Intern
ati
o
n
a
l
Jo
u
r
n
a
l
of
P
o
we
r El
ec
tr
on
i
c
s
an
d D
r
i
v
e
S
y
stem
(I
JPE
D
S)
V
o
l.
11
, N
o
. 2, Jun
e
20
20
, pp
. 57
1
~
57
9
I
SSN
:
208
8-8
6
9
4
, D
O
I:
10.
115
91
/i
jp
e
d
s.v
1
1
.i2
.
p
p57
1-5
79
5
71
Jo
urn
a
l
h
o
me
pa
ge
: h
t
t
p
:/
/ijpe
d
s.
i
a
e
s
c
o
re.
c
o
m
Active cell balancin
g for electri
c
vehi
cle battery m
a
nagem
e
nt
system
Th
i
r
uv
on
asun
dari
Dur
a
i
s
a
m
y
,
De
e
p
a
k
a
l
i
y
aper
um
al
De
pa
rt
me
nt
o
f
Ele
c
t
r
ic
a
l
a
n
d
Elec
t
ron
i
c
s
En
gi
ne
erin
g,
Am
rita
Sc
h
o
ol
of
E
n
g
i
ne
e
r
ing
,
In
dia
A
r
ticle In
fo
A
B
S
T
RAC
T
A
r
tic
le
h
i
st
o
r
y:
Rec
e
i
v
ed
Se
p 5
,
20
19
Rev
i
sed
No
v 11
, 20
19
Acc
e
pt
e
d
Fe
b 4, 2
0
2
0
T
h
e
shri
nk in
acc
e
ssibi
l
it
y of
p
e
t
r
ol
eu
m pro
duc
ts and
in
c
r
em
en
t
in
a
s
set
requ
est are
ev
en
tual
o
u
tco
m
es fo
r El
ectric
a
l Vehi
cles
(
E
Vs). The
battery h
a
s
an
impa
ct o
n
t
h
e p
e
rfo
rman
ce
of
elec
tric
al v
e
hic
l
es,
th
e
d
r
iv
in
g r
a
ng
e
.
Lith
iu
m
io
n
(
L
i-
ion
)
ch
emistry
is
ex
tr
em
ely
s
e
nsi
t
ive
to
ov
erch
ar
ge
and
d
eep
d
i
sc
ha
rg
e, whi
c
h ca
n h
a
rm
th
e b
a
tt
e
r
y,
sh
ort
e
ni
ng
i
t
s p
e
ri
od
o
f
ti
m
e
, a
n
d
even
in
f
l
ict
i
n
g
r
i
sk
y
th
in
gs
.
Th
e
B
a
t
t
er
y
M
a
nage
men
t
S
y
s
t
em
(
B
M
S
)
comp
ris
e
s o
f
th
e
con
s
equ
e
n
t
p
a
rt
s: man
a
gem
e
nt
,
eq
ual
i
za
tion
an
d
prote
c
tion
.
Of th
e thre
e
c
o
mpo
n
ents, equ
a
liza
t
ion
is
tha
t
th
e m
o
st
cru
c
ia
l w
i
th
r
e
s
p
ect to
th
e dur
ab
il
it
y
of
th
e
b
a
tt
e
r
y
f
r
a
mew
o
r
k
. Th
e ab
i
l
i
t
y
o
f
th
e f
u
l
l
p
a
ck
dimin
i
s
h
es
rapid
l
y a
m
id
the
pro
ced
ure wh
ich
lea
d
s to
degr
ad
a
t
io
n of th
e fu
ll
bat
t
e
r
y
f
r
amewo
r
k.
Th
is
co
nd
it
io
n
is
ex
tr
e
m
e
o
n
c
e
th
e b
a
tt
er
y
i
n
c
o
r
p
o
r
at
es
a
more nu
mb
er
of
cells
in
series
an
d
freq
u
e
nt ch
arg
i
n
g
is
con
v
ey
ed
throu
g
h
th
e
b
a
tte
ry
st
rin
g
. Th
e
c
e
l
l i
m
ba
la
nc
e d
u
ri
ng c
h
a
r
gin
g
, d
i
sc
ha
rgi
ng i
s
a
ma
jo
r
is
su
e
in
b
a
t
t
ery
s
y
s
t
ems
u
s
ed
in
EV
s. To
c
i
rcu
m
v
e
nt the
c
e
ll
im
balan
c
e
,
cell
balan
c
ing is
u
s
e
d
.
Cel
l
balan
c
in
g
en
han
c
es batte
ry safety
an
d exten
d
s
b
a
ttery
l
i
fe.
Th
is
pa
pe
r
d
i
sc
usse
s a
b
o
u
t
d
i
ffe
re
n
t
ac
t
i
v
e
ba
l
a
nc
in
g me
th
od to
i
n
c
r
e
a
se
th
e
lif
e
s
p
an
of
the
bat
t
ery
mod
u
l
e. B
a
sed
on
th
e comp
aris
on
,
t
h
e ind
u
cto
r
bas
e
d
ba
lanc
in
g
meth
od
fo
r
6
0
V
b
a
ttery
sy
stem is
imp
l
emen
ted
in
th
e M
A
TLA
B
/S
ims
cape
en
viro
n
m
en
t an
d
the
res
u
lts
ar
e d
i
scus
sed
.
Ke
yw
ords:
Ba
t
t
e
r
y ma
na
g
e
ment
s
y
st
em
C
e
ll
b
a
la
n
c
i
ng
El
ect
ri
c ve
hi
cl
e
Lit
h
iu
m i
o
n b
a
tte
ry
St
at
e
of
cha
r
g
e
Th
is
is a
n
o
p
en
acces
s a
r
ticle
un
d
e
r the
C
C
B
Y
-SA
licens
e
.
Corres
p
o
n
din
g
A
u
t
h
or:
Th
iru
von
a
s
u
nda
r
i
D
u
r
a
isamy,
Depa
rt
me
nt o
f
Ele
c
t
r
i
c
a
l
and
El
e
c
t
r
oni
cs
E
n
gi
nee
r
i
n
g
,
Am
ri
ta
Vi
sh
wa
Vi
d
y
a
p
ee
tha
m
U
n
i
v
e
r
si
ty, A
m
ri
t
a
Sc
hool
of
E
ngi
nee
r
i
ng,
Ba
ngal
o
re,
K
a
rnat
a
k
a
,
In
di
a.
Emai
l:
sun
d
a
r
i
s
a
m
y@
gma
i
l
.
c
o
m
1.
IN
TR
O
DUCTION
B
a
t
t
e
ry frame
wo
rk
s ha
vi
ng
Li
-i
on
c
e
l
l
s are
i
n
cl
i
n
ed
to
fas
t
cel
l
de
te
ri
orat
i
on
a
n
d
b
u
r
st
i
n
t
o
fl
a
m
e
s
or
ca
use
t
o
de
to
n
a
te
.
Int
e
l
l
i
ge
nt
ci
rc
uit
s
a
n
d p
r
og
ra
mmi
n
g
a
dva
nce
m
e
n
ts
a
r
e
set
up
t
o
mo
d
e
ra
te
t
h
ese
i
m
p
e
ndi
ng
t
h
rea
t
s. In
a
m
u
lt
i
ce
ll
ba
t
t
e
r
y pac
k
,
w
h
ic
h
is norma
l
l
y ut
i
l
iz
ed
i
n
E
V
s r
e
st
orat
i
v
e ha
rd
ware
, se
t
t
i
ng c
e
l
ls
i
n
arra
nge
ment
l
e
ads
t
o
t
h
e
l
i
kel
i
ho
o
d
o
f
t
h
e ce
ll
imbal
a
nc
e,
a sl
o
w
, h
o
w
e
ver,
c
o
nsta
nt
deg
r
a
d
a
t
ion o
f
th
e
b
a
tt
er
y.
C
e
lls
ar
e
of
i
n
d
i
stin
gu
i
s
h
a
b
l
e n
a
tu
r
e
.
Th
ere is
con
s
ta
n
tly
sligh
t
ch
ang
e
i
n
th
e co
nd
iti
o
n of
t
h
e St
at
e
o
f
Cha
r
ge
(S
oC
),
c
a
p
ac
it
y,
se
l
f
di
scha
rg
e
,
t
e
mpera
t
ure
a
n
d
i
n
t
e
rna
l
i
m
pe
dance
q
u
a
li
t
i
e
s
,
not
w
i
t
h
st
an
di
ng
for ce
ll
s t
h
a
t
are
a
si
mil
a
r
mo
del
from a
simi
la
r ma
ker
and
e
v
e
n
from
a
si
mil
a
r
c
l
us
t
e
r
of
c
r
e
a
tio
n
[1
].
Wh
en
b
u
ild
ing
mu
lt
i c
e
l
l
p
a
c
k
s
,
m
a
k
e
r
s
typi
ca
ll
y
sep
a
r
a
te ce
lls
w
ith
co
mp
a
r
at
iv
e So
C
ba
se
d
on
th
e
v
o
lta
g
e
. Vo
lta
g
e
d
i
s
s
imi
l
a
r
i
tie
s b
e
tw
e
e
n
t
h
e
ce
lls
ar
ise
a
f
t
e
r
so
me time
du
e
t
o
si
g
n
i
fi
ca
n
t
c
h
ang
e
in
t
h
e
bat
t
e
ry
va
ri
abl
e
s. B
y
c
h
e
c
ki
n
g
t
h
e
v
o
l
t
a
g
e-g
u
i
d
el
i
n
e
poi
nt
of t
h
e
b
a
t
t
e
ry
pac
k
t
h
e c
h
a
r
ge
r re
co
gni
zes
t
h
e full
y
-
c
h
arged
sta
t
e
.
