TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.5, May 2014, pp
. 3671 ~ 36
7
7
DOI: http://dx.doi.org/10.11591/telkomni
ka.v12i5.5016
3671
Re
cei
v
ed O
c
t
ober 3
1
, 201
3; Revi
se
d Decem
b
e
r
16, 2013; Accept
ed Ja
nua
ry 4,
2014
Electro-thermal Modeling of Lithium Ion Batteries
Gaous
sou Hadia FOF
A
NA*, Youton
g ZHANG
Lo
w
Emissi
on
Vehic
l
e Res
ear
ch Lab,
Bei
j
i
n
g
Institute of
T
e
chno
log
y
LABOT
hermique App
liq
ué
e, ENI-ABT
BAMAKO-MALI BP
242
No. 5, Zhong
g
uanc
un So
uth Street, Haidi
a
n
District, Beijin
g 100
08
1, P. R. China
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: fofanamal
i@
ya
ho
o.fr
A
b
st
r
a
ct
In this paper, the el
ectro-ther
ma
l m
ode
l of Lithiu
m-i
on b
a
ttery for electric vehicl
es an
d its relate
d
app
licati
on w
e
r
e
studie
d
. T
h
e
spatia
l v
a
riati
ons of el
ectro
de par
a
m
et
er
and th
e reacti
on he
at ge
ner
ated
insid
e
battery
must
be
cons
i
dere
d
w
h
e
n
d
e
vel
opi
ng
an
electro-th
er
mal
mod
e
l
of Lith
i
u
m-
ion
b
a
ttery for
electric ve
hicl
e
s
, to ensure the app
lica
b
il
ity of the devel
op
ed mod
e
l un
d
e
r different op
eratin
g cond
iti
ons.
T
he results sh
ow
ed that: w
i
th incre
a
si
ng s
t
ate of char
g
e
, the spatia
l va
riatio
ns of net
reaction c
u
rre
nt
dens
ity, lithi
u
m
ion
co
ncent
ration
on
the surface of
acti
ve materi
al pa
rticles, activati
on
overp
o
tenti
a
l
,
equ
ili
briu
m
ele
c
trode p
o
tentia
l and
electr
ic
al
potenti
a
l of so
lid p
has
e are
r
educ
ed, but th
e spati
a
l vari
ati
o
n
of electrica
l
pot
entia
l of el
ectro
l
yte phas
e is e
n
lar
ged.
Ke
y
w
ords
:
lithiu
m
-
i
o
n
b
a
ttery, electroc
he
mic
a
l-ther
mal
coup
lin
g
mo
de
l, poro
u
s e
l
ect
r
ode, c
harg
i
ng
a
n
d
disch
argi
ng, MAT
L
AB
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
Acco
rdi
ng to
the shap
e
of automotive Li
thium-io
n battery (L
IB), automotive LIB
categ
o
rie
s
can be divide
d into squ
a
re LIB and cy
lindrical LIB. Both types of batteries
have
simila
r inte
rn
al st
ru
cture
s
,
mainly in
cludi
ng p
o
si
tive a
nd
n
egative current colle
ct
or
[1],
a
nod
e and
catho
de ele
c
trode
s
a
nd diaph
rag
m
, positive and
neg
ative current
colle
ct
or to
gethe
r
with
electrode
ca
n be
refe
rred
to as pol
e
piece. Po
sitiv
e
and
ne
gati
v
e cu
rre
nt co
llector ge
nerally
con
s
i
s
ts
of al
uminum
foil a
nd
cop
per foi
l
re
sp
ectively [2]. Positive
and
neg
ative ele
c
tro
d
e
s
a
r
e
mainly comp
ose
d
of active substa
nces, the pos
it
ive electro
d
e
active material usually use
s
cob
a
lt aci
d
lithium (Li
C
o
O
2
), mang
an
ese
aci
d
lithium (Li
y
Mn
2
O
4
), or lithium
iron p
h
o
s
ph
ate
(LiFeP
O
4
), the catho
de a
c
tive material g
enerally
use
s
graphite, a
c
etylene ca
rbo
n
black, bea
d
s
,
petrole
um co
ke, carbon
fi
ber and poly
m
er
py
roly
si
s o
r
pyrolysi
s
car
bon, di
aphragm
mai
n
ly
inclu
d
ing poly
e
thylene, pol
ypropylen
e
a
nd so o
n
[3].
