Internati
o
nal
Journal of P
o
wer Elect
roni
cs an
d
Drive
S
y
ste
m
(I
JPE
D
S)
Vol
.
7
,
No
. 2,
J
une
2
0
1
6
,
pp
. 47
2~
48
0
I
S
SN
: 208
8-8
6
9
4
4
72
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJPEDS
Performance Evaluation of Mode
lling and Simulation of Lead
Acid B
a
t
t
eri
es
for Photovoltai
c Applications
A. Selmani*,
A.
Ed
-Dahh
a
k**, M.
Ou
tanou
t
e*, A.
L
a
chhab**,
M.
Guerb
aoui*
and B. B
o
uc
hik
h
i*
* Sensors Electr
onic
& Instrumentation
Team, D
e
partment of Ph
y
s
ics
,
Facu
lty
of
Scien
ces,
Moulay
Isma
ïl
Unive
r
sity
, Me
kne
s
,
Morocc
o
** Modelling S
y
stems Control
an
d Telecommunications
Team,
High School of
Technolog
y
,
Moulay
Isma
ïl
Unive
r
sity
, Me
kne
s
,
Morocc
o
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Sep 22, 2015
Rev
i
sed
Feb 4, 20
16
Accepted
Feb 23, 2016
Lead-
acid
bat
t
er
ies
have
been
th
e m
o
s
t
widel
y
u
s
ed energ
y
s
t
or
a
g
e units
in
stand-alon
e pho
tovoltaic (PV) applicat
ions. To
make a full u
s
e of those
batteries and to
improve their lifecy
c
l
e
,
high p
e
rform
ance
char
ger is
ofte
n
required
.
The i
m
p
lem
e
ntation
of an advance
d
charger need
s
accurat
e
inform
ation on the batte
ries inte
rnal pa
rameters. In this work,
we selected
CIEMAT m
odel because of its
good perform
ance to de
al with
the widest
range of lead acid batteries. The pe
rform
ance
evalua
tion
of t
h
is m
odel is
based on the
co-sim
ulation
L
a
bVIEW
/
Multisi
m
.
W
ith the i
n
tention of
determining
the
impact of th
e ch
arging
process on batteries
,
the b
e
haviour o
f
differen
t
in
tern
al par
a
meters of
th
e ba
tte
r
ie
s
wa
s simu
lated.
During
the
charging m
ode,
the valu
e of the
current m
u
s
t
decre
a
s
e
when th
e batt
eries
’
s
t
ate
of
charg
e
is
clos
e
to
be
full
y charg
e
d.
Keyword:
Battery charge
r
CIEMAT
Lab
V
IE
W/M
u
l
tisim
Lead aci
d
batteries
M
odel
l
i
n
g
Pho
t
ov
o
ltaic
Copyright ©
201
6 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
B
e
nachi
r
B
o
uc
hi
k
h
i
,
Sens
ors
El
ect
r
oni
c
&
Inst
rum
e
nt
at
i
on
Team
, De
part
m
e
nt
of
Phy
s
i
c
s,
Faculty of Scie
nces Me
kne
s,
Moulay Ism
a
ïl Uni
v
ersity
B.P.
1
1201
, Zit
o
un
e, 500
03
,
Mek
n
e
s, Maroc,
E-m
a
il
:
benac
h
i
r
.b
o
u
chi
khi
@
g
m
a
il
.com
1.
INTRODUCTION
Batteries are i
n
fl
u
e
n
tial co
mp
on
en
t in
stand
-
al
o
n
e
PV syste
m
s so
th
ey
are th
e o
r
i
g
in
o
f
th
e failure
an
d
l
o
ss of d
e
p
e
nd
ab
ility. Th
ey g
u
aran
tee an
un
in
terru
p
t
ed
po
wer su
pply to
th
e lo
ad
an
d
co
m
p
en
sate th
e
p
o
wer p
r
o
d
u
c
t
i
o
n
d
e
ficien
cy
wh
en
ev
er weath
e
r
con
d
itio
n
s
are critical. To redu
ce the qu
an
tity of
p
h
y
sical
testing with a specific application,
an acc
urate syste
m
m
o
delling of batteri
es is require
d fo
r an ap
p
r
o
p
riat
e
an
alysis and
sim
u
la
tio
n
.
B
u
t
m
o
d
e
llin
g
and esti
m
a
tio
n
of
batteries state
of cha
r
ge a
r
e
known as
one
of the
m
o
st
co
m
p
l
e
x t
a
sks. M
o
st
of
m
odel
s
necessi
t
a
t
e
t
h
e kn
owl
e
dge
o
f
p
r
o
p
e
r
param
e
t
e
rs wh
ose v
a
l
u
es
hav
e
t
o
b
e
b
u
ilt-in
for each
sp
eci
fic b
a
ttery d
e
sign
an
d cap
acity. Th
is
requ
ires a com
p
le
te testin
g
p
r
o
cess th
at is o
f
ten
bey
o
nd t
h
e us
ual
dat
a
s
h
eet
of t
h
e c
o
nst
r
u
c
t
o
r w
h
i
c
h i
s
at
once
pri
cey
and t
i
m
e consum
i
ng. The
r
e
f
o
r
e
,
bat
t
e
ri
es beha
v
i
ou
r has bee
n
basi
cal
l
y
l
a
bel
l
ed by
m
a
ny
au
t
h
o
r
s, an
d seve
ral
m
a
t
h
em
ati
c
al
m
odel
s
have
bee
n
defi
ned
[
1
]
–
[4
]
.
