Effective solar radiation based benefit and cost analyses for solar water heater development in Taiwan

ContentslistsavailableatSciVerseScienceDirect

Renewable

and

Sustainable

Energy

Reviews

jo u r n al h om ep ag e :w w w . e l s e v i e r . c o m / l o c a t e / r s er

Effective

solar

radiation

based

benefit

and

cost

analyses

for

solar

water

heater

development

in

Taiwan

Tze-Chin

Pan

_,

_Jehng-Jung

_Kao

_,

_Chih-Po

_Wong

a_{InstituteofEnvironmentalEngineering,NationalChiaoTungUniv.,Hsinchu30010,Taiwan,ROC}

b_{DegreeProgramofEnvironmentalTechnologyforSustainability,NationalChiaoTungUniv.,Hsinchu30010,Taiwan,ROC}

a

r

t

i

c

l

e

i

n

f

o

Articlehistory:

Received1May2011

Accepted5January2012

Available online 18 February 2012 Keywords:

Solarwaterheater(SWH)

Effectivesolarradiation

Benefit–costanalysis

Solarenergy

Sustainableenvironmentalsystems

analysis

a

b

s

t

r

a

c

t

Toreducegreenhousegasesemissions,promotingsolarwaterheaters(SWHs)hasbecomean essen-tialnationalpolicyinTaiwan.Toimplementthispolicyeffectively,theapplicabilityofSWHsindifferent regionsmustbeanalyzed.PreviousstudiesgenerallyperformedSWHbenefit–costanalysesbasedontotal annualsolarradiation;however,thismethodmayoverestimateenergyproductionbenefitsbecause,for anSWH,thesolarenergycapturedtodaycannotbepreserved.Therefore,thisstudyproposesthe con-ceptofeffectivesolarradiation(ESR),whichisbasedonpotentialheatoutputestimatedusingtapwater temperatureandsolarradiationineachregion.ThebenefitsofSWHsarethenassessedbasedonthe numberofeffectivedaysandESR,insteadofusingtotalannualsolarradiation.Aprocedureisestablished toevaluatetheapplicabilityofSWHsineachregionbasedonproposedbenefit–costanalyses.Possible outcomesofanationalSWHprogramareestimated.Thesensitivitiesofessentialfactors,including col-lectorefficiency,installationcost,anddiscountrate,arealsoanalyzed.Analyticalresultsshowthatthe ratiosofESRtototalannualsolarradiationforregionsinTaiwanareabout82–89%.Thepaybackperiods varyat6–15yearsfordifferentregionsandheatertypesbeingreplaced.Thenationalprogramisexpected toreducegreenhousegasesemissionsbyapproximately150,000tonseCO2annually.

© 2012 Elsevier Ltd. All rights reserved.

Contents

1. Introduction... 1875

2. Studyarea... 1875

3. Effectivedayandeffectivesolarradiation... 1875

3.1. AnnualE-dayratio ... 1875

3.2. Annualeffectivesolarradiation... 1877

4. Benefitanalysis ... 1878

4.1. Costsavingfromreplacingconventionalenergies ... 1878

4.2. CostavoidedforGHGsandpollutionmitigation... 1878

5. Costanalysis ... 1879

6. Paybackperiodanalysis... 1879

7. NationalSWHprograminTaiwan... 1880

7.1. Nationwidebenefitandcost... 1880

7.2. Governmentalsubsidyvs.associatedbenefits... 1880

8. Sensitivityanalysis... 1881

9. Conclusion ... 1882

Acknowledgment... 1882

References... 1882

Abbreviations:SWH,solarwaterheater;ESR,effectivesolarradiation;E-day,effectiveday;GHGs,greenhousegases;TSP,totalsuspendedparticles;LPG,liquefied

petroleumgas;AR,abundantradiation;HR,highradiation;MR,moderateradiation;SI,smallisland.

∗ Correspondingauthor.Tel.:+88635731869;fax:+88635731759.

E-mailaddress:jjkao@mail.nctu.edu.tw(J.-J.Kao).

1364-0321/$–seefrontmatter © 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Taiwan imports 99% of its energy [1], and emissions of greenhousegases(GHGs)percapitamarkedly exceedtheglobal average.Therefore,thedevelopmentofrenewableenergies,such as solar energy, has become a national policy in Taiwan [2]. However, the amount of solar radiation varies among regions inTaiwan.For example,theamountofsolarradiationin south-ern Taiwan is roughly 1.5 times higher than that in northern Taiwan [3]. Therefore, the applicability and potential benefits of solar water heaters (SWHs) in different regions must be analyzed.

