ArticlePDF Available

Abstract and Figures

Indirect benefits of rooftop photovoltaic (PV) systems for building insulation are quantified through measurements and modeling. Measurements of the thermal conditions throughout a roof profile on a building partially covered by solar photovoltaic (PV) panels were conducted in San Diego, California. Thermal infrared imagery on a clear April day demonstrated that daytime ceiling temperatures under the PV arrays were up to 2.5K cooler than under the exposed roof. Heat flux modeling showed a significant reduction in daytime roof heat flux under the PV array. At night the conditions reversed and the ceiling under the PV arrays was warmer than for the exposed roof indicating insulating properties of PV. Simulations showed no benefit (but also no disadvantage) of the PV covered roof for the annual heating load, but a 5.9kWhm−2 (or 38%) reduction in annual cooling load. The reduced daily variability in rooftop surface temperature under the PV array reduces thermal stresses on the roof and leads to energy savings and/or human comfort benefits especially for rooftop PV on older warehouse buildings.
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)5348087;Fax:(858)5347599;
Address:9500GilmanDr,EBUII580,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,buta5.9kWhm2(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
membranesresultedinseasonalairconditioningenergysavingsof57%onaCaliforniahome
(Akbarietal.,1997a),49%onabungalow,2%to43%inFlorida(ParkerandParkaszi,1997),
and30Whm2d1onaregenerationbuilding(AkbariandRainer,2000).However,theenergy
savingsdependontheroofinsulatingproperties.Increasingtheroofalbedofrom0.09to0.75
onabuildingwithoutinsulationresultedinenergysavingsof28%,whileincreasingthealbedo
from0.30to0.75onabuildingwithR30insulation(anadditionof5.28Km2W1inthermal
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)territorycausedpostPVhouseholdswithair
conditioningtouse0.501kWhlessenergyperdaythanhouseholdswithairconditioningthat
didnothavePVinstalled.
ModelingtheeffectsofbuildingintegratedPV(BIPV)onthemicroclimateoftheurbancanopy
layershowedasignificantreductioninBIPVroofsurfacetemperaturescomparedtoa
conventionalroofwithalbedo0.30andathermalresistanceof1.33Km2W1(Tianetal.,2007).
Aonedimensionaltransientheattransfermodelshowedapeakcoolingloadsavingsof52%
withventilatedBIPVcomparedtotraditionalroofingwithasolarabsorbanceof0.9anda
thermalresistanceof1.33Km2W1(Wangetal.,2006).Aconductionmodelshoweda65%
reductionincoolingloadcomponentthroughaPVroofcomparedtoaconventionalroofwitha
thermalresistanceof2.8Km2W1(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.ThisresultsinasignificantlylowerRValuethannewconstruction,butistypicalof
olderwarehousebuildingswithlarge,flatrooftopsforwhichPVisanattractiveoption.Table1
showsthesiteandbuildingcharacteristics.
Table1:PowellStructuralLaboratory(PoSL)buildingcharacteristics.Thebuildingislocatedat
32o52’50”N,117o14’06”WintheWorldGeodeticSystem1984coordinatesystem(WGS84)and
is1.7kmfromthePacificOceancoastline.
Length(northsouth)Width(eastwest) 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
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
erNorthS
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
osssection
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.Thesamplingfrequencywas1minand5minaverages
werestored.
ApermanentmeteorologicalstationontherooftopofPoSLmonitoredexposedroofsurface
temperature,airtemperature,totalanddiffusesolarirradiance,andwindspeed(Table3).Data
weresampledeverysecondandstoredas5minaverages.TherooftopalbedoandsolarPV
albedoweremeasuredusingaKipp&ZonenCMP3albedometer.Afterthestudy,theTIR
camera,HOBOs,andTN9TIRsensorswerecrosscalibratedontheexposedroofandalinear
regressionwasappliedtoforceagreementbetweenthesensors.AppendixAshowsananalysis
ofthesensitivityofourresultstotemperatureoffsetsinthesensors.
