PERFORMANCE ANALYSIS OF A-SI PHOTOVOLTAIC THERMAL SYSTEM USING OPTIMIZED DIRECT ABSORPTION COLLECTOR

PERFORMANCEANALYSISOFA-SI

PHOTOVOLTAIC/THERMALSYSTEMUSING

OPTIMIZEDDIRECTABSORPTIONCOLLECTOR

JiafeiZhao,1,2MingjiangNi,2,∗ZhongyangLuo,2TaoWang,2YanmeiZhang,2ChunhuiShou,2TingtingWu,2&KefaCen2

1

KeyLaboratoryofOceanEnergyUtilizationandEnergyConversionofMinistryofEducation,DalianUniversityofTechnology,Dalian,116024,P.R.China

StateKeyLaboratoryofCleanEnergyUtilization,InstituteforThermalPowerEngineering,ZhejiangUniversity,Hangzhou,310027,P.R.China

AddressallcorrespondencetoMingjiangNiE-mail:mjn@zju.edu.cn

2

∗

Thispaperextendsourpreviousstudyonthephotovoltaic/thermalsystemfromtheoptimumopticalpropertiesoftheworkingfluidtothesystemperformanceanalysis.Thesystemconsistsofaphotovoltaicmoduleusingana-Sisolarcellandathermalunitbasedonthedirectabsorptioncollector(DAC)concept.Thesystemseparatelyutilizesthesolarradiationduetotheadvantagesoftheworkingfluidabsorbinginfraredradiationfrom760to2000nmandthetransmittedvisiblelightfrom300to760nmbythesolarcell.Inthesystem,thethermalunitabsorbs%oftheinfraredradiationandtransmits84%ofthevisiblelight.Thea-Sisolarcellelectricalefficiencyvariesslightlybetween7.9%and8.1%forvariousworkingfluidinflowtemperatures.Whenreducingthemassflowrateoftheworkingfluid,thethermalefficiencydecreases;however,theoutflowtemperatureoftheworkingfluidreaches77◦Cconstantelectricalefficiencyabout8%.Moreover,theexergeticevaluationwasadoptedtoquantitativelystudytheelectricalenergyandthermalenergyconversion;theresultconfirmstheexistenceofflowratemaximizingthetotalefficiency(optimumflowrate).Finally,whentheincidentsolarirradianceisconcentratedfrom800to4000W/m2withtheoptimumflowrate6kg/handworkingfluidinflowtemperature25◦C,thetotalexergeticefficiencyincreases5%,andthesystemgenerates177◦Chigh-gradeheat,whiletheelectricalefficiencyissacrificedslightly,around1.3%.

KEYWORDS:photovoltaic/thermal,exergy,concentrating,directabsorptioncollector,a-Sisolarcell

1.INTRODUCTION

ingfluidconverts47%ofthesolarradiationinthespec-tralregionfrom200to2000nmintoheat,andtrans-Thisstudyextendsourpreviousinvestigation(Jiafeietmits92%ofthevisiblelightforthephotoelectriccon-al.,2010)intothenonconcentratedandconcentrateda-version.

ThepresentstudyaimstoanalyzetheperformanceofSiphotovoltaic/thermalsystem(PV/TandCPV/T).InJi-afeietal.(2010),theopticalpropertiesoftheworkingana-Siphotovoltaic/thermalsystemusingtheoptimized

fluidindirectabsorptioncollectorwasmodeledbaseddirectabsorptioncollectorwithnonconcentratedandcon-onthedampedoscillatorLorentz-Drudemodelsatisfy-centratedsolarradiation,andassesswhetherthesystemingtheKramers-Kr¨onigrelations(Brewster,1992).Theincreasestheenergyoutputcomparedwiththewatercool-coefficientsofthemodelwereretrievedbytheinverseingsystem.Thestudyfocusedonthesolarradiationtrans-methodbasedongeneticalgorithm,inorderto(i)maxi-ferinthesystemandtheenergyandexergeticefficienciesmizetransmissionofsolarradiationbetween200and760ofthesystem,becausebotharecommonlyusedinPV/Tnm,and(ii)maximizeabsorptionintheinfraredpartofandCPV/Tperformanceevaluations(Yasushietal.,2000;thespectrumfrom760to2000nm.Theoptimizedwork-Coventry,2005;Mittelmanetal.,2007).

c2012byBegellHouse,Inc.1065-5131/12/$35.00󰀁123

124Zhaoetal.

NOMENCLATURE

AcGhkLm˙nqrRTV

absorptance

specificheat(J/kg·K)irradiance(W/m2)

convectionheattransfercoefficient(W/m2·K)

absorptionindexorthermalconductivity(W/m·K)

slabthickness(m)massflowrate(kg/s)refractionindexheatflux(W/m2)reflectioncoefficient

reflectanceandthermalresistance(K/W)transmittanceandtemperature(◦C)Voltage(V)

λκρ

wavelength(m)

absorptioncoefficient(m−1)interfacereflectivity

GreekSymbolsεemissivityηefficiency

σStefan-Boltzmannconstant

Subscriptsairreferstotheairbreferstobottomcalreferstocalculatedresultconvreferstoconvectiondesreferstodesiredperformanceelreferstoelectricalfreferstofluidi,jreferstoindicespvreferstosolarcellspreferstosupportradreferstoradiationthreferstothermaltureferstothermalunit↑referstouppersurface↓referstolowersurface

2.ANALYSIS

2.1Photovoltaic/ThermalSystemconsideredtheworkingfluidinthethermalunit.Then,thea-Sisolar

celllocatedbehindthethermalunitreceivesthetransmit-tedvisiblelighttoperformphotoelectricconversion.