Severalstudies (e.g., Haralambopoulos et al. [4]; Diakoulaki etal.[5];Kaldellisetal.[6])evaluatedtheapplicabilityofvarious SWHdevelopmentprogramsbasedonbenefit–costanalyses,and solarradiationwasthemajorfactorconsideredbythesestudies. Totalannualsolarradiationwasusedtoestimateenergy produc-tionbenefit.However,for anSWH,since solarenergycaptured today cannot generally be stored for later use [4], an analysis based ontotal annual solarradiation mayoverestimate energy productionbenefit.Forinstance,anSWHwithatankvolumeof 250Land4m2 _{collectorsurfacerequiresapproximately16MJof} solarradiationtoheat water to55◦C [7]when tap-water tem-perature is 25◦C and collector efficiency is 50%. If actualsolar radiationtodayis20MJ,thesurplussolarradiationof4MJ can-notbesavedunlessanadditionalwatertankorstoragebattery is installed. However, an additional tank or battery is gener-allynot cost-effectivefor an SWH.Anenhanced methodbased onrequired dailysolar radiationand number of SWHeffective days is applied in this study to improve benefit–cost analy-ses.

Furthermore,ambienttemperaturevariessignificantlyin dif-ferent months and regions, as does the temperature of tap water. For example, water temperature in winter is low and heating this water requires more solar radiation than in sum-mer.Thus, theamountofdailysolarradiation requiredtoheat water to a desired temperature varies. Most previous studies didnotconsidertemperaturevariations,andtheproposedSWH benefit–costanalysismethodisthusmodifiedfurthertoconsider thisvariation.InadditiontoanalyzingtheapplicabilityofSWHs basedontheproposedbenefit–costanalyticalmethod, identify-ing potential environmentalbenefits is necessary for assessing a regionalSWHprogram. Since SWHs canreduce consumption of other energies, such as electricity, fossil fuels, and natu-ral gas, the potential environmental benefits of SWHs include reductionsinemissionsofGHGs,NOx,andtotalsuspended par-ticles(TSP)[5,8,9],generatedbyreplacedenergies,subsequently reducing external costs incurred for these pollutantemissions. Estimatingpotentialenvironmental benefitsis therefore neces-sary when analyzing thetrue benefits and costs of developing SWHs.

The benefits and costs for implementing Taiwan’s national SWH program are assessed. The sensitivities of the effects of major variables, such as collector efficiency, installation cost, and discount rate, are also analyzed and compared. Study results will help policy-makers determine how the effective solar radiation, regional characteristics, and other variables affect the applicability, benefits, and costs for a national SWH program.

Theremainderofthispaperisorganizedasfollows.Thestudy areais firstintroduced, andthe SWHregionis then described. Next,theproposedeffectivedayandeffectivesolarradiation(ESR) areexplained.HowtoestimateSWHbenefits,costs,andthe pay-backperiod is described and used to assess thenational SWH program. Finally, sensitivityanalyses ofvarious parameters are presented.

2. Studyarea

SincetheTropicofCancercrossessouth-centralTaiwan,solar radiation inTaiwan is considerable,and Taiwanis a good can-didatefor SWHs.However,asTable1lists,significantvariation existsintheamountofsolarradiationindifferentregions,suchthat theapplicabilityofSWHsindifferentregionsvariestoo. Appropri-ateregionaldivisionisthusneededtofacilitateplanningofSWH developmentstrategies.Furthermore,thedifferencebetweensolar radiationinbothJulyandDecemberisalsosignificant.Therefore, seasonalsolarradiationvariationsmustbeconsideredwhen ana-lyzingtheapplicabilityofaregionalSWHprogram.

Haralambopoulosetal.[4]andKaldellisetal.[6]dividedregions inGreecebasedprimarilyontheamountofsolarradiation. How-ever,regionsdividedbasedontheamountofsolarradiationmay notmatchadministrativeboundariesandmaycausedifficultiesin SWHprogramsbecauseanSWHdevelopmentpolicyrequiresthe participationoflocalgovernments.Therefore,thisstudydelineated regionsbasedonboththeamountofsolarradiationandthe admin-istrativeboundaries.AslistedinTable1,Taiwanisdividedintofour regions:theabundantradiation(AR)region,thehighradiation(HR) region,themoderateradiation(MR)region,andthesmallisland(SI) region.

