th
o
d
s,
wh
ich
e
it
h
e
r
fo
c
u
s
o
n
S
OC
e
stim
a
ti
o
n
with
o
u
t
c
o
n
si
d
e
rin
g
b
a
tt
e
ry
v
o
lt
a
g
e
o
r
a
p
p
ly
S
M
O
tec
h
n
iq
u
e
s
o
n
ly
to
se
c
o
n
d
-
o
rd
e
r
m
o
d
e
ls,
o
u
r
a
p
p
r
o
a
c
h
e
n
h
a
n
c
e
s
e
stim
a
ti
o
n
a
c
c
u
ra
c
y
b
y
in
c
o
r
p
o
ra
ti
n
g
a
h
ig
h
e
r
-
o
r
d
e
r
m
o
d
e
l
t
h
a
t
b
e
tt
e
r
c
a
p
tu
re
s
th
e
c
o
m
p
lex
b
a
tt
e
r
y
d
y
n
a
m
ics
.
Th
e
p
ro
p
o
se
d
m
e
th
o
d
o
lo
g
y
is
tes
ted
u
n
d
e
r
b
o
t
h
n
o
rm
a
l
a
n
d
fa
u
lt
y
c
h
a
rg
in
g
c
o
n
d
it
io
n
s,
d
e
m
o
n
stra
ti
n
g
su
p
e
ri
o
r
p
e
rfo
rm
a
n
c
e
in
e
stim
a
ti
n
g
b
o
th
S
OC
a
n
d
term
in
a
l
v
o
l
tag
e
o
v
e
r
e
x
ten
d
e
d
p
e
rio
d
s.
Th
e
sim
u
latio
n
re
su
lt
s
c
o
n
firm
th
e
r
o
b
u
st
n
e
ss
o
f
th
e
m
e
th
o
d
,
with
a
c
c
u
ra
te
S
OC
trac
k
in
g
e
v
e
n
in
th
e
p
re
se
n
c
e
o
f
c
h
a
rg
in
g
c
u
rr
e
n
t
fa
u
lt
s,
m
a
k
in
g
it
a
v
iab
le
so
lu
ti
o
n
fo
r
re
a
l
-
wo
r
ld
a
p
p
l
ica
ti
o
n
s
in
b
a
tt
e
ry
m
a
n
a
g
e
m
e
n
t
sy
ste
m
s
(BM
S
).
T
h
is
wo
r
k
c
o
n
tr
ib
u
tes
t
o
im
p
ro
v
in
g
fa
u
lt
-
to
lera
n
t
S
OC
e
stim
a
ti
o
n
stra
teg
ie
s,
a
d
v
a
n
c
in
g
t
h
e
d
e
v
e
l
o
p
m
e
n
t
o
f
sa
fe
r
a
n
d
m
o
re
e
fficie
n
t
e
n
e
rg
y
sto
ra
g
e
tec
h
n
o
lo
g
ies
.
K
ey
w
o
r
d
s
:
E
q
u
iv
alen
t c
ir
c
u
it m
o
d
el
L
ith
iu
m
-
io
n
b
atter
ies
Sli
d
in
g
m
o
d
e
o
b
s
er
v
er
State
esti
m
atio
n
State
o
f
ch
ar
g
e
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
:
Dib
Djalel
Dep
ar
tm
en
t o
f
E
lectr
ical
E
n
g
i
n
ee
r
in
g
,
Facu
lty
o
f
Scien
ce
a
n
d
T
ec
h
n
o
lo
g
y
,
L
ar
b
i
T
eb
ess
i U
n
iv
er
s
ity
T
eb
ess
a,
Alg
er
ia
E
m
ail:
jalel.
d
ib
@
u
n
iv
-
teb
ess
a.
d
z
1.
I
NT
RO
D
UCT
I
O
N
E
n
v
ir
o
n
m
en
tal
p
o
llu
tio
n
r
em
a
in
s
a
cr
itical
g
lo
b
al
is
s
u
e,
lar
g
ely
d
u
e
to
em
is
s
io
n
s
f
r
o
m
c
o
n
v
en
tio
n
al
elec
tr
icity
g
en
er
atio
n
a
n
d
th
e
r
m
al
tr
an
s
p
o
r
tatio
n
s
y
s
tem
s
[
1
]
,
[
2
]
.
I
n
r
esp
o
n
s
e,
th
er
e
is
g
r
o
win
g
in
te
r
est
in
r
en
ewa
b
le
en
er
g
y
an
d
elec
tr
i
c
v
eh
icles,
wh
ich
d
ep
e
n
d
o
n
ad
v
an
ce
d
en
er
g
y
s
to
r
ag
e
tec
h
n
o
lo
g
ies
[
3
]
,
[
4
]
.
L
ith
iu
m
-
io
n
b
atter
ies,
k
n
o
wn
f
o
r
th
eir
ef
f
icien
cy
,
r
ec
y
clab
ili
ty
,
an
d
s
u
itab
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y
ac
r
o
s
s
v
ar
io
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s
ap
p
licatio
n
s
,
ar
e
ce
n
tr
al
to
th
is
tr
an
s
itio
n
[
5
]
,
[
6
]
.
Ho
wev
er
,
a
s
in
g
le
ce
ll
ca
n
n
o
t
m
ee
t
elec
tr
ic
v
eh
icle
en
er
g
y
d
em
a
n
d
s
,
n
ec
ess
itatin
g
b
atter
y
p
ac
k
s
an
d
r
o
b
u
s
t
b
atter
y
m
a
n
ag
em
en
t s
y
s
tem
s
(
B
MS)
[
7
]
-
[
9
]
.
A
k
ey
f
u
n
ctio
n
o
f
th
e
B
MS
is
est
im
atin
g
th
e
s
tate
o
f
c
h
ar
g
e
(
SOC
)
,
wh
ich
ca
n
n
o
t
b
e
d
ir
ec
tly
m
ea
s
u
r
ed
an
d
th
u
s
r
e
q
u
ir
es
e
s
tim
atio
n
alg
o
r
ith
m
s
[
1
0
]
,
[
1
1
]
.
T
h
ese
ar
e
ca
teg
o
r
ize
d
in
t
o
f
o
u
r
m
ain
t
y
p
es:
o
p
en
-
lo
o
p
,
eq
u
iv
ale
n
t
cir
cu
it
m
o
d
el
-
b
ased
,
d
ata
-
d
r
iv
e
n
,
a
n
d
b
o
o
k
k
ee
p
in
g
esti
m
atio
n
m
eth
o
d
s
[
1
2
]
,
[
1
3
]
.
Data
-
d
r
iv
en
m
et
h
o
d
s
s
u
ch
as
n
eu
r
al
n
etwo
r
k
s
an
d
s
u
p
p
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r
t
v
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to
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m
ac
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es
o
f
f
er
h
ig
h
ac
cu
r
ac
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b
u
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r
eq
u
ir
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
R
o
b
u
s
t S
OC
esti
ma
tio
n
fo
r
lith
iu
m
-
io
n
b
a
tter
ies u
n
d
er fa
u
lt
y
ch
a
r
g
in
g
s
ce
n
a
r
io
s
u
s
in
g
…
(
S
o
u
lef
Ma
h
i
d
d
in
e
)
47
s
ig
n
if
ican
t
o
f
f
lin
e
tr
ai
n
in
g
[
1
4
]
-
[
1
6
]
.
B
o
o
k
k
ee
p
i
n
g
m
eth
o
d
s
,
lik
e
co
u
lo
m
b
co
u
n
tin
g
,
e
s
tim
ate
SO
C
u
s
in
g
ch
ar
g
e/d
is
ch
ar
g
e
c
u
r
r
en
ts
[
1
7
]
,
[
1
8
]
.
Op
e
n
-
lo
o
p
m
eth
o
d
s
,
s
u
ch
as
th
e
o
p
en
-
cir
cu
it
v
o
ltag
e
(
OC
V)
tech
n
iq
u
e,
ar
e
s
im
p
le
b
u
t
u
n
s
u
itab
le
f
o
r
r
ea
l
-
tim
e
a
p
p
licatio
n
s
[
1
9
]
.
