Int
ern
at
i
onal
Journ
al of
P
ower E
le
ctr
on
i
cs a
n
d
Drive
S
ystem
(I
J
PE
D
S
)
Vo
l.
11
,
No.
4
,
Decem
be
r 202
0
, p
p.
1987
~
1994
IS
S
N:
20
88
-
8694
,
DOI: 10
.11
591/
ij
peds
.
v11.i
4
.
pp
1987
-
1994
1987
Journ
al
h
om
e
page
:
http:
//
ij
pe
ds
.i
aescore.c
om
Modeli
ng of
batter
y pack
sizing f
or ele
ctric v
eh
i
cles
V.
Sandeep
1
,
Suchitr
a Shas
tri
2
, A
r
gh
y
a
S
ardar
3
, Suren
der R
e
ddy S
al
kut
i
4
1
Depa
rtment of
El
e
ct
ri
ca
l
Eng
in
ee
ring
,
Na
ti
ona
l Ins
ti
tut
e
of Te
ch
nology
Andhra
Prade
sh,
Ind
ia
2
Depa
rtment of
El
e
ct
ri
ca
l
Eng
in
ee
ring
,
C
ent
ra
l U
nive
rsity
of
Ka
rna
ta
k
a, Ka
l
abur
agi
,
Indi
a
3
Te
chno
logy
Inf
orma
ti
on
Forec
a
sting
and
As
sessm
ent Counc
i
l, New
Delhi,
Ind
ia
4
Depa
rtment of
Rai
lro
ad
and
E
lectr
i
ca
l
Eng
ine
er
i
ng,
Woosong
Univer
sity
,
Da
ej
eo
n,
Repub
li
c
of
Korea
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
N
ov
23
, 201
9
Re
vised
A
pr
26
, 2
0
20
Accepte
d
M
a
y
19
, 20
20
The
pap
er
pr
ese
nts
the
m
at
h
ematica
l
modeling
for
batter
y
p
ack
sizi
ng
to
eva
lu
at
e
th
e
ve
hic
l
e
en
erg
y
co
nsumpti
on
by
using
the
der
iv
at
ion
fro
m
Para
metric
Anal
yti
c
al
Model
of
Vehic
l
e
En
erg
y
Consumpti
on
(PA
MV
EC)
by
Simpson
in
R
Studio.
Th
e
a
ss
ess
of
storage
bat
t
eri
es
for
el
e
c
tri
c
veh
ic
l
es
(EVs)
appl
icati
o
n
is
pre
sente
d
i
n
thi
s
pape
r
.
Th
e
main
source
o
f
power
i
n
EVs
are
b
at
t
eri
e
s
and
to
prope
r
l
y
optimi
ze
their
use
in
them,
a
par
ametr
i
c
vehi
c
le
dynami
c
mod
el
is
creat
ed
and
fa
ct
or
s
li
ke
ba
tt
ery
ma
ss
,
ene
rgy
nee
ded
for
th
e
EV
etc.
are
pre
dic
t
ed
using
inp
uts
such
as
ba
ttery
spec
ifi
c
ene
rgy,
ran
g
e
etc.
An
assess
me
n
t
of
ou
tput
par
a
me
t
ers
is
p
erf
or
me
d
by
using
diffe
ren
t
b
at
t
eri
e
s a
nd
co
mpa
r
ed t
o
determ
in
e
b
est
batter
y
for EV a
ppli
c
at
ion
.
Ke
yw
or
d
s
:
Ba
tt
ery
p
a
ck
sizi
ng
Brakin
g
l
os
ses
Ele
ct
ric v
e
hicle
s
Stor
a
ge batt
er
y
Kinetic
ene
r
gy
Op
ti
miza
ti
on
This
is an
open
acc
ess arti
cl
e
un
der
the
CC
BY
-
SA
l
ic
ense
.
Corres
pond
in
g
Aut
h
or
:
Su
r
en
der Re
dd
y
Sal
ku
ti
,
Dep
a
rtme
nt of
Ra
il
ro
ad
a
nd E
le
ct
rical
En
gi
ne
erin
g,
Woos
ong U
nive
rsity,
17
-
2,
Ja
ya
ng
-
Don
g,
D
ong
-
G
u,
Daejeo
n 3
4606, Re
public o
f
K
orea.
Emai
l:
su
re
nde
r@wsu.ac
.
kr
NOME
N
CLA
TURE
a
Acceler
atio
n
Veh
icle ac
c
elera
ti
o
n
(
m
/s
2
)
g
Acceler
atio
n
du
e to g
ravity
ρ
Den
sity
of air
(~
1
.
2
kg
/m
3
)
m
Mass o
f
v
eh
icle
Aerod
y
n
am
ic drag
co
eff
ici
en
t
Fron
tal ar
ea
(
2
)
Ro
llin
g
r
esis
tan
ce c
o
eff
icien
t
Cell cap
acity
Gravitatio
n
al acc
e
l
eration
(
9
.81
m
/s
2
)
Disch
arge r
at
e of
c
ell
Ro
ad
grad
ien
t (
%)
Cell v
o
ltag
e
Facto
r
to
accou
n
t
for
th
e
rotatio
n
al
i
n
ertia
o
f
th
e
p
o
we
r
tr
ain
(
= 1.1
or
1.2
)
f
Ratio
between
tota
l cell
w
eig
h
t to b
attery weigh
t
Total jo
u
rney
tim
e
Gradien
t of veh
icl
e with respect
to ro
ad
Ro
o
t m
ean cu
b
ed
velo
cities
v
Vo
ltag
e
Av
erage velo
city
Ro
ad
load
po
wer
(
W
)
Gradien
t compo
n
e
n
t
Veh
icle sp
eed (
m
/s
)
1.
INTROD
U
CTION
Re
new
a
ble
e
ne
rgy
res
ources
(RERs
)
plays
a
ve
ry
sig
nific
ant
r
ole
i
n
pla
nn
i
ng
a
nd
op
e
rati
on
due
to
no
emissi
on
s
a
nd
cl
ean
el
ect
rici
ty
pro
duct
ion.
D
uri
ng
the
la
st
few year
s
,
a
w
ide
i
ns
ta
ll
at
ion
of
RER
s
h
a
s
bee
n
prom
oted
to
t
he
power
s
ys
te
m.
The
e
ne
rgy
producti
on
f
r
om
these
RER
s
is
the
le
adin
g
so
l
ution
t
oward
s
t
he
decar
bonizat
io
n
of
t
he
s
ociet
y
a
nd
t
he
sec
uri
ty
of
ene
r
gy
s
upply.
Howe
ve
r,
var
i
ou
s
issue
s
of
inter
mit
te
ncy
of
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
D
ri
S
ys
t,
V
ol
.
11
, N
o.
4
,
D
ecembe
r
2020
:
1987
–
1994
1988
RER
s
a
nd
the
const
raints
f
or
the
c
onnecti
on
of
el
ect
ric
ve
hicle
s
(EVs)
sh
oul
d
be
ef
fe
ct
ively
a
ddress
ed
[
1]
.
Energ
y
st
or
a
ge
co
uld
be
one
op
ti
on
t
o
handl
e
the
un
ce
rtai
nt
y
of
RER
s.
More
e
ff
ic
ie
nt
operati
on
of
ma
rk
et
is
require
d
to
acc
om
m
odat
e
flex
ible
dema
nd
a
nd
el
ect
ric
ve
hi
cl
e
(EV
)
c
ha
r
ging
an
d
disch
arg
i
ng.
EV
is
a
typ
e
of
ve
hicle
that
us
es
el
ect
rici
ty
to
r
un.
T
he
r
e
are
t
hr
ee
m
a
in
co
mpo
nen
ts
in
E
Vs,
i.e.,
e
le
ct
ric
mo
to
r,
batte
ry
pack
a
nd
a
no
n
-
c
onve
ntio
nal
transmissi
on
t
hat
trans
fers
th
e
mo
to
r
po
wer
to
the
w
heels.