Figure1showstheschematicofthephotovoltaic/thermal

2.2Assumptions

systemwithemphasisonthedirectabsorptioncollector

consideredinthisstudy.ThesystemconsistsofathermalInordertomaketheproblemmathematicallytrackable,unitplacedaboveaPVmoduleseparatedbyanairgapthefollowingassumptionsaremade:ofarbitrarythickness.ThusthethermalunitneednotbegluedtothePVmoduletoextractheat.Thisarrangement1.Theincidentradiationisassumedtobecollimatedavoidsthemostcomplicatedfabricationtechniqueincon-andnormaltothesystem.

ventionalPV/TandCPV/Tsystems(Zondagetal.,2004).

2.Thespectralrangeconsideredisfrom300to2000InthePVmodule,thecommerciallyavailableamorphous

nmwhere94%ofthesolarradiationisconcentrated.silicon(a-Si)solarcellwasusedtogenerateelectricity.It

producesmostofthepowerinthevisiblespectralrange

3.Eachlayerofthesystemishomogeneousand

of300to760nm.Moreover,theoptimizeddirectabsorp-isotropic.

tionworkingfluidwasusedinthethermalunitduetoitsabsorptionintheinfraredspectrumandhightrans-4.Theworkingfluidisabsorbingbutnonscatteringand

mittanceforvisiblelight(Jiafeietal.,2010).Thetopnonemitting.andbottomslabsofthethermalunitaremadeofsilicon

5.Thea-Sisolarcellproducesmostofthepowerindioxideglass.Inthesystem,first,theinfraredportionof

thevisiblewavelengths,overthespectralrangefromtheincidentsolarradiationisdirectlyabsorbedandcon-300to760nm(Partain,1995;Shihshouetal.,2007).vertedintothermalenergy(photothermalconversion)by

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PerfomanceAnalysisofa-SiPhotovoltaic/ThermalSystem125

collimated incident solar radiation (G)qair1,convtop slabworking fluidToutqfqf,out2bottom slabairsolar cellsupportqspqair5,convqair3,convqf,out1qsky,radqt,glGfL2ĸL1ķTt,glTt,glTinThermal unitTb,glqb,glqair3,radL3Gpvqair4,convqair4,radĺĻqair5,radTaTpvTspĹTb,glPV moduleFIG.1:Structureofthesystemconsideredalongwithheatfluxesandtemperaturesusedforperformanceanalysis.6.Thedensity,heatcapacity,andthethermalconduc-tivityoftheoptimizedworkingfluidareassumedtobeequaltothoseofwater.7.Theworkingfluidofthethermalunitremainsliquid,anditsopticalpropertiesareindependentoftemper-ature.

theworkingfluid,andthetopandbottomglassslabsaregivenbyModest(2003):

Ri,λ

ρi,i+1(1−ρi−1,i)2e−2κiLi

=ρi−1,i+

1−ρi−1,iρi,i+1e−2κiLi

(1−ρi−1,i)(1−ρi,i+1)e−κiLi

1−ρi−1,iρi,i+1e−2κiLi

(1)(2)

Ti,λ=

2.3GoverningEquations

Toanalyzethesolarradiationtransferinthesystem,and

(ni−nj)2+(ki−kj)2todeterminetheenergyandexergeticefficienciesoftheρi,j=and(ni+nj)2+(ki+kj)2system,twomodelsarerequired.First,theradiationtrans-fermodelpredictshowmuchincidentsolarenergyisab-4πki

(3)κ=isorbedbythethermalunitandreceivedbythea-Sisolarλ

cell.Second,thethermalmodeldeterminestheworking

ThespectralabsorptanceAtu,λandtransmittanceTtu,λof

temperatureofthethermalunitandPVmodule.

thethermalunitisexpressedas(Modest,2003)2.3.1RadiationTransferintheSystem

Inthea-Siphotovoltaic/thermalsystemconsidered,thethermalunitconsistsofthreeslabsasshowninFig.1.ThespectralreflectanceRi,λandtransmittanceTi,λof

Atu,λ=1−R1,λ−[T1,λ(T1,λR2,λ+T2,λT3,λ)]󰀂󰀃2/(1−R1,λR2,λ)(1−R2,λR3,λ)−R1,λR3,λT2(4),λTtu,λ=

T1,λT2,λT3,λ

2(5)(1−R1,λR2,λ)(1−R2,λR3,λ)−R1,λR3,λT2,λ

whereLiisthethicknessoftheslabi.Fortheincident

radiationwithwavelengthλ,thereflectivityρi,joftheinterfacebetweenslabsiandjandtheabsorptioncoeffi-cientκiofslabiareexpressedas

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126Zhaoetal.

Thus,overthearbitraryspectralrangefromλitoλj,EpvisthesolarenergyconvertedintoelectricitybythetheincidentsolarenergyabsorbedbythethermalunitPVmodule.Gtu,λi−λjcanbewrittenasSincethea-Sisolarcellconsideredproducesmostof

thepowerinthevisiblewavelengths,theelectricalgener-λ󰀆jatedbythesolarcellissuchthatAtu,λIbλ(Ts)dλλ

Epv=ηel,visGpv,vis(9)Gtu,λi−λj=GAtu,λi−λj=Giλ(6)

󰀆j

IbλdλwherethePVmoduleefficiencyηel,visiscalculatedfromλi

thevisiblelightoftheincidentsolarradiation.Thevisible

wheretheaverageabsorptanceAtu,λi−λjofthethermalportionirradiancereceivedbythePVmoduleisdenotedunitisdefinedastheratiooftheenergyabsorbedtothein-byGpv,vis.ForthePVmodule,theelectricalefficiencyiscidentsolarenergybetweenλiandλj(Jiafeietal.,2010),alsogivenby(Charalambousetal.,2007)Ibλ(Ts)istheblackbodyspectralintensityatthesuntem-VMPPIMPPG

ηel,vis==ηel,pv(10)peratureTs,andGisthetotalincidentsolarirradianceon

GvisSGvis

thesystem.

