Abs ac —This esea ch wo k p esen s he simula ion
based s udy o a comme cial sola cell o analyzing he
eal- ime beha io o a PV module. The ma hema ical
modelling is based on Equi alen ci cui o he sola cell
and demons a ing he p ac ical app oach o using he
single diode i e pa ame e s (IM5P) mechanism. This
esea ch in ol es pu ely ma hema ical o mula ion o
ex ac he unknown pa ame e s o PV cell by applying
he Lambe W unc ion. The I – V and P – V
cha ac e is ics a e emula ed unde di e en empe a u e
and adia ion le els by using he Linea Technology’s
LTSpice simula o .
Keywo ds— Ene gy Ha es ing, I – V & P – V Cu e,
Sola Equi alen Ci cui , Lambe W unc ion.
I. INTRODUCTION
HE wo ld is acing huge ene gy c ises and we will
un ou o uel coal and gases by 2071 as i is
p edic ed by CIA (Cen al In elligence Agency) [1].This
is an ala ming si ua ion which emphasizes he
esea che s and scien is s a ound he globe o make
al e na i e possible solu ions. Ene gy ha es ing is he
only hope o o e come his issue, howe e , enewable
ene gy sou ces can be u ilized o ackle mos o he
ene gy hung y de ices whe he i is in o m o a la ge-
scale applica ions like sola sys ems powe gene a o s o
a small scale domes ic use like cell phone, Ipods, and
wi eless senso ne wo ks, elabo a ed in a ecen e iew
by A. S. Adila, A. Husam, J. H. Sana G. Husi [2]. The
mos iable sou ce which can equip g eene ways
success ully since las decade is sola ene gy.
The Pho o ol aic ma ke ha e seen apid g ow h o sola
powe sys ems ha en e ains he possible gap o
enewable ene gy in e p e a ion o bo h mac o and
mic o sys ems as epo ed in Ren21 [3]. A Pho o ol aic
sys em con e s he sunligh di ec ly in o elec ici y and
he main de ice is sola cell in he sys em. Sola cell
a ays a e o med by g ouping hem oge he . The
elec onic con e e s play a iable ole o p ocessing he
elec ici y om he PV sys em as de ined by M. G.
Villal a, J. R. Gazoli, E. R. Filho [4]. A sola cell is
made o semiconduc o diode which is exposed o ligh
and consis s o a ious ypes o semiconduc o s using
di e en manu ac u ing p ocesses as e iewed by A. S.
Sed a, K. C. Smi h [5]. M.A. El awil, Z. Zhao discussed
ha he incoming sola adia ions and he in insic
p ope ies a e esponsible o he elec ic ene gy
gene a ion in a sola cell [6]. The sola adia ion is
composed o pho ons o a ious ene gies, some o hem
a e abso bed a p-n junc ion as shown in Fig 1., desc ibed
in Union o Conce ned Scien is s [7]. I he pho ons wi h
ene gies a e lowe han he bandgap o he sola cell, hey
a e useless and will no gene a e elec ic cu en o
ol age. Whe eas, pho ons wi h ene gy highe han he
bandgap will gene a e elec ici y and he ene gy
co esponding o he bandgap will be used only. The
emaining ene gy is dissipa ed as hea in he body o
sola cell as men ioned by J. Bikane ia, S. P. Joshi, A. R.
Joshi [8].
Fig 1. Schema ic diag am demons a ing he ope a ion o p-n
junc ion o a Sola Cell
SIMULATING THE ELECTRICAL
CHARACTERISTICS OF A PHOTOVOLTAIC
CELL BASED ON A SINGLE-DIODE
EQUIVALENT CIRCUIT MODEL
Syeda Adila AFGHAN1, Husam ALMUSAWI2, Husi GEZA3
1Uni e si y o Deb ecen, Doc o al School o In o ma ics, [email protected]
2 Uni e si y o Deb ecen, [email protected]
3 Uni e si y o Deb ecen, [email protected]
T
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Despi e o widely adop ed enewable sola solu ion,
he e’s s ill lack o unde s anding he pe o mance
e iciency and powe ex ac ion, when i comes o he
selec ion o sola panels o a ays by he end use s. Many
ma hema ical models a e highligh ed o demons a ing
he non-linea esponse o a PV sys em as highligh by E.