Wh
il
e
dri
vi
ng,
the
batte
ry
powe
r
i
s
us
e
d
a
nd
de
pl
et
ing
it
s
sup
ply
.
T
he
batte
rie
s
in
E
Vs
need
to
be
cha
r
ged
r
egu
la
rly
.
The
ba
tt
ery
EVs
offer
ab
out
(
100
-
15
0)
km
dri
vi
ng
ra
nge
befor
e
nee
di
ng
t
o
be
rec
ha
rg
e
d
[2].
B
ut
act
ual
dri
vi
ng
range
dep
e
nds
on
t
he
dri
vi
ng
st
yle,
s
peed
dr
i
ven,
cl
imat
e
con
t
ro
l
us
age
and
weathe
r.
EVs
us
e
lo
w
dra
g
aerod
yn
a
mic s
hap
e
s, use
high
ly adva
nced te
chnolo
gy, re
duced
weig
ht and
fuel costs
and
zero emi
ssio
ns [
3]
.
EVs
a
re
co
ns
i
der
e
d
as
a
n
i
mporta
nt
te
ch
no
l
ogy
to
re
duce
fo
s
sil
fu
el
consu
mp
ti
on,
emissi
ons
an
d
energ
y
c
onsumpti
on.
But,
the
E
Vs
re
quir
e
la
rger
batte
r
y
pac
ks
t
o
re
ach
acce
ptable
ra
ng
e
le
vels
.
T
he
dev
el
opment
of
ne
w
batte
ries
wit
h
highe
r
s
pecific
e
ne
rgy
c
ou
l
d
re
du
ce
the
mass
an
d
t
he
cost
of
E
V
s
a
nd
increase
thei
r
dr
i
ving
ra
ng
e
[
4].
The
desig
n
and
opti
miza
ti
on
of
t
he
batte
ry
pack
i
n
an
EV
is
essenti
al
for
the
integrati
on
of
EVs
i
nto
gl
ob
a
l
mar
ket
[
5].
E
Vs
ca
n
al
s
o
be
us
e
d
t
o
s
moot
h
ou
t
the
va
ry
i
ng
fl
uctuati
ons
in
t
he
energ
y
pro
file
of
outp
ut
ene
r
gy
ge
ner
at
e
d
by
the
s
ources
.
Energ
y
sto
ra
ge
from
el
ect
ric
veh
ic
le
s’
batte
ries
ca
n
act
as
a
networ
k
of
m
ob
il
e
sto
rag
e
s
ys
te
ms
,
wh
ic
h
can
al
s
o
help
to
s
uppor
t
the
gr
id
by
pr
ov
i
ding
real
ba
ckup
powe
r
an
d
imp
rovin
g
the
e
ne
rgy
pr
of
il
e
by
pro
vid
in
g
reac
ti
ve
power
c
ompe
ns
at
io
n.
T
her
e
fore,
batte
ries
are
consi
der
e
d
on
e
of
the
wi
de
ly
us
e
d
e
nerg
y
st
or
a
ge
s
ys
te
ms
[6].
E
Vs
are
c
heap
e
r
to
run
co
mp
a
red
to
conve
ntion
al
pe
tr
ol/diese
l
ve
hicle
s,
t
hey
a
r
e
ec
o
-
fr
ie
ndl
y,
c
heap
e
r
to
m
ai
ntain,
an
d
c
an
be
c
harge
d
f
rom
RER
s su
c
h
as
s
olar, wi
nd and
geo
t
hermal
, et
c.
The
batte
ries
us
e
d
f
or
E
Vs
are
le
ad
-
aci
d,
nickel
-
base
d,
a
nd
li
thium
-
io
n.
Lea
d
-
aci
d
ba
tt
eries
wer
e
us
e
d
in
E
Vs
i
n
earl
y
gen
e
ra
ti
on
[
7].
T
he
pr
ese
nt
tre
nd
f
or
el
ect
ric
mobil
it
y
is
towa
r
ds
us
in
g
li
thiu
m
-
io
n
batte
ry.
As
le
a
d
-
aci
d
batte
ries
are
of
lo
w
c
os
t
but
the
y
ha
ve
lo
w
s
pecif
ic
energ
y
a
nd
hav
e
m
or
e
we
igh
t
.
Nickel
-
meta
l
hydri
de
batte
rie
s
wer
e
al
s
o
promin
e
nce
for
t
he
use
of
E
Vs
,
bu
t
li
thiu
m
-
io
n
batte
ries
a
re
more
promi
nen
ce
to
wards t
he use
of ele
ct
ric an
d hyb
rid
E
Vs
[8].
A
batte
r
y
-
pow
ered
E
V
m
od
el
al
on
g
with
a
simple
simu
la
ti
on
-
based
it
erati
ve
meth
od
of
batte
r
y
siz
ing
is
propo
sed
i
n
[9].
Re
f
eren
ce
[
10]
pr
opos
es
a
ne
w
batte
ry
c
oo
li
ng
syst
em
for
hy
dro
gen
f
ueled
hybri
d
EVs
t
hat
ac
hieves
more
e
ff
ic
ie
nt
co
olin
g
a
nd
dri
vi
ng,
whic
h
inc
reases
ve
hicle
dri
ving
range
a
nd
e
nhance
s
veh
ic
le
safet
y
by
mai
ntainin
g
the
ba
tt
eries
a
t
opti
mum
ope
rati
ng
c
onditi
ons.
A
c
us
to
me
r
a
da
ption
c
os
t
that
decr
e
ase
s
with
batte
r
y
e
ne
rgy
ca
pacit
y
is
pro
po
se
d
in
r
efere
nce
[11
].
Re
fer
e
nce
[
12]
pr
ov
i
des
a
basic
gu
i
deline
f
or
c
el
l
sel
ect
ion
and
i
nteg
rati
on
of
cel
l
f
or
t
he
EVs
batte
ry
pack.
A
n
e
ff
e
ct
ive
batte
ry
t
hermal
mana
geme
nt
s
ys
te
m
s
olu
ti
on
is
prese
nted
in
re
fer
e
nc
e
[
13]
.
Var
i
ous
E
V
batte
r
y
te
ch
no
l
og
ie
s
a
re
pr
esented
in
[
14].
Mo
de
li
ng
a
nd
sim
ulati
on
of
batte
r
y
E
Vs
has
show
n
i
n
re
fe
re
nce
[15]
that
t
he
c
ho
ic
e
of
batte
ry
te
chnolo
gy
has
a
high
im
pact
on
ve
hicle
pe
r
forma
nce.
Re
f
eren
ce
[
16]
pr
opos
es
a
math
emat
ic
model
f
o
r
t
he
simulat
ion
of
batte
ry
pack
s
base
d
on
el
em
ent
wise
cal
cu
la
ti
on
s
of
matr
ic
es.
T
he
st
udy
a
nd
modeli
ng
of
a
li
thium
-
io
n bat
te
ry
cell
is
pr
e
s
ented
i
n refe
re
nce
[17].
Fo
r
c
onstr
uction
of
fu
t
ur
e
s
cenari
os
,
tre
nds
in
e
nerg
y
st
or
a
ge
te
ch
no
l
ogie
s
wer
e
disc
us
se
d
i
n
this
pap
e
r.
A
sim
ul
at
ion
m
od
el
wh
ic
h
ta
kes
ve
hicle
par
a
met
ers
an
d
cel
l
pa
rameters
(s
pe
ci
fic
energ
y,
volt
age,
discha
rg
e
rate
et
c.)
as
in
puts
an
d
pr
ov
i
de
s
est
imat
es
th
e
energ
y
sto
ra
ge
re
quireme
nt
fo
r
the
veh
i
cl
e
is
dev
el
op
e
d
[
18]
.
It
is
obser
ve
d
that
f
o
r
li
kely
fu
t
ur
e
scena
rio
s
of
batte
ry
te
chnolo
gy,
t
her
e
cou
l
d
be
si
gn
if
ic
ant
po
sit
ive
im
pac
t
on
t
he
co
st
and
/
or
pe
rform
ance
of
E
Vs.