Du
e
t
o
i
n
t
e
rna
l
para
me
t
e
r va
ri
at
i
ons,
a
n
y
ce
ll
i
n
t
h
e
bat
t
ery
pack
ma
y
re
ach
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-8
6
94
Int
J
P
o
w
Ele
c
& D
r
i
S
y
st, V
o
l
.
1
1
,
N
o
.
2, Ju
ne
20
2
0
:
5
7
1
–
579
57
2
t
h
e o
v
erv
o
l
t
a
g
e l
i
mi
t c
o
mpa
r
es to ot
her
ce
l
l
s i
n
t
h
e st
ri
ng
. The
co
n
d
i
t
i
on o
f
the
o
v
e
r
c
h
a
r
ge
d ce
ll
wo
rsens
f
u
r
t
h
e
r
b
y
rep
eate
d
ch
arg
e
and
d
i
sch
a
r
g
e
c
y
cl
es an
d
it
s
l
ead
s t
o
cap
ac
it
y
d
e
te
ri
or
ati
o
n
.
To
gi
ve a
d
yna
mic
sol
u
t
i
o
n
fo
r
t
h
i
s
i
s
s
u
e w
h
i
l
e c
onsi
d
eri
ng
t
h
e age
a
l
on
g
wi
th t
h
e
w
o
rki
ng st
at
es o
f
t
h
e bat
t
e
ri
e
s
, t
h
e B
M
S
w
oul
d a
t
te
mpt
t
o
i
n
t
e
grat
e o
n
e
of the
t
w
o cel
l
equa
li
za
t
i
o
n
t
e
c
hni
que
s t
o
ba
l
a
nc
e
th
e
ce
ll
s a
n
d
t
o
p
r
ev
e
n
t
t
h
e
m
fro
m g
e
tti
n
g
ov
er
emph
a
s
i
z
ed
[
2
]
:
t
h
e
pass
iv
e and
ac
t
i
v
e
c
e
l
l
e
q
u
a
liza
tio
n
.
Th
e
h
i
g
h
vo
ltag
e
ce
ll
is id
enti
fi
ed
an
d t
h
e
e
x
c
e
s
s
en
erg
y
is
d
i
ssi
p
a
t
e
d
ac
ro
s
s
th
e
r
e
si
sto
r
un
ti
l it
s volt
a
g
e
mat
c
hes wi
t
h
t
h
e we
a
k
cel
l
s
in t
h
e p
a
ssi
ve s
c
heme
[3
]. In t
h
e
act
i
v
e t
o
pol
og
y t
h
e
o
v
e
r
c
h
a
r
ge
d ce
ll
ene
r
g
y
is
eva
c
uat
e
d a
nd
gi
v
e
n
t
o
t
h
e
u
n
d
e
r
c
h
a
r
ge
d ce
l
l
s
by
usi
ng e
n
e
r
g
y
tra
n
sfe
r
ri
n
g
e
l
e
m
e
n
ts [4].
The Fi
gu
re
1 sho
w
s
t
h
e di
ffe
r
e
n
t
ce
ll
ba
l
a
nci
n
g t
o
pol
og
i
e
s
w
h
i
c
h
i
s
a
v
ai
l
a
bl
e
fo
r t
h
e
bat
t
e
ry
p
o
w
ere
d
s
y
st
em
.
Thi
s
p
a
pe
r
di
sc
usses a
b
o
u
t
t
h
e
v
a
ri
ous a
c
t
i
ve
ba
la
nci
n
g t
o
p
o
l
ogi
e
s
al
o
n
g
w
i
t
h
it
s e
qual
i
zat
i
on s
p
e
e
d
,
appl
i
cat
i
o
n, si
z
e
,
c
o
st,
desig
n
a
n
d
e
f
fi
ci
en
c
y
.
Se
ct
io
n
2
expl
ai
n
s
t
h
e
v
a
ri
ous ce
l
l
bal
a
nc
i
ng t
o
p
o
lo
g
i
es an
d
t
h
e
bal
a
nci
n
g
t
e
chni
que
s a
r
e
c
o
m
p
are
d
. S
e
c
t
i
on 3
re
p
r
ese
n
t
s
t
h
e
i
n
d
u
ct
o
r
-
b
ase
d
t
o
p
o
l
o
gy
im
pl
eme
n
t
e
d
for
6
0
V
Li
-
ion
ba
tte
ry
sy
ste
m
in
MA
TLA
B
/Sim
sca
p
e
and
th
e
sim
u
la
tion
r
e
su
lts
a
r
e
d
i
sc
u
ssed
f
o
llowe
d
b
y
th
e
con
c
lusi
on
.
Fi
gu
re
1. Ba
l
a
nci
n
g
t
o
p
o
l
ogi
es
2.
BALANCING TOPOLO
GI
E
S
2.1. Ac
ti
ve
ce
ll
bal
a
nc
in
g
m
e
th
od
In
th
is b
a
lan
c
i
n
g sch
e
me,
th
e e
x
ce
ss
en
ergy
is s
h
if
ted
f
r
o
m
t
h
e o
v
e
rch
a
rg
ed
ce
ll
t
o
t
h
e
w
eak
e
r
c
e
l
l
i
n
t
h
e
pack
. U
n
l
i
k
e
passi
ve
bal
a
nci
n
g
sc
he
me,
he
re
e
n
e
r
gy
i
s
not
wa
st
e
d
as
hea
t
i
n
ste
a
d
it
i
s
t
r
a
n
sfe
r
re
d t
o
ot
he
r
ce
ll
s.
2.1.
1.
C
a
p
a
ci
tor
b
a
sed
t
o
p
o
l
ogie
s
In a ca
paci
t
o
r-ba
s
e
d
to
pol
og
y as re
pre
s
ent
e
d i
n
Fi
gu
re 2
,
the
capa
c
i
t
o
r
s
a
r
e use
d
fo
r excha
n
gin
g
une
q
u
al
cha
r
g
e
amo
ng
n
u
m
e
ro
us
c
e
l
l
s
i
n
the
ba
t
t
e
r
y
p
ack. Si
ngle
S
w
i
t
ched C
a
pa
c
i
t
o
r ut
i
l
i
z
e
s
a
si
ngl
e
ca
paci
t
o
r,
ma
kes t
h
e s
y
st
e
m
mo
re c
o
st
-pr
oduc
ti
ve
t
h
a
n
d
o
uble
ti
e
r
e
d
s
w
i
t
ched
ca
pa
ci
tor a
n
d s
w
i
t
c
hed
ca
paci
t
o
r [
5
].
S
w
i
t
c
h
e
d
C
a
pa
c
i
t
o
r t
r
a
n
sfe
r
s
ene
r
g
y
bet
w
ee
n adj
ace
nt c
e
l
l
s. In
order t
o
re
duce
t
h
e
ba
la
nci
n
g
t
i
m
e
a
c
h
ai
n st
ru
c
t
u
r
ed
sw
i
t
ch
ed
cap
a
c
i
t
o
r
top
o
l
og
y w
a
s
in
t
r
odu
c
e
d
[6
]
an
d se
r
i
e
s
-p
a
r
al
le
l sw
i
t
c
h
ed
cap
a
c
i
t
o
r
and
equa
li
ze
r fo
r
v
a
rio
u
s s
p
ee
d
re
qui
reme
nt
[7
].
A
c
o
uple
o
f
c
h
ange
s
made
t
o
sw
it
che
d
c
a
p
a
c
i
tor
st
ra
te
g
y
re
sul
t
s
i
n
D
o
ubl
e-
Tie
r
ed S
w
it
che
d
C
a
pa
ci
tor
(D
TS
C
)
.
T
h
e
uni
qu
eness i
n
t
h
is i
s
, 2 c
a
pac
i
t
o
rs
are
use
d
for
e
n
erg
y
shutt
l
i
ng
p
u
rp
o
s
es.
Fo
r
m
o
re
s
e
ri
es c
o
nnec
t
e
d
c
e
l
l
s t
h
e
ba
la
nci
n
g spee
d
o
f
DTS
C
is sl
owe
r
a
n
d
i
t
i
s
ove
rcome
i
n
[8] b
y
usi
n
g
re
so
n
a
nt
t
o
pol
ogi
es
.
Mo
d
u
l
a
ri
ze
d
sw
it
che
d
ca
pa
ci
tor
i
s
a di
ffe
re
nt
t
ype
o
f
capa
c
i
t
ive
st
ora
g
e
devi
ce
t
o
p
o
l
o
gy w
h
i
c
h a
l
s
o
i
n
cl
ude
s
s
hut
tl
i
ng
c
a
p
ac
it
o
r
t
echni
que
s [9
-1
1].
It
i
n
c
l
u
d
e
s
bat
t
e
ry
pac
k
modul
a
r
iz
at
i
o
n
,
spl
i
t
t
i
ng
t
h
e
bat
t
e
ry
st
ri
n
g
in
to
mo
du
le
s or
grou
p
s
. To
r
e
d
u
c
e
th
e
s
w
i
t
c
h
in
g
lo
sse
s
,
co
ndu
c
tio
n
l
o
sse
s
a
n
d
to
impr
ov
e
t
h
e ba
la
nci
n
g s
p
ee
d
re
s
o
n
a
nt
swi
t
c
h
e
d
ca
pa
c
i
tor,
base
d
on
t
h
at
t
h
e
bal
a
nci
n
g
i
s
use
d
[1
2,
13
].
