TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.7, July 201
4, pp
. 4928 ~ 49
3
3
DOI: 10.115
9
1
/telkomni
ka.
v
12i7.536
3
4928
Re
cei
v
ed
De
cem
ber 1
4
, 2013; Re
vi
sed
Febr
uary 19,
2014; Accept
ed March 7, 2
014
Theoretical Study of Multiple Solar Cells System as a
Function of Temperature
Has
sane
Be
n Slimane*,
Ben Mou
ssa
Dennai, and
Helmaoui Abderra
chid
Labor
ator
y
of Semico
nductor
s
Devices Ph
ysics,
Phy
s
ics Depart
m
ent, Univers
i
ty
of Bechar, P.O. Box
417
Bechar, Alg
e
ri
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: hassan
e
_
ben
@
y
ah
oo.fr
A
b
st
r
a
ct
A simulati
on
mode
l has
be
en
perfor
m
e
d
on
mater
i
als
as Ge, Si, GaAs, AlGaAs and th
e
valu
es o
f
gaps E
gk
of hy
pothetic
al
mat
e
rials, th
e calc
ulati
on of
the
corresponding m
a
x
i
m
u
m
efficiency was carri
ed
out for mu
ltiga
p
solar ce
lls s
ystem
s co
upl
e
d
in spl
i
tting
mo
de. T
he effects of an opti
c
al cou
p
li
ng b
y
a
dichr
o
ic
mirr
or
betw
een
in
de
pen
de
nt sol
a
r
cells, a
n
d
sol
a
r cells
cou
p
l
e
d
in s
e
ries
h
a
v
e
b
een
a
nalys
ed.
One p
a
rticul
ar
result
of o
u
r
study
is t
hat t
he c
oup
lin
g
by
a d
i
chr
o
ic
mir
r
or betw
e
e
n
a
n
in
de
pe
nde
nt cel
l
gives an inter
e
st
ing efficiency.
Ke
y
w
ords
:
mu
ltiple s
o
lar ce
lls
, Dichroïc system
,
multi
j
u
n
cti
on, Ttande
m s
o
lar ce
lls
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
The a
nalysi
s
of singl
e-ju
nction sol
a
r
cell
perfo
rma
n
ce
sho
w
s that t
w
o m
a
jor l
o
sse
s
a
r
e
due to
we
ak
photon
s a
nd
exce
ss phot
o
n
en
ergy [1
].
The
wea
k
ph
otons are n
o
t ab
sorbed
by
the
cell b
e
cau
s
e
their e
nergy i
s
lo
we
r than
the
ene
rgy b
and g
ap th
at do not
create
more
than
o
ne
electron
-hole
pair. Thi
s
excess photo
n
e
nergy is di
ssi
pated in the form of heat.
The multiju
nction app
roa
c
h
req
u
ire
s
that
inci
d
ent ph
otons
be di
re
ct
ed on
to the j
unctio
n
that is tune
d
to the ph
oto
n
’s e
nergy. In gen
er
al
th
e sol
a
r
sp
ect
r
um
can
be
split by u
s
in
g a
dich
roïc mi
rror (filter an
d reflecto
r)
syst
em, if
the subcell
s
are ele
c
tri
c
ally inde
pend
ent, so they
need the
external lo
ad ci
rcuit (ca
s
e
of fig 1.a). Howe
ver, if the sub
c
ell
s
are co
n
necte
d in seri
es,
the total photocu
r
rent ca
n be no large
r
than the sm
all
e
st photo
c
u
r
rent of any of the su
bcells.
The aim of o
u
r wo
rk is a comprehe
nsiv
e study
of
t
he mult
iple sol
a
r cell
s sy
st
e
m
in t
w
o
main pa
rts:
The first is t
o
com
p
a
r
e
usin
g a the
o
r
etical
mod
e
l
betwe
en th
e two
syste
m
s
(inde
pen
dent and seri
es co
nne
cted syst
ems).
For
th
e
se
con
d
pa
rt we
study t
he
factors that li
mit
perfo
rman
ce
for sola
r cell
s di
ch
roi
c
m
ode
with a
simple
system
of two
cell
s.