E
q
u
iv
alen
t
cir
cu
it
m
o
d
el
(
E
C
M)
-
b
ased
m
et
h
o
d
s
,
wh
ich
o
f
f
er
h
ig
h
ac
cu
r
ac
y
,
m
o
d
el
b
atter
y
d
y
n
am
ics
th
r
o
u
g
h
r
elatio
n
s
h
ip
s
am
o
n
g
v
o
l
tag
e,
cu
r
r
en
t,
a
n
d
OC
V
[
2
0
]
-
[
2
2
]
.
T
h
e
alg
o
r
ith
m
s
u
s
in
g
eq
u
iv
alen
t
cir
c
u
it
m
o
d
els
in
clu
d
e
th
e
t
r
ac
e
-
f
r
ee
Kalm
an
f
ilter
[
2
3
]
.
Ho
wev
er
,
th
is
f
ilter
ca
n
p
r
o
d
u
ce
s
ig
n
if
ican
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er
r
o
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a
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tab
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to
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elia
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a
f
ir
s
t
-
o
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d
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T
ay
lo
r
ex
p
a
n
s
io
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f
o
r
n
o
n
lin
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ar
f
u
n
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s
.
T
o
m
itig
ate
th
es
e
is
s
u
es,
th
e
tr
ac
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-
f
r
ee
Kalm
an
f
ilter
em
p
lo
y
s
a
tr
ac
e
-
f
r
ee
tr
an
s
f
o
r
m
[
6
]
,
w
h
ich
en
h
a
n
ce
s
esti
m
atio
n
ac
cu
r
ac
y
b
u
t in
c
u
r
s
h
ig
h
er
co
m
p
u
tatio
n
al
co
s
ts
.
Up
o
n
r
ev
iewin
g
th
e
liter
atu
r
e
,
we
id
en
tifie
d
a
s
ig
n
if
ican
t
g
ap
in
ac
cu
r
ately
esti
m
atin
g
th
e
SOC
o
f
L
i
-
io
n
b
atter
ies
u
n
d
er
b
o
th
n
o
r
m
al
o
p
er
atin
g
co
n
d
itio
n
s
an
d
f
au
lt
s
ce
n
ar
io
s
,
p
ar
ticu
lar
l
y
f
au
lts
r
elate
d
to
cu
r
r
en
t
an
o
m
alies.
M
o
s
t
ex
is
tin
g
s
tu
d
ies
p
r
ed
o
m
i
n
an
tly
r
ely
o
n
s
ec
o
n
d
-
o
r
d
er
e
q
u
iv
al
en
t
cir
cu
it
m
o
d
els,
wh
ich
co
n
s
tr
ain
b
o
th
th
e
a
cc
u
r
ac
y
a
n
d
g
en
er
al
ap
p
licab
ili
ty
o
f
SOC
esti
m
atio
n
m
eth
o
d
s
.
T
o
a
d
d
r
ess
th
e
af
o
r
em
en
tio
n
ed
ch
allen
g
es,
v
ar
io
u
s
s
tu
d
ies
h
av
e
em
p
lo
y
e
d
s
lid
in
g
m
o
d
e
o
b
s
er
v
er
s
(
S
MO
)
,
wh
ich
h
av
e
d
em
o
n
s
tr
ated
ef
f
ec
tiv
en
ess
in
en
h
an
cin
g
SOC
esti
m
atio
n
.
Ho
wev
er
,
th
eir
p
e
r
f
o
r
m
an
ce
i
s
h
ig
h
ly
d
ep
e
n
d
en
t
o
n
th
e
ap
p
r
o
p
r
iate
s
elec
tio
n
o
f
s
witch
in
g
g
ai
n
s
.
T
o
im
p
r
o
v
e
b
o
th
ac
cu
r
ac
y
a
n
d
r
o
b
u
s
tn
ess
,
r
esear
ch
er
s
h
av
e
p
r
o
p
o
s
ed
SMO
with
ad
a
p
tiv
e
g
ain
m
ec
h
an
is
m
s
an
d
tem
p
er
a
tu
r
e
-
s
en
s
itiv
e
b
atter
y
m
o
d
els
[
2
4
]
,
[
2
5
]
.
Desp
ite
th
ese
ad
v
an
ce
m
en
ts
,
m
an
y
ex
i
s
tin
g
ap
p
r
o
ac
h
es
ar
e
s
till
lim
it
ed
b
y
th
e
u
s
e
o
f
lo
wer
-
o
r
d
er
b
atter
y
m
o
d
els
an
d
ca
n
n
o
t
r
eliab
l
y
o
p
er
ate
u
n
d
e
r
ch
ar
g
i
n
g
a
n
o
m
alies.
Ad
d
iti
o
n
ally
,
th
e
co
m
p
u
tatio
n
al
co
m
p
lex
ity
o
f
s
o
m
e
m
eth
o
d
s
h
am
p
er
s
r
ea
l
-
tim
e
d
ep
lo
y
m
en
t
i
n
em
b
e
d
d
ed
s
y
s
tem
s
[
2
6
]
-
[
2
9
]
.
I
n
r
esp
o
n
s
e
,
th
i
s
s
tu
d
y
p
r
o
p
o
s
es
an
ef
f
icien
t
s
lid
in
g
m
o
d
e
o
b
s
er
v
er
with
ad
ap
tiv
e
g
ain
,
in
teg
r
ated
in
to
a
th
ir
d
-
o
r
d
er
E
C
M
to
ca
p
tu
r
e
b
atter
y
d
y
n
am
ics
an
d
d
if
f
u
s
io
n
ef
f
e
cts.
Desig
n
ed
f
o
r
r
o
b
u
s
tn
ess
u
n
d
e
r
cu
r
r
en
t
-
lev
el
f
au
lts
,
it
m
ain
tain
s
SO
C
esti
m
atio
n
ac
cu
r
ac
y
o
v
e
r
tim
e
.
A
f
au
lt
s
ce
n
ar
io
was
s
im
u
lated
to
v
alid
ate
its
er
r
o
r
d
etec
t
io
n
an
d
m
itig
atio
n
ca
p
ab
ilit
ies in
SOC
es
tim
atio
n
.
T
h
e
p
ap
er
in
clu
d
es
in
to
s
ev
er
al
s
ec
tio
n
s
f
o
llo
win
g
th
e
in
tr
o
d
u
ctio
n
:
Sectio
n
2
o
n
t
h
e
s
lid
in
g
m
o
d
e
o
b
s
er
v
er
d
esig
n
,
s
ec
tio
n
3
o
n
r
esu
lts
u
n
d
er
n
o
r
m
al
an
d
f
au
lt
co
n
d
itio
n
s
,
s
ec
tio
n
4
co
m
p
ar
in
g
with
p
r
ev
io
u
s
s
tu
d
ies,
an
d
s
ec
tio
n
5
c
o
n
clu
d
i
n
g
with
co
n
t
r
ib
u
tio
n
s
a
n
d
f
u
tu
r
e
wo
r
k
.
2.
CO
M
P
AR
E
H
E
NS
I
V
E
T
H
E
O
RE
T
I
CA
L
B
A
SI
S
Acc
u
r
ate
b
atter
y
m
o
d
elin
g
is
ess
en
tial
f
o
r
p
r
ed
ictin
g
lith
iu
m
-
io
n
p
e
r
f
o
r
m
an
ce
in
E
Vs
an
d
en
er
g
y
s
to
r
ag
e
s
y
s
tem
s
.
Am
o
n
g
v
ar
i
o
u
s
m
eth
o
d
s
,
E
C
M
is
p
r
ef
er
r
ed
in
B
MS
f
o
r
th
eir
b
alan
c
e
o
f
ac
c
u
r
ac
y
a
n
d
s
im
p
licity
.
T
h
is
s
tu
d
y
u
s
es a
th
ir
d
-
o
r
d
er
E
C
M
with
m
u
ltip
le
R
C
b
r
an
ch
es to
ca
p
tu
r
e
d
if
f
u
s
io
n
ef
f
ec
ts
.
2
.
1
.
