Actual Optical and Thermal Performance of PV Modules

8/3/2019 Actual Optical and Thermal Performance of PV Modules

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ELSEVIER Solar Energy Materials and Solar Cells 41 /4 2 (1996) 557-574

A ctual op t ica l and therm al performance ofP V - m o d u l e s

S. Krauter , R. H anitschUniversity o f Techno logy Berlin, Electrical Ma chines Institute, D-10587 Berlin, G erman y

AbstractActual eff ic ien cy of photovolta ic generators is of ten lower than predicted by s tandard testcondit ions (STC) or s tandard operat ing condit ions (SOC). This is mainly caused by an underest i-mation o f ref lect ion losses and so lar cel l temperature in the mo dule . To get more ac curate resultsin predicting the actual perform ance of PV-m odules , the parameters inf luencing inco min g (opticalparameters) and outg oin g po w er flow (electrical and thermal parameters) were investigated by

simulat ion and som e verifying experim ents a t the Un iversi ty of New South W ales and theAustralian desert.

1 . O p t i c a l p a r a m e t e r sI n o r d e r t o p r e c i s e l y r e p r e s e n t t h e a c t u a l o p t i c a l c o n d i t i o n s i n t h e m o d u l e , a m o d e l f o r

t h e e n c a p s u la t i o n o f t h e c e ll w a s d e v e l o p e d w h i c h d e t e r m i n e s t h e i n s o la t i on r e a c h i n g t h ec e l l f r o m s u n a n d s k y i r r a d i a n c e . T h i s w a s d o n e b y m o d e l l i n g t h e o p t i c a l p r o c e s s e so c c u r r i n g o u t s i d e a n d i n s i d e t h e e n c ~ / p s u l a t i o n ( d i r e c t a n d d i f f u s e i r r a d i a n c e , r e f l e c t i o n ,a b s o r p t i o n ) .1 .1 . M o d e l l i n g o f i r r a d i a n c e

A s a n i n p u t f o r th e t h r e e s la b o p t i c a l s y s t e m o f t h e s o l a r m o d u l e e n c a p s u l a t i o n as o p h i s t i c a te d m o d e l l i n g o f th e i r r a d ia n c e o n t o t h e m o d u l e w a s c a r r i e d o u t . T h e r e f l e c t i o nl o s s e s a t a P V - m o d u l e w e r e m o d e l e d a s a f u n c t i o n o f i n c i d e n c e a n g l e , s t a t e o fp o l a r i z a t i o n , s p e c t r a l i r r a d ia n c e , a n d t h e o p t i c a l p r o p e r t i e s o f t h e e n c a p s u l a t i o n m a t e r i -a ls .0927-0248 /96/$15.00 1996 Elsevier Science B.V. All rights reservedSSDI 0 9 2 7 - 0 2 4 8 ( 9 5 ) 0 0 1 4 3 - 3


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5 5 8 S . K r a u te r , R . H a n i t s ch / S o l a r E n er g y Ma t e r i a l s a n d S o l a r C el ls 4 1 / 4 2 ( 19 9 6) 5 5 7 - 5 7 41 5 0 0 -o

. ~ . . , 1 0 0 0 -

~ . , 5 0 0 -

0

J Ts = 90*= AM 1.00T = 70*= AM 1.06Ys = 50*= AM 1.317s = 30*= AM 2.00

~*= AM 5 .76

5 0 0 1 0 0 0 ~ 5 0 C 2 0 0 0 2 5 0 0W a v e l e n g t h [ r i m ]

F i g . 1 . I n t e r p o l a t e d b e a m s p e c t r a f o r v a r i o u s T s-

1.1.1. Direct irradianceT h e d i r e c t i r r a d i a n c e i s u n p o l a r i z e d a n d t h e a n g l e o f i n c i d e n c e i s d e r i v e d f r o m t h e

a s t r o n o m i c a l p a r a m e t e r s a t t h e ti m e o f d a y a n d d a y o f t h e y e a r a n d g e o g r a p h i c a l l o c a t i o n[1 ] . The ac tua l t e r r e s t r i a l spec t rum o f t he sun was i n t e rpo la t ed f rom the CIE- spec t r a [2 ] :T h e C I E - s p e c t r a a r e g i v e n fo r fo u r d is c r e t e a ir m a s s e s o n l y ( A M 1 , A M 1 .5 , A M 2 , A M5 .6 ) . I n te r m e d i a t e v a lu e s o f s u n e l e v a t i o n a n g l es % h a v e b e e n c o m p u t e d b y e x p o n e n t i a li n t e rpo la t i on . The ca l cu l a t ed r e su l t s a t Ts = 10 - 90 a r e show n in F ig . 1 .

1.1.2. Diffuse irradianceT h e d i f f u s e i r r a d i a n c e w a s m o d e l e d a s a n o n - h o m o g e n o u s i l l u m i n a t e d h a l f - s p h e r e a t

t h e s k y o v e r th e m o d u l e . T h e s p a t ia l d i s tr i b u ti o n o f t h e s k y s p h e r e w a s m o d e l l e da c c o r d i n g t o D I N 5 0 3 4 p a r t 2 [3 ]. A c o n t o u r p l o t o f t h e i r r a d ia n c e l e v e l s o f a p r o j e c t i o no f t h e s k y d o m e o n t h e h o r iz o n t a l a t a s u n e l e v a t i o n o f 3 0 is s h o w n i n F ig . 2 .

B e c a u s e e a c h s c a t t e r i n g p r o c e s s c a u s e s a d i f f e r e n t s t a t e o f p o l a r i z a t i o n o f t h es c a t te r e d a s w e l l a s o f th e t r a n s m i t t e d c o m p o n e n t o f a r a y , t h e d i f f u s e i r r a d ia n c e i sp o l a r i z e d ( F i g . 3 ). B e c a u s e t h e r e f l e c ti o n l o s s e s a t th e P V - m o d u l e d e p e n d o n t h e s t at e o fp o l a r i z a ti o n t o w a r d s t h e p l a n e o f i n c i d e n c e ( s e e b e l o w ) , t h i s e f f e c t h a s a l s o b e e na c c o u n t e d f o r .

E a c h w a v e l e n g t h - b a n d o f t h e s p e c t r u m [2 ] o f e a c h p o i n t a t t h e s k y - d o m e ( a t a s p at i a ld i s t ance o f 15 ) w a s r a y t r a c e d t h r o u g h t h e m o d u l e e n c a p s u l a t i o n a c c o r d i n g t o th e a n g l eo f i nc idence and s t a t e o f po l a r i za t i on .

