Tadeua, Carlos Henggeler Antunesc,d

(1)

ContentslistsavailableatScienceDirect

Sustainable

Cities

and

Society

j o u r n a l ho me p a g e :w w w . e l s e v i e r . c o m / l o c a t e / s c s

A

comparison

between

cost

optimality

and

return

on

investment

for

energy

retrofit

in

buildings-A

real

options

perspective

Sérgio

Fernando

Tadeu

a,∗

_,

_Rafael

_F.

_Alexandre

b,1

_,

_António

_J.B.

_Tadeu

a

_,

Carlos

Henggeler

Antunes

c,d,2

_,

_Nuno

_A.V.

_Simões

a

_,

_Patrícia

_Pereira

_da

_Silva

d,e,3

a_Department_of_Civil_{Engineering–FCTUC,}_University_of_Coimbra,_Rua_Sílvio_Lima–Pólo_II,_3030-790_Coimbra,_Portugal b_Department_of_Computer_and_Systems,_Federal_University_of_Ouro_Preto,_Rua_37,_115,_35931-008_João_Monlevade,_Brazil c_Department_of_Electrical_and_Computer_{Engineering–FCTUC,}_University_of_Coimbra,_Pólo_II,_3030-290_Coimbra,_Portugal d_INESC_Coimbra,_Rua_Antero_de_Quental,_199,_3030-030_Coimbra,_Portugal

e_Faculty_of_Economics,_University_of_Coimbra,_Av._Dias_da_Silva,_165,_3004-512_Coimbra,_Portugal

a

r

t

i

c

l

e

i

n

f

o

Articlehistory:

Received7July2015

Receivedinrevisedform

11November2015

Accepted13November2015

Availableonline28November2015

Keywords:

Costoptimality

Realoptions

Energyretrofit

Geneticalgorithms

Sustainablebuildings

a

b

s

t

r

a

c

t

EuropeanUnion(EU)regulationsaimtoensurethattheenergyperformanceofbuildingsmeetsthe cost-optimalitycriteriaforenergyefficiencymeasures.ThemethodologicalframeworkproposedinEU DelegatedRegulation244isaddressedtonationalauthorities(notinvestors);theoptimalcostlevelis calculatedtodevelopregulationsapplicableatdomesticlevel.Despitethecomplexityandthelarge num-berofpossiblecombinationsofeconomicallyviableefficiencymeasures,therealoptionsforimproving energyperformanceavailabletodecisionmakersinbuildingretrofitcanbeestablished.Ourstudy con-sidersamulti-objectiveoptimizationapproachtoidentifytheminimumglobalcostandprimaryenergy needsof154,000combinationsofenergyefficiencymeasures.Theproposedmodelissolvedbythe NSGA-IImulti-objectiveevolutionaryalgorithm.Asaresult,thecost-optimallevelsandareturnoninvestment approacharecomparedforasetofsuitablesolutionsforareferencebuilding.Eighteencombinationsof retrofitmeasuresareselectedandananalysisoftheinfluenceofrealoptionsoninvestmentsisproposed. Weshowthatasoundmethodologicalapproachtodeterminingtheadvantagesofthistypeofinvestment shouldbeofferedsothatMemberStatescanprovidevaluableinformationandensurethattheminimum requirementsareprofitabletomostinvestors.

1. Introduction

FollowingtheEnergyPerformanceofBuildingsDirective(EPBD)

(EPBD, 2010), MemberStates shall complywith theDelegated Regulation244/2012(EU,2012)tocalculatethecostofenergy

effi-ciencymeasuresappliedtoreferencebuildingsovertheestimated

economiclifecycle.Commoninformation,suchaslong-term

esti-matesofcarbonpricesandtheevolutionofenergyprices(expected

∗_{Corresponding}_author._Tel.:₊₃₅₁_913734586.

