Inter
national
J
our
nal
of
Electrical
and
Computer
Engineering
(IJECE)
V
ol.
16,
No.
5,
October
2026,
pp.
2294
∼
2303
ISSN:
2088-8708,
DOI:
10.11591/ijece.v16i5.pp2294-2303
❒
2294
Modeling
and
perf
ormance
analysis
of
batteries
in
PV
systems
Abdelfettah
Boussaid
1,2,3
,
Hadjer
Bounechba
1,3
,
Seif
El-Islam
Chelli
3,4
,
Salah
Hammoudi
1,2
1
Uni
v
ersit
´
e
Constantine
1,
Fr
`
eres
Mentouri,
Constantine,
Algeria
2
Institut
des
Sciences
et
des
T
echniques
Appliqu
´
ees-IST
A,
Constantine,
Algeria
3
Laboratoire
d’
´
electrotechnique
Constantine-LEC,
Constantine,
Algeria
4
Department
of
Electrical
Engineering,
Uni
v
ersit
´
e
Badji
Mokhtar
-Annaba,
Annaba,
Algeria
Article
Inf
o
Article
history:
Recei
v
ed
Sep
21,
2025
Re
vised
Jun
10,
2026
Accepted
Jul
22,
2026
K
eyw
ords:
Batteries
ef
cienc
y
Char
ging
mode
Dischar
ging
mode
Photo
v
oltaic
batteries
Solar
ener
gy
ABSTRA
CT
This
res
earch
paper
comprehensi
v
ely
e
xamines
photo
v
oltaic
batteries,
essential
elements
of
susta
inable
solar
ener
gy
systems.
This
research
incl
udes
a
pre-
cise
mathematical
model
de
v
elopment
t
o
represent
beha
vior
and
performance
of
these
batteries,
in
order
to
better
understand
the
storage
and
use
of
electri-
cal
ener
gy
generated
by
solar
panels.
In
addition,
a
complete
simulation
w
as
carried
out
to
e
v
aluate
the
performance
of
these
models
under
v
arious
operating
conditions,
thus
contrib
uting
to
impro
v
e
our
understanding
on
v
arious
f
actors
that
inuence
batteries
ef
cienc
y
in
real
situations
.
In
the
eld
of
battery
man-
agement,
their
performances
were
e
xamined,
such
as
char
ging
and
dischar
ging
mode
as
well
as
continuous
monitoring
of
the
battery
status.
The
objecti
v
e
is
to
strengthen
the
use
ef
cienc
y
of
solar
ener
gy
and
impro
v
e
its
sustainability
,
thus
contrib
uting
to
achie
ving
the
global
sustainability
goals
and
reducing
harmful
emissions
associated
with
traditional
ener
gies.
This
is
an
open
access
article
under
the
CC
BY
-SA
license
.
Corresponding
A
uthor:
Abdelfettah
Boussaid
Institute
of
Science
and
Applied
T
echnics,
Uni
v
ersite
Constantine
1
Fr
`
eres
Mentouri
2500,
Algeria
Email:
Abdlfettah.Boussaid@lec-umc.or
g
Nomenclatur
e
V
batt
Battery
v
oltage
S
O
C
The
state
of
char
ge
of
the
battery
n
b
Number
of
cells
constituting
the
battery
△
T
The
battery
heating
E
b
The
electromoti
v
e
force
V
batt
ch
battery
v
oltage
in
char
ging
mode
I
batt
The
current
of
the
battery
V
batt
disch
battery
v
oltage
in
dischar
ging
mode
R
b
The
internal
resistance
of
a
battery
cell
W
ener
gy
(
W
h/k
g
)
R
b
ch
The
internal
resistance
of
a
battery
cell
in
char
ging
mode
P
po
wer
(
W
/
k
g
)
R
b
disch
The
internal
resistance
of
a
battery
cell
in
dischar
ging
mode
t
P
assage
time
of
the
current
(s)
C
10
The
battery
capacity
dischar
ged
in
10
hours
E
a
v
erage
v
oltage
(V)
I
10
dischar
ged
current
in
10
hours,
C
10
=
10
∗
I
10
1.
INTR
ODUCTION
In
the
current
global
conte
xt
of
transition
to
rene
w
able
and
sustainable
ener
gy
sources,
photo
v
oltaic
systems
occup
y
a
prominent
place
as
alternati
v
e
solution
for
clean
ener
gy
production.
Photo
v
oltaic
batteries
play
a
crucial
role
in
these
s
ystems,
storing
the
electrical
ener
gy
produced
by
the
solar
panels
f
or
later
use.
J
ournal
homepage:
http://ijece
.iaescor
e
.com
Evaluation Warning : The document was created with Spire.PDF for Python.
Int
J
Elec
&
Comp
Eng
ISSN:
2088-8708
❒
2295
The
de
v
elopment
and
impro
v
ement
of
photo
v
oltaic
batteries
performances
are
essential
to
maximize
the
use
of
solar
ener
gy
and
ensure
the
clean
ener
gy
sources
sustainability
[1]–[3].
