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Thermal Time Constant of PV Roof Tiles Working under Different Conditions

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Dariusz Kurz at Poznan University of Technology
Dariusz Kurz
Nawrowski
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This paper presents different types of photovoltaic (PV) roof tiles integrating PV cells with roof covering. Selected elastic photovoltaic roof tiles were characterised for their material and electrical characteristics. Practical aspects of using PV roof tiles are discussed, alongside the benefits and drawbacks of their installation on the roof. Thermal resistance, heat transfer coefficient and thermal capacity were identified for elastic PV roof tiles and roof construction built of boards and PV roof tiles, according to valid standards and legal regulations. The resistance–capacity (RC) models of PV roof tiles and roofs are proposed according to the time constants identified for the analysed systems. The energy balance of the studied systems (PV roof tiles alone and the roof as a whole) is presented, based on which temperature changes in the PV cells of the roof tiles working under different environmental conditions were identified. The timing of PV cells’ temperature change obtained by material data and energy balance analyses were compared. The relationship between the temperature change times of PV cells and the thermal resistance and heat capacity of the whole system are demonstrated, alongside environmental parameters.
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Sustainability2019,11,2344;doi:10.3390/su11082344www.mdpi.com/journal/sustainability
Article
ThermalTimeConstantofPVRoofTilesWorking
underDifferentConditions
DariuszKurz*andRyszardNawrowski
PoznańUniversityofTechnology,FacultyofElectricalEngineering,InstituteofElectricalEngineeringand
Electronics,St.Piotrowo3a,60‐965Poznań,Poland;ryszard.nawrowski@put.poznan.pl
*Correspondence:dariusz.kurz@put.poznan.pl
Received:14March2019;Accepted:16April2019;Published:18April2019
Abstract:Thispaperpresentsdifferenttypesofphotovoltaic(PV)rooftilesintegratingPVcells
withroofcovering.Selectedelasticphotovoltaicrooftileswerecharacterisedfortheirmaterialand
electricalcharacteristics.PracticalaspectsofusingPVrooftilesarediscussed,alongsidethe
benefitsanddrawbacksoftheirinstallationontheroof.Thermalresistance,heattransfercoefficient
andthermalcapacitywereidentifiedforelasticPVrooftilesandroofconstructionbuiltofboards
andPVrooftiles,accordingtovalidstandardsandlegalregulations.Theresistance–capacity(RC)
modelsofPVrooftilesandroofsareproposedaccordingtothetimeconstantsidentifiedforthe
analysedsystems.Theenergybalanceofthestudiedsystems(PVrooftilesaloneandtheroofasa
whole)ispresented,basedonwhichtemperaturechangesinthePVcellsoftherooftilesworking
underdifferentenvironmentalconditionswereidentified.ThetimingofPVcells’temperature
changeobtainedbymaterialdataandenergybalanceanalyseswerecompared.Therelationship
betweenthetemperaturechangetimesofPVcellsandthethermalresistanceandheatcapacityof
thewholesystemaredemonstrated,alongsideenvironmentalparameters.
Keywords:photovoltaicrooftile;heattransfercoefficient;thermalresistance;thermalcapacity;
energyyield;RCmodel;BIPV
1.Introduction
Photovoltaic(PV)rooftilesblendPVcellswithroofcovering.ThistypeofPVitemenablesthe
optimaluseofsolarenergyinlightoftheirrelevantexposureandroofslope.Therearedifferent
typesofPVrooftilesavailable—somelookliketraditionalPVpanelsinglazedandmetal‐framed
designs,whileothersareelasticmodulesorPVcellsintegratedwithceramictiles(Figure1).
(a)(b)(c)
Figure1.Differenttypesofphotovoltaic(PV)rooftiles:(a)rigidglassPVrooftilesinmetalframes
[1];(b)elasticPVrooftiles[2];(c)ceramicPVrooftiles[3].
ThedimensionsofPVrooftilesareselectedinsuchawaythattheycanbefittedinbetween
traditionalroofcoveringitems(i.e.,ceramictilesorbitumencovering).ThestandardheightofPV
Sustainability2019,11,23442of14
rooftilesisca.40cm,whiletheirwidthrangesfromseveralcentimetrestoseveralmetres.They
replaceseveralceramictilesorarowortoplayerofasphaltroofingfelt.Thesmallertheitem,the
easieritistofillthewholeroofwithPVelements,whichincreasesthecostofaPVsystemcompared
tolargerrooftiles[4,5].
PVcellsinphotovoltaicrooftilesareexposedtomoresevereworkingconditionscomparedto
traditionalPVpanelsinstalledonasupportingstructureseveralcentimetresabovetheroofsurface.
Thelackofnaturalairmovement(wind)onthebackofthePVmodule,whichreducesthe
temperatureofPVcells,contributestoalowerpower‐generatingefficiencyofsolarrooftiles.The
heatreleasedbythebottomsideoftherooftilesisaccumulatedintheairgapbetweenthebottom
surfaceoftheroofandtheatticinsulatinglayerinthecaseofrigidPVrooftileswithconstruction
similartotheconstructionoftraditionalPVpanelsorPVceramicrooftiles,oritmaybetransferred
furtherintotheroofstructureasinthecaseofelasticPVrooftilesfixed(glued)totheroof
construction(e.g.,onthetoplayerofasphaltroofingfeltandboards).Thedegreeandrateofheat
exchangefromthePVrooftiletotheroof,environment,oratticdependsonthetypeofPVrooftile,
itsinstallation,theparticularinsulationmaterialsoftheroofandatticuse.ThebottomsideofPV
rooftilescanonlybecooledandventedbyairinthespacesbetweenroofslats.Theauthorsin[6,7]
indicatealackofconfirmatorydataconcerningtheefficiencyofPVrooftiles,whichpreventsthe
popularisationofthistechnology.Theauthorsin[8–10]presentdifferentstudiesontheproductivity
andenergylossquantitiesinbuilding‐integratedphotovoltaic(BIPV)systemscomposedofdifferent
photovoltaicitems(rooftiles,glasspanes,shutters,wall‐mounteditemsetc.).Anumberofstudies
havebeencarriedoutonmethodsofPVcellventilation(whenthecellsareintegratedwitharoofor
wall),heatremovalandtheiruseandimpactontheenergyefficiencyofthesystem.In[11,12]itwas
revealedthataddingaventilatingductofarelevantsizebehindPVitemsincreasestheir
energy‐generationefficiency.Gan[13]demonstratedthattheoptimumheightofthegapbetween
thepanelandtheroofisabout0.125m,regardlessoftheinclinationangle.TheauthorsusedCFD
modellingtopresenttheresultsofstudiesfordifferentPVmodules’installationparametersand
scenariosin[14–16].InordertoanalysethetemperaturechangesofPVcells,Gunawanetal.[7]
examinedpanelsinstalledonaroofwithanairgap(standardinstallationonasupportingstructure),
built‐ininacoldroof(withnothermalinsulation),built‐ininahotroof(withmineralwool
insulation)andinstalledonaroofwithAmerican‐styleshingles.Additionally,forcomparison,a
panelwasfixedtoastructurewhichenableditsfreecoolingbythewind,andaweatherstationwas
installedtocollectdataoninsolation,ambienttemperature,windforceandprecipitationintheUK.