E-mailaddresses:sergio.tadeu@itecons.uc.pt(S.F.Tadeu),

rfalexandre@decea.ufop.br(R.F.Alexandre),tadeu@itecons.uc.pt(A.J.B.Tadeu),

ch@deec.uc.pt(C.H.Antunes),nasimoes@itecons.uc.pt(N.A.V.Simões),

patsilva@fe.uc.pt(P.P.d.Silva).

URLs: http://www.uc.pt/fctuc/dec. (S.F. Tadeu), http://www.uc.pt/fctuc/dec.

(A.J.B.Tadeu),http://www.uc.pt/fctuc/dec.(N.A.V.Simões).

1 _web:_{http://www.ufop.br}

2 _web:_{http://www.uc.pt/fctuc/deec}

3 _web:_{http://www.uc.pt/fe.uc.pt}

upto2050),isprovidedbytheEuropeanCommission(Eurostat–EU

Energy,2013;Eurostat,2014).

InJuly2013,Portugalsentthenationwidereport(DGEG,2013)

specified in Article 6 of the Delegated Regulation (EU, 2012)

containingthedataandassumptionsusedforcost-optimal

calcu-lations.However,thisreportonlyreferstonewbuildings,which

annuallyrepresentedlessthan1%ofPortugal’sbuildingstock(INE,

2013).Thecost-optimalmeasureswereselectedusingtheMonte

Carlosimulationtechniques.Itneitherincludesasensitivity

anal-ysisofthediscountratesandtheevolutionofenergyprices,nor

indicatestheuseof renewable energy sourcesrequired in (EU,

2012).

Whentransposingthemethodologicalframeworkproposedin

EPBD(2010),thePortugueselegislationestablishedamethodology forcalculatingtheeconomicfeasibility(REH,2013).However,this

methodologyonlyappliestowholesaleandretailbuildingtrade

servicesinthefollowingsituations:(1)designandconstructionof

newbuildings;(2)“majorrenovation”oftheenvelopeor

techni-calsystemsinexistingbuildings;and(3)energyassessmentand

http://dx.doi.org/10.1016/j.scs.2015.11.002

(2)

maintenanceofnewandexistingbuildingsundergoingmajor

ren-ovationundertheenergycertificationsystemforbuildings.

TheOrder(extract)15793-L/2013(Despacho,2013)statesthat

projectsarecontingentuponeconomicfeasibility,withmandatory

implementationwhentherelevantstudyshowsthatthereareno

technical,legaloradministrativelimitationsorconstraintsonthe

installationandthesimplepaybackperiodiseightyearsorless.

Theterm“majorrenovations”mentionedbyEPBDistransposed

intothenationalcontextaschangesintheenvelopeand/or

tech-nicalsystemsamountingto25%ormoreofthebuildingmarket

value.Thus,aninvestmentanalysistoassessprofitabilityshould

notberestrictedtoameresimplepaybackperiodstudy.However,

despitetheinherentriskanduncertainty,energyretrofitprojects

offeroptionsandflexibilityformakingsubsequentdecisionsthat

affectthefuturecashflowsandtheprojectlifecycle.

Inshort,Portugalfacesthesamedifficultiesofothercountriesin

theEU-28:thelargeamountofpossiblecombinationsofefficiency

measuresforenergyretrofitofbuildingshinderstheselectionof

thecost-optimalonesandthelackofaclearpolicydoesnotattract

privateinvestment.

Theaimof this studyis tocontextualizethereal optionsin

energyretrofitofbuildingsandshowthebestoptionsonthereturn

oninvestmentcriteria(ROI),basedonPortuguesemarketprices.

Thegoalisnottoassignquantitativeandabsolutevaluestothese

options,buttovaluemeasuresmoreprofitablethanthebusiness

asusual(BAU)scenario.Amulti-objectiveoptimizationproblem

designedtominimizetheglobalcostandprimaryenergyneedsof

theenergyefficiencymeasuresisdeveloped.Section2discussesthe

risks,uncertaintiesandrelevanceofapplyingrealoptionstheory

tocostoptimalitystudiesontheenergyretrofitofbuildings.The

methodologyandacasestudyarepresentedinSection3.In

Sec-tion4,illustrativeresultsarepresentedandtheirimplicationsfrom

theperspectiveofrealoptionsarediscussed.Someconclusionsare

drawninSection5.