The
rst
battery
w
as
in
v
ented
during
a
scient
ic
contro
v
ersy
between
the
bio-ph
ysicist
Luig
i
Gal
v
ani
and
the
Italian
engineer
Al
essandr
o
V
ol
ta
.
Originally
used
as
a
DC
v
oltage
source
for
e
xperimental
purposes,
this
technology
has
been
impro
v
ed
o
v
er
decades
to
become
the
main
means
of
electrochemical
storage
in
our
portable
electrical
appliances.
No
w
adays,
battery
research
is
v
ery
acti
v
e,
with
a
wide
v
ariety
of
future
batteries
w
aiting
to
be
de
v
eloped
in
chemical
laboratories
and
among
researchers.
This
historical
re
vie
w
of
battery
technologies
is
f
ar
from
e
xhausti
v
e,
b
ut
it
highlights
the
e
v
olution
of
the
most
signicant
batteries
and
accumulators,
as
well
as
technological
adv
ances
that
ha
v
e
led
to
ne
w
applications.
Inno
v
ation
in
this
eld
of
research
has
gi
v
en
rise
to
man
y
in
v
entions,
and
batteries
di
v
ersity
is
constantly
gro
wing
[4]–[7].
Ener
gy
storage
in
v
olv
es
the
capture
of
produced
ener
gy
at
a
gi
v
en
moment
with
a
vie
w
to
its
sub-
sequent
use.
The
de
vice
or
apparatus
responsible
for
storing
this
ener
gy
is
called
an
accumulator
o
r
battery
.
This
ener
gy
storage
process
aims
to
con
v
ert
forms
of
ener
gy
that
are
dif
cult
to
store
into
forms
that
are
more
con
v
enient
or
economical
to
store
[8]–[14].
Ener
gy
needs
and
research
for
ef
cient
w
ays
to
store
it
are
increasingly
pressing
concerns.
That
is
wh
y
this
sector
has
been
gro
wing
steadily
o
v
er
the
past
fe
w
years.
T
o
use
an
accumulator
or
a
battery
ef
fecti
v
ely
,
it
is
essential
to
understand
their
operation,
their
dynamics
and
the
parameters
that
can
inuence
their
performance.
The
main
challenge
with
these
de
vices
is
to
maintain
their
service
life
for
as
long
as
poss
ible
and
to
optimize
their
ener
gy
use.
The
second
part
addresses
batteries
operation
and
their
essential
characteristics
[15]–[18].
There
are
se
v
eral
methods
of
ener
gy
storage,
among
which
batteries,
super
-capaci
tors
and
f
uel
c
ells
that
occup
y
an
important
place.
Although
these
three
methods
use
dif
ferent
ener
gy
con
v
ersion
and
storage
mechanisms,
the
y
share
se
v
eral
electrochemical
characteristics.
The
ener
gy
production
tak
es
pl
ace
at
the
in-
terf
ace
between
the
electrode
and
the
electrolyte.
The
transport
of
electrons
and
ions
constitutes
tw
o
distinct
processes
the
electrolyte
acts
as
an
ionic
conductor
and
plays
the
role
of
an
electronic
insulator
[19]–[22].
The
battery
is
a
de
vice
that
stores
electricity
in
chemical
form
and
that
can
w
ork
re
v
ersibly
(in
curre
n
t
rather
than
v
oltage).
It
is
characterized
by
its
capacity
and
its
mass
ener
gy
.
The
chemical
ener
gy
stored
in
each
cell
is
directly
con
v
erted
into
electrical
ener
gy
when
the
battery
terminals
are
connected
to
an
electrical
equipment.
The
battery
operation
is
based
on
the
chemical
reaction
between
electrodes
and
electrolyte,
which
leads
to
oxidation-reduction.
Indeed,
the
ne
g
ati
v
e
electrode
under
goes
oxidation,
thus
releasing
electrons,
while
the
positi
v
e
electrode
under
goes
a
reduction,
by
absorbing
electrons.
This
electrical
char
ges
imbalance
generates
the
electromoti
v
e
force
(EMF)
of
the
accumulator
[23]–[25].
The
inte
gration
of
batteries
in
photo
v
oltaic
systems,
whether
connected
to
the
grid
or
autonomous,
presents
signicant
challenges
ranging
from
economic
feasibility
to
comple
x
technical
management.
The
main
obstacle
remains
the
high
cost
of
the
initial
in
v
es
tment,
which
signicantly
af
fects
the
o
v
erall
protability
of
the
system.
This
research
paper
aims
to
pro
vide
a
complete
analysis
of
photo
v
oltaic
batteries
by
studying
their
models
and
simulating
their
performance
under
v
arious
operati
n
g
conditions.