Electro
c
h
e
mi
cal-th
erm
a
l couplin
g mod
e
l sh
ould
be
in a rea
s
on
able mo
del, i
n
clu
d
ing
some
con
s
id
ering
facto
r
s and
a
s
sum
p
tions of the
pre
m
ise, e
n
su
ring
the
appli
c
ability
and
rationality of t
he mo
del [4]. In ord
e
r to
e
n
su
re th
e ele
c
tro
-
the
r
mal
cou
p
ling
mod
e
l for p
r
e
d
icti
ng
power chara
c
teri
stics and
the te
mperature ri
se ch
ara
c
teri
stic
s of automotive LIB pack, the
electrode parameters spati
a
l
differen
c
e and
rea
c
tion
heat gen
erated by the bat
tery cha
r
ge
a
nd
discha
rge
proce
s
s mu
st be consi
d
e
r
e
d
in the pr
ocess of mod
e
l
i
ng [5]. Therefore, this
pa
per
con
s
id
ere
d
th
e spatial va
ri
ations of n
e
t
rea
c
tion
current de
nsity, li
thium io
n
con
c
entration
on
the
surfa
c
e
of
active material
particl
es,
a
c
tivation
overpo
tential, equili
brium
ele
c
tro
de p
o
tential
an
d
electri
c
al p
o
tential of soli
d phase in establ
i
s
hi
ng automotive L
I
B electro
c
h
e
mistry-t
herm
a
l
cou
p
ling m
o
d
e
l. Then, thi
s
article
u
s
ed t
he e
s
t
abli
s
he
d ele
c
tro
c
he
mical
-
thermal
cou
p
ling m
o
del
to simulate the sp
ace dist
ribution of el
ectro
de pa
ra
meters and i
n
ternal b
a
ttery heat generated
rate und
er dif
f
erent wo
rkin
g con
d
ition
s
.
2. Rese
arch
Metho
d
LIB Solid-sol
ution pha
se
interface ele
c
tro
c
he
mical
rea
c
tion p
r
o
c
e
ss
can
be
actually
decompo
se
d
into forward
and reverse
reacti
o
n
. Ensu
ring the
electrode o
n
the two phase
interface forward/reverse reactio
n
rate
and a
c
ti
vation ene
rgy barrier chan
ging
extent is the key
to cal
c
ulate
net cu
rrent. Acco
rdi
ng to
the prin
cipl
e
of kinetic
re
acti
on, the e
x
chan
ge
current
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 5, May 2014: 3671 – 36
77
3672
den
sity
i
0
(A/cm
2
)
on th
e
two p
h
a
s
e i
n
terface,
nam
ely the inte
rf
ace
re
actio
n
is i
n
dyn
a
m
i
c
equilib
rium, the forward/re
verse
rea
c
tio
n
rate
can be
cal
c
ulate
d
by the Equation
(1) [6]:
ma
x
0
aa
c
aa
a
es
s
e
s
e
ik
F
c
c
c
c
(1)
In whic
h,
k
i
s
the
ele
c
tro
de rea
c
tion
rate co
nsta
nt (cathod
e, a
node
);
F
i
s
Fara
day
c
o
ns
tant;
c
e
i
s
lithium
-ion
con
c
e
n
tration
in the soluti
on ph
ase;
c
sma
x
is maximum lithium ion
con
c
e
n
tration
of solid phcase (cath
ode
, anode);
c
se
indicates the
lithium ion concentratio
n
o
n
the solid
and
liquid ph
ase
interface (th
e
activ
e
mat
e
rial p
a
rticl
e
s
surfa
c
e,
mo
l/c
m
3
);
a
a
is the
anodi
c el
ectron tran
sfe
r
coefficient,
0<a
a
<1
, un
de
r n
o
rmal
circu
m
stan
ce
s,
a
a
=0
.
5
; while
a
c
i
s
the
ccathod
e ele
c
tron t
r
an
sfer coeffici
ent,
0<
a
c
<1
, und
er norm
a
l ci
rcu
m
stan
ce
s,
a
c
=0.