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
Act
i
v
e
ce
l
l
bal
anc
i
n
g
for
el
ec
tri
c
vehi
c
le
b
a
t
t
e
r
y m
ana
ge
me
nt
sy
st
e
m
(T
hi
ruv
o
n
a
sun
d
a
ri
Dur
a
i
s
am
y
)
5
73
2.1.
2.
Ind
u
c
t
o
r
s/
tran
sform
e
rs-b
ased
top
o
logy
In
duc
t
o
r
/
tra
n
s
f
ormer ba
se
d a
c
t
i
ve e
qua
l
i
z
e
r a
s
re
pre
s
e
n
te
d in
F
i
g
u
re
3
trans
f
e
r
s
ene
r
gy a
m
o
n
g
mu
l
tip
l
e
ce
lls
w
ith
th
e h
e
l
p
of ma
gn
et
ic
compo
n
e
n
t
s
su
c
h
a
s
in
d
u
ct
o
r
s
a
n
d tr
an
sf
orm
e
rs.
S
i
ng
le
I
ndu
cto
r
C
e
l
l
Ba
l
a
nci
ng i
s
b
a
sed
on t
h
e
b
u
c
k
b
o
o
st
t
e
c
h
niq
u
e
s
whe
r
e
ener
g
y
tra
n
sfe
r
t
a
kes
pl
ac
e f
r
o
m
hi
ghl
y c
h
a
r
ge
d
bat
t
e
ry
t
o
l
o
w
cha
r
ge
d
bat
t
e
ry
a
n
d t
o
a
c
h
i
e
ve
t
h
i
s
v
o
lt
a
g
e
,
m
o
ni
tori
ng
c
i
rcui
ts a
r
e
re
qui
red
f
o
r e
v
er
y
b
a
t
t
e
r
y
[1
4].
M
u
l
t
i
pl
e
i
nduc
t
o
r c
e
l
l
b
a
l
a
n
c
i
n
g
t
o
po
lo
gy us
ing
m
o
re
th
an on
e i
ndu
ct
or
t
o
b
a
l
a
nc
e
th
e mu
lti
p
le
ce
ll
s
si
mu
lta
n
e
o
u
s
l
y
.
Ce
ll
b
a
la
n
c
ing
b
a
sed
on
optim
iz
ed
c
e
l
l
to c
e
l
l
, an
y c
e
l
l
to a
ny ce
ll
a
n
d
p
a
r
a
l
l
el
indu
c
t
or
a
r
c
h
it
ec
tur
e
is
d
i
s
c
u
ssed
in
[15
-
18
]
.
In t
h
e si
n
g
l
e
t
r
a
n
sf
o
r
mer
cel
l
t
o
p
o
l
ogi
es
o
n
l
y
o
n
e
t
r
a
n
sfo
r
mer
is
use
d
t
o
share
t
h
e
cha
r
g
e
be
t
w
e
e
n
th
e
b
a
tt
er
ie
s
wit
h
f
a
s
t
e
q
u
a
l
i
zat
io
n
sp
e
e
d
a
n
d
low
magn
et
ic
lo
sse
s
[
1
9
,
20
].
It
tr
an
sf
er
s
e
n
e
r
gy
from
a p
a
c
k
t
o
t
h
e
un
de
rcha
rg
e
d
ce
ll
c
a
l
l
e
d
as
pa
ck
t
o
ce
ll
met
h
o
d
an
d
o
v
e
r
c
h
a
r
ge
d
c
e
l
l
to
t
h
e
ent
i
re
pa
ck
ca
l
l
e
d
as
ce
l
l
t
o
p
a
ck
me
thod
. M
u
lti
p
l
e
tra
n
sfo
r
mer
t
o
po
log
i
es
c
a
n
b
a
lan
c
e
m
o
r
e
th
an
on
e
ce
ll
a
t
t
h
e
tim
e
of
imb
a
l
a
n
c
e
.
2.1.
3.
C
o
n
v
er
ter
b
a
sed
t
o
p
o
l
ogy
Thi
s
dy
na
mi
c
ce
ll
equal
i
za
ti
on
c
i
rcui
t
a
s
re
prese
n
t
e
d
i
n
F
i
gu
re 4
bal
a
n
c
es
t
h
e i
m
ba
la
nced
ce
ll
s in
th
e
p
a
c
k
thro
ug
h
a DC-
D
C
co
nv
er
te
r [21
,
2
2
],
fo
r
ex
a
m
p
l
e
,
bu
c
k
-b
oo
st or
for
w
ard c
o
nv
ert
e
r
.
Con
v
e
r
t
er
base
d
to
pol
ogi
es a
r
e
very e
f
fi
c
i
e
n
t
an
d
ha
ve a
go
o
d
c
ont
rol
o
v
e
r
t
h
e
po
we
r
fl
ow
[23
-
25].
In a
forw
ard
c
o
nv
ert
e
r
,
in
pr
e
s
e
n
ce
of vo
l
t
a
g
e d
i
f
f
e
r
e
n
ce,
t
h
e c
e
l
l
w
h
ic
h
i
s
h
a
v
i
ng
h
i
gh e
n
ergy
is tr
a
n
sf
err
e
d
t
o
t
h
e
o
t
h
e
r
w
e
ak
c
e
l
l
s th
ro
ugh
t
r
an
sforme
r
w
i
n
d
i
ng
s, d
i
od
e
s
a
nd swi
t
che
s
[2
6]. In
t
h
e Fl
y ba
c
k
co
n
v
erte
r-ba
sed
ce
ll
b
a
la
n
cer
, wh
en
th
e
au
x
i
l
i
ar
y
sid
e
sw
i
t
ch
is
tur
n
ed
o
n
,
t
h
e
ene
r
gy
g
e
ts d
e
live
r
ed
t
o
ce
lls w
ith
low
v
o
l
ta
g
e
f
r
o
m
hi
gh
v
o
lt
age
c
e
l
l
s
t
h
ro
ug
h t
h
e
di
ode
si
nc
e
t
h
e
esti
mat
i
on o
f
hi
gh
v
o
l
t
a
g
e o
n
a
ny ce
l
l
s ge
ts
pu
t
a
w
ay
i
n
th
e
tr
a
n
sfo
r
me
r [2
7]
.
F
u
l
l
-
b
ri
dge
C
o
nve
rt
er i
s
al
so
cal
l
e
d a
s
full
y c
ont
rol
l
ed c
o
n
v
e
r
t
e
r. B
oos
t
and
buc
k m
ode a
r
e t
w
o
mode
s
of
o
p
e
r
at
i
on
of
ful
l
-
b
ri
dge c
o
nve
rt
er
[2
8
]
. T
h
e
c
u
k
c
o
nve
rt
er i
s
l
i
ke
buc
k-
b
o
o
s
t
c
e
l
l
bal
a
nc
er. It
ca
n
in
c
r
em
e
n
t
o
r
d
e
cr
e
a
se th
e
ou
tpu
t
v
o
l
tag
e
.
I
t
c
a
n
b
e
a
p
p
lic
ab
l
e
fo
r
b
a
la
n
c
ing
on
ly th
e n
e
ig
hbo
ur
ing ce
ll
s
[2
9,
3
0
].
Th
e
buc
k
boost
t
o
p
o
l
o
gy
i
s
use
d
whe
r
e
t
h
e
v
o
lt
age
devi
a
t
i
o
ns
a
m
o
n
g
the
ce
ll
s
are
mi
n
i
m
u
m
an
d
t
h
e
a
p
pli
c
a
t
ion
s
n
e
e
d
hig
h
bal
a
nci
n
g
c
u
rre
n
ts
[31
]
.
Q
u
a
s
i
-
Re
sona
n
t
co
n
v
erte
r i
s
a
hig
h
l
y
ef
fi
ci
ent
c
onve
rt
er
beca
u
s
e t
h
e
s
w
i
t
che
s
are
on
&
off
at
z
e
r
o
vol
ta
ge
a
nd/
o
r
zero
cu
rre
n
t
.
I
n
t
h
is e
q
ual
i
z
e
r
in
duc
t
o
rs
&
capa
c
i
t
ors
are
made
as
t
h
e
re
son
a
nt
t
a
n
k
t
o
a
t
t
a
i
n
th
e
ZC
S
fu
n
c
tio
n [3
2]. R
a
mp Co
nv
er
te
r
i
s
a
ddi
ti
o
n
al
l
y
a
n
enha
nc
em
ent
f
o
r t
h
e
mul
t
i
pl
e
wi
n
d
i
ng t
r
a
n
sf
orme
r
e
q
u
a
l
i
z
a
t
i
on
c
i
r
c
u
it.
Th
is
t
o
po
log
y
ju
st
n
e
e
d
s o
n
e
add
ition
a
l
(op
tio
n
a
l)
tw
i
s
tin
g
for
t
h
e
p
a
i
r
of
ce
lls r
a
th
e
r
th
a
n
on
e
f
o
r ever
y ce
ll [
33]
.
F
i
gu
re
2.
C
a
pa
c
i
tor B
a
se
d
F
i
gu
re 3.