The
study
includes
the
de
v
elop-
ment
of
precise
mathematical
models
of
these
batteries,
as
well
as,
the
analysis
of
battery
management
systems
in
order
to
impro
v
e
their
ef
cienc
y
and
ensure
a
longer
service
life.
Understanding
the
operation
of
photo-
v
oltaic
batteries
and
impro
ving
management
techniques
greatly
contrib
utes
to
optimize
solar
ener
gy
use
and
reducing
dependence
on
fossil
fuels.
This
research
paper
,
gi
v
es
a
signicant
scientic
contrib
ution
that
addresses
the
challenges
associ
ated
with
rene
w
able
ener
gy
and
support
global
ef
forts
for
a
more
sustainable
and
clean
future.
Enhancing
the
ef
cienc
y
and
sustainability
of
photo
v
oltaic
batteries
is
a
crucial
step
to
w
ard
meeting
rene
w
able
ener
gy
goals.
Furthermore,
it
plays
a
vital
role
in
strengthening
our
ability
to
combat
climate
change
and
achie
v
e
sustainable
de
v
elopment
w
orldwide.
2.
B
A
TTER
Y
CHARA
CTERISTICS
V
arious
forms
of
batteries
characterized
by
their
structure
or
technology
,
are
a
v
ailable.
Ho
we
v
er
,
the
inte
gration
of
these
dif
ferent
technologies
into
electrical
appliances
requires
compliance
with
certain
condi-
tions.
Among
them:
−
A
high
po
wer
density
(po
wer/
weight
ratio
in
W
/k
g
)
which
f
a
v
ors
signicant
accelerations.
−
An
e
xcellent
ener
gy
density
(
W
h/k
g
)
,
synon
ymous
with
e
xtended
autonomy
.
Modeling
and
performance
analysis
of
batteries
in
PV
systems
(Abdelfettah
Boussaid)
Evaluation Warning : The document was created with Spire.PDF for Python.
2296
❒
ISSN:
2088-8708
−
A
stable
v
oltage
that
guarantees
constant
performance.
−
A
long
service
life,
measured
in
the
number
of
char
ge
/
dischar
ge
c
ycles,
resulting
in
a
reduct
ion
in
costs
for
the
user
.
−
Minimal
maintenance
and
rec
ycling
possibility
.
2.1.
The
mass
ener
gy
density
(
W
h/k
g
)
The
mass
density
,
or
specic
ener
gy
,
is
one
of
the
important
characteristics
of
an
accumulator
,
it
corresponds
to
the
amount
of
ener
gy
(
W
h/k
g
)
,
that
could
be
restored
re
g
arding
i
ts
mass.
The
electri
cal
ener
gy
is
gi
v
en
by
,
dw
=
E
.I
.dt
(1)
The
v
alue
of
theoretical
mass
ener
gy
density
is
t
he
product
of
theoretical
mass
capacity
by
the
accumulator
theoretical
v
oltage
which
is
gi
v
en
by
,
W
(
w
h/g
)
=
E
(
v
ol
ts
)
×
C
(
Ah/g
)
(2)
2.2.
The
mass
po
wer
density
(
W
/k
g
)
Some
applications
require
high
po
wer
,
which
implies
that
both
v
oltage
and
current
must
be
high.
T
o
achie
v
e
this,
it
is
necessary
to
select
electrochemical
combinations
for
electrodes
which
ha
v
e
a
high
open-
circuit
potential
as
possible
and
that
sho
w
f
ast
beha
vior
with
lo
w
o
v
er
v
oltages.
The
accumulator
po
wer
is
determined
by
the
follo
wing
equation,
P
=
W
t
(3)
3.
B
A
TTER
Y
MODELLING
T
o
simulate
the
battery
beha
vior
,
it
is
necessary
to
ha
v
e
a
good
model
that
tak
es
into
account
all
its
parameters.
Unfortunatel
y
,
there
is
no
really
precise
model,
the
y
all
ha
v
e
a
ws.
W
e
ha
v
e
opted
for
the
CIEMA
T
model
(Centre
de
In
v
estig
aciones
Ener
g
´
eticas,
Medioambientales
y
T
ecnol
´
ogicas)
de
v
eloped
by
a
Spanish
research
center
[26].
It
is
relati
v
ely
complete
and
tak
es
into
account
the
temperature.
I
t
is
called
the
”uni
v
ersal”
model
because
it
does
not
require
parameters
or
e
xperimental
determinations,
unlik
e
other
commonly
used
models.
Although
it
has
some
dra
wbacks,
such
as
the
v
oltage
jump
when
switching
from
the
char
ge
c
ycle
to
the
dischar
ge
c
ycle
and
the
ne
glect
of
self-dischar
ge,
it
is
relati
v
ely
accurate.
Researchers
opted
for
this
mathematical
model
in
order
to
simulate
the
battery
beha
vior
,
i
n
order
to
analyze
v
arious
ener
gy
o
ws
according
to
problems
types
to
be
studied.