TheauthordemonstratedthatPVcellsinstalledonAmerican‐stylewoodshinglesreachedthe
highesttemperaturesbecauseheatexchangeintheircasewasmostdifficult,andtheheatreleasedat
thebackofthepanelheatedthePVcellsfurther.Yu‐Huietal.[17]proposedandexperimentally
revisedaphoto–electro–thermalmodel(PETmodel)forPVmodules,basedonwhichthey
confirmedthegeneratedelectricalenergydependenceonPVcelltemperature.In[18],theauthors
studiedthetemperatureofPVcellsworkingunderdifferentenvironmentalconditions,considering
suchthermalprocessesasconvectionandradiation.Theyproposednewvaluesofthecoefficientsof
convectiveheattransferbasedonaliteraturereviewandtheirownstudiesfordifferentconditions.
Theobtainedresultswereconfirmedbyotherscientificpapers[19–21].Trzmiel[22]presentsa
mathematicalmodelofathin‐filmPVpaneldevelopedwiththeuseofaPVcellsingle‐diodeelectric
modelandtemperaturerelationships,basedontheirownmeasurementdata.Heatexchange
betweenPVrooftiles,theroofstructureandaircanoccurinthreephysicallydifferentways:
convection,radiationandconduction.WithregardtotheroofconstructionandarrangementofPV
rooftilesontheroof,heatexchangebyconductionandconvectionhavethegreatestshare,while
radiationprocessescanbeneglected[23].
Basedonaliteraturereviewandourownstudiesitcanbeconcludedthatthetemperatureof
PVcellshasasignificantimpactonPVconversionefficiencyandthequantityofgeneratedelectrical
energy,whichisparticularlyevidentinthecaseofPVcellsintegratedwiththebuilding(BIPVitems)
[24–26].Thephoto–electro–thermal(PET)andresistance–capacity(RC)modelsofPVcellsavailable
intheliteraturearedescribedandverifiedfortraditionalPVpanels,butthereisnoconfirmed
Sustainability2019,11,23443of14
validitytestofthesemodelsforcellsbuiltinPVrooftilesintegratedwiththeroof.Therefore,we
attemptedtodeterminethethermaltimeconstantofPVcellsintegratedwithPVroofsgluedtothe
roofstructure(basedontheRCmodel)andtodeterminethemaximumtemperaturesthattheycan
achieveindifferentworkingconditions(usingthePETmodel).IntheRCandPETmodels,we
consideredtheparametersoftheroofstructure(thermalresistanceandthermalcapacityofthe
board)towhichthesolarroofwasgluedandconsideredthetemperaturechangesofthePVrooftiles
integratedintotheroofandworkinginvariousenvironmentalconditions.Byknowingthewarming
andcoolingratesofPVcells—whichareaffectedbyheatprocessesinthesystem—onecanidentify
energylossesrelatedtotemperaturechangesinthecells,whichhelpsinthemorepreciseestimation
ofthepossibleelectricalenergyyield.
2.TestObject—DescriptionofanElasticPVRoofTile
OurtestobjectwasaTegosolarPVL68elasticPVrooftile(ofTegola,VittorioVeneto,Italy),
presentedinFigure2.ThePVrooftileweighsabout4kgandconsistsoftwoparts:bitumen
substrateandaUni‐SolarelasticPVmodule.ThePVmodulewithamaximumpowerof68W
consistsofelevenseriallyconnectedsolarcells.Thecellsarebasedontriple‐junctionamorphous
silicon.Eachcellisfeaturedwithaby‐passdiodesolderedinparallel,whichenablescurrentflowifa
partofthemoduleisshaded.Althoughtheefficiencyofcellsbasedonamorphoussiliconisfairly
low(6%–10%),theyaremuchcheapertoproducethancrystallinesiliconcellsandcanbe
manufacturedinanyshapeandsize[27].
ThereferencePVrooftilewascomposedoffourmainlayers(showninFigure3),including[27]:
ETFE(ethylene‐tetrafluoroethylene,alsoknownasTefzel)—durablepolymerresistanttowater
andmoisture,withhightensilestrength,highlytransparentandresistanttoUVlight;itisalso
usedfortheproperencapsulationofPVcellsensuringtheirproperelectricalinsulation.
PVcells—11triple‐junctionPVcellsmadeofamorphoussiliconwithdifferentadmixturesto
improvesensitivitytoabsorptionoflightintheblue,greenandredcolourranges;thetotal
thicknessofthePVcellwasca.1μm,dimensions:239×356mmandca.10%efficiency.
Connectiongrid—stainlesssteelconnectionsofPVcells.
PVDFbottomlaminate(polyvinylidene‐fluoride)—thermoplasticpolymerwithahighdegree
ofPVDFcrystallisation;itprovidesadditionalprotectionofPVcellsfrommoistureand
atmosphericconditions,properelectricalinsulation,andmechanical,thermalandchemical
protection.
Figure2.Photovoltaicrooftile(TegosolarPVL68)[27].
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Figure3.ConstructionofTegosolarPVL68photovoltaicelasticrooftile,where1:
ethylene‐tetrafluoroethylene(ETFE);2:siliconcell(a‐Siforblue‐colourradiation);3:siliconcell
(a‐SiGeforgreen‐colourradiation);4:siliconcell(a‐SiGeforred‐colourradiation);5:stainlesssteel
foil(–);6:polyvinylidene‐fluoride(PVDF)baselayers[27].