To
colle
ct t
h
e
cha
r
a
c
teri
stics of photovo
l
taic co
mpo
n
ent, and
det
ermin
e
its b
ehavior,
we
must stu
d
y the
followin
g
parameters: Sho
r
t-ci
rcuit cu
rre
nt; t
he open circuit voltage;
the efficiency
photovoltaics
Figure 1. Multijunctio
n
Sola
r Cell
s:
(a) Se
rie
s
co
nne
cted di
chroïc syste
m
, (b) Indep
end
e
n
t dichroïc
system
2.
Conv
ersion Efficiency
Of Single Solar Cell
Und
e
r ill
umin
ation, the
cell
may be
re
prese
n
ted
by a
n
eq
uivalent
circuit b
a
sed
on the
singl
e-di
ode
model,
a
s
sh
own
in
Fi
gu
re
2.
T
he cell is
d
e
scri
bed
as a curre
n
t sou
r
ce
in
pa
rallel
with the jun
c
tion as:
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Theo
retical Study of Multip
le Solar Cells S
ystem
as a Functio
n
of…
(Ha
s
sane Be
n Slim
ane)
4929
Sh
d
ph
I
I
I
I
(1)
whith:
1
IR
V
nkT
q
exp
I
I
S
0
d
sh
S
Sh
R
IR
V
I
Whe
r
e
ph
I
rep
r
e
s
ent the ph
ot
ocu
r
rent,
d
I
cu
rrent flowing th
roug
h cell wit
hout illuminat
ion
0
I
is
the s
a
turation c
u
rrent;
S
R
and
Sh
R
are respe
c
tively seri
es
resistan
ce an
d shunt re
si
stan
ce,
n
is
the ideality factor, q i
s
ele
m
entary el
ect
r
on
ch
a
r
g
e
, k is the Boltzmann
con
s
ta
nt, and T is t
h
e
absolute tem
peratu
r
e.
Figure 2. Equivalent Circuit
of Solar Cell
s
The da
rk
satu
ration current
can be d
e
scribed by:
kT
/
E
e
0
g
K
I
(2)
Whe
r
e
2
/
1
p
p
D
2
/
1
n
n
A
v
c
e
D
.
N
1
D
.
N
1
N
.
N
.
q
K
If every photon having
an
energy hv > E
g
contribut
ed one mi
no
rity carrie
r
to the sh
ort
circuit cu
rrent
. The photo
c
u
rre
nt can b
e
related to inco
ming light as
follows:
g
E
ph
ph
ph
ph
dE
)
E
(
N
Qq
I
(3)
Q
is overall cell
quantum efficien
cy,
g
E
is the band g
ap of the cell a
nd
ph
N
is numbe
r
of
photon
s which have ene
rgi
e
s in the ra
ng
)
dE
,
E
(
ph
ph
.
The maximum output power of the illum
i
nated so
lar cell corresp
onds to the point on the
curre
n
t–volta
ge cu
rve wh
ere
produ
ct of
volt
age
a
nd
cu
rre
nt re
ach
e
s maxim
u
m value
wh
ich
mean
s that first derivative d(IV)/
dV, must be equal to zero, i.e.:
m
m
m
V
V
sh
S
S
0
ph
V
V
V
V
dV
V
.
R
IR
V
1
)
IR
V
(
nkT
q
exp
I
I
d
dV
)
V
.
I
(
d
dV
dP
(4)
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 7, July 201
4: 4928 – 49
33
4930
Solving Equ
a
tion (4
) giv
e
s an im
plicit
relation from whi
c
h v
a
lue of voltage
m
V
corre
s
p
ondin
g
to maximum powe
r
poi
n
t
may be deri
v
ed:
1
V
nkT
q
)
IR
V
(
nkT
q
exp
1
I
I
m
S
m
0
ph
(5)
The cu
rrent at
maximum
power
I
mp
is
easily
cal
c
ul
a
t
ed from
the
relation
(1)
)
(
m
m
V
I
, the cell
para
m
eters a
r
e cal
c
ul
ated
from the sa
m
e
equatio
n as follows:
a) For
OC
V
V
and
0
I
(
OC
V
: the open-ci
rcuit voltage)
sh
S
OC
S
OC
0
ph
R
IR
V
1
IR
V
nkT
q
exp
I
I
0
(6)
b) For
sh
I
I
and V=0
(
sh
I
: the short-ci
rcuit
current
)
sh
S
sh
S
sh
0
ph
sh
R
R
I
1
R
I
nkT
q
exp
I
I
I
(7)
Usi
ng definiti
on of the sola
r cell conv
e
r
si
on efficien
cy it may be written:
G
P
m
(8)
Whe
r
e
m
P
is maximum po
wer
of the cell an
d
0
G
is the value
of the total p
o
we
r glob
al irradia
n
ce
of the incide
n
t
photon flux (AM1.5) given
by [3].