The
battery
is
represented
by
only
tw
o
components:
a
v
oltage
source
and
an
internal
resistor
,
as
sho
wn
in
Figure
1.
Figure
1.
Equi
v
alent
electrical
diagram
of
a
battery
of
n
elements
The
follo
wing
(4)and
(5)
describes
the
ph
ysical
phenomena
of
char
ging
and
dischar
ging
res
pecti
v
ely:
V
batt
=
n
b
.E
b
+
n
b
.R
b
.I
batt
(4)
V
batt
=
n
b
.E
b
−
n
b
.R
b
.I
batt
(5)
Int
J
Elec
&
Comp
Eng,
V
ol.
16,
No.
5,
October
2026:
2294-2303
Evaluation Warning : The document was created with Spire.PDF for Python.
Int
J
Elec
&
Comp
Eng
ISSN:
2088-8708
❒
2297
3.1.
Equations
of
inter
nal
r
esistance
at
char
ge
and
dischar
ge
modes
The
battery
internal
resistance
does
not
ha
v
e
a
x
ed
v
alue,
b
ut
a
v
ariable
v
alue
that
changes
d
e
pending
on
the
state
of
char
ge,
temperature
v
ariation,
as
well
as
when
char
ging
or
dischar
ging
the
battery
.
One
can
observ
e
this
on
Figure
2,
on
the
other
hand,
Char
ging
and
dischar
ging
beha
vior
could
be
gi
v
en
by
(6)
and
(7)
respecti
v
ely
.
Figure
2.
Equi
v
alent
model
of
the
battery
R
b
ch
=
1
C
10
.
6
1
+
|
I
batt
|
0
.
86
+
0
.
84
(1
−
S
O
C
)
1
.
2
+
0
.
036
1
−
0
.
025
△
T
(6)
R
b
disch
=
1
C
10
.
4
1
+
|
I
batt
|
1
.
3
+
0
.
27
S
O
C
1
.
5
+
0
.
02
1
−
0
.
007
△
T
(7)
3.2.
Equations
of
v
oltage
at
char
ge
and
dischar
ge
modes
The
battery
v
oltage
v
aries
depending
on
t
he
state
of
char
ge
and
temperature
changes.
Which
is
ob-
serv
ed
in
Figure
2.
V
oltage
equations
in
char
ging
mode
are
gi
v
en
by
,
V
batt
ch
=
n
b
.
[2
+
0
.
16
.S
O
C
]+
n
b
.
|
I
batt
|
C
10
.
6
1
+
|
I
batt
|
0
.
86
+
0
.
48
(1
−
S
O
C
)
1
.
2
+0
.
036
.
1
−
0
.
025
△
T
(8)
On
the
other
hand,
the
v
oltage
equation
in
dischar
ge
mode
is
gi
v
en
by
,
V
batt
disch
=
n
b
.
[1
.
965
+
0
.
12
.S
O
C
]
−
n
b
.
|
I
batt
|
C
10
.
4
1
+
|
I
batt
|
1
.
3
+
0
.
27
(
S
O
C
)
1
.
5
+0
.
02
.
1
−
0
.
007
△
T
(9)
3.3.
Equations
of
capacity
c
batt
T
o
highlight
the
ph
ysical
phenomena
that
go
v
ern
the
storage
system
operation,
based
on
the
capacity
,
in
accordance
with
the
proposed
models
i
n
literature,
it
is
necessary
to
tak
e
into
account
the
temperature.
The
capacity
model
C
batt
indicates
the
amount
of
ener
gy
that
the
battery
can
return
in
function
of
the
a
v
erage
dischar
ge
current
I
batt
,
This
capacity
is
dened
by:
C
batt
C
10
=
1
.
67
1
+
0
.
67
.
(
I
batt
I
10
)
0
.
9
.
(1
+
0
.
005
△
T
)
(10)
The
capacity
model
is
e
xpressed
in
current
I
10
and
stand
for
the
operating
re
gime
C
10
,
wherein
△
T
is
the
heating
with
respect
to
an
ambient
temperature
which
is
equal
to
25
◦
C
.
4.
RESUL
TS
AND
DISCUSSION
4.1.
Inter
nal
r
esistance
beha
vior
at
dischar
ge
modes
The
internal
resistance
of
the
battery
when
dischar
ging
decreases,
the
current
direction
is
the
same
as
the
electromoti
v
e
force
direction,
see
Figure
3.
In
case
when
the
state
of
char
ge
related
to
the
battery
increases,
the
electromoti
v
e
force
increases,
resulting
in
dischar
ging
the
current
f
aster
.
This
f
act
leads
to
an
increase
in
the
v
alue
of
the
dischar
ge
current.
Besides,
more
the
temperature
increases,
a
decrease
in
the
internal
resistance
v
alue
is
mark
ed,
so
it
dischar
ges
f
aster
.
Modeling
and
performance
analysis
of
batteries
in
PV
systems
(Abdelfettah
Boussaid)
Evaluation Warning : The document was created with Spire.PDF for Python.