To
av
oi
d
t
h
ose m
a
t
h
em
at
ical
desc
ri
pt
i
o
n
s
w
h
i
l
e
e
v
al
ua
t
i
ng
bat
t
e
ri
es
out
put
v
o
l
t
a
ge,
a
ne
w
fu
zzy b
a
sed
mo
d
e
l fo
r
Nick
el
Cad
m
iu
m
(Ni-Cd
) b
a
tteries
was p
r
o
p
o
s
ed
[5]. Also
, th
e ex
ten
d
e
d
Kalm
an
filter
is able to keep an exce
p
tion
a
l p
r
ecisi
o
n
i
n
SOC estim
a
tio
n
of Lith
ium
-
io
n
b
a
tteries [6
]. Ho
wev
e
r, th
e
adva
ntage
of t
h
e battery m
odels el
aborate
d
by Monegon and CIEMAT
is
unde
rline
d
unde
r their abi
lity
to
cope
wi
t
h
t
h
e
wi
dest
ra
nge
o
f
l
ead
aci
d
b
a
t
t
e
ri
es an
d
re
q
u
i
r
es
fe
w m
a
nufact
ure
pa
ra
m
e
t
e
rs [7]
–
[
1
1
]
. Th
e
v
a
lid
ity o
f
su
ch
m
o
d
e
ls was
an
alysed
in
term o
f
th
ei
r capab
ility to
rep
r
esen
t vo
ltag
e
ev
o
l
u
tio
n
of b
a
t
t
eries
du
ri
n
g
c
h
ar
ge and
di
sc
har
g
e pr
ocesses
.
As a
res
u
l
t
,
CIEM
AT m
odel
proofs
a
good re
presentation c
o
m
p
ared
t
o
M
o
neg
o
n
m
odel
[12]
.
S
o
,
we c
hos
e t
h
e f
o
rm
er
m
odel
as a
n
eq
ui
val
e
nt
ci
rc
ui
t
st
ruct
u
r
e
fo
r l
ead-aci
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 7,
No
.
2,
Ju
ne 20
16
:
472
–
4
80
47
3
b
a
tteries si
mu
latio
n
.
Th
is
m
o
d
e
l an
d its i
m
p
l
e
m
e
n
tatio
n
wh
ich is b
a
sed
on
th
e co-simu
l
atio
n
LabVIE
W/Mul
tisim are described in detail. This co-sim
ula
tion is able to provide accura
te sim
u
lation results
and a ve
ry
fast
sim
u
l
a
ti
on spee
d. The
r
e
b
y
,
i
t
reveal
s t
h
e st
ro
n
g
i
n
st
ant
a
ne
ou
s rel
a
t
i
ons
hi
p bet
w
e
e
n t
h
e
internal
batteri
es pa
ram
e
ters and
the c
h
a
r
gi
ng
cu
rre
nt
rate.
2.
BATTERY MODEL
2.
1.
Equivale
n
t Ci
rcuit
Ou
r st
u
d
y
i
s
fo
un
de
d o
n
t
h
e
m
odel
t
h
at
was est
a
bl
i
s
hed
b
y
“C
ent
r
o
de I
nve
st
i
g
aci
o
n
es
Ener
gét
i
cas,
Medioam
b
ientales y Tecnológicas” (C
IEM
A
T
)
an
d
base
d
o
n
t
h
e
ci
rc
ui
t
sho
w
n i
n
Fi
gu
re
1. T
h
i
s
e
q
ui
val
e
n
t
circuit is com
pos
ed
of a
vol
tage source
V
1
in
series
with in
tern
al
resist
an
ce
R
1
wh
ich th
eir ch
aracteristic
s
depe
n
d
s
o
n
s
o
m
e
param
e
t
e
rs suc
h
as i
n
t
e
r
n
a
l
t
e
m
p
erat
ure
(
T
) a
n
d
SOC
.
Fi
gu
re
1.
B
a
t
t
e
ry
m
odel
eq
ui
v
a
l
e
nt
ci
rcui
t
The i
m
pl
em
ent
a
t
i
on o
f
t
h
e
m
odel
of
n
s
c
e
lls in series
im
plies necess
a
rily assigni
ng dissim
i
lar
expressi
ons t
o
the values
of
V
1
and
R
1
in
each
d
i
fferen
t m
o
d
e
.
We li
m
i
t o
u
r
stud
y to
th
e two
m
a
in
m
o
d
e
s of
ope
rat
i
o
n:
cha
r
ge a
nd
di
sch
a
rge
.
Fo
r t
h
i
s
reaso
n
, m
a
t
h
em
at
i
cal form
ul
at
i
ons ar
e gi
ven
by
t
h
e fo
l
l
o
wi
n
g
equat
i
o
ns:
Ch
argi
n
g
mo
de
The electrom
o
tive force
V
1
an
d
th
e in
tern
al
resisto
r
R
1
are
fun
c
t
i
ons
of t
h
e i
n
t
e
r
n
al
co
m
ponent
s o
f
th
e b
a
ttery:
1
1
0.
8
6
1.
2
10
11
(2
0
.
1
6
)
60
.
4
8
0.
036
1
0
.
025
1(
1
)
s
bat
s
ba
t
ba
t
b
a
t
Vn
S
O
C
I
Rn
T
CI
S
O
C
VV
R
I
(1
)
Whe
r
e
n
s
is t
h
e cells nu
m
b
er,
T
is th
e v
a
riatio
n
of th
e b
a
ttery in
tern
al temp
erat
u
r
e (
T
bat
) ,
SO
C
is th
e
b
a
ttery
state of charge at a
given time,
I
bat
is
th
e in
stan
tan
e
o
u
s
b
a
ttery cu
rren
t
,
V
bat
is th
e
in
stan
tan
e
ou
s b
a
ttery
vol
t
a
ge
, a
n
d
C
10
is th
e
rated
cap
acity.
Discharging mode
The m
a
the
m
atical equati
ons
a
r
e a
n
alogous t
o
those
fo
und
at charging m
ode
with
a sort of differe
n
ce
conce
r
ni
n
g
t
h
e
val
u
e
s
.
1
1
1.
3
1
.
5
10
11
2.