Theconstructionofthereferencephotovoltaicrooftile,basedonatriple‐junctionstructure
(withtheadditionofGeindifferentamountsinindividualpartsofthePVcells)ispresentedin
Figure3,whileitsmostimportanttechnicalparametersareshowninTable1.Thestructurewhich
generatedelectricalenergyconsistedofstainless‐steelfoil,onwhichthreelayersofamorphous
silicon,atransparentelectrodeandconnectiongridsocketswereapplied.Thestructurewascoated
withanETFEpolymerfilm,whichprotectedthemodulefromwaterandpreventeddirtdeposition.
Becausethelowefficiencyofamorphouscellsismainlycausedbythepoorabsorptionoflow‐energy
infraredradiation,eachofthethreelayersofamorphoussiliconwasresponsiblefortheabsorption
ofdifferentsolarradiationwavelengths[28].
IndividualparametersofthemateriallayersmakingupthePVrooftileandroofstructureson
whichthetilescanbeinstalled,arepresentedinTable2.TheconnectionpathsofPVcellswerenot
consideredinthedeliberationswithregardtotheirsmallsizecomparedtothetotalareaofPVrooftiles.
Table1.TegosolarPVL68photovoltaicrooftiledata(inSTC)[27,29].
ParameterSymbolandunitValue
MaximumpowerratingP
max
(W)68
OpencircuitvoltageU
oc
(V)23.1
VoltageatthemaximumpowerpointU
m
(V)16.5
ShortcircuitcurrentI
sc
(A)5.1
CurrentatthemaximumpowerpointI
m
(A)4.13
Temperaturecoefficientofshort‐circuitcurrent
Isc
(mA/°C)5.1
Temperaturecoefficientofopen‐circuitvoltage
Uoc
(mV/°C)−88
Uoc
(%/°C)−0.38
Temperaturecoefficientofshort‐circuitcurrent
Isc
(mA/°C)5.1
Isc
(%/°C)0.1
TemperaturecoefficientofvoltageatMPP
Umpp
(mV/°C)−51
Umpp
(%/°C)−0.31
TemperaturecoefficientofcurrentatMPP
Impp
(mA/°C)4.1
Impp
(%/°C)0.1
Temperaturecoefficientofpower
P
(mW/°C)−143
P
(%/°C)−0.21
Panelefficiency
p
(%)7.26
DimensionsofPVcellswidth×height(mm)239×356
NumberofPVcellsinthepanelN
s
(pcs.)11
TypeofPVcells‐ triple‐junction,amorphous
Paneldimensions(global)width×height×thickness(mm)2880×395×2.5
Panelarea(global)S(m
2
)1.138
Panelarea(active)S
a
(m
2
)0.936
Panelweightm(kg)3.9
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Table2.MaterialdataofPVL68photovoltaicrooftilelayersandroof.
Parameter
Layer
Thickness
dm(m)
Specificheat
cp,n(J/kgK)
Density
n(kg/m3)
Thermalconductivity
k(W/mK)
ETFE 0.5×10−3[27,29]1000[30]1800[30]0.24[30]
PVcell1×10−6[27,29]677[18,19,31]3200[18,19,31]170[18,31,32]
Gridconnection10×10−9[27,29]460[33]7900[33]17[33]
PVDF2×10−3[27,29]1120[34]1800[34]0.12[34]
Pineboard25×10−31600[33]450[35]0.35[35]
ThephotovoltaicmoduleofthereferencePVrooftilehasanadhesivelayeronitsbottomsideto
facilitateitsfixingtotheroofstructure.ThedimensionsofthePVpanelwerethesameasthe
dimensionsofstandardroof‐coveringitems(bitumen—shinglesorasphaltroofingfelt),which
makesembeddingthePVrooftilesintotheroofstructureveryeasy.Inadditiontoelectricalcurrent
generation,aPVrooftileensurestheappropriateroofstrengthandwaterinsulation,muchlike
traditionalroofcovering.AccordingtotherecommendationsofthePVrooftilesmanufacturer,
standardroofcoveringistobeusedca.0.5mfromtheouteredgesoftheroof[27].
3.ThermalResistanceandThermalCapacityoftheRoofandPVRoofTiles
ByknowingtheconstructionandmaterialparametersofPVrooftilelayersaswellastheroof
structure,onecanidentifythethermalresistanceandthermalcapacityofeachlayerandtheentire
PVrooftilebasedoncurrentlegalregulationsandstandardsconcerningbuildingmaterials.PN‐EN
ISO6946:2017“Buildingcomponentsandbuildingelements.Thermalresistanceandthermal
transmittance.Calculationmethods”isthestandardvalidcurrentlyinPoland[36].Thethermal
resistanceandthermalcapacityofahomogeneouslayercanbeidentifiedbasedonthefollowing
equations[18,36,37]:
k
d
Rm
th ,(1)
mnpnth dcC .
,(2)
whereRthisthematerial(layer)thermalresistance(m2K/W),Cthisthematerial(layer)thermal
capacity(J/m2K),dmisthelayerthickness(m),kisthethermalconductivitycoefficientofthematerial
(W/mK),
nisthematerialdensity(kg/m3),andcp,nisthematerialspecificheat(J/kgK).
ThevaluesofthermalresistanceandthermalcapacityofPVrooftilelayersandroofstructure,
identifiedaccordingtoEquations(1)and(2),arecollectedinTable3.Individualthermalresistance
valuesRthdescribethematerialresistancetotransmitheat,whilethermalcapacityvaluesCthreferto
theabilitytoabsorbandtransmitheat.Heattransmittance(conduction)betweenthemateriallayers
(buildingcomponentlayers)isaprocessinvolvinginertmovementenergytransmittanceby
adjacentparticles;itisoneofthreekindsofheattransfer,withconvectionandradiationbeingthe
othertwo.Theprocessstrictlydependsonthematerialparametersofthelayers.
Table3.CalculatedRthandCthvaluesofPVPVL68materials(layers)androofcomponents.