2298
❒
ISSN:
2088-8708
Figure
3.
Equi
v
alent
model
of
the
battery
in
dischar
ge
mode
From
Figure
4,
in
a
temperature
of
25
◦
C
and
a
state
of
char
ge
30%,
the
internal
resistance
equals
to
0
.
0233
Ω
.
When
the
temperature
increases
to
50
◦
C
with
the
same
mentioned
state
of
char
ge
30%,
the
internal
resistance
mo
v
es
to
0
.
0173
Ω
.
On
the
other
hand,
if
the
temperature
is
x
ed
to
35
◦
C
and
the
state
of
char
ge
is
changed
from
80%
to
10%,
the
internal
resistance
v
aries
from
0
.
0117
Ω
to
0
.
0733
Ω
respecti
v
ely
.
From
these
results
it
is
ob
vious
that
the
internal
resistance
is
related
to
temperature
and
state
of
char
ge.
Indeed,
when
temperature
increases,
the
internal
resistance
decreases,
in
opposition,
when
state
of
char
ge
decreases,
the
internal
resistance
increases
in
dischar
ge
mode.
1
0
2
0
3
0
4
0
5
0
6
0
7
0
2
5
3
0
3
5
4
0
4
5
5
0
5
5
6
0
0
,
0
0
,
1
0
,
2
0
,
3
0
,
4
T
(
°
C
)
R
b
d
i
s
c
h
S
O
C
(
%
)
Figure
4.
Internal
resistance
v
ariation
in
the
dischar
ge
mode
in
function
of
dif
ferent
temperatures
and
dif
ferent
state
of
char
ge
Figure
5
stands
for
internal
resist
ance
v
ariation
at
the
dischar
ge
mode
depending
on
the
state
of
char
ge
and
dischar
ging
current.
On
can
notice
that,
at
a
x
ed
v
alue
of
state
of
char
ge
30%
with
dif
ferent
current
v
alue
of
0.2
A
and
1.7
A,
the
internal
resistance
v
aries
from
0
.
0431
Ω
to
0
.
0247
Ω
respecti
v
ely
.
No
w
,
if
the
current
is
x
ed
at
1.2
A
and
v
aries
the
state
of
char
ge
from
90%
to
30%,
the
internal
resistance
mo
v
es
from
0
.
0173
Ω
to
0
.
0283
Ω
.
From
these
results,
it
is
concluded
that,
the
internal
resistance
decreases
when
the
dischar
ge
current
increases.
In
opposition,
the
internal
resistance
increases
by
the
state
of
char
ge
decreasing
in
dischar
ging
mode.
0
,
0
0
,
4
0
,
8
1
,
2
1
,
6
2
,
0
2
,
4
2
,
8
0
2
0
4
0
6
0
8
0
1
0
0
0
,
0
0
0
,
0
2
0
,
0
4
0
,
0
6
0
,
0
8
0
,
1
0
S
O
C
(
%
)
R
b
d
i
s
c
h
I
b
a
t
(
A
)
Figure
5.
Internal
resistance
v
ariation
in
the
dischar
ge
mode
in
function
of
dischar
ging
current
and
state
of
char
ge
Int
J
Elec
&
Comp
Eng,
V
ol.
16,
No.
5,
October
2026:
2294-2303
Evaluation Warning : The document was created with Spire.PDF for Python.
Int
J
Elec
&
Comp
Eng
ISSN:
2088-8708
❒
2299
4.2.
Inter
nal
r
esistance
beha
vior
at
char
ging
modes
The
equi
v
alent
model
of
the
battery
in
char
ging
mode
is
sho
wn
in
Figure
6.
In
this
case,
t
he
i
nternal
resistance
of
the
battery
when
char
ging
is
considered,
the
char
ging
current
direction
is
opposite
to
the
electro-
moti
v
e
force.
Besides,
when
the
state
of
char
ge
increases,
the
electromoti
v
e
force
increases,
obstructing
the
mo
v
ement
of
the
char
ging
current,
therefore
its
v
alue
decreases,
which
leads
to
an
increase
in
the
v
alue
of
the
internal
resistance.
Ho
we
v
er
,
as
with
an
increase
in
temperature,
the
v
alue
of
the
internal
resistance
decreases,
as
sho
wn
in
Figure
7.
Figure
6.
Equi
v
alent
model
of
the
battery
in
char
ging
mode
F
or
instance,
at
a
temperature
of
25
o
C
and
a
state
of
char
ge
of
30%
the
internal
resistance
of
the
battery
is
equal
to
0.0139
Ω
and
at
a
temperature
of
35
o
C
and
a
same
state
of
char
ge,
the
internal
resistance
of
the
batte
ry
is
equal
to
Ω
.
In
opposition,
if
a
x
ed
v
alue
of
temperature
is
considered
as
35
o
C
for
tw
o
dif
ferent
v
alues
of
state
of
char
ge
which
are
40%
and
90%
,
the
obtained
v
alues
of
internal
resistances
are
gi
v
en
respecti
v
ely
by
0.0048
Ω
and
0.0121
Ω
.