B
a
t
t
er
y
m
o
delin
g
T
h
is
s
tu
d
y
u
s
es
a
(
3
-
R
C
)
m
o
d
el
f
o
r
SOC
esti
m
atio
n
,
w
h
ich
b
etter
ca
p
tu
r
es
b
atter
y
d
y
n
am
ics
an
d
tr
an
s
ien
t
b
eh
a
v
io
r
th
an
th
e
s
i
m
p
ler
2
-
R
C
m
o
d
el.
Desp
ite
its
co
m
p
lex
ity
,
it
im
p
r
o
v
es
ac
cu
r
ac
y
u
n
d
e
r
f
au
lt
co
n
d
itio
n
s
an
d
s
u
p
p
o
r
ts
r
ea
l
-
ti
m
e
f
au
lt d
etec
tio
n
in
B
MS.
2
.
1
.
1
.
M
o
del
d
escript
io
n:
wh
en
t
he
ba
t
t
er
y
is
o
pera
t
ing
n
o
rm
a
lly
B
atter
y
m
o
d
els
v
ar
y
in
co
m
p
l
ex
ity
an
d
ar
e
ty
p
ically
class
if
ied
in
to
f
o
u
r
ty
p
es:
em
p
ir
ical,
eq
u
iv
alen
t
cir
cu
it,
elec
tr
o
ch
e
m
ical,
an
d
d
ata
-
d
r
iv
en
m
o
d
els
(
Fig
u
r
e
1
)
[
2
9
]
.
T
h
e
elec
tr
o
ch
em
ic
al
m
o
d
el
d
escr
ib
es
in
ter
n
al
r
ea
ctio
n
s
an
d
u
n
d
er
p
i
n
s
o
th
er
m
o
d
els.
T
h
e
E
C
M
s
im
p
lifie
s
th
ese
r
ea
ctio
n
s
u
s
in
g
cir
cu
it
elem
en
ts
,
s
h
ar
in
g
p
ar
a
m
eter
s
with
th
e
el
ec
tr
o
ch
em
ical
m
o
d
el
to
ef
f
ec
tiv
ely
r
ep
r
esen
t b
atter
y
b
eh
av
io
r
[
3
0
]
.
Fig
u
r
e
1
.
T
h
e
class
if
icatio
n
s
o
f
b
atter
y
m
o
d
ellin
g
m
eth
o
d
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
5
,
No
.
1
,
Ma
r
ch
20
2
6
:
4
6
-
5
8
48
Am
o
n
g
v
a
r
io
u
s
m
o
d
els,
th
e
E
C
M
is
wid
ely
u
s
ed
in
B
MS
d
u
e
to
its
s
im
p
lici
ty
an
d
lo
w
co
m
p
u
tatio
n
al
co
s
t.
T
h
is
s
tu
d
y
em
p
lo
y
s
a
th
i
r
d
-
o
r
d
er
E
C
M
[
3
1
]
.
Fig
u
r
e
2
f
o
r
SOC
esti
m
atio
n
an
d
d
y
n
am
ic
an
aly
s
is
.
T
h
e
m
o
d
el
c
o
n
s
is
ts
o
f
an
OC
V
s
o
u
r
ce
d
e
p
en
d
e
n
t
o
n
SOC
,
an
o
h
m
ic
r
esis
tan
ce
(
R
₀)
r
ep
r
esen
tin
g
in
ter
n
al
lo
s
s
es,
an
d
th
r
ee
R
C
p
air
s
(
R
₁C
₁,
R
₂
C
₂,
R
₃
C
₃)
to
ca
p
tu
r
e
tr
an
s
ien
t
an
d
d
if
f
u
s
io
n
e
f
f
ec
ts
.
T
h
e
b
atter
y
cu
r
r
en
t
(
I
_
b
at)
f
lo
ws
th
r
o
u
g
h
th
e
cir
cu
it,
in
f
lu
e
n
cin
g
th
e
ter
m
in
al
v
o
ltag
e
(
Vb
at)
,
wh
ic
h
i
s
m
ea
s
u
r
ed
at
th
e
o
u
tp
u
t.
T
h
is
co
n
f
ig
u
r
atio
n
im
p
r
o
v
es a
cc
u
r
ac
y
in
m
o
d
elin
g
t
h
e
b
atter
y
’
s
n
o
n
lin
ea
r
.
Fig
u
r
e
2
.
E
q
u
iv
alen
t c
ir
c
u
it m
o
d
el
o
f
L
i
-
io
n
b
atter
y
T
h
e
in
ter
n
al
s
tates
o
f
th
e
L
i
-
io
n
b
atter
y
a
r
e
d
escr
ib
e
d
b
y
(
1
)
-
(
3
)
.
T
h
ese
eq
u
atio
n
s
d
ef
in
e
th
e
b
atter
y
’
s
in
ter
n
al
b
eh
av
io
r
.
1
=
1
1
.
1
−
1
(
1
)
2
=
2
2
.
2
−
2
(
2
)
3
=
3
3
.
3
−
3
(
3
)
T
h
e
d
er
iv
ativ
e
o
f
th
e
SOC
o
f
a
b
atter
y
with
r
esp
ec
t
to
tim
e
ca
n
b
e
ex
p
r
ess
ed
in
(
4
)
,
wh
er
e
QC
r
ep
r
esen
ts
th
e
ce
ll's
ch
ar
g
e
ca
p
ac
ity
in
(
Ah
)
.
̇
=
−
.
3600
(
4
)
Acc
o
r
d
in
g
t
o
elec
tr
ical
cir
cu
it
th
eo
r
y
,
t
h
e
v
o
ltag
e
at
th
e
b
atte
r
y
ter
m
in
als ca
n
b
e
ex
p
r
ess
ed
b
y
(
5
)
an
d
(
6
).
=
(
)
−
0
−
1
−
2
−
3
(
5
)
=
−
(
)
+
1
+
2
+
3
0
(
6
)
2
.
1
.
2
.
M
o
del descript
io
n:
wi
t
h c
urre
nt
f
a
ult
An
y
u
n
e
x
p
ec
ted
b
eh
av
i
o
r
in
a
co
n
tr
o
lled
p
r
o
ce
s
s
is
co
n
s
id
e
r
ed
a
f
a
u
lt.
I
n
b
atter
ies,
f
au
lts
ca
n
o
cc
u
r
in
th
e
ce
ll,
s
en
s
o
r
s
,
o
r
in
ter
n
al
co
m
p
o
n
en
ts
.
As
s
h
o
w
n
in
Fig
u
r
e
3
,
f
au
lts
ar
e
class
if
ied
b
y
th
eir
tim
e
-
v
ar
y
in
g
b
eh
av
io
r
as
s
u
d
d
e
n
,
in
ter
m
it
ten
t,
o
r
g
r
ad
u
al.
E
f
f
ec
tiv
e
b
atter
y
m
o
n
ito
r
in
g
is
ess
en
tial
f
o
r
d
etec
tin
g
an
d
m
an
ag
in
g
s
u
ch
f
a
u
lts
[
3
2
]
.
Fig
u
r
e
3
.
E
q
u
iv
alen
t c
ir
c
u
it m
o
d
el
o
f
a
L
i
-
io
n
b
atter
y
with
f
au
lt c
u
r
r
en
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
R
o
b
u
s
t S
OC
esti
ma
tio
n
fo
r
lith
iu
m
-
io
n
b
a
tter
ies u
n
d
er fa
u
lt
y
ch
a
r
g
in
g
s
ce
n
a
r
io
s
u
s
in
g
…
(
S
o
u
lef
Ma
h
i
d
d
in
e
)
49
T
h
e
m
o
d
el
in
Fig
u
r
e
3
co
n
s
is
ts
o
f
R
0
,
th
e
th
r
ee
p
air
s
R
C
,
th
e
o
p
e
n
cir
c
u
it
v
o
ltag
e
OC
V,
V
1
,
V
2
,
V
3
,
an
d
V
bat
,
wh
ic
h
we
h
a
v
e
alr
ea
d
y
d
e
f
in
ed
;
I
b
a
is
th
e
k
n
o
wn
i
n
p
u
t
c
u
r
r
en
t
o
f
th
e
b
atter
y
.