Parameter
Layer
Rth
C
th
(m2K/W)(J/m2K)
ETFE2.08×10−3900
PVcell10×10−92.17
Gridconnection0.1×10−93.6×10−3
PVDF16.66×10−34029.78
Pineboard71.43×10−318,000
ThetotalvalueofthermalresistanceRTHandthermalcapacityCTHofaPVrooftileoraroofis
thetotalofthermalresistanceandthermalcapacityvaluesofalllayersintheanalysedstructure,
whichisexpressedbythefollowingequations[18,36]:
Sustainability2019,11,23446of14
i
ithTH RR ,(3)
i
ithTH CC .(4)
TheabovementionedEquations(3)and(4)wereusedtocalculatethevaluesofthermal
resistanceandthermalcapacityofthereferencePVL68PVrooftile,whichamountedto18.74×10−3
m2K/Wand4931.95J/m2Krespectively.Theroofstructureinthedeliberationswastreatedasa
homogeneouslayercomposedonlyofpineboards,withouttakingothercomponents(e.g.,rafters)
intoaccount,whichwouldnotgreatlyaffecttheidentifiedRCtimeconstantvaluesduetothesmall
sizeofthecomponentscomparedtotheroofslopearea.Detailsofthemethodusedtoidentifythe
totalresistanceofaroofcomposedofdifferentlayers,takingallcomponentsintoaccount,are
presentedin[38].
WhenEquation(1)istransformedintoonewhichenablesthedeterminationofthecoefficientof
thermalconductivity(thermalconductance)kofaPVrooftile,thefollowingrelationshipis
obtained:
th
m
R
d
k.(5)
ThecoefficientofthermalconductivitykofthestudiedPVPVL68rooftilewas0.13W/mK,that
is,muchlowerthanthevalueofkforstandardceramictiles(i.e.,1W/mK,accordingtostandard
[36])andslightlylowerthanthecoefficientvalueforthetoplayerofasphaltroofingfelt(forwhichit
amountsto0.18W/mK).ThismeansthatthereferencePVL68photovoltaicrooftileprovidedbetter
thermalinsulationoftheroofthanceramicorbitumenroofcovering,whichwouldcontributetoa
lowercoolingrateofthebuildingatticinwinterandaslowerheatingrateinsummer.Theentire
analysedroofstructure,composedofpineboardsandPVrooftiles,hadathermaltransmittanceof
0.31W/mK,atotalthermalresistanceamountingto90.17×10−3m2K/Wandtotalthermalcapacityof
22,931.95J/m2K.
4.RCCircuitModel
Thematerialparametersofrooftilelayersaswellasatmosphericconditions(e.g.,wind
directionandspeed,irradiance,ambienttemperature)greatlyaffectthetemperatureofPVcells
constitutingthephotovoltaicrooftile.AworkingPVrooftilealsogeneratesheatasaresultofits
internalprocesses.Aresistance–capacity(RC)modelofaphotovoltaicrooftilehelpstoidentify
temperaturechangesofthePVcells,whicharethePVrooftilecomponents,withasuddenchangein
theirworkingconditions(particularlyatmosphericconditionsandirradiance).Thetemperatureof
PVcellsinphotovoltaicrooftileschangesexponentiallywithadiscontinuous(sudden)changein
irradiance,whiletheRCtimeconstantofaPVrooftileisdefinedasthetimenecessarytoreach63%
ofthetotaltemperaturechangevalue.TheproposedRCmodelofthestudiedPVrooftilehelpsto
identifyitsτRCundervariableworkingconditions.ThermalmechanismsofPVrooftileswere
expressedbycorrelatingtheirelectricalequivalents(resistanceandcapacity)withthermalresistance
andthermalcapacity,usedfordefiningheattransmittanceintheirlayers.Figure4presentsa
substitutewiringdiagramfortheRCmodelofastudiedsinglePVL68photovoltaicrooftile(Figure
4a)andfortheentireroofstructurewithbuilt‐inPVrooftiles(Figure4b).Figure4a,bcoversthePV
cellasawhole(i.e.,assemblyofthethreelayersofcellslistedinFigure3).IPV,UPV(Figure4a,b)isa
photovoltaiccurrentandvoltageofsolarcells,respectively.PPVisaelectricpowergeneratedbya
solarrooftile,calculatedasmultiplicationoftheIPVandUPV.
RthfrontandRthbackstandfortheresistanceofheattransferontheouterRseandinnerRsisurfaceof
theitemrespectively.Theresistancevalues,dependingonthedirectionoftheheatstreamflow,
werespecifiedin[36]PN‐ENISO6946:2017andarepresentedinTable4.
Sustainability2019,11,23447of14
(a)
(b)
Figure4.Equivalentelectricalcircuitfortheresistance–capacity(RC)modelfor:(a)asinglePVL68
photovoltaicrooftile;(b)theentireroofcomposedofpineboardandPVL68photovoltaicrooftiles.
Table4.Valuesoftheheattransferresistanceonthesurfaceandairlayers,dependingontheheat
streamflowdirection[36].
Heattransfer
resistance(m
2
K/W)
Heatstreamdirection
UpHorizontal*Down
R
si
0.100.130.17
R
se
0.040.040.04
*Valuesapplyingtothehorizontaldirectionwereusedincasethedirectionofaheatstreamwas
deflectedby±30°fromthehorizontalplaneandwhenitwaspossibletochangetheheatstream
direction.
ThetimeconstantofthereferencePVrooftileortheentireroofconstructioncanbeidentified
accordingtoEquation(6),basedonidentifiedthermalresistanceandheatcapacityvalues(Tables3
and4)andwiringdiagramspresentedinFigure4:

THbackthfrontthTHRC
CRRR
.(6)
TheidentifiedtimeconstantvaluesforthePVL68photovoltaicrooftileandtheentireroof
amountedtoτ
RCpv
=18.80minandτ
RCroof
=99.43min,respectively.Intheanalysisoftheentireroof
constructionwithPVrooftiles,theRCtimeconstantvalueincreasedduetothehighheatcapacityof
woodboardslaidunderthephotovoltaicrooftiles.
5.HeatBalanceoftheRoofandPhotovoltaicRoofTiles
ItwasassumedthatthePVrooftiletemperaturewasuniformlydistributedonitsdifferent
layersandthatthetemperatureofallPVcellswasthesame.Inthecaseofphotovoltaicrooftiles,it
sufficestotakeconductiveandconvectiveheatexchangeintoaccount,whileneglectingradiation.