3. Effectivedayandeffectivesolarradiation

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]. Smin

z,d =

V·Ds·H·tz,d

SWH·A (1)

whereSmin

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₎

Meandailysolar radiation(MJ/m2₎ July December Abundantradiation (AR) 5000–6000 TC 5286 18.4 12.3 CY 5857 19.7 13.1 KS 5174 17.7 10.6 PD 5093 16.7 10.9 TD 5551 23.1 10.5 Highradiation(HR) 4000–5000 HC 4433 19.2 8.3 NT 4262 14.7 10.9 TN 4961 16.9 10.6 Middleradiation(MR) 3000–4000 TP 3841 15.7 7.3 IL 3758 19.2 5.6 HL 3953 21.0 7.9

Smallisland(SI) 3000–5000

KM 4624 18.8 9.3

PH 4080 17.8 8.1

MT 3973 18.8 7.0

istemperaturedifference(◦C)betweenthehotwaterheatedbyan SWHandtapwaterondayd;SWHiscollectorefficiencyofanSWH; andAissurfaceareaofasolarcollector(m2_).

Whenavailablesolar radiation onone dayexceeds Smin

z,d, an

SWHcanheattapwatertothedesiredtemperature,andthedayis regardedasanE-day.Sincesolarradiationvariesamongregions, thenumberofeffectivedaysalsodiffersamongregions.Theannual E-dayratioisthencalculatedusingthefollowingequation:

For DRz,d>Sminz,d, Ez,d=1, For DRz,d<Sminz,d, Ez,d=0, REz=



whereDRz,dissolarradiationondaydforregionz;Ez,disabinary variableindicatingwhetherdaydinregionzisanE-day;REzisthe annualE-dayratioinregionz;andYisthenumberofdaysinastudy year(usually365days).E-daysarethosedaysonwhichanSWH providessufficienthotwaterusingonlysolarenergy.Theannual E-dayratioisanusefulindexwhenassessingtheapplicabilityof SWHsindifferentregions.TheSmin

z,d valueisestimatedforatypical familySWHwitha250-Lstoragetankproviding55◦Cwater.The solarcollectorsurfaceareais4m2_{andcollectorefficiencyis50%,} theminimumacceptableefficiencyin Taiwan[12].Regionaltap watertemperaturesareestimatedbasedondataobtainedbyChang [13].Fig.1showstheSmin

z,d valuesforthetypicalSWHindifferent

12 11 10 9 8 7 6 5 4 3 2 1 Month 12 14 16 18 20 Minimum required solar radiation (MJ/m 2) AR HR MR SI

Fig.1.Minimumrequiredsolarradiationfordifferentregions.

monthsandregionsinTaiwan.TheSmin

z,d valueinwinterishigher 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 MR HR AR Region 0 0.2 0.4 0.6

Annual E-day ratio

(a)

Monthly E-day ratio AR

HR MR SI

(b)

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

12 11 10 9 8 7 6 5 4 3 2 1 0 200 400 600 Solar radiation (MJ/m 2)

(a)

(b)

(c)

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 Smin

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=Smin z,d,

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

ESRz= Y





whereERz,disESRondaydinregionz;ESRz istheannualESRin regionz;andRESRzistheratioofESRtototalsolarradiationin regionz.WhendaydisanE-dayandDRz,d>Smin

z,d,surplussolar radiationdoesnotprovideadditionalenergysavings.Therefore,in Eq.(3),whenEz,d=1,ERz,d=Smin

z,d,notDRz,d.WhenDRz,d<Sz,dmin, 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

/m

)

Rat

io

of ESR

/

to

ta

l s

o

la

r radia

ti

on

Fig.4.AnnualESRsandratiosofESRtototalsolarradiationindifferentregions.

Fig.4showstheannualESRsandratiosofESRtototalregional solarradiationindifferentregions.Althoughtotalsolarradiation intheARregionexceedsthatintheHRregion,theirESRvaluesare similarat4522and4194MJ/m2_{,respectively,becausetheESRratio} (82%)intheARregionislowerthanthat(89%)fortheHRregion.

4. Benefitanalysis

ThebenefitsofanSWHincludecostsavingsbyreplacing con-ventionalenergiesandpollutionmitigation[14].Thecostsavings from replacing conventional energies can be estimated by the amountofeffectiveenergygeneratedunderannualESRandthe priceofreplacedenergies.Costsavingsduetopollutionmitigation aredeterminedbasedonthereductionintheamountofGHGsand airpollutants.ThedetailsoftheSWHbenefitanalysisareasfollows.

