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Solar nergy

Vol. 32. No, 5. pp. 603 607, 1984 DO38-092X/84 3.00+ ,DO

Printed in Great Britain. ~; 1984 Pergamon Press Ltd.

C H R C T E R I Z T I O N O F P V R R Y O U T P U T

U S I N G S M L L N U M B E R O F

M E S U R E D P R M E T E R S

S. SINGER, B. ROZENSHTEIN an d S. SURAZI

Facul ty o f Engineer ing , Tel A viv Univers i ty , Ram at A viv , Tel Aviv , Israel

(Received 7 July 1981; revision accepted29 November 1982)

Ab st rac t - -Th e purpose of the p resen t s tudy was to develop a sufficien tly good f i t fo r the mea sured I - V

curve of a PV m odule and ar ray using on ly th ree easily measurab le parameters : - - t he open-ci rcu i t vo l tage

Vow); - - t he shor t -ci rcu i t curren t Isc); - - t he max imum power Pro)- W ith an addi t ional th ree parame ters

(OV,,,./OT;OVSOQ;OlsJOT

i t is possib le to descr ibe any I -V curve, ta k ing in to a ccount cel l temperature

T and so lar rad iat ion Q . This method has been tes ted on var ious so lar ar ra y panels as wel l as on a s ing le

l0 cm d ia . so lar cel l. The d i f ference between the real curve an d the proposed f it was fou nd to be less than

3 percen t fo r a f ixed temp erature and rad iat ion and abo ut 6 percen t fo r var ious com binat io ns o f

t em p era tu re an d r ad i a t i o n .

l . INTRODUCTION

A p h o t o v o l t a i c P V ) m o d u l e i s a r e c t a n g u l a r m a t r i x

c o n s i s t i n g o f s o l a r c e ll s a r r a n g e d i n s e r i e s a n d p a r a l l e l

c o n n e c t i o n . T h e o u t p u t o f t h e P V m o d u l e i s d e s c r i b e d

b y it s c u r r e n t - v o l t a g e I - V ) c u r v e , w h i c h v a r i e s a s a

f u n c t i o n o f t e m p e r a t u r e T a n d r a d i a t i o n i n t e n s i t y Q ,

s u c h t h a t 1 = I V , Q , T ) .

T h e m a n u f a c t u r e r u s u a l l y p r o v i d e s m a n y I - V

g r a p h s c o r r e s p o n d i n g t o d i f f e r e n t r a d i a t i o n l e v e l s a t

s t a n d a r d t e m p e r a t u r e , a n d t o d i f fe r e n t c e ll te m -

p e r a t u r e s a t s t a n d a r d r a d i a t i o n .

S i n c e d a t a i n s u c h f o r m a r e n o t p r a c t i c a l f or

c a l c u l a t i o n s , s ev e r a l m o d e l s o f P V c e l l s h a v e b e e n

d e v e l o p e d [ I - 5 ] w i t h I - V c u r v e s t h a t c l e a r ly a p p r o x i -

m a t e t h e m e a s u r e d I - V c u r v e o f t h e P V c e ll . H o w -

e v e r, t h e se m o d e l s i n v o l v e a l a rg e n u m b e r o f p a r a m -

e t e r s t h a t a r e d i f f i c u l t t o m e a s u r e . O t h e r m o d e l s , s u c h

a s t h a t r e p o r t e d b y S l o n i m [ 6 ] , p r o v i d e a l i n e a r f it

w h i c h i s s i m p l e a n d e a s i l y s u i t e d t o c a l c u l a t i o n s a n d .

c o r r e s p o n d s s u f f ic i e nt ly , e x c e p t a t t h e m a x i m u m

p o w e r p o i n t .