ThevalueofelectricalenergygeneratedbyPVrooftilesandthequantityofsolarenergyreaching
thePVmodulesurfacewerealsoconsidered.Thethermalbalanceequation(PETmodel,
photo‐electro‐thermal)canbeformulatedasfollows[17]:
Sustainability2019,11,23448of14
convpvsolar
pv
TH QPQ
dt
dT
CS ,(7)
whereSisthePVmodulesurface(m2),CTHisthePVrooftilethermalcapacity(J/m2K),TpvisthePV
celltemperature(K),QsolaristhesolarenergyreachingthePVmodulesurface(W),Ppvistheelectrical
powergeneratedbythePVmodule(W)andQconvrepresentstheconvectiveheatlosses(W).
ThepowerdensityvalueofsolarradiationreachingthePVmodulesurfacecanbeidentified
fromEquation(8)[17]:
ESQsolar
,(8)
where
isthePVmodulecoefficientofsolarradiationabsorption,whosevaluerangedfrom70%to
90%,andEisthesolarradiationpowerdensity(W/m2).
ThetotalvalueofconvectiveheatlossesisthetotalofforcedconvectionheatonthePVmodule
frontsurfaceandfreeconvectionheatofthemodulerearpart,whereasfreeconvectionisminor
comparedtoforcedconvectionandcanbeneglected.Convectiveheatlossescanbeidentifiedfrom
Equation(9)[17]:
ambpvconvconv TThSQ ,(9)
wherehconvisthecoefficientofconvectiveheatexchange(W/m2K)andTambistheambient
temperature(K).
Thecoefficientofconvectiveheatexchangehconvdependsonthewindspeed
wind(m/s),whichis
expressedbyEquation(10)[18]:
windconv
h
56.255.8 .(10)
Thehconvcoefficientwasdeterminedexperimentallybytheauthorsin[18],whoalsoreviewed
theothercoefficientsofEquation(10)dependingonthedeterminationmethods—inawindtunnel
orduringrealmeasurements—andobtainedonthebasisofthefundamentaltheoryofheat
exchangeandcriterionnumbers.
Itwasassumedthatinnaturalconditions,thechangeintheambienttemperatureatirradiance
changeswasslowenoughtobeconsideredasaconstantvalue.UponincludingEquations(8)–(10),a
relationshipforthemomentarytemperaturevalueofPVcellswasobtainedinEquation(7)asan
analyticalsolutionofthefirst‐orderPETdifferentialequation:

amb
conv
pv
TH
conv
pv T
hS
PES
t
C
h
tT
exp1 .(11)
Anassumptionwasmadethatundernaturalconditions,ambienttemperaturechangeatirradiance
changeoccursslowlyenoughtobeconsideredafixedvalue.
ThePVcelltemperaturevalueofthereferencestandalonerooftile(Figure5a)andbuilt‐inroof
tilefixedtowoodboards(Figure5b)wasidentifiedforthreedifferentenvironmentalconditions:
a) test1:E=1000W/m2,
wind=3m/s,Tamb=30C;
b) test2:E=600W/m2,
wind=3m/s,Tamb=30C;
c) test3:E=600W/m2,
wind=2m/s,Tamb=30C.
ThemaximumtemperaturevaluesofPVcellsinaworkingPVL68rooftileamountedto81.26,59.08
and67.45Crespectivelyforthethreedifferentsetsofenvironmentalconditions,whichremained
unchangedduringtheanalysis.ThevalueofthedifferenceinthePVcellstemperatureandambient
temperature(presentedinFigure5)wasidentifiedbasedonthefollowingequation:
ambpvpv TtTT )( .(12)
Sustainability2019,11,23449of14
(a)
(b)
Figure5.TemperaturechangeofPVcellsofPVL68photovoltaicrooftilesunderdifferent
environmentalconditions:(a)standalonerooftile;(b)rooftilefixed(glued)totheroofboards.
4.Discussion
Thevaluesoftimeconstants
RCofPVcellsinastandalonerooftileandatilebuiltintotheroof,
workingunderdifferentconditions,arelistedinTable5.
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Table5.Specificationsoftimeconstantvalues
RCofPVcellsinaPVL68rooftileworkingunder
differentconditionsasstandaloneandbuilt‐inversions,andvaluesdeterminedbasedonmaterial
data.
PVcellin:
τRC(min)
MaterialdataForcedconvectionFreeconvection
test1test2test3test1test2test3
StandalonePVrooftile18.805.325.326.2720.8120.8120.81
Built‐inPVrooftile99.4323.8023.7628.2595.5895.7695.49
test1:E=1000W/m2,
wind=3m/s,Tamb=30C;test2:E=600W/m2,
wind=3m/s,Tamb=30C;test3:E=
600W/m2,
wind=2m/s,Tamb=30C.
OnecanobserveahighconvergencewhencomparingthetimeconstantsofaPVrooftile
obtainedfrommaterialdataandidentifiedfromtheenergybalanceequation,butonlyinthecaseof
freeconvection.ThePETmodel,alsotakingintoaccountforcedconvection,givesrealvaluesofthe
timeresponseoftemperaturechangesofPVcellstothecurrentlyprevailingenvironmental
conditionsofthePVrooftile(windspeed,irradiance)inwhichthePVtileswork.Underunchanged
ambientconditions,afterca.5–6min,thetemperatureofPVcellsinastandalonerooftilewould
changeby63%comparedtotheirpotentialmaximumvalue.Theproposedroofstructurecomposed
ofwoodboardsandPVrooftileswascharacterisedbyatimeconstantintherangeof23–28min,that
is,fourtofivetimeslongerthanthetimeconstantofthestandalonerooftile.Notethatduetoits
structure,aPVrooftilewillneverworkasastandaloneitem,butwillalwaysbeintegratedwitha
substratesuchastheroofofabuilding.Achangeintheirradiancevaluewillcausedirectly
proportionalchangesinthetemperaturevaluesthataPVcellcanreach.Theirradiancevaluedidnot
greatlyaffectthevalueofthesystemtimeconstant,whileareducedwindspeed(atunchanged
irradiancevalue)contributedtothePVrooftilebecomingconsiderablyheated,andtoanincreasein
thevalueofthesystemtimeconstant.
