I
nte
rna
t
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na
l J
o
urna
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f
P
o
wer
E
lect
ro
nics
a
nd
Driv
e
S
y
s
t
em
s
(
I
J
P
E
DS)
Vo
l.
1
6
,
No
.
1
,
Ma
r
ch
2
0
2
5
,
p
p
.
4
4
0
~
4
4
7
I
SS
N:
2
0
8
8
-
8
6
9
4
,
DOI
: 1
0
.
1
1
5
9
1
/ijp
ed
s
.
v
1
6
.
i1
.
p
p
4
4
0
-
447
440
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
p
e
d
s
.
ia
esco
r
e.
co
m
Efficien
t
S
O
C
esti
ma
tion for ele
ctri
c vehicles
:
E
x
tend
ed
K
a
lma
n f
il
ter
a
pp
ro
a
ch f
o
r lit
h
ium
-
io
n battery sy
ste
ms
M
er
iem
M
o
s
s
a
d
dek
,
E
l Meh
di L
a
a
dis
s
i,
So
ha
ib B
o
uza
i
d,
Abdelo
wa
hed H
a
j
j
a
j
i
La
b
o
r
a
t
o
r
y
o
f
E
n
g
i
n
e
e
r
i
n
g
S
c
i
e
n
c
e
s
f
o
r
E
n
e
r
g
y
(
La
b
S
I
P
E)
,
N
a
t
i
o
n
a
l
S
c
h
o
o
l
o
f
A
p
p
l
i
e
d
S
c
i
e
n
c
e
s,
C
h
o
u
a
i
b
D
o
u
k
k
a
l
i
U
n
i
v
e
r
si
t
y
,
E
l
Ja
d
i
d
a
,
M
o
r
o
c
c
o
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Ma
y
2
0
,
2
0
2
4
R
ev
is
ed
No
v
6
,
2
0
2
4
Acc
ep
ted
No
v
2
8
,
2
0
2
4
Th
is
st
u
d
y
in
v
e
stig
a
tes
t
h
e
e
sti
m
a
ti
o
n
o
f
th
e
sta
te
o
f
c
h
a
r
g
e
(S
OC)
in
li
th
i
u
m
-
io
n
b
a
tt
e
ries
b
y
u
ti
li
z
in
g
t
h
e
e
x
ten
d
e
d
Ka
lma
n
fil
ter
(EKF
)
a
lg
o
rit
h
m
.
A
sim
u
latio
n
m
o
d
e
l
wa
s
d
e
v
e
l
o
p
e
d
in
M
ATLAB,
in
te
g
ra
ti
n
g
t
h
e
Th
e
v
e
n
i
n
m
o
d
e
l
wit
h
th
e
EKF
a
lg
o
rit
h
m
t
o
a
ss
e
ss
S
OC
lev
e
ls.
Th
e
re
su
lt
s
fro
m
th
e
sim
u
latio
n
s
c
o
n
firm
t
h
e
a
c
c
u
ra
c
y
a
n
d
re
li
a
b
il
it
y
o
f
th
e
p
r
o
p
o
se
d
a
p
p
r
o
a
c
h
i
n
e
stim
a
ti
n
g
S
OC.
M
o
re
o
v
e
r,
a
S
imu
li
n
k
-
b
a
se
d
m
o
d
e
l
o
f
th
e
Th
e
v
e
n
i
n
e
q
u
iv
a
len
t
c
ircu
it
a
n
d
t
h
e
EKF
a
l
g
o
rit
h
m
wa
s
imp
lem
e
n
ted
to
f
u
rt
h
e
r
v
e
rify
th
e
e
ffe
c
ti
v
e
n
e
ss
o
f
t
h
e
EKF
i
n
S
OC
e
stim
a
ti
o
n
.
T
h
is
re
se
a
rc
h
u
n
d
e
rsc
o
re
s
th
e
p
o
ten
ti
a
l
o
f
th
e
EKF
a
lg
o
rit
h
m
to
d
e
li
v
e
r
p
re
c
ise
S
OC
e
stim
a
tes
,
wh
ich
is
c
ru
c
ial
fo
r
o
p
ti
m
izin
g
b
a
tt
e
ry
m
a
n
a
g
e
m
e
n
t
sy
ste
m
s,
p
a
rt
icu
larly
in
e
lec
tri
c
v
e
h
icle
s.
K
ey
w
o
r
d
s
:
B
atter
y
m
an
ag
em
en
t sy
s
tem
E
lectr
ic
v
eh
icle
E
x
ten
d
ed
Kalm
a
n
f
ilter
L
ith
iu
m
-
io
n
b
atter
y
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
:
Me
r
iem
Mo
s
s
ad
d
ek
L
ab
o
r
ato
r
y
o
f
E
n
g
i
n
ee
r
in
g
Scien
ce
s
f
o
r
E
n
er
g
y
(
L
ab
SIPE
)
,
Natio
n
al
Sch
o
o
l o
f
Ap
p
lied
Sc
ien
ce
s
C
h
o
u
aib
Do
u
k
k
ali
Un
iv
er
s
ity
E
l Jad
id
a,
Mo
r
o
cc
o
E
m
ail:
m
o
s
s
ad
d
ek
m
er
y
e
m
@
g
m
ail.
co
m
,
m
o
s
s
ad
d
e
k
.
m
@
u
cd
.
ac
.
m
a
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
g
lo
b
al
s
h
if
t
to
war
d
s
s
u
s
tain
ab
le
en
er
g
y
s
o
lu
tio
n
s
h
as
p
o
s
itio
n
ed
elec
tr
ic
v
eh
icles
(
E
Vs)
at
th
e
f
o
r
ef
r
o
n
t o
f
ef
f
o
r
ts
to
r
ed
u
ce
g
r
ee
n
h
o
u
s
e
g
as e
m
is
s
io
n
s
an
d
d
ep
en
d
e
n
ce
o
n
f
o
s
s
il
f
u
els [
1
]
.
T
h
e
Un
ited
States
,
J
ap
an
,
an
d
C
h
in
a
h
av
e
em
e
r
g
ed
as
th
e
p
r
im
ar
y
m
ar
k
ets
d
r
iv
in
g
th
e
a
d
o
p
tio
n
o
f
E
Vs,
wi
th
s
ales
s
h
o
win
g
a
co
n
s
is
ten
t u
p
war
d
tr
en
d
s
in
ce
th
e
ea
r
ly
2
0
0
0
s
[
2
]
.
Desp
ite
th
ese
g
ain
s
,
th
e
wid
esp
r
ea
d
ad
o
p
tio
n
o
f
E
Vs is
s
till
co
n
s
tr
ain
ed
b
y
s
ig
n
if
ican
t
ch
al
len
g
es,
in
clu
d
i
n
g
h
ig
h
m
an
u
f
a
ctu
r
in
g
c
o
s
ts
,
lim
ited
d
r
i
v
i
n
g
r
an
g
e,
a
n
d
c
o
n
ce
r
n
s
r
eg
ar
d
in
g
b
atter
y
lo
n
g
ev
ity
a
n
d
r
eliab
ilit
y
[
3
]
.