Similarly,overthearbitraryspectralrangefromλitoηel,pv=η0[1−β(Tpv−Ta)](11)λj,theincidentsolarenergyreceivedbythePVmodule

wherethevisiblepartofsolarirradianceisGvis.Thesys-Gpv,λi−λjisgivenby

temcollectorsurfaceareaisS.ThevoltageVMPPandthecurrentIMPPcorrespondtothemaximumpower,whereλj

󰀆

theproductofcurrentandvoltageismaximum.Theelec-Ttu,λIbλ(Ts)dλλtricalefficiencyηel,pvofthePVmoduleisforthesolar

Gpv,λi−λj=GTtu,λi−λj=Giλ(7)

radiationspectrum.Theelectricalefficiencyη0isforthe󰀆j

Ibλdλa-Sisolarcellworkingat25◦C.Thesolarcelltempera-λi

tureandtheambientairtemperaturearedenotedbyTpv

WheretheaveragetransmittanceTtu,λi−λjofthethermalandTa,respectively.Thetemperaturecoefficientβistheunitisdefinedastheratiooftheenergytransmittedoftheelectricalefficiencyreductionforeverydegreecentigradethermalunittotheincidentsolarenergybetweenλiandoftemperaturerise.Inaddition,thevisibleportionirradi-ancereceivedbythePVmoduleiscalculatedfromλj(Jiafeietal.,2010).

2.3.2EnergyConversionintheSystem

Energybalanceequationsareformulatedtodeterminethe

workingtemperatureofthethermalunitandthePVmod-ulewithnonconcentratedandconcentratedsolarradia-tion.Thesystemisassumedtooperateatsteadystate.Figure1schematicallyindicatestheheatfluxesandtem-peraturesinthesystem.

First,theenergyconversionequationforthePVmod-ulecanbewrittenas(Zondagetal.,2003)

GpvApv−Epv=qsp+qair4,conv+qair4,rad

(8)

Gpv,vis=GTtu,λ3−λ4

(12)

whereTtu,λ3−λ4istheaveragetransmittanceofthether-malunitbetweenλ3=300nmandλ4=760nm.Thus,Eq.(8)canbewrittenas

GpvApv−ηpv,visGpv,vis=qsp+qair4,conv+qair4,rad(13)TheheatfluxacrossthePVmoduleqspis

qsp=qair5,conv+qair5,rad

(14)

wheretheheatfluxbetweenthesolarcellandthesupportisqsp,andtheheatfluxesbetweenthePVcellandthesurroundingsbyconvectionandradiationaredenotedbyqair4,convandqair4,rad,respectively.TheabsorptanceofthePVcelloverthesolarradiationspectrumisApv.TheirradianceGpvreceivedbythePVmodulebetweenλ1=300nmandλ2=2000nmiscalculatedbasedonEq.(7).

wheretheheatconvectionbetweenthesupportandtheairisqair5,conv,andthenetradiationfluxexchangedbetweenthesupportandtheairisqair5,rad.

Moreover,theenergybalanceoftheworkingfluidcanbeexpressedas(Zondagetal.,2003)

GfAf,λ1−λ2=qf+qf,out1+qf,out2

(15)

whereqf,out1andqf,out2aretheconvectiveheatfluxesthroughtheworkingfluidtothetopandbottomglass

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PerfomanceAnalysisofa-SiPhotovoltaic/ThermalSystem127

slabs,respectively.Thethermalenergycollectedbytheworkingfluidinthethermalunitisdenotedbyqf.TheaverageabsorptanceoftheworkingfluidisdenotedbyAf,λ1−λ2.TheirradiancereceivedbytheworkingfluidGfiswrittenas

Gf=GTgl,λ1−λ2

(16)

760nm.Thethermalefficiencyofthesystemisdefinedas(Zondagetal.,2003)

ηth=m˙

cp(Tout−Tin)

GS

(22)

whereTgl,λ1−λ2istheaveragetransmittanceofthetopsilicondioxideglassslabbetweenλ1=300nmandλ2=2000nm.

Theenergybalancesatthetopandbottomglassaregivenby

qf,out1=qt,gl(17)

qf,out2=qb,gl

(18)

wheretheconductiveheatfluxesinthetopandbottom

glassslabsareqt,glandqb,gl,respectively.Furthermore,theenergybalanceofthetopandbottomglassslabscanalsobeexpressedas(Zondagetal.,2003)

qt,gl=qair1,conv+qair1,radqb,gl=qair3,conv+qair3,rad

(19)(20)

wherem˙istheworkingfluidmassflowrateinthether-malunit,andcpistheheatcapacityoftheworkingfluid.TheinflowandtheoutflowworkingfluidtemperaturesaredenotedbyTinandTout,respectively.Furthermore,thethermalefficiencyisconventionallyshownasafunctionofreducedtemperaturedefinedas(Charalambous,2007)

Tred=(Tin−Ta)/G

(23)

wheretheheatconvectionexchangesbetweentheglassslabsandairaredenotedbyqair1,convandqair3,conv.Inaddition,qair1,radandqair3,radarethenetradiationfluxexchangedbetweenthetopglassslabandthesky,andbetweenthebottomglassslabandtheair,respectively.Therefore,inthesystem,thethermalmodelconsistsofsevenenergybalanceequations[Eqs.(13)–(15)andEqs.(17)–(20)]solvedforsevenunknowntemperatures(Tpv,Tout,Tt,gl↑,Tt,gl↓,Tb,gl↑,Tb,gl↓,andTsp).Theex-pressionsfortheheatfluxesinEqs.(13)–(20)asafunc-tionofthetemperaturesofthesystemareprovidedintheAppendix.Oncethetemperaturesaredetermined,theper-formanceofthesystemwithnonconcentratedandcon-centratedsolarradiationcanbeanalyzed.