1.2. Optical parameters of the encapsulation1.2.1. Reflective losses under realistic conditions

I n e a r l i e r w o r k , e s t i m a t i o n s o f r e f l e c t i v e l o s s e s a t t h e s u r f a c e o f P V - m o d u l e s h a v eb e e n b a s e d o n n o r m a l i n c id e n c e a n d a m o u n t t o 2 - 4 % o f t h e in s o l at io n . T h i s i s c o r r e c to n l y f o r t r a c k i n g s y s t e m s w i t h o u t a n y d i f f u s e i n s o l a t i o n ( a s i n s p a c e ) . F o r n o n - t r a c k i n gs y s t e m s d ir e c t i n so l a t io n i s p e r p e n d i c u l a r t o t h e m o d u l e o n l y t w i c e a y e a r . A t o t h e rt i m e s t h e r e f l e c t e d c o m p o n e n t i n c r e a s e s a c c o r d i n g t o t h e F R E S N E L e q u a t i o n s ( s e e


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S . K r a u t e r , R . H a n i t s c h / S o l a r E n e r g y M a t e r i al s a n d S o l a r C e l l s 4 1 / 4 2 ( 1 9 9 6 ) 5 5 7 - 5 7 4 559

Nl

, , i , ,

Fi g . 2 . Non- i so t rop i c d i s tr i bu t i on o f d i f fu se i r r ad i ance ( acco rd i ng t o DIN 5034) fo r a sun e l ev a t i on o f 30 andc l e a r s k y in W m - 2 s r - I ( p r o j e c t io n f r o m s k y d o m e ) .

b e l o w ) . T h e d i f f e r e n t e n c a p s u l a t i o n l a y e r s c a u s e m u l t i p l e r e f l e c t i o n s i n s i d e a n d a m o n gt h e s l a b s ( s e e a l s o s c h e m e i n F i g . 4 ) . D u e t o o p t i c a l d i s p e r s i o n o f t h e m a t e r i a l s t h etransmit tance a l so depends on the incoming spec trum.

/ i:~ ' x ,~~.' _..'.,'r ' k : ' " ' ", " i ~ k " . . . . . . . . . ... . . . . , ~ . . : . . . . ~ . . . . ~ , \ ~ ! \/ ~ ' ~ : .. . . . . . . , .. " . " . : . 'k ' .. " : ' ; - - - / . . ~ \ . . . . " \ ~ : . . . . . . . . . . . . . \; : ; I ~ . ' ~ - ~ " ~ " r ' ~ . ' - . . ' , ~ ' v . ~ , ~ . . . '

w l _ x i _ ~ . - D L ,W ~ , ( , :k ~ ~ x ~ . .' ." .. '. f . 4 _ ~ " ~ ". -z - I[ - ~ - ~ - . . ' ~ . ' ~ 4 - , , , . ' - Z ~ . . . " ~ . -~ . .. .. ~ . .. .. .. - m ~ . .7i ~ / - - 0 ' , x ' . . . . .$ - '~ ] . . .. .. .. ...-> ........

-

F i g . 3 . D e g r e e o f p o l a r iz a t i o n ( in % ) a n d d i r e c t i o n s o f p l a n e s o f p o l a r i z a ti o n ( a r ro w s ) o f d i f f u s e i r ra d i a n c e a t as u n e l e v a t io n o f 3 0 * (p r o j e c t i o n f r o m t h e s k y d o m e ) .


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560 S . K r a u te r , R . H a n i t s ch / S o l a r E n er g y Ma t e r i a l s a n d S o l a r C e l ls 4 1 / 4 2 ( 19 9 6) 5 5 7 - 5 7 4

iF i g . 4 . R a y t r a c i n g t h r o u g h t h e m o d u l e l a y e r s .

T h e a b b r e v i a t i o n A R C i n F ig . 4 s t a n d s f o r t h e a n t i - re f l e c t iv e - c o a t i n g o f t h e s o l a r c e l l,i t c o n s i s ts o f T i O 2 o r a n o t h e r o p t i c a l m a t e r i a l t o b r i d g e o v e r t h e r e f r a c t i v e in d i c e s o fs i li c o n a n d f r o n t c o v e r . E V A i s t h e p o t t a n t e t h y l e n e - v i n y l - a c e t a t e w h i c h s e r v e s a s am e c h a n i c a l , t h e r m a l a n d o p t i c a l i n t e r f a c e b e t w e e n t h e s o l a r c e l l s a n d t h e g l a s s c o v e r .

1 . 2 . 2 . N o n - n o r m a l i n c i d e n c eI n g e n e r a l , i n c i d e n c e o f i n s o l a ti o n i s n o n - n o r m a l . T h e r e f l e c t a n c e c a n b e c a l c u l a t e db y t h e F R E S N E L e q u a t i o n s ( s e e , e . g . , B o r n a n d W o l f [ 4 ] ) a s a f u n c t i o n o f a n g l e o fi n c i d e n c e 0 in ( s e e F i g . 5 ) . T h e c o m p o n e n t s o f t h e d i r e c t io n o f p o l a r i z a ti o n p a r a l le l ( 1 1 ) o rp e r p e n d i c u l a r (_ 1_ ) t o t h e a n g l e o f i n c i d e n c e a r e c a l c u l a t e d s e p a r a t e l y f r o m e a c h o t h e r .N o r m a l i z e d r e f l e c t i o n ( R i p R . ) a n d t r a n s m i s s i o n (T I I, T ) a r e g i v e n as :

t a n 2 ( 0 i n - - 0 o u t ) s in2 ( 0 i n - - 0 o u t )RII = tan2 (0in + 0ut A R s in2(0 in + 0ut , (1 )( T II = 1 - R I I ) A ( T = 1 - R ) . (2 )

T h e a n g l e o f r e f r a c t i o n is g i v e n a s:

Oout = ar cs in ( ~1 sin Oin ) ( 3 )

F i g . 5 . I n c i d e n c e o n a s u r f a c e a t 0 m .


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S. Krauter, R. Hanitsch / Solar Energy Materials and Solar Cel ls 41 /4 2 (1996) 55 7-5 74 56 1

1 .2 .3 . Mo del l ing o f a p lane s labInc i den t i n so l a t i on has t o pas s t h rough t w o op t i ca l boundary l aye r s and sus t a i n

a t t enua t ion by abso rp t i on i ns i de t he ma t e r i a l. Th e r e f l ec t i on a t t he l ow er bou ndary i s no tl os t compl e t e l y , bu t bounced up and fo rw ard t h rough t he s l ab a t dec r eas i ng i n t ens i t y(Fig . 6) .