2. Risk,uncertaintyandrealoptionsinenergyretrofitof buildings

The evidence of financial gains of energy efficiency

invest-mentsinexistingbuildingsistoourknowledgestillratherlimited

(Christersson, Vimpari, & Junnila, 2015). The energy retrofit of

buildings involves irreversibility issues and the possibility of

deferralassociatedwiththeinvestment.Thisinvestmentcanbe

consideredlowrisk,butalsowithlittleornoliquidity.Traditional

investmentanalysiscriteria,suchasthenetpresentvalue(NPV),

tendtounderestimateitsvaluesince,ingeneral,theydonot

incor-porateoperationalflexibilityissuesandotherstrategicfactorsin

the calculationprocess, in particular the possibility of deferral

(Soares,1996).

Althoughthereissomecommitmenttokeepagivensolutionfor

alongtimeoncethedecisiontoimplementhasbeenmade,itis

pos-sibletorevertpreviousdecisionswhencircumstancesand/orthe

technologychange.Forexample,heatingsystems,whether

con-ventionalor basedonrenewable energy sources(RES), maybe

replacedbyan alternativesystemattheend oftheirlifecycle,

appreciablyshorterthanthe30-yearperiodrecommendedin(EU,

2012).Buildingownerscanthendecidetoredirecttheir

invest-ment,which denotes a certainstrategic adaptability.Therefore,

realoptionsincreasethevalueoftheprojectandshouldbeadded

totheNPV.Thegreaterthenumberofoptionsandtheassociated

uncertainty,thehighertheprojectvalue(Silva,1999).

The selection of actions to improve energy efficiency in

buildingsis aprobleminvolvingmultiple,incommensurate and

generally conflicting axes of evaluation of the merits of those

actions. These problems may be tackled using multi-objective

optimization models,in which the setof potential alternatives

is implicitly defined by constraints defining a feasible region

andmultipleobjectivefunctionsareoptimized,ormulti-criteria

decisionanalysis,inwhichthealternativesareexplicitlyknown

a-prioritobeappraisedby(qualitativeand/orquantitative)multiple

criteria.Simulationtechniquesarealsousedtodealwiththis

prob-lem,ingeneralfocusingonparticularaspectsratherthanfollowing

aglobalapproach(Asadi,Silva,Antunes,Dias,&Glicksman,2014; Caccavelli&Gugerli,2002;Chidiac,Catania,&Morofsky,2011a; Chidiac,Catania,Morofsky,&Foo,2011b;Diakaki,Grigoroudis,& Kolokotsa,2008;Doukas,Nychtis,&Psarras,2009;Soaresetal.,in press;Verbruggen,AlMarchohi,&Janssens,2011).

Itisnotalwayspossibletoestablishnumericaltechniqueseither

directlyaddressing thestochasticprocess(Monte Carlo

simula-tion,forexample)orbasedontheresultingdifferentialequations

(Pindyck,1988).MonteCarlo techniquescomputetheexpected

valueand thedispersion(standard deviation) ofa variable (for

example,cashflow),consideringthevariationrangeandthe

proba-bilitydistributionofasetofuncertainparameters.However,these

techniquesdo not distinguishbetween technicaland economic

uncertainty,sotheiruseincost-optimalapproachesisnot

appro-priate.Itshouldbenotedthatfutureeconomicuncertaintyoverlaps

technicalperformanceuncertainty,soitcannotbeeasilydefined

inaprobabilisticmanner(Rysanek&Choudhary,2013).TheMonte

Carlosimulationtechniquesarethereforelimitedandcannot

opti-mizetheprofitabilityofenergyefficiencymeasuresinbuildings.

Insteadofsimulatingallthecombinations,thecomputationtime

canbesignificantlyreducedthroughtheuseofgeneticalgorithms

tocopewiththecombinatorialnatureoftheproblem.