085
0.
12
(
1
-
)
40
.
2
7
0.
02
1
0
.
007
1
s
bat
s
bat
ba
t
b
a
t
Vn
S
O
C
I
Rn
T
CI
S
O
C
VV
R
I
(2
)
2.
2.
Capaci
tor
Model
The capaci
t
y
m
odel
i
s
defi
n
e
d by
t
h
e fol
l
owi
ng e
quat
i
o
n (3
). T
h
e val
u
e of t
h
e i
n
t
e
r
n
al
capaci
t
y
(
C
bat
) is settled
fro
m
th
e exp
r
essi
on
of th
e cu
rren
t
I
10
,
w
h
i
c
h m
a
t
c
h up
t
o
t
h
e
ope
rat
i
ng
spee
d
of t
h
e rat
e
d
cap
acity o
f
th
e
b
a
ttery
C
10
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Perfo
r
man
ce Eva
l
ua
tio
n o
f
Mo
d
e
lling
a
n
d
S
i
mu
l
a
tio
n o
f
Lea
d
Acid Ba
tteri
es fo
r …
(
B
e
n
a
c
hi
r B
ouc
hi
k
h
i
)
47
4
0.
9
10
10
1.67
1
0
.005
(
T
25
)
10
.
6
7
ba
t
bat
ba
t
C
C
I
I
(3
)
The instanta
ne
ous calculate
d capacity
C
bat
is
u
s
ed
to
esti
m
a
te th
e
SOC
[1
3
]
, as dem
onst
r
a
t
ed i
n
t
h
e equa
t
i
ons
bel
o
w:
()
(
1
)
0(
)
1
ba
t
bat
I
SOC
t
SOC
t
C
SO
C
t
(4
)
2.
3.
Thermal Model
Equ
a
tio
n
(
5
)
ev
alu
a
tes th
e chan
g
e
in
electrolyte te
m
p
eratu
r
e, du
e to th
e intern
al resistiv
e lo
sses
and
the am
bient tem
p
erature
[9], [14]
.
The
t
h
erm
a
l
m
odel
i
s
de
fi
ne
d
by
a
first ord
e
r
d
i
fferen
tial equ
a
tion
with
param
e
t
e
rs fo
r
t
h
erm
a
l
resi
st
ance a
n
d
cap
aci
t
a
nce. T
h
i
s
has
bee
n
do
ne
by
t
h
e
fol
l
o
wi
n
g
e
quat
i
o
n:
0
0
(1
)
1
()
t
ba
t
a
bat
s
oo
TT
Tt
T
P
d
CR
(5
)
Whe
r
e
T
bat
is t
h
e b
a
ttery’s tem
p
eratu
r
e in
°C;
T
0
is th
e b
a
ttery’s in
itial
te
m
p
eratu
r
e in
°C
, expected
to be
equal t
o
the
ne
arby am
bient te
m
p
erature;
P
s
is th
e
R
1
I
bat
2
powe
r los
s
of the internal
resis
t
ance
R
1
in
Watts;
R
o
is th
e th
erm
a
l
resistan
ce in
°C/W
atts;
C
o
is th
e th
erm
a
l cap
acitan
ce in
Jo
u
l
es/°
C
;
is an
in
teg
r
ation
ti
me
v
a
riab
le; and
t
is th
e sim
u
latio
n
tim
e in
seco
nd
s.
Ev
en
tho
ugh
th
e b
a
ttery m
o
du
le is co
m
p
o
s
ed
of m
o
re than one elem
ent, a single tem
p
erature for the
electro
lyte o
f
th
e co
m
p
lete
mo
du
le
was adop
ted
.
3.
BATTERY MODEL SIMULATION ST
RUCT
URE
Th
e
Nation
a
l
In
stru
m
e
n
t
s Co
mm
u
n
ity p
r
esen
ts th
e prin
cip
l
e
o
f
co-si
m
u
l
atio
n
usin
g th
e two
si
m
u
lato
rs LabVIEW and
Multisi
m
[1
5
]
. Th
erefore,
th
e
battery
m
o
d
e
lli
n
g
an
d
sim
u
lat
i
o
n
are
d
e
v
e
l
o
p
e
d
i
n
th
e fo
llowing
man
n
e
r. Firstly, th
e stag
e ci
rcu
itry is
d
e
si
g
n
e
d
i
n
M
u
ltisi
m
wh
ich con
t
ain
s
t
h
ree parts: an
equi
val
e
nt
ci
rc
ui
t
m
odel
,
a char
ge o
r
di
sch
a
rge m
ode swi
t
cher, a
nd a t
h
erm
a
l
m
odel
.
The
n
t
h
e Lab
V
IE
W
code t
o
m
oni
t
o
r t
h
e ci
rc
ui
t
i
s
devel
o
pe
d,
l
o
cat
ed i
n
si
de
of a Lab
V
IE
W
c
o
nt
r
o
l
bl
o
c
, and c
o
u
p
l
e
d t
o
t
h
e
Mu
ltisi
m
circu
it fo
r co-sim
u
l
atio
n
.
Th
e two sim
u
lato
rs u
s
ually ex
ch
ang
e
d
a
ta in
a syn
c
hron
ised and
v
a
riab
le
ti
m
e
step
m
a
n
n
er. Th
e flowch
art
o
f
t
h
e prop
o
s
ed
La
bVIEW
/
M
u
ltisi
m
b
a
ttery
m
o
d
e
l sim
u
la
tio
n
is sho
w
n
i
n
the Figure
2.
Fig
u
re
2
.
Flowch
art
o
f
th
e
prop
o
s
ed LabVIEW
/
M
u
ltisi
m
b
a
ttery
m
o
d
e
l si
m
u
la
tio
n
LabVIEW code send
s two
d
i
fferen
t
typ
e
s of d
a
ta t
o
M
u
ltisi
m
circu
itry.
