Content uploaded by Jan Kleissl
Author content
All content in this area was uploaded by Jan Kleissl on Jul 10, 2018
Content may be subject to copyright.
1
EffectsofSolarPhotovoltaicPanelsonRoofHeatTransfer
AnthonyDomingueza,JanKleissla,andJeffreyC.Luvallb
aUniversityofCalifornia,SanDiego,DepartmentofMechanicalandAerospaceEngineering
bNASA,MarshallSpaceFlightCenter,AL35812,USA
Correspondingauthor
JanKleissl,jkleissl@ucsd.edu
Office:(858)534‐8087;Fax:(858)534‐7599;
Address:9500GilmanDr,EBUII–580,UniversityofCalifornia,SanDiego,LaJolla,CA,92093‐
0411
Abstract
Indirectbenefitsofrooftopphotovoltaic(PV)systemsforbuildinginsulationarequantified
throughmeasurementsandmodeling.Measurementsofthethermalconditionsthroughouta
roofprofileonabuildingpartiallycoveredbysolarphotovoltaic(PV)panelswereconductedin
SanDiego,California.ThermalinfraredimageryonaclearAprildaydemonstratedthatdaytime
ceilingtemperaturesunderthePVarrayswereupto2.5Kcoolerthanundertheexposedroof.
HeatfluxmodelingshowedasignificantreductionindaytimeroofheatfluxunderthePVarray.
AtnighttheconditionsreversedandtheceilingunderthePVarrayswaswarmerthanforthe
exposedroofindicatinginsulatingpropertiesofPV.Simulationsshowednobenefit(butalsono
disadvantage)ofthePVcoveredrooffortheannualheatingload,buta5.9kWhm‐2(or38%)
reductioninannualcoolingload.Thereduceddailyvariabilityinrooftopsurfacetemperature
underthePVarrayreducesthermalstressesontheroofandleadstoenergysavingsand/or
humancomfortbenefitsespeciallyforrooftopPVonolderwarehousebuildings.
Keywords:Buildingenergyuse;coolingload;photovoltaic;roofheatflux;thermalinfrared
camera
2
1. Introduction
BuildingHeating,VentilationandAirConditioning(HVAC)isamajorcontributortourban
energyuse.Especiallyinpoorlyinsulated,singlestorybuildingswithlargesurfaceareasuchas
warehouses,mostoftheheatentersthroughtheroof.Increasingroofalbedo(orsolar
reflectance)reducescoolingloadinsunnyandhotclimates.Installingreflectiveroof
membranesresultedinseasonalair‐conditioningenergysavingsof57%onaCaliforniahome
(Akbarietal.,1997a),49%onabungalow,2%to43%inFlorida(ParkerandParkaszi,1997),
and30Whm‐2d‐1onaregenerationbuilding(AkbariandRainer,2000).However,theenergy
savingsdependontheroofinsulatingproperties.Increasingtheroofalbedofrom0.09to0.75
onabuildingwithoutinsulationresultedinenergysavingsof28%,whileincreasingthealbedo
from0.30to0.75onabuildingwithR‐30insulation(anadditionof5.28Km2W‐1inthermal
resistance)resultedinsavingsofonly5%(SimpsonandMcPherson,1997).
Shadetreesplantednearresidentialbuildingsresultedinaseasonalcoolingenergysavingsof
30%andpeakdemandsavingsof27%and42%intwoSacramento,CAresidences(Akbarietal.,
1997b).
Arooftop‘modification’whoseimpactoncoolingloadshasnotbeenexaminedexperimentally
issolarphotovoltaic(PV)arrays.InCaliforniaalone,overaGW(109Watts,correspondingto
about1km2ofrooftopspace)inresidentialandcommercialrooftopPVareapprovedorinthe
planningstages.AnindicationoftheinfluenceofPVoncoolingcomesfromanevaluationof
residentialbuildingenergyuseat260sitesinsouthernCaliforniapreandpostinstallationofa
PVsystem,whichindicatedthatACenergyuseinhighcoolingdegreedayconditionsdecreased
comparedtoareferencesample(ITRONInc.,2010).A1degreeincreaseindailyaverage
3
temperatureinSanDiegoGas&Electric(SDG&E)territorycausedpost‐PVhouseholdswithair
conditioningtouse0.501kWhlessenergyperdaythanhouseholdswithairconditioningthat
didnothavePVinstalled.
ModelingtheeffectsofbuildingintegratedPV(BIPV)onthemicroclimateoftheurbancanopy
layershowedasignificantreductioninBIPVroofsurfacetemperaturescomparedtoa
conventionalroofwithalbedo0.30andathermalresistanceof1.33Km2W‐1(Tianetal.,2007).
Aonedimensionaltransientheattransfermodelshowedapeakcoolingloadsavingsof52%
withventilatedBIPVcomparedtotraditionalroofingwithasolarabsorbanceof0.9anda
thermalresistanceof1.33Km2W‐1(Wangetal.,2006).Aconductionmodelshoweda65%
reductionincoolingloadcomponentthroughaPVroofcomparedtoaconventionalroofwitha
thermalresistanceof2.8Km2W‐1(Yangetal.,2001).
Inthisstudy,weinvestigateabuildingpartiallycoveredbyaflushandhorizontalsolarPVarray
andanoffsetandtiltedsolarPVarray(Section2).Meteorologicalandrooftemperature
measurements(includingthermalimagery)wereconducted(Section3).Section4describesa
roofconductionmodeltoestimateaverageandpeakcoolingenergydifferencesfortheroof
sectionswithandwithoutPV.InSection5wepresentafullroofenergybalancemodelto
calculateannualroofheatingandcoolingloadswithandwithoutPV.Conclusionsarepresented
insection6.
2. Experimentalsetup
2.1. Buildingandlocation
4
ThebuildingusedinthisstudyisthePowellStructuralLaboratory(PoSL)attheUniversityof
California,SanDiego(Fig.1;Tables1,2).ItisahollowconcretecubewithoutHVACsystem.
Therearenowindowsexceptforasmallpartiallyshadedrowofwindowsontheeastandwest
sidesneartheroof.Onworkdaysthebuildingiscooledbynaturalventilationthroughagateon
thesouthfaceofthebuilding(manycoastalbuildingsinSanDiegolackHVACsystemsasthe
seabreezeskeeptheindoorenvironmentcomfortableformostoftheyear).Duetosafetyand
productivityconsiderations,theexperimenthadtobeconductedonaweekendday,whenall
doorswereclosedandthebuildingwas‘ventilated’onlythroughinfiltration.PoSLhas2solar
PVarraysontherooftop;oneistiltedsouthat4.4degreesandelevated0.10moffoftheroof
surfaceandtheotherishorizontalandflushwiththeroofsurface(Fig.2).Theroofis0.20m
thickandcomposedofmeshreinforcedinsulatingconcreteand24GAcorrugatedsteelontop
oftrusses.ThisresultsinasignificantlylowerR‐Valuethannewconstruction,butistypicalof
olderwarehousebuildingswithlarge,flatrooftopsforwhichPVisanattractiveoption.Table1
showsthesiteandbuildingcharacteristics.