Ind
u
c
t
or/
T
r
a
n
as
fo
rm
er
B
a
s
e
d
F
i
gure
4. C
o
nv
erte
r B
a
se
d
2.2. C
o
mp
ar
i
s
on
o
f
acti
ve b
a
l
a
n
c
i
n
g t
o
p
o
l
ogi
es
The
Ta
bl
e.1
com
p
are
s
t
h
e
vari
o
u
s cel
l
bal
a
nc
in
g t
o
pol
og
i
e
s
ba
se
d o
n
t
h
e
bal
a
nc
in
g spe
e
d
,
r
e
l
i
a
b
ili
ty
,
co
n
t
r
o
l s
t
r
a
t
e
gy
,
ef
fi
ci
en
c
y
, e
t
c.
Th
e c
o
n
t
r
o
l
syste
m
and
p
l
an
p
e
r
s
p
e
ct
iv
es
are th
e
two
sign
ifi
c
a
n
t cr
it
er
ia
s
for
th
e cho
i
c
e
o
f
a
c
t
i
v
e
c
e
l
l
b
a
la
n
c
i
ng to
polo
g
i
e
s
. Co
n
t
rol qu
ali
t
ie
s a
r
e
id
en
tif
i
e
d
w
i
th
d
e
p
e
n
d
a
b
ilit
y
and m
e
t
hods
o
f
ac
tiv
i
ty
,
w
h
ich
com
p
ri
ses
of c
h
arge
a
n
d
di
sc
ha
rge c
o
nt
rol
[34
,
35
].
B
a
si
c
co
nt
rol
i
m
pl
ie
s be
tt
er de
pen
d
abi
l
it
y. In l
i
g
ht o
f
th
e
cor
r
e
l
a
ti
on
t
h
e
ind
u
c
t
o
r-b
a
s
ed
t
o
po
l
ogy
i
s
t
h
e b
e
t
t
e
r
topol
o
g
y
f
o
r
ch
a
r
g
i
n
g
a
s
w
e
l
l
a
s
disc
h
a
rg
e
b
a
la
nc
in
g
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-8
6
94
Int
J
P
o
w
Ele
c
& D
r
i
S
y
st, V
o
l
.
1
1
,
N
o
.
2, Ju
ne
20
2
0
:
5
7
1
–
579
57
4
Ta
ble
1. C
o
mp
ariso
n
of a
c
t
i
v
e
c
e
l
l
bal
a
nc
i
n
g
t
o
p
o
l
o
gi
es
T
ype Bal
a
nci
ng
spee
d
Re
lia
bility Contr
o
l
str
a
t
e
gy
Cost
Siz
e
C
h
ar
ge &
Dis
c
h
a
r
g
e
Eff
i
c
i
en
c
y
Ap
pl
ica
tion
S
i
ngle sw
itche
d
c
a
pa
citor
Low
M
e
di
um
H
a
r
d
H
i
gh
Bulk
B
o
th
H
i
gh ++
/++
+
Multi
ple
Ca
pac
itor
s
Ve
ry low
M
e
di
um
M
oder
a
t
e
M
e
dium
M
o
de
r
a
te
B
o
th
H
i
gh
++
/++
+
S
i
ngle/
Mu
l
tiple
I
nductor
s
M
e
dium
M
e
di
um
H
a
r
d
M
e
dium M
o
de
r
a
te
B
o
th
M
e
dium ++
/++
+
S
i
ngle T
r
ansf
or
m
e
r
Low
L
o
w
H
a
r
d
L
o
w
M
o
de
r
a
te
C
h
ar
ge
a
l
one
Lo
w +
+
Multi
ple
Tra
n
s
f
o
r
mer
Low
L
o
w
M
oder
a
t
e
L
o
w
Com
p
ac
t
C
h
ar
ge
a
l
one
Lo
w +
+
F
o
r
w
ar
d
Conver
t
e
r
M
e
dium
M
e
di
um
H
a
r
d
M
e
dium M
o
de
r
a
te
B
o
th
M
e
dium ++
F
l
y bac
k
conver
t
e
r
Low
L
o
w
M
oder
a
t
e
M
e
dium
M
o
de
r
a
te
B
o
th
M
e
dium
++
F
u
l
l
bri
dge conve
rt
er
High
M
e
di
um
H
a
r
d
L
o
w
Com
p
ac
t
B
o
th
H
i
gh
++
Cuk c
onver
t
e
r
M
e
dium
M
e
di
um
H
a
r
d
M
e
dium M
o
de
r
a
te
B
o
th
M
e
dium ++
/++
+
Buc
k
or
/boost
c
onver
t
e
r
High H
i
gh
H
a
r
d
M
e
dium
M
o
de
r
a
te
B
o
th
H
i
gh
++
/++
+
Q
u
asi
-
r
e
sona
nt
c
onver
t
e
r
L
o
w Ve
ry
lo
w
Ha
rd
Lo
w
Mo
d
e
ra
te
Bo
th
Med
i
u
m
+
+
/+
++
Ra
m
p
conve
rt
er
Low
V
e
r
y
low
H
a
r
d
L
o
w
M
o
de
r
a
te
B
o
th
L
o
w
++
+ -
L
o
w pow
er,
++ -
M
e
dium
pow
er,
++
+ - Hi
g
h
pow
e
r
3.
In
du
c
t
o
r
ba
sed a
c
tiv
e
cell
ba
la
ncing
The
i
n
duct
o
r b
a
sed
act
i
v
e cel
l
ba
la
nci
n
g
t
o
pol
o
g
y
i
s
ac
t
u
a
l
i
z
e
d
f
o
r 60
V
Li
-i
o
n
bat
t
e
r
y
frame
wo
rk
whi
c
h c
o
m
p
ri
se
s
of 1
6
cel
l
s
a
s
soc
i
a
t
ed i
n
an
arra
n
g
em
e
n
t
.
R
e
gul
ar i
n
duct
o
r-ba
se
d
t
o
p
o
l
ogy set
s
asi
d
e
a
great
dea
l
o
f
ef
fo
rt
to exc
h
a
n
ge t
h
e
char
ge
from t
h
e
p
r
inc
i
pa
l ce
ll
t
o
t
h
e l
a
st
cel
l
i
n
t
h
e strin
g
.
So, t
h
e effect
i
v
ene
s
s
o
f
the
tr
a
d
iti
on
al
to
po
lo
gy
isn
'
t sa
tisf
a
ct
ory
.
In
th
e
pr
opo
sed
c
e
l
l
b
a
la
n
c
i
n
g
top
o
l
o
g
y
a
sma
l
le
r
n
u
mb
er
o
f
switches
and
i
n
ductor
s
are utilized [17,
18] contras
t
ed
with
c
onve
ntional indu
ct
o
r
-bas
ed tec
h
niques
which
lessen
t
h
e p
o
w
er
mi
sf
ort
u
n
e
s
a
n
d
i
m
pro
v
e t
h
e
p
r
o
f
i
c
i
e
nc
y. T
h
e s
q
uare
cha
r
t o
f
1
6
cel
l
in
duc
t
o
r-base
d
ce
l
l
a
d
j
u
st
in
g
t
opol
o
g
y
i
s
ap
pea
r
e
d
i
n
Fi
g
u
r
e
5
w
h
ic
h c
o
mp
ri
se
s o
f
'
n
'
l
i
t
h
i
u
m i
o
n ce
l
l
s
and
(n
-1) i
n
d
u
ct
o
r
s a
n
d
(2n
-
2)
swi
t
c
h
es so
ab
solut
e
l
y
for 16
ce
ll
s
15
in
duc
t
o
rs an
d
30 s
w
i
t
c
h
es
a
r
e
ut
il
i
zed.
Fi
gu
re
5. Pr
o
pose
d
i
n
d
u
ct
or-ba
s
e
d
t
o
p
o
lo
gy
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t
J
P
o
w
Elec
& Dri
Sy
st
I
SSN
: 208
8-8
6
9
4
A
c
ti
ve
c
e
ll b
a
l
a
n
c
i
n
g fo
r el
ec
tri
c
ve
h
i
c
l
e
ba
t
t
e
r
y ma
nag
e
m
en
t sy
ste
m
(Th
i
ru
vo
na
su
nda
ri
D
u
ra
isa
m
y
)
5
75
3.
1.
C
o
n
t
r
o
l
m
e
th
od
ol
o
g
y
The
c
o
n
t
r
o
l
met
h
odo
log
y
e
x
e
c
u
t
ed
in
t
h
is to
po
lo
gy
i
s
b
a
s
e
d
on
the
v
o
lta
g
e
d
e
vi
at
io
n
am
ong
th
e
c
e
l
l
s.
Ri
gh
t
of
f t
h
e b
a
t
,
all
th
e
c
e
ll v
o
ltage
s a
r
e
est
i
ma
te
d
.
Th
e
pro
c
e
s
s o
f
ac
qu
ir
i
n
g
ab
n
o
rm
al
b
a
tte
ry
c
e
l
l
s
a
n
d
t
h
e a
p
pl
ic
at
ion
of
act
i
v
e c
e
l
l
ba
la
nci
n
g
i
s
de
sc
ri
be
d in
F
i
gu
re
6.
F
i
gu
r
e
6.
Ac
t
i
v
e
bal
a
nci
ng
c
o
nt
r
o
l
f
l
o
w
c
h
art
3.
1.
1.
F
i
r
s
t
st
age
Th
e vo
ltag
e
d
i
stin
ctio
n b
e
t
w
een
t
h
e
od
d nu
mb
er
e
d
cells
(
C
1
,
C3
...