Table3:Sensortype,make,model,andheightaboverooflevel(ARL)formeasurementsonthe
PoSLroof(Fig.2).TheTN9accuracyisgivenforthe1535oCtemperaturerange.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
kWhm2,whichwaslargerthanatypicalAprilday.Figure4bshowsthewindspeed,which
followstypicalseabreezepatterns(cf.annualaverageuinFig.4b)withcalmwindsuntil0800
PST,increasesto5ms1at1400PSTanddecreasestolessthan1ms1by2030PST.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
enclosedairspacebetweenthepanelsandtherooflimitshorizontaladvectionofheat.The
ceilingcoveredbytheflushPVarrayhasthehighesttemperatureatnightduetotheinsulating
propertiesoftheenclosedairbetweenroofandsolararrayandtheincreaseinincident
longwaveradiationfromthepanelcomparedtothesky.
4. Simulationofroofheatflux
Theresultsinsection3haveshownmarkeddifferencesinthethermalresponseofaroof
underneathasolarpanelcomparedtothatofanexposedroof.However,todeterminethe
potentialHVACenergysavingsassociatedwithsolarPVpanelstheroofheatfluxintotheair
conditionedspace(orroofcoolingload)isthemostrelevantvariable.Quantifyingthisheatflux
independentlyforeachsurfaceisdifficult,sinceconvectiveandradiative(andtoalesserextent
conductive)exchangeofheatbetweenceilingareasthroughtheroomairandwallandfloor
surfacesbluntsthetruedifferencesbetweentheceilingtemperaturesundereachrooftype.
13
TheconductionheatfluxthroughtheroofcanbemodeledusingaCrankNicholsonmethod
(UnderwoodandYik,2004)appliedtotheonedimensionaltransientheatconductionequation

 
(1)
usingadiscretizationof32layers.Theboundaryconditionsarethemeasuredrooftopsurface
andinteriorceilingsurfacetemperatures.Theeffectsoftheupperroofmembraneandlower
corrugatedsteel(Fig.2)werenegligible,astheyarethinandhavehighthermalconductivityin
comparisontotheinsulatingconcrete,sothemodelwassimplifiedbydefiningtheentireroof
asmeshreinforcedinsulatingconcrete.Thethermalpropertiesusedinthemodelwerethermal
conductivityk=0.38Wm1K1,densityρ=1200kgm3,andheatcapacitycp=1000Jkg1K1
(ThermalPropertiesofConcrete,2010),resultinginathermaldiffusivityof3.2x107m2s1and
thermalresistanceof0.526Km2W1(abouttheequivalentofR3insulation).Themodelwas
validatedagainstananalyticalsolutionforablockwithuniforminitialtemperaturebeing
submergedintoaliquidwithconstantuniformtemperature(UnderwoodandYik,2004).Since
thesystemisquasiperiodiconcleardays,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.Timeseriesofsimulated1Dtemperatureprofilethrougha.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
whereΔxisthenumericaldiscretizationdistancebetweenrooflayers.Thisanalysiscannotbe
conductedfortheflushPVarrayastheexteriorrooftemperaturewasnotavailabletodrivethe
conductionmodel.AppendixBshowsanattempttoestimatetheflusharrayheatflux.
Figure6cshowstheresultingheatfluxthroughtheexposedroofandtheroofunderthetilted
array.Asexpectedtheheatfluxisnegative(upward)intheearlymorning.Theminimum
between09001000PSTisaresultoftheheatlossattheroofsurfacethroughthenightbut
likelyamplifiedbysolarradiativeheatingoftheinteriorandceilingthroughthewindowsinthe
earlymorningaswellasincreasedconvectiveheatingfromtheinteriorairtemperature.At
1300PST(exposedroof)and1900PST(tiltedPV)theheatfluxbecomespositive(downward)
withalargerpeakfortheexposedroofthanthePVcoveredroofat1930PST.Theheatfluxes
remainpositivethroughthenightconsistentwiththetimelagofheattransferthroughthe
roof.Generally,therelativelysmallthermaldiffusivityoftheroofunderconsiderationcauses
secondaryeffects(ceilingbuildinginteraction,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
Interiorconvectiveheattransfercoefficient1.25Wm2K1(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
n1Rooftemperatureatprevioustimestepn1
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
obtainedusingtheDOE2convectionmodel(Eqs.68,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=
1.25Wm2K1wasusedfortheinteriorheattransfercoefficient(ASHRAE,2005b).