P r o p o s e d h e r e i n i s a p h e n o m e n o l o g i c a l f i t w h i c h

a l s o ta k e s i n t o a c c o u n t t h e d a t a c o r r e s p o n d i n g t o t h e

m a x i m u m p o w e r p o i n t . U s i n g t hr e e b a s ic p a r a m e t e rs ,

t he I - V c u r v e a t c o n s t a n t t e m p e r a t u re a n d r a d i a t i o n

i s d e s c r ib e d , a n d , u s i n g t h r e e a d d i t i o n a l p a r a m e t e r s ,

t h e i n f l u e n c e o f v a r i a b l e t e m p e r a t u r e a n d r a d i a t i o n

i n t e n s i t y i s d e t e r m i n e d . T h e m a i n a d v a n t a g e o f o u r f i t

i s t h e v e r y l i m i t e d n u m b e r o f e a s i ly m e a s u r a b l e

p a r a m e t e r s n e c e s s a r y t o o b t a i n s u f fi c ie n t a c c u r a c y .

W e b e l i e ve t h a t s u c h a n a p p r o a c h i s p r o b a b l y m o r e

u s e f u l t o t h e s y s t e m d e s i g n e r t h a n a b a s i c t h e o r e t i c a l

a p p r o a c h .

2. DESCRIPTION OF THE I-V CURVE OF A SINGLE

SOLAR CELL USING THREE PARAMETERS

T h e c l a s s ic a l e q u a t i o n d e s c r i b i n g t h e I V c u r v e o f

tNat ional Physical Laboratory of Israel .

a s in g le so l ar c el l i s [7 , 8 ] :

: 1

w h e r e I i s t h e c u r r e n t a n d V t h e v o l t a g e , I 0 t h e d i o d e

s a t u r a t i o n c u r r e n t , I L t h e l i g h t - g e n e r a te d c u r r e n t , R

t h e s e r ie s r e s i s t a n c e , q t h e e l e c t r o n i c c h a r g e , k t h e

B o l t z m a n n c o n s ta n t , T th e te m p e r a t u r e K ) a n d A

a d i m e n s i o n l e s s f a c t o r .

E q u a t i o n 1 ) d e s c r i b e s t h e I V c u r v e q u i t e w e ll , b u t

t h e p a r a m e t e r s c a n n o t b e m e a s u r e d i n a s i m p l e

m a n n e r . W e t h e r e f o r e h a v e d e v e l o p e d a fi t b a s e d o n

a s m a l l e r n u m b e r o f p a r a m e t e r s w h i c h c a n b e m e a -

s u r e d e a si ly . T h e s e i n c l u d e F i g . 1 ): - - t h e o p e n - c i r c u i t

v o l t a g e (Voc); - - t h e s h o r t - c i rc u i t c u r r e n t (Isc);- - t h e

m a x i m u m p o w e r (Pro)

O u r m o d e l r e li e s o n e q n 1 ) b u t u s e s t he f o l l o w i n g

s i m p l i f i c a t i o n :

e x p ( q / AKT ) V ~ > 1; IL ~ I~c-

S u b s t i t u t i n g 2 =

q / A K T ,

t h e I - V c u r v e c a n b e e x -

p ressed as :

I = I~ cll - ( ~ ) e x p 2 ( V + I R )] . 2 )

i s c Pm = V

m oc l l ~

Fig. 1 . I -V curve of a so lar cel l and hype rbola o f a constan t

power P , ,) tange nt to the curve.

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604

S S I N G E R e t a l

S i n c e 2 a n d R a r e u n k n o w n , t w o c o n d i t i o n s a r e

requi re d to ena ble u se o f th is f i t: (a ) I f I = 0, then

V = VoD

( b ) A t t h e m a x i m u m p o w e r p o i n t t h e f i t i s

t a n g e n t t o t h e h y p e r b o l a P m = I V . C o n d i t i o n ( a )

yields:

V o

v l z o

i

in

or :

I A)i~i O 0.92 SUN

(~.l ,16'- \

o 3 r 4

I . l i e

I

t R

i]O.li.4 [ ~ l ~V Vi

0 I 2 3 4 5

Fig. 2 . I -V for Module TSG-P (AEG) when

lo/Is

s taken

as 10 -s and 10-~0. N ote resulting different calculated values

of R and 2.

1 L c \

) 3 )

I t w a s f o u n d t h a t a t y p i c a l v a l u e f o r t h e r a t i o

Io/I,