I
n
this
wor
k,
it
is
assume
d
tha
t
there
is
no
c
ha
ng
e
i
n
the
veh
ic
le
des
ign
or
co
mpo
ne
nt
siz
in
g.
T
he
ve
hicle
is
ass
ume
d
to
re
m
ai
n
same
as
in
it
s
pr
ese
nt
f
or
m
,
e
xcep
t
the
fact
that
th
e
batte
r
y
pac
k
is
co
ns
tr
ucted
with
cel
ls
of
e
mer
ging
te
ch
nolo
gies.
The
refor
e
,
it
is
possible
to
hav
e
hi
gh
e
r
be
nef
it
s
as
c
omp
ared
t
o
th
e
res
ults
sho
wn
in
t
he
pr
ese
nt
wor
k.
T
he
a
ppli
cat
ion
of
these
ba
tt
eries
for
E
Vs
is
pre
sented
i
n
this
pap
e
r.
The
ma
in
source
of
powe
r
in
EVs
a
re
batte
ries
a
nd
to
pro
per
l
y
opti
mize
their
us
e
i
n
t
he
m,
a
pa
ramet
ric
ve
hicle
dynamic
model
i
s
create
d
a
nd
f
act
or
s
su
c
h
as
batte
ry
mass
,
energ
y
need
e
d
for
a
n
EV
ar
e
predict
ed
by
us
i
ng
i
nputs
li
ke
batte
r
y
s
pecific
ene
r
gy,
ra
nge
et
c
[
19].
A
n
assess
ment
of
ou
t
pu
t
par
a
me
te
rs
is
pe
rformed
by
us
i
ng
dif
fer
e
nt
batt
eries,
a
nd
c
ompa
red
t
o
determine
best
ba
tt
ery
f
or
EV
a
ppli
cat
ion.
The
re
main
der
of
this
pap
e
r
is
organ
iz
e
d
a
s
fo
ll
ows:
Sect
ion
2
prese
nts
the
detai
le
d
m
at
hemati
cal
modeli
ng
of
ba
tt
ery
pack
siz
ing
.
Sim
ulati
on
resu
lt
s
a
nd
discuss
i
on
is
pr
ese
nted
in
S
ect
ion
3.
Final
ly,
the
con
t
rib
ution
s
with c
on
cl
ud
i
ng
remarks
are prese
nted
in Se
ct
ion
4.
2.
MA
T
HEM
AT
ICA
L
MODE
LING
OF B
A
TT
ERY
P
A
C
K
SIZI
NG
The
predict
io
n
of
range
an
d
performa
nce
of
el
ect
ric
ve
hicle
s
(E
Vs)
is
i
mporta
nt.
T
hre
e
imp
or
ta
nt
par
a
mete
rs
i
n
this re
gard a
re rang
e
p
e
r
c
harg
e o
f
b
at
te
r
y,
m
aximum s
pee
d and acc
el
erati
on. De
velo
pm
e
nt
o
f
a
mathemat
ic
al
model
to
est
im
at
e
these
pe
rfo
rm
a
nce
par
a
m
et
ers
f
or
var
i
ous
hypotheti
ca
l
fu
t
ur
e
batte
ri
es
will
require
c
onsid
erati
on
of
fun
da
mental
eq
uations
of
the
ve
hi
cl
e
dynamics.
The
pe
rfo
rma
nc
e
of
a
giv
e
n
ve
hicle
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t J
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ow Elec
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ys
t
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Mo
deling of
ba
tt
ery
pa
ck
sizi
ng fo
r elec
tri
c v
ehicl
es
(V
. San
deep)
1989
dep
e
nds
to
a
l
arg
e
e
xtent
on
the
dri
ving
c
ycle
it
fo
ll
ows
.
A
dr
ivi
ng
cy
cl
e
is
ti
me
vs
sp
ee
d
pro
file
of
t
he
veh
ic
le
.
Since
there
a
re
in
fi
nite
num
be
r
of
possibil
it
ie
s
for
s
uc
h
dr
i
vin
g
patte
rn
in
real
li
fe,
ty
pical
ly
a
sta
nd
a
rd
ti
me
vs
sp
ee
d
pro
file
is
def
i
ned
ba
sed
on
sta
ti
sti
cal
analy
ses
a
nd
s
uc
h
a
sta
nd
ard
dri
vi
ng
c
yc
le
is
acce
pted
for
va
ri
ous
re
gula
to
ry
pur
poses
[
20]
.
Mo
dified
I
nd
ia
n
D
rivi
ng
Cycle
(
M
I
DC)
is
the
dri
ving
cycle
acce
pted
in
I
ndia
.
T
he
f
uel
econom
y
of
ve
hicle
s
are
te
s
te
d
wit
h
r
espe
ct
to
this
dri
vi
ng
cycle.
Ve
hicle
man
uf
act
ur
e
rs
in
I
ndia
re
po
rt
mil
eage/f
uel
eco
nomy
wit
h
re
sp
ect
t
o
t
his
M
I
DC
dri
ving
c
ycle.
Si
mil
arly,
sta
nd
a
rd
dri
vi
ng
c
ycles
are
av
ai
la
ble
in
ot
her
co
un
t
ries
suc
h
as
U
nited
Stat
es
of
Amer
ic
a
,
Eu
rope,
an
d
J
apan
et
c.
By
usi
ng
sta
nd
a
rd
math
emat
ic
al
equ
at
ion
s
a
nd
s
pr
ea
ds
he
et
s,
the
si
mu
la
ti
on
can
be
do
ne
in
MATL
AB
and
E
xce
l
s
hee
ts.
I
nputs
t
o
m
od
el
a
re
va
rio
us
ve
hicle
at
trib
utes
s
uch
as
m
ass
of
t
he
veh
i
cl
e,
it
s
dime
nsi
on
s
,
gear
rati
o,
w
he
el
base
s
peed,
mo
to
r
power
e
tc
.,
an
d
it
is
ne
cessar
y
to
have
a
good
performa
nce
of
the
veh
ic
le
so
that
it
can
achieve
th
e
ta
rg
et
of
a
c
urr
e
nt
IC
en
gin
e
veh
ic
le
.
Anot
her
im
portant
aspect
f
or
E
V
s
is
it
s
range
[
21
-
22].
A
mathe
mati
cal
mo
del
is
de
velo
ped
t
o
ca
lc
ulate
the
range
of
ve
hicle
base
d
on
the
t
yp
e
of
batte
ry an
d
it
s
capaci
ty.
Fig
ure 1 de
picts t
he roa
d
l
oad eq
ua
ti
on
s
of E
V.
Figure
1
.
Flo
w
cha
rt of c
ucko
o
sea
rch al
gori
thm.
2.1.
Po
wer
c
onsump
tion by
a vehicl
e
Wh
il
e
r
unning
,
a
ve
hicle
nee
ds
t
o
overc
ome
f
our
f
or
ces
opposi
ng,
the
y
are
m
otio
n
-
a
erod
yn
a
mic
dr
a
g,
r
olli
ng
re
sist
ance,
a
c
ompone
nt
of
it
s
w
ei
gh
t
de
pe
nd
i
ng
on
t
he
gradie
nt,
a
nd
i
ts
ine
rtia
.
Sinc
e
t
he
powe
r
consu
mp
ti
on
is
obta
ine
d
by
m
ulti
ply
in
g
t
he
f
or
ce
with
velo
ci
ty,
a
nd
since
the
velocit
y
of
the
veh
ic
le
c
ha
ng
e
s
con
ti
nu
ously
duri
ng
it
s
m
ov
e
ment.
Ty
pical
ly,
simulat
ors
are
us
ed
to
est
imat
e
powe
r
c
on
s
umpti
on
at
each
simulat
ion
ste
p
s.
T
he
ene
r
gy
co
nsum
ptio
n
is
ob
ta
i
ned
by
inte
gr
at
in
g
t
he
po
wer
consu
mp
ti
on
values
ov
e
r
ti
me
[23
].