C
1
5)
with its con
tig
uo
us
e
v
en
n
u
mb
er
e
d
c
e
ll
(
C
2
,
C4
..
..
C
1
6
)
is
mo
r
e
th
an
the
thr
e
sh
o
l
d vo
l
t
ag
e
(2
0mV
)
, at
tha
t
po
i
n
t
th
e ov
erc
h
arg
e
d c
e
l
l
is sw
it
ch
ed on
&
th
e indu
c
t
or is ch
a
r
g
e
d
.
Wh
en t
h
e
v
o
l
ta
ge d
i
stin
c
t
i
on is und
e
r
n
e
a
t
h n
o
rm
al
t
h
e
n
th
e sw
itc
h
is tu
r
n
e
d
o
ff,
th
e stor
ed
en
e
r
g
y
i
n
t
h
e induc
to
r
i
s
g
i
v
e
n
t
o
t
h
e low
ch
a
r
g
e
d
ce
ll thr
oug
h
t
h
e bod
y
d
i
o
d
e
of
th
e
sw
it
ch
.
Th
e
vo
lta
g
e
a
c
r
o
ss
th
e
i
ndu
c
t
or
L1
,
(1
)
(2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-8
6
94
Int
J
P
o
w
Ele
c
& D
r
i
S
y
st, V
o
l
.
1
1
,
N
o
.
2, Ju
ne
20
2
0
:
5
7
1
–
579
57
6
W
h
ere,
k
= 2, 3....
.
8
, and
j
=
3, 5.
.
....15
F
o
r
i
n
st
a
n
ce
,
i
f
the
v
o
l
t
a
g
e
c
o
nt
ra
st bet
w
ee
n
od
d nu
mbe
r
ed
c
e
l
l
s is more
t
h
an 2
0
m
V
c
ont
ra
st wit
h
eve
n
n
u
m
b
ere
d
cel
l
s
,
od
d
n
u
m
be
red
swi
t
ch
es S1
...
S
1
5
a
r
e
o
n
an
d t
h
e
e
n
erg
y
i
s
st
ore
d
i
n
t
h
e i
n
d
u
ct
or.
When
it
i
s
b
e
low
th
e
th
r
e
sh
o
l
d
,
th
e
sw
it
ch
e
s
ar
e
turn
e
d
of
f,
th
e i
ndu
ct
or
en
erg
y
is
g
i
v
e
n
to
t
h
e
e
v
e
n
ce
lls
.
3.1.
2.
S
e
c
o
n
d
sta
g
e
In
t
h
e
sec
o
n
d
s
t
a
g
e,
t
h
e i
n
it
i
a
l
two ce
ll
v
o
lt
age
(
V
1
+ V
2
) i
s
c
o
ntrast
e
d
w
i
t
h
t
h
e
ne
xt t
w
o
c
e
l
l
vol
t
a
ge
(V
3
+
V
4
)
i
n
the
ev
en
t t
h
at it
i
s
mo
re
t
h
an 20mV
,
a
t
th
at po
in
t th
e pr
of
ound
ly
c
h
a
r
g
e
d
c
e
ll sw
i
t
ch
is
tur
n
e
d
on
.
Th
e
stra
te
gy
is
sam
e
for th
e
r
e
ma
in
ing
c
e
ll
s
.
(3
)
+
(4
)
W
h
ere
,
k =
1
0
,
11
, 12
,
j
=
5, 7,
9.
.. 15
and
i
= 6
,
8,
1
0
.
.
.
.
.
1
6
3.1.
3.
T
h
i
r
d
s
t
a
g
e
In
th
is st
ag
e
,
t
h
e
c
e
ll vo
lta
g
es (V
1
+ V
2
+ V
3
+ V
4
)
a
r
e c
ont
rast
ed
wi
th
(V
5
+ V
6
+
V
7
+
V
8
) a
nd
th
e
c
e
ll
v
o
lta
ge
s (V
9
+ V
10
+ V
11
+
V
12
)
a
r
e con
t
ra
sted
w
i
th
(
V
13
+ V
14
+
V
15
+
V
16
). In
light
of
t
h
e
voltage
devi
at
i
o
n t
h
e
c
o
rre
s
pon
di
n
g
s
w
i
t
c
he
s
a
r
e t
u
rne
d
o
n
.
(5
)
(6)
3.1.
4.
F
o
ur
th
sta
g
e
In t
h
is st
age
t
h
e t
op
8
cel
l
v
o
l
ta
ges a
r
e
c
ont
rast
ed
w
i
t
h
t
h
e
bott
o
m 8 c
e
l
l
volt
a
ge
s. T
h
e
com
p
ari
n
g
ce
ll
sw
it
che
s
a
r
e tu
rne
d
o
n
de
pen
d
e
n
t
o
n
t
h
e
vol
t
a
ge
co
nt
ra
s
t
.
(7)
Thi
s
pr
o
pose
d
i
n
duct
o
r-ba
se
d t
o
p
o
l
o
gie
s
c
a
n
e
v
e
n
o
u
t
to
p,
c
e
nt
re
a
n
d
base
ce
ll
s a
t
t
h
e
sa
me
ti
me
w
i
t
h
mo
re
p
r
om
in
e
n
t
equ
a
liz
a
tio
n
sp
e
e
d
c
o
n
t
r
a
st
ed w
i
th t
h
e
r
e
gu
la
r te
chn
i
qu
e
.
3.2. Si
mu
l
a
tio
n
r
e
sul
t
s
S
o
a
s
t
o
chec
k
t
h
e
use
f
ul
ness
o
f
the
f
r
ame
w
o
r
k
,
t
h
e
pr
op
ose
d
m
o
del
i
s
si
mula
t
e
d
und
e
r
c
h
ar
gin
g
con
d
i
t
i
on
i
n
t
h
e
MA
TLAB
/
Si
msc
a
pe
e
nvi
ro
nme
n
t
.
T
h
e
ba
tt
ery
m
odel
para
met
e
r
va
l
u
es are
t
a
ke
n
fr
om
the lookup table.
The
voltag
e differe
n
ce bet
w
een
t
h
e cell
s is m
a
de
by
c
h
anging t
h
e
initial condition
of
charge
(
S
o
C
) of
t
h
e
p
a
ck.
Th
e li
thiu
m
i
o
n c
e
l
ls ar
e
ch
arg
e
d a
t
CC
-
C
V mode.
Th
e 16 c
e
lls
ar
e asso
ci
ated
in
arra
nge
ment
so a
s
t
o
get
t
h
e
6
0
V
. T
h
e ca
p
a
ci
t
y
o
f
ea
ch
c
e
l
l
i
s
3
.
3
A
h. T
h
e
i
n
d
u
ct
o
r
va
l
u
e sel
ect
e
d
fo
r t
h
is
t
opol
o
g
y
is
6
0
mH.
F
o
r eve
r
y
c
e
l
l
, t
h
e
te
rmina
l
v
o
l
t
a
g
e
,
ope
n ci
rc
uit
v
o
lt
age
,
t
e
m
p
era
t
ure
a
n
d
S
o
C a
r
e
det
e
rmi
n
ed
.
In
l
i
ght
o
f
t
h
e
te
rmina
l
v
o
lt
a
g
e
of
t
h
e
cel
l
s
t
h
e
equal
i
zat
i
o
n t
e
c
hni
que
i
s
e
x
e
c
ut
ed.
F
i
gu
re 7.
C
e
l
l
1 & Ce
ll
2
s
u
b
s
yst
e
m i
n
M
a
t
l
a
b
Fi
gu
re
8. Ind
u
c
t
or
1 v
o
l
t
a
g
e & cu
rre
n
t
wa
ve
forms
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
Act
i
v
e
ce
l
l
bal
anc
i
n
g
for
el
ec
tri
c
vehi
c
le
b
a
t
t
e
r
y m
ana
ge
me
nt
sy
st
e
m
(T
hi
ruv
o
n
a
sun
d
a
ri
Dur
a
i
s
am
y
)
5
77
Init
i
a
l
l
y
t
h
e v
o
l
ta
ge di
ff
ere
n
c
e
bet
w
ee
n
the
ce
ll
1
and t
h
e
c
e
l
l
2 i
s
25
mV
. The
ce
ll
s a
r
e
char
ge
d at
con
s
i
s
te
nt
cu
rre
n
t
an
d st
ea
dy
volt
a
ge
m
ode
.
The c
e
l
l
s a
r
e
char
ge
d a
t
0.5
C
rat
e
. W
h
e
n
t
h
e c
e
l
l
s
are
c
o
me
t
o
t
h
res
hol
d c
h
a
r
ge
v
o
lt
a
g
e
(
3
.7
), t
h
e
c
e
l
l
bal
a
nci
n
g t
e
c
hni
qu
e
i
s
e
x
ec
ut
ed.
F
i
g
u
re
7
re
pre
s
ent
s
t
h
e
s
u
bsys
t
e
m
for
ce
ll
1
an
d
cel
l
2 i
n
MAT
L
AB
/Si
m
sca
p
e.
F
i
gure
9. V
o
lt
age
&
c
u
rre
n
t
w
a
vef
o
rms
of
ce
l
l
1
&
2
F
i
gure
10.