I n o r d e r to e st a b li s h a c o m m o n n o m e n c l a t u r e , e a c h l a y e r i s m a r k e d b y a n i n d e x " k " ,t he u p p e r m e d i u m b y t h e i n d ex " k - 1 " a n d t h e l o w e r m e d i u m b y " k + I " . T h e a n g leo f i n c i d e n c e a t t h e t ra n s it io n f r o m m e d i u m " k - 1 " t o t h e m e d i u m " k " i s m a r k e d b yO , the an gle o f ref rac t ion by Ok+ 1. Th e o pt ica l t rans i t ions are den oted b y the indices ofmed i a i n t he o rde r o f t he r ad i a t i on pas s i ng t h rough t hem " k , k + 1" ( e . g ., T01) . Th et r ansmi t ted pa r t s i o f t he ir r ad i ance on s lab k a r e ma rked a s Wk, , th e r e f l ec t ed ones a sPk,r A d i s t inc t i on be t w ee n t he p l anes o f po l a r i za t i on i s no t ma de any m ore i n t h i s o r thefo l l ow i ng sec t i ons i n o rde r t o keep t he fo rmul as s i mpl e . So fo r t he gene ra l l y usedva r i ab l e s R and T , t he spec i f i c com pon en t s R II , R and TII , T a r e t o be i nse r ted . Thei nc i den t i r r ad i ance i s a l so n o rma l i zed t o E = 1 . Th e a t t enua t ion o f a r ay E k a f t e r apas sage t h rough a s l ab k , i s de t e rm i ned by t he coe f f i c i en t o f abso rp t i on ak (A ) o f thema t e r i a l , i ts t h i cknes s d k and t he i nc i dence an g l e 0 k on t he c ons i de r ed s lab k :

= e x p - k c o s 0 k ] - ( 4 )Th ere fo re , r e f l ec t i on l os ses R o t o ccu r a t t he i nc i den t bou nda ry su r f ace o f s l ab 1 and

R t2 on i ts l ow e r su r f ace , w h i l e t he r em a i n i ng t r ansmi t t ed pa r t cons i st s o f :Tt , t = T0tTl2exp - a t . (5 )

The i n t e rna l r e f l ec t i on R t2 i s com put ed t he s ame as R o t us i ng Eq . ( 1 ) , a s w e l l , t he newi nc i dence ang l e 0 2 f o r t he l ow er l aye r 2 ac cord i ng t o Eq . ( 2 ) . The i n t e rna l r e f l ec t i on att he boundary 1 -2 pas ses t h rough l aye r 1 aga i n , and i s a t t enua t ed accord i ng l y . A t t hebou ndary 0 -1 t h i s r ay i s r e f r ac t ed onc e more , w h i l e a com pon en t T~0 pas ses i n t om e d i u m 0 . T h e r e f l ec t e d c o m p o n e n t R t 0 r e a c h e s b o u n d a r y 1 - 2 a t te n u a t e d , w h e r eano t he r pa r t T t 2 pene t r a t e s l aye r 2.

( - 3 a t d t )T I ' 2 ~ " T l R t 2 R l T t 2 e x p cosO'----~ " ( 6 )

n o

T1z" Tl2"n 2 - * T I , 1 - - ~ ' T I , 2F i g . 6 . T r a n s m i s s i o n t h r o u g h a p l a n e s l a b .


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5 6 2 S. Krauter, R. Hanitsch / Solar Energy Materials and Solar Cells 41/42 (1996) 557-574S u m m i n g u p a l l tr a n s m i t t e d f r a c t io n s o f t h e l a y e r 1 :

[ _ O t l d l ~ o [ [ ) ] i - IC O S O 1 ( 7 )

T h i s i n f i n i t e s e r i e s i s a g e o m e t r i c a l o n e a n d c a n b e s u m m a r i z e d :[ - - l d lr o , r , 2 e x p ) ( 8 )

1 - Rl2 Rl0 ex p cos01B e c a u s e r a d i a t io n i s b e i n g a b s o r b e d i n t h e s l a b , th e r e f l e c t i v i ty p o f a s l a b h a s t o b ec o m p u t e d e x p l i c i t l y , b e c a u s e O 1 - r . T h e r e f l e c t e d c o m p o n e n t s P l ,i o f a s la b 1 a r e t ob e c a l c u l a t e d ( f i r st o n e t r iv i a l O l , l R01) as:

( - 2 a ' d l )= , ( 9 )P l , 2 T m R t 2 T l o e x p cos01 ~

1 o )l .3 = T o lR 2 2 R lo T lo e x p cos0-----~ '

P I . i > I = TolRI21R{o2Tme x p c s 0 1 ( 1 1 )Thi s i n f in i t e s e r i e s i s a geom et r i ca l s e r i e s aga in :

T m R l 2 T l 0 e x p ( --201dlcosOlp l = R o l + ( _ 2 a l d l ) ( 12 )

1 - R l o R l 2 e x p c o s0 1

1 . 2 .4 . I n t e r n a l tr a n s m is s io n a n d r e fle c t io nK n o w l e d g e o f t h e i n t e r n a l t r a n s m i s s i o n i s n e c e s s a r y t o d e t e r m i n e t h e t r a n s m i s s i o no f m u l t i p l e l a y e r s y s t e m s , f o r e x a m p l e Y j : t h e t r a n s m i t t a n c e o f s l a b 1 , w h e n i t i si l l u m i n a t e d f r o m r e f l e c t i o n s c o m i n g o u t o f s l a b 2 . T o d i s t i n g u i s h i n t e r n a l t r a n s m i t t a n c ea n d i n t e r n a l r e f l e c t a n c e f r o m t h e e x t e r n a l o n e s , a b a r o v e r t h e v a r i a b l e i s u s e d .