4.1. Costsavingfromreplacingconventionalenergies

TheenergysavingsbySWHsfordifferentregionsinTaiwanare estimatedbythefollowedequation:

BEz=ESRz×A×SWH (6)

CBEfz=_HVfBEz_×f ×EPf (7)

whereBEzistotalenergyreductioninregionz;CBEfziscost sav-ingsfromenergysourcef (e.g.,electricity,diesel,naturalgas,and liquefiedpetroleumgas(LPG))inregionz;HVfistheheatingvalue ofenergysourcef;f istheheatingefficiencyofenergysourcef; andEPfistheunitpriceofenergysourcef.InEq.(6),totalenergy reductionistheeffectiveenergygeneratedbyanSWH.The mone-tarybenefitofreplacingconventionalenergiesisdeterminedusing Eq.(7).

Table2liststotalenergyreductionandcostsavingsbyreplacing conventionalenergiesforafamilySWH,basedontheheatingvalue, heatingefficiency,andenergypriceinTable3[1,15–19].SinceESR isthemajorfactoraffectingtotalenergyreduction,total energy reductionsintheARandHRregionsaremarkedlyhigherthanthat intheMRregion.Thepriceofdieselhasincreasedinrecentyears, andheatingwater withdieselis expensive.Therefore, usingan SWHtoreplaceadieselheatingsystemcansavemorethanwhen replacingwaterheatersfueledwithotherenergies.

Fig.5. (a)Pollutantreductionsand(b)costavoidedforreducingGHGsandpollutant

emissionsfordifferentenergiesintheARregion.

4.2. CostavoidedforGHGsandpollutionmitigation

Eqs.(8)and(9)estimatereductionsinpollutantsemittedbya conventionalenergyandthecostsavingbypollutionmitigation, respectively. BPfp,z= BEz HVf×f ×EF f p (8) CBPzf=



whereBPfp,zisthereductioninairpollutantp(e.g.,GHGs,TSP,NOx, andSOx)whenreplacingenergysourcefbyanSWHinregionz;EF_if istheemissionfactorofairpollutantpforconventionalenergyf; CBPzistotalcostavoidedbyreducingGHGsandpollutantemissions inregionz;andTEpisthecostavoidedfortreatingpollutantp.

Table3liststheemissionfactorsforeachpollutantfromfour conventional energies—electricity, diesel, natural gas, and LPG. Fig.5(a)shows thebenefit of pollutionmitigation byreplacing differentenergies.Roughly40%oftheelectricityinTaiwanis gener-atedbycoal-firedplants[1].Coal-firedplantsgenerallyemitmore pollutantsthanotherpowerplants.Therefore,replacingelectricity hasthelargestpollutionemissionreduction.Localcostsfor reduc-ing1metrictonofGHGs,TSP,NOx,andSOxareroughlyNT$800, NT$15,365,NT$26,985,andNT$26,242,respectively[20].Although theunitcostofGHGsremovalissignificantlylowerthanthosefor

Table2

Totalenergyreductionandcostsaving.

Region Totalenergyreduction(MJ) Costsaving(NT$)

Electricity Diesel Naturalgas LPG

AR 9044 7481 8842 4400 5281

HR 8388 6939 8200 4081 4898

MR 7112 5883 6953 3460 4153

SI 7938 6566 7761 3862 4635

Table3

Datafordifferentenergysources.

Source Heatingvalue[15] Heatingefficiency [16]

Price(2007)[1] Emissionfactor e[19]

eCO2[16] TSP[17] NOx[17] SOx[17]

Electricity 860kcal/kWh 90% 2.68NT$/kWh 660g/kWh 0.022g/kWh[18] 0.292g/kWh[18] 0.344g/kWh[18] 1.47%

Diesel 8400kcal/L 80% 27.5NT$/L 2700g/L 0.24g/L 0.24g/L 0.0009g/L 9.71%

Naturalgas 8900kcal/m3 _{80% 14.5NT$/m}3 _2100g/m3 _0.179g/m3 _1.50g/m3 _0.0096g/m3 _8.86%

LPG 6700kcal/L 80% 13.1NT$/L 1740g/L 0.054g/L 1.74g/L 0.391g/L 8.30%

otherpollutants,total costreduction forGHGs, asillustratedin Fig.5(b),isthehighestbecausethereductioninGHGsemissions islarge.