3.
Conv
ersion Efficiency
of Mult
iple-Cell Photov
oltai
c
S
y
stem
3.1. Subcells Electrically
Indepen
d
en
t
In the ca
se o
f
sub
c
ells
ele
c
tri
c
ally inde
p
ende
nt the conversion
effi
cien
cy of the
system
is cal
c
ul
ated
as a si
mple sum of the efficien
cie
s
corresp
ondi
ng to particula
r cell
s.
i
n
i
T
(9)
3.2. Series-c
onnec
t
ed Su
bcells
For
any set o
f
n
se
rie
s
-co
n
necte
d sub
c
e
lls (or, in
dee
d
,
any so
rt of t
w
o-te
rmin
al e
l
ement
or d
e
vice
) whose indi
vid
u
a
l cu
rrent–vo
l
tage
)
V
J
(
curve
s
are de
scribe
d
by
)
(
J
V
i
for the i
th
device, the J
–V
curve fo
r the se
rie
s
-co
n
necte
d set is
simply:
n
i
i
)
J
(
V
)
J
(
V
(10)
That i
s
, the v
o
ltage
at a
gi
ven current i
s
equ
al
to t
he
sum
of the
su
bcell
voltage
s at that
curre
n
t. Each individual
sub
c
ell
will
have its o
w
n maximum
-
power p
o
int
(
)
mi
mi
J
V
,
whi
c
h
maximizes
)
(
.
J
V
J
i
.
Ho
wever, in t
he se
rie
s
-co
n
necte
d multip
le cell
s, the currents th
rou
gh ea
ch
of the subcell
s
are
con
s
trai
ned to have the sam
e
valu
e, and theref
ore ea
ch
sub
c
ell will be a
b
l
e
to ope
rate
at
its m
a
ximu
m-po
we
r
poi
nt only if
mi
J
is
the same for all the
subcells, that
is,
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Theo
retical Study of Multip
le Solar Cells S
ystem
as a Functio
n
of…
(Ha
s
sane Be
n Slim
ane)
4931
mn
2
m
1
m
J
=
=
J
=
J
........
. If this is th
e ca
se, the
n
the maximu
m power
out
put of the
co
mbined
multiple-cell
s
is the
sum
of
the maximu
m po
wer out
puts
(
)
mi
mi
J
V
.
of the
subcells. O
n
t
he othe
r
hand, if the
sub
c
ell
s
do
not all have
the sam
e
val
ue for
mi
J
, then in their
seri
e
s
-con
ne
cted
multiple-cell
s
combi
nation
,
some of th
e sub
c
ell
s
m
u
st ne
ce
ssarily
operate a
w
ay from th
eir
maximum-po
wer p
o
ints,
so the
total
cu
rre
nt can
be
no la
rge
r
th
a
n
the
sm
alle
st cu
rre
nt of
a
n
y o
f
the sub
c
ell
s
a
nd the maxim
u
m gene
rate
d power is
cal
c
ulate
d
as:
∑
n
i
mi
mT
J
V
J
=
P
)
(
.
(11)
The efficien
cy of the multiple cell p
hoto
v
oltaic syste
m
therefo
r
e:
G
P
mT
T
(12)
The variatio
n
of band ga
ps with tem
p
erat
u
r
e can
be expre
s
se
d app
roximat
e
ly by
a
universal fun
c
tion.