Thesystemswithnonconcentratedandconcentratedso-larradiationsupplydifferentformsofenergysuchaselectricityandheat.However,theelectricalandthermalenergyproducedbycombinedutilizationarenotessen-tiallythesameinnature.Theenergyanalysisapproachhassomedeficiencies.Theenergyconceptisnotsensi-tivetotheassumeddirectionoftheprocess.Italsodoesnotdistinguishthequalityoftheenergy(Petela,2008).Therefore,toquantitativelyevaluatetheusefulnessoftheenergyobtained,theconceptofexergyisadoptedinthisstudy.Sincetheelectricalenergywillnotbeaffectedbytheenvironment,itcanbeconvertedintoanequalamountofwork.Therefore,iftheincidentirradianceisG,andtheelectricalefficiencyofthesystemisηel,thentheelectricalexergyisgivenbyFujisawaandTani(1997)andYasushietal.(2000):

ee=ηelG=ξelG

andξel=ηel

(24)

whereeeistheelectricalexergy,andξelistheelectricalexergeticefficiency.Moreover,inordertotransformthethermalenergyintomechanicalwork,ahigh-temperatureheatsourceandadumpoflow-temperatureheatarere-quired.ThemagnitudeoftransformablethermalenergytoworkisrestrictedbytheCarnotefficiencyηc.Ifthe2.3.3PerformanceAnalysis

temperatureofthesystemisT1andthatoftheenviron-First,sincethesolarcellreceivedpartoftheincidentir-mentisT0,thethermalexergyisdefinedasthemaximumradianceonthesystemforphotoelectricalconversion,thevalueofthework,thatis,theeffectiveenergy,whichcanrelationshipbetweenelectricalefficiencyofthePVmod-betakenoutfromthesystem.Thethermalexergyethanduleηel,pvandtheelectricalefficiencyofthesystemηelthethermalexergeticefficiencyξthcanbewrittenas(Ya-canbeexpressedassushietal.,2000)

󰀅󰀄

ηel=ηel,pvTtu,λ3−λ4(21)T0

ηthGandeth=ηcηthG=ξthG=1−T1

whereTtu,λ3−λ4isthethermalunitaveragetransmit-ξth=ηcηth(25)tanceoverthevisiblelightspectrumfrom300nmtoλ2=

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128Zhaoetal.

Therefore,thesyntheticexergyofthesystemisthetotalvalueoftheelectricalandthermalexerties.Thetotalex-ergeticefficiencyofthesystemispresentedas(Yasushietal.,2000)

ξsys=ξel+ξth(26)2.4ClosureLaws

ThesilicaglasstopandbottomslabshavethicknessL1=

L3=1cm,therefractiveindexn1=n3=1.45,andab-sorptionindexk1=k3=0overthewavelengthrangefrom200to2000nm.ThethicknessoftheworkingfluidlayerisL3=3cm.ThedesiredtransmittanceandabsorptanceofthethermalunitareTdessλg=1.0from300to760nmandAdes,λ=1.0from760to2000nm(Brewster,1992).Thesystemissurroundedbyair(nair=1.0andkair=0).Moreover,withrespecttothesupport(PVlaminate),aPE-Al-tedlarlayerofthicknessLtedlar=0.1mmwithconductionktedlar=0.2W/m·KandanEVAlayerofthicknessLEVA=0.5mmwithconductionKEVA=0.35W/m·Kareassumed(Zondagetal.,2003).Thus,thethermalresistanceofthesupportcanbedeterminedasRsp=Rtedlar+REVA,whereRtedlarandREVAarethethermalresistancesofthePE-Al-tedlarlayerandEVAlayer.Forthecommerciallyavailableamorphoussili-consolarcell,thetemperaturecoefficientβis0.3%/◦C,andtheefficiencyη0is0.98attheambienttemperatureTa=25◦C(Greenetal.,2009).Furthermore,whentheReynoldsnumberconsideredissmallerthan2300,thevalueoftheNusseltnumberis6.70forarectangularchan-nelatconstantheatflux(Rohsenow,1985).Thus,thecon-vectiveheattransfercoefficientbetweentheglassplate

andtheworkingfluidishf=42W/m2·K.Sincethetemperatureofthesolarcellwouldbelowerthanthatofthebottomglass,thefreeconvectionbetweenthesolarcellandtheglassisneglected(Chowetal.,2007).Ineval-uatingthesystemperformance,theskytemperatureTskyisnotcriticalandcanbesimplytakenasequivalenttotheambientairtemperature(Chowetal.,2008).Finally,toassesstheperformanceofthesystem,thevaluesofcoef-ficientsusedinthesimulationsaresummarizedinTable1.3.RESULTSANDDISCUSSION

ThissectionreportstheradiativepropertiesofthePV/Tsystemusingtheoptimizedworkingfluid.ItcomparestheenergyandexergeticefficienciesofthePV/Tsystemus-ingtheoptimizedworkingfluidandwater,anddiscussestheeffectofthefluidmassflowrate,theinflowtemper-ature,andtheirradianceontheperformanceofthePV/Tsystem.