Arangeofrealoptionscanbeconsideredininvestmentsinthe

energyretrofitofbuildings.Buildingownersmaydecidetodefer,

abandon,contract,expandorexchange aparticularsolutionfor

insulation,heating,cooling,domestichotwater(DHW)oruseof

RESon-siteasexplainedbelow.

Option of waiting or deferral: when there is no regulatory

requirement,thebuildingownercanpostponethe

implementa-tionofaspecificenergyefficiencymeasure.Itisstraightforwardto

determinetheoptimalinvestmenttimewhenthereisno

uncer-tainty,sinceitissufficienttocalculatetheprojectNPVassociated

withvariousstartdatesandselecttheonewiththehighervalue.

However,thissimpleruledoesnotapplyinanuncertaincontext

(Silva,1999).Oneexample is theuncertainty offuture interest ratesthataffecttherequiredreturnrate(thecostofcapital)used

asthediscountrate.Dealingwithuncertaintyisstillmore

diffi-cultwhendifferentscenarios fortheevolutionof energyprices

areconsidered.Thecombinationofalltheseissueswilldetermine

theattractivenessofenergyefficiencymeasures.Forexample,the

replacementofsystemsmayinvolveawaitingvalue,especiallyfor

fuelswitching.Inthecaseofhighlyvolatileprices,waitingbecomes

amore profitableoption.However,thereisnowaitingvaluein

buildingenveloperetrofitwhenenergypricepresentsamoderate

andsmoothincreasing(Kumbaroglu&Madlener,2012).

Option to abandon or exchange: technically, abandonment

occurswhenthedecisionmakerchooseswaivingtheprojectstillin

theinvestmentstart-upphase,andexchangeiswaivinginthe

oper-ationalphase.Theoptimaltimeofthiswaiveristhepointwhere,

whencomparingfutureexpectedcashflows,immediate

abandon-menthasthehighestadjustedvalue(Robichek&VanHorne,1967).

Inthecaseofrehabilitationinvestment,theabandonmentoption

appearsmeaningless.

Optiontocontractorexpand:theexpansionoptionhas

vari-ousapplicationsinpilotprojectsandresearchanddevelopment

projects.TheseprojectscanhavenegativeNPVinafirstapproach,

buttheycanturnouttobequitevaluablewitharelativelysmall

investment,since theycancollectinformation leadingtolarger

(3)

canberepresented,forexample,byinstallinginsulationat

differ-entstagesorbymodules.Theresultscanbeassessedbyenergy

audits(Dall,Speccher,&Bruni,2012)andwhenexperiencesare

goodthereareargumentsfortheexpansionofinvestment.Inthe

oppositescenario,decisionmakersmaynotinvestinsubsequent

stepsandshrinktheinvestmentinitiallyplanned.Similarly,itis

possibletoimplementRESonasmallscaleandexpandthemasthe

energyproductionpotentialisconfirmed.

Insummary, theoptions frameworkindicatesthat, allother

thingsbeingequal,thevalueofmanagementflexibility(premium

option)isgreaterunderuncertainty;it mayincrease inperiods

ofhighinterestratesandcangrowinlongerinvestmentprojects

orthosethatcanbedeferred.Greateruncertainty,higherinterest

ratesorleavingmoretimebeforetheimplementationofaproject

(evenindicatingdelayinreceivingorsavingcash flows)do not

necessarilyrepresentaworseinvestmentopportunity(Silva,1999).

Weemphasizethatthetimeofretrofitimplementationaswell

asthereinforcementoftheenergyperformancelevelofbuilding

retrofitting,asstatedintheEPBDorinnationalregulations,shall

betakenasconstraintsoverwhichtheownerorinvestordoesnot

havemuchfreedomtodeferordelaywhenitcomestodeferringor

delayingimplementationoftheenergyefficiencymeasures.