C
en
tr
al
to
th
ese
ch
allen
g
es
is
th
e
p
er
f
o
r
m
an
ce
o
f
lith
iu
m
-
io
n
b
atter
ies
[
4
]
,
wh
ich
p
la
y
a
cr
i
tical
r
o
le
in
d
eter
m
in
in
g
th
e
e
f
f
icien
cy
,
r
a
n
g
e,
p
o
wer
o
u
tp
u
t,
an
d
o
v
e
r
all
co
s
t
-
ef
f
ec
tiv
e
n
ess
o
f
E
Vs
[
5
]
.
L
ith
i
u
m
-
io
n
b
atter
ies
ar
e
wid
ely
f
av
o
r
ed
f
o
r
en
e
r
g
y
s
to
r
ag
e
i
n
E
Vs
b
ec
au
s
e
o
f
th
eir
ex
ce
p
tio
n
al
en
er
g
y
d
e
n
s
ity
,
ex
ce
llen
t p
o
wer
p
er
f
o
r
m
an
ce
,
an
d
m
in
im
al
s
elf
-
d
is
ch
ar
g
e
r
ates [
6
]
.
T
h
e
ev
o
lu
tio
n
o
f
th
ese
b
atter
ies,
p
a
r
ticu
lar
ly
th
r
o
u
g
h
th
e
u
s
e
o
f
o
r
g
an
ic
el
ec
tr
o
ly
tes,
h
as
led
to
s
ig
n
if
ica
n
t
im
p
r
o
v
em
e
n
ts
in
en
er
g
y
d
en
s
ity
,
en
ab
lin
g
lo
n
g
er
d
r
iv
in
g
r
an
g
es
an
d
co
n
tr
i
b
u
tin
g
to
th
e
in
cr
ea
s
in
g
p
o
p
u
la
r
ity
o
f
p
lu
g
-
in
h
y
b
r
id
elec
tr
ic
v
eh
icles
(
PHEV
s
)
an
d
f
u
lly
elec
tr
ic
v
eh
icles
[
7
]
.
Or
g
an
ic
elec
tr
o
ly
te
s
allo
w
f
o
r
s
tab
le
o
p
er
atio
n
at
h
ig
h
er
v
o
ltag
es,
wh
ich
h
as
b
ee
n
in
s
tr
u
m
e
n
tal
in
t
h
e
ad
v
an
ce
m
en
t
o
f
lith
iu
m
-
i
o
n
tec
h
n
o
l
o
g
y
[
8
]
.
Ho
wev
e
r
,
d
esp
ite
th
ese
ad
v
an
ce
s
,
th
e
i
n
h
er
en
t
lim
itatio
n
s
o
f
lith
iu
m
-
i
o
n
b
atter
ies,
s
u
ch
as
d
e
g
r
ad
at
io
n
o
v
e
r
tim
e
an
d
s
en
s
itiv
ity
to
o
p
er
atin
g
c
o
n
d
iti
o
n
s
,
co
n
tin
u
e
to
p
o
s
e
ch
allen
g
es to
th
eir
wid
esp
r
ea
d
a
d
o
p
tio
n
[
9
]
.
An
ess
en
tial
co
m
p
o
n
en
t
o
f
b
at
ter
y
m
an
a
g
em
en
t
in
elec
tr
ic
v
eh
icles
is
ac
cu
r
ately
esti
m
atin
g
th
e
s
tate
o
f
ch
ar
g
e
(
SOC
)
,
wh
ich
p
r
o
v
i
d
es
r
ea
l
-
tim
e
in
f
o
r
m
atio
n
o
n
t
h
e
r
em
ain
in
g
en
er
g
y
ca
p
ac
ity
o
f
th
e
b
atter
y
[
1
0
]
.
Acc
u
r
ate
SOC
esti
m
atio
n
is
v
ital
f
o
r
m
ax
im
izin
g
b
atter
y
ef
f
icien
cy
,
p
r
o
lo
n
g
in
g
its
life
s
p
an
,
an
d
en
s
u
r
in
g
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2
0
8
8
-
8
6
9
4
E
fficien
t S
OC
esti
ma
tio
n
fo
r
e
lectric v
eh
icles:
ex
ten
d
ed
K
a
lma
n
filt
er a
p
p
r
o
a
ch
f
o
r
…
(
Mer
iem
Mo
s
s
a
d
d
ek
)
441
s
af
e
an
d
ef
f
ec
tiv
e
o
p
er
atio
n
o
f
E
Vs.
Sev
er
al
tech
n
iq
u
es
h
av
e
b
ee
n
d
ev
elo
p
ed
to
esti
m
ate
SOC
,
ea
ch
with
d
is
tin
ct
s
tr
en
g
th
s
an
d
wea
k
n
ess
es
[
6
]
,
[
1
1
]
.
C
o
u
lo
m
b
co
u
n
tin
g
is
am
o
n
g
th
e
s
im
p
le
m
eth
o
d
s
u
s
ed
to
d
eter
m
in
e
th
e
b
atter
y
'
s
s
tate
o
f
ch
ar
g
e
(
S
OC
)
;
th
is
ap
p
r
o
ac
h
r
elies
o
n
t
h
e
in
teg
r
atio
n
o
f
in
p
u
t
an
d
o
u
tp
u
t
cu
r
r
e
n
ts
o
f
th
e
b
atter
y
o
v
er
tim
e.
Desp
ite
its
s
im
p
licity
,
th
is
m
eth
o
d
is
p
r
o
n
e
to
cu
m
u
lativ
e
er
r
o
r
s
,
p
ar
tic
u
lar
ly
as
th
e
b
atter
y
ag
es
o
r
its
ca
p
ac
ity
ch
an
g
es
[
1
2
]
.
An
o
t
h
er
wid
ely
u
s
ed
tec
h
n
iq
u
e
is
th
e
o
p
en
-
cir
cu
it
v
o
ltag
e
(
OC
V)
m
eth
o
d
,
wh
ich
esti
m
ates
SO
C
b
y
m
ea
s
u
r
in
g
th
e
b
atter
y
’
s
ter
m
in
al
v
o
ltag
e
[
1
3
]
,
[
1
4
]
.
T
h
e
n
o
n
lin
ea
r
ity
b
etwe
en
v
o
ltag
e
an
d
SOC
,
tem
p
er
at
u
r
e
f
lu
ctu
a
tio
n
s
,
an
d
h
y
s
ter
esis
ef
f
ec
ts
ca
n
im
p
ac
t
th
e
ac
c
u
r
ac
y
o
f
th
i
s
m
eth
o
d
,
th
o
u
g
h
it
r
em
ain
s
co
s
t
-
ef
f
ec
tiv
e
an
d
ea
s
y
to
u
s
e
[
1
5
]
.
T
h
ese
c
h
allen
g
es
h
ig
h
lig
h
t
th
e
n
ec
ess
ity
f
o
r
m
o
r
e
a
d
v
an
ce
d
ap
p
r
o
ac
h
es to
ad
d
r
ess
th
e
co
m
p
lex
an
d
n
o
n
lin
ea
r
n
atu
r
e
o
f
SOC
esti
m
atio
n
in
lith
iu
m
-
io
n
b
atter
ie
[
1
6
]
.
T
h
e
ex
ten
d
ed
Kalm
an
f
ilter
(
E
KF
)
is
th
e
m
o
s
t
ap
p
licab
le
m
eth
o
d
in
th
e
f
ield
o
f
E
Vs
f
o
r
esti
m
atin
g
b
atter
y
s
tate
o
f
ch
ar
g
e,
d
u
e
to
its
s
tr
o
n
g
ca
p
ab
ilit
y
to
h
an
d
l
e
th
e
n
o
n
lin
ea
r
ities
ch
a
r
ac
ter
i
s
tic
o
f
s
u
ch
b
atter
y
s
y
s
tem
s
[
1
2
]
,
an
d
also
f
o
r
esti
m
atin
g
b
atter
y
p
ar
am
eter
s
an
d
s
tates
[
1
7
]
.