Table1:PowellStructuralLaboratory(PoSL)buildingcharacteristics.Thebuildingislocatedat
32o52’50”N,117o14’06”WintheWorldGeodeticSystem1984coordinatesystem(WGS84)and
is1.7kmfromthePacificOceancoastline.
Length(north‐south)Width(east‐west) HeightRooftopareaMeasuredRoofAlbedo
36.6m19.2m18.0m703m20.218
Table2:PoSLflushPVarraycharacteristics(seealsoFig.1c).ThetiltedPVarrayisidenticalto
theflusharraywiththeexceptionofthe4.4degreesouthtilt(measuredaverageof14panels
onthee
d
panel).
Lengt
6.01
m
Fig.1.a.
TIRcam
e
Google
E
d
geofthea
r
h
Widt
m
7.80
m
Photograph
e
racircled,f
i
E
arthimage
o
r
ray)andal
h
#ofpa
m
8X4=
ofPoSLfac
i
i
eldofview
o
fPoSL(No
r
engthof6.
9
nelsPan
32K
y
i
ngSouth;b
shownbyb
l
r
thisup)wi
t
9
9m.Theto
t
elType
y
ocera
.Photograp
l
uelines,an
t
htiltedarr
a
t
alratedD
C
Solar
Reflectanc
e
0.178
hofPoSLfr
o
dPVlocati
o
a
yontheN
o
C
outputis1
3
e
Sol
a
o
minsidefa
o
noutlinedi
n
o
rthsideof
t
3
kW(200
W
a
rConversi
o
Efficiency
0.08
cingNorth
w
n
green;c.
t
heroofan
d
5
W
per
o
n
w
ith
d
flusharr
a
larger(T
a
Fig.2.S
o
disconti
n
variable
d
allowing
ceilingt
e
image(F
2.2. Equ
i
2.2.1. I
n
Datawe
r
Insideth
pointed
a
viewwa
s
partially
a
yinthece
n
a
ble2).
o
uth(left)to
n
uitiesatth
e
d
efinitions
s
airflowbet
w
e
mperature
s
ig.3).
i
pment
n
teriormea
s
r
etakenfro
m
ebuilding,
a
a
ttheceilin
g
s
notsuffici
e
theceiling
u
n
ter.Thelar
g
North(righ
t
e
verticalda
s
s
eeTable3).
w
eenpanel
a
s
T
c
,T
cs
and
s
urements
m
1500PST
a
FLIRA320
t
g
torecord
t
e
nttocaptu
r
u
nderthefl
u
g
erNorth‐S
o
t
)verticalcr
s
hedlines)
w
ThePVpa
n
a
ndroof,w
h
T
cflat
arere
p
Friday,Apri
l
t
hermalinfr
a
t
helongwav
r
etheentir
e
u
sharrayan
d
o
uthpanel
s
oss‐section
w
ithschem
a
n
elsare1.4
m
h
iletheflat
p
p
resentative
l
17,2009t
o
a
red(TIR)c
a
eirradiance
e
ceiling,th
e
d
theexpos
e
s
pacingmak
ofthePoSL
a
ticofallex
t
m
long.The
t
panelsaref
l
ofdifferen
t
o
0600PST
M
a
merawith
a
(Fig.1b).Si
e
TIRcamer
a
e
dpartoft
h
esthetilte
d
roof(tosca
t
eriormeas
u
tiltedPVpa
n
l
ushtothe
r
t
areaswithi
M
onday,Ap
r
a
45
o
wide
a
nceeventh
e
a
waspositi
o
h
eroof,and
d
arrayappe
a
leexceptfo
r
u
rements(f
o
n
elsarerais
r
oofsurface
.
ntheTIRca
r
il20,2009.
a
nglelensw
a
e
wideangl
e
o
nedtoima
g
thefullare
a
6
a
r
r
o
r
ed
.
The
mera
a
s
e
g
e
a
underth
through
o
Stefan’s
tempera
t
conducti
Fig.3.a.
denotes
trussest
h
isvisible
represe
n
tempera
t
theceili
n
etiltedarra
y
o
utthestud
y
lawassumi
n
t
urestotha
t
ngepoxy.
ThermalIR
c
temperatur
e
h
atarebel
o
asacoolar
e
n
tativeofth
e
t
ure.b.Pho
t
n
gprovidel
a
y
(Fig.3).TI
R
y
period.Th
n
ganemissi
v
t
ofaconta
c
c
ameraima
g
e
inK.Horiz
wtheceilin
g
e
ainthece
n
e
ceilingun
d
t
ographoft
a
ndmarksto
R
imagesco
n
esurfacete
v
ityof0.95.
c
tthermoco
g
eofceiling
ontalandv
e
g
atadiffer
e
n
ter.Pixels
w
d
erneathea
c
heceilingfr
visuallyge
o
n
taining32
0
mperature
o
Thisassum
p
uplesensor
at1710PS
T
e
rticallines
t
e
nttemper
a
w
ithinblack
c
hrooftype
omsamea
n
o
referencet
h
0
x240pixels
o
feachpixe
p
tionwasv
e
affixedtot
h
T
onApril1
9
t
hroughthe
a
ture.Thef
o
rectangles
w
andwereu
n
gle.Theco
o
heimages.
weretaken
lwascomp
u
e
rifiedbyco
m
h
eceilingw
i
9
,2009.The
imageresu
l
o
otprintoft
h
w
erechose
n
sedtoobta
i
o
ler(turned
every5mi
n
u
tedusing
m
paringTIR
i
thheat
colorbar
l
tfromsteel
h
etiltedPV
n
as
i
nitsaverag
off)lamps
o
7
n
utes
R
array
e
o
n
8
2.2.2. Exteriormeasurements
SurfacetemperaturewasmeasuredbyaffixingHOBOProV2externaltemperaturesensors
usingheatconductingepoxytoboththeundersideofthetiltedsolarpanelsandthesurfaceof
theroofunderthesolarpanel(Fig.2).Anairtemperatureprobewasmounted0.1mabovethe
roofsurfaceunderthetiltedarray.Thespaceundertheflusharraywasinaccessiblesono
measurementscouldbetakenthere.Thesamplingfrequencywas1‐minand5‐minaverages
werestored.