I
ts
r
ef
er
en
c
e
d
ir
ec
tio
n
r
ef
er
s
to
th
e
d
is
ch
ar
g
e
p
r
o
c
ess
(
+)
an
d
th
e
ch
ar
g
in
g
p
r
o
ce
s
s
(
-
)
.
I
Fault
is
th
e
f
au
lt
cu
r
r
en
t,
wh
ich
is
u
n
id
ir
ec
tio
n
al
an
d
is
ac
tu
ally
u
n
k
n
o
wn
b
ec
au
s
e
it
is
d
u
e
t
o
s
ev
er
al
r
ea
s
o
n
s
(
s
en
s
o
r
er
r
o
r
,
s
h
o
r
t
cir
cu
it,
wr
o
n
g
ch
ar
g
er
s
elec
tio
n
t
o
s
p
ee
d
u
p
th
e
ch
a
r
g
in
g
p
r
o
ce
s
s
)
.
I
in
p
u
t
is
th
e
in
p
u
t
cu
r
r
en
t
o
f
th
e
b
atter
y
a
n
d
is
d
eter
m
in
ed
b
y
Kir
ch
h
o
f
f
'
s
cir
c
u
it law
.
I
n
th
e
ca
s
e
o
f
f
au
lt,
as
s
h
o
wn
in
(
7
)
.
=
+
(
7
)
B
u
t w
h
en
th
e
b
atter
y
is
o
p
er
at
in
g
n
o
r
m
ally
,
=
0
an
d
th
u
s
=
.
3.
M
E
T
H
O
D
T
h
is
s
tu
d
y
ad
o
p
ts
a
s
tr
u
ctu
r
e
d
ex
p
e
r
im
en
tal
ap
p
r
o
ac
h
,
u
s
in
g
a
t
h
ir
d
-
o
r
d
er
E
C
M
an
d
SMO
with
alg
o
r
ith
m
ic
ju
s
tific
atio
n
f
o
r
r
o
b
u
s
t
SOC
esti
m
atio
n
.
C
o
u
lo
m
b
co
u
n
tin
g
is
ap
p
lied
f
o
r
tr
ac
k
in
g
SOC
,
wh
ile
th
e
th
ir
d
-
o
r
d
er
m
o
d
el
en
s
u
r
es
h
ig
h
er
d
y
n
am
ic
ac
cu
r
ac
y
th
a
n
s
ec
o
n
d
-
o
r
d
er
m
o
d
els.
T
o
ass
ess
th
e
r
o
b
u
s
tn
ess
o
f
th
e
SOC
esti
m
atio
n
m
eth
o
d
,
s
en
s
o
r
b
ias
an
d
cu
r
r
en
t
d
r
if
t
f
a
u
lts
wer
e
s
im
u
lated
o
v
er
1
1
h
o
u
r
s
.
T
h
is
lo
n
g
-
ter
m
test
h
ig
h
lig
h
ts
th
e
SMO
o
b
s
er
v
er
’
s
s
tab
ilit
y
u
n
d
er
u
n
d
etec
te
d
f
au
lts
.
Fu
tu
r
e
wo
r
k
will
test
p
er
f
o
r
m
an
ce
u
s
in
g
s
tan
d
ar
d
ch
ar
g
in
g
p
r
o
f
iles
lik
e
C
C
C
V
an
d
C
PC
V
.
C
o
u
lo
m
b
c
o
u
n
tin
g
is
wid
ely
u
s
ed
f
o
r
SOC
esti
m
atio
n
b
u
t
s
u
f
f
er
s
f
r
o
m
er
r
o
r
ac
cu
m
u
latio
n
d
u
e
to
s
en
s
o
r
in
ac
cu
r
ac
ies
an
d
v
o
ltag
e
f
lu
ctu
atio
n
s
,
esp
ec
ially
o
v
er
tim
e
o
r
u
n
d
er
a
b
n
o
r
m
al
co
n
d
i
tio
n
s
.
Mo
r
e
r
o
b
u
s
t
alter
n
ativ
es,
lik
e
th
e
SMO
wi
th
an
E
C
M,
b
etter
h
an
d
le
d
y
n
am
ic
b
eh
av
io
r
s
an
d
r
e
d
u
ce
lo
n
g
-
ter
m
esti
m
atio
n
er
r
o
r
s
.
T
h
e
SMO
is
s
elec
ted
d
u
e
to
its
r
o
b
u
s
tn
ess
ag
ain
s
t
m
ea
s
u
r
em
en
t
n
o
is
e
a
n
d
p
a
r
am
eter
v
a
r
iatio
n
s
.
T
ab
le
1
r
e
p
r
esen
ts
I
n
f
o
r
m
atio
n
ab
o
u
t
th
e
u
s
ed
b
atter
y
.
T
ab
le
1
.
I
n
f
o
r
m
atio
n
a
b
o
u
t th
e
u
s
ed
b
atter
y
Li
-
i
o
n
b
a
t
t
e
r
y
V
a
r
i
a
b
l
e
V
a
l
u
e
P
a
r
a
me
t
e
r
M
a
x
i
m
u
m
v
o
l
t
a
g
e
4
.
5
V
N
o
mi
n
a
l
v
o
l
t
a
g
e
3
.
7
V
b
a
t
t
e
r
y
c
u
r
r
e
n
t
10
A
R
0
0
.
0
0
1
4
Ω
R
1
0
.
0
0
2
4
Ω
C
1
2
4
0
0
0
F
R
2
0
.
0
0
3
0
Ω
C
2
2
6
0
0
0
F
R
3
0
.
0
0
4
0
Ω
C
3
2
7
0
0
0
F
3
.
1
.
Sli
din
g
m
o
de
o
bs
er
v
er
T
h
e
SMO
is
a
s
tate
m
o
n
ito
r
in
g
tech
n
iq
u
e
v
alu
ed
f
o
r
its
s
im
p
licity
an
d
lo
w
co
m
p
u
tatio
n
al
d
em
an
d
,
as
it
d
o
es
n
o
t
r
e
q
u
ir
e
a
c
o
m
p
l
ex
m
ath
em
atica
l
m
o
d
el
o
f
th
e
co
n
tr
o
lled
s
y
s
tem
a
n
d
is
i
n
s
en
s
itiv
e
to
p
a
r
am
eter
v
ar
iatio
n
s
.
T
h
is
m
ak
es
it
an
e
f
f
ec
tiv
e
s
tr
ateg
y
f
o
r
d
esig
n
in
g
m
o
n
it
o
r
in
g
s
y
s
tem
s
th
at
ca
n
ac
cu
r
ately
m
ea
s
u
r
e
an
d
ef
f
icien
tly
tr
ac
k
th
e
s
tates
o
f
n
o
n
lin
ea
r
s
y
s
tem
s
.
T
h
e
m
o
n
ito
r
is
also
r
esis
tan
t
to
e
x
ter
n
al
d
is
tu
r
b
an
ce
s
an
d
n
o
is
e,
d
em
o
n
s
tr
atin
g
ex
c
ellen
t
p
er
f
o
r
m
a
n
ce
in
r
ea
l
-
wo
r
l
d
ap
p
licatio
n
s
.
W
h
en
ca
lcu
latin
g
th
e
SOC
o
f
a
L
i
-
io
n
b
atter
y
,
f
ac
to
r
s
s
u
ch
as
co
m
p
u
tatio
n
al
co
m
p
lex
ity
,
f
lex
ib
ilit
y
,
an
d
co
n
v
e
r
g
en
ce
s
p
ee
d
m
u
s
t
b
e
co
n
s
id
er
ed
.
I
ts
h
ig
h
r
esis
tan
ce
to
in
ter
f
e
r
en
ce
in
d
icate
s
ex
ce
p
tio
n
al
r
o
b
u
s
tn
ess
,
allo
win
g
it
to
m
ain
tain
p
e
r
f
o
r
m
a
n
ce
ev
e
n
in
th
e
p
r
esen
ce
o
f
b
atter
y
-
lev
el
d
is
tu
r
b
an
ce
s
.