M. G. Rod igues, R. Melicio, V. M. F. Mendes and J. P.
S. Ca alao [9]. The common echnique is o model he
sola equi alen ci cui and amongs all possible
pa ame ic models, he single diode model is he popula
one, which is also known as 1M5P (Single Mechanism,
Fi e Pa ame e s). I is used o p edic he eal- ime
beha io o a sola cell men ioned by Ye ayew and
Jyo hsna [10]. Fo I – V and P – V cha ac e is ics, he
complica ed p ocedu e is equi ed which in ol es ce ain
equa ions and calcula ions. The sola cell in ol es non-
linea and exponen ial exp essions ha esul s he
equa ions as implici , which is complica ed, i e a i e, and
ime consuming. J. Cubas, S. Pindado, C. D. Manuel [11]
demons a ed in hei esea ch ha he explici echnique
is equi ed which consis s o analy ical o mula ion wi h
use o Lambe W unc ion o making he pa ame ic
model simple . In his pape , he single diode equi alen
ci cui is being modelled o a comme cial sola cell o
ob aining he unknown pa ame e s om he
manu ac u e ’s da ashee . Ma lab is used o he
o mula ion o he explici exp essions whe eas, he
LTSpice ci cui simula o is used o model and simula e
he pe o mance o sola cell by demons a ing he I – V
and P – V cu es a empe a u e and i adia ions
a ia ions o sola equi alen ci cui .
II. MODELLING OF SOLAR CELL
A. Ideal Single Diode Model o Pho o ol aic Cell
The pho o ol aic echnology is based on he p inciple
o elec on hole c ea ion in each cell ha consis s o wo
di e en laye s; p ype and n ype. Howe e , The I - V
cu e cha ac e is ics o a sola cell a e like he
exponen ial cha ac e is ics o he ideal diode as desc ibed
by Walke [12]. To unde s and he phenomenon o any
sola cell, panel o an a ay, i is needed o de i e he
elec ical pa ame e s o PV cell in o he equi alen
ci cui as a necessa y equi emen . As shown in he Fig.
2, he ideal sola cell consis s o cu en sou ce IL, which
is pa allel o he diode ID. The model con aining 3
pa ame e s also known as 1M3P (Single mechanism
h ee pa ame e s) sugges ed by M. Azzouzi, D. Popescu
and M. Bouchahdane [13].
Fig. 2. Ideal Single Diode Model (1M3P)
The e o e, he equa ion can be de i ed by using he
Ki chho ’s law:
Whe e ID equals o,
The ou pu cu en is ep esen ed by he ollowing
non-linea I – V equa ion:
Howe e , his model does no be able o p oduce
accu a e esul s o modelling I – V and P – V cu es o a
sola cell.
Fig. 3 Single Diode Equi alen Ci cui (1M5P)
B. Single Diode Model wi h Se ies and Shun Resis o s
To speci y he mos popula and p ac ical unc ioning
o a sola cell, M. Wol and H. Rauschenbach [14]
deno ed he ep esen a ion o losses by he esis o s as
shown in he Fig. 3, ha ing a cu en sou ce connec ed in
pa allel wi h a diode and wo esis o s, one in se ies and
o he in pa allel.
Azzouzi, Popescu and Bouchahdane [13] also
men ioned ha his model composed o i e pa ame e s
o which i known as 1M5P (Single mechanism, i e
pa ame e s), as cu en , ol age, and powe cu es can be
easily deduced by his model by calcula ing he i e
unknown pa ame e s. Mos ly he sho ci cui , open
ci cui and maximum powe poin s a e included in he
da ashee o sola cells as illus a ed in Fig. 4.
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Fig. 4. I – V and P – V cha ac e is ics o a ypical sola cell
III. MATHMATICAL MODELING OF SINGLE DIODE EQUIVALENT
CIRCUIT
A. Wa aa, A. M. Ash a , A. Fouad, S. Saad [15]
desc ibed ha i is impo an o de i e he cha ac e is ics
equa ions o sola cell o calcula ing he i e-
pa ame e s o an equi alen sola ci cui . Conside ing he
Fig. 3, he equa ion is gi en as:
To ully de ine he ela ionship be ween he ou pu
cu en o pho o ol aic cell and he e minal ol age o
he single diode model is gi en by he ollowing
equa ion:
Along wi h The mal Vol age;
[V]
Whe e IL deno es he cu en gene a ed by he
incidence o ligh , ID deno es he diode cu en , RS
ep esen s he se ies esis ance, o leakage cu en Rsh is
deno ed as Shun esis o , a is he ideali y ac o , V is he
he mal ol age, q as an elec on cha ge, he Bol zman
cons an K; he n as numbe o cells in se ies and T as he
empe a u e.