[ - - a l d tT l ex p ~ c - - ~ 1 ) ( 1 3 )

1 - R l o R l 2 e x p c o s0 1A t th e b o u n d a r y b e t w e e n s l a b 2 a n d s l a b 1 , T2~ i s n e g l e c t e d b e c a u s e i t h a s b e e n a l r e a d y


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S. Krauter, R. Hanitsch / Solar Energy Materials and Solar Cells 41/42 (1996) 557-574 563

acco unte d for by the ne t re f lec t iv i ty of the low er s labs. In te rna l re f lec t iv i ty ~ i s se t upt h e s a m e w a y :

R lo T t2 ex p ( -cos012qdt )p l ~ - ( _ 2 C r l d l ) . ( 1 4 )

1 - R l2 R ,0 ex p cos0"---~The t ransi t ion f rom slab 2 to s lab 1 (T21) i s a lso neglec ted .1 .2 . 5. T r a n s m i t t a n c e t h r o u g h t w o s la b s

A n op t i c a l sy s t e m c ons i s t ing o f s l a b 1 a nd s l a b 2 n ow w i l l be e xa m ine d (F ig . 7 ). Inaddi t ion to the in te rna l re f lec t ions ins ide each s lab there a re a lso re f lec t ion s over 2 s labs(be tw e e n the uppe r bound a ry o f the o the r s l ab a nd the low e r bound a ry o f the low e r s la b )to be cons idered . In ord er to keep the p ic ture s im ple , the rays and the i r in f in i te se r ies a resum me d up a s s l a b t ra nsmi t t a nc e s z a nd s l a b re f l e c t a nc e s p . Th i s i s done in F ig . 7 a ndi s ma rke d by bo ld a r row s .The fo l low ing f ra c t ion ou t l ine s the m os t d i r e c t w a y in to s la b3:

z ' r 2 (15)T12,1 "~- T I 2I t shou ld be me n t ione d tha t fo r t he c om bina t ion o f the s l a b t r a nsmi t t anc e s r l a nd r 2

the r e f l e c tion a t t he bounda ry 1 - 2 ha s be e n t a ke n in to a c c oun t in r~ a s w e l l a s in r 2 . SoT~2 ha s to be c ompe nsa te d onc e in r , 2 . A c c o rd ing ly th i s ha s to be done fo r fu r the rcom bina t ions o f s labs rk+ i . The re f lec ted par t ~ l " ( P2 - R21)" T~-21 f rom inside layer 2e n te r s s l ab 1 a nd i s r e f le c t e d a t t he boun da ry 1 - 0 ba c k in to s l ab 1 by lo s ing 1. F romsla b 1 the f r a c t ion P l r e a c he s sl a b 2 .The f ra c t ion ~ c a n be t re a t e d in the same w a y a sthe d i rec t in com ing par t and , there fore , has the sam e a t tenua t ion z 2 . T~-2~ as tha t in s lab2 when i t en te rs s lab 3 . This resu l ts in :

p 2 - R l 2 ) r2r12 ,2 = T122 ( 16 )

n o

n l ~ - R z ~

n

n 3 - r - r 2-r,2., =F i g . 7 . T r a n s m i s s i o n th r o u g h a t w o s l ab s y s t e m .


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564 s. Krauter, R. Hanitsch Solar Energy Materials and Solar Cells 41/42 (1996) 557-574A g a i n a f r a c t i o n / 92 - R I 2 i s r e f l e c t e d f r o m s l a b 2 in t o s l a b 1 . S u m m a r i z e d , t h e t o t a l

t r a n s m i t t a n c e i s :T I T 2 ~ [ ( D 2 - R 1 2 ) P 1 ] i - I

" 2 " 1 2 T l 2 i=,[ ~ , ( 1 7 )T IT27"12 = T 12 - - ( P 2 - - R I 2 ) P l " ( 1 8 )

T h e i n n e r r e f l e c t i v i t y P21 o f t h e s l a b s y s t e m i s:~ ' 2 7 2 P lP 21 = P 2 + ( 1 9 )T I2 - - P I ( P 2 - - R I 2 ) '

w h i l e 2 c a n b e e x p r e s s e d a c c o r d i n g t o E q . ( 1 3 ).1.2.6. Transmittance through three slabs

T h e m o d u l e e n c a p s u l a t i o n i s n o w c o n s i d e r e d a s th r e e s l a b s o f d i ff e r e n t o p ti c a lp r o p e r t i e s . T h e u p p e r t w o - s l a b - s y s t e m i s t r e a t e d b y i t s i n p u t a n d o u t p u t p r o p e r t i e s a s as i n g le s l a b s y s t e m a n d t h e r e fo r e t h e s a m e p r o c e d u r e a s d e s c r ib e d a b o v e i n c h a p t e r 1 .2 .5c o u l d b e u s e d r e c u r s i v e l y : z I i s s u b s t i t u t e d b y 7 -1 2, ~ '2 b y 7 -3 , T l 2 b y T E a , SO t h e f i r s tf r a c t i o n o f 7 -~ 23 c o u l d b e w r i t t e n a s :

T I 2 T 3T 1 2 3 . 1 = T 2 3 (20)

F o r t h e c o m b i n a t i o n o f th e s l a b t r a n s m i t t a n c e s 7 -12 a n d 7 -3 th e r e f l e c t i o n a t b o u n d a r y2 - 3 h a s b e e n t a k e n i n t o a c c o u n t i n 7 -12 a s w e l l a s i n r 3 . S o T 23 h a s t o b e c o m p e n s a t e do n c e i n 7 1 2 3 . T h e r e f l e c t e d p a r t 7 1 z . ( P 3 - R 2 3 ) " T2 31 f r o m i n s i d e l a y e r 3 e n t e r s s l a bs y s t e m I - 2 a n d i s r e f l e c te d a t t h e b o u n d a r y l - 0 b a c k i n t o s la b s y s t e m 1 2 b y l o s i n g 1 2.F r o m s l a b s y s t e m I - 2 t h e f r a c t i o n ~ 21 r e a c h e s s l a b 3 . T h e f r a c t i o n P 21 c a n b e t r e a t e di n th e s a m e w a y a s t h e d ir e c t i n c o m i n g p a r t a n d t h e r e f o r e h a s t h e s a m e a t t e n u a t io n7 -3 " T ~ I a s t h a t i n s l a b 3 w h e n i t e n t e r s s l a b 4 . T h i s r e s u l t s i n :

r 1 2 ( P 3 - - R23) P 2 1 T 3T t 2 3 , 2 = T 2 3 ( 2 1 )

n I

n 2

n 3

n 4 TI23A 7"12a,Fig. 8. Transm ission through a three slab system .