5
. Acco
rdi
ng
to the p
r
in
cip
l
e of
kineti
c
s
rea
c
tion, the
activation
overpote
n
tial
chara
c
te
rizes the two p
h
a
s
e
interface acti
vation energy barri
er chan
ging extent,
se
U
(2)
Whe
r
e,
s
is t
he
solid
pha
se voltag
e
(
V
);
e
is
poten
tial of the
solution
(
V
);
U
is
balan
ce
d ele
c
trod
e p
o
tenti
a
l (
V
);
U
i
s
m
a
inly dete
r
mi
ned by th
e te
mperature
of
the battery
a
n
d
the electrode
stoichiomet
r
ic ratio
ma
x
/
se
s
cc
, their specifi
c
relatio
n
shi
p
sho
u
ld
be confi
r
med
by
fitting test d
a
ta. About
electrochemi
c
al-th
e
rm
al couplin
g
mo
d
e
l,
the relati
onship between
positive an
d negative ele
c
trode
U
a
nd
is de
scribe
d b
a
se
d on batte
ry temperatu
r
e kno
w
n.
Anode:
-5
1
.
5
0
.
5
-4
-
1
8
.
00
229
2
.
17
65
10
5
.
06
47
12.
578
8.6
3
2
2
1
0
0.
460
16
e
x
p
1
5
0
.0
6
0
.55
364
e
x
p
2
.43
2
6
0
.
9
2
U
(3)
Catho
de:
115
6
54
3
2
85
.68
1
35
7.7
6
1
3
.
8
9
5
55
.65
2
8
1
.
0
6
7
6
.
64
8
13
.1
98
3
0.3
0987
e
x
p
5
.657
U
(4)
U
chan
ging
along
with th
e ch
ang
e of
the ba
ttery te
mperature
is
usu
a
lly de
scribed by
temperature coeffici
ent
/
UT
,
/
UT
mainly depe
n
d
s on LIB
, usually setting
known to
cha
r
a
c
ter te
mperature
coefficient
/
UT
; the relation
sh
ip bet
wee
n
and
state
o
f
cha
r
ge
(SOC
) s
how
s
in (5).
10
0
0.01
SO
C
(5)
In which,
1
is a
stoichi
o
metri
c
ratio in th
e battery full ch
arge
state (S
OC=10
0
%);
0
is
a
stoichiomet
r
ic ratio
after th
e batte
ry emi
tting t
he
rate
d capa
city (S
OC=0%); S
O
C i
s
e
qual
to
the
ratio of the re
maining p
o
wer and b
a
ttery capa
city,
0
1
e
Q
Q
SO
C
QQ
(6)
In the formul
a,
Q
e
is the remainin
g po
wer i
n
the cu
rre
nt time,
Q
is the whole
power of
battery,
Q
0
is discha
rge
ca
pacity, usu
a
ll
y SO
C is
belong to [0.2, 0.8] [7].
Figure 1 sh
o
w
s the a
c
tive
material pa
rticle
s LiFePO
4
and Li
x
C
6
of
positive an
d negative
electrode
s ha
ppen with th
e redu
ction
reactio
n
, temperatu
r
e co
efficient
/
UT
c
h
an
ge
s
a
l
o
ng
with the
cha
n
ge of ele
c
tro
de stoi
chi
o
m
e
tric
ratio
[8]. As sho
w
n i
n
Figure 2, the
same
amo
u
n
t
of lithium io
n
in diffe
rent
SOC, the
en
tropy
chan
ge
extent is ve
ry differe
nt b
y
finishin
g d
e
-
intercalation
reactio
n
and re-inte
r
calatio
n
rea
c
tion.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Electro
-
the
r
m
a
l Modelin
g o
f
Lithium
Ion
Batteries
(Ga
ousso
u Ha
dia
FOFANA)
3673
Figure 1. (a)
SOC on vari
a
t
ion of battery voltage
versus de
pth of dischar
ge (DO
D
); (b
) variati
on
of battery voltage versu
s
b
a
ttery temperature
/
UT
Figure 2. Positive and Neg
a
ti
ve Electrod
es versu
s
SO
C
Figure 2
sh
o
w
s that with
the de
crea
se
of
the SO
C, the op
en
circu
i
t voltage am
plitude o
f
the modelin
g
objects d
e
creases g
r
ad
u
a
lly. Accord
i
n
gly, the smaller the SOC i
s
, the smalle
r
U
cha
ngin
g
alo
ng with
cha
nging i
s
. Ho
wever, a
s
for the two ph
a
s
e inte
rface i
n
unit volume
of
the ele
c
trod
e
electrochem
ical rea
c
tion
net cu
rrent
j
,
j
spa
c
e
distrib
u
tion i
s
different un
der
different SO
C duri
ng
cha
r
gi
ng an
d di
sch
a
rgin
g,
j
inc
r
ea
s
e
s
w
i
th
th
e
d
e
c
r
e
as
e o
f
th
e
SOC
.