5. Costanalysis

ToassesstheapplicabilityofTaiwan’snationalSWHprogram,a costanalysiswasfirstimplemented.Thefollowingequations, sim-ilartothoseusedbyKaldellisetal.[6],areappliedtoestimatethe annualcostofanSWH. AC=(FC+MC−S)·











whereACistheannualcostofanSWHfornoperatingyears;FCis initialinstallationcost;MC iscurrentvalueoftotalmaintenance cost;Sis thegovernmentsubsidy; iis thediscountrate;MR is annualmaintenancecost;fisaverageinflationrate;mistheratio ofannualmaintenancecosttoinitialinstallationcost;and˛isthe subsidyratebasedoncollectorarea.

InEq.(10),annualcostofanSWHisestimatedbasedoninitial installationcost,totalmaintenancecost,andthegovernment sub-sidy.Eq.(11)determinesthecurrentvalueoftotalmaintenance costbasedonannualmaintenancecost,withanannualincrease rateequal totheaverageinflation rateand localdiscount rate. Annualmaintenancecostisassumedtobeafixedfraction(m)of initialinstallationcost,asinEq.(12).InTaiwan,thegovernment subsidyisbasedonthesurfaceareaofasolarcollector.Therefore, Eq.(13)determinesthesubsidyamountbymultiplyingthesubsidy ratebythesurfaceareaofasolarcollector.

ForafamilySWHinTaiwan,typicalinstallationcostisroughly NT$66,000;annualmaintenance costis about3%ofinstallation cost;nationaldiscountrateis1.86%;andtheinflationrateis1.08%. Sincea subsidyis aneffectivepolicytool inducing residentsto installanSWH,threesubsidyratesarecompared.Thefirstsubsidy rateiszero,andthesecondis2250NT$/m2_{,whichisthecurrent} subsidyrateinTaiwan.Somelocalgovernmentshaveraisedthe subsidyrateto4500NT$/m2_{,whichisthethirdrate.}

SincetheSWHsinstalledinTaiwan’sfourregionsaresimilar, theSWHcostsforthefourregionsareassumedthesame.Fig.6

comparesannual costs of anSWH withdifferent subsidyrates andyearsofoperation.TheannualcostsforanSWHoperatingfor 6–15yearsare20–10%ofthatforanSWHoperatingforonly1year. Therefore,ensuringthatanSWHcanoperateforatleast6yearsis essential;otherwise,anSWHmaynotbecost-effective. Further-more,annualcostsanddifferencesinannualcostswithdifferent subsidyratesdecreaseastheoperatingperiodincreases.Payback periodsofanSWHwithdifferentsubsidyratesareestimatedand discussedinthenextsection.

6. Paybackperiodanalysis

ThepaybackperiodisthedurationrequiredforanSWH invest-menttopayforitself,andcanbeusedtomeasuretheeconomic feasibilityofinstallinganSWH[21,22].Thepaybackperiodis deter-minedbycomparingannualcostandannualbenefitforanSWH. Asmentioned,annualcostofanSWHcanbederivedbyEq.(6). Annualbenefit,asdeterminedbythecostsavingbyreplacinga

15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

Number of operating years 1

10 100

Annual cost and benefit (NT$ 1,000)

No subsidy NT$2,250/m NT$4,500/m Electricity Diesel Natural gas LPG

Fig.6. Annualcostsandbenefitsforvariedsubsidyrates,replaceddifferentenergies,

conventionalenergy,canbeestimatedbyEq.(14),whichissimilar totheequationusedbyKaldellisetal.[6].

ABfz=CBEfz×













whereABfzistheannualcostsavingbyreplacingenergyfinregionz; CBEfz,derivedbyEq.(7),isthecostsavingbyreplacingenergysource f;eistheannualrateofmarketpricechangeforareplaced con-ventionalenergy;andnisthenumberofSWHoperatingyears.The annualcostandannualbenefitvaryfordifferentoperatingyears. Andthepaybackperiodequalstheoperatingyearsinwhichannual benefitisequaltoorgreaterthanannualcost.