Howe
ver,
a
pa
rametric
a
ppr
oa
ch
f
or
est
imat
ing
ve
hicle
ene
rgy
c
onsumpti
on
has
bee
n
i
ntrod
uced
by
Simps
on
et
al
.
in
ref
e
ren
ce
[
24].
The
m
od
e
l
dev
el
oped
by
them
is
kn
own
as
Para
metri
c
A
nalytic
al
V
ehicl
e
Energ
y
C
on
s
umpti
on (
PAM
VEC)
.
T
he
f
un
dame
ntal
co
nc
ept
of
this
ap
proach
is
to d
e
-
c
ouple
the
total
tract
ive
forces
int
o
tw
o
sep
arate
cat
e
gories.
Fi
rst
one
co
mprise
s
t
he
aer
odynami
c
dr
a
g
a
nd
ro
ll
ing
resist
ance,
wh
ic
h
are
non
-
rec
ov
e
rab
le
.
The
ot
he
r
one
c
omp
rise
s
the
gr
a
dient
r
el
at
ed
f
or
ce
a
nd
ine
rtia
,
wh
ic
h
re
su
lt
in
cha
ng
e
in
po
te
ntial
or
kin
et
ic
energ
y
of
the
veh
ic
le
,
and
ca
n
be
rec
ov
e
re
d.
Sim
pson
et
al
.
hav
e
sh
ow
n
that
a
dri
vin
g
cycle
ca
n
be
r
epr
ese
nted
by
four
pa
ram
et
e
r
s:
avera
ge
sp
e
ed,
r
oo
t
mean
cub
e
d
vel
ocity
,
vel
ocity
rati
o,
an
d
char
act
e
risti
c accel
erati
on
[
25].
2.2.
A
verage
r
oad lo
ad p
ow
e
r
The
m
od
el
in
g
of
ve
hicle
e
nerg
y
c
onsum
ption
is
ap
pro
ached
by
t
he
pa
ramet
ric
de
scriptio
n
of
fo
ll
owin
g ro
a
d l
oad eq
uatio
ns [
26]
,
=
+
+
+
(1)
=
1
2
3
+
+
+
(2)
Eq
uation
(
1)
is
the
ave
rag
e
r
oa
d
loa
d
power
equ
at
io
n,
an
d
i
t
con
sist
s
of
four
c
omp
on
e
nts
.
an
d
are
irre
ve
rsibl
e
powe
r
losse
s
du
e
to
ae
rod
ynamic
a
nd
ro
ll
ing
dr
a
g,
w
herea
s
an
d
are
the
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
D
ri
S
ys
t,
V
ol
.
11
, N
o.
4
,
D
ecembe
r
2020
:
1987
–
1994
1990
powe
r
f
or
veh
i
cl
e
acce
le
rati
o
n
an
d
hill
-
cl
imbin
g,
r
ep
rese
nting
the
pote
ntial
and
kin
et
ic
energ
y,
a
nd
t
he
y
are
recovera
ble
[27]. T
his ass
umpti
on ma
kes
and
equ
al
to
zer
o,
i.e
.,
∫
=
0
∫
0
=
0
0
(3)
In
orde
r
t
o
paramet
erize
the
r
oad
loa
d
e
qu
at
ion
,
it
is
ass
ume
d
t
hat
a
ve
hi
cl
e’s
jour
ney
is
de
fine
d
as
includi
ng the
re
tur
n
trip
to
it
s point
of d
e
par
t
ur
e
[28].
Simil
arly,
∫
=
0
∫
=
0
0
0
(4)
These
a
re
valid
as
the
net
c
ha
ng
e
in
sp
ee
d
an
d
el
evati
on
i
s
zer
o.
Since
,
t
he
veh
ic
le
retu
rn
s
ove
r
the
journe
y
t
o
it
s point
of d
e
par
t
ure, t
he
el
evati
on a
nd n
et
c
ha
nge in
s
peed is z
ero.
=
1
2
3
+
(5)
wh
e
re
=
1
∫
0
an
d
=
√
1
∫
3
0
3
.
T
he
dri
ving
patte
rn
velocit
y
r
at
io
(Ʌ)
is
de
fine
d
as
the r
at
io
of
to
. F
r
om t
his,
the
av
e
rag
e
road
l
oad po
wer i
s e
xpresse
d
as
[2
9],
=
1
2
Ʌ
3
3
+
(6)
Eq
uations
(
5)
and
(
6)
acc
ou
nt
s
f
or
gravit
at
ion
al
ene
r
gy
an
d
i
ner
ti
al
losse
s
as
a
par
t
of
veh
ic
le
r
oa
d
load. T
hese tw
o
lo
sses a
re
due to ine
ff
ic
ie
nt
mecha
nisms i
n ve
hicle
pow
e
r t
rain.
2.3. A
verage
b
rakin
g
lo
sses
The
fr
ic
ti
on
br
akes
dissipates
the
gra
vitat
iona
l
energy
an
d
kin
et
ic
ene
r
gy
store
d
wit
hin
t
he
ine
rtia
of
the
ve
hicle
[30
].
T
he
ave
rag
e
rate
of
e
nerg
y
store
d
is
deter
mined
within
t
he
inerti
a
of
a
veh
ic
le
.
T
her
e
f
or
e
,
to
der
i
ve
the
av
e
r
age
rate o
f
e
ne
rgy
st
or
a
ge, t
he
foll
ow
i
ng equati
on is c
on
si
der
e
d.
=
(
+
)
(7)
Let
=
+
.
T
he
grad
ie
nt
co
mpo
nent
and
acce
le
rat
ion
both
can
be
re
pr
ese
nted
by
sin
gle
acce
le
rati
on
te
rm.
T
he
a
ve
ra
ge
rate
of
e
nergy
sto
ra
ge
i
n
ve
hicle
ine
rtia
(
)
is
w
ritt
en
by
assumi
ng
the
gr
a
dient
of zer
o,
i.e
.,
=
1
∫
|
≥
0
0
(8)
Her
e
,
to
s
ubsti
tute
a
par
a
me
tric
eq
uatio
n,
po
sit
ive
acce
le
rati
on
ki
netic
energ
y
per
unit
distance
(P
K
E)
is
int
rod
uced, which
is a
meas
ur
e
o
f
a
ccel
erati
on
w
ork
re
quired
in
a
dri
ving
patte
r
n.
PKE
is
the
s
um
of
distances
betw
een
the
s
quare
s
of
t
he
fi
nal
and
i
niti
al
velo
ci
ti
es
in
su
cce
ssive
acce
le
rat
ion
,
div
i
ding
by
total
trip
distance.