ApermanentmeteorologicalstationontherooftopofPoSLmonitoredexposedroofsurface
temperature,airtemperature,totalanddiffusesolarirradiance,andwindspeed(Table3).Data
weresampledeverysecondandstoredas5‐minaverages.TherooftopalbedoandsolarPV
albedoweremeasuredusingaKipp&ZonenCMP3albedometer.Afterthestudy,theTIR
camera,HOBOs,andTN9TIRsensorswerecross‐calibratedontheexposedroofandalinear
regressionwasappliedtoforceagreementbetweenthesensors.AppendixAshowsananalysis
ofthesensitivityofourresultstotemperatureoffsetsinthesensors.
Table3:Sensortype,make,model,andheightaboverooflevel(ARL)formeasurementsonthe
PoSLroof(Fig.2).TheTN9accuracyisgivenforthe15‐35oCtemperaturerange.Fullrange
accuracyis2oC.
MeasurementVariable SensorHeightAccuracy
RoofsurfacetemperatureTrZyTempTN9TIR 1.41m0.6oC
AirtemperatureTaSensirionSHT75T/RH1.93m0.4oC
GlobalhorizontalincidentsolarGHILiCorSZ200pyranometer 2.26m3%
9
irradiance
DiffusehorizontalsolarirradianceDIFFDynamaxSPN1
pyranometer
2.27m5%
WindspeeduDaviswindsensor2.00m5%
TemperaturesundertiltedPVarray:
RoofsurfacetemperatureTrsHoboProV20.0m0.2oC
AirtemperatureundertiltedarrayTasHoboProV20.1m0.2oC
PVbackpaneltemperatureTpHoboProV20.17m0.2oC
3. Measurementresults
3.1. Solarradiation,windspeed,andoutsideairtemperature
OnlydataforSunday,April19,2009areanalyzed,becauseitwastheclearestdaywithafew
cloudsfrom0730to1000PST(Fig.4a).Thedailyglobalhorizontalsolarirradiationwas7.72
kWhm‐2,whichwaslargerthanatypicalAprilday.Figure4bshowsthewindspeed,which
followstypicalseabreezepatterns(cf.annualaverageuinFig.4b)withcalmwindsuntil0800
PST,increasesto5ms‐1at1400PSTanddecreasestolessthan1ms‐1by2030PST.Theair
temperaturecycle(Fig.5a)hasasmalldiurnalamplitude.Overallthemeteorologicalconditions
onApril19wererepresentativeforcoastalsouthernCaliforniawheremuchofthegrowthinPV
isexpectedtooccur.
10
Fig.4.a.Diffuseandglobalhorizontalincidentsolarirradianceandb.windspeedonApril19,
2009(seeTable3fordetailsonsensorsandmeasurementlocations).
3.2. Roofandceilingtemperatures
Figure5ashowsthetemperaturesofoutsideair,roof,andceilingfortheexposedroof.The
roofsurfacetemperaturepeaksatnoonandishigherthantheairandceilingsurface
temperaturesduringdaylighthours,asitisheateddirectlybysolarradiation.Theceiling
surfacetemperaturepeaksat1737PSTduetoatimelaginthetransportofheatfromthe
exteriorroofsurfacetotheinteriorceilingsurface.
Figure5bshowsthetemperaturesunderthetiltedPVarray.Thebackpaneltemperatureofthe
solarpanelissimilartotherooftemperaturefortheexposedroof.However,sincetheroof
surfaceunderneaththePVpanelisshadeditstemperatureissignificantlylowerthanforthe
exposedroof.Theairtemperatureinthegapbetweenthepanelandtheroofislowerthanthe
backpaneltemperatureandrooftemperatureunderthepanels,buthigherthantheair
temperatureat1.93mabovetheroof.Toconcludetheroofunderthesolarpanelsisheatedby
0
200
400
600
800
1000
Solar Radiation [Wm
-2]
a)
GHI
DIFF
April average GHI
00:00 04:00 08:00 12:00 16:00 20:00 00:00
0
1
2
3
4
5
6
Time [P ST]
wind speed [ms-1]
b)
u
April average u
Annual average u
11
longwaveradiationfromthepanelundersideanddiffuseradiationfromthesky(whichissmall
giventhesmalltiltangle),thesumofwhichislessthanthesolarirradiancetotheexposedroof.
Convectionofairthroughtheairspacebelowthepanelresultsinheatremoval.Atnight,the
roofsurfaceunderthesolarpanelsremainswarmer,duetothereductioninradiativecooling
tothesky.
Fig.5.a.Ceilingsurface(Tc),roofsurface(Tr)andoutsideairtemperature(Ta)measurements
fortheexposedroof.b.Ceilingsurface(Tcs),roofsurface(Trs),outsideair(Tas),andbackpanel
temperature(Tp),measurementsunderthetiltedPVarray.c.Interiorceilingsurface
10
20
30
40
50
60
Temperature [oC]
a)
Tc
Tr
Ta
10
20
30
40
50
60
Temperature [oC]
b)
Tcs
Trs
Tas
Tp
00:00 04:00 08:00 12:00 16:00 20:00
24
26
28
30
32
34
36
Time [PST]
Temperature [oC]
c)
Exposed Roof
Tilted PV array
Flat PV array
12
temperaturesunderexposedroof,tiltedPVarray,andflatPVarrayaveragedoverareas
identifiedinFig.3.
Theinteriorceilingsurfacetemperatures(belowtheexposedroof,tiltedPVarray,andflushPV
array)areredrawnforclarityinFigure5c.From0900to2100PSTtheceilingundertheexposed
roofiswarmerthantheceilingunderneaththeflushpanels,whichinturniswarmerthanthe
ceilingunderneaththetiltedpanels.Themaximumtemperaturedifferencebetweenexposed
roofandtiltedPVis2.5oCat1700PST.ThetemperatureoftheceilingunderneaththeflushPV
arrayisbetweentheothercasesduringthedaytime,asitprovidesshadingtotheroof,butthe
enclosedairspacebetweenthepanelsandtherooflimitshorizontaladvectionofheat.The
ceilingcoveredbytheflushPVarrayhasthehighesttemperatureatnightduetotheinsulating
propertiesoftheenclosedairbetweenroofandsolararrayandtheincreaseinincident
longwaveradiationfromthepanelcomparedtothesky.