B
a
t
t
e
ry
ce
ll
SoC
F
i
gure
8
S
h
ow
s the
vol
ta
ge
a
n
d
c
u
rre
n
t
w
a
vef
o
rms
of
t
h
e
i
n
d
u
c
t
o
r
1 du
rin
g
bal
a
nci
n
g. The cel
l
1
v
o
l
t
a
g
e
is h
i
g
h
er
th
an
th
e
c
e
ll 2
v
o
ltag
e
, sw
itch
S1
is tur
n
ed
o
n
. Th
e
i
nduc
to
r1
is c
h
a
r
g
e
d
t
h
ro
ug
h S
1
.O
n
ce
t
h
e
vol
ta
ge
di
ffe
r
e
n
c
e
be
twe
e
n
t
h
e t
w
o c
e
l
l
s
a
r
e
le
ss t
h
a
n
20mV
,
s
w
i
t
c
h
S1 t
u
rne
d
of
f.
At
58
00
s t
h
e
e
n
erg
y
store
d
in the
i
n
duct
o
r
1
i
s
gi
v
e
n to ce
ll
2
t
h
rou
g
h
t
h
e
bo
d
y
di
o
d
e o
f
the
s
w
i
t
ch
S
2
. Si
nc
e
t
h
e t
h
res
h
ol
d
vol
ta
ge
l
i
mi
ts bet
w
ee
n
t
h
e cel
l
s
a
r
e
le
ss,
t
h
e
ce
ll
v
o
l
t
age
varia
t
io
ns
a
r
e
not
ver
y
hi
g
h
as
sho
w
n i
n
F
i
gu
re
9.
Thi
s
ba
la
nci
n
g
t
o
p
o
l
o
gy
t
o
ok
5
0
mi
nute
s
t
o
ba
la
nce
t
h
e
c
e
l
l
vol
t
a
ge
e
q
u
a
l
l
y
a
n
d i
t
t
o
o
k
a
r
o
u
n
d
2
h
our
s fo
r
c
o
mp
le
te
ch
a
r
g
i
ng.
Sin
ce t
h
e
wh
o
l
e c
e
ll v
o
ltag
e
s a
r
e
b
a
la
n
c
e
d
to t
h
e
sa
me
le
v
e
l,
th
e So
C o
f
t
h
e
c
e
l
l
s
are
t
h
e same at
t
h
e e
nd
of
c
h
a
r
ge
w
h
i
c
h is a
ppea
r
e
d
in Fi
gu
re
10
. The c
h
ar
gin
g
proce
dure ha
p
p
en
s
i
n
a
n
amb
i
en
t
temp
era
t
u
r
e
o
f
aroun
d
2
0
˚
C. Amid
c
h
ar
g
i
n
g
t
h
e
te
mp
er
atu
r
es of t
h
e
ce
ll
s
a
r
e
in
cr
ea
sin
g
u
p
t
o
24
.7
5
˚
C app
e
are
d
in
F
i
gu
r
e
11
.
In t
h
e
se
c
o
n
d
s
t
a
g
e ce
l
l
1 & c
e
l
l
2 v
o
lt
a
g
es
are
co
mpa
r
e
d
wit
h
ce
ll
3 &
cel
l
4 v
o
lt
age
s
. Thi
r
d st
age
ce
ll
1, 2, 3
&
4 volt
a
ges
are
com
p
are
d
wi
th
c
e
l
l
5, 6,
7 & 8 vol
t
a
ges
.
F
o
rt
h
st
age
c
e
l
l
1,
2, 3,
4
,
5, 6, 7
&
8
v
o
l
t
a
g
e
s
ar
e comp
ar
ed
w
i
th
cel
l 9
,
1
0
, 1
1
, 12
,
13
,
14
,
15
& 16
v
o
lta
g
e
s.
Figur
e
11
.
Battery cell tem
p
e
r
atur
e
F
i
gure
12.
C
h
a
r
g
i
ng
cu
rre
nt a
n
d
v
o
l
t
a
ge
A
m
i
d
c
h
a
r
gi
n
g
,
t
h
e
c
e
l
l
s
a
r
e
c
h
a
r
ge
d at
st
ea
dy c
u
rre
nt
how
e
v
er
t
h
e
vol
t
a
ge
i
s
di
ffe
r
i
n
g.
When
th
e
c
e
l
l
ach
ie
ve
s th
e mo
st ex
tre
m
e li
mit v
o
l
ta
g
e
th
e
n
i
t
mov
e
s t
o
th
e ste
a
d
y
v
o
ltag
e
m
o
d
e
w
h
e
r
e
i
t
k
eep
s u
p
th
e
v
o
l
ta
ge
as
a
c
o
n
s
tan
t
an
d th
e cu
rr
en
t w
i
ll
ach
ie
v
e
th
e
b
a
se v
a
l
u
e.
Th
is
r
e
la
tio
n
sh
i
p
is
a
p
p
e
a
r
ed
in
Fi
gu
re
1
2
.
4.
CO
NCL
U
S
I
O
N
D
i
ve
rse
a
c
t
i
v
e
c
e
l
l
bal
a
nc
in
g
t
o
p
o
l
ogie
s
a
r
e
di
sc
ussed
i
n
t
h
i
s
pa
pe
r.
Ind
u
ct
o
r
ba
sed
t
o
pol
o
g
y
is
pi
cke
d
u
p
fo
r
uti
l
i
zat
i
on ba
se
d
on
t
h
e
a
s
se
ss
ment
a
n
d a
n
al
ysis.
The
p
r
op
ose
d
t
o
p
o
l
ogy
c
a
n a
l
t
e
r
to
p,
mi
ddl
e
and
ba
se
ce
ll
s si
mul
t
a
neo
u
sl
y
wi
th
a
sma
l
l
e
r
n
u
m
b
er
of
part
s
t
h
a
n
sta
n
dard
i
n
duct
o
r-
base
d s
y
ste
m
s.
T
h
e
cont
rol
st
ra
t
e
gi
es im
pl
ement
e
d
o
n
t
h
e
swi
t
c
he
s
a
r
e
ba
se
d
on
t
h
e
volt
a
ge
diffe
r
e
n
ce
be
t
w
een
t
h
e
ce
ll
s. S
i
m
p
l
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-8
6
94
Int
J
P
o
w
Ele
c
& D
r
i
S
y
st, V
o
l
.
1
1
,
N
o
.
2, Ju
ne
20
2
0
:
5
7
1
–
579
57
8
cont
rol
a
n
d fa
s
t
eq
ual
i
za
ti
on a
r
e
t
h
e
a
dva
nt
ag
e
s
o
f
t
h
i
s
t
o
p
o
l
o
g
y
co
mpa
r
e
d
t
o
the
c
onve
nti
onal
in
duc
t
o
r-
base
d
t
opol
o
g
y
.
T
h
e
16
-ce
l
l i
n
du
c
t
or-base
d
e
qua
li
z
a
t
ion t
o
p
o
l
o
g
y
i
s
si
mul
a
t
e
d i
n
MA
TLAB/
S
i
m
s
ca
pe a
n
d
t
h
e
i
d
eal
ce
ll
equal
i
zat
i
o
n i
s
e
s
ta
bli
s
he
d
a
n
d c
h
ecke
d
fr
om
t
h
e
re
-e
na
c
t
ment
yi
el
d.
ACKNOW
LE
DG
E
M
ENT
Thi
s
wo
rk ha
s bee
n
su
pp
ort
e
d by
R
obe
rt
B
o
sch
E
ngi
ne
erin
g a
n
d
B
u
si
ne
ss S
o
l
u
ti
o
n
Li
mit
e
d,
B
a
n
g
al
o
r
e
,
In
di
a.
RE
FERE
NC
E
S
[1]
M.
A
.
Hannan
,
et a
l
.
,
"State-of-the-Art and
Energy Managem
e
nt
Sys
t
em of
L
i
t
hium-Ion Batteries
i
n
El
ectric
Veh
i
cl
e Ap
plica
tion
s
: Iss
u
es
and
Recomm
end
a
tio
n
s
,
"
in
I
E
EE
Access
,
v
o
l.
6
,
pp
. 1
9
3
6
2
-1
937
8,
20
18
.
[2] Z
.
B.
Om
ariba,
et a
l
.
,
"Re
v
iew o
f
Ba
tt
e
r
y
Ce
ll Bal
a
nc
in
g
Me
th
o
dolo
g
i
e
s for Opt
i
m
i
z
i
ng
Bat
t
ery Pa
c
k
P
e
rforman
ce
in
Ele
c
tric Veh
i
cle
s
,"
in
I
E
EE A
c
cess
,
vo
l.
7,
p
p
.
12
933
5-1
2
9
352
, 2
0
1
9
.
[3] Amin,
et al
.
,
"P
a
s
si
ve
b
a
la
nc
i
ng b
a
tt
e
r
y
m
a
na
gem
e
n
t
sy
st
e
m
u
s
ing
MOSFE
T
i
n
te
rn
al
r
e
si
st
a
n
c
e
a
s
b
a
l
a
n
c
i
ng
resistor,"
20
17 In
te
rn
at
io
na
l
Co
n
f
e
r
e
n
ce
o
n
S
u
stai
na
bl
e
E
n
e
r
gy
En
g
i
n
e
e
r
i
n
g
a
nd A
p
p
lic
a
t
i
on (ICS
E
E
A
)
,
Jakarta,
p
p
.
15
1-1
55,
2017
.
[4] M.
Caspa
r
,
et al.