I
t
is
a
n
o
n
lin
ea
r
e
x
ten
s
io
n
o
f
th
e
lin
ea
r
Kalm
an
f
ilter
an
d
o
p
er
ates b
y
lin
ea
r
izin
g
n
o
n
lin
ea
r
f
u
n
ctio
n
s
th
r
o
u
g
h
th
e
u
s
e
o
f
p
a
r
tial d
er
i
v
ativ
es a
n
d
a
f
ir
s
t
-
o
r
d
er
T
ay
lo
r
s
er
ies ex
p
an
s
io
n
[
1
8
]
.
T
h
e
E
KF w
as u
s
ed
b
o
th
f
o
r
th
e
id
en
t
if
icatio
n
o
f
b
atter
y
m
o
d
el
p
ar
am
eter
s
an
d
f
o
r
s
tate
esti
m
atio
n
[
1
9
]
.
T
h
e
esti
m
atio
n
p
r
o
ce
s
s
in
v
o
lv
es
ca
lcu
latio
n
o
f
th
e
J
ac
o
b
ian
m
atr
ix
,
wh
ich
ca
n
in
f
lu
en
ce
th
e
ac
cu
r
ac
y
o
f
th
e
esti
m
ated
SOC
v
alu
e
[
20
]
.
Ho
wev
er
,
th
e
E
KF
is
n
o
t
with
o
u
t
its
lim
itatio
n
s
.
I
ts
r
elian
ce
o
n
f
ir
s
t
-
o
r
d
er
a
p
p
r
o
x
im
atio
n
s
ca
n
in
tr
o
d
u
ce
e
r
r
o
r
s
,
p
ar
ticu
lar
ly
in
s
y
s
tem
s
with
s
ig
n
if
ican
t
n
o
n
lin
ea
r
ities
[
1
3
]
.
Mo
r
eo
v
er
,
th
e
E
KF's
p
er
f
o
r
m
an
ce
is
h
ig
h
ly
d
ep
en
d
e
n
t
o
n
th
e
ac
cu
r
ac
y
o
f
p
r
io
r
k
n
o
wled
g
e
r
eg
ar
d
in
g
s
y
s
tem
n
o
is
e,
wh
ich
,
if
in
ac
cu
r
ate,
ca
n
lead
t
o
esti
m
atio
n
er
r
o
r
s
an
d
ev
e
n
d
iv
e
r
g
en
ce
f
r
o
m
th
e
tr
u
e
SOC
[
2
1
]
.
I
n
r
esp
o
n
s
e
to
th
ese
ch
allen
g
es,
v
ar
io
u
s
en
h
a
n
ce
m
en
ts
to
th
e
E
KF
h
av
e
b
ee
n
p
r
o
p
o
s
ed
in
r
ec
en
t
y
ea
r
s
.
On
e
s
u
ch
im
p
r
o
v
em
e
n
t
is
th
e
E
KF
wh
ich
in
co
r
p
o
r
ates
ad
ap
tiv
e
p
ar
a
m
eter
u
p
d
ates
to
ac
co
u
n
t
f
o
r
ch
an
g
es
in
th
e
b
atter
y
'
s
ch
ar
ac
ter
is
t
ics
o
v
er
tim
e,
s
u
ch
as
ag
in
g
[
2
2
]
.
T
h
is
ad
ap
tatio
n
im
p
r
o
v
es
th
e
ac
cu
r
ac
y
o
f
SOC
esti
m
atio
n
,
p
ar
ticu
lar
ly
in
r
ea
l
-
tim
e
ap
p
licatio
n
s
wh
er
e
th
e
b
atter
y
'
s
co
n
d
itio
n
m
ay
ch
an
g
e
d
y
n
am
ically
[
2
3
]
.
On
e
lim
itatio
n
o
f
th
e
E
KF
alg
o
r
ith
m
is
th
at
its
lin
ea
r
izatio
n
o
n
ly
p
r
o
v
i
d
es
f
ir
s
t
-
o
r
d
er
ac
c
u
r
ac
y
,
as
it
r
elies
o
n
f
ir
s
t
-
o
r
d
er
T
a
y
lo
r
e
x
p
an
s
io
n
.
C
o
n
s
eq
u
en
tly
,
th
e
p
er
f
o
r
m
an
c
e
o
f
th
e
E
KF
is
h
ig
h
ly
d
ep
e
n
d
en
t
o
n
th
e
ac
c
u
r
ac
y
o
f
th
e
b
atter
y
m
o
d
el
p
ar
am
eter
s
an
d
p
r
i
o
r
k
n
o
wled
g
e
o
f
s
y
s
tem
n
o
is
e.
I
f
th
e
p
r
io
r
k
n
o
wled
g
e
is
in
ac
cu
r
ate,
th
e
esti
m
atio
n
p
r
o
ce
s
s
m
ay
r
esu
lt
in
d
iv
er
g
e
n
ce
er
r
o
r
s
[
2
4
]
.
Fo
r
in
s
tan
ce
,
th
e
au
th
o
r
s
in
[
1
8
]
p
r
o
p
o
s
ed
a
n
I
m
p
r
o
v
e
d
E
KF
f
o
r
o
n
lin
e
SOC
esti
m
atio
n
,
wh
ich
ad
ap
ts
b
atter
y
m
o
d
el
p
ar
am
eter
s
in
r
ea
l
tim
e
to
ac
c
o
u
n
t
f
o
r
b
atter
y
ag
in
g
.
T
h
e
I
-
E
KF
m
eth
o
d
d
e
m
o
n
s
tr
ated
th
at
th
e
SOC
e
s
tim
ated
f
r
o
m
a
s
in
g
le
ce
ll
co
u
ld
b
e
ac
cu
r
ately
u
s
ed
to
r
ep
r
esen
t
th
e
SOC
o
f
an
en
tire
b
atter
y
p
ac
k
in
E
Vs.
Ad
d
itio
n
ally
,
a
r
o
b
u
s
t
E
KF
was
u
tili
ze
d
f
o
r
SOC
est
i
m
atio
n
u
s
in
g
a
f
i
v
e
-
R
C
b
atter
y
m
o
d
el
to
e
v
alu
ate
th
e
alg
o
r
ith
m
’
s
p
er
f
o
r
m
an
ce
[
2
5
]
.
T
h
e
s
tu
d
y
ex
p
lo
r
e
d
th
e
s
en
s
itiv
ity
o
f
SO
C
es
tim
atio
n
to
d
i
f
f
er
en
t
in
itial
co
n
d
itio
n
s
,
an
d
th
e
r
esu
lts
s
h
o
wed
th
at
r
o
b
u
s
t
E
KF
co
u
ld
ef
f
ec
tiv
ely
m
in
im
ize
er
r
o
r
s
ca
u
s
e
d
b
y
in
co
r
r
ec
t
in
itial
SOC
v
alu
es.