At th
e
s
a
me time, due to
dynamic chang
e co
mpletely dete
r
mine
d by
j
, henc
e
,
incre
a
se
s
wit
h
t
he
decrea
s
e of
the SOC. After re
sp
ective
ly us
ing (1
) and (2
) dete
r
mine the ex
cha
nge
curre
n
t
den
sity and activation pote
n
tial, and then comp
uti
ng automotive LIB electrod
es
solid - solutio
n
pha
se interfa
c
e re
actio
n
ra
te. By
Butler-Volmer eq
uat
ion j is sh
own
in (7) in detai
l:
0
exp
e
xp
a
S
EI
c
S
EI
e
bat
e
bat
e
an
F
R
j
a
n
F
R
j
js
i
RT
s
R
T
s
(7)
Whe
r
e,
j
i
s
t
he two p
h
a
s
e interfa
c
e
i
n
unit volu
m
e
of the
ele
c
trode
ele
c
tro
c
hemi
c
al
rea
c
tion net curre
n
t,
A/c
m
3
;
s
e
is the
averag
e a
c
tive
area
pe
r unit
volume;
R=8.
314
J/(m
ol-K)
is
the gen
eral
g
a
s
con
s
tant;
T
bat
is the bat
tery tempe
r
at
ure,
K
, and
th
is pa
per u
s
ed
T
bat
=273
+2
5
K
;
R
SEI
is the act
i
ve material p
a
rticle
s su
rfa
c
e pa
ssive film area
resi
st
ance,
-cm
2
.
Acco
rdi
ng to
ohm'
s
la
w, the cha
r
ge t
r
ansfe
r
flux p
r
odu
ce
d by
arbitrary
cro
s
s-se
ction
con
d
u
c
tors u
nder th
e actio
n
of electri
c
al
driving
force
is equ
al to the pro
d
u
c
t of the cro
s
s-sect
ion
electri
c
pote
n
t
ial gradie
n
t and the co
ndu
ctivity. Comb
ined with the l
a
w of co
nservation of electric
cha
r
ge, th
e relation
ship
b
e
twee
n the
solid ph
ase in
poro
u
s ele
c
trode p
o
tential
gradi
ent a
nd
the
net rea
c
tion current den
sity is sho
w
n in (8):
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02-4
046
TELKOM
NI
KA
Vol. 12, No. 5, May 2014: 3671 – 36
77
3674
ef
f
s
j
xx
(8)
The bou
nda
ry condition
s:
0
,
0;
0;
,
;,
,
.
ef
f
e
f
f
ef
f
e
f
f
ss
s
s
np
e
e
I
I
x
x
xL
xL
x
Sx
x
x
S
In whic
h,
I
is the b
a
ttery
cha
r
gin
g
an
d disch
a
rgi
n
g cu
rrent,
I>0
indi
cate
s chargi
ng
p
r
oc
es
s
,
I<0
sho
w
s disch
a
rgin
g proce
ss,
A
;
S
e
=1.
0
452
×10
4
is th
e total activa
tion are
a
in the
battery pol
e
piece,
cm
2
;
ef
f
is the
effectiv
e ele
c
tri
c
al
condu
ctivity of soli
d ph
ase
electroni
c,
S/c
m
;
ef
f
can be
calculated by
(9):
ef
f
p
e
s
(9)
In whic
h,
is solid ph
ase el
ectro
n
ic co
nd
uctivity,
S/c
m
;
s
is LIB po
sitive and n
egati
v
e
electrode
a
c
tive material
volume fra
c
ti
on;
pe
=1.5
i
s
Brugge
ma
n po
ro
sity factor.