I
t
is ex
pr
e
ssed
by usin
g [31
],
=
∑
(
2
−
2
)
=
∑
(
2
−
2
)
∫
0
(9)
The
a
ve
rag
e
rate
of
kin
et
i
c
ene
rgy
(
KE
)
sto
ra
ge
[32]
in
a
ve
hicle
duri
ng
dri
vi
ng
cycle
is
represe
nted b
y,
×
=
∑
(
2
−
2
)
(10)
The
a
ver
a
ge
r
a
te
o
f
K
E
sto
rage
in a
ve
hicle
mass
durin
g
a
dr
i
ving
patte
rn is ex
pr
e
ssed
a
s,
=
∑
(
1
2
2
−
1
2
2
)
(11)
The
e
quat
ion f
or ene
rgy st
or
a
ge wit
hin
ve
hi
cl
e inertia
is
giv
en
by,
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N: 20
88
-
8
694
Mo
deling of
ba
tt
ery
pa
ck
sizi
ng fo
r elec
tri
c v
ehicl
es
(V
. San
deep)
1991
=
1
2
(12)
The
a
bove
e
quat
ion
is
a
paramet
ric
ex
pr
es
sion
for
the
a
ve
rag
e
rate
of
e
nerg
y
sto
rag
e
,
wh
ic
h
is
a
consi
ste
nt form o
f
in e
quat
ion (
1). T
her
e
f
ore, t
he
c
har
act
e
risti
c accel
erati
on (
ã
)
ca
n be e
xpresse
d
as
,
ã
=
1
2
PKE
=
1
2
∑
(
2
−
2
)
v
avg
T
(13)
The
a
ver
a
ge
ra
te
of
e
ne
rgy
st
or
a
ge
i
n
the
ve
hicle
inerti
a
over
a
dr
i
ving
c
yc
le
,
assu
min
g
a
flat
r
oad
is
giv
e
n by,
=
(
ã
)
(14)
The
a
ver
a
ge
br
akin
g
lo
sses
ca
n
be
def
i
ned
by u
sin
g
t
h
e
re
ge
ner
at
ive
bra
kin
g
f
racti
on
(
),
an
d
it
can
be
e
xpress
ed
as
,
=
(
1
−
)
(15)
The
n,
t
he
can
be
e
xpresse
d
a
s,
=
(
1
−
)
(
ã
)
(16)
The
eq
uatio
ns
(6)
a
nd
(16
)
ca
n
be
co
mb
i
ned
to
get
the
ave
rag
e
po
wer
re
quireme
nt
at
the
outp
ut
o
n
the
dri
ve
n
axle
of
a
veh
ic
le
,
i
.e.,
power
at
dri
ve
s
haf
t
is
eq
ual
to
po
wer
due
to
r
oa
d
loa
d
an
d
power
due
to
br
a
king
[33
],
a
nd it
can be
ex
pr
ess
ed
as,
−
=
1
2
3
3
+
+
(
1
−
)
(
ã
)
(17)
As
te
nd
s
to
1,
br
a
king
losse
s tend
to b
ec
om
e
zero
,
t
he
pote
ntial
and
k
ineti
c
energy
is returne
d
for
recapt
ur
e
of
the
powe
r
trai
n.
If
the
re
w
ou
l
d
be
10
0%
e
ff
ic
ie
nc
y
of
st
or
a
ge
m
echan
is
m
a
nd
ene
rgy
recapt
ur
e,
no e
nerg
y
c
on
s
ump
ti
on
would af
fe
ct
d
ue
to g
rav
it
at
ion
a
nd ine
rtia
.
3.
RESU
LT
S
AND DI
SCUS
S
ION
In
t
his
pa
pe
r,
a
sp
r
eads
heet
model
is
de
vel
op
e
d
t
o
cal
cul
at
e
the
pa
rame
te
rs
of
the
Mo
dified
I
nd
ia
n
Dr
i
ving
Cycle
(M
ID
C
),
name
ly,
a
ver
a
ge
velocit
y,
root
mea
n
cu
be
d
veloci
ty,
velocit
y
rati
o
an
d
c
har
act
e
risti
c
acce
le
rati
on
.
T
o
m
odel
the
i
mp
act
of
batte
ry
te
c
hnol
ogy,
it
is
importa
nt
to
pre
dict
th
e
pe
rformance
of
a
veh
ic
le
base
d
i
n
te
r
ms
of
c
rite
ria’s,
su
c
h
as:
top
sp
ee
d,
i
.e.
,
ma
ximum
s
pe
ed
of
t
he
ve
hi
cl
e
(k
m/
h)
,
dr
iving
range,
an
d
acc
el
erati
on
ti
me,
i.e.,
ti
me
ta
ke
n
for
the
ve
hi
cl
e
to
reac
h
f
rom
mi
nimum
sp
ee
d
t
o
ma
xi
mu
m
sp
ee
d(
s
)
(Ta
bl
e
1)
.
T
he
m
odel
c
onside
rs
input
ve
hicle
sp
eci
ficat
io
ns
and
s
om
e
deta
il
s
ab
ou
t
the
energ
y
s
tora
ge
te
ch
nol
ogy
us
e
d
a
re
s
pecific
e
nerg
y,
sp
eci
fic
powe
r,
cel
l
vo
lt
age
et
c.
The
main
ou
t
pu
ts
obta
in
ed
a
re
the
ma
xim
um
sp
ee
d,
ra
nge
an
d
acce
le
ra
ti
on
ti
me.
A
ft
er
e
xtracti
ng
the
ve
hicle
pa
rameters
f
orm
the
sp
eci
ficat
io
ns
t
able, the
n
t
he
t
yr
e
outer
diam
et
er
an
d mot
or
base spee
d
ca
n be calc
ulate
d.
The
Indian
dri
ving
c
ycle,
i.e.
,
sp
ee
d
vs
ti
me
gr
a
ph
is
dep
ic
te
d
in
Fig
ur
e
2.
The
pa
ramete
rs
of
India
n
dr
i
ving
c
ycle
ta
ken
from
spreads
heet
cal
c
ulati
on
a
re
as
fo
ll
ows:
t
otal
ti
me
is
196s,
total
distance
<
-
1022.
67km,
<
−
5
.
22
,
<
−
3
.
26
,
ℎ
<
−
0
.
27
and
vel
ocity
rati
o
<
-
0.6
2.
Var
i
ous
c
onsta
nts
consi
der
e
d
i
n
t
his
pa
pe
r
are
i
s
1.2
25,
g
is
9.81,
is
0.3,
is
0.01,
k
is
1.1
,
is
0.3.
O
nce
t
he
veh
ic
le
at
tribu
te
s
are
obta
ined
,
t
he
m
otor
a
nd
tr
ans
missi
on
e
ff
ic
ie
ncies
a
re
assu
med,
a
nd
oth
e
r
s
uc
h
c
onsta
nt
s.
T
he
necessa
ry
valu
es
of
and
ar
e
cal
culat
ed
from
the
velocit
ie
s
ob
ta
ine
d
f
r
om
the
dr
i
ve
c
ycles.
A
nd
oth
e
r param
et
ers
s
uch as i
niti
al
cell
mass a
nd ma
xim
um ac
cel
erati
on
a
re a
lso ca
lc
ulate
d.
The
ve
hicle
dy
namics
eq
uatio
ns
are
now
eva
luate
d
an
d
the
batte
ry
ma
ss
is
opti
mize
d.
Th
e
e
qu
at
io
ns
for
mathe
mati
cal
m
od
el
is
ta
ken
f
r
om
P
arametric
A
na
lyti
cal
Mod
el
of
Ve
hicle
Energ
y
Co
ns
umpti
o
n
(P
A
MVEC)
by
Sim
pson.
It
ex
plains
the
energ
y
c
on
s
umpti
on
m
od
e
l
wh
ic
h
pre
dicts
the
total
energ
y
consu
med
by
the
veh
ic
le
,
by
pa
rametric
dr
i
ving
c
ycle
and
veh
ic
le
at
tribu
te
s
as
an
input.
The
deri
vation
ou
tl
ines
the
pa
rametric
form
ul
at
ion
of
ro
a
d l
oad eq
uatio
n.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
D
ri
S
ys
t,
V
ol
.
11
, N
o.
4
,
D
ecembe
r
2020
:
1987
–
1994
1992
The
obta
ine
d
r
esults
by
us
i
ng
the
pro
po
se
d
appr
oach
a
re:
batte
ry
powe
r
is
17920W,
ba
tt
ery
ene
rgy
is
12185.6
W
h,
maxim
um
sp
e
ed
is
101.0
9
m
/s,
mo
t
or
base
sp
ee
d
is
95
54.
14r
pm
,
acc
el
er
at
ion
ti
me
is
20.
63
s
and ene
r
gy con
su
m
ptio
n per k
m is
160.8
7Wh
.
Table
1.
T
ech
ni
cal
v
ehicl
e s
pe
ci
ficat
ion
of
M
a
hindra's
e2O Pl
us
elec
tric
veh
ic
le
.