9/18

S. Krauter, R. Hanitsch / Solar Energy Materials and Solar Cells 41/42 (1996) 557-574 56 5Again a fraction P3-223 is reflected from slab 3 into slab system 1-2. Summarized,

the total transmittance is:T I 2 T 3 pc ( P 3 - - R 2 3 ) P 2 1 ] i - I

] 1 -" 1 2 3 = T23 i= T2 3 ] ( 2 2 )T12T3: (23)3"123 T23 - - ( 03 - - R 2 3 ) P21

This "1"12 consists of the components 1 - 1 2 3 1 1 and TI23 j_ which are to be multipl ied bythe components of the according directions of polarization.1 . 3 . O p t i c a l t r a n s m i t t a n c e

1 .3 .1 . T r a n s m i t t a n c e o f a r e a l e n c a p s u l a t i o nUsing the model for an optical three-slab-system mentioned above, the transmittancesfor real modules and their dependence on the refractive indices of the two front slabshave been investigated. A plot of the transmittance as a function of incident angle for asimulation of a real module (PQ 40/50 supplied by ASE, former Telefunken Sys-temtechnik in Wedel, Germany) at a wavelength of 800 nm (max. spectral efficiency) isshown in Fig. 9.1.3.2. V a r i a t i o n o f n I a n d n 2

The dependency of the transmittance on the refractive indices of the two front slabshas also been examined. The results for the simulations to determine the relativeirradiance reaching the cell as a function of the refractive indices nj and n 2 (n 3 = 2.30,n 4 = 3.69) at the top slabs are shown in Fig. l0 for 0 = 0 and unpolarized insolation.

An increase of the angle of incidence shows a shift of the maximum transmittancetowards lower refractive indices, especially of the top slab. This is caused by theincreasing reflection losses at the air boundary layer (n o = 1.00) to the upper front layer

10

0 . 8 -8

0 . 6 -.=_t - 0 . 4 -

I - -0 . 2

0 .00

] I . . . . . I [ ] q r

. . . . . . . . . . . . . e ~ \ \ \a r a ll e l p o l a n z " ' ' " \. . . . . p e r p e n d i c u l a r p o l a ri z e d " ' - . ~ \- - u n p o l a r i z e d " ' . . ~ \ \a ir 2 \ \: n = l) / ~ " \ \ \ ~

1 0 2 0 , 30 4 0 5 0 6 0 7 0 8 0 9 0a n g l e o f i n c i d e n c e i n d e g r e e s

Fig. 9. Transmission of encapsulation (PQ 40/50).


10/18

566 S. Krauter, R. Hanitsch Solar Energy Materials and Solar Cells 41 /42 (1996) 557-574/ , / / ' > ~ , , . ,

2 . 2 0 : / / ~ / / ~ t ; 8 8~ / /2.1o-/> ~ / \2 . 0 0 - ~ ~ /

x 1 9 o ' ~ %/ /l ) 1 . 7 0 -._ 1 . 5 o :--,.,o-. /mzAk.-4

1 . 2 0 21 . 0 0 1 . 1 0 1 . 2 0 1 . 3 0 1 . 4 0 1 . 5 0 1 . 6 0 1 . 7 0 1 . 8 0 1 . 9 0

r e f r a c t i v e i n d e x nFig. 10. Contour of transmittance as a function of the refractive indices o f the two top layers n I and n z(n 3 = 2.30, n o = 3.69). * : standard modules.

n L, w h i l e t h e l o s s e s a t t h e l o w e r b o u n d a r i e s i n c r e a s e t o a m u c h s m a l l e r e x t e n d d u e t o t h er e d u c e d i n c i d e n c e a n g l e s r e s u lt in g f r o m t h e p r e v i o u s a n g l e o f r ef r a c t io n .

1.3.3. Comparison o f different modelsA s s h o w n i n F i g . 1 1 , t h e u s u a l l y u s e d n o r m a l i n c i d e n c e g i v e s o n l y a p e a k v a l u e o f

t h e re a l t r a n s m i t t a n c e o f t he e n c a p s u l a t i o n s y s t e m o n c e d u r i n g a d a y , e s p e c i a l l y i f o n l yt h e a i r / g l a s s t r a n s i t i o n is r e g a r d e d .

1

0 . ~ 5 ... ... ... ... - - ~ .~ - - - -. ~. '~ ..-- .- -- ..-~ ---= ~- . . . . . ...............

0 . 9 . . . . . .. . . . . . . . . . . . . . J . . . . . . . . . . . . . . .8

" ~ o . 6 . . . . . . . . . . , . .. . ~ . . ~ I ......I-"

0. 75 .... ........l ' , ~

o z r , , V ; , , , , . . . . , . . . . ~ . . . . . . ~ J . . . . ,4 6 1 0 1 2 1 4 1 6 1 8 2 0

t i m e o f d a yFig. 11. Transmittance o f an encapsulat ion o f a standard PV module (PQ 4 0/ 50 ) ove r a day (March 21 at34S) calculated with different models.


11/18

S. Krauter, R. Hanitsch / Solar Energy Materials and Solar Cells 41/42 (1996) 557-574

, 5 C ~ C

~ 4 C ~

3 C

r ~ r ~ r ~ h 9 0 r r ~ O O t J le o l O V U " ~Fi g . 12 . Ref l ec t i on l o sses a t d i r ec t i r r ad i ance (S ite : 34 .5N, Module : PQ 4 0/5 0, f i xed sou t hward ) .

5 67

1 . 3. 4 . A c c u m u l a t e d r e f l e c t i o n l o s s e s o v e r a d a yT h e m o d e l d e s c r i b e d a b o v e w a s a l s o u s e d f o r a s i m u l a t i o n o v e r o n e d a y f o r a

s t anda rd modu l e r epea t i ng t he ca l cu l a t i on each 15 mi nu t es w i t h t he i r co r r e spond i ngi nc i den t ang l e s and spec t r a .

The t o t a l r e f l ec t i on l os ses o f a t h r ee l aye r encapsu l a t i on o f a s t anda rd modu l e (PQ4 0 / 5 0 ) d u r i n g a d a y a r e 1 5 . 5 % o f th e i n c o m i n g g l o b a l r a d ia t io n f o r a n a d e q u at e m o d u l ee l eva t i on ang l e ( s ee F igs . 12 and 13) . Fo r h igh e l ev a t i on ang l e s ( 50 -90 ) , t he r e f l ec t i onl os ses i nc r ease up t o 42 . 5% fo r d i r ec t rad i a t ion . P o l a r i za t i on o f d i f fuse r ad ia t i on l ow er s

5 0 i3 0 " ~

2 0 " 6~ o ~

" ' ) ~ ? h 9 o ~ / r f l o d u l e eFi g . 13 . Ref l ec t i on fo r d i f fu se i r r ad i ance (S ite : 34 .5N, Module : PQ 4 0/5 0, f i xed sou t hward ) .


12/18

568 S. Krauter, R. Hanitsch Solar Energy Materials and Solar Cells 41/42 (1996) 557-574the d i f fuse inc idence by 0 .5 - 5% [5] and the in f luence o f op t i ca l d i spe rs ion is a round 1%[6,7].