Fig.6showsannualcostswithdifferentsubsidyratesandthe annualcostsavingbyreplacingdifferentenergieswithatypical SWHinstalledintheARregion.AsshowninFig.6andTable2, thecostsavingofreplacingdieselishigherthanthatofreplacing otherconventionalenergiesbecausethedieselpricehasincreased substantiallyinrecentyears.Theannualbenefitofreplacing elec-tricityduringthefirstfewyearsishigherthanthatofreplacingLPG andnaturalgas.However,sincethepriceofelectricityiscontrolled bythegovernmentanddoesnotincreasesignificantly,themarket pricechangerate,e,forelectricity,aslistedinTable3,issmaller thanthatofotherenergies.After14or10years,theannualbenefit ofreplacingelectricityislowerthanthatofreplacingLPGornatural gas.

Theintersectionoftheannualcostandannualbenefitcurvesis thepaybackperiod.Sinceenergygeneratedbydieselperdollaris lowerthanthatbyotherenergies,thecostsavingfordieselishigher thanthoseforotherenergies,andthepaybackperiodofdieselis shortest.Ifthepriceofdieselremainshigh,thegovernmentshould encouragethoseusingdieselheatingsystemstoinstallanSWH.

Sincethepaybackperiodmarkedlyinfluencesresident willing-nesstoinstallSWHs,subsidiesarefrequentlyprovidedtoshorten thepaybackperiodandincreaseincentivetoadoptSWHs.AsFig.6 shows,intheARregionwithoutasubsidy,thepaybackperiodfor replacinganelectricitywater heateris 13years.Whenthe sub-sidyrateisNT$2250/m2_{,thepaybackperiodis11years,betterthan} thatforreplacinganaturalgaswaterheater.Ifthesubsidyrateis increasedtoNT$4500/m2_{,thepaybackperiodisreduced} signifi-cantlyto9years,whichisclosetothatforreplacinganLPGwater heater.Table4liststhepaybackperiodsforthefourregionsunder asubsidyrateofNT$2250/m2_{.Thepaybackperioddecreasesas} theamountofsolarradiationincreases.Mostpaybackperiodsare 11–13years,excludingthoseforreplacingelectricityandnatural gaswaterheatersintheMRregion.Thoseforreplacingdieselwater heatersareonly6–8yearsbecausethepriceofdieselandits mar-ketpricechangeratearebothhigh.Thecostsavingforreplacing electricityinthefirstyearishigherthanthoseforreplacingnatural gasandLPG.However,thepaybackperiodforreplacing electric-ityisnotshorterthanthoseforreplacingdieselandLPGbecause thelocalmarketpricechangerate,e,forelectricityissmallerthan thoseforotherenergies.

7. NationalSWHprograminTaiwan

ToachieveenergyindependenceandreduceGHGsemissions, the government implemented a national program called the NationalScienceand TechnologyProgramfor Energy[23]; pro-motingSWHuseisoneoftheprogram’sprimarytasks.Thegoal oftheprogramistoassist150,000householdsininstallingSWHs during2010–2014.ThetypicalsurfaceareaofahouseholdSWH solarcollectoris4m2_{and,thus,approximately600,000m}2_ofsolar collectorswill beinstalled duringthis 5-yearperiod. Analyzing expectedcostandbenefitsofSWHinstallationisessentialwhen

evaluatingtheeffectivenessofthisnationalprogram.Thebenefits ofinstallingSWHsvarymarkedlyasregionshavedifferentamounts of solar radiation. The probable SWH distribution is estimated basedonhistoricaldataofSWHinstallation[24],salesvolumeof conventionalheaters[25],andtheratioofconventional heaters replacedbySWHsindifferentregionsinTaiwan,aslistedinTable5. Programeffectivenessisevaluatedusingtwoapproaches.First, nationwide benefit and cost of theprogram are estimated and analyzed for overall effectiveness. Second, government invest-ment,includingsubsidy,iscomparedwithpublicbenefitgained byreducingpollutantandGHGsemissions.Thesetwoapproaches aredescribedinthefollowingsections.

7.1. Nationwidebenefitandcost

Toanalyzenationwidebenefitandcost,totalannualcostsaving fromreplacingconventionalenergiesandthecostofinstallingand maintainingSWHsareestimatedandcompared.Totalannualcost savingfromreplacingaconventionalenergyinregionz,TABz,is determinedbyEq.(15).