As
a
conclusion
for
this
case
of
study
,
the
internal
resistance
of
the
battery
in
char
ging
mode
depends
on
temperature
and
the
state
of
char
ge.
3
0
4
0
5
0
6
0
7
0
8
0
9
0
2
4
2
6
2
8
3
0
3
2
3
4
3
6
3
8
4
0
0
,
0
0
0
0
,
0
0
5
0
,
0
1
0
0
,
0
1
5
0
,
0
2
0
0
,
0
2
5
0
,
0
3
0
0
,
0
3
5
T
(
°
C
)
R
b
c
h
S
O
C
(
%
)
Figure
7.
Internal
resistance
v
ariation
in
char
ging
mode
in
function
of
temperatures
and
state
of
char
ge
A
second
case
of
study
is
consi
d
e
red
which
consists
of
discuss
ing
the
internal
resistance
beha
vior
under
v
arious
v
alues
of
current
and
state
of
char
ge.
Indeed,
from
Figure
8,
it
is
noticeable
at
a
x
ed
v
alue
of
state
of
char
ge
equals
30%,
the
internal
resistance
stands
for
0.0222
Ω
for
a
char
ging
currents
of
0.2
A
and
equals
to
0.0130
Ω
for
a
char
ging
currents
of
1.7
A.
Equally
,
for
x
ed
v
alue
of
char
ging
current
of
1.2
A,
the
internal
resistance
equals
to
0.0142
Ω
and
0.0239
Ω
corresponding
for
the
state
of
char
ge
20%
and
80%
respecti
v
ely
.
From
the
abo
v
e
mentioned
results,
one
can
notice
that,
the
internal
resistance
decreases
with
the
char
ging
current
increase.
Whereas,
it
increases
with
state
of
char
ge
increase.
4.3.
Battery
v
oltage
in
char
ging
mode
When
char
ging
the
battery
,
the
v
oltage
equation
of
the
battery
is
gi
v
en
by
the
follo
wing
form
:
V
batt
=
E
b
+
R
b
.I
batt
(11)
According
to
the
pre
vious
equations,
the
battery
v
oltage
increases
with
state
of
char
ge
increasing.
This
is
due
to
the
f
act
that
the
internal
resistance
of
the
battery
increases
with
the
state
of
char
ge
increases.
Nonetheless,
when
the
temperature
increases,
the
battery
v
oltage
decreases.
This
is
due
to
the
decrease
in
the
internal
resistance
of
the
battery
.
Modeling
and
performance
analysis
of
batteries
in
PV
systems
(Abdelfettah
Boussaid)
Evaluation Warning : The document was created with Spire.PDF for Python.
2300
❒
ISSN:
2088-8708
0
1
2
3
4
5
0
2
0
4
0
6
0
8
0
1
0
0
0
,
0
0
5
0
,
0
1
0
0
,
0
1
5
0
,
0
2
0
0
,
0
2
5
0
,
0
3
0
0
,
0
3
5
0
,
0
4
0
0
,
0
4
5
S
O
C
(
%
)
R
b
c
h
I
b
a
t
(
A
)
Figure
8.
Internal
resistance
v
ariation
in
char
ging
mode
in
function
of
char
ging
current
and
state
of
char
ge
From
Figure
9,
it
is
ob
vious
that,
for
the
same
state
of
char
ge
v
alue
that
equals
to
30%,
the
corre-
sponding
battery
v
oltages
are
2.0038
V
and
1.9968
V
which
stand
for
25
o
C
and
55
o
C
v
alues
of
temperature
respecti
v
ely
.
On
the
other
hand,
for
a
x
ed
v
alue
of
temperature
at
40
o
C,
the
obtained
char
ging
v
oltage
with
a
stat
of
char
ge
of
10%
is
1.9683
V
,
and
2.0963
V
for
state
of
char
ge
of
90%.
From
these
res
ults,
the
battery
v
oltage
decreases
with
temperature
increases
and
it
increases
with
the
state
of
char
ge
increase.
0
1
0
2
0
3
0
4
0
5
0
6
0
7
0
8
0
9
0
0
2
0
4
0
6
0
8
0
1
0
0
1
,
9
4
1
,
9
6
1
,
9
8
2
,
0
0
2
,
0
2
2
,
0
4
2
,
0
6
2
,
0
8
2
,
1
0
2
,
1
2
2
,
1
4
S
O
C
(
%
)
V
b
a
t
t
c
h
T
(
°
C
)
Figure
9.
Char
ging
v
oltage
of
the
battery
v
ariation
in
function
of
temperatures
and
state
of
char
ge
4.4.