Agreatertimeconstantisdesiredwhiletheelementsbecomeheatedduringphotovoltaic
processes,sothatthetemperatureofPVcellsdoesnotincreasetooquicklyanddoesnotreachtoo
highavalue,butratherhasanegativeimpactduringsystemcooling,whenthetemperatureofPV
cellsisreducedasquicklyaspossible.ThePVcelltemperaturesreachedforthethreepresented
cases(Tpvtest1=81.26C,Tpvtest2=59.08C,Tpvtest3=67.45C)fortheanalysedPVrooftilewitha
temperaturecoefficientofpowerchange
P=−0.21%/°Cmaycontributetoareductioninthe
generatedpowervaluebyamaximumof11.81%,7.16%and8.91%respectively.
InitialexperimentalresearchwasalsocarriedoutinvolvingthemeasurementofthePVcells’
temperatureofthefree‐standingPVtileandthePVtilebuiltintotheroof(gluedtotheboards)
underrealenvironmentalconditions.ThetemperaturechartofPVcellsandtheambientconditions
isshowninFigure6.
Duringthetest,theirradianceEwaschangedintherangeof70–330W/m2,windspeed
inthe
range0.5–3.1m/s,andambienttemperatureTambintherange9.1–10.4C.Withtheincreaseof
irradiance,thetemperatureofPVcellsincreased,bothtiles:free‐standing(Tpv,free‐standing)and
builtintotheroof(Tpv,built‐in).ThemaximumtemperatureofthePVcellsofrooftilesbuiltintothe
roofwas24.6C,anditwas2Clowerthanthetemperatureoffree‐standingtilecellsatanambient
temperatureof10.4C.ThePVcellsofthefree‐standingtilereactedfastertochangesinirradiance
andwindspeed.ThemostvisibletemperaturechangesofthePVcellsofafree‐standingtilewere
seenaroundat12:30–14:00atthehighestwindspeeds.Ontheotherhand,thetemperatureofPV
cellsinrooftilesintegratedwiththeroofdecreasedslowerandmoreuniformly.Additionally,atthe
endofthemeasurementtime,whentheirradiancedecreasedsignificantly,thetemperatureofthe
PVcellsofthefree‐standingtiledecreasedfasterthanthoseinthetilebuiltintotheroof.
Sustainability2019,11,234411of14
Figure6.ChartoftemperaturechangesofPVcellsinfree‐standingconfigurationandas
roof‐mountedsolarrooftiles,aswellastheambientconditionsprevailingduringthetests.E:
irradiance;T
amb
:ambienttemperature;
:windspeed.
ThisstudyconfirmsthesimulationresultsofchangesintherateofheatingandcoolingofPV
cellsdependingontheconditionoftheiroperation(free‐standingorintegratedwiththeroof).By
gluingPVtilestotheroofstructure,theoverallsystemcapacityincreases,thankstowhichthe
temperaturedecomposesintheentiremassandincreasesmoreslowly,butalsoslowsthereleaseof
heattothesurroundings.
5.Conclusions
ThispaperpresentsknownRCandPETmodelsofphotovoltaiccellsthatmakeuptraditional
PVpanelsandhasbeenadaptedtodeterminethethermaltimeconstantofcellsincludedinthe
photovoltaicrooftiles.TheywereconfirmedtobecorrectforthePVrooftiles,butonlyinthecaseof
theiroperationasafree‐standingelement,liketraditionalPVpanelsandnotintegratedwiththe
roof.DifferencesinthevaluesofthethermaltimeconstantofPVrooftileswerealsoshown
dependingonthemodelused(RCorPET).TheRCmodel,basedonthematerialdataofthePVroof
tilelayers,doesnotconsidertheweatherconditionsinwhichthetileworks.UsingthePETmodel
(consideringonlytheprocessofthefreeconvectionofheatexchange),convergentvaluesofthetime
constantwereobtainedwiththevaluesobtainedbymeansoftheRCmodel(ca.19–21min).Theuse
ofthePETmodelallowedmoreaccuratetimeconstantresultstobeobtained(ca.5–6min),becauseit
considersdifferentformsofheatexchangeaswellasthecurrentweatherconditions(i.e.,irradiance,
ambienttemperature,windspeed).Furthermore,itwasshownthattheavailablemodelscannotbe
usedtodeterminethethermaltimeconstantofPVrooftilesintegratedintheroof,duetothe
additionalthermalcapacityandthermalresistanceoftheroofstructurewithwhichtheyare
integrated.TheauthorsmodifiedtheavailableRCmodelwithamemberrepresentingaroof
structure(composedofboards),takingintoaccountitsthermalresistanceandthermalcapacity.
Also,inthePETmodel,thetotalthermalcapacityofthesystemwastakenintoaccount,whichisthe
sumofthethermalcapacitiesofthePVrooftileandtheroofstructure.Accountingfortheroof
structureinbothmodelscausedaboutafive‐foldincreaseinthevalueofthethermaltimeconstant
Sustainability2019,11,234412of14
ofPVcells.Theearlierdependencesofchangesinthetimeconstantvalue(takingintoaccountonly
thefreeconvection)werealsometintheanalysisoftheentireroofwithPVrooftiles.
Insimulationtestsnos.1and2,theirradiancechangeof400W/m2atawindspeedof3m/s
causedadifferenceinthemaximumtemperatureofthePVcellsrooftileof22C.During
experimentalinvestigations,withirradianceof330W/m2andwindspeedof3.1m/s,the
temperatureofPVcellsincreasedbyapprox.14–16Caboveambienttemperature,confirmingthe
correctnessoftheproposedRCmodelofphotovoltaicrooftiles.
Theexperimentaltestscarriedoutalsoconfirmedthechangesinthevaluesofthethermaltime
constantsofthePVcellsoffree‐standingandintegratedphotovoltaicrooftiles.Thetemperatureof
thePVcellsofafree‐standingrooftilequicklyrespondedtochangesintheenvironmentinwhichit
workedcomparedtoaPVrooftilebuiltintotheroof.However,furtherlong‐termstudiesare
necessary,underdifferentenvironmentalconditions,sothatthevaluesofthetimeconstantsofthe
testedsystemsfromexperimentalresearchcanbeunambiguouslydetermined.