3. Casestudy

Thebuildingunderstudyisa2-bedroomsingle-familydwelling

builtbefore1960.Thecalculationsuseclimatedatafromthecity

ofAmarante,locatedincentralregionofPortugal,with1570◦_C_of

heatingdegreedays(HDD)(REH,2013).Itwasdefinedasa

refer-encebuildingrepresentativeofdetachedhousesfromthisperiod

ofconstruction.Thegeometricandthermalcharacteristicsofthis

buildingwereestablishedusingstatistical dataprovidedbythe

NationalAgencyforEnergy(ADENE),availableintheEnergy

Certi-ficationSystem(ECS)database(DGEG,2013),whichcontainsmore

than800,000certificates.

This buildingoccupies 80m2_, _it _has _a _heating _system _with

nominal efficiency of 1.00 and a DHW system with nominal

efficiencyof0.60. Theoriginalthermaltransmittancevalues (U

-value)for the roof, walls and ground floor are 2.80, 2.00 and

1.65[W/(m2◦_C)], _{respectively.} _The _thermal _insulation _option _is

expandedpolystyrene(EPS)withthicknessesrangingfrom30to

180mm.It isassumed thatinsulation isappliedtotheexterior

fac¸ade,theroofingslabandthegroundfloor.Thereferencebuilding

hassingle-glazedwoodenframedwindowswithasolarheatgain

coefficientgwof0.85andathermaltransmittancevalueUof5.10

[W/(m2◦_C)],_which_are_replaced_in_some_retrofit_packages_(set_of

measurestobeappliedtothebuilding).Theoptionsforwindows

replacementhaveUvaluesrangingfrom1.21to2.45[W/(m2◦_C)]

andcoefficientsgwfrom0.30to0.59.

Theenergyretrofitpackagescombine10solutionsforroof,10

forexteriorwallsand10forgroundfloorthermalinsulation,11

optionsforwindowsreplacementandtheuseof4different

heat-ingandDHWsystems,plus4optionsforRES.Atotalof154,000

packageswereobtaineddiscounting22,000adversecombinations.

TheheatingandDHWsystemsdefinedasenergyefficiencyretrofit

measuresareanairconditioner(AC)(forheatingonly),abiomass

boiler(BM)andagasboiler(GB)forbothheatingandDHW.The

technicalperformancedetailswerebasedonthemostwidelyused

systems in thePortuguese market (CYPE, 2014)and an annual

maintenancecostof1%oftheinitialinvestmentwasconsidered.

Table 1 shows thepossible combinations of heating and DHW

systems.Thesesetofcombinationswerecomparedwiththe

heat-ingandDHWsystemsdefinedforthereferencebuilding(electric

heater,EH,andgaswaterheater,GWH).TheoptionsforRESarea

solarthermalthermosyphonsystem—STT,asolarthermalforced

circulationsystem—STC,andaphotovoltaicpanel—PV,asshown

inTable2.ThePVproductionisforself-consumption,whichmeans thatthereisnofeed-intariff.Thesystemusesbatteriestostorethe

surpluselectricityproduced.Theefficienciesofrenewableenergy

sourcesareindicatedinPortugueselegislation(REH,2013)andthe

systemsizeswereselectedtopreventwasteofenergyinallthe

simulatedscenarios.

3.1. Methodology

Theenergyneedswerecalculatedusingtheseasonal

method-ologyofENISO13790:2008(European,2008),asitwasadopted

inPortugal. Thecalculationisfirstperformedassuming

perma-nentuseofheatingsystemsthroughoutthewinter.However,since

therealenergyconsumption islower thantheestimatedvalue

obtainedwiththeseasonalmethod,aconsumptionreductionfactor

wasconsideredtakingintoaccounttheheatinghabitsnationwide.

Consideringtherecenttrendofgrowinguseofelectricalheating

systemsandtheimprovementintheirefficiency,thisenergysource

wasusedasareference.Accordingtothelatestsurvey(2010)by

thenationalstatisticsinstitute(ICESD,2010)(InstitutoNacionalde Estatística,2011),51.7%ofhouseholdsusedelectricityforheating.