4. Simulationofroofheatflux
Theresultsinsection3haveshownmarkeddifferencesinthethermalresponseofaroof
underneathasolarpanelcomparedtothatofanexposedroof.However,todeterminethe
potentialHVACenergysavingsassociatedwithsolarPVpanelstheroofheatfluxintotheair
conditionedspace(orroofcoolingload)isthemostrelevantvariable.Quantifyingthisheatflux
independentlyforeachsurfaceisdifficult,sinceconvectiveandradiative(andtoalesserextent
conductive)exchangeofheatbetweenceilingareasthroughtheroomairandwallandfloor
surfacesbluntsthetruedifferencesbetweentheceilingtemperaturesundereachrooftype.
13
TheconductionheatfluxthroughtheroofcanbemodeledusingaCrank‐Nicholsonmethod
(UnderwoodandYik,2004)appliedtotheone‐dimensionaltransientheatconductionequation
(1)
usingadiscretizationof32layers.Theboundaryconditionsarethemeasuredrooftopsurface
andinteriorceilingsurfacetemperatures.Theeffectsoftheupperroofmembraneandlower
corrugatedsteel(Fig.2)werenegligible,astheyarethinandhavehighthermalconductivityin
comparisontotheinsulatingconcrete,sothemodelwassimplifiedbydefiningtheentireroof
asmeshreinforcedinsulatingconcrete.Thethermalpropertiesusedinthemodelwerethermal
conductivityk=0.38Wm‐1K‐1,densityρ=1200kgm‐3,andheatcapacitycp=1000Jkg‐1K‐1
(ThermalPropertiesofConcrete,2010),resultinginathermaldiffusivityof3.2x10‐7m2s‐1and
thermalresistanceof0.526Km2W‐1(abouttheequivalentofR‐3insulation).Themodelwas
validatedagainstananalyticalsolutionforablockwithuniforminitialtemperaturebeing
submergedintoaliquidwithconstantuniformtemperature(UnderwoodandYik,2004).Since
thesystemisquasi‐periodiconcleardays,theinitialtemperatureprofileintheroofwas
estimatedbytakingthetemperatureprofileattheendofthedayandaddingalinearfitsothat
thesurfacetemperaturesmatchtheinitialmeasuredsurfacetemperatures.
Fromthemodeledrooftemperatureprofileatimelaginheatpenetrationfromrooftopto
ceilingisapparent(Fig.6).Fortheexposedroof,thecoolingandheatingoftheuppersurface
drivestheheatconductionthroughtheroof(Fig.6a).UnderthetiltedPVarrayhowever,while
heatingfromthetopisdominant,heatingfromthebottomalsooccurs(Fig.6b).Thoughthe
interiorairtemperaturewasnotmeasured,theundersideofaconcreteblocksurfacewithin
thebuildingcapturedbytheTIRcamera(bottomrightofFig.3a)wassignificantlylargerthan
14
theoutsideairtemperatureandtypicaltemperatureforairconditionedbuildings.Thefactthat
buildingisnotventilatedorairconditionedleadstoanincreaseinindoorairtemperatureand
reductioninroofheatflux.
Fig.6.Timeseriesofsimulated1‐Dtemperatureprofilethrougha.theexposedroofandb.the
roofunderthetiltedPVarray.ThecolorbarshowstemperatureinoC.c.Conductiveheatflux
frombottomrooflayertoceilingsurfacefortheexposedroofandthetiltedPVarray(negative
meansupwardfluxasperEq.2).
Giventheenergybalanceattheceiling,theheatfluxintotheindoorbuildingair(orroofcooling
load)shouldbeequaltotheconductiveheatfluxintothebottomrooflayer(layer32)
3231 TT
x
k
q
,(2)
Depth [m]
Time [PST]
a)
00:00 06:00 12:00 18:00
0
.05
.10
.15
.20
Time [PST]
b)
00:00 06:00 12:00 18:00
0
.05
.10
.15
.20 15
20
25
30
35
40
00:00 04:00 08:00 12:00 16:00 20:00 00:00
-40
-30
-20
-10
0
10
20
Time [PST]
Heat Flux [Wm
-2
]
c)
exposed roof
tilted PV array
15
whereΔxisthenumericaldiscretizationdistancebetweenrooflayers.Thisanalysiscannotbe
conductedfortheflushPVarrayastheexteriorrooftemperaturewasnotavailabletodrivethe
conductionmodel.AppendixBshowsanattempttoestimatetheflusharrayheatflux.
Figure6cshowstheresultingheatfluxthroughtheexposedroofandtheroofunderthetilted
array.Asexpectedtheheatfluxisnegative(upward)intheearlymorning.Theminimum
between0900‐1000PSTisaresultoftheheatlossattheroofsurfacethroughthenightbut
likelyamplifiedbysolarradiativeheatingoftheinteriorandceilingthroughthewindowsinthe
earlymorningaswellasincreasedconvectiveheatingfromtheinteriorairtemperature.At
1300PST(exposedroof)and1900PST(tiltedPV)theheatfluxbecomespositive(downward)
withalargerpeakfortheexposedroofthanthePVcoveredroofat1930PST.Theheatfluxes
remainpositivethroughthenightconsistentwiththetimelagofheattransferthroughthe
roof.Generally,therelativelysmallthermaldiffusivityoftheroofunderconsiderationcauses
secondaryeffects(ceiling‐buildinginteraction,windowshortwavetransmission)tohavea
significantinfluenceonthemodeledconductiveheatfluxesneartheceiling.
5. Modelingannualroofheatflux
5.1.Roofheatflux
Table4:Variablesusedintheannualroofheatfluxmodelandtheirsources.
TermDescriptionSource
aVelocitycoefficientinhcforexposed
roof/PVcoveredroof
18.65/14.82(Palyvos,2008)
bVelocityexponentinhcforexposedroof/PV
coveredroof
0.605/0.420(Palyvos,2008)
hcExteriorconvectiveheattransfercoefficient DOE‐2model(Eq.9)
h
i
Interiorconvectiveheattransfercoefficient1.25Wm‐2K‐1(ASHRAE2005b)
SVFSkyviewfactorofroofunderPVpanel0.0817(Calculatedfrompanelangle)
16
uWindspeedMeasured2mARL
DIFFDiffuseirradiationMeasured
GHIGlobalHorizontalIrradiationMeasured
R
f
Surfaceroughnessmultiplierinhc2.17forstucco
RHRelativehumidityMeasured2mARL
TaAirtemperatureMeasured2mARL
TiInteriorairtemperaturePrescribedas23.3oC(coolingday)or
21.7oC(heatingday)
T
p
PVpaneltemperatureModeled(JonesandUnderwood,2001)
Tr
n‐1Rooftemperatureatprevioustimestepn‐1
T1TemperatureatfirstrooflayerFromCrankNicolsonmodel
α RoofsurfacealbedoMeasured0.218
εrRoofemissivityAssumed0.95
εpPVemissivityAssumed0.95
Themodeldescribedinsection4wasexpandedtosimulatetheenvelopeheatfluxoverayear
forcedusingcontinuousmeteorologicalobservationsfromthePoSLroof(topofTable3).Table
4showsalistofallvariablesusedintheannualroofheatfluxmodel.Fortheexposedroof,
theseare(inthisorderinEqs.3and4)netshortwave(solar)radiation,incominglongwave
radiation,outgoinglongwaveradiation,convection,conductionintotheroof,andchangein
internalenergy(storage).ForthePVcoveredroof,globalsolarradiationisreplacedbydiffuse,
andincominglongwaveradiationcomesfromboththesolarpanelandtheskyweightedby
theirrelativeskyviewfactors(SVF)(Eq.4).