Th
e
first typ
e
is th
e static
p
a
ram
e
ters u
s
ed
to
d
e
fin
e
th
e th
erm
a
l
m
o
d
e
l,
s
u
ch
as
th
e amb
i
e
n
t te
mp
e
r
a
t
u
r
e
(
T_
a
), the in
itial te
m
p
eratu
r
e
(
T_o
), the the
r
mal resistance
(
R_o
) and the therm
a
l capacitance (
C_o
). Th
e second
typ
e
is th
e in
stan
tan
e
ous
p
a
ram
e
ters which
ev
alu
a
te t
h
e
b
a
ttery circu
it p
a
ram
e
ter
s
su
ch as t
h
e vo
ltag
e
sou
r
ce (
V_1
), th
e in
tern
al
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
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:
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94
I
J
PED
S
Vo
l. 7,
No
.
2,
Ju
ne 20
16
:
472
–
4
80
47
5
resistance (
R_1
) a
n
d the inte
rnal ca
pacitanc
e (
C
_
bat
).
On
the othe
r side,
the calculation of t
hose
pa
ra
meters
with
in
LabVIEW
co
d
e
d
e
pen
d
s on
the data sen
t
b
y
Mu
ltisi
m
stag
e su
ch
as t
h
e in
stan
tan
e
ou
s b
a
ttery
te
m
p
erature (
T_
ba
t
) eval
uat
e
d by
t
h
e t
h
er
m
a
l
m
odel
bloc an
d t
h
e sense
d
cur
r
ent
(
I
_se
n
se
) t
h
r
o
u
gh t
h
e
equi
val
e
nt
ci
rc
ui
t
.
3.
1.
Multisim Sta
g
e
The e
q
ui
val
e
nt
ci
rcui
t
i
n
Fi
g
u
re
3
-
a i
s
c
o
m
pos
ed
o
f
a
v
o
l
t
a
ge co
nt
r
o
l
l
e
d
so
urce
V
1
in series with a
vol
t
a
ge c
o
nt
rol
l
ed resi
st
or
R
1
.
The val
u
e
s
of
V
1
and
R
1
de
pe
nd
on t
h
e
bat
t
e
ry
ope
rat
i
on m
ode at
a gi
ve
n
t
i
m
e
and va
ried
wit
h
tem
p
erature
and SOC. T
h
e
resi
stance
also
varie
d
wit
h
the se
nse
d
c
u
rrent (
I_s
e
nse
)
flo
w
ing
th
ro
ugh
th
e curren
t
p
r
ob
e
XC
P1
.
The c
h
ar
ge a
n
d di
sc
ha
rge m
ode s
w
i
t
c
her
K
1
is sh
own
in
Fig
u
re
3
-
b
.
It offers th
e
po
ssib
i
l
ity to
switch
betwee
n two
m
odes accordi
ng to the se
nt
value by m
ean of the term
ina
l
Sw
_1
. At
cha
r
gi
ng t
i
m
e (
Sw
_1
=
5
V) t
h
e
p
o
sitiv
e b
a
ttery
p
i
n
(2) is link
e
d to
t
h
e co
n
t
ro
lled cu
rren
t sou
r
ce (
I_c
h
arge
)
.
B
u
t
at d
i
scharg
ing ti
m
e
(
Sw
_1
=
0
V)
t
h
e c
o
n
n
ect
i
o
n i
s
swi
t
c
he
d t
o
t
h
e
vol
t
a
ge
c
ont
rol
l
e
d
resi
st
o
r
(
R2
) in
stead
.
Th
e t
h
erm
a
l Mo
d
e
l i
n
Fi
g
u
re
3
-
c trails the b
a
ttery’s
el
e
c
t
r
ol
y
t
e t
e
m
p
erat
ure
.
It
i
s
c
o
m
posed
of
t
w
o
vol
t
a
ge
c
ont
r
o
l
l
e
d so
urce
s
eq
1
and
eq2
wh
ich
ev
al
u
a
te
th
e in
stan
tan
e
o
u
s
b
a
ttery tem
p
eratu
r
e (
T_
bat
). L
.
Castaner a
nd
S. Silvestre
pre
s
ent the
use of ‘sdt
’ PS
p
i
ce fu
n
c
tion
wh
ich
is th
e ti
m
e
in
te
g
r
al
o
p
e
ration
[16
]
.
We
u
s
e t
h
is fun
c
tio
n to
so
l
v
e
th
e equ
a
tion
(5) as t
h
e
fo
llowi
n
g
:
Vol
t
a
ge
co
nt
r
o
l
l
e
d so
urce
eq1
:
_*
_
,
2
_
/
ao
V
R
b
a
t
p
w
r
abs
V
I
s
e
ns
e
V
T
bat
V
T
V
R
(6
)
Vol
t
a
ge
co
nt
r
o
l
l
e
d so
urce
eq2
:
20
/
oo
VT
s
d
t
V
V
C
(7
)
The calc
u
lation
of battery te
m
p
erature
V(T
_
bat)
is b
a
sed
o
n
th
e in
tern
al
resistan
ce
V(R_bat)
and t
h
e
i
n
st
ant
a
ne
o
u
s s
e
nse
d
cu
rre
nt
t
h
r
o
ug
h t
h
e
bat
t
ery
V(I_se
nse)
. More
over, t
h
e
values
of the a
m
bient te
m
p
erature
V(T
a
)
, the thermal resistance
V(R
o
)
, th
e b
a
t
t
ery in
itial te
mp
erat
u
r
e
V(T
o
)
and the t
h
erm
a
l capacitance
V(C
o
)
are set at th
e beg
i
nn
ing
of th
e si
m
u
latio
n
and
sen
t
to
Mu
ltisi
m
b
y
Lab
V
IEW
-
M
u
ltisi
m
termin
als su
ch
as
T_a
,
R_o
,
T
_o
an
d
C_
o
. Fi
nally
the evaluate
d te
m
p
erature
V(T
_
ba
t)
i
s
sent
t
o
LabV
IE
W code
by
t
h
e
T_bat
termin
al.