,
"S
yste
m
a
tic
Com
p
a
r
i
s
o
n
of Ac
ti
ve
Bala
nc
i
n
g
:
A Model
-
Based
Quant
itati
v
e
Anal
ysis,
"
i
n
IEEE
T
r
a
n
s
a
ction
s
on
Veh
i
cular
T
echn
o
logy,
v
o
l.
6
7
, no.
2
,
pp.
92
0-9
3
4
,
Fe
b
.
20
18.
[5] Mohamed
Daow
d,
et a
l
.
,
"S
ingle
S
w
itched
Cap
a
citor B
a
ttery
Bal
a
ncing
S
y
ste
m
Enhan
c
emen
ts,"
Ener
gies,
vol
. 6,
p
p
.
21
49
-21
7
, 201
3.
[6] M.
Ki
m,
et
a
l
.
,
"A
Ch
a
i
n
Struc
t
u
r
e
of Switc
he
d
C
a
pac
i
to
r for
Im
p
r
ov
e
d
Ce
l
l
Ba
la
nc
i
n
g
Sp
ee
d
o
f
L
ith
iu
m
-Io
n
B
a
tt
e
r
ies
,
"
in
IEEE T
r
ans
actio
n
s
on
Ind
u
s
t
r
i
al
El
ectr
o
n
i
cs
, v
o
l
.
61,
n
o
.
8
,
pp.
3
9
8
9
-
39
99
,
Au
g 2
014.
[7]
Y.
Ye
and
K. W. E. Ch
eng
,
"
M
od
ellin
g
an
d
A
n
aly
s
is of
S
e
r
i
es–
P
a
r
allel
S
w
itch
ed-C
apac
ito
r
Vo
lt
age
Equ
a
lizer
for
Batte
r
y/S
uper
ca
paci
to
r
S
t
rin
g
s
,
"
in
IEE
E
Jou
r
na
l of
Emer
ging
a
nd S
e
lec
t
ed
T
o
pi
c
s
in
Power
El
e
c
tr
onics
, v
o
l
.
3,
no
. 4
,
p
p
.
977
-9
8
3
,
De
c 2
015
.
[8] Y.
Y
e
,
et
a
l
.
,
"
T
op
olog
y, M
o
d
e
ll
ing
,
and
Des
i
g
n
of S
w
itch
ed
-Cap
acitor-Based
Ce
l
l
B
a
lan
c
ing
S
y
stems
an
d
Th
e
i
r
Ba
l
a
n
c
i
n
g
Ex
pl
ora
t
i
on,
"
in
IEE
E
Tran
sac
t
io
ns
on
Po
we
r
Ele
c
t
r
o
n
i
c
s
,
vo
l.
32
,
no
. 6
,
pp
. 4
4
4
4
-44
5
4
,
J
un
20
17.
[9]
Y. S
h
ang
,
N
.
Cu
i,
B.
Du
an
and
C.
Zh
ang
,
"
A
n
a
ly
sis
and
O
p
ti
miz
a
tio
n
of
S
t
ar
-S
tru
c
tu
red
S
w
it
ched-Cap
acitor
Eq
ualizers
for
S
e
ries-Con
ne
ct
ed Battery
St
ri
ngs
,
" i
n
IEE
E
Tr
an
sa
ctions
o
n
Pow
e
r Ele
ctro
ni
cs
,
vo
l.
33,
n
o
.
1
1
,
pp
. 9
6
3
1
-9
646
,
N
o
v
.
20
18
.
[1
0] Y.
S
h
a
n
g,
et
al.
,
"
A
Del
t
a-S
t
ru
ctu
r
ed
S
w
itch
ed
-Ca
p
ac
itor
Eq
ua
liz
e
r for
S
e
ries
-Conn
ected
B
a
tte
ry S
t
rin
g
s,"
in
IEEE
Tr
an
sa
ctio
ns
on
Power
Ele
c
tro
n
ics
, vo
l.
34, no
.
1
,
p
p
. 4
5
2
-
4
6
1
,
Ja
n
.
20
19.
[1
1] Y.
Sha
ng,
et al
.
,
"A
n Opt
i
mi
zed
M
e
s
h
-
S
tr
u
c
tu
r
e
d
S
w
it
ch
ed
-C
ap
a
c
it
or
E
q
u
a
li
zer
f
o
r
L
i
t
h
i
u
m-
I
o
n
B
a
t
t
e
r
y
S
t
r
i
ng
s,"
in
IEE
E
Tra
n
sac
t
io
ns on
Tra
n
sp
orta
ti
on
El
ec
tri
f
i
c
at
io
n
,
vo
l.
5
,
no
.
1,
pp
.
2
52-2
6
1
,
M
a
rch 2
0
1
9
.
[1
2] S.
Go
od
a
r
z
i
,
et a
l
.
,
"
D
es
ig
n and
imp
l
emen
tin
g
o
f
a nov
e
l
reson
a
nt
sw
itched
-
c
ap
acitor
co
nv
erter
fo
r
imp
r
ov
in
g
balancing
speed
of
l
i
t
h
i
u
m-ion
batte
ry
cell
s,
"
20
16 7th
Po
we
r Ele
ctro
ni
c
s
a
n
d
D
r
ive Sys
t
e
m
s Tech
no
lo
gies
Con
f
er
enc
e
(
P
EDS
T
C),
Tehr
an,
pp.
20
4-2
1
0
,
20
16
.
[1
3]
Fa
rz
a
n
M
o
g
h
a
dda
m
,
A
a
n
d
Van d
e
n
Bo
ssc
h
e, A. "A
c
e
ll
e
q
u
a
liz
a
t
i
on m
e
tho
d
ba
se
d
o
n
reson
a
nt
switc
he
d
capacit
or
balancing
for
L
i
thium i
o
n ba
tteri
es,
"
Pr
es
ente
d
a
t
the 20
18 9th
In
ter
n
a
t
io
na
l Conferen
ce
on
Mech
an
ica
l
an
d Aero
sp
ace
Eng
i
ne
er
in
g
(IC
M
AE)
,
IEEE,
pp
.
33
7-34
1,
20
18
.
[1
4] Ri
gv
e
n
d
r
a
Ku
ma
r
Va
rd
ha
n,
et a
l
.
,
"Mo
d
e
l
in
g
o
f
sin
g
l
e
in
duc
to
r
ba
se
d bat
t
e
ry
ba
lan
c
in
g circ
ui
t for
hy
b
r
id
e
l
e
c
tr
ic
veh
i
c
l
es,"
I
E
CON -43
r
d
An
nu
al
Con
f
er
e
n
c
e
of
th
e IE
EE
Indu
stria
l
Elec
t
r
onics
So
c
i
ety,
pp.
2
2
9
3
-
2298
,
20
17
.
[1
5] B.
Do
ng
,
et a
l
.
,
"
P
arall
e
l Arch
itec
t
ure
fo
r Battery
Charg
e
Eq
ual
i
z
a
t
ion
,
"
I
E
E
E
T
r
ans
actio
n
s
on
Po
wer Electron
i
cs
,
v
o
l
.
3
0
,
no.
9,
pp.
4
9
0
6
-
49
13,
Se
pt
2
0
1
5
.
[16] Z
h
ou,
et a
l
.
,
"
A
n
a
n
y-cel
l(s
)
-t
o-an
y-ce
ll(s) eq
ualizer b
a
s
e
d o
n
b
i
d
i
re
ction
a
l
ind
u
ctor
co
nver
t
ers fo
r seri
es
c
o
nn
e
c
te
d bat
t
e
r
y
st
rin
g
,
"
20
16
I
E
EE 11
th
Con
f
e
r
en
ce
o
n
In
du
str
i
al
El
ec
tr
oni
cs
a
n
d
A
p
p
l
i
c
a
t
ion
s
(
I
C
IE
A)
,
H
e
fei
,
p
p
.
25
11
-25
1
5
,
20
16
.
[17
]
A.
F
.
M
o
g
h
add
a
m and
A
.
V
a
n
D
e
n Bos
s
ch
e, "
A
n A
c
tive
Cell
Eq
ualiza
t
ion
Te
ch
nique
fo
r Lith
i
u
m
Io
n B
a
tteri
es
Ba
se
d on
In
d
u
c
t
or Ba
la
nci
n
g
,
"
9t
h
Inte
rna
tion
a
l
Confe
r
e
n
ce
o
n
Me
c
h
a
n
i
c
al
an
d
Ae
ro
sp
ac
e En
gin
e
e
r
i
n
g
(ICMAE
)
,
Bu
d
a
pe
st,
pp.
27
4-2
78,
20
18.
[18
]
Ali F
a
rzan
M
o
g
h
ad
dam an
d Alex
V
a
n
D
e
n Boss
che, "A
n efficien
t equ
a
lizing
meth
od
for
l
i
t
h
i
u
m-ion batt
er
ies
bas
e
d on
coup
le
d
in
du
c
t
or b
a
la
n
c
in
g,"
Electron
i
c
s
, v
o
l.
8,
pp
.
1
3
6
,
20
19
.
[1
9] Y.
Sha
n
g,
et al
.
,
"
A
M
o
d
u
l
a
r
i
zat
io
n M
e
tho
d
f
o
r
B
a
tt
e
r
y Eq
ua
l
i
z
e
r
s Us
in
g M
u
l
t
i
w
i
n
d
i
n
g
T
r
ans
f
o
r
mer
s
,"
in
IEEE
T
r
a
n
s
a
ction
s
on
Veh
i
cular
T
echn
o
logy,
vo
l.