TABz=PA·RIz·



(ABfz·Hfz) (15)

wherePAisthetotalestimatedareaofallSWHsolarcollectors installedundertheprogram,600,000m2_{;RIz isthenationalratio} ofSWHsinstalledinregionz,aslistedinTable5;ABfzistheannual benefitofcostsavingfromreplacingenergyfinregionz,as deter-minedbyEq.(14);andHzf istheratioofinstalledSWHcollectors replacingheatersthatuseenergyfinregionz.

In addition to the cost saving of replacing a conventional energy,pollutionmitigationisanessentialSWHbenefit.Theannual amountofpollutionmitigated,TBPz,andannualcostavoidedfor reducingGHGsandpollutantemissions,TAPz,arecalculatedbythe followingequations;whereBPfp,zisGHGsandairpollutant emis-sionreductions,asdeterminedbyEq.(8).

TBPp,z=PA·RIz·





Althoughasubsidyisapolicycostfortheprogram,itismainlya monetarytransferoffundsfromthegovernmenttoaresidentandis notacostofinstallingSWHs.Thesubsidyisthereforenotincluded whenestimatingnationalannualcost.

For15operatingyears,theannualcostsavingsfromreplacing conventionalenergy(TABz)plusthecostavoidedtoreduceGHGs andpollutantemissions(TAPz)isNT$1534 million.Accordingto theestimatedcostsavingsandcostforimplementingthenational SWHprogram,thenetbenefitfortheprogramisapproximately NT$449million.AsillustratedinFig.7,withoutconsideringcost ofreducingGHGsandpollutantemissions,theprogrampayback periodis12years.Byconsideringtheseavoidedcosts,thepayback isreducedto11years.

7.2. Governmentalsubsidyvs.associatedbenefits

Evaluating the effectiveness of the program and analyzing whetherbenefitsgainedfromprogramimplementationexceedits costsareimportant.Theprimarycostofprogramimplementation isthesubsidyprovidedtoresidentswhoinstallSWHs.Thissubsidy ispaidatthetimeatwhichanSWHisinstalled.Thecurrentsubsidy rateis2250NT$/m2_{.Approximately600,000m}2_{ofSWHcollectors} willbeinstalledundertheprogramand,thus,thetotalamountof subsidiesisNT$1350million.

Table4

PaybackperiodsunderthesubsidyrateofNT$2250/m2_{forreplacingdifferentenergiesindifferentregions.}

Region Paybackperiod(year)

Electricity Diesel Naturalgas LPG

AR 11 6 12 11

HR 12 7 13 11

MR 15 8 15 13

SI 13 7 13 11

Table5

TheSWHinstallationratiosandratioforreplacingdifferentconventionalheatersindifferentregions.

Region(z) Installationratio(RIz) Ratioforreplacingtraditionalheater(Hfz)

Electricity Diesel Naturalgas LPG

AR 47.6% 32.56% 3.87% 14.02% 49.55%

HR 42.0% 33.26% 1.89% 20.21% 44.64%

MR 10.1% 31.65% 6.63% 27.26% 34.45%

SI 0.2% 23.29% 31.54% 0.00% 45.17%

ThemajorpublicbenefitofSWHsisreducingGHGsand pollut-antemissions.Sincethisbenefitisestimatedannually,theinitial one-timesubsidyis converted intoan annualvalue forease of comparison.Theannualizedsubsidyandannualcostavoidedfor reducingGHGsandpollutantemissionswithdifferentoperating yearsforSWHsarecomparedinFig.8.IfanSWHoperatingperiod exceeds12years,thepublicbenefitoftheprogramexceedsthe subsidy.

8. Sensitivityanalysis

Since someparameters usedin this study, suchascollector efficiency,installationcost, anddiscountrate,maychangewith technicaloreconomicdevelopmentsandsignificantlyalter assess-mentresults.Thesensitivityanalysisisthusimplemented,aslisted inTable6.TheminimumacceptedcollectorefficiencyofanSWH is50%in Taiwan[12].Accordingtoasolarratingand certifica-tionreport[26],collectorefficienciesforsomeSWHsexceed80%. Thus,netbenefitswithcollectorefficienciesof50%,65%,and80% areanalyzed. Thepriceofan SWHvaries; thecurrentrange in

15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

Number of operating years

100 1000 10000 100000

Annual cost and benefit (million NT$)

Annual cost

Cost saving for replacing tradiational energies Cost avoided for reducing GHGs and pollutants emissions Total benefits

Fig.7. AnnualcostandbenefitsofimplementingthenationalSWHprogram.