Fi
gu
re
3.
a-
Eq
ui
val
e
nt
ci
rcui
t
m
odel
,
b
-
C
h
a
r
ge
o
r
di
scha
rg
e m
ode swi
t
c
h
e
r, c
-
T
h
erm
a
l
m
odel
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Perfo
r
man
ce Eva
l
ua
tio
n o
f
Mo
d
e
lling
a
n
d
S
i
mu
l
a
tio
n o
f
Lea
d
Acid Ba
tteri
es fo
r …
(
B
e
n
a
c
hi
r B
ouc
hi
k
h
i
)
47
6
3.
2.
La
bVIEW Stag
e
Eq
uat
i
ons
(
1
-
4
) w
h
i
c
h
desc
ri
be t
h
e e
v
ol
ut
i
o
n
of i
n
t
e
rnal
b
a
t
t
e
ry
param
e
ters a
nd t
h
e st
a
t
e of c
h
ar
ge
are i
m
pl
em
ented as se
pa
rat
e
col
l
a
b
o
rat
i
n
g
bl
oc
ks as
sh
ow
n i
n
Fi
g
u
re
4. T
h
e
r
ef
ore
,
t
h
e La
bV
IE
W
bl
oc
k
d
i
agram
to
co
n
t
ro
l th
e Mu
lti
si
m
b
a
ttery circu
itry con
t
ain
s
th
ree m
a
j
o
r parts: “Mu
ltisim
Battery circ
u
itry”,
“B
at
t
e
ry
m
ode
l
param
e
t
e
rs est
i
m
a
t
i
ons” a
n
d
“SOC
e
s
t
i
m
a
t
i
on”
bl
ock
.
T
h
e
l
a
st
t
w
o
bl
o
c
s
exec
ut
e t
h
e c
o
nt
r
o
l
syste
m
a
l
g
o
r
it
h
m
s wh
ich
esti
m
a
te
th
e b
a
tte
ry
m
o
d
e
l p
a
rameters. After th
at, th
e esti
m
a
ted
v
a
lu
es are
sen
t
to
th
e Mu
ltisim
ci
rcu
it.
Fi
gu
re
4.
Lab
V
IE
W bl
ock
di
a
g
ram
of
b
a
ttery
m
o
d
e
l p
a
rameters estim
a
tio
n
3.
2.
1.
Battery Mode
l Par
a
meters
Estimation Bloc
The “B
at
t
e
ry
m
odel
param
e
t
e
rs est
i
m
a
t
i
on” bl
oc
is a La
bVIE
W case s
t
ructure.
It estim
a
tes, for
every
o
p
e
r
at
i
o
n m
ode (cha
r
g
e o
r
di
sc
har
g
e)
, t
h
e i
n
st
a
n
t
a
ne
ou
s val
u
e of m
odel
p
a
ram
e
t
e
rs whi
c
h are
capacitance
C
_
bat
by
u
s
i
n
g e
quat
i
o
ns
(1
) a
n
d
(
2
)
, in
tern
al
v
o
ltag
e
(
V_1
)
an
d in
tern
al resisto
r
(
R_1
) by
usi
n
g
eq
u
a
tion
s
(3
) an
d (4
).
3.
2.
2.
SOC
estim
a
ti
on
bloc
After th
e estimatio
n
o
f
th
e i
n
tern
al p
a
ram
e
ters, th
e “SOC
Esti
m
atio
n
”
blo
c
is th
en
ab
le to
estim
a
t
e
t
h
e ne
w i
n
st
a
n
t
a
ne
ou
s val
u
e of S
O
C
by
usi
n
g t
h
e eq
uat
i
on
(4
), as
descri
bed i
n
Fi
gu
re 5
.
He
n
ce, t
h
e
calcu
latio
n
of
SOC is b
a
sed on
t
h
e
b
a
ttery cu
rren
t (
I
_ba
t
), th
e esti
m
a
ted
cap
acity (
C_
ba
t
) and t
h
e SOC
hi
st
ory
t
h
at
i
s
st
ore
d
by
t
h
e “M
em
ory
”
bl
oc
k. The
out
put
of t
h
i
s
m
e
m
o
r
y
bl
oc i
s
l
i
m
i
t
e
d bet
w
ee
n 0 a
nd
1 by
the “Saturation” bloc
which presents
th
e i
n
st
ant
a
ne
ou
s est
i
m
a
t
e
d val
u
e
o
f
SOC
.
Fi
gu
re
2.
B
a
t
t
e
ry
st
at
e o
f
c
h
ar
ge est
i
m
ati
on
b
l
ock
4.
RESULTS
A
N
D
DI
SC
US
S
I
ONS
4.
1.
Simula
ti
o
n
Results
Fi
gu
re
6
rep
r
e
s
ent
s
t
h
e
f
r
o
n
t
pa
nel
o
f
t
h
e
pr
o
pose
d
Lab
V
IE
W
g
r
ap
hi
c
a
l
user
i
n
t
e
r
f
a
ce (
G
U
I) t
o
sim
u
l
a
t
e
t
h
e i
n
st
ant
a
ne
ous
ba
t
t
e
ry
m
odel
pa
ram
e
t
e
rs evol
u
t
i
on.
Du
ri
n
g
t
h
e char
gi
n
g
a
n
d
di
scha
rgi
n
g
m
ode
, i
t
g
u
a
ran
ties th
e o
b
s
erv
a
tio
n
o
f
th
e b
e
h
a
v
i
ou
r o
f
th
ose in
tern
al p
a
ram
e
ters with
th
e p
o
s
sib
ility
o
f
settin
g
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 7,
No
.