I
n
th
is
s
tu
d
y
,
we
p
r
o
p
o
s
e
d
e
v
e
lo
p
in
g
a
co
m
p
r
eh
en
s
iv
e
e
q
u
iv
alen
t
cir
cu
it
m
o
d
el
(
E
C
M)
o
f
a
lith
iu
m
-
io
n
b
atter
y
,
in
c
o
r
p
o
r
atin
g
t
h
e
d
y
n
am
ic
ch
a
r
ac
ter
is
tics
o
f
th
e
b
atter
y
,
s
u
ch
as
r
esis
tan
ce
,
ca
p
a
citan
ce
,
an
d
v
o
ltag
e
s
o
u
r
ce
s
.
T
h
is
m
o
d
el
will
s
er
v
e
as
th
e
b
asis
f
o
r
f
o
r
m
u
latin
g
a
s
tate
eq
u
atio
n
m
o
d
el,
wh
ich
will
th
en
b
e
im
p
lem
en
ted
in
MA
T
L
AB
/
Si
m
u
lin
k
f
o
r
s
im
u
latio
n
.
T
h
e
s
im
u
latio
n
r
esu
lts
will
p
r
o
v
id
e
a
f
o
u
n
d
atio
n
f
o
r
in
teg
r
atin
g
th
e
m
o
d
el
in
to
an
E
KF
alg
o
r
ith
m
to
esti
m
ate
SO
C
.
T
h
e
ef
f
ec
tiv
en
ess
o
f
th
e
p
r
o
p
o
s
ed
m
eth
o
d
will
b
e
ev
alu
ated
b
y
c
o
m
p
ar
i
n
g
th
e
esti
m
ated
SO
C
v
alu
es
with
ac
tu
al
SOC
v
alu
es
o
b
tain
ed
f
r
o
m
ex
p
er
im
en
tal
m
ea
s
u
r
em
en
ts
.
T
h
is
wo
r
k
co
n
t
r
ib
u
tes
to
t
h
e
ex
is
tin
g
b
o
d
y
o
f
k
n
o
wled
g
e
b
y
in
tr
o
d
u
cin
g
a
r
e
f
in
ed
b
atter
y
m
o
d
el
th
at
m
o
r
e
ac
cu
r
ately
ca
p
tu
r
es
th
e
n
o
n
lin
ea
r
b
eh
a
v
io
r
o
f
lith
i
u
m
-
io
n
b
atter
ies,
a
n
d
b
y
p
r
o
p
o
s
in
g
an
im
p
r
o
v
e
d
E
KF a
lg
o
r
ith
m
th
at
ac
co
u
n
ts
f
o
r
b
atter
y
a
g
in
g
a
n
d
o
t
h
er
d
y
n
am
ic
f
ac
to
r
s
,
th
er
eb
y
en
h
an
cin
g
th
e
ac
cu
r
ac
y
an
d
r
eliab
ilit
y
o
f
SOC
esti
m
atio
n
.
Fin
ally
,
th
e
s
tu
d
y
p
r
o
v
id
es
a
r
i
g
o
r
o
u
s
ev
alu
atio
n
o
f
th
e
p
r
o
p
o
s
ed
m
eth
o
d
th
r
o
u
g
h
s
im
u
latio
n
s
an
d
ex
p
e
r
im
en
tal
v
alid
atio
n
,
d
em
o
n
s
tr
atin
g
its
p
o
ten
tial
ap
p
licab
ilit
y
i
n
r
ea
l
-
wo
r
ld
E
V
b
atter
y
m
an
ag
em
en
t sy
s
tem
s
.
T
h
e
s
tr
u
ctu
r
e
o
f
th
is
m
an
u
s
cr
ip
t
is
as
f
o
llo
ws:
i)
Sectio
n
2
o
f
f
er
s
a
co
m
p
r
eh
e
n
s
iv
e
r
ev
i
ew
o
f
th
e
liter
atu
r
e,
d
is
cu
s
s
in
g
b
o
th
th
e
s
tr
en
g
th
s
an
d
lim
itatio
n
s
o
f
p
r
ev
io
u
s
r
esear
ch
o
n
SOC
esti
m
atio
n
;
ii)
I
n
s
ec
tio
n
3
,
th
e
m
et
h
o
d
o
lo
g
y
is
o
u
tlin
ed
,
co
v
er
i
n
g
th
e
d
ev
elo
p
m
en
t
o
f
th
e
b
atter
y
m
o
d
el
a
n
d
th
e
ap
p
l
icatio
n
o
f
t
h
e
E
KF
alg
o
r
ith
m
;
iii)
Sectio
n
4
p
r
esen
ts
th
e
s
im
u
latio
n
an
d
ex
p
er
i
m
en
tal
r
esu
lts
,
wh
ile
s
ec
tio
n
5
p
r
o
v
id
es
an
in
-
d
e
p
th
d
is
cu
s
s
io
n
o
f
th
ese
f
in
d
in
g
s
;
an
d
iv
)
L
astl
y
,
s
ec
tio
n
6
co
n
clu
d
es
th
e
p
ap
er
,
s
u
m
m
ar
izin
g
th
e
m
ain
co
n
tr
ib
u
tio
n
s
an
d
p
r
o
p
o
s
in
g
d
ir
ec
tio
n
s
f
o
r
f
u
tu
r
e
r
esear
ch
.
2.
M
E
T
H
O
D
T
o
ac
cu
r
ately
esti
m
ate
th
e
SOC
o
f
a
b
atter
y
,
it
is
n
ec
ess
ar
y
to
co
n
s
tr
u
ct
an
eq
u
i
v
alen
t
m
o
d
el
th
at
n
o
t
o
n
ly
o
f
f
er
s
h
ig
h
p
r
ec
is
io
n
b
u
t
also
ac
cu
r
ately
ca
p
tu
r
es
th
e
d
y
n
am
ic
b
e
h
av
io
r
o
f
th
e
b
at
ter
y
.
Mo
r
eo
v
e
r
,
to
f
ac
ilit
ate
p
r
ac
tical
im
p
lem
en
ta
tio
n
in
en
g
in
ee
r
in
g
ap
p
licatio
n
s
,
th
e
m
o
d
el'
s
co
m
p
lex
ity
m
u
s
t
b
e
k
ep
t
in
ch
ec
k
.
T
h
e
m
o
s
t
co
m
m
o
n
ly
u
s
ed
eq
u
iv
alen
t
m
o
d
els
f
o
r
L
i
-
io
n
b
a
tter
ies
in
clu
d
e
t
h
e
R
in
t
m
o
d
el
[
2
6
]
,
th
e
T
h
ev
e
n
in
m
o
d
el
[
2
7
]
,
an
d
th
e
R
n
g
v
m
o
d
el
[
2
8
]
.
Am
o
n
g
th
ese,
th
e
T
h
ev
en
in
m
o
d
el
is
p
ar
ticu
lar
ly
ef
f
ec
tiv
e
in
q
u
ick
ly
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.
1
6
,
No
.
1
,
Ma
r
c
h
2
0
2
5
:
440
-
447
442
ca
p
tu
r
in
g
th
e
o
p
er
atin
g
s
tate
o
f
th
e
L
i
-
io
n
b
atter
y
with
o
u
t
in
t
r
o
d
u
cin
g
s
ig
n
if
ican
t
d
elay
s
,
th
u
s
en
s
u
r
in
g
r
eliab
le
ac
cu
r
ac
y
o
v
er
e
x
ten
d
ed
s
im
u
latio
n
s
.