Equations3and4werecoupledtotheheatconductionmodel(Section4)tocalculatetheheat
fluxintothebuildingfromexteriorboundaryconditionsofTa,u,RH,GHI,andDIFFandinterior
boundaryconditionofconstantairtemperature(Ti).SinceEqs.3and4arenonlinear,
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)of5.48Wm2
andameanbiaserror(MBE)of4.40Wm2.ThePVcoveredroofhadanRMSEof2.18Wm2
andaMBEof1.72Wm2.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
onHVACsetpointsandhoursofoperationusedinotherairconditionedcommercialbuildings
oncampusforcoolingdays,Ti=23.3oC(74oF),andabuildingscheduleof08002000PSTare
assumed.FortheheatingdaysTi=21.7oC(71oF)anda24hourbuildingscheduleareassumed.
ThejustificationsforthebuildingschedulesarediscussedattheendofSection5.
Theroofcoolingandheatingloadanalysiswasrunbymonth(Table5)forallof2009which
included155coolingdaysand210heatingdays.
Table5:Meanmonthlyroofheatfluxcontributionstocoolingandheatingloadsfor2009.
Coolingloadisaverageloadduring08002000PSToncoolingdays.Heatingloadisaverageload
overtheentireheatingday.Negativeheatingloadmeansthattheroofheatflowsintothe
buildingonaheatingday.Numbersinitalicsrepresentmonthswith2orlessdaysofcoolingor
heating.CDD:coolingdegreedays.HDD:heatingdegreedays.
MonthCDD/HDDmeancoolingload[Wm2]meanheatingload[Wm2]
[oCd]Exposed
roof
PVcoveredExposed
roof
PVcovered
133.4/79.4 2.330.933.403.38
25.33/1202.701.152.062.78
35.56/1185.114.080.750.70
417.4/96.112.85.79‐1.99‐0.77
53.05/38.211.74.223.52‐3.43
64.44/13.38.066.48‐4.09‐4.07
21
780.6/0.5911.46.622.70‐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(4.8Wm2)occurredinJuly,whichwaswarmandmostly
clear.Onclearcoolingdaysthebenefitsofshadingaremaximizedcausingalargereductionin
coolingloadcomparedtotheexposedroof(e.g.Fig.9).Onovercastcoolingdaystheexposed
roofisalsoshadedbycloudssothePVcoolingloadissimilartotheexposedroofcoolingload.
InJune2009(acloudymonth)averagecoolingloadsdifferedbylessthan1.6Wm2.
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.measuredGHIonJuly1213,2009.Hot,cloudfreeconditions
resultinthegreatestcoolingloadsavingsunderthePVarraywithameandaily(08002000)coolingload
of13.9Wm2fortheexposedroofand6.19Wm2forthePVcoveredroof.
Fig.10.a.Modeledroofheatingloadandb.measuredGHIonDecember1112,2009.Coldandcloudy
daysresultinthegreatestreductioninheatingloadunderthePVarray,withameanheatingloadof
5.96Wm2fortheexposedroofand4.03Wm2forthePVcoveredroof.
-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&Eas12001800PST.Thedailyvariabilityinrooftopsurface
temperatureunderthePVarraywashalfthatoftheexposedroof,indicatingareductionin
thermalstressesoftheroofstructure.TheceilingtemperaturesunderatiltedPVarrayoffset
fromtheroofallowingheatadvectionwerecoolerthanunderaflatarraywhichwasmounted
flushwiththeroof.Atnightwithcalmwindstheconditionsreversedandtheceilingunderthe
PVarrayswaswarmerthantheceilingundertheexposedroof,especiallyfortheflushPVarray.
