Future Work
Whenworkingonathesislikethis,there willalwaysbeareasandideaswhih
annot befurther investigated dueto lakoftime. Inthesetionsbelowsome
ofmythoughtsareoutlined.
The multiple state models are evaluated to be less workable than the single
statemodels,due tohigh residualvaluesand,in general,theinstabilityof the
models. Inafutureanalysis itouldbeinterestingtoinvestigatehowtoattain
afuntional and reliablemultiple statemodels. The residualsofthe extended
non-linearsinglestatemodelrevealthattheworsepreditionsarefoundduring
thedayhours,whihis themostimportantperiod toget agoodpreditionof
sinethemosteletriityinproduedinthisperiod. Thisindiationsthatthere
isstill roomforimprovementsof themodel.
The primary fous of the thesis has been to identify models whih are able
to desribetheolleteddatain asatisfatoryway. Theanalysisof thevalues
and the size ofthe parametershavebeengiven lowerpriority. In somefuture
workit ouldbeof greatinterestto investigateand understand theestimated
parameters. This shallbeseenin thelightofthemodeltype,namelygrey-box
modelling,wheretheestimatedparametersshould atuallyestimatetrue
phys-ial parameters.
measuredvariables. Ifforinstanemoremeasurementsofthemodule
tempera-turewereavailable,itwouldbepossibletoonstrutamultiplemodelonsisting
ofthreestates.
With regard to the thermal images it would also be of advantage if thermal
images from the spei days of theapplied datawere taken. Also the
state-mentsaboutthepossiblyinueneofhumidityandtheangleofthewindspeed
ouldbeinterstingtotest inthemodels.
Inrelationtotheset-upwithnsintheairgapafurtheranalysiswherethe
re-sultsareomparedtotheomplexempirialequationsontainingtheReynolds
numberortheNusseltoeientouldbearriedout. Thesenumbersare an
the help desriptionthe when dealingwith turbulentwind and dierenies in
temperature,whihistheasewiththese data.
It ouldalsobeexitingtoarry outaost-benetanalysis,whihdetermines
inenergyandeonomistermswhetherthereisabenitofapplyingthefored
veloityoftheairgap.
Conlusion
The analyses of this thesis have proven that it is possible to model the
tem-peratureofthemodule. Itisfoundthatthephotovoltaimoduleisomplexin
many ways. The improvementsandndings ofthis thesiswill bedisussed in
thesetionbelow. Due tothesubdisussionsandonlusionsattheendof the
hapters,thishapter willappearasaombineddisussionandonlusion.
Thestohastistatespaemodelshaveproventobeexellentwithaviewto
han-dling theutuationsofthemeasureddata. Comparedto theRC-modelsrst
desribed,thestohastistatemodelsappliedareabletomodelnon-linearities.
Inthe modelling proessit is proventhat thenon-linearinuene ofthe wind
andtheinfraredradiationaresigniant.
Theanalysesofthemodelshaverevealedthat theextendedsinglestatemodel
had the overall best performane. The likelihood ratio test stressed the
nd-ing. Also theanalyses of the residualsstrengthened that theextended model
has the most qualied way of desribing the data. Sine the analysis of the
residuals shown signs of possible improvements, it has been attempted to
ex-tendthemodelfrombeingsinglestatetoonsistofmultiplestates. Due tothe
knowledgeastothehangingheatdistribution,thedynamialparameter
f
wasimplementedin themodeltodeterminethedegreeofinueneofthemeasured
topandbottomtemperaturesrespetively. Theresultsofthesemodelsarevery
to estimate the model. Espeially the ausal and logisti funtion give rises
to problems, whih werehard to solve despitemany attempts. It analso be
disussed whether
f
is dened appropriate. Even though the residual values got worse ompared to the singlestate models it is presumed that there is apotentialin movingfromsingleto multiple statemodels. Thisisstatedin the
lightoftheindiationsofthepartialorrelationsplotfortheneessityofextra
states in the model. Also the fat that the worse preditions of the module
temperaturesourduringthedayhours,wherethemostamountofeletriity
isprodued. Thismakesitessentialtoimprovethemodelperformane. Ithas
tobementionedthatthemodelswherensturntheforedairowintoa
turbu-lentairow,donothavethesamediultiesofpreditingduringthedayhours.
Itanbedeterminedthattheperformaneoftheestimatedsinglestatemodels
isimprovedomparedtothesimilarmodelsin theartile[Jiménezetal.2006℄,
whihgaveraisetothisthesis. Theprimaryreasonisthehangeofoutput
vari-ablefromtheaveragetemperaturetothetoptemperature. Furthermoreitdoes
alsoinuenethatthealulatedirradianeisappliedinsteadofthemeasured.