0 1
,
∆
∆
(3)
0
1
1
∗
,
∆
∆
(4)
Thedownwellinglongwaveradiationfromtheskywascalculatedusing(CIMIS2010)
,
.(5)
17
Thecloudfraction,f,iscalculatedbasedontheratioofmeasuredGHItoclearskyGHIand
variesfrom0.595(verycloudy)to1(clear).Thenetemissivityisbasedonthevaporpressure
(ea,calculatedfromRHandT)as 0.34 0.14.ThePVpaneltemperature(Tp)is
neededtocalculate,andwasmodeledusinganenergybalancemethod(Jonesand
Underwood,2001).
Modelresultsaremostsensitivetotheconvectiveheattransfercoefficient(hc)thatwas
obtainedusingtheDOE‐2convectionmodel(Eqs.6‐8,ASHRAE,2005b)asacombinationofthe
coefficientsfornaturalconvection(hn)andforcedconvectionoverasmoothsurface(hc,glass).
1.520|
|
(upwardheatflow)or(6a)
0.4958|
|
(downwardheatflow)(6b)
,
(7)
,
(8)
Theconstantsaandbwerechosenbasedonwindtunnelmeasurementsoverasmoothsurface
fortheexposedroofandmeasurementsona6thfloorrecessedsurface,whichexperiencesa
similardropinwindspeedsfromthefreestream,forthePVcoveredroof(Palyvos,2008).hi=
1.25Wm‐2K‐1wasusedfortheinteriorheattransfercoefficient(ASHRAE,2005b).
Equations3and4werecoupledtotheheatconductionmodel(Section4)tocalculatetheheat
fluxintothebuildingfromexteriorboundaryconditionsofTa,u,RH,GHI,andDIFFandinterior
boundaryconditionofconstantairtemperature(Ti).SinceEqs.3and4arenon‐linear,
Newton’smethod(Eq.9)isusedtoiterativelysolvefortheroofsurfacetemperature.In
Newton’smethod,Trattheprevioustimestepisusedastheinitialguess(xi)andEqs.3and4
18
andtheirderivatives(FandF’)areusediterativelyuntilTratthecurrenttimestep(xi+1)
converges.
(9)
Theroofheatfluxintothebuildingisthencalculatedfromtheinteriorceilingsurface
temperatureandtheassignedinteriorairtemperatureby
.
5.2Validation
Themodelwasvalidatedagainstthedataobtainedintheintensivestudyperiod.Fig.7shows
themodeledandmeasuredroofsurfacetemperatures,andFig.8showsthemodeledheatflux
intothebuildingagainsttheheatfluxcalculatedinSection4basedonthemeasuredroof
temperature.Theexposedroofheatfluxhadarootmeansquareerror(RMSE)of5.48Wm‐2
andameanbiaserror(MBE)of4.40Wm‐2.ThePVcoveredroofhadanRMSEof2.18Wm‐2
andaMBEof1.72Wm‐2.Consideringthecomplexenvironmentofabuildingrooftopthe
agreementwasconsideredsufficientforvalidation.
19
Fig.7.MeasuredandmodeledroofsurfacetemperatureusingEqs.3and4fora.theexposed
roofandb.PVcoveredroofforApril19,2009.
Fig.8.Heatfluxfromtheceilingtobuildingair(positivevalueequalsfluxintobuilding)
computedusingtheconductionmodelofSection4usingthemeasuredTr(Fig.6,Section4)and
themodeledTr(Eqs.3and4)duringApril19,2009fora)exposedroofandb)PVcoveredroof.
10
20
30
40
50
60
Temperature [
o
C]
a)
T
r
modeled T
r
00:00 06:00 12:00 18:00
10
20
30
40
50
60
Time [PST]
Temperature [
o
C]
b)
T
rs
modeled T
rs
-40
-20
0
20
40
Heat Flux [Wm
-2
]
a) from measured T
r
from modeled T
r
00:00 06:00 12:00 18:00 00:00
-40
-20
0
20
40
Time [PST]
Heat Flux [Wm
-2
]
b) from measured T
rs
from modeled T
rs
20
5.3Roofcoolingload
Theroofheatfluxcontributiontocoolingandheatingloadsisestimatedbydividingthedaysof
theyearintocooling(averageofdailymaximumandminimumoutsideairtemperaturegreater
than18.3oC(65oF))andheating(averageofdailymaximumandminimumtemperatureless
than18.3oC(65oF))days.Forcooling(heating)daysthetotaldailynetincoming(outgoing)
heatfluxisassumedtoconstitutethedailyHVACloadrelatedtotheroofenvelopeflux.Based
onHVACsetpointsandhoursofoperationusedinotherair‐conditionedcommercialbuildings
oncampusforcoolingdays,Ti=23.3oC(74oF),andabuildingscheduleof0800–2000PSTare
assumed.FortheheatingdaysTi=21.7oC(71oF)anda24hourbuildingscheduleareassumed.
ThejustificationsforthebuildingschedulesarediscussedattheendofSection5.
Theroofcoolingandheatingloadanalysiswasrunbymonth(Table5)forallof2009which
included155coolingdaysand210heatingdays.
Table5:Meanmonthlyroofheatfluxcontributionstocoolingandheatingloadsfor2009.
Coolingloadisaverageloadduring0800‐2000PSToncoolingdays.Heatingloadisaverageload
overtheentireheatingday.Negativeheatingloadmeansthattheroofheatflowsintothe
buildingonaheatingday.Numbersinitalicsrepresentmonthswith2orlessdaysofcoolingor
heating.CDD:coolingdegreedays.HDD:heatingdegreedays.