Sola cell is equi ed o be cha ac e ized by he sho
ci cui cu en Isc, he open ci cui ol age Voc, and
ideali y ac o a. Equa ion (4) can be ew i en as:
Sho Ci cui cu en : I = Isc, o V=0
Open ci cui Vol age: I = 0 o V = Voc
Maximum powe poin equa ion: I = Imp, o V =
Vmp
A. Requi ed Equa ions o Calcula ing Unknown
Pa ame e s
In o de o ob ain he alue o se ies esis o , i is need
o calcula e he implici exp ession, which is uns able and
ime consuming a he same ime, o he sake o making
exp ession decoupled, analy ical o mula ion is equi ed
o make i explici . The e o e, he implici cu en -
ol age exp ession is con e ed as an explici one by
applying he echnique o sol e he ol age as a unc ion
o cu en and ice e sa, i is in ended o make use o
popula s a egy as sugges ed by J. Ami , S. Sandeep, K.
A inashi [16], Villegas [17], K. Robe s, S. R. Vallu i
[18] ha is known as Lambe W unc ion.
Fo calcula ing Rs:
Whe e,
(9)
Fo calcula ing Rsh:
Fo calcula ing I0:
Fo calcula ing IL:
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IV. METHODOLOGY
A. Pa ame e Iden i ica ion and Calcula ion om
Manu ac u e ’s Da ashee
In o de o e alua e he unknown pa ame e s (IL, IO,
Rs, Rsh) and o simpli y he calcula ions o speci ic
model, P. M. Cuce, E. Cuce [19] elabo a ed ha he
ideali y ac o should be conside ed as gene ic alue
which is sugges ed o monoc ys alline cell ype as a =
1.2 and is independen o any empe a u e and
i adia ion. The ollowing p ocedu e is ollowed o
calcula ing he pa ame e s om manu ac u e ’s
da ashee .
1) App oxima ing he ideali y ac o a as 1.2 o
Monoc ys alline Cell
2) Calcula ing he Se ies Resis ance Rs wi h
Equa ion (8)
Calcula ing he Shun Resis ance Rsh wi h Equa ion
(10)
3) Calcula ing he Sa u a ion Cu en IO wi h
Equa ion (11)
4) Calcula ing he Pho odiode Cu en IL wi h
Equa ion (12)
The elec ical cha ac e is ics a e gi en in he TABLE
I, which demons a es he pe quisi e da a o inse ion in
o he exp essions. The inpu pa ame e s om he
da ashee a (STC) S anda d Tes Condi ions a e 1000
W/m2 inciden no mal adiance, Cell empe a u e is 25
0C and Ai Mass AM1.5g.
TABLE I
ELECTRICAL SPECIFICATIONS OF IXOLAR SOLARMD SLMD481H08L
I – V Cu e
Cha ac e is ics
Speci ica ions
Uni s
Open Ci cui
Vol age (Voc)
5.04
V
Sho Ci cui
Cu en (Isc)
0.2
A
Vol age a
maximum powe poin
(Vmpp)
4.0
V
Cu en a
maximum powe poin
(Impp)
0.178
A
Maximum Peak
Powe (Pmpp)
0.714
W
Tempe a u e
Coe icien s o Isc
(alpha)
0.12
mA/(cm2)
K
Tempe a u e
Coe icien o Voc
(be a)
-2.1
mV/K
The ob ained pa ame e s a e demons a ed in TABLE
II, whe e he unknown pa ame e s ha e been calcula ed
by he de ined equa ions and pushing he ideali y ac o
as cons an and independen .
TABLE II
CALCULATED PARAMETERS OF IXOLAR SOLARMD SLMD481H08L
B. Simula ing he Sola Equi alen Ci cui
In his pape , he comme cial sola cell iXola
Sola MD SLMD481H08L [20] is being selec ed o
analyzing I – V and P – V cu es based on ma hema ical
o mula ion and using he Linea Technology’s LTSpice
(Linea Technology Simula ion P og am wi h In eg a ed
Ci cui Emphasis) so wa e. Howe e , he ob ained
alues will be modelled on he sola equi alen ci cui o
e ol ing he beha io o sola module on simula o . As
de ined in sec ion IV. A, he inpu pa ame e s ha e been
calcula ed o modelling and simula ion pu pose o sola
equi alen ci cui as shown in Fig. 5.