Theannualelectricityconsumptionforheatingperhousingunit

was418.6[kWh](0.036[toe]),forbuildingswithanaveragearea

of106.6[m2_]_and_an_average_heated_area_of_50.6_[m2_]_(47.5%_of_the

totalarea).Thus,theactualannualconsumptionoffinalenergywas

8.3[kWh/m2_]_of_the_heated_area.

Table1

HeatingandDHWsystemcombinations.

Heatingsystem DHWsystem

h,k Equipment Fuel Efficiency Power[kW] Investment[D] w,k Equipment Fuel Efficiency Power[kW] Investment[D]

h,1 Electricheater Electricity 1.00 9.6 908 w,1 Gaswaterheater Gas 0.60 9.4 325

h,2 Airconditioner Electricity 4.30 8.6 4948 w,2 Gaswaterheater Gas 0.78 9.4 542

h,3 Biomassboiler Pellets 0.92 4.8–16 4776 w,3 Biomassboiler Pellets 0.92 4.8–16 3053

h,4 Gasboiler Gas 0.93 7–23.6 1520 w,4 Gasboiler Gas 0.83 7–23.6 972

Obs.:h,kidentifieseachheatingsystemandw,kidentifieseachDHWsystem,whereh,1combinesonlywithw,1andsoon.Thevaluesoftheinitialinvestmentcostinclude

taxesandfees.Itwasassumedthat39%oftheinvestmentassociatedwithBMandGBisrelativetoDHW.

Table2

Renewableenergysources(RES)systems.

r,k Equipment Energysource Energyproduced Surface[m2_] _Investment_[D]

r,1 Solarthermalthermosyphon Solar Thermal 1.92 1989

r,2 Solarthermalforcedcirculation Solar Thermal 2.02 3319

r,3 Photovoltaicpanel Solar Electricity 11.62 12855

(4)

According to the Energy Certification System (ECS) (DGEG,

2013), the final average for energy used for heating is 61.6

[kWh/m2_]._This_is_the_result_of_the_seasonal_method_calculations

assumingpermanentheating.Establishingarelationshipbetween

thetwosetsofdatashowsthatthefinalheatingenergy

consump-tionreportedbyICESDrepresents13.4%oftheestimatedvalues

availableintheECS.

Thus,a consumptionreduction factor(occupancypattern)of

0.134wasappliedtobeclosertothePortugueseheatinghabits.

Forexample,inthereferencebuilding,theaveragemonthlyenergy

billjustforheatingandDHWisD _336.40,_considering_100%_of_the

estimatedenergyneedsbytheseasonalmethodandD _86.96_with

thereductionfactor(13.4%).

TheenergypricetrendhasbeenestimatedbytheEUcovering

theperiodupto2050(Eurostat–EUEnergy,2013).Theenergycosts

forelectricity(D _0.2375/kW_h)_and_natural_gas₍D _0.1004/kW_h)

wereobtainedfromdataprovidedbythePortugueseregulatorfor

energyservices(ERSE)(ERSE,2009).Theenergy costforpellets

(D _0.0492/kW_h)_was_based_on_current_market_cost._The_primary

energy conversionfactors considered were2.5kWhep/kWh for

electricityand1kWhep/kWhforgasandpellets,accordingtoOrder

(extract)D-15793/2013(extrato,2013).Theprimaryenergy

con-versionfactorsconsideredforRESwere1.0kWhep/kWh,evenfor

electricityproducedbyphotovoltaicpanelssinceitisusedonlyin

self-consumptionmode.

Theeconomicanalysisofconventionalsystemsrecommended

inISO15459(EuropeanCommitteeforStandardization,2007)was

extendedandadaptedtothepreviousselectionofRES,insulation

optionsandwindows.Thesolutionswerecomparedwithrespect

toprofitabilityincommoncostunits,whichwereeurosper

kilo-watthour[D_/k_Wh]_for_equipment_(systems)_and_euro_per_thermal

resistance[D_/_r_]_in_the_case_of_insulation_and_windows_(building

envelope).Initialinvestmentandmaintenancecostswereprovided

bymanufacturersassociations or obtainedthrough samplingof

quotationsfromtheconsumermarket(CYPE,2014).For

replace-mentcosts,itwasconsideredalifespan(L)foreveryperiodof:50

years(L=50)forinsulation,40years(L=40)forwindowsand20

years(L=20)forallsystems,includingRES.