Hen
c
e,
the
catho
de:
0.58
ef
f
; the anode:
0.05
ef
f
.
Gene
rally, du
e to po
rou
s
electrode
co
ndu
ctiv
ity and diffusio
n
coefficient va
ri
ation a
r
e
much
small
e
r, so the el
e
c
tri
c
potentia
l gradi
ent an
d con
c
e
n
trati
on gradie
n
t are lithium i
on
(po
s
itive ch
arge) d
r
iving force in the
sol
u
tion pha
se d
u
r
ing the m
o
ve
. Hen
c
e, it ca
nnot be a
b
le t
o
dire
ctly use o
h
m's la
w to describ
e the net curr
ent de
nsity and sol
u
tion pha
se
electri
c
pote
n
t
ial
gradi
ent, and
the equatio
n modificatio
n
[9] is sho
w
n b
e
low:
ln
0
c
ef
f
e
f
f
ee
j
D
xx
x
x
(10)
The bou
nda
ry condition
s:
0,
0
;
,
0
.
ee
xx
L
x
x
In whic
h,
k
eff
is
lithium
-io
n
effective
ele
c
tric
al
condu
ct
ivity of soluti
on p
h
a
s
e,
S/
c
m
; the
catho
de:
k
eff
=3.
9
×1
0
-4
; the di
aph
rag
m
:
k
eff
=7.21×
10
-4
; the
a
node:
k
eff
=3
.87×1
0
-4
;
eff
D
is
effective diffu
sion
al cond
u
c
tivity coeffici
ent of solutio
n
pha
se,
A/
cm
. The
k
eff
ca
lculatio
n form
ula
is sh
own in (1
1).
ef
f
p
e
e
(11)
Whe
r
e,
e
is t
he ele
c
trode
porosity, th
at is to
say
e
is
the volume frac
tion
of the
electrolyte;
is lithium i
on
con
d
u
c
tivity of solution
pha
se,
S/c
m
,
is
compl
e
tely determined by
electrolyte co
mpositio
n. And acco
rdi
n
g
to the theory of strong sol
u
tion,
eff
D
can b
e
cal
c
ulated
by the (12):
22
ln
00
11
1
ln
ef
f
e
f
f
RT
RT
df
ef
f
ba
t
b
at
tt
D
Fd
c
F
e
(12
)
In which,
1
f
as the electrolyte activity coefficient [10][11];
0
0.363
t
for lithium ion
transfe
re
nce numbe
r.
As for LIB
ch
arge
an
d di
scharg
e
p
r
o
c
e
d
u
re,
part
of th
e inn
e
r
heat
gene
rated
rai
s
e
s
the
temperature
of the battery
itself, anoth
e
r tra
n
smit
s to the battery
surfa
c
e
se
n
d
ing out into
the
surro
undi
ng
environ
ment
by co
ndu
ctive effect. So
many
phy
sical
an
d
chemi
c
al paramete
r
s i
n
LIB are associate
d
with
battery temperatu
r
e
val
ues, in
cludin
g
the electrode re
actio
n
rate
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Electro
-
the
r
m
a
l Modelin
g o
f
Lithium
Ion
Batteries
(Ga
ousso
u Ha
dia
FOFANA)
3675
con
s
tant, the lithium ion diffusion
coeffici
ent, electr
o
n
i
c
ele
c
trical condu
ctivity of the solid ph
a
s
e
and solution
pha
se lithium
ion diffusion
coeffici
ent an
d electri
c
al
co
ndu
ctivity.
3. Results a
nd Analy
s
is
Rea
s
o
nably cal
c
ulatin
g the spatial di
stributi
on of p
a
ram
e
ters in
LIB electrod
es and
internal
heat
gene
rated
rat
e
is to en
su
re
that
the mod
e
l ca
n be a
p
p
lied to
predi
ct automotive L
I
B
pack p
o
wer cha
r
a
c
teri
sti
c
s and
the
temperature
rise.
