Design and analysis of a new toroidal Finel lens for three junction GaAs battery

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1 Itertiol Core Jourl of Egieerig Vol.5 No. 09 ISSN: Deig d lyi of ew toroidl Fiel le for three juctio GA ttery Xioh Niu, Chgqig Zhu Deprtmet of Vehicle d Electricl Egieerig,Army Egieerig Uiverity,Chi Shijizhug Cmpu Uiverity, Shijizhug, Heei , Chi Atrct The trditiol ulr Freel le uig igle wvelegth deig, focu o the deig of focl ple uiform ditriutio, i the deig of the wvelegth of the light icidet h etter uiformity, ut the u light diperio pheomeo fter the icidet, the greter the cloer to the le edge regio of focl pot width, led to the focl ple of the ueve ditriutio of eergy. A lot of light to the outide, d with the focl legth decree, the uiformity will e further reduced. Therefore,thi pper i of wide pectrl orptio,repectively GIP/GIA/Ge multi juctio olr cell, coiderig the diperio curve of refrctio d le mteril pectrl repoe rte i ech u cell, the toru focl pot improved deig method d multi wvelegth comitio deig, optimize the deig of the Freel le. The imultio reult how tht the cocetrtio uiformity reche 8% while the cocetrtig efficiecy reche 80% i the rge of 0.3 μm-.8 μm Keyword Opticl device deig;toru Freel Le ;Uiformity;o imgig optic.. Itroductio The third geertio photovoltic ytem i compoed of four prt: cocetrtor, photovoltic cell, dy-to-dy ytem d rditor. It icree the icidet eergy o the urfce of photovoltic cell y cocetrtor, o tht the photovoltic ytem c oti high efficiecy output while reducig the required re of photovoltic cell, reducig the cot of power geertio [,], d h rod propect for developmet. Becue the poit-focued Freel le ed o igle-wvelegth deig i widely ued i cocetrtig photovoltic ytem, there re my techicl prolem uch low utiliztio rte of photovoltic cell d ueve irrditio, which mke the urfce of photovoltic cell overhet loclly, cue cell dmge, reduce photoelectric coverio efficiecy d icree the cot of power geertio [3]. I order to improve the irrditio uiformity, the ecodry cocetrtor i uully ued, ut it will icree the lie lo d cot, d mke the mechicl tructure more complex. I order to improve the ove prolem, ew toroidl Freel le for GIP/GIA/Ge multijuctio olr cell i deiged i thi pper. PMMA rei i elected the le mteril. Coiderig the ditriutio of olr rod pectrum irrditio, the diperio chrcteritic of PMMA mteril d the pectrl repoe chrcteritic of three-juctio GA cell, the trditiol deig method of toroidl Freel le i improved. The le i divided ito everl mi wvelegth to deig, the focu ditriutio i chged, d the prolem of optimum deig prmeter electio i olved y uig the improved prticle wrm optimiztio lgorithm. The deig ojective re follow: the cocetrtig efficiecy of the le reche 80%, the irrditio uiformity reche 74%, d the geometric cocetrtig rtio i more th 300 time uder the pectrl repoe d of GIP/GIA/Ge ttery d AM.5D tdrd ulight. 37

2 Itertiol Core Jourl of Egieerig Vol.5 No. 09 ISSN: Clcultig Method of Mi Opticl Prmeter of Le. Mthemticl Model of Cocetrtig Efficiecy The opticl lo of Freel le c e roughly divided ito five ctegorie: reflectio lo, orptio lo, techologicl lo, tructurl lo d tructio lo. Reflectio lo d tructio lo re the mi cue of opticl lo. A how i Fig., whe rod-pectrum light ource i icidet, the received d of photovoltic cell i oly lmd λ ~λ l md λ l due to the diperio pheomeo, d the received rditio eergy i clled tructio lo. o R R l F l f Fig. Schemtic digrm of the priciple of tructio Tructed wvelegth c e clculted y the followig formul i(rct R / F) rct( ) () co(rct R / F) m i i( ) () l l i i( ) (3) c d e f (4) Accordig to formul () ~ (3), the refrctive idex NL d NS correpodig to wvelegth lmd λ l d lmd λ c e otied. Amog them, NM i the mi wvelegth ued i the deig of the igle tooth, d the the criticl wvelegth of lmd λ l d lmd λ re clculted ccordig to Schoot formul (4). Reflectio lo c e clculted y Freel formul. co t co co (5) co t p co co The trmittce formul i The trmittce T i r p co t co co t co p p T T (7) T i the trmiio fctor of le mteril. Coiderig oth tructio lo d reflectio lo, the igle-tooth focuig efficiecy i follow (6) 38