66
,
n
o
.
1
0
,
pp
.
87
10
-
872
2,
Oct
.
20
17
.
[2
0]
A. F.
Mo
gha
dd
am
a
n
d
A.
Va
n
de
n
Bossc
h
e,
"M
u
l
t
i
-Win
d
i
n
g
E
q
u
a
liz
a
tio
n
T
e
c
hni
qu
e
for Lit
h
i
u
m
I
o
n
Ba
tte
rie
s
for Elec
tric
al Veh
i
c
l
es,"
20
18 7th
In
te
rna
t
io
na
l C
o
n
f
e
r
e
n
c
e
on R
e
n
e
wa
b
l
e
E
n
e
r
g
y
Re
se
a
r
c
h
and
Ap
p
l
i
c
atio
ns
(ICR
ERA)
, Pa
ri
s
,
pp.
13
9-1
43,
20
18
.
[21
]
Y. M
a
, Ah
san
u
z
zam
an an
d A
.
P
r
odi
ć
,
"A hardware effici
ent
lit
h
i
um-i
on cell
bal
a
ncing
techni
que utili
zing l
o
w-
vo
lu
me
h
ybrid
DC-DC
con
v
erter,
"
I
E
CON
201
7
- 4
3
rd
Ann
u
a
l
Co
nferen
ce
of
the I
E
EE Industri
a
l
El
ectronics
So
cie
t
y,
Be
ijin
g
,
pp
.
56
6-5
7
0
,
20
17
.
[22] Yew
e
n
Wei,
et al.
,
"Swit
c
h Matri
x
Algor
i
thm f
o
r Series L
i
thium
Batt
ery
Pac
k
E
q
uili
bri
u
m
Base
d
on
D
e
ri
ve
d
Accel
era
t
ion
In
fo
rmatio
n Gau
s
s
-
Seidel,"
Ma
th
ematica
l
Pr
obl
ems
in
En
gin
eering
,
Article
ID 80
754
53
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
Act
i
v
e
ce
l
l
bal
anc
i
n
g
for
el
ec
tri
c
vehi
c
le
b
a
t
t
e
r
y m
ana
ge
me
nt
sy
st
e
m
(T
hi
ruv
o
n
a
sun
d
a
ri
Dur
a
i
s
am
y
)
5
79
9
p
a
ge
s,
20
19.
[23]
Z
.
Amjadi
and
S. S.
W
illi
amson,
"Power-El
ect
ro
nics-B
ased Sol
u
t
i
ons for
Pl
ug-in
Hybri
d
Elect
r
i
c
Vehi
cl
e Energy
S
t
o
r
age
and
M
a
n
a
gem
e
nt
Sy
ste
m
s,"
in
I
EEE T
r
ans
actio
n
s
o
n
In
d
u
s
t
r
i
al
Electro
nics
, v
o
l. 57
, no. 2
,
pp. 60
8
-
61
6,
F
e
b 201
0.
[24
]
S
.
S
r
eelaks
h
m
i
an
d K. Deepa
,
"F
u
zzy
b
a
sed b
i
direct
io
nal con
v
er
ter,"
In
ter
natio
na
l
Co
nferen
ce on
Circu
i
ts,
Po
we
r
an
d Comp
utin
g T
ech
nolog
ies
[ICCPCT
-2
01
5]
,
Na
ge
rc
o
il, 20
15
,
p
p
.
1
-
6, 20
1
5
.
[25] Y.
Ma,
et al
.
,
"E
qualizat
ion
of
Li
thiu
m-Ion
Battery
P
ack
Bas
e
d
on
F
u
zzy
Logi
c Control
in E
l
ectric
Vehicl
e,
"
in
IEE
E
Tra
n
sac
t
io
ns on
Ind
u
strial
El
e
c
tron
ic
s
,
v
o
l. 6
5
,
no
.
8
,
pp
.
67
62
-67
71,
Au
g.
201
8.
[2
6] Y.
Sh
a
n
g,
et a
l
.
,
"A
n A
u
to
matic
Eq
ualizer B
a
se
d o
n
F
o
rward–
Fly
-
back Conv
erter for Se
ries-Co
n
n
ected
Battery
St
rin
g
s,
"
IEEE T
r
a
n
sac
t
io
ns on
Ind
u
stri
al
E
l
e
c
tron
ic
s
,
vo
l.
6
4
,
no.
7,
pp
.
5
380
-53
9
1
,
Ju
ly
20
17
.
[2
7]
Ka
li
ya
pe
ru
m
a
l.De
e
p
a
,
et a
l
.
,
"
A
ctive
clamp
z
e
ro v
o
l
t
ag
e s
w
itching
mul
t
ipl
e
ou
tp
ut
fly-b
a
c
k
co
nve
rter
w
i
th
vo
ltag
e d
o
u
b
l
e
r,"
Inter
n
a
t
ion
a
l
Review on
Mod
eli
n
g
an
d
S
i
m
u
la
ti
on
s
, vo
l.
6
,
p
p
.
3
5
1
-
35
9, 20
13
.
[28]
E
.
C
h
atzinikolaou
and D.
J. Rog
e
r
s
,
"El
e
ctrochemical
cel
l
balan
c
i
n
g usi
ng a
ful
l
-b
ridge multil
ev
el
converter and
ps
eud
o
-o
pen c
i
r
c
uit vo
ltag
e
me
asu
r
e
m
en
ts
,"
8
t
h IET In
te
rna
t
io
n
a
l Co
nf
e
r
e
n
c
e
on Po
we
r
E
l
e
c
t
ro
n
i
c
s
,
Mac
hi
n
e
s
and Drives (PEMD
2016)
, G
l
as
go
w, p
p
.
1-6
,
20
16
.
[29] Q.
Ouyang,
et
a
l
.
,
"SOC
E
s
tim
ation-Based
Quasi-
Sl
id
ing M
o
d
e
C
ontrol
fo
r C
e
ll B
a
la
ncing
i
n
Lithium-Ion B
a
t
t
ery
P
acks
,
"
in
IEE
E
T
r
an
sactio
ns
on
Ind
u
s
t
r
i
a
l
E
l
ec
tron
ics
, v
o
l
.
65
,
n
o
.
4
,
p
p
.
34
27
-3
43
6,
April
201
8.
[30
]
Ali F
a
rz
an M
o
g
h
a
dd
am
an
d Alex
V
a
n Den
Bo
s
s
ch
e,
"
A ´Cuk
Co
nverter
Cel
l
Ba
lan
c
ing
Te
ch
niqu
e
b
y
Using
C
o
u
p
l
e
d I
n
du
cto
r
s
f
o
r
Li
thi
u
m
-
B
a
s
e
d
B
a
tt
er
ies
,
"
En
ergies
,
vo
l.
1
2
,
pp
. 2
881
, 2
0
1
9
.
[3
1] Sh
ub
ia
o
,
et a
l
.
,
"
A
No
vel
Lay
e
red
Bidirec
t
io
na
l
Eq
ualizer
B
a
sed
on
a Buck-Boost Conver
te
r for
Series-Connected
Bat
t
ery Stri
ngs
,
"
En
ergi
es
, vo
l.
1
0
, 20
17
.
[32] Y.
Sha
n
g,
et
a
l
.
,
"
A
Ce
l
l
-t
o-Cel
l
Ba
t
t
ery
E
q
ual
i
zer
W
i
t
h
Ze
ro
-Cu
r
re
nt
S
w
i
t
c
h
in
g
an
d
Ze
ro
-Vol
ta
g
e
Ga
p
Ba
se
d
on
Qu
asi-Reson
a
nt
LC Conv
er
ter
a
n
d Bo
os
t Co
nv
e
r
ter,"
IEEE
Transactions
on Power
El
ec
tronics,
vo
l. 30
,
no
.
7
,
p
p
.
37
31
-37
4
7
,
J
u
ly
20
15
.
[
3
3
]
T.
Go
tw
a
l
d
,
et
a
l
.
,
“Eq
u
a
lizatio
n
of EV
and
H
E
V
b
a
tte
ri
es with a ra
m
p
co
nv
erter
”
,
IEE
E
Tr
an
sa
ctio
ns
on
A
e
ro
sp
ac
e
a
nd
El
ec
tro
n
i
c
Sy
stems
,
vo
l.
33
,
n
o
.
1
,
p
p
.
307
-31
2
,
J
a
n.
19
97
.
[34
]
Thiruv
on
as
un
dari.D, K
.
D
e
epa,
"
E
l
ectr
i
c
V
e
hic
l
e B
a
tt
ery
M
o
d
e
lling
M
e
th
o
d
s
Bas
e
d on
S
t
ate o
f
Ch
arg
e
-R
eview,"
Jou
r
n
a
l of
Gr
ee
n Eng
i
n
eerin
g
(2
02
0 in
pres
s).
[35] S.
Narayan
a
swamy,
et al.
,
"M
o
d
u
l
ar
A
c
tive Ch
ar
ge Bal
a
ncing
for
S
calab
le
B
a
tter
y
P
acks,"
IEEE T
r
ans
actio
n
s
on
V
e
ry
La
rg
e
-
Sc
ale
In
te
grat
io
n
(VLS
I)
S
y
ste
m
s
,
vol.
25,
no.
3,
p
p
. 974
-98
7
,
Ma
rc
h
2
0
17
.
Evaluation Warning : The document was created with Spire.PDF for Python.