To illu
strate th
e rationality of the
electrochemi
c
al-therm
al coupling mo
del establi
s
hed
in this paper,
this section
will sim
u
late t
he
spatial di
strib
u
tion of the net curre
n
t den
sity,
lithiu
m
ion con
c
e
n
tration, the activation ov
er
potential, ele
c
trod
e potenti
a
l based on t
he m
odel of the battery un
der 80% SO
C [12].
Figure 3
~
Fig
u
re
6 p
r
e
s
en
ted LIB seco
nds
pul
se
ch
argin
g
a
nd
d
i
scharging, th
e SO
C
cha
ngin
g
effects the
spat
ial dist
ributio
n of the
net
rea
c
tion i
n
p
o
sitive an
d n
egative ele
c
trod
e
cur
r
e
n
t
den
si
t
y
j
, active material lithi
um-io
n
con
c
entration
an
d the
ratio
of the maxi
mum
c
o
nc
en
tr
a
t
io
n
c
se
/c
sm
ax
, the
activation
over p
o
tential
, balan
ce
d ele
c
trod
e p
o
tenti
a
l
U
. Fi
gure
3
sho
w
s SO
C=80%
re
sp
e
c
tively, the t
e
mpe
r
ature
of the
battery is
25
℃
, and
ch
arging
an
d
discha
rgin
g currents a
r
e 5
C
.
(a) SO
C=80
%, Pulse cha
r
ge
(b) SO
C=80
%, Pulse discharg
e
Figure 3. The
Spatial Distri
bution of j in the
Battery Pulse Charging
and Di
scha
rgi
ng und
er 80
%
SOC (
T
bat
=25
℃
, I=
5C
)
Figure 3 i
ndi
cates
und
er
8
0
% SOC, i
n
t
he in
itial
mo
ment of the
L
I
B pulse
charging
and
discha
rgin
g,
a pe
ak of
j
is
alway
s
p
r
od
u
c
ed
ne
ar the
electrode
a
r
e
a
of th
e di
aph
ragm,
but
alo
ng
with p
r
og
re
ss throu
gh th
e
cha
r
gin
g
a
n
d
disch
a
rgi
ng,
j
in th
e p
o
si
tive and
neg
ative ele
c
trod
es
grad
ually ten
d
to be uniformly distribute
d
along t
he x axes. Howe
ver, with the battery cha
r
gi
ng
and
discha
rg
ing p
r
og
re
ssi
ng, hete
r
og
e
neou
s
rea
c
ti
on rate
will
grad
ually le
a
d
to the
spa
t
ial
variation in
creasi
ng of
c
se
/c
sm
ax
.
(a) SO
C=80
%, Pulse cha
r
ge
(b) SO
C=80
%, Pulse discharg
e
Figure 4. The
spatial di
strib
u
tion of cse/csma
x in the b
a
ttery pulse
chargi
ng an
d d
i
scharging
unde
r 80% SOC (
T
bat
=25
℃
, I=
5C
)
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 5, May 2014: 3671 – 36
77
3676
As
sho
w
n
in
Figure 4,
the
sm
aller the
distan
ce
of th
e a
c
tive mate
rial
parti
cle
s
and th
e
diaph
rag
m
is, the bigger l
i
thium ion co
nce
n
tration
i
n
crea
se
s or
redu
ce
s.
Rel
a
tively larger or
smaller
c
se
/c
sma
x
will result
in lithium io
ns de
-inte
r
cal
a
tion re
actio
n
and re
-inte
r
calation rea
c
tion
more e
nergy con
s
um
ed.