15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

Number of operating years

0 500 1000 1500

Annualized subsidy and benefit

(Million NT$)

Annualized subsidy

Annual cost avoided for reducing GHGs and pollutants emissions

Fig.8. Annualizedsubsidyvs.annualbenefitfordifferentSWHoperatingyears.

TaiwanisroughlyNT$40,000–89,000,andthetypicalpriceisabout NT$66,000. Therefore, the prices of NT$66,000, NT$46,200, and NT$85,800,whichare1,0.7,and1.3timesthetypicalprice, respec-tively,areanalyzed.Thediscountratesinlastfewyearsvariedat 1.25–3.62%[27].Therefore,discountratesof1%,1.86%,and3%are analyzed.

ThenetannualbenefitslistedinTable6arenationwide ben-efitsestimatedwithanoperatinglifetimeof15years.Asheating efficiencyincreasesby15%from50%to65%,netannualbenefit increasesroughly38%.However,ascollectorefficiencyincreasesby 30%from50%to80%,netannualbenefitincreasesonly19%because for E-days, as the extra energy from increasing collector effi-ciencycannotcontributesignificantlytobenefits.Ifonlycollector

Table6

Sensitivityanalysisofcollectorefficiency,installationcost,andthediscountrate.

Parameter Values Netannualbenefit

(millionNT$) Collectorefficiency 50% 449 65% 614 80% 700 Installationcost(NT$) 46,200 775 66,000 449 85,800 123 Discountrate 1.00% 511 1.86% 449 3.00% 365

efficiencyisimproved, thenetbenefitdoesnot increase signif-icantly.However, as collectorefficiency increases,the required collectorsurfaceandassociatedinstallationcostlikelydecline sig-nificantlyalthough predictingthiscost reduction isdifficult.As installationcostdeclinesby30%,theannualnetbenefitcanincrease about73%.Therefore,thegovernmentshouldencourageSWH man-ufacturerstodeveloplow-costSWHstoincreasebenefit.Moreover, thelowdiscountratecanincreasenetbenefitandisadvantageous forSWHdevelopment.

9. Conclusion

Sincesolarradiationcapturedtodaycannotbeusedlater,the conventionalmethodthatusestotalannualsolarradiationmay overestimatetheenergyproductionofanSWH.Thisstudythus proposedtheESRandE-daysbasedontapwatertemperatureand solarradiationtoimprovetheSWHenergysavingestimation.Total annualsolarradiationintheARregionismarkedlyhigherthanthat inotherregions;however,theESRvaluesoftheARandHRregions aresimilar.FortheARregion,theratioofESRtototalannualsolar radiationisabout82%.IftheSWHenergyproductionisestimated basedontotalannualsolarradiation,SWHenergyproductionwill beoverestimatedby18%.TheproposedESRisexpectedtoimprove theestimation.

TwomajorbenefitsofinstallingSWHsareassessed.Oneisthe costsavinggeneratedbyreplacingconventionalenergies,andthe otherisavoidingthecostsassociatedwithreducingGHGsand pol-lutantemissions.Thecostsavingofreplacingconventionalenergies isroughly11timesthecostavoidedtoreduceGHGsandpollutant emissions.ThepaybackperiodsofanSWHindifferentregionsare alsodetermined.AlthoughtotalannualsolarradiationintheAR regionismarkedlyhigherthanthatintheHRregion,thepayback periodsintheARandHRregionsareclosebecausetheESRsin bothregionsaresimilar.ThepaybackperiodforanSWH replac-ingadieselheateris6–8years,significantlyshorterthanthosefor replacingwaterheaterspoweredbyotherconventionalenergies becausetheprice/heatunitofdieselishigherthanthoseofother conventionalenergies.

The annual net benefit for the national SWH development program is approximately NT$449 million. Additionally, GHGs emissionscanbereducedbyapproximately150,000tonsyearly. BycomparingsubsidycostandthebenefitofreducingGHGsand pollutant emissions, the payback period for the national SWH development program is roughly 13years. Increasing collector efficiencycanreducetheminimumrequiredsolarradiationand increasethenumber ofE-days. However,theadditional benefit gainedbyincreasingthecollectorefficiencyfrom65%to80%isless thanthatfrom50%to65%becausetheadditionalenergygenerated onE-dayscannotresultinadditionalbenefit.

Acknowledgment

TheauthorswouldliketothankNationalScienceCouncilofthe Republicof China,for providingpartialfinancial supportof this studyunderContractNo.NSC99-2221-E-009-039.

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