Para
m
eter
Valu
e
Para
m
eter
Valu
e
Top
sp
eed
8
5
km/h
Grade sp
eed
1
0
kmph
Tar
g
et
rang
e
1
4
0
km
Ov
erall
g
ea
r
1
0
.83
Acceler
atio
n
m
in
i
m
u
m
sp
eed
0
kmph
W
h
eel diamete
r
1
4
inch
Acceler
atio
n
m
ax
i
m
u
m
sp
eed
6
0
kmph
Sid
e wall
h
eig
h
t
9
9
m
m
Acceler
atio
n
tim
e
9
.5 s
Moto
r
p
o
wer
1
9
kW
Glid
er
m
ass
1
2
5
7
k
g
Moto
r
to
rqu
e
7
0
Nm
Pass
en
g
er
weig
h
t
3
2
0
kg
Co
n
su
m
p
tio
n
8
8
Wh
/k
m
Cell sp
ecific en
erg
y
1
7
0
Wh
/k
g
Battery
capacity
2
8
0
Ah
Gradien
t PC
18%
Nu
m
b
er
o
f
m
o
d
u
le
s
16
Fron
tal ar
ea
2
.49
6
m
2
Nu
m
b
er
o
f
cells
64
Pack
vo
ltag
e
7
2
V
Battery
kW
h
1
5
kW
h
Cell cap
acity
7
0
Ah
Battery
weigh
t
1
1
2
kg
Disch
arge r
at
e
0
.5 C
Cell sp
ecific
p
o
we
r
2
0
0
W/k
g
Cell v
o
ltag
e
3
.2 v
Grade sp
eed
1
0
kmph
Cell to
battery
w
ei
g
h
t
0
.8
Ov
erall
g
ea
r
1
0
.83
Figure
2. I
nd
ia
n dr
i
ving c
ycle.
3.1.
I
mp
act
s
of futur
e de
vel
op
men
ts
in
en
ergy st
or
ag
e
te
chno
l
og
ie
s
on EVs
Ra
ng
e/
mil
eage
:
The
mil
eage
of
ve
hicle
can
be
i
mpro
ve
d
if
the
sp
eci
fic
ene
rgy
of
the
batte
r
y
increases
. Th
is
r
esults i
n
l
onge
r
dri
ving
rang
e for
the
sa
me
batte
ry
mass. Hence
, one wil
l need
lesse
r
stop
s
f
or
chargin
g,
al
s
o
le
ading
t
o
le
ss
er
impact
on
th
e
gr
id
.
T
he
goa
l
is
to
achieve
the
ra
ng
e
i
n
an
EV
eq
ual
to
w
hat
is
seen
i
n
a
petr
ol
eum
base
d
ve
hicle
s
f
or
the
same
am
ount
of
f
uel
(t
o
ac
hi
eve
s
pecific
pow
e
r
cl
os
e
t
o
that
of
gas
oline/diese
l
in batt
eries).
Ba
tt
ery
mas
s
r
edu
ct
io
n
f
or
sa
me
power
:
I
f
t
he
powe
r
is
ke
pt
same
a
nd
th
e
sp
eci
fic
e
nergy
inc
rease
d,
then
the
mass
can
be
re
du
ce
d
du
e
t
o
inc
reas
e
in
ene
rgy
ou
t
pu
t
per
kg
wei
gh
t.
This
in
-
tu
r
n
ef
fects
the
lo
a
d
of
the v
e
hicle
a
nd d
ec
reases t
he e
nerg
y
c
on
s
ume
d per
km, a
dd
ing
t
o
the
inc
re
ase in
range.
Lifecycle
im
pro
veme
nt:
De
velo
pm
e
nt
in
batte
ries
co
uld
al
so
pote
ntia
ll
y
aff
ect
the
increase
in
li
fecy
cl
es
of
t
he
b
at
te
r
y,
lea
din
g t
o
l
onge
r ba
tt
ery
li
feti
mes,
and h
e
nce i
ncrea
sing t
he
li
fe
of the
batte
r
y.
Faste
r
c
hargin
g:
De
velo
pm
e
nt
in
batte
ries
co
uld
pote
ntial
ly
le
ad
to
f
ast
er
cha
r
ging
(w
it
h
same
chargin
g p
ow
e
r)
from
the ele
ct
ro
c
hemical
c
hange i
n
the
ba
tt
eries.
4.
CONCL
US
I
O
NS
This
pa
per
has
anal
yzed
the
po
s
sible
fu
t
ur
e
imp
roveme
nts
in
e
ne
rgy
stora
ge
te
c
hnologi
es
that
ha
ve
var
i
ou
s
a
ppli
cat
ion
s
s
uch
as
el
ect
ric
veh
ic
le
s
(EV
s
).
M
odel
ing
of
batt
ery
pac
k
siz
in
g
f
or
E
Vs
has
been
pr
ese
nted
in
this
w
ork.
T
he
ob
je
ct
ive
of
t
his
pap
e
r
is
to
c
ondu
ct
and
anal
yz
e
the
im
pac
ts
of
fu
t
ur
ist
ic
/e
mer
ging
batte
ry
te
chnolo
gies.
It
i
s
not
po
s
sible
t
o
c
onsider
detai
le
d
batte
r
y
c
har
act
erist
ic
s
s
uch
a
s
it
s
char
ge
-
discharge
c
har
act
e
risti
cs
et
c.,
as
su
c
h
data
are
no
t
a
vaila
ble
f
or
t
he
emer
gi
ng
batte
r
y
c
he
mi
stry.
Su
c
h
iss
ues
a
r
e
ty
pical
ly
co
nsi
der
e
d
at
the
t
ime
of
act
ual
desig
n
of
the
veh
ic
le
batte
r
y
pa
ck
.
H
ow
e
ve
r,
this
work
does
not
require
a
deta
il
ed
desig
n
of
veh
ic
le
batte
r
y
pack.
The
fu
t
ur
e
wor
k
can
be
f
ocused
on
flow
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N: 20
88
-
8
694
Mo
deling of
ba
tt
ery
pa
ck
sizi
ng fo
r elec
tri
c v
ehicl
es
(V
. San
deep)
1993
batte
ries
an
d
t
heir
us
e
i
n
E
V
s
an
d
th
ei
r
im
pa
ct
s
on
E
Vs.
A
s
the
flo
w
batt
eries
are
al
s
o
more
ef
fici
ent
than
t
he
rech
a
rg
ea
ble
ba
tt
eries,
bu
t
th
e
disad
van
ta
ge
is
of
it
s
struct
ur
e
.
The
refo
re,
mo
re
c
oncent
r
at
ion
on
re
duci
ng
t
he
structu
re a
nd
weig
ht of t
he
fl
ow b
at
te
ries c
a
n be
done.
ACKN
OWLE
DGE
MENTS
This
re
searc
h
work
ha
s
be
en
carried
out
bas
ed
on
the
s
upport
of
“
Ce
ntral
U
niv
er
sit
y
of
Karnata
ka
’
s
Acad
e
mic
Re
search
Fun
ding
-
(
2019
-
2020
)
”
an
d
“
Woos
ong
Un
i
ver
sit
y's
Aca
de
mic
Re
search
Fun
ding
-
(20
19
-
20
20)
”
.
REFERE
NCE
S
[1]
S.C.
A.
de
Almei
da,
F.
L.
A.
Viei
r
a,
“
Modeli
ng
an
d
Analysis
of
an
El
e
ct
r
ic
Veh
ic
l
e
using
PA
MV
E
C
”
,
Enge
nhari
a
Térm
ic
a
(Therm
al
Eng
ine
ering)
,
vol.
17
,
no
.
2
,
pp
.
37
-
40
,
De
c. 20
18.
[2]
M.
Mathe
w,
Q.
H.
Kong,
J.
Mc
Grory,
M.
Fow
ler,
“
Simu
la
t
ion
of
li
thi
u
m
ion
b
at
t
ery
rep
l
acem
en
t
in
a
ba
tt
ery
pac
k
for
applic
at
ion
i
n
elec
tr
ic ve
hi
cles
”
,
Journal
o
f P
ower
Source
s
,
v
ol.
349
,
pp
.
94
-
1
04,
May
2017.
[3]
E.