ThetemperatureofrooftilePVcellsdidnotchangeabruptlyasaresultofrapidchangesin
ambientconditions,andthiswasrelatedtoheatenergyaccumulationintheitem’smass.Hence,the
determinedtimeconstantofaPVrooftileandtheentireroofhelpedtoestimatethespeedof
changesinPVcellsduringheatingandcooling.Inturn,thechangesdeterminetheelectricalenergy
generationefficiency.Alengthoftimeofbetweenthreeandfivetimeconstantswasassumedasthe
timenecessarytoreachthemaximumtemperatureofanitem.Theknowledgeofthermalprocesses
andPVcelltemperaturechangesenablesmorepreciseestimationoftheamountofelectricalenergy
generatedbyaphotovoltaicsystembuiltintoaroof,dependingontheroofstructuretype.Thebetter
theroofinsulation,thehigherthetimeconstantvalueofthesystemandthelongerthetime
necessaryforPVcellstobecomeheatedandtocooldown.Thesystemcoolingtimehasaspecial
significance,afterreductioninthemomentaryirradiancevalue.
AuthorContributions:D.K.:conceptualisation,methodology,writing—originaldraftpreparation,
writing—reviewandediting;R.N.:conceptualisation,formalanalysis,writing—reviewandediting,
supervision.
Funding:ThisresearchwasfundedbyPolishGovernment,MinistryofScienceandHigherEducation.
ConflictsofInterest:Theauthorsdeclarenoconflictofinterest.
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In this study, a polymer composite is made using chemically treated jute fiber and waste floor tile powder as an alternative source for roof tile application. The wear qualities were examined at various ages, and the outcomes were optimized. In order to improve the wetting properties of the jute fiber, it was chemically treated. MINITAB software was used to develop Taguchi method parameters such as jute fiber percentage, waste tile powder percentage, and NaOH chemical treatment using the MINITAB software. It was determined that hardness was the most important characteristic in terms of wear properties after the specimens were subjected to ageing and abrasion wear testing and hardness tests were carried out as per normal protocols. As a result of the waste tile powder addition, the surface and core pore formation rates were reduced and the wear index rates were low. Jute fiber with 15%, 9% tile powder, and 5% NaOH treatment were found to have the lowest wear index of the other specimen compositions tested, according to the wear index. Specimen made with 5% jute fiber addition, 9% tile powder inclusion, and 10% NaOH treatment, on the other hand, had more hardness. Degradation of the fibers and delamination are side effects of the ageing process. The wear resistance of the surface was increased by the use of waste tile powder.
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... The newest publications are related to the issues of ecology, economics, etc., in particular the implementation and application of hybrid energy conversion systems in Poland [21,22]. There have also been publications on non-silicon PV modules [23], studies of weather and climate conditions on the efficiency of solar energy conversion [24], etc. ...
Renewable Energy in Ukraine-Poland Region: Comparison, Critical Analysis, and Opportunities
Chapter
Full-text available
  • Sep 2020
Fundamental and applied research on renewable energy is actively supported for the development of world science and maintaining the energy independence and security of different countries. This section analyzes the publications of scientists from two countries—Ukraine and Poland—in the field of “thermoelectricity,” “photoelectricity,” and “bioenergy” to find regularities in each state and to determine the prospects for joint research. Ukraine and Poland share a common border and have similar climatic conditions and historical heritage, but Poland is a member of the EU, and its legislation in the field of renewable energy complies with the regulations of the European Community. Ukraine is making every effort to develop renewable energy. Comparison of the state of research in these countries is also an example of the analysis of the situation at the borders of EU countries and may answer questions related to sustainable development, the mass transition to renewable energy, and the refusal to use fossil fuels and nuclear power plants. The analysis is based on the results of data published in the international scientific databases Web of Science and Scopus. The most advanced areas of research in each country are identified, analyzed, and aimed at practical application.
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Watertightness Design and Experimental Evaluation of a Solar Panel Structure for Building Integrated Photovoltaics (BIPV) Roofs
Chapter
  • Feb 2024
Building integrated photovoltaic (BIPV) roof technology is gaining popularity and its durability is of concern to different interest groups—watertightness is an important aspect. This study proposes an optimized solar panel structure for BIPV roofs, which aims to achieve watertightness performance; further, watertightness experiments with static and dynamic rainfall (the max wind speed level was 12) were conducted based on GB/T 15227–2019 standard through third-party testing. The results show that the BIPV roof system proposed has good watertightness performance; the water leakage grade is “not severe”. In addition, this study compares the technology application differences of three BIPV roof prototypes and discusses the effectiveness of red dyed test strips in characterizing water leakages. The proposed structure can be a reference for architects and engineers in the early design stage of BIPV roofs, which effectively enhances the durability and the cost investment of waterproofing materials.
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Plus minus zero: carbon dioxide emissions of plus energy buildings in operation under consideration of hourly German carbon dioxide emission factors for past, present and future
Article
Full-text available
  • Sep 2022
The energy supply of private household buildings accounted for 16 % of the total German CO 2 -emission in 2020. To fulfil the targets of a climate neutral building sector in 2045, both, energy efficiency as well as on-site use of Renewable Energies in buildings are needed. One concept of a climate neutral building is the so-called Efficiency House Plus, that features large photovoltaic systems making it seemingly energy self-sufficient and CO 2 -negative by feeding in more electric energy into the grid than needed for its operation on a yearly basis. In fact, houses of this type are highly grid dependent especially during winter months due to their solely electrically based energy supply and a missing long term energy storage. This paper analyses the CO 2 -emission of Energy Efficiency Plus houses more in detail on a timely resolved basis for the German electric supply system of the year 2013, 2021 and a perspective one 2030. An alternative calculation approach for simplified normative evaluation of such buildings is proposed.
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Power Performance Loss Factor Analysis of the a-Si BIPV Window System Based on the Measured Data of the BIPV Test Facility
Article
Full-text available
  • Sep 2018
The application of a building-integrated photovoltaic (BIPV) module to an elevation means that the factors causing performance losses in a BIPV are relatively high compared to a photovoltaic (PV) that is installed at the optimal angle. Therefore, it is essential to evaluate the performance loss factors of BIPV and to examine the characteristics of each performance loss factor. Measured data were used to analyze the performance and loss factors (module temperature, dust and soiling, power conditioning system (PCS) standby mode, direct current–alternating current (DC-AC) conversion loss). A performance ratio of International Electrotechnical Commission (IEC) 61724 was used to power the generation performance analysis. The impact analysis of each loss factor is analyzed by using difference of the power generation, the module efficiency, irradiation, and the performance ratio according to the existence of a loss factor. The performance ratio analysis result of this BIPV system shows a range of 66.8–69.5%. The range of performance loss due to each loss factor was as follows; module temperature: 2.2–6.0%, dust and soiling: 2.2–23.1%, PCS standby loss: 4.9–15.7%, DC–AC conversion loss: 4.1–8.0%. Because the effects of the loss factors are different depending on the installation conditions, the performance loss of the system should be minimized by taking this into consideration in the design stage in the BIPV.