T
o
esti
m
ate
th
e
SOC
u
s
in
g
th
e
ad
ap
tiv
e
s
lid
in
g
m
o
d
e
o
b
s
er
v
er
,
it
is
ess
en
tia
l
to
estab
lis
h
a
m
ath
em
atica
l
m
o
d
el
o
f
th
e
L
i
-
io
n
b
atter
y
s
y
s
tem
an
d
d
er
i
v
e
th
e
s
tate
-
s
p
ac
e
eq
u
atio
n
s
.
Fo
llo
win
g
t
h
is
,
th
e
d
esig
n
o
f
th
e
r
elev
a
n
t
SM
O
is
im
p
lem
en
ted
to
m
o
n
ito
r
th
e
b
atter
y
'
s
s
tate
v
ar
iab
les f
o
r
SOC
esti
m
atio
n
[
3
3
]
-
[
3
5
]
.
T
h
e
s
tate
eq
u
atio
n
s
o
f
th
e
b
att
er
y
s
y
s
tem
ca
n
b
e
d
er
iv
ed
th
r
o
u
g
h
a
s
y
s
tem
atic
p
r
o
ce
s
s
.
T
h
is
p
r
o
ce
s
s
is
o
u
tlin
ed
in
(
8
)
–
(
1
2
)
.
̇
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1
+
2
(
)
−
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1
−
4
2
−
5
3
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3600
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+
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1
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(
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.
1
−
.
3600
.
2
−
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3
+
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2
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9
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1
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1
2
.
1
−
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3600
.
+
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3
(
1
0
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̇
2
=
1
2
2
.
1
−
1
1
.
+
∆
4
(
1
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
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2
2
5
2
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8
7
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p
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wer
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Vo
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1
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Ma
r
ch
20
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6
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3
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1
3
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3
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2
.
+
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5
(
1
2
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a
1
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C
3
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2
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1
C
1
C
3
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1
C
2
)
/(
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1
C
2
C
3
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;
a
2
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C
3
C
2
+C
1
C
3
+C
1
C
2
)
/(
C
1
C
2
C
3
);
a
3
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C
3
C
2
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1
C
2
C
3
+C
3
R
1
+R
1
C
2
)
/(
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1
C
2
C
3
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;
a
4
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R
2
C
3
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2
C
2
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1
C
3
+R
2
C
2
C
3
)
/(
R
2
C
2
C
3
);
a
5
= (
C
3
C
2
+R
3
C
3
+C
3
RC
1
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2
R
2
C
1
)
/(
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3
C
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2
.
T
h
e
s
tate
eq
u
atio
n
ca
n
b
e
e
x
p
r
ess
ed
co
n
cisely
in
ter
m
s
o
f
m
a
tr
ices,
as sh
o
wn
in
(
1
3
)
-
(
15
)
.
{
(
)
̇
=
(
)
+
(
)
+
∆
(
)
=
(
)
(
1
3
)
[
̇
̇
1
̇
2
̇
3
̇
]
=
[
1
6
0
0
0
2
6
0
0
0
3
6
7
0
0
4
6
0
8
0
5
6
0
0
9
]
.
[
1
2
3
]
−
[
1
2
3
4
5
]
+
∆
(
1
4
)
=
[
1
0
0
0
0
]
.
[
1
2
3
]
(
1
5
)
T
h
e
in
p
u
ts
an
d
o
u
tp
u
ts
o
f
t
h
e
cir
cle
m
o
d
el
wer
e
d
ef
in
ed
as
U(
t)
=
I
bat
an
d
y
(
t)
=
V
bat
in
r
o
w,
s
y
s
tem
co
n
d
itio
n
v
a
r
iab
les
ar
e
ch
o
s
en
as
V
bat,
SO
C
,
V
1
,
V
2
,
V
3
.
T
h
e
OC
V
o
f
th
e
elec
tr
ical
cir
cu
it
is
ex
p
r
ess
ed
as
a
f
u
n
ctio
n
o
f
th
e
s
tate
o
f
ch
ar
g
e
(
SOC
)
u
s
in
g
th
e
p
iece
wis
e
lin
ea
r
ap
p
r
o
x
im
atio
n
m
eth
o
d
,
as
s
h
o
wn
in
(
1
6
)
.
(
)
=
+
(
1
6
)
T
h
e
OC
V
d
er
iv
ativ
e
o
f
th
e
elec
tr
ical
cir
cu
it
is
ex
p
r
ess
ed
as
a
f
u
n
ctio
n
o
f
th
e
s
tate
o
f
ch
a
r
g
e
(
SOC
)
u
s
in
g
th
e
p
iece
wis
e
lin
ea
r
ap
p
r
o
x
im
atio
n
m
eth
o
d
,
as sh
o
wn
in
(
1
7
)
.
̇
(
)
=
−
3600
.
(
1
7
)
W
h
er
e
an
d
ar
e
co
n
s
tan
t
v
alu
es
in
ev
er
y
1
0
%
o
f
SOC
,
wh
ich
allo
w
u
s
to
r
ep
r
esen
t
th
e
tim
e
d
er
iv
ativ
e
o
f
in
ea
ch
1
0
% o
f
SOC
.
T
o
ac
cu
r
ately
esti
m
ate
th
e
s
tate
o
f
ch
ar
g
e,
SMO
eq
u
atio
n
s
a
r
e
p
r
o
p
o
s
ed
.
T
h
ese
eq
u
atio
n
s
ar
e
s
h
o
wn
in
(
1
8
)
–
(
2
2
)
.
̂
̇
=
1
+
2
(
)
−
1
.
+
1
(
)
(
1
8
)
̂
̇
=
3
−
3
(
)
+
3
.
1
+
3
.
2
+
3
.
3
+
2
(
)
(
1
9
)
1
̂
̇
=
4
.
1
−
2
.
+
∆
3
+
3
(
1
)
(
2
0
)
2
̂
̇
=
5
.
1
−
3
.
+
∆
4
+
4
(
2
)
(
2
1
)
3
̂
̇
=
6
.
3
−
4
.
+
∆
5
+
5
(
3
)
(
2
2
)
W
h
er
e
(
)
{
+
1
,
>
0
−
1
,
<
0
.
T
h
e
s
tate
er
r
o
r
is
s
h
o
wn
in
(
2
3
)
.
{
=
−
̂
=
−
̂
=
1
=
1
−
1
̂
2
=
2
−
2
̂
3
=
3
−
3
̂
(
2
3
)
B
y
s
u
b
tr
ac
tin
g
(
2
0
)
-
(
2
4
)
f
r
o
m
(
1
0
)
-
(
1
4
)
,
we
o
b
tain
th
e
e
r
r
o
r
d
y
n
am
ics
eb
at,
eso
c,
ev
1
,
ev
2
,
ev
3
,
as
s
h
o
wn
in
(
2
4
)
-
(
2
8
)
.
̇
=
1
+
2
+
∆
1
−
1
(
)
(
2
4
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
R
o
b
u
s
t S
OC
esti
ma
tio
n
fo
r
lith
iu
m
-
io
n
b
a
tter
ies u
n
d
er fa
u
lt
y
ch
a
r
g
in
g
s
ce
n
a
r
io
s
u
s
in
g
…
(
S
o
u
lef
Ma
h
i
d
d
in
e
)
51
̇
=
3
−
3
+
3
.
1
+
3
.
2
+
3
.
3
+
∆
2
−
2
(
)
(
2
5
)
1
̇
=
4
.
1
+
∆
2
−
3
(
1
)
(
2
6
)
2
̇
=
5
.
2
+
∆
2
−
4
(
2
)
(
2
7
)
3
̇
=
6
.
3
+
∆
2
−
5
(
3
)
(
2
8
)
B
ased
o
n
L
y
ap
u
n
o
v
'
s
s
tab
ili
ty
th
eo
r
y
,
th
e
asy
m
p
t
o
tic
co
n
v
er
g
en
ce
o
f
th
e
ter
m
i
n
al
v
o
ltag
e
er
r
o
r
ca
n
b
e
p
r
o
v
en
b
y
ch
o
o
s
in
g
a
ca
n
d
id
ate
L
y
ap
u
n
o
v
f
u
n
ctio
n
,
as sh
o
wn
i
n
(
2
9
)
.