T
h
e
eq
u
iv
alen
t
cir
c
u
it
m
o
d
e
l
is
a
well
-
es
tab
lis
h
ed
ap
p
r
o
ac
h
,
f
r
eq
u
en
tly
ap
p
lied
ac
r
o
s
s
v
ar
io
u
s
ap
p
licatio
n
s
d
ep
e
n
d
in
g
o
n
th
e
ty
p
e
o
f
b
atter
y
.
R
esear
ch
er
s
in
th
e
f
ield
h
a
v
e
cr
ea
te
d
s
e
v
er
al
m
o
d
els,
o
f
te
n
r
ef
in
in
g
th
em
th
r
o
u
g
h
ex
ten
s
iv
e
test
in
g
to
g
en
er
alize
th
eir
u
s
e
f
o
r
d
if
f
er
en
t
b
atter
y
ty
p
es.
T
h
e
f
o
llo
win
g
s
ec
tio
n
o
u
tlin
es so
m
e
o
f
th
e
m
o
d
els
d
is
cu
s
s
ed
in
th
e
liter
atu
r
e.
On
e
o
f
th
e
m
o
s
t c
o
m
m
o
n
ly
u
s
ed
m
o
d
els is
T
h
ev
en
i
n
’
s
m
o
d
el,
d
ep
icted
in
Fig
u
r
e
1
.
I
n
th
is
m
o
d
el,
th
e
co
m
p
o
n
en
ts
o
f
th
e
eq
u
iv
alen
t
cir
cu
it
a
r
e
c
o
n
s
id
er
ed
co
n
s
tan
t
,
with
d
if
f
er
e
n
ce
s
b
etwe
en
th
e
ch
ar
g
in
g
an
d
d
is
ch
ar
g
in
g
s
tates.
Ho
wev
er
,
in
r
ea
lity
,
t
h
ese
p
ar
am
eter
s
also
v
a
r
y
ac
co
r
d
in
g
to
th
e
b
atter
y
’
s
s
tate
o
f
ch
a
r
g
e
an
d
d
is
ch
ar
g
e
r
ate
[
2
9
].
Fig
u
r
e
1
.
T
h
ev
en
i
n
b
atter
y
m
o
d
el
2
.
1
.
St
a
t
e
o
f
cha
rg
e
estima
t
i
o
n ba
s
ed
o
n E
K
F
T
h
e
E
KF
alg
o
r
ith
m
r
ep
r
esen
ts
th
e
ad
v
an
ce
d
Kalm
an
f
ilte
r
d
esig
n
ed
to
ac
co
m
m
o
d
ate
non
-
lin
ea
r
s
y
s
tem
m
o
d
els.
It
f
i
n
d
s
ex
t
en
s
iv
e
ap
p
licatio
n
in
ad
d
r
es
s
in
g
s
tate
esti
m
atio
n
ch
allen
g
es,
p
ar
ticu
lar
ly
in
esti
m
atin
g
th
e
SOC
f
o
r
lith
iu
m
-
io
n
b
atter
ies
in
E
Vs.
Op
er
atin
g
on
a
m
ath
em
atica
l
m
o
d
el
of
th
e
b
atter
y
'
s
b
eh
av
io
r
,
th
e
E
KF
in
teg
r
ates
r
ea
l
-
tim
e
m
ea
s
u
r
em
en
ts
with
p
r
ed
icted
s
tates,
u
n
d
e
r
tak
in
g
i
ter
ativ
e
u
p
d
ates
to
en
h
an
ce
t
h
e
p
r
ec
is
io
n
of
s
tate
esti
m
ates
[
30
]
.
T
h
e
p
r
o
ce
d
u
r
al
s
tep
s
in
v
o
lv
ed
in
im
p
lem
en
tin
g
th
e
E
KF
alg
o
r
ith
m
f
o
r
b
atter
y
s
tate
esti
m
atio
n
ar
e
as
f
o
llo
ws:
‐
State
an
d
m
ea
s
u
r
em
en
t
m
o
d
el
s
d
ef
in
itio
n
:
Sp
ec
if
y
th
e
s
tate
v
ec
to
r
,
o
u
tlin
in
g
th
e
p
ar
am
ete
r
s
o
f
in
ter
est
f
o
r
esti
m
atio
n
.
‐
I
n
itializatio
n
: Set
th
e
in
itial v
a
lu
es f
o
r
th
e
s
tate
v
ec
to
r
a
n
d
its
co
v
ar
ian
ce
m
atr
ix
,
r
ef
lectin
g
th
e
p
r
elim
in
ar
y
esti
m
ate
an
d
u
n
ce
r
tain
ty
r
eg
ar
d
in
g
th
e
b
atter
y
'
s
SOC
an
d
o
th
er
p
ar
am
eter
s
.
‐
Pre
d
ictio
n
p
h
ase
:
E
m
p
lo
y
th
e
n
o
n
-
lin
ea
r
s
y
s
tem
m
o
d
el
to
p
r
o
ject
th
e
s
u
b
s
eq
u
en
t
s
tate
(
SOC
an
d
o
th
er
p
ar
am
eter
s
)
,
tak
in
g
in
to
ac
c
o
u
n
t th
e
p
r
esen
t state
esti
m
ate
an
d
s
y
s
tem
in
p
u
ts
(
e.
g
.
,
cu
r
r
en
t,
v
o
ltag
e)
.
‐
C
o
v
ar
ian
ce
p
r
ed
ictio
n
:
Utilize
th
e
J
ac
o
b
ian
m
atr
ix
an
d
th
e
co
v
ar
ian
ce
m
atr
ix
o
f
th
e
p
r
esen
t
s
tate
to
p
r
o
ject
th
e
co
v
ar
ian
ce
m
atr
ix
f
o
r
th
e
s
u
b
s
eq
u
en
t
s
tate
esti
m
ate.
T
h
is
m
atr
ix
q
u
an
tifie
s
th
e
u
n
ce
r
tain
ty
ass
o
ciate
d
with
th
e
p
r
o
jecte
d
s
tate.
‐
Up
d
ate
p
h
ase
:
C
o
llect
r
ea
l
-
ti
m
e
m
ea
s
u
r
em
en
ts
f
r
o
m
s
en
s
o
r
s
(
e.
g
.
,
b
atter
y
v
o
ltag
e
,
cu
r
r
e
n
t)
an
d
co
m
p
a
r
e
th
em
with
th
e
p
r
o
jecte
d
m
ea
s
u
r
em
en
ts
d
er
iv
ed
f
r
o
m
th
e
m
ea
s
u
r
em
en
t m
o
d
el.
‐
State
u
p
d
ate
:
E
n
h
a
n
ce
th
e
s
tate
esti
m
ate
b
y
co
m
b
in
in
g
th
e
p
r
o
jecte
d
s
tate
with
th
e
Kalm
a
n
g
ain
-
weig
h
ted
m
ea
s
u
r
em
en
t
r
esid
u
al.
T
h
is
p
r
o
ce
s
s
y
ield
s
an
im
p
r
o
v
ed
esti
m
ate
o
f
th
e
b
atter
y
'
s
SO
C
an
d
o
th
er
p
ar
a
m
eter
s
.
‐
C
o
v
ar
ian
ce
u
p
d
ate
:
Ad
j
u
s
t
th
e
co
v
ar
ia
n
ce
m
atr
i
x
o
f
th
e
s
tate
esti
m
ate
u
s
in
g
th
e
Kalm
a
n
g
ain
an
d
th
e
co
v
ar
ian
ce
m
atr
ix
o
f
th
e
s
en
s
o
r
m
ea
s
u
r
em
en
ts
.