24
Largeindoorairandsurfacetemperaturescausedtheroofheatflux(definedasconductive
heatfluxfromthebottomrooflayertotheceiling)underthetiltedPVarraytobeupwardfor
mostoftheday.Themeandaytimeheatflux(12002000PST)undertheexposedroofinthe
modelwas14.0Wm2largerthanunderthetiltedPVarray.Themaximumdownwardheatflux
was18.7Wm2fortheexposedroofand7.0Wm2underthetiltedPVarray,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%to9.69kWhm2from15.6kWhm2fortheexposedroof.
ConsideringthetotalannualPVenergyproductionof148kWhm2,theannualcoolingload
reductionof5.91kWhm2enhancestheannualnetenergybalanceofPVby4%.Thebenefits
weregreatestinJuly(awarmandsunnymonth),withadifferenceindailycoolingloadof57.36
Whm2andanaveragedailyPVarrayelectricityproductionof570Whm2,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
mayhaveconductedheathorizontallywhichisnotaccountedforinour1dmodelagain
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
n1Rooftemperatureatprevioustimestep
TIRThermalInfrared
α Roofsurfacealbedo
εnetNetemissivityofair
εrRoofemissivity
εpPVemissivity
ρ Densityofroofmaterial
σ StefanBoltzmannconstant
ΔxDiscretizedspacingofrooflayers
AppendixA:SensitivityAnalysis
Thesensitivityoftheheatfluxcalculationtothesurfacetemperatureswasanalyzedbyvarying
theoffsetbetweenroofsurfacetemperaturesTrsandTrandtheceilingtemperaturesacquired
28
bytheTIRcamera(Tc).Figure12showsthatoffsettingexposedroofandPVcoveredroof
measurementshasasmalleffectonreductioninpeakheatfluxanddifferenceinmeandaytime
heatflux.OffsettingTrsandTrwithina+‐0.5oCwindow(atypicaluncertaintyofathermistor)
resultsinarangeof55%‐69%reductioninpeakheatfluxandameandaytimeheatflux
differenceof12.215.9Wm2.Thesenarrowrangesshowthatourheatfluxresultsarerobust.
Fig.11:Sensitivityofa.reductionofpeakroofheatflux[%/100]andb.differenceinmean
daytime(1200‐2000PST)heatflux[Wm2]tooffsetsinexposedroof(Tr)andPVroof(Trs)
surfacetemperatures(seeFig.6cforaplotofthisheatfluxfortheexposedroofandPVroof).
AppendixB:ExtensionofconductiveheatfluxanalysistoincludeflushPVarray
Inamannersimilartothederivationofsolairorenvironmentaltemperaturesoutdoors,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(12002000
PST)is7.25Wm2lessthanundertheexposedroofand6.78Wm2greaterthanthatunderthe
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.Peakpowerandcoolingenergysavingsofhighalbedo
roofs,EnergyandBuildings25(1997a)117126
H.Akbari,D.M.Kurn,S.E.Bretz,J.W.Hanford,Peakpowerandcoolingenergysavingsofshade
trees,EnergyandBuildings25(1997b)139148
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/70B3F447ADF548D38DF0
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.28:89(2008)801808.
D.S.ParkerandS.F.Barkaszi,Roofsolarreflectanceandcoolingenergyuse:fieldresearch
resultsfromFlorida,EnergyandBuildings25(1997)105115
J.R.Simpson,E.G.McPherson,Theeffectsofroofalbedomodificationoncoolingloadsofscale
modelresidencesinTucson,Arizona,EnergyandBuildings25(1997)127137
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)18911901
C.P.UnderwoodandF.W.H.Yik,ModelingMethodsforEnergyinBuildings,BlackwellPublishing
Ltd(2004)
Y.Wang,W.Tian,J.Ren,L.Zhu,andQ.Wang,Influenceofabuilding’sintegratedphotovoltaics
onheatingandcoolingloads,AppliedEnergy84(2006)9831003
32
H.X.Yang,J.Burnett,Z.ZhuandL.Lu,Asimulationstudyontheenergyperformanceof
photovoltaicroofs,ASHRAETrans107(2001)(2),129–135
... Photovoltaic (PV) roofs and thermal coating solutions are becoming increasingly popular as strategies for energy efficiency and comfort enhancement in buildings. Photovoltaic roofs offer numerous advantages, such as local electricity production and shading for various surfaces [17][18][19]. Studies have shown that the success of energy reduction strategies with photovoltaic panels depends on the size of the PV panel system and the availability of roof space. ...
