All the remaining variables in the analysis are input variables. The use of
these variables will make it possible to predit the module temperature. The
analyseswillhelptoidentifytheinuenefromdierentvariablesonthemodule
temperature.
7.4.1 The ambient temperature
Itisobviousthattheambienttemperaturehasaninueneontheperformane
of thePV module,sinethewhole frontareaofthe module isin ontatwith
the ambient temperature. In Figure 7.4 the temperature measurements are
shown. Likethepastvariablesthereisalear24hoursperiodiity. Theambient
temperaturehasalowvariation omparedto themeasuredwind speedshown
in Figure7.7. Aroundnoonthelargestutuationsare found.
Theambientairtemperatureismeasuredbyusingaventilateddoubleshielded
PT100sensorItisonstrutedin suhawaythatthetemperatureismeasured
inside the equipment. This implies that the temperature is not aeted by
0 500 1000 1500 2000 2500 3000 3500 4000 4500 16
18 20 22 24 26 28 30 32 34
Time [min]
Temperature [ ° C]
Inlet temperature Outlet temperatur
Figure7.5: Plotoftheinletandoutlettemperature
7.4.1.1 The temperature of theair ow behind the module
BetweenthePVmoduleandtheopaquewoodenboardisamehaniallydriven
airow. Thisentailsthat theowanbeontrolledand measuredaurately,
sine it is possible to get a onstant ow in ontrast to naturally ventilated
systems. Theairowanbesetatfourdierentonstantveloitylevels. Figure
7.5showsthetwotemperatures,thein-andoutlet temperatures,onwhihthe
alulationof
∆T
isbased. Inthedata set both aalulatedandameasured∆T
isavailable.Thetwovariablesareplotted inFigure7.6.TomeasuretheairowaSwemair300instrumentisapplied.
TheairowbehindthePVmoduleoolsdownthemodule. Thethermalsystem
andtherebytheeletrialsystemofthePV modulebeomesmoreeientthe
highertheforedairowbeomes[Gandiniet al.n.d.℄.
7.4.1.2 The measurementof the wind speed
InFigure7.7aplotofthemeasuredwindspeedanbeseen. Thegurereveals
that the wind onditions at the siteutuate. A movingaverage wind speed
withmeasurementintervalsof20minutesispresent. Thereasonwhythis
trans-formationofthewindspeedistakenintoonsiderationisthatthePVmodule,
in theory, mightbemoreinuenedbythe moreonstant wind onditions. A
0 500 1000 1500 2000 2500 3000 3500 4000 4500
−1 0 1 2 3 4 5
Time [min]
Temperature [ ° C]
∆T measured
∆T calculated
Figure7.6: Plotofthetemperaturesoftheventilatedairgapbehindthemodule
An anemometer has been used to measure the wind speed. The anemometer
wasplaed on the roof of the pent just above the module. When measuring
wind it is important to plae the equipment lose to the site, sine the wind
onditionsutuateovershortdistanes.
OnemajorproblematinatureofthetestsiteisthatthewindinIspraisrather
limited. Thewindspeedisseldomabove2m/s. Thisanbealimitationofthe
sopeofthemodels.
7.4.1.3 The irradiane on the PVmodule
Themostimportantvariablewhen dealingwith PVmodulesistheirradiane.
The irradiationis representedin the data setin twoversions. A pyranometer
is applied to ollet theirradiane data. The pyranometer isplaed about20
entimetresfromthemodule. Thereisariskthatasystematierrorisattahed
tothismeasurement. Thepyranometerisplaedonawoodenpillaratahinge.
If the srewsare not fastenedproperly, a twist of theequipmentmay leadto
an inorretlymeasuredirradiane ompared to theirradiane of themodule.
Amorepreisewayto desribetheirradianeisbyalulation,sinetheshort
iruiturrent,
I sc
,ofthemoduleoverawiderangeisproportionaltothesolar radiation. In the models both measures are applied in order to nd the bestdesribingvariable. InFigure 7.8thetwovariablesareplotted.
0 500 1000 1500 2000 2500 3000 3500 4000 4500 0
0.5 1 1.5 2 2.5 3 3.5
Time [min]
Wind [m/s]
Measured wind speed Moving average wind speed Lowpass filtered wind speed
Figure7.7: Plotofthemeasuredwindspeed,aalulatedmovingaverage
ver-sionofthewindandalowpassltrationofwindspeed
0 500 1000 1500 2000 2500 3000 3500 4000 4500
−100 0 100 200 300 400 500 600 700
Time [min]
Irradiance [W/m 2 ]
Measured irradiance Calculated irradiance
Figure7.8: Themeasuredandalulatedirradianeofthemodule
Single State Models
-Model identiation
8.1 Thermal models
Thepurposeofthishapteristoidentifythebestmodelto preditthemodule
temperature. All themodelsareonstrutedinaordanewiththethreeheat
transfer priniples deribed in Setion 2.4. Introdutorilyadesription of the
modelsisoutlined. All themodelsin thishapter areestimatedbothfora
24-hourperiod,the16thofAugust2002, andforthethree-dayperiod,16-18thof
August 2002. Thisoers abasisforomparing theinuene ofthenumberof
observationsontheresiduals,theunertaintiesofthemodelandtheparameter
estimates. Inthesearh forasatisfatorymodelseveraldierentmodels,both
linearandnon-linear,havebeenestimatedandtested. Subsequentlytheresults
ofthemodelswillbeanalysedandomparedinordertodeterminewhihmodel
ormodels will suit the data thebest. The best model will also be applied in
someofthefollowinghapters.
The models applied in this hapter is developed in onnetion to the artile