2,
Ju
ne 20
16
:
472
–
4
80
47
7
b
a
tteries d
a
tash
eet p
a
ram
e
ters v
a
lu
es m
a
n
u
a
lly. Ad
d
itio
n
a
lly, we can
tes
t
th
e i
m
p
act
o
f
th
e cu
rren
t
rate o
n
b
a
tteries ch
argin
g
or
d
i
sch
a
rgin
g
pro
c
ess: Du
ri
n
g
th
e ch
arg
i
ng
m
o
d
e
t
h
e GUI g
i
v
e
s t
h
e po
ssib
ility to
d
e
fi
n
e
d
i
rectly th
e v
a
lu
e o
f
t
h
e curren
t, bu
t du
ri
n
g
th
e d
i
sch
a
rg
ing
m
o
d
e
, th
is valu
e is d
e
fi
n
e
d b
y
v
a
rying
the load
resistance
value. More
over, the be
ha
vi
our
of each
battery
can be
sim
u
lated at any gi
ve
n internal pa
ra
meters
'
in
itial co
nd
itio
n
s
, su
ch as t
h
e in
tern
al tem
p
eratu
r
e an
d th
e state of ch
arge. In
t
h
e
n
e
x
t
l
i
n
e
s, t
h
e sim
u
latio
n
resu
lts ob
tain
ed
du
ri
n
g
t
h
e
ch
arg
i
ng
m
o
de will b
e
p
r
esen
ted
.
Firstly, we set b
a
ttery
m
o
d
e
ls p
a
rameters
(
ba
ttery 1
) as fo
llo
w:
Battery Mo
d
e
l
Param
e
ters:
n
s
= 6 a
n
d
C
10
= 19
0 Ah
;
Th
erm
a
l Mo
d
e
l Param
e
ters:
C_
o
= 15 Wh/°C,
R_o
= 0.2 °C/W
,
T_o
=
25 °C an
d
T_
a
= 25
°C.
After t
h
at we
set th
e sim
u
lat
i
o
n
p
a
ram
e
ters b
y
cho
o
sing
the b
a
ttery fu
n
c
t
i
o
n
m
o
d
e
(C
h
a
rg
e) and
setting
th
e
in
itial b
a
ttery state o
f
ch
arg
e
(
SOC
_
1
=
0.
1)
.
Fi
nal
l
y
, we
fi
x
t
h
e c
h
ar
gi
n
g
c
u
r
r
ent
(
I
_
bat
= 1
A
)
.
Fig
u
re 3
.
Lead acid
b
a
ttery p
a
ram
e
ters
si
m
u
l
a
tio
n
GUI un
der
co
-sim
u
l
atio
n
LabVIEW/Mu
ltisi
m
4.
2.
Discussions
To eval
uate the perform
a
nce of
the
propos
ed m
e
thod of the m
ode
lling a
nd sim
u
lation of lead aci
d
b
a
tteries, a seco
nd
b
a
ttery (
ba
ttery 2
) is
b
e
i
n
g sim
u
lated
with
th
e sam
e
th
erm
a
l p
a
rameters and
sim
u
latio
n
co
nd
itio
ns. The b
a
ttery m
o
d
e
l p
a
ram
e
ters are:
n
s
= 6
,
C
10
= 29
6 Ah
.
Figu
re 7-a sho
w
s th
e evo
l
utio
n
o
f
in
tern
al resistan
ce
for th
e two
b
a
tteries during
t
h
e ch
arg
i
ng
regim
e
. The contin
u
o
u
s
cu
rv
e refer
s
to
ba
ttery 1
. Its inte
rnal resistance
jum
p
s from
0.32
Ω
(
SOC
= 0.9)
t
o
4.
53
Ω
(
SO
C
= 0.
9
9
)
.
T
h
e
d
a
she
d
c
u
r
v
e
re
fers
to
ba
ttery 2
.
Its i
n
ternal resistance
jum
p
s from
0.22
Ω
(
SOC
=0.9) to
2.91
Ω
(
SOC
=
0.99).
As a
res
u
lt, when batterie
s
are c
h
a
r
gi
ng,
the values
of internal resista
n
ce
a
r
e
i
n
fl
ue
nce
d
by
t
h
e st
at
e o
f
c
h
arge
. M
o
reo
v
e
r
, t
h
ose
va
l
u
es
increase
ra
pidly whe
n
the
batteries approa
ch the
fully cha
r
ge
d
s
t
ate.
Fi
gu
re 7
-
b s
h
ows t
h
e ev
ol
u
t
i
on o
f
t
h
e va
ri
at
i
on o
f
i
n
t
e
rnal
t
e
m
p
erat
ure fo
r
ba
ttery 2
at three
char
gi
n
g
c
u
r
r
e
n
t
rat
e
s.
T
h
e a
m
ount
o
f
t
h
i
s
vari
at
i
o
n i
s
g
o
v
er
ne
d
by
b
o
t
h
t
h
e c
h
ar
gi
n
g
c
u
r
r
ent
a
n
d t
h
e
st
at
e of
charge.
During constant cha
r
ging curre
nt, t
h
e tem
p
erature
variation inc
r
eas
es fo
llo
wi
ng
th
e SOC. B
u
t, wh
en
we approac
h
the fully charged state,
the internal te
m
p
erature val
u
e ri
s
e
s quic
k
ly with increasi
n
g charging
current. Furthe
rm
ore, the i
n
ternal tem
p
erature influe
nces t
h
e internal
capacity. As a resu
lt, th
e cap
acity v
a
lu
e
o
f
th
e
b
a
ttery b
eco
m
e
s h
i
g
h
e
r wh
en
it is clo
s
e to
b
e
fu
lly ch
arg
e
d
.