2 . T h e r m a l p a r a m e t e r s

PV mo dules sho w redu ced vo l t age and e f f i c iency a t e l eva ted ce l l t empera tu res (by0 .4 -0 .5 % K- ~ fo r c rys ta l line s il i con so la r ce l l s [8 ] ) . The ce l l t empera tu re a t a ce r t a inhea t f low d ens i ty t)heat A - l ( absorbed i r rad iance minu s gene ra ted PV pow er dens i ty ) isde te rmined by the hea t cond uc t iv i ty o f the encapsu la t ion and by the hea t t r ans fe r to theenv i ron me nt which cons i s t s o f convec t ive hea t t r ans fe r and the he a t rad ia t ion exchangea m o n g m o d u l e a n d s k y o r g r o u n d . A s k e tc h o f t h e i n c o m i n g a n d t h e o u t g o i n g en e r g yf lows o f a PV-m odule i s g iven in F ig . 14.2.1. Thermal proce ss inside the PV-mo dule

Afte r absorp t ion o f the incom ing rad ia tion in the so la r ce l l a por t ion o f i t i s conve r tedin to e lec t r i c i ty and d ive r ted . The rema in ing hea t f low ge t s f rom the ce l l th rough theencapsu la t ion to the su r face o f the module ( s t eady s t a te hea t f low) o r inc reases thetempera tu re o f the module (non-s teady s t a te hea t f low) . A t conven t iona l s t anda rdmo dules the the rma l cap ac i ty i s re la t ive ly low , so a s imple s t eady s t a te hea t f low cou ldbe used .2.2. Heat dissipation by convection

Convec t ive hea t f lows can no t be t rea ted in a c losed ma themat ica l mode l and ,the re fo re , have to be computed by i t e ra t ion o r approx ima t ion . The convec t ive hea tt rans fe r coe f f i c ien t h c i s a bu lky func t ion o f the ac tua l a i r (TA) and module su r facetempera tu re (TM) , a i r v i s cos i ty , the rma l conduc t iv i ty and hea t capac i ty , cha rac te r i s t i cl eng th and e leva t ion ang le o f the m odule and f ina l ly speed and d i rec t ion o f wind . Themode l s used have been based on the ex tens ive work by Mehl [9 ] .

Q e a t r - t r a n s .

q o o o w , : h o I T M - Q , o . o nFig. 14. Balance of energy f low s at a PV module

%A


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S. Krauter, R. Hanitsch Solar Energy Materials and Solar Cells 4 1 /4 2 (1996) 557-574 5 6 9

,.)

0 )t- -

5 6 -

5 2JQ)o . 5 0E

[ I - E ] 2 0 0 W a t t . h o r i z o n t a l l y m o u n t e d4a ,n~.2,o0 wQt,. ve~!~.,,~..,~.~.t;d, . . . , . . . . . . . . . , . . . . ,0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0

m o d u l e e l e v o t io n i n d e g r e e sF i g . 1 5 . C e l l t e m p e r a t u r e a t a h e a t f l o w o f 2 0 0 W i n a M 5 5 m o d u l e ( 4 0 0 W m - 2 ) f o r T a m bie n = T sk y = 2 4 . 9 C ,n a t u r a l c o n v e c t i o n .

R e s u l t s o f m e a s u r e m e n t s a r e p lo t t e d in F i g . 1 5. T h e e l e v a t i o n a n g l e o f t h e m o d u l e h a sl it tl e i n f lu e n c e o n t h e n a t u r a l c o n v e c t i v e h e a t t r a n s f e r c o e f f i c ie n t i n t h e 2 0 - 8 0 e l e v a t i o n a n g l e r a n g e ( < 0 . 2 % ) . H o w e v e r , a t a l m o s t h o r iz o n t a l p o s i t i o n ( 0 0 - 2 0 a n g le o fm o d u l e e l e v a t i o n ) t he e n e r g y o u t p u t o f th e m o d u l e d e c r e a s e s b y a p p r o x i m a t e l y 0 . 7 %d u e t o e l e v a t e d c e l l t e m p e r a t u r e . H o r i z o n t a l , i n s t e a d o f v e r t i c a l m o u n t i n g o f a s t a n d a r dm o d u l e i n c r e a s e s e f f i c i e n c y b y 0 . 3 % . H e a t i n g w a s d o n e b y f o r c i n g a n e l e c t r ic a l p o w e rd i s s ipa t ion in t he ce l l s (u s ing ce l l s a s d iodes i n fo rward d i r ec t ion ) . To min imizer a d i a t i o n e x c h a n g e t h e t e s t s w e r e c a r r i e d o u t i n a h u g e h a l l w i t h t h e w a l l t e m p e r a t u r e s(~ __ _A T s k y ) e q u a l t o a i r t e m p e r a t u r e TA .2.3. Heat radiation exchange

T h e t o ta l r a d ia t i v e h e a t f lo w f r o m t h e m o d u l e 0 r~ d to t h e e n v i r o n m e n t c o n s i s ts o f t h ec o m p o n e n t s o f t h e r a d i a t i o n e x c h a n g e o f t h e f r o n t ( F ) a n d r e a r s i d e s ( R ) o f t h e m o d u l ewi th t he sky and the g round (G) : t)Fsky , ORsky , 0FC and 0 R e . Th ese co m po nen t s a r ef u n c t i o n s o f t h e t e m p e r a t u r e o f t h e m o d u l e s u r f a c e ( TF , TR) , t he t empera tu re o f t heg r o u n d Tc , t h e e q u i v a l e n t s k y t e m p e r a t u r e s T s k y [ 1 0 - 1 2 ] a n d t h e a c c o r d i n g e m i s s i v i t i e se . A l s o t h e s e c o m p o n e n t s a re d e t e r m i n e d b y t h e s o c a ll e d " r a d i a t i o n s h a p e f a c t o r " ( o r" v i e w f a c t o r " ) ~ 0;., t h e r a d i a ti v e su r f a c e a r e a A o f t h e m o d u l e a n d t h e S t e f a n - B o l t z -8m a n n c o n s t a n t t r ~ 5 . 6 7 - 1 0 - W m - 2 K - 4 ) [13].