Aftertheusefulenergyneedsfor154,000packagesof

meas-ureswereobtained,theirglobalcostinthefinancialperspective

describedin(EU,2012)(consideringonlythereturnoninvestment)

wascalculated.A6%nominaldiscountrate(excludinginflation)

wasappliedtothevariouscostsincurredinaneconomiclifecycleof 30years,thisbeingthevaluecurrentlyofferedbycreditlines espe-ciallydedicatedtoretrofitprojects(BuildingsPerformanceInstitute Europe,2013).Inadditiontothecriteriarequiredby(EU,2012),four

indicatorswerecalculated:simpleandadjustedpaybackperiod,

internalrateofreturnoninvestment(IRR)andreturnon

invest-ment(ROI).

Followingthecostoptimalityconcept,theobjectivefunctionsf1

andf2representtheprimaryenergyneedsandglobalcost,

respec-tively.Weconsideramulti-objectiveoptimizationproblem(MOP)

inaminimizationcontext.Thus,aMOPisdefinedasfollows(Marler &Arora,2004).Let

Ᏺ

₌

f1,f2

,fi:Rn⇒R,i=1,2,theMOPbeing

definedas:

Minimize:→y=→f(→x)=[f1(→x),f2(→x)] (1)

→x=[x1,...,xn]∈⊆Rn (2)

→y=[y1=f1(→x),y2=f2(→x)]∈⊆Rm (3)

where,→xisavectorofndecisionvariables,while→yrepresents

a2-dimensionalobjectivevectormappingsolutions→x ∈into

theobjectivefunctionspace.Theobjectivefunctionsaredefined

byEqs.(4)and(5).

Fig.1. Representationofthedecisionvariables.

Eachcomponentofthe→xvectorcorrespondstoadecision

variable,i.e.,specifiesthecostandcorrespondingtechnical charac-teristicslinkedtoeachretrofitoption.Thus,forroof(#1),walls(#2),

groundfloor(#3)andwindows(#4),thetechnicalcharacteristicis

thermaltransmittancevalueU.Forheating(#5)andDHW(#6),the

technicalcharacteristicisefficiencyandforRES(#7)isenergy

pro-duction.Fig.1showsthesolutionrepresentation(encoding),where

eachvectorpositionhasasetofpossiblevalidvalues:

3.1.1. Primaryenergyneeds

Inthisstudy,thecoolingneedswerenotconsidered.According

tothePortugueselegislation,itisallowedtoneglectthecooling

needsoncetheriskofoverheatingisminimal.Thus,thetotal

pri-maryenergyneeds,PE,resultfromthesumoftheheatingenergy

needs,Eh,k,anddomestichotwaterproduction,Ew,k,lessany

con-tributionsfromrenewableenergysourcesperm2_of_floor_area,_E

r,k

(adaptedfrom(REH,2013)):

f1(→x)=PE (→x)=

K_h

k=0

fh,k(x5)Eh,k(x5) h,k(x5) Ph,k(x5)

+

Kw

k=0

fw,k(x6)Ew,k(x6) w,k(x6) Pw,k

(x6)

−

Kr

k=0

Er,k(x7)Pr,k(x7)

(4)

where,agiven systemkislinkedtoasingleenergy source;Kh,

KwandKrarethenumberofsystemsforspaceheating,DHWand

renewableenergyproduction,respectively;fh,kandfw,karethe

per-centageoftheenergyneedsprovidedbyeachsystemk;Ph,k,Pw,k

andPr,karetheconversionfactorbetweenfinalenergyandprimary energyofeachsystemk;h,kandw,karetheefficiencyofeach

sys-temandx5tox7aretheassociateddecisionvariables,becausethese

variableshaveadirecteffectonthetwoobjectivefunctions,while

thevariablesx1tox4affecttheusefulenergyneedsand,indirectly,

theobjectivefunctions(seeFig.1).