3.1RadiativePropertiesoftheSystem

Toachievethemaximumabsorptionintheinfraredspec-trumandthemaximumtransmittanceinthevisible,theopticalpropertiesoftheworkingfluidwereretrievedbasedontheinversemethodinthepreviouspaper(Ji-afeietal.,2010).Figure2showstheretrievedcomplexindexofrefractionoftheworkingfluidasafunctionofwavelengthfortheworkingfluidwithTdes,λ=1.0from300to760nm,Ades,λ=1.0from760to2000nmforthethicknessL2=0.03m.Moreover,toevaluatetheperfor-manceofthethermalunitusingoptimizedworkingfluid

TABLE1:ThevaluesofcoefficientsusedintheperformanceanalysisVariable

AmbienttemperatureAbsorptioncoefficientCoefficientofheattransferEmissivityofsolarcellEmissivityofglass

HeatcapacityofworkingfluidHeatconductionthroughglassHeatconductionthroughworkingfluidHydraulicdiameterinthermalunit

Inflowtemperature

Nusseltnumberinthermalunit

SymbolTaApvhwεpvεglcpkglKfδfTinNuf

Value250.92100.900.904.2×103

0.900.620.03256.70

Unit◦C–W/m2·K

––J/kg·KW/m·KW/m·Km◦C2.12

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PerfomanceAnalysisofa-SiPhotovoltaic/ThermalSystem129

1.54Optimized reractive index, ncal,OOoptimized working fluid,L2=0.03m1.521.501.481.461.4430050070090011001300150017001900 O Wavelength, O (nm)(a)10󰀔󰀑(󰀎󰀓󰀓0Optimized absorption index, k cal,O󰀔󰀑(󰀐󰀓󰀔10O-1optimized working fluid,L2=0.03m󰀔󰀑(󰀐󰀓󰀕10-2FIG.3:ThetransmittanceofthethermalunitofthesystemusingtheoptimizedworkingfluidasafunctionofwavelengthwithTdes,λg=1.0from300to760nm,Ades,λg=1.0from760to2000nm,comparedwiththatofthesystemusingwater,andthespectralresponseofthea-Sisolarcellusedinthesystem.

thesolarinfraredradiationfrom760to2000nmforpho-tothermalconversion,andaccepts84%ofthevisiblelightfrom300to2000nmforphotoelectricalconversion.Theaveragetransmittanceofthethermalunitusingtheop-timizedworkingfluidoverthevisiblelightisabout6%lowerthanthatofthethermalunitusingwater,whichwouldleadtotheelectricalefficiencydecrease.However,theaverageabsorptanceofthethermalunitusingtheop-timizedworkingfluidovertheinfraredradiationisabout22%higherthanthatofthewatersystem.Therelativede-creaseintheelectricalefficiencywouldbecompensatedbyboththeeffectivethermalconversionoftheoptimizedworkingfluidandthesmallincreasingtemperatureofthesolarcell,especiallywiththeconcentratingsystem.3.2PerformanceoftheSystem

BasedonEqs.(1)–(7),thesolarradiationtransferinthesystemwasdetermined.Forthespectralrangefromλ1=300nmandλ2=2000nm,thesolarenergyabsorbedbytheoptimizedworkingfluidisGfAf,λ1−λ2=0.47G,andtheenergyabsorbedbythesolarcellisGpvApv=0.45G.Similarly,whenwaterissubstitutedfortheopti-mizedworkingfluid,GwaterAwater,λ1−λ2=0.26GandGpvApv=0.63G.Notethatusingtheoptimizedworking

󰀔󰀑(󰀐󰀓󰀖10-3󰀔󰀑(󰀐󰀓󰀗10-4󰀔󰀑(󰀐󰀓󰀘10-5󰀔󰀑(󰀐󰀓󰀙10-6󰀔󰀑(󰀐󰀓󰀚10-7󰀔󰀑(󰀐󰀓󰀛10-8300500700Wavelength, O (nm)90011001300150017001900(b)

FIG.2:Theretrievedrefractiveindex(a)andabsorptionindex(b)asafunctionofwavelengthfortheoptimizedworkingfluidwithTdes,λ=1.0from300to760nm,Ades,λ=1.0from760to2000nmforthethicknessL2=0.03m.

andwater,Fig.3comparesthespectraltransmittanceofthethermalunitbetween300and2000nmusingeithertheoptimizedworkingfluidorwater,andshowsthespec-tralresponseofthea-Sisolarcellinthesystem.There-sultsindicatethattheoptimizedsystemabsorbs%of

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130Zhaoetal.

fluid,lessenergyisabsorbedbythesolarcell,andover-heatingofthesolarcellisprevented.Additionally,moreenergyisusedforthethermalconversion.Thesevaluesweresubstitutedtotheenergyconversionequations.Theefficienciesofthesystemwithnonconcentratedandcon-centratedsolarradiationwerecalculatedasafunctionoftheworkingfluidmassflowrate,theworkingfluidinflowtemperature,andtheincidentsolarirradiance.

ingfluidinflowtemperatures.Comparedwiththeconven-tionalPV/Tsystem,theresultindicatesthattheelectricalefficiencyofthesystemconsideredisindependentoftheworkingfluidinflowtemperature.

Furthermore,Fig.5showsthetemperatureofthesolarcellandtheoutflowtemperatureoftheworkingfluidforthesystemusingtheoptimizedworkingfluidandwaterasafunctionofthemassflowrate.Figures6and7com-paretheenergyandexergeticefficienciesofthesystemusingtheoptimizedworkingfluidandwaterwithrespect3.2.1PerformanceoftheSystemwithNonconcentrated