MonthCDD/HDDmeancoolingload[Wm‐2]meanheatingload[Wm‐2]
[oCd]Exposed
roof
PVcoveredExposed
roof
PVcovered
133.4/79.4 2.330.933.403.38
25.33/1202.701.152.062.78
35.56/1185.114.08‐0.750.70
417.4/96.112.85.79‐1.99‐0.77
53.05/38.211.74.22‐3.52‐3.43
64.44/13.38.066.48‐4.09‐4.07
21
780.6/0.5911.46.62‐2.70‐5.83
8106/010.417.27N/AN/A
9100/09.736.31N/AN/A
1030.4/20.66.133.27‐1.41‐1.16
1110.1/60.64.101.710.701.22
123.69/1352.252.683.513.12
Total400/6838.385.21‐0.270.16
Themaximumcoolingloadreduction(4.8Wm‐2)occurredinJuly,whichwaswarmandmostly
clear.Onclearcoolingdaysthebenefitsofshadingaremaximizedcausingalargereductionin
coolingloadcomparedtotheexposedroof(e.g.Fig.9).Onovercastcoolingdaystheexposed
roofisalsoshadedbycloudssothePVcoolingloadissimilartotheexposedroofcoolingload.
InJune2009(acloudymonth)averagecoolingloadsdifferedbylessthan1.6Wm‐2.
Onheatingdaystheincreasedlongwaveradiationfromthepanelbecomesabenefitonall
nights(especiallyclearnights)and(toalesserextent)oncloudydays.Forexample,twocloudy
heatingdaysinDecemberhadalowerheatingloadforPVduringdaytimeandatnight(Fig.10).
Onclearheatingdaystheexposedroofhasalowerdaytimeheatingloadduetotheincreased
solarirradiation.Sinceonlytheroofcontributiontotheheatingloadwascalculated,thesolar
radiationcontributionleadstoanegativeheatingloadformanymonthlyaverages,i.e.theroof
heatfluxisactingtoreducetheheatingloadcausedbywallheatfluxesandinfiltration.Dueto
themoderateairtemperaturesandsignificantsolarirradiationinSanDiegowinterstheannual
meanroofheatingloadisnearlyzeroforbothcases;theheatlossesdrivenbytheinsideto
outsidetemperaturegradientareovercomebyheatgainthroughabsorptionofsolarradiation.
22
Fig.9.a.Modeledroofcoolingloadandb.measuredGHIonJuly12‐13,2009.Hot,cloud‐freeconditions
resultinthegreatestcoolingloadsavingsunderthePVarraywithameandaily(0800‐2000)coolingload
of13.9Wm‐2fortheexposedroofand6.19Wm‐2forthePVcoveredroof.
Fig.10.a.Modeledroofheatingloadandb.measuredGHIonDecember11‐12,2009.Coldandcloudy
daysresultinthegreatestreductioninheatingloadunderthePVarray,withameanheatingloadof
5.96Wm‐2fortheexposedroofand4.03Wm‐2forthePVcoveredroof.
-10
0
10
20
30
roof cooling load [W m
-2
]
a) exposed roof
PV covered roof
00:00 06:00 12:00 18:00 00:00 06:00 12:00 18:00 00:00
0
200
400
600
800
1000
Time [PST]
GHI [W m
-2
]
b)
-5
0
5
10
roof heating load [W m
-2
]
a)
exposed roof
PV covered roof
00:00 06:00 12:00 18:00 00:00 06:00 12:00 18:00 00:00
0
100
200
300
400
500
Time [PST]
GHI [W m
-2
]
b)
23
Theannualcoolingorheatingloadmodelhasseveralshortcomings.Thecoolingloads
representonlytheloadnecessarytomaintainTi=23.3oCduringtheday.The‘startup’loadto
cooltothedesiredTiinthemorningatthebeginningofHVACoperationisnotconsidered.For
coolingload,theeffectofignoringthestartuploadissmall,sincethegenerallycoolnights
wouldresultinTi<23.3oCatthebeginningofHVACoperation.However,fortheheatingload
the‘startup’loadcanbesignificant,andwasaccountedforbyusinga24hbuildingschedulefor
theheatingload.Theinteriorboundaryconditiondoesnotaccountforlongwaveradiativeheat
exchangebetweenbuildingenvelopesurfaces.Whiletheabsoluteresultsmaynotbeaccurate
orrepresentative,thedifferencesbetweentheexposedroofandthePVcoveredroofsurface
temperatureandheatfluxesareconsideratecorrect.
6. DiscussionandConclusions
Carefulmeasurementsofthethermalconditionsthroughoutaroofprofileonabuilding
partiallycoveredbysolarphotovoltaic(PV)panelswereconducted.Thermalinfrared(TIR)
imagerydemonstratedthatceilingtemperaturesunderthePVarrayswereupto2.5Klower
thanundertheexposedroofat1700PST,atimethatlieswithintheintervalofpeakenergy
demand,definedbySDG&Eas1200–1800PST.Thedailyvariabilityinrooftopsurface
temperatureunderthePVarraywashalfthatoftheexposedroof,indicatingareductionin
thermalstressesoftheroofstructure.TheceilingtemperaturesunderatiltedPVarrayoffset
fromtheroofallowingheatadvectionwerecoolerthanunderaflatarraywhichwasmounted
flushwiththeroof.Atnightwithcalmwindstheconditionsreversedandtheceilingunderthe
PVarrayswaswarmerthantheceilingundertheexposedroof,especiallyfortheflushPVarray.
24
Largeindoorairandsurfacetemperaturescausedtheroofheatflux(definedasconductive
heatfluxfromthebottomrooflayertotheceiling)underthetiltedPVarraytobeupwardfor
mostoftheday.Themeandaytimeheatflux(1200–2000PST)undertheexposedroofinthe
modelwas14.0Wm‐2largerthanunderthetiltedPVarray.Themaximumdownwardheatflux
was18.7Wm‐2fortheexposedroofand7.0Wm‐2underthetiltedPVarray,a63%reduction
duetothePVarray.Thereductioninheatfluxiscomparabletothe65%reductionincooling
loadshownbythemodelin(Yangetal.,2001)andthe52%reductionofsummertimepeak
coolingloadfromthesimulationin(Wangetal.,2006).Asensitivityanalysisofourresultsto
temperaturemeasurementuncertaintyconfirmstherobustnessofthedifferenceinroofheat
fluxunderexposedandPVcoveredroof(AppendixA).