{
=
1
2
2
̇
=
−
̇
(
2
9
)
T
h
e
tim
e
d
er
i
v
ativ
e
o
f
a
L
y
a
p
u
n
o
v
f
u
n
ctio
n
f
ilter
m
u
s
t
b
e
n
eg
ativ
e
to
en
s
u
r
e
a
s
lid
in
g
r
eg
im
e
,
a
n
d
af
ter
d
ev
elo
p
in
g
th
e
ex
p
r
ess
io
n
s
o
f
(
V_
(
v
_
b
at)
)
̇
,
L
1
>>
1
is
t
h
e
v
alu
e
o
f
L
1
th
at
e
n
s
u
r
es
(
V_
(
v
_
b
at)
)
̇
<0
.
All
s
y
m
b
o
ls
th
at
h
av
e
b
ee
n
u
s
ed
in
th
e
eq
u
atio
n
s
s
h
o
u
ld
b
e
d
e
f
in
ed
in
th
e
f
o
llo
win
g
tex
t.
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
e
p
r
o
p
o
s
ed
m
eth
o
d
im
p
r
o
v
es
SOC
esti
m
atio
n
ac
cu
r
ac
y
a
n
d
b
atter
y
s
af
ety
u
n
d
er
f
a
u
lt
c
o
n
d
itio
n
s
.
An
SMO
was
test
ed
o
n
a
th
ir
d
-
g
en
er
atio
n
L
i
-
i
o
n
b
atter
y
u
s
in
g
b
o
th
n
o
r
m
al
an
d
f
au
lt
cu
r
r
en
ts
to
esti
m
ate
s
y
s
tem
s
tates
(
Vb
at,
SOC
,
V1
,
V2
,
a
n
d
V
3
)
.
Fu
t
u
r
e
w
o
r
k
will
f
o
cu
s
o
n
r
ea
l
-
tim
e
im
p
lem
en
tatio
n
a
n
d
ad
ap
tiv
e
g
ain
o
p
tim
izatio
n
.
P
o
lar
izatio
n
v
o
ltag
es
(
V1
,
V2
,
V3
)
wer
e
v
alid
ated
b
y
c
o
m
p
a
r
in
g
SMO
esti
m
ates
to
b
en
ch
m
a
r
k
E
C
M
v
alu
es.
R
MSE
an
aly
s
is
co
n
f
ir
m
ed
th
e
m
eth
o
d
’
s
ac
cu
r
ac
y
u
n
d
er
b
o
th
n
o
r
m
al
an
d
f
a
u
lt
co
n
d
itio
n
s
.
T
h
is
s
tu
d
y
aim
s
to
im
p
r
o
v
e
t
h
e
ac
cu
r
ac
y
an
d
r
o
b
u
s
tn
ess
o
f
(
SOC
)
an
d
ter
m
in
al
v
o
ltag
e
esti
m
atio
n
u
n
d
er
b
o
t
h
n
o
r
m
al
a
n
d
f
au
lt
y
co
n
d
itio
n
s
.
Un
lik
e
p
r
e
v
io
u
s
wo
r
k
s
th
at
u
s
e
s
ec
o
n
d
-
o
r
d
er
m
o
d
els
o
r
s
h
o
r
t
s
im
u
latio
n
d
u
r
atio
n
s
[
3
2
]
,
[
3
6
]
,
it
em
p
lo
y
s
a
th
ir
d
-
o
r
d
e
r
E
C
M
co
m
b
in
ed
with
a
n
a
d
ap
tiv
e
SMO.
T
h
is
ap
p
r
o
ac
h
en
h
an
ce
s
d
y
n
am
ic
p
er
f
o
r
m
a
n
ce
,
e
x
ten
d
s
o
p
er
atio
n
al
tim
e
u
p
to
4
0
,
0
0
0
s
ec
o
n
d
s
f
ar
s
u
r
p
ass
in
g
th
e
d
u
r
atio
n
s
h
an
d
led
b
y
m
o
d
els
in
[
3
6
]
-
[
3
8
]
,
wh
ich
ar
e
lim
ited
to
less
th
an
1
4
,
0
0
0
,
1
,
8
0
0
,
an
d
9
0
0
s
ec
o
n
d
s
r
esp
ec
tiv
ely
,
an
d
s
im
u
ltan
eo
u
s
ly
esti
m
ates
SO
C
,
v
o
ltag
e,
a
n
d
p
o
lar
izatio
n
p
o
ten
tials
(
V₁,
V₂,
V₃)
,
o
f
f
er
i
n
g
a
m
o
r
e
co
m
p
r
eh
e
n
s
iv
e
an
d
f
au
lt
-
to
ler
an
t so
lu
tio
n
f
o
r
b
atter
y
m
an
ag
em
en
t sy
s
tem
s
.
4
.
1
.
B
a
t
t
er
y
curr
ent
a
na
ly
s
i
s
T
h
is
s
tu
d
y
s
im
u
lated
co
m
m
o
n
f
au
lts
lik
e
s
en
s
o
r
b
ias
an
d
cu
r
r
en
t
d
r
if
t
to
test
th
e
SOC
esti
m
atio
n
m
eth
o
d
'
s
r
o
b
u
s
tn
ess
.
T
h
e
1
1
-
h
o
u
r
f
a
u
lt
an
aly
s
is
ass
ess
ed
th
e
SMO
-
b
ased
o
b
s
er
v
er
’
s
p
er
f
o
r
m
an
ce
u
n
d
er
lo
n
g
-
ter
m
f
au
lt
co
n
d
itio
n
s
,
r
ef
lect
in
g
s
ce
n
ar
io
s
wh
er
e
a
B
MS
m
ay
n
o
t
ac
t
im
m
ed
iately
.
T
h
is
ex
ten
d
e
d
test
h
ig
h
lig
h
ts
th
e
m
et
h
o
d
’
s
lo
n
g
-
ter
m
ac
cu
r
ac
y
a
n
d
s
tab
ilit
y
.
T
h
e
3
-
R
C
m
o
d
el
en
h
an
c
es
SOC
es
tim
atio
n
ac
cu
r
ac
y
b
y
b
etter
ca
p
t
u
r
in
g
v
o
ltag
e
f
lu
ctu
atio
n
s
an
d
tr
an
s
ien
t
d
y
n
am
ics
u
n
d
er
f
a
u
lt
co
n
d
itio
n
s
.
I
ts
ad
d
ed
co
m
p
lex
ity
is
ju
s
tifie
d
f
o
r
r
ea
l
-
tim
e,
f
au
lt
-
to
ler
a
n
t BMS.
Fig
u
r
e
4
s
h
o
ws
b
atter
y
cu
r
r
e
n
t
u
n
d
e
r
n
o
r
m
al
an
d
f
au
lty
co
n
d
itio
n
s
.
I
n
Fig
u
r
e
4
(
a)
,
t
h
e
h
ea
lth
y
b
atter
y
ex
h
ib
its
a
s
tab
le
an
d
co
n
s
is
ten
t
cu
r
r
en
t
p
r
o
f
ile.
I
n
co
n
tr
ast,
Fig
u
r
e
4
(
b
)
s
h
o
ws
a
f
au
lty
b
atter
y
with
f
lu
ctu
atio
n
s
ca
u
s
ed
b
y
is
s
u
es
s
u
ch
as
s
en
s
o
r
er
r
o
r
s
,
s
h
o
r
t
cir
cu
its
,
o
r
im
p
r
o
p
e
r
ch
ar
g
e
r
u
s
e.
T
h
ese
d
ev
iatio
n
s
h
ig
h
lig
h
t th
e
im
p
ac
t o
f
f
au
lts
o
n
p
er
f
o
r
m
a
n
ce
an
d
th
e
n
ee
d
f
o
r
ef
f
ec
tiv
e
f
au
lt d
etec
tio
n
in
B
MS.
(
a)
(
b
)
Fig
u
r
e
4
.
B
atter
y
cu
r
r
en
t
:
(
a
)
b
atter
y
cu
r
r
e
n
t in
o
p
er
atin
g
n
o
r
m
ally
an
d
(
b
)
b
atter
y
cu
r
r
en
t
with
f
au
lt
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
5
,
No
.
1
,
Ma
r
ch
20
2
6
:
4
6
-
5
8
52
4
.
2
.