3 Itertiol Core Jourl of Egieerig Vol.5 No. 09 ISSN: E l E i i i 800 E Ei 300 ( ) T ( ) T d d I the formul Ei i the um of the rditio eergy trmitted to the olr cell y differet wvelegth light o the firt igle tooth, E i the rditio eergy of the firt igle tooth light o the urfce of the le, d Ei (λ) i the rditio eergy of the icidet light with the wvelegth of λ. The the totl rditio efficiecy of the le to the olr pectrum i 总 i S i, i,,3,... (9) i I the formul, Si i the re of the firt errted tooth d N i the totl umer of errted teeth.. Clcultio Model of Focl Spot Sptil Uiformity of Toroidl Freel Le The focl ple i divided ito y regio ed o the midpoit of the photocell. The width of igle wvelegth light trmitted through igle errted urfce fll o the focl ple i S, o y wvelegth refrcted y the errted urfce fll ito oe or more regio. A how i Figure, the light ry re refrcted d the fll ito the X d x+ regio. R (8) r r Fig. Clcultio model of ptil uiformity of focl pot Firtly, the th igle tooth iclitio gle i determied ccordig to formul (). Whe the wvelegth of icidet light i lmd, the coordite of the light fllig poit re determied ccordig to formul (0): d R t(rci(i ) ) F (0) The re where the ldig poit elog x i The re where the ldig poit elog x i E( ) T r R S r Ex r ( x r ) O E x 39 d x () E( ) T r R S r r ( x r ) E(λ) i the rditio eergy of the icidet light, d the trmittce of the light with wvelegth λ trvel through the th igle tooth. By clcultig the eergy ditriutio i ech regio of the focl ple fter the refrctio of micro light o ll wtooth, the uiformity of the cocetrtio ditriutio i meured y the mximum d verge of the iteity of light. The me vlue of irrdice ditriutio o the output urfce i defied follow E x x+... d... (y-) y AVE E x y x y () (3) (4)

4 Itertiol Core Jourl of Egieerig Vol.5 No. 09 ISSN: The uiformity of cocetrtio ditriutio c e expreed 3. Optiml deig of ew toroidl Freel le 3. Coidertio for Optimum Deig E MAX E 00% (5) E AVE The ew toroidl Freel le i mily deiged ccordig to PMMA ilic gel diperio chrcteritic, AM.5D olr pectrl chrcteritic d pectrl repoe chrcteritic of GIP/GIA/Ge multi-juctio olr cell, o tht ech juctio olr cell c oti higher rditio uiformity d lrger effective rditio eergy. The diperio chrcteritic of PMMA mteril c e otied from Schoot formul i Sectio.. The pecific prmeter re how i Tle. T Schoot coefficiet f c d e Figure 3 how the GIP/GIA/Ge qutum efficiecy (EQE) mp. The repoe d of top cell, middle cell d ottom cell re micro, micro d micro, repectively. Fig.3 Spectrl repoe of three juctio GIP/GIA/Ge photovoltic cell with differet juctio The deig of trditiol toroidl Freel le motly ue 0.55 um the mi wvelegth. Tkig the trditiol toroidl Freel le with rdiu of 90 mm d ditce of 0.3 mm exmple, the irrdice ditriutio o the focl ple with rdiu of 5 mm i imulted y TrcePro ry trcig oftwre. Whe the icidet light wvelegth i 0.55 um d icidet verticlly, the imultio reult re how i Fig. 4 (). The rditio uiformity of focl ple clculted y formul (5) i 8%, d the ditriutio i firly uiform. Coiderig the divergece gle of ulight d it wide pectrum, 75 equl-pced icidet light i ued to imulte the ulight i the micro d of AM.5D tdrd. The divergece hlf-gle i et to 0.5 mrd. Figure 4 () how tht whe the pectrl repoe d of the top ttery i icidet, the irrditio eergy mily cocetrte o the ceter of the focl ple. Thi i ecue the deig method doe ot coider the focl ple ditriutio of differet wvelegth whe the rod pectrl icidece occur, which reult i the low irrditio uiformity of the top ttery focl ple, d the clculted irrditio uiformity i oly 59%. From Figure 4 (c) d Figure 4 (d), we c ee tht the focuig efficiecy of the le i the repoe d of the ottom ttery d the middle ttery i low, 60% d 54% repectively. Accordig to the formul of. ectio tructio wvelegth, the lower limit wvelegth of 0.65 um i the repoe d of the ottom ttery fll to the right oudry of the focl ple fter refrctio y the 05 rig le, which how tht the le re outide the 05 rig h o effect o the ottom 40