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Diurnal Thermal Behavior of Photovoltaic Panel with Phase Change Materials under Different Weather Conditions
Article
Full-text available
  • Dec 2017
The electric power generation efficiency of photovoltaic (PV) panels depends on the solar irradiation flux and the operating temperature of the solar cell. To increase the power generation efficiency of a PV system, this study evaluated the feasibility of phase change materials (PCMs) to reduce the temperature rise of solar cells operating under the climate in Seoul, Korea. For this purpose, two PCMs with different phase change characteristics were prepared and the phase change temperatures and thermal conductivities were compared. The diurnal thermal behavior of PV panels with PCMs under the Seoul climate was evaluated using a 2-D transient thermal analysis program. This paper discusses the heat flow characteristics though the PV cell with PCMs and the effects of the PCM types and macro-packed PCM (MPPCM) methods on the operating temperatures under different weather conditions. Selection of the PCM type was more important than the MMPCM methods when PCMs were used to enhance the performance of PV panels and the mean operating temperature of PV cell and total heat flux from the surface could be reduced by increasing the heat transfer rate through the honeycomb grid steel container for PCMs. Considering the mean operating temperature reduction of 4°C by PCM in this study, an efficiency improvement of approximately 2% can be estimated under the weather conditions of Seoul.
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Analysis of the impact of thermal resistance of the roof on the performance of photovoltaic roof tiles
Article
Full-text available
  • Jan 2017
The paper explores the issues related to the impact of thermal resistance of the roof on the electrical parameters of photovoltaic roof tiles. The methodology of determination of the thermal resistance and thermal transmittance factor was presented in accordance with the applicable legal regulations and standards. A test station was presented for the purpose of measurement of the parameters of photovoltaic roof tiles depending on the structure of the roof substrate. Detailed analysis of selected building components as well as their impact on the design thermal resistance factor and thermal transmittance factor was carried out. Results of our own studies, which indicated a relation between the type of the roof structure and the values of the electricity generated by photovoltaic tiles, were presented. Based on the calculations, it was concluded that the generated outputs in the respective constructions differ by maximum 6%. For cells with the highest temperature, the performance of the PV roof tiles on the respective roof constructions fell within the range between 0.4% and 1.2% (depending on the conducted measurement) and amounted to 8.76% (in reference to 9.97% for roof tiles with the lowest temperature).
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Voltage-Dependent Temperature Coefficient of the I–V Curves of Crystalline Silicon Photovoltaic Modules
Article
  • Nov 2017
The temperature dependence of the I–V curves of various kinds of commercial crystalline silicon photovoltaic modules is investigated, based on experiments by using a solar simulator and a thermostatic chamber. The temperature coefficient (TC) of the output voltage of the modules with p-n junction technology is found to closely agree with a formula as a function of their output voltage per cell and temperature, throughout the voltage range of about 0.5–0.7 V per cell, which is important for estimating the P $_{\rm{max}}$ , fill factor, and V $_{\rm{oc}}$ of the modules. The formula is derived from a one-diode model, and reproduces the TC of the I–V curves within ±5% relative error without adjusting the parameter for each module. The formula is successfully applied for translating the modules' I–V curves.
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Determination of a mathematical model of the thin-film photovoltaic panel (CIS) based on measurement data
Article
  • Sep 2017
In this paper the author attempted to determine the most accurate mathematical model of the photovoltaic panel composed of a monolithic structure of series connected Copper Indium Diselenide (CIS) based solar cells, based on its actual measurement data. The purpose of this paper has been achieved by implementing the original applications which, using the methods of approximation, made it possible to design the final mathematical model of the tested panel, characterized by the minimum of error modelling. Using the known literature on the operation of similar facilities, the model parameters were determined directly from the collection of random measurement data; then the obtained models were verified by several different statistical methods. As a result, the best model was selected, based on the smallest dispersion of the theoretical values (simulated) calculated from the model relative to the actual measurements. The model will be used in practice in the future to evaluate the condition (inefficiency, use) of photovoltaic panels, what will be the theme of following articles. © 2017, Polish Academy of Sciences Branch Lublin. All rights reserved.
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A computational fluid dynamic study of PV cell temperatures in novel platform and standard arrangements
Article
  • Mar 2017
  • SOL ENERGY
Solar systems using photovoltaic (PV) modules must operate in climatic regions that range from relatively benign to hostile. The performance, lifetime and failure rate of the modules at the heart of these systems vary considerably with environmental factors and particularly temperature. The degree to which the design of PV system platforms influences module temperatures and consequently stress outcomes is investigated. The aim is to estimate the PV-cell temperature of modules in novel platforms from the physical properties of their materials in a way that may be readily adapted to address unique conditions. The ability to analyse the thermal impact of new solar system features and elements is important to enable thermal analysis during the design phase. A coupled computational fluid dynamic – finite element model with material properties is used to predict the PV-cell nominal temperature. It is shown that a novel PV-platform is 5 °C cooler in no wind conditions due to passive convection.
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Heat flow in installations with photovoltaic tiles
Conference Paper
  • Sep 2016
The paper presents methods for determining similarity numbers do define the density of heat flux in a system. An installation was analysed with photovoltaic tiles located on the roof of a building. The values of similarity numbers and heat flux were determined, and the type of the system was defined for the case analysed.
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Operating temperatures of open-rack installed photovoltaic inverters
Article
  • Nov 2016
  • SOL ENERGY
This paper presents a model for evaluating the heat-sink and component temperatures of open-rack installed photovoltaic inverters. These temperatures can be used for predicting inverter reliability. Inverter heat-sink temperatures were measured for inverters connected to three grid-connected PV (photovoltaic) test systems in Golden, Colorado, US. A model is proposed for calculating the inverter heat-sink temperature based on the ambient temperature, the ratio of the consumed power to the rated power of the inverter, and the measured wind speed. To verify and study this model, more than one year of inverter DC/AC power, irradiance, wind speed, and heat sink temperature rise data were collected and analyzed. The model is shown to be accurate in predicting average inverter temperatures, but will require further refinement for prediction of transient temperatures.
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