T
T
-
)
0
(
E
)
T
(
E
2
g
g
(13)
Whe
r
e
α
and
β
are
co
nsta
n
t
s spe
c
ific to
each semi
co
ndu
ct
or. It is
clea
r that a
s
t
he temp
eratu
r
e
increa
se
s, the intrinsi
c co
nce
n
tration i
n
crea
se
s, an
d thus re
co
mbination in
crea
se
s, and
cell
perfo
rman
ce
i
s
im
paired. B
and
gap
na
rrowin
g, referre
d
to
earli
er, i
s
a
red
u
ctio
n i
n
ba
nd
gap
d
ue
to high dopi
n
g
and al
so se
rves to in
cre
a
s
e
i
n
and impai
r solar
cell pe
rforman
c
e.
4. Resul
t
s
I
n
t
h
is se
ct
io
n we
con
s
ide
r
as
so
ciat
io
n
s
wit
h
p
a
rt
ic
u
l
ar mat
e
rial
s su
ch a
s
Ge,
S
i
,
and
GaAs fo
r the
dich
roi
c
mod
e
of two cells and thr
ee
ce
lls, then we
will cal
c
ul
ate
the efficien
cy
for
the indep
end
ent system a
nd the
syste
m
conn
ecte
d in seri
es.
The efficie
n
c
y of a solar cell can
be incre
a
sed sub
s
tanti
a
lly by usin
g dicroi
c
multijunctio
n
sola
r
cell
s. T
he the
o
ritical
limit to the
AM1.5 efficie
n
cy of
a to
w
band
ga
p
cel
l
is
about 5
6
% [4]. The cu
rrent
-voltage of t
w
o sol
a
r
cell
s i
s
obtai
ned fro
m
the Equati
on (1
). Fig
u
re
3
sho
w
h
o
w t
w
o sol
a
r
cell
s
with different
energy
gap
s
Eg (AlGaA
s)
and Eg
(Si) d
e
vide the in
ci
dent
energy cu
rre
nt of the AM1.5 spe
c
trum.
Figure 3. J–V
Characte
ri
stics of Seri
es Con
n
e
c
ted
Sola
r Cells AlGaAs/Si
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 7, July 201
4: 4928 – 49
33
4932
The en
ergy
current first fall
s on the
cell
with
the great
er en
ergy g
a
p
Eg(AlGaA
s), whi
c
h
)
(
AlGaAs
Eg
≥
ν
h
absorbs
all p
hoton
s with
)
(
AlGaAs
Eg
<
ν
h
a
nd tra
n
smit
s
all photo
n
s
wi
th the
cell b
ehin
d
, with the lower
energy gap, t
hen a
b
sorb
s t
he ph
oton
s with
)
(
)
(
AlGaAs
Eg
<
ν
h
≤
Si
Eg
.
The Ta
ble 1
l
i
sts the
efficie
n
cy for th
e in
depe
ndent
sy
stem a
nd the
system
co
nn
ected i
n
seri
e
s
.
Energy ga
p, simulate
d efficien
cy of each cell in two j
unctio
n
dichroic sy
stem.
Table 1. Efficiency of the tow multiple
solar c
e
ll
s
y
s
t
em for different cas
e
s
Dichr
o
ïc sy
stem
2.086eV/GaAs
1.798eV/Si
1.495eV/Ge
GaA
s
/Ge
Independent s
y
s
t
em
η
=32.10%
η
=35.93%
η
=28.72%
η
=31.93%
S
y
stem connecte
d in series
η
=27.34%
η
=33.19%
η
=27.26%
η
=25.52%
The Figure 4 sho
w
that the voltage at
the open circuit voltage decrea
s
e with
increa
sing
te
mperature,
while th
e
cu
rre
nt den
si
ty
J is rel
a
tively indep
ende
nt
of tempe
r
atu
r
e.
Solar
cell
s a
r
e sensitive t
o
tempe
r
atu
r
e. Incr
ea
se
s
in tempe
r
atu
r
e re
du
ce the
band
ga
p of
a
semi
con
d
u
c
tor (Equ
ation (13
)) In a solar cell, the p
a
ram
e
ter mo
st affected b
y
an increa
se in
temperature i
s
the ope
n-circuit volt
age a
nd the co
nversion effici
en
cy.