Itertiol Core Jourl of Egieerig Vol.5 No. 09 ISSN: 44-895 ttery. The lower limit wvelegth of 0.

ottom d middle cell repodig wve d, d the irrditio of the top cell i ot uiform. The imultio reult re how i Fig. 4 (e). c d e Fig.

Deig Method T trditiol toru Fiel le 0.35~ 0.65~ 0.67 0.95 4 0.86~.75 0.38~.

propoed. A how i Fig. 5, the le i divided ito three regio: I, I d I 3.

5 Itertiol Core Jourl of Egieerig Vol.5 No. 09 ISSN: ttery. The lower limit wvelegth of 0.86 um i the repoe d of the cetrl cell i refrcted y the 4t rig le d fll o the right oudry of the focl ple, which how tht the le re outide the 4t rig h o effect o the cetrl cell. Whe the whole cell repod to the icidet wve d, the eergy lo of the log wve prt i eriou, which led to the low cocetrtio efficiecy of the ottom d middle cell repodig wve d, d the irrditio of the top cell i ot uiform. The imultio reult re how i Fig. 4 (e). c d e Fig. 4 the cocetrtio ditriutio of the covetiol toru Fiel le t differet wvelegth Proceig imultio dt wvelegth(μm) 3. Deig Method T trditiol toru Fiel le 0.35~ 0.65~ ~ ~.8 efficiecy 8% 60% 54% 73% Evee 59% 77% 8% 53% Bed o the hortcomig of trditiol toroidl Freel le, ew deig method of toroidl Freel le i propoed. A how i Fig. 5, the le i divided ito three regio: I, I d I 3. Accordig to the pectrl repoe chrcteritic of GIP/GIA/Ge multi-juctio olr cell, lmd, lmd d lmd 3 re ued the mi wvelegth of the deig, i.e. 0.55, 0.75 d.5 micro. The focl ple re D, D d D3 regio repectively, d d, D d D3 re the focl pcig of the three regio. Thi deig method h two mi dvtge: ) The mi deig wvelegth of le D, D d D3 elog to the repoe ceter d of ech juctio ttery, repectively. It reduce the tructio lo of log wve i the outer rig of the le, improve the

Itertiol Core Jourl of Egieerig Vol.5 No. 09 ISSN: 44-895 focuig efficiecy i the repoe d of the middle d ottom tterie, d improve the uiformity of the multipectrl ditriutio of the focl ple.

6 Itertiol Core Jourl of Egieerig Vol.5 No. 09 ISSN: focuig efficiecy i the repoe d of the middle d ottom tterie, d improve the uiformity of the multipectrl ditriutio of the focl ple. ) Optimizig ech regio with differet focl pcig improve the ptil ditriutio uiformity of illumitio iteity. R R R L I I I3 f Fig.5 A ew chemtic digrm of ew toru Fiel Accordig to Figure 5, there re R R ( -) R (8) L R r (9) r i i i i i i, c d e f i,,3 (0) r d, 0.55m; I () r 0 D ( - I ) d, 0.75m I I ; D D ( - I I ) d,.5m I I 3 ; 3 () (3) i(rct( L / f )) rct( ) (4) co(rct( L / f )) i I the formul, I i the refrctive idex of the le mteril correpodig to lmd i, R i the ditce etwee the ceter poit of the th rig wtooth d the cetrl xi, d RN i the ditce etwee the focl pot poitio of the th rig wtooth d the cetrl xi. From thi, the height gle lph of the w teeth of ech rig le c e clculted. 4. Modelig d Simultio of ew toroidl Freel le 4. Le Prmeter Settig d Modelig o` r D D The deig of the le ivolve ix vrile d h cotrit. I order to oti the optiml olutio, the mixed pelty fuctio method ed o prticle wrm optimiztio i ued to olve the prmeter. The optimum prmeter re clculted y uig MATLAB. Le ize: R = 90 mm, rig tooth width: R = 0.3 mm, focl legth: f = 80 mm, focl ple re: D =.05 mm, D = 3.3 mm, D3 = 0.96 mm, focu itervl D = 0.05 mm, D = 0.03 mm, D3 = 0.00 mm. The cocetrtio rtio i 366 time. Accordig to the prmeter otied, the model i etlihed y SolidWork how i Figure 6. D3 d d d3 Fig. 6 imultio model of ew toroidl Fiel le 4