T
h
is
s
tep
m
in
im
izes
th
e
u
n
ce
r
tain
ty
in
th
e
s
tate
es
tim
ate
af
ter
in
co
r
p
o
r
atin
g
r
ea
l
-
tim
e
m
ea
s
u
r
em
en
ts
.
T
h
e
ap
p
licatio
n
o
f
th
e
E
KF
s
er
v
es
to
allev
iate
th
e
in
f
lu
en
ce
o
f
n
o
is
e,
y
ield
in
g
ac
cu
r
ate
SOC
esti
m
atio
n
o
u
tco
m
es.
W
h
en
d
ea
lin
g
with
n
o
n
lin
ea
r
s
y
s
tem
s
,
th
e
d
is
cr
ete
-
tim
e
s
tate
s
p
ac
e
m
o
d
el
is
ex
p
r
ess
ed
in
(
1
)
.
=
(
−
1
,
−
1
)
+
−
1
,
=
(
,
)
+
(
1
)
W
h
er
e,
th
e
f
u
n
ctio
n
X
t
is
th
e
b
atter
y
d
y
n
am
ics
s
tate
eq
u
atio
n
,
an
d
th
e
f
u
n
ctio
n
Y
t
is
th
e
b
atter
y
o
u
t
p
u
t
s
tate
eq
u
atio
n
.
T
h
e
f
u
n
ctio
n
(
−
1
,
−
1
)
is
t
h
e
s
tate
tr
an
s
itio
n
f
u
n
ctio
n
,
an
d
th
e
f
u
n
ctio
n
(
,
)
is
th
e
m
ea
s
u
r
em
en
t o
r
o
b
s
er
v
atio
n
f
u
n
ctio
n
o
f
th
e
n
o
n
lin
ea
r
s
y
s
te
m
.
T
h
e
p
ar
am
eter
s
o
f
th
e
s
tate
s
p
ac
e
m
o
d
el
ar
e:
X
t
is
th
e
s
tate
v
ec
to
r
,
Y
t
d
en
o
tes
th
e
o
b
s
er
v
atio
n
v
ec
to
r
,
U
t
s
ig
n
if
ies th
e
in
p
u
t
v
ec
to
r
,
W
t
s
tan
d
s
f
o
r
p
r
o
ce
s
s
n
o
is
e,
an
d
V
t
r
ep
r
esen
ts
Gau
s
s
ian
wh
ite
m
ea
s
u
r
em
en
t
n
o
is
e.
T
h
e
T
ay
lo
r
s
er
ies
ex
p
an
s
io
n
o
f
th
e
n
o
n
lin
ea
r
o
b
s
er
v
atio
n
f
u
n
ctio
n
,
as sh
o
wn
in
(
2
)
-
(
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:
2
0
8
8
-
8
6
9
4
E
fficien
t S
OC
esti
ma
tio
n
fo
r
e
lectric v
eh
icles:
ex
ten
d
ed
K
a
lma
n
filt
er a
p
p
r
o
a
ch
f
o
r
…
(
Mer
iem
Mo
s
s
a
d
d
ek
)
443
g
(
,
)
≈
g
(
̂
,
)
+
(
,
)
|
=
̂
(
−
̂
)
an
d
=
(
,
)
|
=
̂
(
2
)
=
+
(
̂
,
)
−
̂
+
(
3
)
o
f
th
em
,
(
̂
,
)
−
̂
h
as n
o
f
u
n
ctio
n
al
r
el
atio
n
s
h
ip
with
,
s
o
it is
d
ir
ec
tly
r
eg
ar
d
e
d
as
.
=
+
+
(
4
)
[
]
=
[
1
0
0
(
∆
2
)
]
[
−
1
−
1
]
+
[
−
∆
2
−
(
1
−
∆
2
)
]
−
1
+
[
1
−
1
2
−
1
]
(
5
)
=
[
(
)
−
1
]
[
]
−
1
+
(
6
)
T
h
e
f
o
r
m
u
la
an
d
th
e
p
r
o
ce
s
s
o
f
th
e
ex
ten
d
ed
Kalm
an
ca
lc
u
la
tio
n
as (
7
)
.
̂
̅
=
−
1
̂
−
1
+
−
1
−
1
̂
̅
=
−
1
̂
−
1
+
−
1
+
=
̂
−
(
̂
−
+
)
−
1
̂
=
̂
−
+
(
−
̂
−
−
)
=
(
−
)
−
(
7
)
T
h
e
f
u
n
ctio
n
in
g
o
f
th
e
E
KF
ad
h
er
es
to
a
f
u
n
d
am
e
n
tal
p
r
in
cip
le
en
co
m
p
ass
in
g
m
u
lti
p
le
s
tag
es.
I
n
itially
,
it
co
m
p
u
tes
th
e
a
p
r
i
o
r
i
esti
m
ate
v
alu
e
b
ased
o
n
th
e
s
tate
q
u
an
tity
f
r
o
m
th
e
p
r
ec
ed
in
g
tim
e
s
tep
an
d
s
u
b
s
eq
u
en
tly
ascer
tain
s
th
e
co
v
ar
ian
ce
m
at
r
ix
o
f
th
e
esti
m
atio
n
er
r
o
r
.
T
h
ese
co
m
p
u
t
ed
v
alu
es
ar
e
th
e
n
em
p
lo
y
ed
in
th
e
f
o
r
m
u
latio
n
o
f
th
e
tem
p
o
r
al
u
p
d
ate
eq
u
atio
n
s
.
Su
b
s
eq
u
en
tly
,
th
e
g
ain
co
e
f
f
icien
t
is
d
er
iv
ed
b
ased
o
n
th
e
ex
is
tin
g
o
b
s
er
v
at
io
n
m
atr
ix
.
Fo
llo
win
g
th
is
,
th
e
o
p
tim
al
tem
p
o
r
al
v
alu
e
is
co
m
p
u
ted
u
tili
zin
g
th
e
a
p
r
io
r
i
esti
m
ate
v
alu
e
o
f
th
e
s
tate
q
u
an
tity
an
d
th
e
cu
r
r
en
t
o
b
s
er
v
atio
n
v
alu
e,
u
ltima
t
ely
,
th
e
co
v
ar
ian
ce
er
r
o
r
m
at
r
ix
is
ad
ju
s
ted
ac
co
r
d
in
g
ly
.
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
I
n
th
is
r
esear
ch
,
a
MA
T
L
AB
-
b
ased
s
im
u
latio
n
p
latf
o
r
m
wa
s
u
s
ed
to
d
esig
n
an
d
im
p
lem
e
n
t
a
SOC
esti
m
atio
n
m
o
d
el
th
at
i
n
teg
r
at
es
th
e
T
h
ev
en
i
n
eq
u
iv
alen
t
cir
cu
it
with
E
KF
alg
o
r
ith
m
s
.
T
h
i
s
m
eth
o
d
in
v
o
lv
e
d
co
u
p
lin
g
t
h
e
lith
iu
m
-
io
n
b
atte
r
y
m
o
d
el
with
th
e
E
KF
alg
o
r
ith
m
,
as
d
ep
icted
in
Fig
u
r
e
2
.