tothemassflowrate.Asintuitivelyexpected,duetowa-Radiation

ter’shightransmissionintherangeofvisiblelight,the

Figure4showsthethermalandelectricalefficienciesofelectricalefficiencyusingwaterisabout0.3%higherthanthesystemsusingtheoptimizedworkingfluidandwa-thatobtainedwiththeoptimizedworkingfluid.However,terasafunctionofreducedtemperature.Whenthein-intheoptimizedPV/Tsystem,theworkingfluiddirectlyflowtemperatureincreasesfrom25◦Cto50◦Cthesys-absorbsmostoftheinfraredradiation.Thesolarenergytem,thethermalefficienciesofthesystemusingtheop-absorbedbytheworkingfluidisabout47%ofthein-timizedworkingfluidandwaterbothdecrease.However,cidentirradiance.Thusthethermalefficiencyachieved,thePVmoduleisseparatedfromthethermalunit,andthewhenusingtheoptimizedworkingfluid,isabout2%–workingfluidhaslittleeffectonthePVmodule.Whenin-16%higherthanthatachievedwithwater.Theoutflowcreasingtheworkingfluidinflowtemperature,thework-temperatureoftheoptimizedworkingfluidreaches77◦CingtemperatureofthesolarcellinthePVmodulechangeswiththedecreaseofthemassflowrate.Ontheotherhand,slightly,andtheelectricalefficiencyofthesystemre-intheoptimizedPV/Tsystem,thePVmodulereceivedmainsconstantforbothusingtheoptimizedworkingfluidonly6%oftheinfraredradiation.Theinfraredpartoftheandwater.Thea-Sisolarcellelectricalefficiencyintheoptimizedsystemisaround7.9%–8.1%forvariouswork-800.6Temperature, Tpv and Tout (ć)Thermal and electrical efficiency, Kth Kel0.5optimized working fluid, Kthoptimized working fluid, Kelwater, Kthwater, Kel70optimized working fluid, Tpvoptimized working fluid, Tout60water, Tpvwater, Tout0.4500.3400.2300.120000.0050.010.0150.020.025200.030.0350.0040.0080.0120.0160.02FIG.5:ThetemperatureofthePVmoduleandtheout-FIG.4:Thethermalandelectricalefficienciesofthesys-flowtemperatureoftheworkingfluidforthesystemus-temsusingtheoptimizedworkingfluidandwaterasaingtheoptimizedworkingfluidandwaterasafunctionfunctionofreducedtemperaturewiththefixedincidentofmassflowratewiththefixedincidentsolarradiancesolarradianceG=800W/m2andmassflowrateofwork-G=800W/m2andworkingfluidinflowtemperatureingfluidm˙=76kg/h.Tin=25◦C.

Reduced temperature, Tred (Km/W)Mass flow rate, (kg/s)󰀆mJournalofEnhancedHeatTransfer

PerfomanceAnalysisofa-SiPhotovoltaic/ThermalSystem131

0.60.50.40.3optimized working fluid, Kthoptimized working fluid, Kelwater, Kthwater, Kel0.10.2000.0040.0080.0120.0160.02lowerthanthoseofthethermalunitisallowed.TheresultsconfirmthatintheoptimizedsystemthethermalunitandthePVmodulehavelittleeffectoneachother,andthesystemelectricalefficiencyisindependentoftheworkingfluidmassflowrates.Additionally,theexergeticefficien-ciesofthesystemusingtheoptimizedworkingfluidandwaterwerecalculatedbasedonEqs.(24)–(26).Theex-ergeticefficiencyoftheoptimizedPV/Tsystemishigherthatofthewatersystemwithvariousmassflowratesfrom1to76kg/h.Whentheworkingfluidmassflowrateisaround6kg/h,theoptimizedsystemachievesthehighestexergeticefficiency,10.5%,asshowninFig.7.TheresultconfirmstheexistenceofoptimumflowratemaximizingthePV/Tsystemefficiency.

3.3PerformanceoftheSystemwith

ConcentratedRadiation

TheoutflowtemperaturesoftheworkingfluidfortheCPV/TsystemusingtheoptimizedworkingfluidandwateratdifferentincidentsolarirradianceareshowninTable2.Inthesystemwiththedirectabsorptioncol-lector,thethermalunitandthePVmoduleindepen-dentlyachievephotothermalandphotoelectricalconver-sion.ContrarytotheconventionalCPV/Tsystem,thethermalunitdoesnotextractheatfromthePVmodule,andthethermalunithasnothermallimitationsfromthePVmodule.Therefore,theworkingfluidinthethermalunitcangeneratehigh-temperatureheatwithoutnegativeeffectsonthePVmodule’selectricalefficiency.Whentheincidentsolarirradianceincreasesfrom800to4000W/m2(theconcentrationratioisfrom1to5),theoutflowtemperatureofthesystemusingtheoptimizedworkingfluidreaches177◦C.Thethermalunittemperaturegener-atedbytheoptimizedsystemisabout40◦Chigherthanthatofthewatersystem.

Figure8showsthethermalandelectricalefficienciesoftheCPV/Tsystemasafunctionoftheincidentsolarir-radiancewiththefixedoptimumflowrate6kg/h.There-sultsindicatethatwhentheincidentirradianceincreases,thethermalefficiencyoftheCP/Tsystemdoesnotde-crease.ThethermalefficiencyoftheoptimizedCPV/Tsystemisalwaysaround27%,andisabout8%higherthanthatofthewatersystem.Themainreasonforthisresultisthatthewaterdoesnotabsorbthesolarinfraredradiationasmuchastheoptimizedworkingfluidinthethermalunit.Furthermore,thethermalunitusingtheop-timizeddirectabsorptioncollectorpreventstherapidriseintemperatureatthePVmodule.Withtheincreaseoftheincidentsolarirradiancefrom800to4000W/m2,the

Thermal and electrical efficiency, KthKelMass flow rate, (kg/s)󰀆mFIG.6:Thethermalandelectricalefficienciesofthesys-temsusingtheoptimizedworkingfluidandwaterasa

functionofmassflowratewiththefixedincidentsolarradianceG=800W/m2andworkingfluidinflowtemper-atureTin=25◦C.

0.120.11Total exergetic efficiency, [sys0.10.090.080.070.060.050.0400.0040.0080.0120.0160.02optimized working fluid, [syswater, [sysMass flow rate, (kg/s)󰀆mFIG.7:Thetotalexergeticefficienciesofthesystemsus-ingtheoptimizedworkingfluidandwaterasafunction

ofmassflowratewiththefixedincidentsolarradianceG=800W/m2andworkingfluidinflowtemperatureTin=25◦C.

solarradiationhaslittleeffectonthePVmodule.There-fore,whenthemassflowratedecreases,thePVmod-uletemperatureisalwaysaround42◦Candatemperature

Volume19,Number2,2012

132Zhaoetal.

TABLE2:TheoutflowtemperaturesoftheworkingfluidforthesystemusingtheoptimizedworkingfluidandwateratdifferentincidentsolarirradianceIrradianceG(W/m2)

8001600240032004000

OutflowtemperatureTf,out(◦C)

5684117147177

OutflowtemperatureTwater,out(◦C)

476992114137

Thermal and electrical efficiency, KthKel0.30.20.180.250.2Exergetic efficiencies, [th,[el,[sys0.160.140.120.10.080.060.040.020800optimized working fluid, [thoptimized working fluid, [eloptimized working fluid, [syswater, [thwater, [elwater, [sysoptimized working fluid, Kth0.150.1optimized working fluid, Kelwater, Kthwater, Kel0.0508001200160020002400280032003600400012001600200024002800320036004000Irradiance, G (W/m)2Irradiance, GCR (W/m)2FIG.8:Thethermalandelectricalefficienciesofthesys-temsusingtheoptimizedworkingfluidandwaterasafunctionoftheincidentsolarirradiancewiththefixedmassflowrateofworkingfluidm˙=6kg/handworking

◦

fluidinflowtemperatureTin=25C.

electricalefficiencyofthesystemusingtheoptimizedworkingfluidonlydecreases1.3%,andbecomeshigherthanthatofthesystemusingwater.Theseresultsindicatethattheoptimizedsystemwithconcentratedsolarradi-ationhashighelectricalefficiency,andgenerateshigh-gradeheatwithconstantthermalefficiency.

Thesystemwithconcentratedsolarradiationsuppliesdifferentformsofenergy.Toquantitativelyevaluatetheusefulnessoftheenergyobtained,theexergyefficien-ciesofthesystemwerecalculated.Figure9showstheexergyefficienciesoftheCPV/Tsystemusingtheopti-mizedworkingfluidandwaterasafunctionoftheinci-dentsolarirradiance.Whentheincidentsolarirradianceincreasesfrom800to4000W/m2,theelectricalexer-

FIG.9:Exergeticefficienciesofthesystemusingtheop-timizedworkingfluidandwaterasafunctionofthein-cidentsolarirradiancewiththefixedmassflowrateofworkingfluidm˙=6kg/handworkingfluidinflowtem-peratureTin=25◦C.

geticefficiencyoftheoptimizedsystemξelissacrificedslightly,about1.3%.However,thethermalexergeticeffi-ciencyoftheoptimizedsystemξthquicklygoesupfrom2.6%to9.0%,andthesystemtotalexergeticefficiencyξsysincreasesfrom10.5%to15.2%.Inaddition,itisclearfromthefigurethatthetotalexergeticefficiencyξsysofthesystemusingtheoptimizedworkingfluidbecomeshigherthanthatofthesystemusingwaterfrom1%to5%,astheincidentsolarirradianceincreasesfrom800to4000W/m2.Overall,thestudyresultssuggestthatusingtheoptimizeddirectabsorptioncollectorisabestoptionintheCPV/Tsystem,thetotalexergeticefficiencyoftheCPV/Tsystemincreasesalongwiththeincidentsolarir-radiance.

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PerfomanceAnalysisofa-SiPhotovoltaic/ThermalSystem133

4.CONCLUSION

Thispaperextendsourpreviousstudy,andfocusesontheperformanceevaluationofthephotovoltaic/thermalsys-temusingtheoptimizeddirectabsorptioncollector.Theradiativepropertiesandefficienciesoftheoptimizedsys-temwithnonconcentratedandconcentratedsolarradia-tionwerecalculatedbasedontheradiationtransferandtheenergyconversionequations.Thefollowingconclu-sionscanbedrawn:

1.Intheoptimizedsystem,thethermalunitabsorbs%oftheinfraredradiationforphotothermalcon-version,andthePVmoduleaccepts84%ofthevisi-blelightforphotoelectricalconversion,respectively.ThethermalunitandthePVmoduleindependentlyachieveenergyconversion.

2.Whenusingthenonconcentratedsolarradiation,theelectricalefficiencyofthePV/Tsystemvariesslightlybetween7.9%and8.1%forvariousworkingfluidinflowtemperatures.Moreover,whenreducingthemassflowrateoftheworkingfluid,thethermalefficiencydecreases;however,theoutflowtempera-tureoftheworkingfluidreaches77◦Cconstantelec-tricalefficiency,about8%.Theexergeticefficiency

ofthePV/Tsystemisabout10.5%withtheoptimumModest,M.F.,RadiativeHeatTransfer,SanDiego,CA:Aca-demicPress,2003.

massflowrate6kg/h.3.IntheoptimizedCPV/Tsystem,whentheincidentsolarirradianceincreasesfrom800to4000W/m2,theelectricalefficiencyofthesystemissacrificedslightly,about1.3%.Thethermalefficiencyremainsconstantat27%.Thesystemgenerates177◦Cwork-ingfluid.Furthermore,thesystemtotalexergeticef-ficiencyincreasesfrom10.5%to15.2%.ACKNOWLEDGMENTS

Petela,R.,Anapproachtotheexergyanalysisofphotosynthesis,Sol.Energy,vol.82,pp.311–328,2008.

Charalambous,P.G.,Maidment,G.G.,Kalogirou,S.S.,andYiakoumetti,K.,Photovoltaicthermal(PV/T)collector:Areview,Appl.Therm.Eng.,vol.27,pp.275–286,2007.

Chow,T.T.,Ji,J.,andHe,W.,Photovoltaic-thermalcollectorsystemfordomesticapplication,J.SolarEnergyEng.,vol.129,pp.205–209,2007.

Chow,T.T.,He,W.,Chan,A.L.S.,Fong,K.F.,Lin,Z.,andJi,J.,Computermodelingandexperimentalvalidationofabuilding-integratedphotovoltaicandwaterheatsystem,Appl.Therm.Eng.,vol.28,pp.1356–13,2008.