Itertiol Core Jourl of Egieerig Vol.5 No. 09 ISSN: 44-895 4. Opticl imultio I order to verify the ove deig method, TrcePro i ued for ry trcig. Uder the icidet coditio of 0.35-0.67, 0.65-0.95, 0.86-.

7 Itertiol Core Jourl of Egieerig Vol.5 No. 09 ISSN: Opticl imultio I order to verify the ove deig method, TrcePro i ued for ry trcig. Uder the icidet coditio of , , d micro, the ew toroidl Freel le i imulted d it irrdice ditriutio o the focl ple with rdiu of 5 mm i lyzed. The imultio reult re how i Figure 7. c d Fig. 8 the cocetrtio ditriutio of the ew toroidl Fiel le t differet wvelegth Proceig imultio dt wvelegth(μm) T3 ew type of toru Fiel le 0.35~ 0.65~ ~ ~.8 efficiecy 83% 80% 83% 8% Evee 74% 8% 8% 80% A how i Tle 3, the ew toroidl Freel le h high cocetrtio efficiecy d rditio uiformity i the whole pectrum d the repoe d of the juctio photovoltic cell. The uiformity of focl ple irrditio i more th 74%, the focuig efficiecy i more th 80%, d the geometric focuig rtio i 366 time, which chieve the optimiztio gol. 5. Cocluio The third geertio photovoltic ytem h rod propect for developmet. The power geertio efficiecy of the whole ytem i ffected y irrditio uiformity d cocetrtio efficiecy. I thi pper, y etlihig mthemticl model, uig the deig method of multi-pricipl wvelegth d vrile focu itervl, the improved hyrid prticle wrm optimiztio lgorithm i ued to elect the optiml deig prmeter. The imultio reult how tht the ew toroidl Freel le c cocetrte light uiformly d efficietly o ll juctio photovoltic cell. The cocetrtig efficiecy i more th 80%, the irrditio uiformity i more th 74%, d the geometricl cocetrtig rtio i 366 time. Compred with the trditiol toroidl Freel le, the opticl performce h ee igifictly improved, the deig gol h ee chieved, d the correcte of the deig method h ee verified. 43

8 Itertiol Core Jourl of Egieerig Vol.5 No. 09 ISSN: Referece [] Whitefield G R, Betley R W, Wethery C K, et l. The developmet of mll cocetrtig pv ytem[a]. 9th IEEE PV SC[C]. New Orle, [] Bur C. Triple-juctio Ⅲ-Ⅴed cocetrtor olr cell perpective d chllege[j]. Jourl of Solr Eergy Egieerig, 007, 9( 3): 58 [3] Ti Wei, Wg Yipig. Progre of cocetrtor photovoltic ytem [J]. Jourl of olr eergy, 005, 6 (4): [4] Zhg Li, Che Zhimig, Dog Qimi, et l. Deig d lyi of toroidl focl pot Freel cocetrtor [J]. ler d optoelectroic, 0, 49 (9): 90 [5] Ouyg Choge, prcticl optimiztio techology [M]: Huei ciece d Techology Pre, 986:

Spherical refracting surface. Here, the outgoing rays are on the opposite side of the surface from the Incoming rays.

$Spherical refracting surface. Here, the outgoing rays are on the opposite side of the surface from the Incoming rays.$ Sphericl refrctig urfce Here, the outgoig ry re o the oppoite ide of the urfce from the Icomig ry. The oject i t P. Icomig ry PB d PV form imge t P. All prxil ry from P which trike the phericl urfce will