(a) SO
C=80
%, Pulse cha
r
ge
(b) SO
C=80
%, Pulse discharg
e
Figure 5. The
Spatial Distri
bution of
in the Battery Pulse Charging
and Di
scha
rgi
ng und
er
80% SOC (
T
ba
t
=25
℃
, I=
5C
)
Figure 6 indi
cates the
sp
atial distri
bution
U
of po
sitive and n
egative
electrode i
s
simila
r
to the
c
se
/c
smax
spatial
di
stribution
in
Fi
gure
5
wh
en
Ch
argi
ng, th
e
U
value
of
the po
sitive a
n
d
negative ele
c
trode
s g
r
ad
u
a
lly redu
ce
s
along th
e
x
axis
. In c
o
ntras
t,
U
in
crea
se
s alo
ng th
e
x
axis. Becau
s
e the lithium
ion
con
c
e
n
tration
c
sm
ax
is
smalle
r in
the cath
ode
active mate
ri
al
particl
es than
the a
nod
e’s
c
sm
ax
, that the sa
me
amou
nt of lithi
um
i
ons in th
e
ca
thode
pro
g
re
ss
de-inte
rcalati
on
rea
c
tion and re
-intercalation rea
c
ti
on cau
s
e
s
bi
gger
chan
ge
of
c
se
/c
sm
ax
than
positive
rea
c
ti
on. So g
ene
rally sp
eaki
ng,
a b
a
ttery cha
r
ging
an
d di
scha
rgin
g in
th
e same
cu
rre
n
t
and differe
nt SOC, the sp
ace di
strib
u
tion variation
of negative
U
is more ap
p
a
rent alo
ng the
x
axis than that
of positive
U
.
Figure 6. The
Spatial Distri
bution of
U
in
the Battery Pulse
Cha
r
gin
g
and Di
scha
rging u
nde
r
80% SOC (
T
ba
t
=25
℃
, I=
5C
)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Electro
-
the
r
m
a
l Modelin
g o
f
Lithium
Ion
Batteries
(Ga
ousso
u Ha
dia
FOFANA)
3677
4. Conclusio
n
Electro
c
h
e
mi
cal-th
erm
a
l cou
p
ling mo
del shoul
d con
s
id
er so
me
mo
re
fa
ctors
a
n
d
assumptio
n
s
to build a re
a
s
on
able mo
d
e
l to ens
ure t
he appli
c
a
b
ility and ration
al
ity of the model.
An ele
c
tro
-
th
ermal
mo
del
of LIB for ele
c
tri
c
vehi
cle
s
is d
e
velop
ed
based
on th
e
poro
u
s ele
c
trod
e
theory with
consi
deri
ng th
e spatial va
ri
ations of el
ectrode p
a
ra
me
ter and
rea
c
ti
on heat, an
d
the
solutio
n
for the mo
del to
the effect
s
of SOC,
current rate
an
d
tempe
r
ature
on the
spat
ial
variation
s
of
electrode
pa
rameter
and
h
eat gen
eratio
n ba
sed
on M
A
TLAB langu
age. Th
e results
indicate that: the spatial
distrib
u
tion
and dyna
mic chan
ge p
r
o
c
e
ss i
s
simil
a
r to
j
, SOC
redu
ction
will
increa
se th
e s
patial dist
ribution difference
of
. The spatial
dist
ribution
U
of
positive a
nd
negative ele
c
trode i
s
si
milar to the
c
se
/c
sm
ax
spatial distrib
u
tion.
Whe
n
a batt
e
ry
cha
r
gin
g
a
nd
discha
rgin
g i
n
the
sam
e
current a
nd dif
f
erent SO
C, t
he
spa
c
e
dist
ribution
variat
ion
of negative
U
is mo
re
app
a
r
ent al
ong th
e
x
axis tha
n
that of po
sitive
U
. Ele
c
tro
c
hemical-th
e
rmal
cou
p
ling mo
d
e
l to simulate
the spa
c
e di
stributio
n of electrode p
a
rameters an
d internal b
a
ttery
heat gen
erat
ed rate un
de
r different wo
rking
con
d
ition
s
is rea
s
ona
b
l
e and a
c
cept
able.
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ces
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g
H
y
u
p
J
eon, Se
un
g Man Ba
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hermal mod
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li
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y
l
i
ndr
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Lithi
u
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W
u
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d
-ord
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C
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ngi
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her
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u
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i L
i
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a
n
g
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a
n
g
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l
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E
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hn,
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Y
ang
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ang.
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he
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o
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e
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a
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gy Conv
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ge
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ang Z
h
ifu, pen
g lia
n
y
u
n
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engc
h
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ge an
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h
a
rge ch
aracter
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stics of Li-io
n
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onthly
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16
8.
[8]
Yong
hu
ang
Ye
, Yixian
g S
h
i,
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he
ng
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,
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un
Le
e,
Xi
an
gmin
g H
e
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x
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n bat
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r Source
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yl
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e
w
m
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n
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e N
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hmutz, Jea
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arie T
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