Fig. 5 Single diode Equi alen ci cui o iXola Sola MD
SLMD481H08L
V. RESULTS AND DISCUSSIONS
A. I – V and P – V cu e simula ion
The gene a ed I – V and P – V cu e o comme cial
sola cell has been plo ed as demons a ed in Fig. 6 and
Fig. 7. The simula ions a e ma hema ically o mula ed
based on he da ashee in o ma ion. These plo s a e being
u he simula ed based on wo a ia ions o sola
equi alen ci cui . The en i onmen dependence has been
modelled o analyze he PV cell esponse and he
cha ac e is ics poin s o adequa e he ou pu pe o mance
o he cell. Fo his pu pose, he empe a u e and
i adia ions le els a e adop ed o con igu e he sys em
esponse in he eal- ime en i onmen .
Pa ame e s
Calcula ed Values
I0
9.0837e-10
IL
0.2009
Rs
1.7795
Rsh
398.4280
a
1.2
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Fig. 6. I – V cu e o Sola Equi alen Ci cui o iXola
Sola MD SLMD481H08L
Fig. 7. P – V cu e o Sola Equi alen Ci cui o iXola
Sola MD SLMD481H08L
B. E ec o sola i adia ion on I – V cu e
The simula ion is being pe o med on he same sola
ci cui o di e en le els o sola i adia ion, which
a ies om 200 W/m2 o 1000 W/m2 by main aining he
empe a u e cons an a 25 oC. I can be seen in Fig. 8,
ha he gene a ed cu en depends on he inciden ligh ,
as long as he i adia ion is inc easing he cu en also
inc eases. As he e is sligh change o ol age wi h
espec o he inc emen o he cu en .
Fig. 8. Sola I adia ion le els om 200 W/m2 o 1000 W/m2 a
25 0C
C. E ec o empe a u e on I – V and P – V cu e.
In his simula ion, he empe a u e is being a ied om
15 0C o 85 0C and keeping he i adia ion le el cons an
a 1000 W/m2. Fig. 9 and Fig. 10, shows he I – V and P
– V cu e gene a ed on di e en empe a u e anges. As
i is clea ly indica ed ha by a ying he empe a u e
om low o high, he ol age is being a ec ed.
Inc easing he empe a u e causing he dec eased ol age
and maximum powe poin a he same ime. While he
cu en gene a ed by inciden ligh emained cons an .
Fig. 9. I – V Cha ac e is ics o Tempe a u e a ia ion be ween
15 0C o 85 0C a 1000 W/m2
VI. CONCLUSION
In his esea ch wo k, he comme cial sola cell is
being examined o p edic he sola cell esponse on he
simula o based on he I – V and P – V cha ac e is ics.
Fo such s udy, he sola cell is being modelled as a
single diode equi alen ci cui (1M5P), he only sou ce
a ailable is he manu ac u e ’s da ashee ha is being
conside ed o ex ac he unknown pa ame e s. Ce ain
calcula ion and explici exp essions ha e been pe o med
o ge mos o he op imal alues o he module. This
way he calcula ion is being done on he Ma lab so wa e
and he ob ained pa ame e s we e simula ed on LTSpice
simula o on he equi alen ci cui . The esul s ha e been
analyzed on he wo cases; one on he empe a u e
a ia ion and keeping i adia ion cons an and second on
he i adia ion le els keeping empe a u e cons an . The
plo s o I -V cu es indica e ha as a as empe a u e
inc eases he cell cu en sligh ly inc eases and he
Fig. 10. P – V Cha ac e is ics o Tempe a u e a ia ion
be ween 15 0C o 85 0C a 1000 W/m2
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ol age is being dec eased. I is obse ed ha P – V
cha ac e is ics o sola cell deno es he dec ease in
ol age as he empe a u e is being dec eased which
p opo ionally a ec s he powe ou pu o he cell.
Howe e , he inc emen in he i adia ion le els also
inc eases he ou pu powe . Finally, his simula ion based
s udy p o ides he end use s o es ablish he ealis ic
ma hema ical modelling o sola cell, panel o an a ay o
es ima e he elec ical beha io o PV sys ems o
planning hei own sys ems.
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Janua y 2017).
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