Battery
v
oltage
in
dischar
ging
mode
When
dischar
ging
the
battery
,
the
v
oltage
equation
of
the
battery
is
gi
v
en
by
the
follo
wing
form
:
V
batt
=
E
b
−
R
b
.I
batt
(12)
According
to
(12)
and
Figure
10,
the
battery
v
oltage
decreases
when
the
state
of
char
ge
decreases,
and
this
is
due
to
the
f
act
that
the
internal
resistance
of
the
battery
increases
as
the
state
of
char
ge
decreases.
Ho
w-
e
v
er
,
when
the
tem
perature
increases,
the
battery
v
oltage
increases,
this
is
due
to
the
decrease
in
the
internal
resistance
of
the
battery
which
related
mainly
to
the
temperature
increases.
0
1
0
2
0
3
0
4
0
5
0
6
0
7
0
8
0
9
0
0
2
0
4
0
6
0
8
0
1
0
0
1
,
8
5
1
,
9
0
1
,
9
5
2
,
0
0
2
,
0
5
S
O
C
(
%
)
V
b
a
t
t
d
i
s
c
h
T
(
°
C
)
Figure
10.
Dischar
ging
v
oltage
of
the
battery
v
ariation
in
function
of
temperatures
and
state
of
char
ge
Int
J
Elec
&
Comp
Eng,
V
ol.
16,
No.
5,
October
2026:
2294-2303
Evaluation Warning : The document was created with Spire.PDF for Python.
Int
J
Elec
&
Comp
Eng
ISSN:
2088-8708
❒
2301
4.5.
Capacity
c
batt
The
equi
v
alent
model
of
the
battery
capacity
is
sho
wn
in
Figure
11.
From
the
obtained
results
in
Figure
12,
it
is
clear
that
the
battery
capacity
is
af
fected
by
temperature
and
current
changes.
Indeed,
when
the
temperature
increases,
the
battery
capacity
increases
and
decreases
when
the
current
increases.
F
or
instance,
if
the
temperature
change
from
25
◦
C
to
50
◦
C
,
the
battery
capacity
changes
from
162.32
Ah
to
192.51
Ah
respecti
v
ely
for
a
current
v
alue
of
1
A
.
On
the
contrary
,
for
the
same
temperature
v
alue
of
40
◦
C
and
the
current
changes
from
2
A
to
6
A
,
the
obtained
battery
capacities
are
173.14
Ah
and
140.82
Ah
respecti
v
ely
.
Figure
11.
Equi
v
alent
model
of
the
battery
capacity
1
0
2
0
3
0
4
0
5
0
6
0
0
2
4
6
8
1
0
1
0
0
1
2
0
1
4
0
1
6
0
1
8
0
2
0
0
I
b
a
t
t
(
A
)
C
b
a
t
t
T
(
°
C
)
Figure
12.
Battery
capacity
in
function
of
current
for
dif
ferent
temperatures
5.
CONCLUSION
This
research
study
pro
vides
an
in-depth
analysis
of
the
CIEMA
T
model
used
to
simulate
the
batter
-
ies
beha
vior
.
This
paper
presents
detailed
fundamental
equations
that
go
v
ern
internal
resistance
and
battery
v
oltage
in
char
ge
and
dischar
ge
modes,
taking
into
account
crucial
f
actors
such
as
the
state
of
char
ge
(SOC),
temperature
and
battery
current.
The
obtained
results
by
simulation
clearly
sho
w
that
the
internal
resistance
and
the
battery
v
olt
age
v
ary
considerably
depending
on
these
parameters.
In
particular
,
the
internal
resistance
decreases
with
temperature
and
char
ging
current
increasing.
Ne
v
ertheless,
it
increases
when
the
state
of
char
ge
decreases
during
dischar
ge
mode.
Con
v
ersely
,
the
internal
resistance
increases
with
the
state
of
char
ge
increas-
ing
in
char
ging
mode.
The
simulation
of
batteries
m
ak
es
it
possible
to
nd
the
”golden
mean”
between
the
storage
capacity
and
the
surf
ace
of
panels
in
photo
v
oltaic
systems
which
could
be
considered
as
a
future
step
of
this
w
ork.
FUNDING
INFORMA
TION
Authors
state
no
funding
in
v
olv
ed.
A
UTHOR
CONTRIB
UTIONS
ST
A
TEMENT
This
journal
uses
the
Contrib
utor
Roles
T
axonomy
(CRediT)
to
recognize
indi
vidual
author
contrib
u-
tions,
reduce
authorship
disputes,
and
f
acilitate
collaboration.