T
h
e
T
h
ev
en
i
n
m
o
d
el
s
im
p
lifie
s
th
e
b
atter
y
in
to
an
eq
u
iv
alen
t
cir
cu
it
co
m
p
r
is
in
g
a
s
er
ies
r
es
is
tan
ce
an
d
an
in
te
r
n
al
v
o
ltag
e
s
o
u
r
ce
,
allo
win
g
f
o
r
ac
cu
r
ate
s
im
u
lati
o
n
o
f
th
e
b
atter
y
'
s
elec
tr
ical
r
esp
o
n
s
e
u
n
d
er
v
a
r
y
in
g
o
p
er
ati
n
g
co
n
d
iti
o
n
s
.
T
h
e
E
KF
alg
o
r
ith
m
p
r
o
ce
s
s
es
m
ea
s
u
r
ed
d
ata
alo
n
g
s
id
e
th
e
b
atter
y
'
s
d
y
n
am
ic
m
o
d
els
to
p
r
o
v
id
e
m
o
r
e
ac
cu
r
ate
SOC
esti
m
ates
th
an
co
n
v
e
n
tio
n
al
m
eth
o
d
s
.
Utilizin
g
th
ese
to
o
ls
in
th
e
MA
T
L
AB
en
v
ir
o
n
m
e
n
t
en
a
b
les
co
m
p
r
eh
e
n
s
iv
e
s
im
u
latio
n
o
f
lith
iu
m
-
io
n
b
atter
y
p
er
f
o
r
m
a
n
ce
,
th
e
f
in
e
-
tu
n
in
g
o
f
m
o
d
el
p
ar
am
eter
s
b
ased
o
n
ex
p
er
im
en
tal
d
ata,
an
d
im
p
r
o
v
ed
p
r
ec
is
io
n
in
SOC
esti
m
at
io
n
.
T
h
is
a
p
p
r
o
ac
h
o
v
er
c
o
m
e
s
th
e
lim
itatio
n
s
o
f
s
tatic
e
s
tim
atio
n
tech
n
iq
u
es
b
y
co
n
s
id
er
in
g
d
y
n
a
m
ic
SOC
f
lu
ctu
atio
n
s
,
d
eliv
er
in
g
r
el
iab
le
o
u
tc
o
m
es
f
o
r
p
r
ac
tical
ap
p
licatio
n
s
s
u
ch
as
en
er
g
y
m
an
ag
em
e
n
t in
elec
tr
i
c
v
eh
icles.
Fig
u
r
e
2
illu
s
tr
ates
th
e
s
im
u
la
tio
n
m
o
d
el
u
s
ed
f
o
r
esti
m
atin
g
th
e
SOC
o
f
th
e
b
atter
y
.
T
o
ass
es
s
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
p
r
o
p
o
s
ed
esti
m
atio
n
m
o
d
el,
th
e
s
im
u
latio
n
r
esu
lts
f
o
r
SOC
wer
e
ev
al
u
ated
b
y
an
aly
zin
g
th
e
in
p
u
t
cu
r
r
en
t
an
d
lo
ad
v
o
lt
ag
e,
as
s
h
o
wn
in
F
ig
u
r
es
3
a
n
d
4
.
T
h
is
p
r
o
ce
s
s
in
v
o
lv
es
v
er
if
y
in
g
th
e
ac
c
u
r
ac
y
o
f
th
e
SOC
esti
m
atio
n
m
o
d
el
b
y
e
x
am
in
in
g
h
o
w
v
ar
iatio
n
s
in
in
p
u
t
cu
r
r
en
t
an
d
lo
a
d
v
o
lt
ag
e
af
f
ec
t
th
e
SOC
r
esu
lts
.
T
h
e
d
ata
p
r
esen
ted
i
n
th
e
r
ef
er
e
n
ce
d
f
ig
u
r
es
e
n
ab
le
a
co
m
p
a
r
is
o
n
b
etwe
en
th
e
esti
m
ated
SOC
v
alu
es
an
d
th
e
ac
tu
al
m
ea
s
u
r
em
en
ts
,
wh
ich
h
elp
s
d
eter
m
in
e
th
e
m
o
d
el’
s
p
er
f
o
r
m
an
ce
u
n
d
er
d
if
f
er
en
t
o
p
er
atio
n
al
co
n
d
itio
n
s
.
B
y
an
aly
zi
n
g
th
e
i
n
p
u
t
c
u
r
r
e
n
t
an
d
l
o
ad
v
o
ltag
e,
in
s
ig
h
ts
ca
n
b
e
g
ain
e
d
i
n
to
h
o
w
well
th
e
m
o
d
el
ad
ap
ts
to
v
ar
io
u
s
o
p
er
atin
g
s
ce
n
ar
io
s
an
d
m
ain
tain
s
ac
cu
r
ate
SOC
esti
m
atio
n
s
.
T
h
is
v
alid
atio
n
en
s
u
r
es
t
h
e
m
o
d
el’
s
r
o
b
u
s
tn
ess
an
d
its
s
u
it
ab
ilit
y
f
o
r
p
r
ac
tical
ap
p
licatio
n
s
s
u
ch
as
en
er
g
y
m
an
a
g
em
en
t
in
b
atter
y
s
y
s
tem
s
.
T
h
e
SOC
esti
m
atio
n
m
o
d
el
p
r
o
p
o
s
ed
,
as
d
ep
icted
in
Fig
u
r
e
2
,
was
ass
e
s
s
ed
b
ased
o
n
s
im
u
latio
n
r
esu
lts
o
b
tain
ed
u
n
d
er
s
p
ec
if
ic
co
n
d
iti
o
n
s
o
f
lo
ad
in
p
u
t
cu
r
r
en
t
an
d
l
o
ad
v
o
ltag
e.
T
o
ev
al
u
ate
th
e
m
o
d
el'
s
p
er
f
o
r
m
an
ce
,
lo
ad
v
o
ltag
e
an
d
cu
r
r
en
t
p
r
o
f
iles
,
d
er
iv
ed
f
r
o
m
E
A
p
o
wer
co
n
tr
o
l,
wer
e
an
al
y
ze
d
.
T
h
e
d
ata
ac
q
u
is
itio
n
p
r
o
ce
s
s
was m
an
ag
ed
th
r
o
u
g
h
th
e
L
a
b
View
in
ter
f
ac
e.
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.
1
6
,
No
.
1
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Ma
r
c
h
2
0
2
5
:
440
-
447
444
Fig
u
r
e
2
.
Simu
lin
k
m
o
d
el
Fig
u
r
e
3
.
C
u
r
r
e
n
t p
r
o
f
ile
Fig
u
r
e
4
.
Vo
ltag
e
p
r
o
f
ile
Fu
r
th
er
m
o
r
e
,
th
e
ac
cu
r
ac
y
o
f
th
e
E
KF
alg
o
r
ith
m
was
ev
alu
ated
,
an
d
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
SOC
esti
m
atio
n
m
eth
o
d
s
was
d
eter
m
in
ed
b
y
e
x
am
in
in
g
t
h
e
esti
m
atio
n
r
esu
lts
p
r
esen
ted
in
Fig
u
r
e
5
.
T
h
is
ev
alu
atio
n
in
v
o
lv
ed
a
d
etailed
an
al
y
s
is
o
f
th
e
m
o
d
el'
s
p
er
f
o
r
m
an
ce
in
p
r
ed
ictin
g
th
e
SOC
an
d
its
a
b
ilit
y
to
ac
cu
r
ately
r
ef
lect
ch
an
g
es
in
l
o
ad
c
o
n
d
iti
o
n
s
.