Th
is is wh
y b
a
tteries
requ
ire a lon
g
p
e
ri
od
of
t
i
m
e
i
n
o
r
de
r t
o
be
f
u
l
l
y
ch
arge
d.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Perfo
r
man
ce Eva
l
ua
tio
n o
f
Mo
d
e
lling
a
n
d
S
i
mu
l
a
tio
n o
f
Lea
d
Acid Ba
tteri
es fo
r …
(
B
e
n
a
c
hi
r B
ouc
hi
k
h
i
)
47
8
(a)
(b
)
Fi
gu
re
7.
Ev
ol
ut
i
o
n
o
f
i
n
t
e
r
n
al
param
e
t
e
rs at
char
gi
n
g
tim
e
,
a- Internal res
i
stance,
b- Internal
tem
p
erature.
Trad
ition
a
l ch
arg
i
n
g
techn
i
ques o
f
lead
acid
b
a
tteries
eith
er u
s
e con
s
tan
t
cu
rren
t or con
s
t
a
n
t
v
o
ltag
e
t
o
cha
r
ge
bat
t
e
ri
es,
or
com
b
i
n
e t
h
e
s
e t
w
o s
c
hem
e
s. C
onst
a
nt
cu
rra
nt
i
s
pract
i
cal
at
t
h
e
be
gi
n
n
i
n
g
of
bat
t
e
ry
ch
arg
i
ng
wh
ile th
e b
a
ttery vo
ltag
e
is lo
w.
Wh
en
th
e
b
a
ttery v
o
ltage increases to
a
prede
f
ine
d
val
u
e, the
char
ger
shi
f
t
s
t
o
t
h
e c
o
nst
a
nt
vol
t
a
ge
m
ode.
Ho
we
ver
,
w
h
e
n
u
p
c
o
m
i
ng t
h
e ful
l
y
cha
r
ge
d st
at
e, t
h
e
val
u
e o
f
in
ter
n
al r
e
sistan
ce in
cr
ease rap
i
d
l
y wh
ich
cau
s
es an
expon
en
tial dr
op
o
f
th
e cur
r
e
n
t
. Th
er
ef
or
e,
f
u
ll ch
arg
e
tak
e
s a long
ti
m
e
s wh
ich
lead
s to
v
e
ry im
p
o
r
tan
t
ch
ang
e
on
t
h
e b
a
tt
ery te
m
p
erature. Th
is
fact has an
im
port
a
nt
i
n
fl
u
e
nce
on t
h
e
pe
rf
orm
a
nce an
d
l
i
f
et
im
e of t
h
e
bat
t
e
ri
es.
To
ove
rc
om
e t
hose sh
ort
c
om
i
ngs, w
e
in
ten
d
to
im
p
r
o
v
e
th
e
p
e
rfo
rman
ce of th
e
ch
arg
i
ng
p
r
o
c
ess b
y
an
in
tellig
en
t ch
arg
i
n
g
alg
o
rith
m
wh
ich
can
accurately dete
rm
ine that the charging c
u
rre
n
t is necessa
ry. A fuzzy logic syste
m
has be
en impl
eme
n
ted to
cont
rol
t
h
e flow of
cha
r
ging current
o
f
Lithiu
m
-
io
n
b
a
ttery [17
]
. Th
is con
t
ro
ller
will u
s
e two i
np
uts whi
c
h
are voltage a
nd tempe
r
atu
r
e
.
Th
e
n
e
w ch
arg
e
r will
b
e
b
a
sed
also on th
e
fu
zzy con
t
ro
ller
wh
ich
takes in
t
o
account the
battery te
m
p
erature va
riations
and the
SO
C
value when adjusting th
e c
h
a
r
gi
ng c
u
rrent.
5.
CO
NCL
USI
O
N
In t
h
i
s
w
o
r
k
we pre
s
ent
a new m
e
t
hod
of si
m
u
l
a
t
i
on of l
ead aci
d
bat
t
e
ri
es para
m
e
t
e
rs. The
i
m
p
l
e
m
en
tatio
n
o
f
th
e
C
I
EMAT
m
o
d
e
l was b
a
sed
o
n
th
e co-sim
u
l
ati
o
n Lab
V
IEW-Mu
ltisi
m
. Th
e circu
itry
stag
e is d
e
si
g
n
ed
in
Mu
ltisim an
d
t
h
e cod
e
of con
t
ro
lli
n
g
o
f
th
is circu
itry is d
e
velop
e
d
i
n
LabVIEW. The two
si
m
u
lato
rs ch
aracteristically
ex
ch
ang
e
d
a
ta in
a syn
c
h
r
on
ized
and
v
a
riab
le ti
m
e
step
m
o
d
e
. Sim
u
latio
n
resu
lts
dem
onstrate the im
pact of the
charging
cu
rren
t on
th
e in
tern
al resistan
ce
,
te
m
p
erature a
n
d the ca
pacitance of
th
e b
a
ttery. At
ch
arg
i
n
g
ti
m
e
, in
tern
als
resistan
ce an
d tem
p
erature inc
r
ease ra
pidly when approac
h
i
n
g the
ful
l
y
cha
r
ge
d s
t
at
e. There
f
ore
,
t
o
i
m
pro
v
e t
h
e per
f
o
rm
ance of t
h
e
bat
t
e
ry
char
gi
n
g
pr
oce
ss by
e
nha
nci
n
g t
h
e
full charge time, the battery charge
r con
t
ro
l algo
rith
m
m
u
st
tak
e
th
e
internal te
m
p
erature a
nd t
h
e SOC
inform
ation into account
whe
n
evaluati
ng the charging current.
As a res
u
lt,
the chargi
ng curre
nt m
u
st drop
wh
en in
tern
al
te
m
p
eratu
r
e or SOC
rises.