B
a
t
t
er
y
v
o
lt
a
g
e
estim
a
t
i
o
n
Fig
u
r
e
5
s
h
o
ws
th
e
esti
m
atio
n
o
f
b
atter
y
te
r
m
in
al
v
o
ltag
e
(
Vb
at)
u
n
d
e
r
n
o
r
m
al
an
d
f
au
lty
co
n
d
itio
n
s
o
v
er
4
0
,
0
0
0
s
ec
o
n
d
s
(
ap
p
r
o
x
i
m
ately
1
1
h
o
u
r
s
)
.
T
h
e
p
r
o
p
o
s
ed
SMO
ac
cu
r
ately
tr
ac
k
s
v
o
l
tag
e
th
r
o
u
g
h
o
u
t
t
h
is
p
er
io
d
,
o
u
tp
er
f
o
r
m
in
g
th
e
m
et
h
o
d
in
[
3
6
]
,
wh
ich
r
e
m
ain
s
r
eliab
le
o
n
ly
u
p
to
1
4
,
0
0
0
s
ec
o
n
d
s
.
Fig
u
r
es
5
(
a)
an
d
5
(
b
)
co
m
p
ar
e
esti
m
ated
an
d
ac
tu
al
Vb
at
u
n
d
er
n
o
r
m
al
a
n
d
f
au
lty
co
n
d
itio
n
s
.
W
h
ile
th
e
m
eth
o
d
in
[
3
6
]
is
r
eliab
le
o
n
l
y
u
p
t
o
1
4
,
0
0
0
s
ec
o
n
d
s
,
th
e
SMO
-
b
ased
esti
m
ato
r
en
s
u
r
es
s
tab
le
v
o
ltag
e
tr
ac
k
in
g
with
m
in
o
r
o
s
cillatio
n
s
in
n
o
r
m
al
co
n
d
it
io
n
s
an
d
clea
r
ly
d
etec
ts
d
ev
iatio
n
s
d
u
r
in
g
f
au
lts
.
T
h
ese
r
esu
lts
co
n
f
ir
m
its
r
o
b
u
s
tn
ess
f
o
r
lo
n
g
-
ter
m
,
r
ea
l
-
tim
e
b
atter
y
m
o
n
ito
r
in
g
an
d
f
a
u
lt d
etec
tio
n
in
B
MS.
(
a)
(
b
)
Fig
u
r
e
5
.
B
atter
y
v
o
ltag
e
:
(
a)
b
atter
y
v
o
ltag
e
in
o
p
er
atin
g
n
o
r
m
ally
an
d
(
b
)
b
atter
y
v
o
ltag
e
with
f
au
lt
4
.
3
.
St
a
t
e
o
f
cha
rg
e
estima
t
i
on
Fig
u
r
e
6
illu
s
tr
ates
SOC
esti
m
atio
n
u
n
d
er
n
o
r
m
al
an
d
f
a
u
lty
co
n
d
itio
n
s
o
v
er
4
0
,
0
0
0
s
e
co
n
d
s
.
T
h
e
p
r
o
p
o
s
ed
SMO
m
eth
o
d
en
s
u
r
es
ac
cu
r
ate
an
d
s
tab
le
tr
ac
k
in
g
th
r
o
u
g
h
o
u
t,
with
m
i
n
im
al
d
ev
iatio
n
in
n
o
r
m
al
o
p
er
atio
n
,
as
s
h
o
wn
in
Fig
u
r
e
6
(
a)
,
an
d
clea
r
f
au
lt
d
etec
tio
n
u
n
d
er
ab
n
o
r
m
al
co
n
d
itio
n
s
,
as
s
h
o
wn
in
Fig
u
r
e
6
(
b
)
.
I
n
co
n
tr
ast,
m
eth
o
d
s
in
[
3
2
]
an
d
[
3
7
]
ar
e
r
eliab
le
o
n
l
y
u
p
to
1
,
0
0
0
an
d
1
,
8
0
0
s
ec
o
n
d
s
,
r
esp
ec
tiv
ely
,
h
ig
h
lig
h
tin
g
th
e
s
u
p
e
r
io
r
r
o
b
u
s
tn
ess
an
d
lo
n
g
-
ter
m
ac
c
u
r
ac
y
o
f
th
e
SMO
-
b
ased
a
p
p
r
o
ac
h
.
(
a)
(
b
)
Fig
u
r
e
6
.
State
o
f
ch
ar
g
e
esti
m
atio
n
:
(
a)
SOC
in
o
p
er
atin
g
n
o
r
m
ally
an
d
(
b
)
SOC
with
f
au
lt
4
.
4
.
Cell
po
la
riza
t
io
n po
t
ent
ia
l e
s
t
im
a
t
io
n
Fig
u
r
es
7
,
8
,
an
d
9
s
h
o
w
th
e
esti
m
ated
ce
ll
p
o
lar
izatio
n
v
o
ltag
es
(
V₁,
V₂,
an
d
V₃)
u
n
d
er
n
o
r
m
al
an
d
f
au
lty
co
n
d
itio
n
s
o
v
er
4
0
,
0
0
0
s
ec
o
n
d
s
.
T
h
is
ex
ten
d
ed
p
er
io
d
en
a
b
les
a
th
o
r
o
u
g
h
ev
alu
ati
o
n
o
f
th
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
’
s
ab
ilit
y
to
tr
ac
k
v
o
ltag
e
d
y
n
am
ics
o
v
er
tim
e.
I
n
co
n
tr
ast,
th
e
m
eth
o
d
in
[
3
8
]
was
test
ed
o
v
er
o
n
ly
9
0
0
s
ec
o
n
d
s
,
lim
itin
g
its
ef
f
ec
tiv
en
ess
f
o
r
lo
n
g
-
ter
m
m
o
n
ito
r
in
g
.
T
h
e
r
esu
lts
h
ig
h
lig
h
t
th
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
’
s
s
u
p
er
io
r
s
tab
ilit
y
,
r
eliab
ilit
y
,
an
d
ac
cu
r
ac
y
ev
en
u
n
d
er
f
au
lt
co
n
d
itio
n
s
,
im
p
r
o
v
in
g
f
a
u
lt
d
etec
tio
n
an
d
o
v
er
all
B
MS
p
er
f
o
r
m
a
n
ce
.
T
h
is
d
em
o
n
s
tr
ates its
r
o
b
u
s
tn
ess
f
o
r
r
ea
l
-
wo
r
ld
e
n
er
g
y
s
to
r
a
g
e
ap
p
licatio
n
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
R
o
b
u
s
t S
OC
esti
ma
tio
n
fo
r
lith
iu
m
-
io
n
b
a
tter
ies u
n
d
er fa
u
lt
y
ch
a
r
g
in
g
s
ce
n
a
r
io
s
u
s
in
g
…
(
S
o
u
lef
Ma
h
i
d
d
in
e
)
53
(
a)
(
b
)
Fig
u
r
e
7
.
First
ce
ll p
o
lar
izatio
n
p
o
ten
tial e
s
tim
atio
n
:
(
a)
V
1
o
p
er
atin
g
n
o
r
m
ally
a
n
d
(
b
)
V
1
with
f
au
lt
(
a)
(
b
)
Fig
u
r
e
8
.
Seco
n
d
ce
ll
p
o
lar
izatio
n
p
o
te
n
tial e
s
tim
atio
n
:
(
a)
V
2
in
o
p
e
r
atin
g
n
o
r
m
ally
a
n
d
(
b
)
V
2
with
f
au
lt
(
a)
(
b
)
Fig
u
r
e
9
.
T
h
ir
d
ce
ll p
o
lar
izatio
n
p
o
te
n
tial e
s
tim
atio
n
:
(
a)
V
3
in
o
p
er
atin
g
n
o
r
m
ally
an
d
(
b
)
V
3
with
f
au
lt
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
5
,
No
.
1
,
Ma
r
ch
20
2
6
:
4
6
-
5
8
54
4
.
5
.
