Effective day and effective solar radiation

Totalannualsolarradiationwasoftenusedtoestimatesolar energyproduction(e.g.,Kaldellisetal.[6],LiandYang[10]),but itmayoverestimatetheenergysavingofaSWHduetoESR. Fur-thermore,solarradiationvariesfordifferentregionsandseasonsin Taiwan;thus,Taiwan’stemporalandspatialcharacteristicsmust beanalyzed.AnenhancedmethodisthusproposedbasedonESR, regionalamountsofsolarradiation,andtapwatertemperatures.

ForanSWH,surplussolarradiationcannotbesavedand,thus, excessivesolarradiationcannotresultin additionalenergy sav-ings.Furthermore,tapwatertemperaturesignificantlyaffectsthe amountofsolarradiationrequiredtoheatwatertoadesired tem-perature.Coldtapwaterrequiresmoresolarradiationtoheatthan warmtapwater. Toevaluatetheapplicabilityof SWHsin each region,thisstudyproposedtwonewindexes,theannualratioof effectivedays(E-days)andannualESR,toassesspotentialenergy savingsfromanSWH.Thevalues ofbothindexesareestimated basedontapwatertemperatureanddailysolarradiationineach region.AnE-dayisadayonwhichsolarradiationexceedsthe min-imumrequiredsolarradiation,andtheESRistotalannualeffective solarradiationusedbyanSWH.Thesetwoindexesaredescribed asfollows.

3.1. AnnualE-dayratio

Beforedescribingthisindex,minimumrequiredsolarradiation isdefined.AnSWHrequiressufficientsolarradiationtoheattap water.Whensolarradiationisinsufficient,anSWHcannotheat enoughhotwaterfordailyusesandrequiresotherenergiestoheat tapwatertoadesiredtemperature—55^◦Cinthisstudy.Thus,the minimumrequiredsolarradiationistheamountofsolarradiation requiredby anSWHtoheat tapwater tothedesired tempera-ture.ItisdeterminedbasedontapwatertemperatureandSWH specifications,andisestimatedbythefollowingequation[11].

S_z,d^min=V·Ds·H·tz,d

SWH·A (1)

whereS^min_z,d isminimumrequiredsolarradiation(MJ/m²)forday dinregionz;VisthevolumeofanSWHstoragetank(L);Dsis waterdensity(kg/L);Histhespecificheat(MJ/kg^◦C)ofwater;td

Table1

Averagesolarradiationoffourregionsduring2006–2008.

Region Range(MJ/m²) Weatherstationcode Annualtotalsolar

radiation(MJ/m²)

istemperaturedifference(^◦C)betweenthehotwaterheatedbyan SWHandtapwaterondayd;SWHiscollectorefficiencyofanSWH;

andAissurfaceareaofasolarcollector(m²).

Whenavailablesolar radiation onone dayexceeds S_z,d^min, an SWHcanheattapwatertothedesiredtemperature,andthedayis regardedasanE-day.Sincesolarradiationvariesamongregions, thenumberofeffectivedaysalsodiffersamongregions.Theannual E-dayratioisthencalculatedusingthefollowingequation:

For DRz,d>S^min_z,d, Ez,d=1,

whereDRz,dissolarradiationondaydforregionz;Ez,disabinary variableindicatingwhetherdaydinregionzisanE-day;REzisthe annualE-dayratioinregionz;andYisthenumberofdaysinastudy year(usually365days).E-daysarethosedaysonwhichanSWH providessufficienthotwaterusingonlysolarenergy.Theannual E-dayratioisanusefulindexwhenassessingtheapplicabilityof SWHsindifferentregions.TheS_z,d^minvalueisestimatedforatypical familySWHwitha250-Lstoragetankproviding55^◦Cwater.The solarcollectorsurfaceareais4m²andcollectorefficiencyis50%, theminimumacceptableefficiencyin Taiwan[12].Regionaltap watertemperaturesareestimatedbasedondataobtainedbyChang [13].Fig.1showstheS^min_z,d valuesforthetypicalSWHindifferent

12

Minimum required solar radiation (MJ/m2)

AR HR MR SI

Fig.1.Minimumrequiredsolarradiationfordifferentregions.

monthsandregionsinTaiwan.TheS_z,d^minvalueinwinterishigher thanthatinsummerbecausetapwaterinwinteriscolderthan insummerand,thus,requiresmoresolarradiationtoheattothe desiredtemperature.