I n g e n e r a l t h i s c a n b e e x p r e s s e d a s f o l l o w s [ 13 ]:G r a d = E Q i j = E r ~ i E j A i~ i j (T i 4 - T j 4 ) ~ " E o r E i c ' j A i ~ i j ( T i 4 - T j 4 ) ( 2 4 )

i j i j l : i j


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57 0 S. Krauter, R. Hanitsch / Solar Energy Materials and Solar Cells 41/42 (1996) 557-574The appr oxim at ion abov e is exact fo r (1 - e /) (1 - e~)~u~ j i ,~ : 1 . App l ied on the

e leva t ion ang le 7M of the mod ule [6] :

a ra d = 1 0 " [ a F e F ( ' s k y ( T 4 - T s~ y)(1 + s in ( 9 0 - 7 M ) ,+ ' c ( T 4 - T d )( 1 - s in ( 9 0 - 7 M ) ) ,- I - aR ' R ( ' s k y ( Z R - T ~ a y ) ( 1 - C OS TM ),-t- e~ (T ~ - T ~) (1 -~t-COS')/M))]. (25)

3 . S i m u l a t i o n

For eve ry so la r pos i t ion dur ing a day , each po in t on the sky sphe re was desc r ibed byi t s spec i f i c spec t rum, po la r i za t ion and inc idence ang le towards the module su r face . A l lcomponen t s were ray - t raced s epa ra te ly un t i l the i r absorp t ion in the so la r ce l l . Af te rs u m m i n g o f a l l ab s o rb e d c o m p o n e n t s t h e b a la n c e o f e n e r g y f l o w s w a s c a r d e d o u t. T h e npower d i s s ipa t ion by e lec t r i ca l load , hea t t r ans fe r to the f ron t and back su r face o f themo dule , hea t d i s s ipa t ion by rad ia t ion exchange wi th the g roun d and the sky , and na tu ra land fo rced conv ec t ion was s imula ted [14]. The qu i t e in te re s t ing re su l t s f rom a s imula t ionof the m odule e f f i c i ency dur ing a da y a re sho wn in F ig . 16. Exp lana t ions fo r cha rac te r is -t ics of the shape are g iven in the f igure .3.1. Verification

The mode l used fo r the de te rmina t ion o f the ce l l t empera tu re was ve r i f i ed bymeasurem ents at" the Ar id Z one Resea rch s t a tion o f the Unive rs i ty o f New Sou th W alesin the Aus t ra l i an dese r t [14] . For the s imula t ion a cons tan t wind speed o f 2 m / s was

0 , 1 3

0 .12> .ot -O~-~ o . 1EO

o . l o ~" 00 o . o 9

0 .08 4 ~

i i i i i i i I i i id l f~ rod lo f lononly,low coi l tomporc~ures

~ ~ ~ ~ 1 ' o I ' ! 1 '2 1 ' ~ 1 ~ 1 ' 5 1 '6 1 '~ 1 8 1 ' 9 2 ot i m e o f d a y

Fig. 16. PV m odule efficiencyduring a day (June 21 at 34.5N, PQ 40 /50 by AS E, r/STC= 0 .10).


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S. Krauter, R. Hanitsch / Solar Energy Materials and Solar Cells 41 / 42 (1996) 557-574 5 7 1

51)

(.~ 40

~ 30

c l.E~ 20

10

[ T _ c e l l , p r e d i c t e d. . .. . .. . .. i J T _ c e l l , m e a s u r e d! J T a m b i e n t i n s i m u l a t i o n/ o T - a m b i e n t , m e a s u r e d............. i

6 7 8 9 10

Fig. 17. M easured cell tem peratures versu s simulation atelevation: 30).

11 12 13 14 15 16 17 18t ime of c l a y

M a r c h 4 i n F o w l e r s G a p ( 3 1 5 ' S , 1 4 1 4 0 ' E , m o d u l e

u s e d a s i n p u t a n d t h e a m b i e n t t e m p e r a t u r e a s s h o w n i n F i g . 1 7 . I t c a n b e s e e n t h a t t h ep r e d i c t e d c e l l t e m p e r a t u r e f o l l o w s a c c u r a t e l y t h e a c t u a l m e a s u r e d o n e w i t h a p e a kd e v i a t i o n o f 3 K , w h i c h o c c u r r e d o n l y w h e n t h e a c t u a l w i n d s p e e d w a s q u i t e d i f f e r e n tf ro m 2 m / s .

T h e t i m e d e p e n d e n c e o f P V m o d u l e e f f i c i e n c y s h o w n i n F ig . 1 6 h a s b e e n v a l i d a t e db y V a n d e n B e r g e t a l . [ 1 5 ] f o r t i m e s f r o m 7 t o 1 7 h r s . T h e e f f i c i e n c y m e a s u r e m e n t sa r o u n d d a w n , w h i c h h a v e t h e g r e a t e s t u n c e r t a i n ty , r e q u i re m o r e s e n s i ti v e m e a s u r i n ge q u i p m e n t a n d a p r e c i se , m a x i m u m - p o w e r - p o i n t t r a c k e r d u e t o t h e l o w i n t e n s i ty l e v e ls .A d d i t i o n a l r e s u l t s w i ll b e p u b l i s h e d a f t e r b e t t e r m e a s u r e m e n t s a r e o b t a i n e d w i thi m p r o v e d e q u i p m e n t .3.2 . Opt ica l improvements

T h e t o ta l r e f l e c ti o n l o s se s c a n b e l o w e r e d f r o m 1 5 . 5% t o 1 1 . 4 % f o r o p t i m a l m a t c h i n gof r e f r ac t ive i nd i ces (n I = 1 .32 a nd n 2 = 1 .75) ; w i th r ea l m a te r i a l s ( e . g . , l ow r e f r ac t iveg la s s a t n I = 1 .43 and po ly -ca rb ona te (PC ) a t n 2 = 1 .60 ) , an ach ieve m en t o f u p to12 .9% i s poss ib l e , wh ich m ean s a ga in in t he da i ly p roduc ed en e rgy o f 3% ( see [6 ,7 ]) .

A n i m p r o v e m e n t o f tr a n s m i t t a n c e a n d c o r r e s p o n d i n g d a i l y g e n e r a t e d e le c t r ic a l e n e r g yi n t h e 5 % r a n g e c o u l d a l s o b e a c h i e v e d b y V - g r o o v e s t r u c tu r e d s u r f a c e s [ 1 6 - 1 8 ] .3.3. The rma l improve ments

A t il t o f th e m o d u l e a z i m u t h t o w a r d s e a s t a ll o w s a b e t t e r p e r f o r m a n c e i n th e m o r n i n gw h e n l o w e r a m b i e n t t e m p e r a t u r e s o c c u r ( o p t i m u m a t 3 5 w i t h a g a i n in e n e r g y o u t p u t o f0 . 4 % ) .