... In warm climates, roofs contribute significantly to the cooling load of buildings, making cool roofs and coating solutions particularly valuable. Research in regions like the Colombian Caribbean, the Mediterranean climate zone of Algeria, and other locations has demonstrated the potential of coating solutions in reducing cooling requirements [17][18][19]. ...
Article
Full-text available
Thermal coating paints offer a passive strategy to reduce heat gain in buildings, improve ventilation, and lower energy consumption. This study investigates the effectiveness of these technologies by comparing different housing structures and environmental conditions. Specifically, it examines thermal envelope solutions for cool roofs in homes along the Colombian Caribbean Coast. We quantify the thermal impacts using experimental data collected from 120 houses across eight municipalities in the Magdalena Department, Colombia. The research details the technology and analytical methods employed, focusing on thermal reductions achieved through thermal coatings to potentially reduce energy demand. A comprehensive measurement system, incorporating temperature and humidity sensors, is developed to assess the impact of the coatings. Thermal comfort is evaluated according to the ASHRAE 55 standard, with temperature reductions calculated for each house treated with thermal coatings. A methodology is applied to evaluate the thermal reduction between a house with a coating solution versus a house without it. The results show a temperature reduction on a house-by-house basis, from 1.5% to 16%. On average, the results yield a significant 7% reduction in thermal load. Additionally, a mobile application is developed to disseminate the results of this research, promoting the social appropriation of science among the involved communities.
... Recent studies suggest that cityscale RPVSP deployment might either decrease or increase urban temperatures [5][6][7] . For example, it has been observed that the deployment of RPVSP on a building not only curtailed greenhouse gas emissions but also reduced annual cooling loads 8 . Similar results have been observed in simulation-based studies and in the case of medium-to-large-scale RPVSP deployment [9][10][11][12] . ...
... As a result, air temperatures around RPVSPs tend to remain higher during the day, particularly in urban building environments. Moreover, higher air temperature was also observed in the gap between the RPVSPs and roof (~0.3 m) compared with the ambient air temperature 8,26 . This increase of 3.2 °C is indicative of the overall impact of the RPVSPs on urban temperature during peak hours at the city scale. ...
... Comparing those two roof types, the BR + PV shows its highest heat gain during summer season of 2.5 kWh/m 2 in July and exhibits during the entire summer months a smaller heat gain through the roof compared to the BR, which has its highest heat gain of 7 kWh/m 2 during the summer months in July as well. The lower convective heat flux of the BR + PV compared to the BR is ascribed to the shade provided by the panels which reduce the short-wave incident on the roofs surface, resulting in lower surface temperatures [14,24,92]. Consequently, the BR is the less appropriate option for reducing heat gain through the roof during the summer season. ...
Article
Full-text available
The European Union has emphasized policies promoting photovoltaic (PV) energy generation to achieve the United Nations' Sustainable Development Goals 7 and 13. Notably, building roofs suitable for PV panels also present opportunities for passive energy-saving methods, such as green roofs. Both approaches impact beyond buildings to the urban level; PV panels intensify the urban heat island (UHI) effect, while well-irrigated green roofs mitigate it. In the Mediterranean region, where cities face challenges from extreme weather events and droughts leading to water restrictions, a comprehensive analysis of the influence of these approaches at both the building and urban levels becomes crucial. This work addresses this gap by employing dynamic simulations of a typical Mediterranean roof, an extensive green roof and a summer-irrigated green roof, all with and without PV panels, under Mediterranean climate. While both green roofs and PV systems prove beneficial at the building level, only irrigated green roofs effectively reduce the UHI impact. Unirrigated green roofs show no benefit on the UHI, whereas PV panels consistently amplify it. Combining an unirrigated green roof with PV panels has the highest UHI impact among all analyzed roof types. Summer irrigation of the extensive green roof can compensate the additional convective heat flux by PV panels, and moreover enhancing heat loss through the roof-a beneficial aspect at the building level during summer. The findings underscore the complexity of defining strategies that meet goals for renewable energy and UHI mitigation, highlighting the need for further research in this area.