In th
e
fu
tu
re
wo
rk
,
we i
n
ten
d
t
o
im
ple
m
ent a fuzzy-c
ontrol-base
d
b
a
ttery ch
arg
e
r to
cop
trad
ition
a
l ch
arg
e
r fail
s. Th
is co
n
t
ro
l is tak
i
n
g
t
h
e
v
a
riatio
n
o
f
tem
p
eratu
r
e and
SOC as
in
pu
t to
adju
st
th
e ch
arg
i
ng
cu
rren
t as an
o
u
tp
u
t
.
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NC
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.
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c
on-M
o
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ccur
a
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ectr
i
ca
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tter
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odel Capab
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al
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a
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odels
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ead-
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es
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.
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.
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.
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,
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t
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.
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ilves
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oltaic Systems Using PSpice
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,
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120–122.
[17]
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l
a,
A. F. Oklil
as,
a
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thild
a,
“
L
ithiu
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y
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i
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y
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BIOGRAP
HI
ES OF
AUTH
ORS
A.
Selmani
is a computer scien
ce teach
er at qu
alif
y
i
ng schoo
l since 2001. Curr
ently
he is a Ph.D.
student at th
e Electron
i
cs Automatic and Biotech
nol
og
y
Laborato
r
y
,
Faculty
of Sciences of Meknes,
Universit
y
Moul
a
y
Ism
a
ïl, Moro
cco.
His resear
c
h
inter
e
sts inc
l
u
d
e fuz
z
y
logi
c c
ontrolle
r based
of
the
climate und
er greenhous
e usi
ng solar
energ
y
equipment.
A.
Ed-dah
hak
r
eceived Ph.D. fr
om
Faculty
of Scien
ces Meknes in 2009. He is a Professor in the
Department of
Electr
i
cal Eng
i
neer
ing, High
School of Technolog
y
Me
knes, Moulay
Ismaïl
Univers
i
t
y
, M
o
r
o
cco. Hi is
a m
e
m
b
er of Laborat
or
y
of El
ectron
i
cs
, Autom
a
tics
a
nd Biotechno
log
y
of the
F
acul
t
y
o
f
S
c
ien
ces
,
M
e
k
n
es
. His
current
area
of r
e
s
ear
ch
includ
es
el
ec
tro
n
ics
,
d
e
ve
lopm
ent
of a s
y
stem
for
m
onitoring th
e
clim
ate and
m
a
na
ging th
e drip
fert
ilizing
irrigation
in
greenhouse.
M
.
O
u
tanoute
is currently
a Ph.D. student at the El
ectro
nics Automatic and Biotechno
lo
g
y
Laborator
y
,
Mo
ulay
Ismaïl University
, Faculty of
S
c
ienc
es
in
M
e
knes
,
M
o
rocco. His
r
e
s
ear
ch
inter
e
sts include advanced modeling and contr
o
l st
rategies of climatic
parameters under a solar
greenhouse.
A.
Lac
hhab
received Ph
.D. fro
m Faculty
of Sciences in
Rab
a
t
in 2000. He is a Professor in High
School of Tech
nolog
y
of Mek
n
es, Moulay
Is
ma
ïl University
, Morocco. He is a Member o
f
Laborator
y
of
Electronic, Auto
ma
tic
and Biotechnolog
y
in
Faculty
of
Scien
c
es in Meknes.
Hi
s
current
ar
ea
of r
e
search
in
cludes
m
odelling
and
a
u
tom
a
tic
contro
l
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Perfo
r
man
ce Eva
l
ua
tio
n o
f
Mo
d
e
lling
a
n
d
S
i
mu
l
a
tio
n o
f
Lea
d
Acid Ba
tteri
es fo
r …
(
B
e
n
a
c
hi
r B
ouc
hi
k
h
i
)
48
0
M. Gu
erb
aou
i
r
eceived Ph.D. fr
om Facult
y
of Scien
ces Meknes in 2014.
He is
a teacher at High
School in
Engineering
Scien
c
e since 1996
.
He
is a memb
er of
Laborator
y
of
Electronics,
Autom
a
tics and
Biotechno
log
y
o
f
the Facu
lt
y of
Sc
ienc
es
, M
e
kn
es
. His
res
ear
ch
inter
e
s
t
s
includ
e
regulating p
a
rameters under
gr
eenhouse b
y
Fu
zzy
logi
c and
use of solar
energ
y
equipment in
the
greenhouse.
B.
Bouc
hikhi
receiv
e
d the Ph.D. degree from
the
Université de d
r
oit, d’E
c
onom
i
e
et des Sci
e
nce
s
d’Aix Marseille
III, in 1982. B
e
n
achir Bou
c
hikhi
wa
s awarded a
Doctor of Scien
ces degree in 19
88
from the Univer
sity
of Nan
c
y
I
.
Dr. Bouchikhi g
o
t a
position o
f
t
itular p
r
ofessor a
t
the Univ
ersit
y
of
Moulay
Ismaïl,
Faculty
of
Scien
ces in Mekn
es, Morocco sin
c
e 1993. He
is th
e director of
th
e
Laborator
y
of
Electronics, Automatic
and Bio
t
ec
hno
log
y
. His
curren
t
research focuses on the
development of
electronic nose and electronic
t
ongue devices for food anal
y
s
is and biomedical
applications and
the con
t
rol of th
e climate
and drip fertirr
i
gation u
nder greenhouse. He is author
an
d
co-author
of ov
er 65 p
a
pers, pu
blished on
inter
n
ation
a
l
journals. During th
e
last 10
y
e
ars he h
a
s
coordinated
a do
zen n
a
tion
a
l and
international pr
ojects
, in
th
e
area of food
safety
, the contro
l of
th
e
climate and
drip
fert
irrigation u
nder greenhouse. He
is
member of th
e H2020-
MSCA-RI
S
E-2014
project TROPSENSE: "Dev
elopment of a non-
invasive breath te
st for early
diagnosis of tropical
diseases He is member of
the Editorial Board
of J
ournal of
Biotechnolg
y
and
Bioengineer
ing.
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