E
s
t
im
a
t
io
n
er
ro
r
a
na
l
y
s
is
Fig
u
r
es
1
0
-
1
4
s
h
o
w
esti
m
atio
n
er
r
o
r
s
f
o
r
b
atter
y
v
o
ltag
e
(
V
b
at)
,
SOC
,
an
d
p
o
la
r
izatio
n
v
o
ltag
es
(
V₁,
V₂,
V₃)
u
n
d
er
n
o
r
m
al
a
n
d
f
a
u
lt
co
n
d
itio
n
s
o
v
er
4
0
,
0
0
0
s
ec
o
n
d
s
.
T
h
is
d
u
r
atio
n
o
f
f
e
r
s
a
s
tr
o
n
g
co
m
p
ar
is
o
n
to
[
3
9
]
a
n
d
[
4
0
]
,
w
h
ich
co
v
er
o
n
ly
2
5
,
0
0
0
a
n
d
1
,
0
6
5
s
ec
o
n
d
s
,
r
esp
ec
tiv
ely
.
T
h
e
n
ea
r
-
ze
r
o
e
r
r
o
r
s
d
em
o
n
s
tr
ate
th
e
p
r
o
p
o
s
ed
m
eth
o
d
’
s
ac
cu
r
ac
y
an
d
r
eliab
ilit
y
in
esti
m
atin
g
s
y
s
tem
s
ta
tes,
ev
en
d
u
r
in
g
f
a
u
lts
.
T
h
e
o
b
s
er
v
er
co
n
s
is
ten
tly
tr
ac
k
s
v
o
ltag
e
a
n
d
SOC
with
h
ig
h
p
r
ec
is
io
n
,
co
n
f
ir
m
in
g
its
r
o
b
u
s
tn
ess
f
o
r
r
ea
l
-
tim
e,
f
au
lt
-
to
ler
an
t BMS a
p
p
licatio
n
s
.
(
a)
(
b
)
Fig
u
r
e
1
0
.
V
bat
esti
m
atio
n
er
r
o
r
:
(
a)
er
r
o
r
V
bat
in
o
p
er
atin
g
n
o
r
m
ally
an
d
(
b
)
e
r
r
o
r
V
bat
with
f
au
lt
(
a)
(
b
)
Fig
u
r
e
1
1
.
State
o
f
ch
ar
g
e
esti
m
atio
n
er
r
o
r
:
(
a)
SOC
er
r
o
r
in
o
p
er
atin
g
n
o
r
m
ally
an
d
(
b
)
SOC
er
r
o
r
with
f
au
lt
(
a)
(
b
)
Fig
u
r
e
1
2
.
First ce
ll p
o
lar
izatio
n
p
o
te
n
tial e
s
tim
atio
n
er
r
o
r
:
(
a)
V
1
er
r
r
o
r
in
o
p
er
atin
g
n
o
r
m
ally
an
d
(
b
)
V
1
er
r
o
r
with
f
au
lt
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
R
o
b
u
s
t S
OC
esti
ma
tio
n
fo
r
lith
iu
m
-
io
n
b
a
tter
ies u
n
d
er fa
u
lt
y
ch
a
r
g
in
g
s
ce
n
a
r
io
s
u
s
in
g
…
(
S
o
u
lef
Ma
h
i
d
d
in
e
)
55
(
a)
(
b
)
Fig
u
r
e
1
3
.
S
ec
o
n
d
ce
ll
p
o
lar
iz
atio
n
p
o
ten
tial e
s
tim
atio
n
er
r
o
r
:
(
a)
V
2
er
r
r
o
r
in
o
p
er
atin
g
n
o
r
m
ally
an
d
(
b
)
V
2
er
r
o
r
with
f
au
lt
(
a)
(
b
)
Fig
u
r
e
1
4
.
T
h
ir
d
ce
ll p
o
lar
izat
io
n
p
o
te
n
tial e
s
tim
atio
n
er
r
o
r
:
(
a)
V
3
er
r
r
o
r
in
o
p
er
atin
g
n
o
r
m
ally
an
d
(
b
)
V
3
er
r
o
r
with
f
au
lt
5.
CO
NCLU
SI
O
N
T
h
is
p
ap
er
p
r
esen
ts
a
n
o
v
el
SMO
d
esig
n
ed
to
ac
cu
r
ately
esti
m
ate
th
e
SO
C
an
d
ter
m
in
al
v
o
ltag
e
o
f
Li
-
io
n
b
atter
ies
u
s
in
g
a
th
ir
d
-
o
r
d
er
E
C
M
with
th
r
ee
r
esis
to
r
–
ca
p
ac
ito
r
(
R
C
)
n
etwo
r
k
s
.
T
h
e
p
r
o
p
o
s
ed
m
et
h
o
d
ef
f
ec
tiv
ely
ca
p
tu
r
es th
e
b
atter
y
’
s
d
y
n
am
ic
b
eh
av
i
o
r
,
p
r
o
v
i
d
in
g
p
r
ec
is
e
SOC
esti
m
atio
n
u
n
d
er
b
o
t
h
n
o
r
m
al
an
d
f
au
lty
c
o
n
d
itio
n
s
.
Simu
latio
n
r
esu
lts
co
n
f
ir
m
its
h
ig
h
ac
cu
r
ac
y
,
r
o
b
u
s
tn
ess
,
an
d
s
u
p
er
io
r
p
er
f
o
r
m
an
ce
co
m
p
ar
ed
t
o
co
n
v
e
n
tio
n
al
ap
p
r
o
ac
h
es.
T
h
e
SMO
also
d
is
tin
g
u
is
h
es
b
etwe
en
n
o
r
m
al
a
n
d
f
au
lt
s
ce
n
ar
io
s
,
m
ak
in
g
it su
itab
le
f
o
r
r
ea
l
-
tim
e
B
MS.
T
h
is
s
tu
d
y
en
h
an
ce
s
b
atter
y
r
eliab
ilit
y
,
s
af
ety
,
an
d
life
s
p
an
,
esp
ec
ially
f
o
r
elec
tr
ic
v
eh
icles
an
d
r
en
ewa
b
le
en
e
r
g
y
s
to
r
ag
e
a
p
p
licatio
n
s
.
T
h
is
s
tu
d
y
p
r
esen
ts
an
esti
m
atio
n
m
et
h
o
d
b
ased
o
n
a
3
-
R
C
b
atter
y
m
o
d
el
th
at
b
alan
ce
s
ac
c
u
r
ac
y
an
d
c
o
m
p
u
tatio
n
al
ef
f
icien
c
y
.
T
h
e
m
eth
o
d
p
e
r
f
o
r
m
s
r
eliab
l
y
ev
e
n
u
n
d
er
f
au
lty
ch
ar
g
in
g
c
o
n
d
itio
n
s
,
m
ak
in
g
i
t
well
-
s
u
ited
f
o
r
p
r
ac
tical
ap
p
licatio
n
s
.
Fu
tu
r
e
wo
r
k
s
h
o
u
ld
f
o
cu
s
o
n
r
ea
l
-
tim
e
v
alid
atio
n
u
s
in
g
ex
p
e
r
im
en
tal
test
b
en
ch
es
an
d
ad
a
p
tiv
e
g
ain
co
n
tr
o
l
t
o
im
p
r
o
v
e
r
o
b
u
s
tn
ess
.
I
n
teg
r
atin
g
SMO
tech
n
iq
u
es
with
m
ac
h
i
n
e
lea
r
n
in
g
c
o
u
ld
e
n
h
an
ce
f
au
lt
d
i
ag
n
o
s
is
an
d
p
r
ed
ictiv
e
ac
cu
r
ac
y
.
Ap
p
ly
i
n
g
th
e
ap
p
r
o
ac
h
to
d
if
f
e
r
en
t
b
atter
y
ch
em
is
tr
ies,
s
u
ch
as
lith
iu
m
-
io
n
a
n
d
s
o
lid
-
s
tate
s
y
s
tem
s
,
an
d
o
p
tim
izin
g
co
m
p
u
tatio
n
al
p
er
f
o
r
m
an
ce
will
s
u
p
p
o
r
t
its
u
s
e
in
lo
w
-
p
o
wer
em
b
ed
d
e
d
an
d
I
o
T
-
b
a
s
ed
en
er
g
y
s
to
r
ag
e
Evaluation Warning : The document was created with Spire.PDF for Python.