... Studies suggest that strategically locating PVSPs on low reflective rooftops could mitigate UHI [5]. However, there are contrasting studies reporting a warming [6,7,8] or cooling effect [9,10,11]. For this reason, it is required comprehensive research using in situ measurements. ...
Article
Full-text available
To achieve the objectives of COP28 for transitioning away from fossil fuels and phasing these out, both natural and technological solutions are essential, necessitating a step-change in how we implement social innovation. Given the significant CO2 emissions produced by the building sector, there is an urgent need for a transformative shift towards a net-zero building stock by mid-century. This transition to zero-energy and zero-emission buildings is difficult due to complex processes and substantial costs. Building integrated photovoltaics (BIPV) offers a promising solution due to the benefits of enhanced energy efficiency and electricity production. The availability of roof and façade space in offices and other types of buildings, especially in large cities, permits photovoltaic integration in both opaque and transparent surfaces. This study investigates the synergistic relationship between solar conversion technologies and nature-based components. Through a meta-analysis of peer-reviewed literature and critical assessment, effective BIPVs with greenery (BIPVGREEN) combinations suitable for various climatic zones are identified. The results highlight the multi-faceted benefits of this integration across a range of techno-economic and social criteria and underscore the feasibility of up-scaling these solutions for broader deployment. Applying a SWOT analysis approach, the internal strengths and weaknesses, as well as the external opportunities and threats for BIPVGREEN deployment, are investigated. The analysis reveals key drivers of synergistic effects and multi-benefits, while also addressing the challenges associated with optimizing performance and reducing investment costs. The strengths of BIPVGREEN in terms of energy efficiency and sustainable decarbonization, along with its potential to mitigate urban and climate temperature increases, enhance its relevance to the built environment, especially for informal settlements. The significance of prioritizing this BIPVGREEN climate mitigation action in low-income vulnerable regions and informal settlements is crucial through the minimum tax financing worldwide and citizen’s engagement in architectural BIPVGREEN co-integration.
Article
Beginning in the early 1990s, photovoltaic (PV) technologies were integrated with building envelopes to reduce peak electrical load and fulfill building energy demands. The PV technologies are referred to be building integrated (BI) PV systems when they are either incorporated or mounted to the envelopes. BIPV system groupings include BIPV roofs, BIPV facades, BIPV windows, and BIPV shadings. In this study, the technology division of photovoltaic cells and the BIPV system groupings are discussed and investigated. This evaluation addresses several variables that impact the BIPV system applications’ functionality and design. The tilt angle of PV shading devices, transmittance, window-to-wall ratio (WWR), and glass orientation are the parameters that have been found. Researchers will find this review paper useful in constructing the BIPV system since it offers opportunities for future study.
Article
Full-text available
The increasing adoption of solar panels as a sustainable energy solution has raised concerns about their potential detrimental effects on residential roofing systems. This research evaluates these impacts, focusing on structural and material considerations. The study identifies common issues such as structural damage, leaks, and material compatibility problems through a mixed-methods approach, combining literature reviews, surveys, interviews, and case studies. Key findings indicate that improper installation is a primary cause of roof damage, with 65% of homeowners reporting structural issues and 50% experiencing leaks. The study proposes several mitigation strategies, including proper training for installers, using compatible materials, regular inspections, and adherence to industry standards. These recommendations aim to help homeowners, installers, and policymakers ensure the integrity of roofing systems while reaping the benefits of solar energy.