Che
ma
l
i,
M
.
Preindl,
P.
Malysz,
A.
E
ma
di
,
"El
ec
tro
c
hem
i
ca
l
and
E
l
ec
trost
at
i
c
En
er
gy
Storage
and
Mana
gement
Sy
stem
s
for
El
e
ct
ri
c
Drive
Vehi
cl
e
s:
Stat
e
-
of
-
the
-
A
rt
Review
and
Future
Tre
nds,"
I
EE
E
Journal
o
f
Eme
rging and
S
el
e
ct
ed
Topics
in
Powe
r
Elec
tron
ic
s
,
vo
l. 4, no. 3, pp. 1117
-
1134,
Sept.
2016
.
[4]
I.
B.
Weinstoc
k
,
“
Re
ce
n
t
adv
an
ce
s
in
th
e
US
Depa
rtment
of
Ene
rgy’s
e
ner
gy
storage
t
ec
hnol
ogy
rese
a
rch
an
d
deve
lop
me
nt
pr
ogra
ms
for
hybr
id
e
lectr
i
c
and
e
le
c
tri
c
veh
icles,
”
Journal
of
Pow
er
Source
s
,
vol
.
110,
no
.
2
,
pp.
471
-
474,
Aug.
2
002.
[5]
P.T
.
Mos
el
ey
,
B
.
Bonnet,
A.
Co
oper
,
M.J.
Ke
ll
a
way,
“
L
ea
d
–
ac
i
d
bat
t
ery
chemi
stry
ada
pt
ed
for
hybrid
elec
tr
ic
vehi
c
le
du
ty,
”
Jo
urnal
of
Powe
r
S
ource
s
,
vol
.
174
,
no.
1,
pp.
49
-
53
,
Nov.
2007.
[6]
G.
Mulder,
N.
Omar
,
S.
Pauwe
ls,
M.
Mee
us,
F.
Le
e
ma
ns,
B
.
Verbrugge
,
W.
D
.
Nijs,
P.V.
Boss
che
,
D.
Six
,
J.V
.
Mierl
o,
“
Comp
a
rison
of
commer
ci
a
l
batter
y
cells
in
re
l
ation
to
m
at
er
ia
l
p
rope
rt
ie
s
,
”
E
lectroc
himi
c
a
Acta
,
vol
.
87
,
pp.
473
-
488
,
Jan
.
2013
.
[7]
T.
K.
Ying,
X.P.
Gao,
W
.
K.
Hu,
F.
Wu,
D.
“
N
oré
us,
Stud
ie
s
o
n
re
cha
rg
ea
bl
e
NiMH
bat
t
eri
es,
”
Int
ernati
ona
l
Journal
of
Hydrogen
En
ergy
,
vo
l.
31
,
no
.
4
,
pp
.
5
25
-
530,
Mar
.
20
06.
[8]
A.M.
Jarushi,
N.
Schofie
ld
,
"Bat
t
ery
and
super
capac
i
tor
com
b
inat
ion
for
a
ser
ie
s
h
ybrid
elec
t
ric
v
e
hic
l
e,
"
5th
I
ET
Inte
rnational
Co
nfe
renc
e
on
Pow
er
Elec
troni
cs,
Mac
hine
s and
D
rive
s
,
Br
ight
on
,
UK
,
2010,
pp
.
1
-
6.
[9]
M.G.
Cari
gn
ano
,
J.M.
Cabello,
S.
Junco,
“
Si
zi
n
g
and
p
erf
orm
an
ce
ana
lysis
of
b
at
t
ery
pa
ck
in
e
l
ec
tr
ic
v
ehicle
s,
”
IEE
E
Biennial C
ongress
of
Arge
nti
na
(
AR
GENC
ON),
Bariloch
e,
2014,
pp
.
240
-
2
44.
[10]
M.
Al
-
Z
areer,
I
.
Dince
r,
M.A
.
Rosen,
“
Perform
a
nce
assess
me
nt
of
a
n
ew
hydrog
en
cooled
pr
ism
at
i
c
b
at
t
ery
pa
ck
arr
angeme
nt
for
hydroge
n
hybrid
elec
tr
ic
vehicle
s
,
”
Ene
rgy
Conver
sion
and
Manage
ment
,
vol
.
173
,
pp.
303
-
319
,
Oct.
2018
.
[11]
M.W
.
Verbrugg
e,
C
.
W
.
W
am
pl
e
r,
“
On t
h
e
opt
imal
siz
ing
of
b
at
t
e
rie
s for
e
lectr
i
c
v
ehi
c
le
s a
nd
the
i
nflue
nc
e
of
f
ast
cha
rge
,
”
Journal
of
Powe
r Sourc
es
,
vol
.
384
,
pp
.
312
-
317,
Apr.
2
018.
[12]
L.
H.
Saw,
Y
.
Y
e,
A
.
A.O.
Ta
y
,
“
Inte
gr
at
ion
issues
of
li
th
ium
-
io
n
batter
y
int
o
e
le
c
tri
c
veh
ic
l
es
bat
t
ery
p
ac
k,
”
Journal
of
Cle
an
er
Production
,
v
ol.
113
,
pp
.
1032
-
1045,
Feb
.
201
6.
[13]
J.
Kim,
J.
Oh,
H.
Lee,
“
Revie
w
on
bat
t
ery
therma
l
ma
nag
eme
nt
sys
te
m
for
elec
tr
ic
v
ehi
c
le
s
”
,
Appl
i
ed
Therm
al
Engi
ne
ering
,
vol
.
149
,
pp
.
192
-
2
12,
Feb
.
2019
.
[14]
R.
Gar
cia
-
Valle,
J.A.
Pec¸
as
Lo
pes
(ed
s.)
,
“
El
e
ct
ri
c
Veh
ic
l
e
Int
egr
ation
int
o
Modern
Pow
er
Ne
tworks,
Pow
e
r
El
e
ct
roni
cs
and
Pow
er
Sy
stem
s,
”
Springer
Sci
en
ce
Busin
ess Med
ia
New
York,
20
13.
[15]
D.
Hülsebusch,
S.
Schwunk,
S.
Caron,
B.
Propf
e,
“
Mode
li
ng
an
d
simul
ation
of
el
e
ct
ri
c
veh
ic
l
es
-
The
eff
ect
of
diffe
ren
t
Li
-
ion
bat
t
ery
technolo
gie
s
,
”
The
25th
World
Bat
t
ery
,
Hybrid
and
Fue
l
Cel
l
El
e
ct
ri
c
Vehic
l
e
Symposiu
m
&
E
xhi
bi
ti
on
,
E
VS
-
25
Shenzhe
n
,
China,
Nov.
5
-
9
,
2010
.
[16]
F.
Chang
,
F.
Ro
em
er
,
M
.
B
aumann,
M.
Lienka
mp,
“
Model
li
ng
and
Ev
al
ua
ti
on
of
B
at
t
ery
Pack
s
with
Diff
ere
n
t
Number
s of
Par
a
ll
eled
C
el
ls,
”
Wo
rld E
l
ec
tri
c Ve
hi
cl
e
Journal
,
vol
.
9,
no
.
8
,
pp
.
1
-
1
5,
2018
.
[17]
E.
Vergori
,
F.
Moce
ra
and
A
.
So
mà
,
"Ba
tt
ery
mo
del
ing
and
si
mulati
on
using
a
pro
gra
mmable
t
esting
equ
ipm
en
t,
"
2017
9th
Compu
te
r Sc
ie
nc
e
and
El
e
ct
ronic
Engi
n
ee
ring (
C
EE
C)
,
Colc
hest
er,
pp.
1
62
-
167
,
2017
[18]
J.
Seo,
S.
Sank
ara
subram
anian,
C.
S.
Ki
m,
P.
Hovington,
J.
Praka
sh,
K.