Inthe aseofthe singlestatemodels both thedata onsistingof one-dayand
three-daymeasurementwereestimated. Whentheperformanewasompared
thethree-daymodelshadonlyalittlelead. Inrelationtotheresidualanalysis
it was disovered that for some of the tests, e.g. the portmanteau lak-of-t
andtheondeneintervalsingeneral,itwasadiultfatorthatthemodels
werebasedonthatmanyobservations. Theanalysesoftheparameterestimates
reveal thattheindividual setof datahasgreat inueneonthesize ofthe
pa-rameters.
There are several irumstanes in relation to the module temperature that
makesitdiulttoobtainasatisfatorydesription. Thethermalimageswere
abreakthroughto realizethatthe heatdistribution of themodule isomplex.
The variation overtime is signiant. Initially the desriptionof the module
temperature wasanaverage betweenthemeasures at thetopand thebottom
of the module. Comparingthe average temperature with the thermal images
it wasdisoveredthat thetongues in the heat distribution rendertheaverage
impossible. Inaordanewiththethermalimagesthetemperatureat thetop
resultedin thebestpreditions. Italsomakesgreatsensetoapplythe
temper-ature atthe topof themodule,sine thehighesttemperatures arefound here
and therebythe worse performane of themodule is desribed. The
tempera-tureofthemodule,that hasto bepredited,isthemostimportantvariableto
beorret,butalsothedesribingvariablesanhelpimprovethedesriptionof
thetemperatureofthemodule. Theanalysisrevealedthatthemodelsbasedon
thealulated
∆T
andontheirradianeobtainedthebestresults. Beforethisanalysis it wasbelieved that altered versionof the ambientwind speedwas
that the utuationsof theambientwind dohaveinuene. The ausallter
whihestimatestheoptimalltrationofthewind revealedthatonlyverylittle
ofthemeasuredwindhastoberemovedinordertoobtaintheoptimal
desrip-tionof themodule temperature. It anbedisussedifit isneessarytoapply
thelterifonlyverylittleimprovementisdisovered. Onestrongargumentfor
keepingtheausal lterinthemodel,denoted asthebest, is thatthewind at
the test sitein Ispra is limited. It an therefore be expeted that the ausal
lterwillbeofhigherappliabilityatsites wherethewindspeedishigherand
maybemoreutuating.
The statements above underlinethe advantages of the abilities of testing the
performaneand thetting ofthese grey-boxmodels. Introdutorilythe
non-linearinueneofthewindwasaddedinboththetermoftheonvetionfrom
theambientairtothemoduleandtheirradianeterm. CTSMlearlyshowthat
thewinddoesnotinuenetheirradianeintothemodule. Intheinvestigation
it beame evident that the irradiane wasmeasured inside the module whih
means that the ambient windspeedshould not inuene theirradiane. This
entailsaredutionofthemodel,whihouldalsobedeterminedonthebasisof
physial knowledge. Thisisoneofthestrengthofgrey-bpxmodelling.
The last and heering nding in this thesis is that the model is able to
dis-riminate dierentveloity levelsand set-up, with orwithoutns in the gap,
from eah other. Theanalyseshaverevealedthat theforedveloityin theair
gap has asigniantly inreasinginuene on theheat transferoeient
be-tweentheambientairandthemodule. Furthermore,thedierenebetweenthe
ambientairtemperatureandthemoduletemperaturewashigherfortheset-up
with ns, where the former laminar air ow is turned into a more turbulent
ow. This underpins the theory of the inuene of ns in air gaps known in
advane. Fortheset-upwithnsintheairgapthepreditionproblemsduring
thedayarenearlyremoved. Thisanbeseenfromtheplotoftheresidualsand
standarddeviationsoftheresidualswhiharethemostsmoothand thelowest
in theentireanalysis.
Aboveseveral improvementsfor inreasingthe levelof desriptionof the
pho-tovoltai module are stated. The analyses have proved to be adequate as to
to modelling themeasure data, thoughthere is stillroomfor further
improve-ments. Asan overall onlusionof themodels itan bepointedoutthat, the
modelsbasedondatawherensareplaedintheairgapgavethebest results.
Thestandarddeviationsarethelowestidentied,andtheresidualsarerandom.
Furthermore,thedesiredinreaseintheperformaneofthemoduleisobtained
due to the inreased heat transferand thederease of the temperature of the
module.
Appendix to the Chapter
Analysis of the Fored
Ventilation in the Air Gap
A.1 The dates of the data olletion
Table A.1: The dates of the data olletion. -denotes that 24 hours data is not
available
Veloityofthefan Nons Fins
6 14thofAugust 12ofAugust
7 -
-10 17thofAugust 7thofAugust
13 28thofAugust 30thofJuly