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5 7 2 S. Krauter, R. Hanitsch / Solar Energy Materials and Solar Cells 41 / 42 (1996) 557-574

7 0 -

6 0 -

0 C _ 5 0 _

. . ~ 4 0 -

" " 2 0o

1 0 -

0 0 ~ 0 0 0 " 0o o t he rm al e n h a n c e d P V - m od u l e

conventional PV-Module, direct ounted' I ' ~ ' I ' I ' I ' I ' I ' I ' + ' I ' I ' I ' I ' I6 7 8 9 1 0 11 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9

s o l a r t i m e o f c l a yF i g . 1 8. C e l l t e m p e r a t u re s o f a c o n ve c t io n a l P V m o d u l e c o m p a r e d t o T O E P V I S m o d u l e d u r in g a d a y f o r h o ta d d c o n d i ti o n s .

A g a i n o f 2 . 6 % w a s a c h i e v e d b y a t t a c h in g a s m a l l w a t e r t an k ( 1 2 . 3 l it e r) to t h eb a c k s i d e o f a m o d u l e t o i n c r e a s e t h e t o t a l h e a t c a p a c i t y . D u r i n g a d a y t h e m i n i m u me f f i c i e n c y i s t h e n d e l a y e d t w o h o u r s f r o m t h e t i m e o f m a x i m u m i n s o l a t i o n a t l o w e r p e a kt e m p e r a tu r e s . A l a t en t h e a t s to r a g e f i lm i s u n d e r d e v e l o p m e n t a n d s h o u l d a l l o w a ni m p r o v e m e n t o f 8 - 1 0 % .

3.4. New modules

C o n t i n u o u s s t u d i e s l e d u s t o t h e T O E P V I S - m o d u l e ( T h e r m a l a n d O p t i c a l E n h a n c e dP V m o d u l e w i t h I n t e gr a t ed S t a n d ) . H e r e t h e t h er m a l c a p a c i t y ( a w a t e r t an k m a d e o u t o f

0 . 1 0 -

_.~ 0 .08-

E o.08-

" 0 . 0 4 .

L u 0 . 0 2 .

O @ . ~ . . o - , o .. + , . o . + . o + . o . .+ o. , 0 " - o , . + . . + . .

O 0 t h e r m a l e n h o n c e d P V - m o d u l ec o n v e n f i o r ' ~ l P V - - m o O u l e ( I ~ 1 0 / 4 0 )

0 . 0 0 , , - , . , , . , , , . , , , 6 7 8 il 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 18S o lo " t im e o f d a yF i g . 1 9. E f f ic i e n c y o f T O E P V I S m o d u l e c o m p a r e d t o a c o n v e n t i o n a l m o d u l e w i t h i n a h o t d ay .


17/18


18/18

574 S. Krauter, R. Hanitsch / Solar Energy Materials and Solar Cells 41 / 42 (1996) 557-5744 . C o n c l u s i o n

T h e m o d e l a n d t h e s i m u l a t io n p r o g r a m d e v e l o p e d a l l o w u s to p r e d i c t o p t i c a l a n dt h e r m a l p e r f o r m a n c e u n d e r r e a l is t ic o p e r a t i n g c o n d i t i o n s , a n d th e y a r e p r o m i s i n g t o o l sf o r e v a l u a t i n g n e w P V p o w e r p l a n t s w i th t h e a i m o f i n c re a s i n g e f f i c ie n c y .

AcknowledgementsT h e a u t h o rs a r e g r a te f u l fo r th e s u p p o r t o f M a r t i n G r e e n , S m a r t W e n h a m a n d t h e ir

t e a m f r o m t h e U N S W C e n t r e f o r P h o t o v o l t a i c D e v i c e s a n d S y s t e m s d u r i n g th e m e a s u r e -m e n t p h a s e i n A u s t r a l i a .

References[1] The Astronomical Alman ac, 198 9 (U S Govt. Printing Office, W ashington, DC, 1988).[2] Commission Internationale d'F.clairage (CIE), Publication No. 85 (1990).[3] DIN 5034 Part 2, German Institute for Standardization (Beuth, Berlin, 1985).[4] M. Born and E. Wo lf, Principles of Optics, 5th ed. (Pergam on, O xford, 1976).[5] S. Krauter and R. Hanitsch, in: Proc. Cairo Int. Conf. on Renewable Energy Sources, Cairo, 1993.[6] S. Krauter, Betriebsmodell der optiscben, thermiscben und elektrischen Parameter van PV-Modulen

(K/Sster Publications, B erlin, 1993).[7] S. Krauter, R. Hanitsch, P. Camp bell and S.R. Wenham , in: Proc. 12 th European P hotovoltaic So lar

Energy Con f., Am sterdam, 19 94, pp. 1194-1197 .[8] S.R. Wenh am, M.A . Green and M.E. W att, Applied Photovoltaics (University o f New S outh Wales,Centre of Photovoltaic System s and Devices, Australia, 1994).

[9] F. Mehl, Theoretische Untersuchung der WSxmetransportmechnismen von solarelektrischen Generatorenzur Bestimmung von Zelltemperaturen, Diploma Thesis at the Institute of Electrical Machines, Universityof Technology B erlin (1993).

[10] W.C. Swinbank, Quarterly J. Royal Meteor. Soc. 89 (1963) 339.[11] A. Whiller, Design Factors Influencing So lar Collectors Lo w Temperature Eng ineering App lications fo r

Solar Energy (ASHRAE, N ew York, 1967).[12] N. Ch. Abid, Contribution a l '6tude de la production de froid a l 'aide de capteurs a caloducs, Diploma

Thesis at the Inst. of Physics, Un iversity o f Constantine, Algeria (1987).[13] V DI-W 'firmeatlas, 6th ed. (V DI Publications, D~sseldorf, 1991).[14] Ph. Strauss, K. Onneken, S. Krauter and R. Hanitsch, Proc. 12 th European Photovoltaic So lar EnergyConf., Amsterdam, 1994, pp. 1198-120 2.[15] R. van den Berg, M . BN inge n and F.W. Sch ulze, Proc. 12 th European P hotovoltaic Solar Energy Conf.,Am sterdam, 1994, pp. 1206-1209.[16] S. Krauter and R. Hanitsch, Proc. 6th Photovoltaic Science and Engineering Conf., Ne w Delhi, 1992, p.

I I1 0 .[17] S. Krauter and R. Hanitsch, Proc. 1 th European P hotovoltaic So lar Energy C onf., Montreux, 1992, pp.

1351-1354.[18] A. Scheydecker, A. Goetzberger and V. Wittwer, Solar Energy 53 (1994) 171-176.

Actual Optical and Thermal Performance of PV Modules

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