Z
agh
ib,
“T
h
ermal
ch
ara
c
te
ri
zation
of
Li
/sulfur
,
Li/
S
–
Li
FePO
4
and
Li
/S
–
Li
V3O
8
c
el
ls
using
Isoth
erm
a
l
Micro
-
Ca
lori
metry
and
A
cc
e
le
r
at
ing
R
at
e
Cal
orimetry
,
”
Jo
urnal
of Powe
r S
ource
s
,
Vol
.
289
,
pp
.
1
–
7
,
2015
.
[19]
J.
La
r
mi
ni
e, J.
L
owry,
“
El
e
ct
ri
c Vehic
l
e
T
ec
hno
l
ogy
Explaine
d
”,
John W
iley
&
S
ons L
td, E
ng
la
n
d,
2003
.
[20]
A.G.
Simpson,
“
Para
metric
Mod
el
li
ng
o
f
Ene
rgy
Consumpti
on
i
n
Road
Vehicle
s
”,
Ph.D
Th
esis,
The
Univer
si
ty
of
Quee
nsland
,
2
005.
[21]
S.S.
Reddy
,
"O
pti
ma
l
op
erati
o
n
ma
n
ageme
nt
of
Grid
-
Conne
c
te
d
mi
cro
g
rids
under
un
ce
rt
ai
nt
y",
Indone
sian
Journal
of
Elec
t
rical
Engi
ne
erin
g
and
Computer
Sci
en
ce
,
vol
.
16
,
no.
3,
pp.
1163
-
1170,
De
c. 2019
.
[22]
H.
He,
R
.
Xion
g,
H.
Guo,
“
Onl
ine
est
im
a
ti
on
o
f
mode
l
p
arame
t
ers
and
sta
te
-
o
f
-
cha
rge
o
f
Li
FeP
O
4
bat
t
eri
es
in
el
e
ct
ri
c
v
ehi
c
le
s,
”
App
li
ed
En
ergy
,
vo
l. 89, no. 1,
pp.
413
-
420
,
Jan
.
2012
.
[23]
V.
Mara
no
,
S.
Onori,
Y.
Gue
z
enne
c
,
G.
R
izzo
ni,
N.
Made
l
la,
"Lit
hium
-
ion
ba
tt
eries
li
fe
esti
m
at
ion
for
plug
-
in
hybrid
e
le
c
tric
v
ehi
c
le
s,"
I
EEE
V
ehi
c
le
Powe
r an
d
Propulsion
Co
nfe
renc
e
,
Dea
rb
orn,
MI,
2009,
p
p.
536
-
543
.
[24]
Z.
Ch
en,
N.
Gu
o,
X.
Li,
J.
Shen
,
R.
Xiao
,
S.
Li,
“
Ba
tt
ery
Pack
Grouping
and
C
apa
c
it
y
I
mprovement
for
E
lectr
i
c
Vehic
l
es
Based
on
a
G
ene
t
ic Alg
orit
hm
,
”
Ene
rgi
e
s
,
vol. 10, pp.
1
-
15,
2017
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
D
ri
S
ys
t,
V
ol
.
11
, N
o.
4
,
D
ecembe
r
2020
:
1987
–
1994
1994
[25]
S.S.
Reddy
,
"
Solving
opti
m
al
gene
ra
ti
on
sche
duli
ng
problem
of
Microgr
id
using
t
ea
ch
ing
le
arn
ing
b
ase
d
opti
mization
al
g
orit
hm",
Indone
s
ian
Journal
o
f
E
le
c
tric
al
Engi
n
e
ering
and
Comp
ute
r
Scienc
e
,
vol
.
17,
no.
3
,
pp
.
1632
-
1638,
Mar
.
2020.
[26]
X.
Hu,
S
.
J.
Mo
ura
,
N.
Murgovs
ki,
B.
Eg
ard
t
,
D.
Cao
,
"Inte
gr
at
e
d
Opti
mi
z
at
ion
of
Ba
tt
ery
Si
zi
n
g,
Ch
arg
ing
,
and
Pow
er
Mana
ge
me
nt
in
Plug
-
In
Hybrid
El
e
ct
r
ic
Vehi
cl
es,
"
IE
E
E
Tr
ansacti
ons
on
Control
Syst
ems
Technol
og
y
,
vol.
24
,
no
.
3
,
pp
.
1036
-
1043
,
Ma
y
2016.
[27]
S.S.
Red
dy
,
“
Multi
-
Obje
ct
iv
e
Based
Opt
im
a
l
Sch
edul
ing
o
f
Microgr
id
Co
nsideri
ng
Unce
r
ta
inties”
,
IEEE
Inte
rnational
C
onfe
renc
e
on
Cutt
ing
-
edg
e
Technol
og
ie
s
in
Engi
ne
ering
(
I
Con
-
CuT
E)
,
No
v.
14
-
16
,
2019
,
Luc
know,
U
tt
ar
Prade
sh,
Ind
ia
.
[28]
B.
Bend
je
di
a,
N
.
Ri
zoug,
M.
B
oukh
nife
r,
F.
Boucha
fa
a,
"H
ybrid
Fuel
Cell/Bat
te
ry
Sourc
e
Si
zing
and
Ene
rgy
Mana
gement for
Automot
i
ve
Ap
pli
c
at
ions",
IFAC
-
Pape
rs
OnL
ine
,
vo
l. 50, no. 1,
pp.
4745
-
4750
,
J
ul.
2017
.
[29]
S.S.
Reddy,
J.Y.
Park,
C.
M.
Ju
ng,
“Opt
im
a
l
O
per
ation
of
Mic
rogrid
Us
ing
Hybrid
Dif
fer
ent
i
al
Evo
lut
ion
an
d
Harm
ony
Sear
ch
Algorit
h
m”
,
Fr
onti
ers
in
Ene
rg
y
,
vo
l. 10, no. 3,
pp.
355
-
362
,
Se
pt.
2016
.
[30]
L.
Zh
ang,
X.
H
u,
Z
.
W
ang,
F.
Sun,
J.
Deng,
D
.
G.
Dorrel
l,
"M
ult
iobjective
Op
ti
mal
Siz
ing
of
Hybrid
Ene
rgy
Storage
Sys
te
m
for
El
e
ct
r
ic
Veh
ic
l
es,
"
IEEE
Tr
ansacti
ons
on
V
ehi
cu
lar
Techno
logy
,
vo
l.
67
,
n
o.
2,
pp
.
1027
-
1035,
Feb
.
2018
.
[31]
S.S.
Reddy,
“Opti
mal
Opera
ti
o
n
of
Microgr
id
conside
ring
R
en
ewa
ble
Ene
rgy
Source
s,
Elec
tric
Vehicle
s
and
Dema
nd
R
esponse”
,
E3S
W
eb
o
f Confe
renc
es,
vo
l
.
87
,
pp
.
1
-
6
,
Ma
r.
2019
.
[32]
E.
T
ara,
S.
Shah
idi
nejad,
S.
Fi
li
z
ade
h,
E.
B
ibe
au
,
"Batt
ery
Stor
ag
e
Sizi
ng
in
a
Re
t
rofit
t
ed
Plug
-
in
Hybrid
El
e
ct
ri
c
Vehic
l
e,
"
I
EEE
Tr
ansacti
ons on Vehicular
Techn
ology
,
vol
.
59
,
n
o
.
6
,
pp
.
2786
-
2
794,
July 2
010
.
[33]
J.
Snous
si,
S.B.
El
gh
al
i
,
M.
Be
nbouzi
d,
M.F.
Mimouni
,
"O
ptimal
Sizi
ng
of
Ene
rgy
Stor
age
Sys
te
ms
Us
ing
Freque
ncy
-
Sepa
rat
ion
-
B
ase
d
En
erg
y
Man
ageme
nt
for
Fue
l
Cell
Hybrid
E
lectr
i
c
Vehic
l
es,
"
IEEE
Tr
ansacti
ons
on
Ve
hi
cul
ar Tec
hn
o
logy
,
vol
.
67
,
n
o.
10
,
pp
.
9337
-
9346,
Oct
.
2018
.
Evaluation Warning : The document was created with Spire.PDF for Python.