Figure 4. Ope
n
Circuit Voltage at Differe
nt Tempe
r
atu
r
es
The T
able
2
lists th
e
efficien
cy at
the
maxim
u
m p
o
wer
point
de
cre
a
se
with
increa
sing
t
e
mpe
r
ature,
while
the
e
ffici
ency of
in
depe
ndent systems
i
s
rel
a
tively
decre
ase
more tha
n
the system co
nne
cted in se
ries
(Relation
s
8 and 1
2
).
Table 2. Efficiency a
s
a Fu
nction of Tem
peratu
r
e in th
e Tow Multipl
e
Solar Cell System
Temper
ature
Independent s
y
s
t
em
S
y
stem connecte
d in series
T=300K
31.81%
26.35%
T=310K
31.13%
25.13%
T=320K
30.19%
23.6%
T=325K
29.87%
22.96%
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Theo
retical Study of Multip
le Solar Cells S
ystem
as a Functio
n
of…
(Ha
s
sane Be
n Slim
ane)
4933
5. Conclu
sion
The inte
rn
al
power l
o
sse
s
ca
usi
ng h
eat
ing of the
cell
s in th
e to
w-cell sy
stem b
a
s
ed
on
AlGaAs/GaA
s-Si i
s
redu
ced to ap
proximately hal
f o
f
corre
s
po
ndi
ng si
ngle
-
cell
system
s fo
r
the
same ill
umin
ation. This
re
ductio
n
is fav
o
rabl
e
to the
desi
gn requi
rement of cell coolin
g ne
ed
ed
to ke
ep th
e
cell tem
p
e
r
at
ure
stabl
e a
n
d
lo
w. In th
e
ele
c
tric
cou
p
ling
of two
different type
s of
sola
r cell
s,
t
he I
(
V
)
ch
ara
c
t
e
rist
i
c
,
whi
c
h
has the mo
re
importa
nt current is mo
dified.
The calculati
ons
de
scribe
d in this p
a
p
e
r were con
ducte
d for th
e AM1.5, the
results
sho
w
s that the efficien
cy of indepe
ndent cou
p
led cells is
intere
sted.
Referen
ces
[1]
Antoni
o L
u
q
ue,
Steven
He
ge
d
u
s. Ha
ndb
ook
of P
hotov
olta
ic
Scienc
e and
Engi
neer
in
g. W
ile
y
e
d
iti
on,
200
3.
[2]
NA Gokcen, JJ Loferski. Efficienc
y of tand
em so
lar ce
ll s
y
stems as a
function of te
mperatur
e an
d
solar e
nerg
y
c
once
n
tratio
n ra
tio.
Solar Ener
gy Materials.
1979; 1; 27
1-28
6.
[3]
B Bea
u
mo
nt, G Nataf, F
Ra
ymond,
C Ver
i
e.
A F
our-C
el
l P
hotovo
l
taic
S
y
s
t
em Base
d
on I
n
P a
nd G
a
A.
16th IEEE Pho
t
ovoltaic s
y
ste
m
Conf. 1982;
595-
600.
[4]
C Veri
e. A crit
erio
n for S
e
lec
t
ion
of Semic
o
nductors
Use
d
in M
u
ltisp
e
ctral H
i
g
h
Efficie
n
c
y
S
o
l
a
r C
e
ll
s
18th IEEE Photovoltaic Spec
ialist Conf., 1985; 528-532.
[5]
JR Leg
uerr
e
e
t
M Lero
y
. U
n
e Etude C
o
mp
arative
d
e
Dis
positifs Ph
otov
oltaïqu
e
s Multi
p
les. Rev
u
e
Ph
y
s
. Ap
pl. (In F
r
ench). 198
4; 19: 889-
90
3.
[6]
H Be
n Sl
iman
e, B D
enn
ai
e
t
A Helm
ao
ui.
Modé
lisati
on
d
’
un s
y
st
ème
di
chroïqu
e
co
up
l
é
e
n
sér
i
e”,
Revu
e des En
ergi
es Ren
ouv
ela
b
les.
F
r
enc
h. 2011; 1
4
(4): 699
–7
06.
[7]
Sze S. Ph
y
s
ics
of Semicond
u
c
tor Devices. John W
i
l
e
y
& S
ons, Ne
w
York,
NY. 1981.
Evaluation Warning : The document was created with Spire.PDF for Python.