Article
A simulation model has been developed to investigate the thermal and electrical energy performance of photovoltaic roofs (PV roofs). Direct numerical simulations of heat transfer and energy conversion of PV roofs are made by introducing a cumulative variable, which can simplify the heat transfer calculation problems. The cumulative variable is inverted to represent the roof surface temperature instead of real surface temperature so that it is easier to deal with thermal radiation heat transfer between the two-layer surfaces of the ventilated PV roofs. Natural ventilation heat transfer in the ventilation gap takes away a large amount of heat, which reduces the cooling load of the buildings. The cooling load reduction, the ventilation gap ratio, and the roof inclination angle are discussed in this paper. It is found that the cooling load component through a PV roof is about 35% compared with the load of a conventional roof.
Article
Energy use and environmental parameters were monitored in three AT and T regeneration buildings during the summer of 2000. These buildings are constructed with concrete and are about 14.9 m2 (160 f2; 10x16 ft)in size. The buildings were initially monitored for about 1 1/2 months to establish a base condition. Then, the roofs of the buildings were painted with a white coating and the monitoring was continued. The original roof reflectances were about 26 percent; after the application of roof coatings the reflectivities increased to about 72 percent. In two of these buildings, we monitored savings of about 0.5kWh per day (8.6 kWh/m2 [0.8 kWh/ft2]). The third building showed a reduction in air-conditioning energy use of about 13kWh per day. These savings probably resulted from the differences in the performance (EER) of the two dissimilar AC units in this building. The estimated annual savings for two of the buildings are about 125kWh per year; at a cost of dollar 0.1/kWh, savings are about dollar 12.5 per year. Obviously, it costs significantly more than this amount to coat the roofs with reflective coating, particularly because of the remote location of the buildings. However, since the prefabricated roofs are already painted green at the factory, painting them with white (reflective) color would bring no additional cost. Hence the payback time for having reflective roofs is nil, and the reflective roofs save an accumulated 370kWh over 30 years of the life of the roof.
Article
Data supporting reductions in cooling load and related demand for electric power possible from increasing building surface albedo are limited. Electrical use of wall-mounted air conditioners, roof temperatures, and related environmental factors were monitored during the summer of 1990 on three initially identical 1/4-scale model buildings situated in rock mulch landscapes in Tucson, Arizona. Model thermodynamic properties were scaled to approximate thermodynamic similarity with full-size buildings. With ceiling insulation of R value 5.28 m2 K W−1 (R-30) installed, increasing roof albedo of the gray composition shingles (0.30 albedo, 0.94 emissivity) by painting one roof silver and another white (0.49 and 0.75 albedos, 0.70 and 0.98 emissivities, respectively) reduced daily total and hourly peak electrical use for air conditioning approximately 5% for the house with white-colored roof compared to either gray or silver-colored roofs. Larger differences were found without ceiling insulation, with daily total and peak hourly demand for houses with white compared to dark brown roofing (0.9 albedo, 0.98 emissivity) reduced 28 and 18%, respectively. Computer simulations of daily total energy use confirmed comparable savings for similar full-sized buildings. White roofs were 20 to 30°C cooler than either silver or dark-colored roofs on hot, sunny days, indicating that expected cooling due to an increase in albedo may not be realized if it is accompanied by a decrease in emissivity. Light colored roofs, by maintaining cooler attic temperatures, may provide savings in addition to those presented here by reducing heat gain to air distribution systems located in the attic space.
Article
Advances in educational technology and its increasing availability in K-12 schools make it incumbent upon colleges of education to look critically at how technology is integrated into teacher preparation programs. In seeking to prepare teachers for the next century, college faculty are increasingly being expected to utilize and model the use of technology; to facilitate its use by their students; and to integrate technology into instruction. Unfortunately, the literature reveals that technology is not systematically integrated into many preparation programs and that the lack of equipment, training, and time often limit opportunities for both faculty and students. This article reports the results of a faculty self-study at Louisiana Tech University regarding: (1) faculty use of technology in planning and instruction; (2) required student use; (3) perceived obstacles to increased use; and (4) faculty interest in professional development in technology.