Expandingthemodeltoutilizeinternalairtemperature(Ti)andoutsidemeteorological
conditions(GHI,DIFF,Ta,RH,andu)asboundaryconditionsallowedfortheroofheatfluxtobe
modeledfortheyear2009toestimateheatingandcoolingloads.Totalannualcoolingloadof
thePVcoveredroofdecreased38%to9.69kWhm‐2from15.6kWhm‐2fortheexposedroof.
ConsideringthetotalannualPVenergyproductionof148kWhm‐2,theannualcoolingload
reductionof5.91kWhm‐2enhancestheannualnetenergybalanceofPVby4%.Thebenefits
weregreatestinJuly(awarmandsunnymonth),withadifferenceindailycoolingloadof57.36
Whm‐2andanaveragedailyPVarrayelectricityproductionof570Whm‐2,resultingina10%
enhancementofthenetenergybalanceofPV.ThedifferencebetweenPVandexposedroof
wasdependentoncloudcover,ascloudydaysincreasedthebenefitsofPVonheatingdaysand
decreasedthebenefitsoncoolingdays.ThedaytimeshadingprovidedbyPVbecomesa
disadvantageonclearheatingdaysaspassiveheatingisreducedcomparedtotheexposed
25
roof.However,thislossinpassiveheatingisaboutbalancedbyareductioninnighttime
radiativeheatlossresultinginoverallsimilarheatingloadforPVcoveredandexposedroof.The
reductioninnighttimeheatlossisexpectedtoreduceheatingenergyuseinmostregionsofthe
world,especiallyforresidentialapplicationswheremostheatingoccursatnight.Thetools
developedinthisstudycanbeusedwithdifferentmeteorologicalforcingdataandroofthermal
propertiestoestimateheatingandcoolingbenefitsofPV.
ThepresentstudyisuniqueastheimpactoftiltedandflushPVarrayscouldbecompared
againstatypicalexposedroofatthesameroofforacommercialuninhabitedbuildingwith
exposedceilingandconsistingonlyofthebuildingenvelope.Consequently,otherfactorsthat
oftenmakeitdifficulttocomparedifferentroofingmodifications,suchasmicrometeorological
conditionsatthesite,influenceofthesurroundingurbanenvironment,occupantbehavior,and
differencesinbuildingthermalpropertiescouldbeexcludedascontributingfactorsinour
study.NeverthelessthisisacasestudyandtheresultsfortheimpactofPVonthebuilding
coolingloadmaynotbegenerallyapplicable.Shortcomingsoftheanalysisoftheintensive
measurementsinSection4arethat(i)thebuildingwasunventilatedreducingroofcoolingload;
(ii)theceilingareasunderthedifferentroofsectionswerethermallycoupledthroughradiative
andconvectiveexchangeviathebuildinginteriorandgroundslabbluntingthethermal
differencesbetweenexposedandPVcoveredceiling;(iii)thecorrugatedsteelontheceiling
mayhaveconductedheathorizontallywhichisnotaccountedforinour1‐dmodelagain
bluntingthethermaldifferencesbetweenexposedandPVcoveredceiling.However,allof
theseshortcomingsacttoreducethebenefitofshadingfromthePVpanel,soourresultscould
beconsideredaconservativeestimateofPVbenefitsforthisparticularbuilding.Forafuture
26
studywerecommendcomparingclimatecontrolled,identicalbuildingsinaneighborhood,one
withandonewithoutaPVarray.
Inaddition,theresultsserveasapotentialexplanationofthereductioninenergyuseonhot
daysfoundbytheCaliforniaSolarInitiativeimpactevaluation(ITRONInc.,2010),which
presumablyalsohavethehighestroofradiationloadingandmaximumshadingbenefitofPV
systems.WiththeexponentialgrowthinrooftopPV,itbecomesmoreimportanttoconsider
theeffectofrooftopPVsystemsonbuildingHVACcosts.ThemodelsforindirectPVeffectson
coolingloadcouldbeusedsimilartoexistingroofcalculatorsforinsulationimprovementsand
roofalbedoincreases(e.g.ASHRAE,2005a;DOECoolRoofCalculator2009;EPARoof
Calculator,2009).
Nomenclature
TermDescription
a Velocitycoefficientinhcforexposed
roof/PVcoveredroof
bVelocityexponentinhcforexposedroof/PV
coveredroof
c
p
Heatcapacityofroofmaterial
eaVaporpressure
fCloudfraction
qConductiveheatflux
hcExteriorconvectiveheattransfercoefficient
hc,glassHeattransfercoefficientoverasmooth
surface
h
i
Interiorconvectiveheattransfercoefficient
hnNaturalconvectionheattransfercoefficient
kThermalconductivityofroofmaterial
uWindspeed
ARLAboveRoofLevel
BIPVBuildingIntegratedPV
CDDCoolingDegreeDays
27
DIFFDiffuseirradiation
GHIGlobalHorizontalIrradiation
HConvective(sensible)heatflux
HDDHeatingDegreeDays
HVACHeating,Ventilating,andAirConditioning
Ld,sk
y
Downwellinglongwaveradiationfromsky
MBEMeanBiasError
PoSLPowellStructuralLaboratory
PSTPacificStandardTime
PVPhotovoltaic
R
f
Surfaceroughnessmultiplierinhc
RHRelativehumidity
RMSERootMeanSquareError
SDG&ESanDiegoGasandElectric
SVFSkyviewfactorofroofunderPVpanel
TaAirtemperature
TasAirtemperatureundertiltedarray
TcCeilingtemperature
TcsCeilingtemperatureundertiltedarray
Tcfla
t
Ceilingtemperatureunderflatarray
T
i
Interiorairtemperature
T
x
Temperatureatxthrooflayer
T
p
PVpaneltemperature
Tr
Roofsurfacetemperature
Trs
Roofsurfacetemperatureundertilted
array
Tr
n‐1Rooftemperatureatprevioustimestep
TIRThermalInfrared
α Roofsurfacealbedo
εnetNetemissivityofair
εrRoofemissivity
εpPVemissivity
ρ Densityofroofmaterial
σ Stefan‐Boltzmannconstant
ΔxDiscretizedspacingofrooflayers
AppendixA:SensitivityAnalysis
Thesensitivityoftheheatfluxcalculationtothesurfacetemperatureswasanalyzedbyvarying
theoffsetbetweenroofsurfacetemperaturesTrsandTrandtheceilingtemperaturesacquired
28
bytheTIRcamera(Tc).Figure12showsthatoffsettingexposedroofandPVcoveredroof
measurementshasasmalleffectonreductioninpeakheatfluxanddifferenceinmeandaytime
heatflux.OffsettingTrsandTrwithina+‐0.5oCwindow(atypicaluncertaintyofathermistor)
resultsinarangeof55%‐69%reductioninpeakheatfluxandameandaytimeheatflux
differenceof12.2–15.9Wm‐2.Thesenarrowrangesshowthatourheatfluxresultsarerobust.