B
y
co
m
p
ar
in
g
th
e
esti
m
ated
SOC
o
u
tco
m
es
with
ac
tu
al
m
ea
s
u
r
em
en
ts
,
th
e
s
tu
d
y
ass
ess
ed
th
e
r
eliab
ilit
y
an
d
p
r
ec
is
io
n
o
f
t
h
e
p
r
o
p
o
s
ed
e
s
tim
atio
n
m
o
d
el
an
d
alg
o
r
ith
m
.
Fig
u
r
e
6
illu
s
tr
at
es
th
e
co
m
p
ar
is
o
n
b
etwe
en
t
h
e
r
ea
l
v
o
ltag
e
an
d
th
e
esti
m
ated
v
o
ltag
e
o
f
t
h
e
b
atter
y
,
d
em
o
n
s
tr
atin
g
th
e
ac
cu
r
ac
y
o
f
th
e
esti
m
atio
n
m
o
d
el.
T
h
e
clo
s
e
alig
n
m
en
t
b
etwe
en
b
o
th
v
o
ltag
e
p
r
o
f
iles
in
d
icate
s
t
h
at
th
e
esti
m
atio
n
alg
o
r
ith
m
e
f
f
ec
tiv
ely
t
r
ac
k
s
t
h
e
ac
tu
al
b
atter
y
v
o
ltag
e,
w
h
ich
is
ess
en
tial
f
o
r
r
eliab
le
S
OC
p
r
ed
ictio
n
an
d
o
p
tim
al
b
atter
y
m
an
ag
em
e
n
t.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2
0
8
8
-
8
6
9
4
E
fficien
t S
OC
esti
ma
tio
n
fo
r
e
lectric v
eh
icles:
ex
ten
d
ed
K
a
lma
n
filt
er a
p
p
r
o
a
ch
f
o
r
…
(
Mer
iem
Mo
s
s
a
d
d
ek
)
445
Fig
u
r
e
5
.
SOC
esti
m
atio
n
u
s
in
g
E
KF a
lg
o
r
ith
m
Fig
u
r
e
6
.
R
ea
l v
o
ltag
e
an
d
esti
m
ated
v
o
ltag
e
4.
CO
NCLU
SI
O
N
T
h
e
E
KF
m
eth
o
d
ex
h
ib
its
r
esil
ien
ce
to
v
ar
iatio
n
s
in
th
e
in
itial
SOC
v
alu
e
an
d
d
em
o
n
s
tr
ates
th
e
ab
ilit
y
to
r
ec
tify
SOC
er
r
o
r
s
,
as
co
r
r
o
b
o
r
ated
th
r
o
u
g
h
d
is
tin
ct
in
p
u
t
ad
ju
s
tm
en
ts
.
I
n
th
e
s
im
u
latio
n
r
esu
lts
,
th
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
d
em
o
n
s
tr
ates
its
ef
f
e
ctiv
en
ess
an
d
ac
cu
r
ac
y
in
ad
d
r
ess
in
g
th
e
o
u
tlin
ed
o
b
jectiv
es,
th
e
SOC
e
s
tim
ated
b
y
th
e
ex
ten
d
ed
Kalm
an
f
ilter
f
o
r
th
e
b
atter
y
is
in
d
icate
d
at
9
0
% a
n
d
1
0
%,
r
esp
ec
tiv
ely
.
T
h
ese
f
ig
u
r
es p
o
r
tr
ay
th
e
v
alu
es
th
e
e
x
ten
d
e
d
Kalm
an
f
ilter
esti
m
ated
,
th
e
ac
tu
al
SOC
v
alu
e,
an
d
th
e
SOC
v
alu
e
in
am
p
er
e
-
h
o
u
r
s
p
lo
tted
to
g
eth
er
.
W
h
en
r
ely
i
n
g
s
o
lely
o
n
th
e
a
m
p
er
e
-
h
o
u
r
in
teg
r
atio
n
m
eth
o
d
,
a
n
er
r
o
n
eo
u
s
in
itial
v
alu
e
p
er
p
etu
ates
er
r
o
r
s
,
s
ig
n
if
ica
n
tly
co
m
p
r
o
m
is
in
g
SOC
esti
m
ati
o
n
p
r
ec
is
io
n
.
Ho
wev
e
r
,
u
tili
zin
g
th
e
E
KF
f
o
r
SOC
esti
m
atio
n
d
em
o
n
s
tr
ates
r
esil
ien
ce
to
in
itial
v
alu
es,
f
ac
ilit
atin
g
r
ap
id
co
r
r
ec
tio
n
o
f
t
h
e
SOC
esti
m
ate
p
r
o
v
id
ed
b
y
th
e
E
KF.
Data
a
n
aly
s
is
o
f
d
ata
in
d
icate
s
th
at
ev
en
wh
en
th
e
in
itial
SOC
d
if
f
er
s
f
r
o
m
th
e
ac
tu
al
SOC
b
y
5
0
%,
th
e
E
KF
a
d
ep
tly
r
ec
tifi
es
th
e
d
is
cr
ep
an
c
y
to
u
n
d
er
5
%.
Fo
llo
win
g
er
r
o
r
co
r
r
ec
tio
n
b
y
th
e
E
KF,
th
e
esti
m
atio
n
er
r
o
r
f
lu
ctu
ates,
p
r
im
ar
ily
in
f
lu
en
ce
d
b
y
ad
d
ed
Gau
s
s
ian
n
o
is
e.
No
n
et
h
el
ess
,
th
e
E
KF
er
r
o
r
g
r
ad
u
ally
d
im
in
is
h
es,
a
n
d
th
e
esti
m
ated
SOC
v
alu
e
c
o
n
s
is
ten
tly
co
n
v
er
g
es
to
war
d
th
e
tr
u
e
v
alu
e.
T
h
e
ex
p
er
im
en
tal
f
in
d
in
g
s
v
alid
ate
th
e
ef
f
icac
y
o
f
th
e
E
KF
alg
o
r
ith
m
in
ca
p
tu
r
in
g
th
e
d
y
n
am
ic
ch
ar
ac
ter
is
tics
o
f
lith
iu
m
-
io
n
b
atter
ies,
en
c
o
m
p
ass
in
g
v
ar
iab
les
s
u
ch
as
ch
a
r
g
e
an
d
d
is
ch
ar
g
e
c
y
cles,
v
a
r
y
in
g
tem
p
er
atu
r
e
co
n
d
itio
n
s
,
an
d
n
o
n
-
lin
ea
r
v
o
lt
ag
e
-
SOC
r
elat
io
n
s
h
ip
s
.
I
n
co
m
p
ar
is
o
n
to
tr
ad
itio
n
al
m
eth
o
d
s
,
th
e
E
KF
ap
p
r
o
ac
h
m
itig
ates
cu
m
u
lativ
e
er
r
o
r
s
an
d
ad
d
r
ess
es
u
n
ce
r
tain
ties
in
b
o
th
th
e
b
atter
y
m
o
d
el
a
n
d
m
ea
s
u
r
em
en
ts
,
y
ield
i
n
g
m
o
r
e
ac
cu
r
ate
SOC
esti
m
atio
n
.
Mo
r
eo
v
e
r
,
th
e
a
d
ap
tab
ilit
y
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