Coventry,J.S.,Performanceofaconcentratingphoto-voltaic/thermalsolarcollector,Sol.Energy,vol.78,pp.211–222,2005.

Fujisawa,T.andTani,T.,Annualexergyevaluationonphotovoltaic-thermalhybridcollector,Sol.EnergyMater.Sol.Cells,vol.47,pp.135–142,1997.

Green,M.A.,Emery,K.,Hishikaw,Y.,andWarta,W.,Solarcellefficiencytables(version34),Prog.Photovolt:Res.Appl.,vol.17,pp.320–326,2009.

Jiafei,Z.,Mingjiang,N.,Chunhui,S.,Yanmei,Z.,Wei,W.,Jixi-ang,Z.,Zhongyang,L.,andKefa,C.,Optimumopticalprop-ertiesoftheworkingfluidindirectabsorptioncollector,J.EnhancedHeatTransfer,vol.18no.(3),pp239–247,2011.Mittelman,G.,Kribus,A.,andDayan,A.,Solarcoolingwithconcentratingphotovoltaic/thermal(CPVT)systems,EnergyConvers.Manage.,vol.48,pp.2481–2490,2007.

Partain,L.D.,SolarCellsandTheirApplications,PaloAlto,CA:JohnWileyandSons,1995.

Rohsenow,W.M.,HandbookofHeatTransferFundamentals,NewYork:McGraw-Hill,1985.Shihshou,L.,Chii,C.C.,Frank,G.,andThomas,P.,Broad-bandanti-reflectioncouplerfora:Sithin-filmsolarcell,J.Phys.D:Appl.Phys.,vol.40,pp.754–758,2007.Yasushi,M.,Toru,F.,andTatsuo,T.,Momentperformanceofphotovoltaic/thermalhybridpanel(Numericalanalysisandexergeticevaluation),ElectricalEng.Jpn.,vol.133,pp.43–51,2000.

TheauthorsgratefullyacknowledgethesupportoftheNationalNaturalScienceFoundationofthePeople’sRe-publicofChinaunderGrantsno.50676082andno.Zondag,H.A.,Vries,D.W.,Helden,W.G.J.,Zolin-gen,R.J.C.,andSteenhoven,A.A.,Theyieldofdifferent

51006017.Theauthorswouldalsoliketoacknowledge

combinedPV-thermalcollectordesigns,Sol.Energy,vol.74,

ProfessorLaurentPilon(UCLA)whosecommentshelpedpp.253–269,2003.improvethemanuscript.REFERENCES

Brewster,M.Q.,ThermalRadiativeTransferandProperties,NewYork:JohnWileyandSons,1992.

Zondag,H.A.,Helden,W.G.J.,Elswijk,M.J.,andBakker,M.,PV-thermalcollectordevelopment–Anoverviewofthelessonslearnt,inProc.of19thEuropeanPVSolarEnergyConf.andExhibition,Paris,France,2004,Hoff-mann,W.,Bal,J.L.,Ossenbrink,H.,Palz,W.,andHelm,P.,eds.,2004.

Volume19,Number2,2012

134Zhaoetal.

APPENDIX:OVERVIEWOFTHEHEATTRANSPORTEQUATIONS

InthePVmodule,theheatfluxacrossthePVsupportcanbewrittenas(Zondagetal.,2003)

qsp=

Tpv−TspRspS

(1)

wherethetemperaturesofthesolarcellandthesupportaredenotedbyTpvandTsp,respectively.Rspisthether-malresistanceofthesupport.Moreover,qair4,rad=

󰀇4󰀁εpvεgl4σTpv−Tb,bl↓

εpv+εgl−εpvεgl

44

qair5,rad=εspσ(Tsp−Ta)

andTb,gl↑;theconvectionheattransfercoefficientforthe

workingfluidovertheglassslabisdenotedbyhf.Thus,qf,out1andqf,out2areexpressedas

󰀄󰀅Tout+Tin

qf,out1=hf−Tt,gl↓(6)

2󰀄󰀅Tout+Tin

−Tb,gl↑(7)qf,out2=hf

2TheheatfluxacrossthetopandbottomglassslabsaregivenbyZondagetal.(2003)

qt,gl=qb,gl=

kgl

(Tt,gl↓−Tb,gl↑)L1

kgl

(Tb,gl↑−Tb,gl↓)L3

(8)(9)

(2)(3)(4)

qair5,conv=hw(Tsp−Ta)

wherethetemperatureofthelowersurfaceofthebottomglassslabisdenotedbyTb,gl↓.Theparametersεpvandεglaretheemissivitiesofthesolarcellandtheglassslabs.Inthethermalunit,thethermalenergycollectedbytheworkingfluidinthethermalunitcanbewrittenas(Zondagetal.,2003)

qf=

mc˙p(Tout−Tin)

S

(5)

wheretheuppersurfaceofthetopglassslabisdenotedbyTt,gl↑.Thethermalconductivityofthetopandbottomglassslabsiskgl,andthethicknessofthetopandbottomglassslabsareL1andL3,respectively.

Moreover,qair1,conv,qair1,rad,andqair3,radaregivenby

qair1,conv=hw(Tt,gl↑−Ta)(10)

44qair1,rad=εglσ(Tt,gl↑−Ta)

(11)

󰀁󰀇4εpvεgl4

−T(12)qair3,rad=σTb,wheretheoutflowandinflowtemperaturesofthework-pvbl↓

εpv+εgl−εpvεgl

ingfluidaredenotedbyToutandTin,respectively.The

temperatureofthelowersurfaceofthetopslabandthewheretheconvectionheattransfercoefficientforthewinduppersurfaceofthebottomslabaredenotedbyTt,gl↓flowoverthetopglassslabisdenotedbyhw.

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