Fig.11:Sensitivityofa.reductionofpeakroofheatflux[%/100]andb.differenceinmean
daytime(1200‐2000PST)heatflux[Wm‐2]tooffsetsinexposedroof(Tr)andPVroof(Trs)
surfacetemperatures(seeFig.6cforaplotofthisheatfluxfortheexposedroofandPVroof).
AppendixB:ExtensionofconductiveheatfluxanalysistoincludeflushPVarray
Inamannersimilartothederivationofsol‐airorenvironmentaltemperaturesoutdoors,the
heatfluxintothebuildingaircanbesimplifiedintosomeoverallindoorheattransfer
coefficienthitimesthedifferenceintheceilingsurfacetemperatureTcandsomeinternal
environmentaltemperatureTie
(A.1)
PV offset [
o
C]
Exposed offset [
o
C]
a)
-2.0 -1.0 0.0 1.0 2.0
-2.0
-1.0
0.0
1.0
2.0 0.3
0.4
0.5
0.6
0.7
PV offset [
o
C]
Exposed offset [
o
C]
b)
-2.0 -1.0 0.0 1.0 2.0
-2.0
-1.0
0.0
1.0
2.0 8
10
12
14
16
18
20
29
KnowingqandTcforboththeexposedroofcaseandthetiltedPVarray(section4)ateachtime
stepallowssolvingforhiandTieforeachtimestepusingthelinearsystemofEq.A.1.Thesecan
inturnbeusedtosolvefortheheatfluxundertheflusharraygiventheceilingtemperature.
Thedaytimeresultsofthisanalysis(Fig.12)showthatthemeandaytimeheatflux(1200‐2000
PST)is7.25Wm‐2lessthanundertheexposedroofand6.78Wm‐2greaterthanthatunderthe
tiltedarray.
Fig.12.Heatfluxthroughthebottomrooflayer(section4.,Eq.2)forallthreerooftypes.The
solutiongoestoinfinity,however,whentheTc,exposedequalsTc,pvorqPVequalsqexposedwhich
occursaround0100and0900PST.
Acknowledgements
AnthonyDominguezwasfundedbytheNASAgraduatestudentresearchersprogram.Kleissl
acknowledgesfundingfromaNSFCAREERawardandtheHellmanfoundation.Thefollowing
UCSDundergraduatestudentswereinstrumentalinthedatacollection:AvneetSingh,Kevin
04:00 08:00 12:00 16:00 20:00
-30
-20
-10
0
10
20
Time [PST]
Heat Flux [Wm
-2
]
exposed roof
tilted PV array
flush PV array
30
Chivatakarn,ThomasMinor,JeremiahFarinella.WethankRonnenLevinsonforcontributinghis
expertiseandthePowellStructuresLaboratorybuildingstaff,especiallyAndrewGunthardt,for
beingsupportiveofourworkandallowingaccesstothebuildingforthemeasurements.
References
H.Akbari,S.Bretz,D.M.Kurn,J.Hanford.Peakpowerandcoolingenergysavingsofhigh‐albedo
roofs,EnergyandBuildings25(1997a)117‐126
H.Akbari,D.M.Kurn,S.E.Bretz,J.W.Hanford,Peakpowerandcoolingenergysavingsofshade
trees,EnergyandBuildings25(1997b)139‐148
H.AkbariandL.Rainer,MeasuredEnergySavingsfromtheApplicationofReflectiveRoofsin3
AT&TRegenerationBuildings(2000).LawrenceBerkeleyNationalLaboratory.PaperLBNL‐
47075.
ASHRAE(2005a),CoolingLoadComponents,MicrosoftExcelspreadsheetcalculatoravailable
throughtheASHRAEbookstore.
ASHRAEToolkitChapter3,ExteriorHeatBalance(2005b).
CIMISevapotranspirationmodel,http://wwwcimis.water.ca.gov/cimis/infoEtoPmEquation.jsp,
accessedSeptember25,2010.
DepartmentofEnergy(DOE)CoolRoofCalculator,
http://www.ornl.gov/sci/roofs%2Bwalls/facts/CoolCalcEnergy.htm,accessedNov16,2009
EnvironmentalProtectionAgency(EPA),2009,http://roofcalc.com/RoofCalcBuildingInput.aspx,
accessedNov16,2009
31
ItronInc.,CPUCCaliforniaSolarInitiative2009ImpactEvaluation,2010,
http://www.cpuc.ca.gov/NR/rdonlyres/70B3F447‐ADF5‐48D3‐8DF0‐
5DCE0E9DD09E/0/2009_CSI_Impact_Report.pdf,accessedJuly13,2010.
A.D.JonesandC.P.Underwood,Athermalmodelforphotovoltaicsystems,SolarEnergy,Vol.
70:4(2001)349‐359.
J.A.Palyvos,Asurveyofwindconvectioncoefficientcorrelationsforbuildingenvelopeenergy
systems’modeling,AppliedThermalEngineeringVol.28:8‐9(2008)801‐808.
D.S.ParkerandS.F.Barkaszi,Roofsolarreflectanceandcoolingenergyuse:fieldresearch
resultsfromFlorida,EnergyandBuildings25(1997)105‐115
J.R.Simpson,E.G.McPherson,Theeffectsofroofalbedomodificationoncoolingloadsofscale
modelresidencesinTucson,Arizona,EnergyandBuildings25(1997)127‐137
ThermalPropertiesofConcrete,http://people.bath.ac.uk/absmaw/BEnv1/properties.pdf,
accessedJanuary22,2010.
W.Tian,Y.Wang,Y.Xie,D.Wu,L.ZhuandJ.Ren,Effectofbuildingintegratedphotovoltaicson
microclimateofurbancanopylayer,BuildingandEnvironment42(2007)1891‐1901
C.P.UnderwoodandF.W.H.Yik,ModelingMethodsforEnergyinBuildings,BlackwellPublishing
Ltd(2004)
Y.Wang,W.Tian,J.Ren,L.Zhu,andQ.Wang,Influenceofabuilding’sintegrated‐photovoltaics
onheatingandcoolingloads,AppliedEnergy84(2006)983‐1003
32
H.X.Yang,J.Burnett,Z.ZhuandL.Lu,Asimulationstudyontheenergyperformanceof
photovoltaicroofs,ASHRAETrans107(2001)(2),129–135