Fig.2showstheannualandmonthlyE-dayratiosofdifferent regionsbasedon2008data.Fig.2(a)presentstheannualE-day ratiosforthefourregions;allexceed30%.TheannualE-dayratio fortheARregion,50%,issignificantlyhigherthanthoseforother regions,andis19%higherthanthatfortheMRregion(31%).

SI

Fig.2. E-dayratiosfordifferentregions:(a)annualE-dayratioand(b)monthly E-dayratio.

12 11 10 9 8 7 6 5 4 3 2 1 0 200 400 600

Solar radiation (MJ/m2)

(a)

12 11 10 9 8 7 6 5 4 3 2 1 0 200 400 600

(b)

12 11 10 9 8 7 6 5 4 3 2 1

Month 0

200 400 600

Solar radiation (MJ/m2)

(c)

12 11 10 9 8 7 6 5 4 3 2 1

Month 0

200 400 600

Total solar radiation ESR

(d)

Fig.3. Monthlyeffectivesolarradiationinthe(a)AR,(b)HR,(c)MR,and(d)SIregions.

Since summer solar radiation is abundant and the required S^min_z,d islow,themonthlyE-dayratiosinsummer,asillustratedin Fig.2(b),aremarkedlyhigherthanthoseinotherseasons.Because winteris typicallycloudy, rainy,andcold insomeregions, and theamountofsolarradiationandtapwatertemperaturearelow, monthlyE-dayratiosforthefourregionsinDecember,January,and Februaryare0%.AlowannualE-dayratioindicatesthatasignificant amountofsupplementalenergy,suchasnaturalgasorelectricity,is neededtoheattapwatertothedesiredtemperatureonnon-E-days.

3.2. Annualeffectivesolarradiation

ToanalyzethebenefitsandcostsofSWHs,anovelindex,annual ESR,isproposed.TheannualESRindexisdeterminedbythe follow-ingequations:

For Ez,d=1, ERz,d=S^min_z,d,

For Ez,d=0, ERz,d=DRz,d, (3)

ESRz=



d=1

ERz,d (4)

RESRz=



d=1DR_z,d (5)

whereERz,disESRondaydinregionz;ESRz istheannualESRin regionz;andRESRzistheratioofESRtototalsolarradiationin regionz.WhendaydisanE-dayandDRz,d>S^min_z,d,surplussolar radiationdoesnotprovideadditionalenergysavings.Therefore,in Eq.(3),whenEz,d=1,ERz,d=S_z,d^min,notDRz,d.WhenDRz,d<S_z,d^min, energysavingistheamountof solarenergy producedbyDRz,d. Thus,ERz,d=DRz,dinEq.(3)whendaydisnotanE-day.TheESRz

valueisthenthesumofallERz,dvaluesinastudyyear.

Fig.3comparesthemonthlyESRsfordifferentregions.TheESR insummerisnotsignificantlyhigherthanthatforotherseasonsin theARandHRregions.Althoughsolarradiationishighinsummer, energysavingsforheatingwaterarelowasthetemperatureoftap waterinsummerisalsohigh.Inwinter,relativelymoresolar radia-tionisneededtoheatwatertothedesiredtemperature.Therefore, almostallsolarradiationinwinterisutilizedtoheatwater,and sur-plussolarradiationinsummercannotresultinadditionalenergy savings.Thus,thebenefitsofSWHsinwintermaynotbelessthan thoseinsummer.

SI MR

HR AR

0 1000 2000 3000 4000 5000

Annual ESR (MJ/m2)

0 0.2 0.4 0.6 0.8 1

Ratio of ESR / total solar radiation

Annual ESR Ratio of ESR

Fig.4.AnnualESRsandratiosofESRtototalsolarradiationindifferentregions.

Fig.4showstheannualESRsandratiosofESRtototalregional solarradiationindifferentregions.Althoughtotalsolarradiation intheARregionexceedsthatintheHRregion,theirESRvaluesare similarat4522and4194MJ/m²,respectively,becausetheESRratio (82%)intheARregionislowerthanthat(89%)fortheHRregion.