Name
of
A
uthor
C
M
So
V
a
F
o
I
R
D
O
E
V
i
Su
P
Fu
Abdelfettah
Boussaid
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
Hadjer
Bounechba
✓
✓
✓
✓
✓
✓
✓
✓
Seif
El-islam
Chelli
✓
✓
✓
✓
✓
✓
✓
Salah
Hammoudi
✓
✓
✓
✓
✓
✓
✓
✓
C
:
C
onceptualization
I
:
I
n
v
estig
ation
V
i
:
V
i
sualization
M
:
M
ethodology
R
:
R
esources
Su
:
Su
pervision
So
:
So
ftw
are
D
:
D
ata
Curation
P
:
P
roject
Administration
V
a
:
V
a
lidation
O
:
Writing
-
O
riginal
Draft
Fu
:
Fu
nding
Acquisition
F
o
:
F
o
rmal
Analysis
E
:
Writing
-
Re
vie
w
&
E
diting
Modeling
and
performance
analysis
of
batteries
in
PV
systems
(Abdelfettah
Boussaid)
Evaluation Warning : The document was created with Spire.PDF for Python.
2302
❒
ISSN:
2088-8708
CONFLICT
OF
INTEREST
ST
A
TEMENT
Authors
state
no
conict
of
interest.
D
A
T
A
A
V
AILABILITY
The
authors
conrm
that
the
data
supporting
the
ndings
of
this
study
are
a
v
ailable
within
the
article.
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Int
J
Elec
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Comp
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ISSN:
2088-8708
❒
2303
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BIOGRAPHIES
OF
A
UTHORS
Abdelfettah
Boussaid
recei
v
ed
the
master
de
gree
in
electrical
engineering
from
Brothers
Mentouri,
Constantine
1
Uni
v
ersity
,
in
2012,
and
the
Ph.D.
in
electrical
engineering
from
Brothers
Mentouri,
Constantine
1
Uni
v
ersity
,
in
2017.
Currently
,
he
is
a
researcher
at
the
Laboratory
of
Elec-
trotechnics
Constantine
(LEC).
He
is
a
professor
at
the
Institute
of
Science
and
Applied
T
echnics,
Uni
v
ersity
Consta
ntine
1.
He
is
the
head
of
the
scientic
council
for
the
Institute
of
Science
and
Applied
T
echnics,
Uni
v
ersity
C
onstantine
1.
His
research
interests
include
control
strate
gies
for
A
C
machine
dri
v
es,
po
wer
electronics,
rene
w
able
ener
gy
,
and
batteries.
He
can
be
conta
cted
at
email:
abdlfettah.boussaid@lec-umc.or
g.
Hadjer
Bounechba
recei
v
ed
the
master
de
gree
in
elect
rical
engineering
from
Brothers
Mentouri,
Constantine
1
Uni
v
ersity
,
in
2012,
and
the
Ph.D.
in
electrical
engineering
from
Brothers
Mentouri,
Constantine
1
Uni
v
ersity
,
in
2017.
Currently
,
she
is
a
researcher
at
the
Laboratory
of
Electrotechnics
Constantine
(LEC).
She
is
a
professor
at
the
Department
of
Electrotechnics,
Uni
v
er
-
sity
Cons
tantine
1.
Her
research
interests
include
rene
w
able
ener
gy
,
po
wer
electronics,
and
storage
systems.
She
can
be
contacted
at
email:
Hadjer
.BOUNECHB
A@lec-umc.or
g.
Seif
El-Islam
Chelli
recei
v
ed
the
master
de
gree
in
electrical
engineering
from
Brothers
Mentouri,
Constantine
1
Uni
v
ersity
,
in
2015,
and
the
Ph.D.
in
electrical
engineering
from
Brothers
Mentouri,
Constantine
1
Uni
v
ersity
,
in
2022.
Currently
,
he
is
a
researcher
at
the
Laboratory
of
Elec-
trotechnics
Cons
tantine
(LEC).
Currently
,
he
is
a
research
professor
in
the
Department
of
Electrical
Engineering
at
Badji
Mokhtar
Uni
v
ersity
,
Annaba,
Algeria.
His
research
interests
include
automatic
control
strate
gies
for
electrical
dri
v
es
and
static
con
v
erters,
and
rene
w
able
ener
gy
.
Email:
seif-el-
islam.cheli@uni
v-annaba.dz.
Salah
Hammoudi
recei
v
ed
the
master
de
gree
in
mechatronics
from
Badji
Mokhtar
Uni-
v
ersity
,
Annaba,
Algeria,
in
2009,
and
the
Ph.D.
in
mechanical
engineering
from
Badji
Mokhtar
Uni
v
ersity
,
Annaba,
Algeria,
in
2017.
Currently
,
he
is
a
professor
at
the
Institute
of
Science
and
Applied
T
echnics,
Uni
v
ersity
Constantine
1,
Algeria.
He
is
the
head
of
the
Mechanics
Department
for
the
Institute
of
Science
and
Applied
T
echnics,
Uni
v
ersity
Constantine
1,
Algeria.
His
research
interests
include
machine
tool
vibrations,
articial
intelligence,
and
rene
w
able
ener
gy
.
He
can
be
contacted
at
email:
salah.hammoudi@umc.edu.dz.
Modeling
and
performance
analysis
of
batteries
in
PV
systems
(Abdelfettah
Boussaid)
Evaluation Warning : The document was created with Spire.PDF for Python.