Theusefulenergyneedsofthebuilding,Eh,kandEw,k,areinput

datatothegeneticalgorithmandwerepreviouslycalculatedby

asoftwaredevelopedforthispurpose,whichfollowsthestandard

seasonalmethodproposedinENISO13790:2008(European,2008)

togetherwithspecificrulesdefinedinthePortugueselegislation

(REH,2013).Thiscalculationusesthedecisionvariablesx1 tox4

toobtainEh,k,sincetheusefulenergyneedsalsodependonthe

insulationthicknessesandwindows,amongotherfactors.

ThecurrentPortugueselegislationdeterminesthatthe

mini-mumenergyrequirementsforexistingbuildingsundergoingmajor

interventionsshouldbeestablishedbasedonreference

parame-tersofthermalandenergyefficiencyappliedtotheenvelopeand

equipmentofthebuilding.Incaseofexistingbuildingsconstructed

before1960itisacceptedthatthevalueofPEcanexceedupto50%

theregulatorylimitsetfornewbuildings.

3.1.2. Globalcost

Theglobalcost,GC (→x,) forsetofmeasuresJ(where,j=0

correspondstotheBAUscenario),referringtostartingyear,i=0,

overtheplanningperiod,resultsfromthesumofthefull

(5)

bythediscountfactor,Di.Inthisstudyaperiod=30yearswas considered:

f2=GC (→x,)= J

j=0

i=0

ICi,j(→x)+ECi,j(→x)

Di (5)

Thediscountfactorforyeari,Di,isbasedontherealdiscount rateRtobecalculatedas:

Di=

₁

1+R/100

i

(6)

Theinvestmentcosts,ICi,j,resultfromabroadconceptoffull

investmentcostandareobtainedfromthesumoftheinitial

invest-ment,Ii,j,themaintenancecosts,Mi,j,thereplacementcosts,Ri,j,less theresidualvalue,Vij:

ICi,j x

= Ii,j+Mi,j+ıiLRi,j−ıiVi,j

(7)

where,ınmistheKroneckerdeltasymboltobecalculatedas:

ınm=

0, if n=/m

1, if n=m (8)

Thereplacementcosts,Ri,j,associatedwitheachsetofmeasures areaddedjustattheendoftherespectivelifespanL.Similarly,the

residualvalue,Vi,j,issubtractedjustattheendofthecalculation

period.

In the case under study, the investment costs, ICi,j, result

fromthesumofthemeasuresobtainedbychanging4elements

(insulation,windows,conventionalsystemsandrenewableenergy

systems),identifiedbythesubscriptsins,win,sysandres, respec-tively:

Ii,j(→x)= Iins,i+Iwin,i+Isys,i+Ires,i

(9)

Inturn,ins(insulation)resultsfromthesumofthe3

enve-lopeelementsthatarechanged,identifiedbythesubscriptsinsroof, inswallsandinsfloor,denotingroof,wallsandgroundfloor, respec-tively:

Iins,i(→x)= Iinsroof,i+Iinswalls,i+Iinsfloor,i

(10)

Similarly,sys (systems) andres (renewableenergy systems)

resultfromthesumofthesystemsthat arechanged,identified

bythesubscriptsh,w,andr(seeTables1and2),respectivelyfor

heating,DHWandRES:

Isys,i(→x)= 4

k=1

(Ih,i,k+Iw,i,k), Ires,i(→x)= 3

k=1

Ir,i,k (11)

ThesameprocedureisappliedtotheotherparametersMi,j,Ri,j

andVi,j.

Theenergycosts,ECi,j,resultfromthesumoftheenergycosts forheating,ECh,i,andtheenergycostsforDWH,ECw,i:

ECi,j(→x)= ECh,i+ECw,i

(12)

TheenergycostsforheatingandDHW,ECh,iandECw,i,result fromthefinalenergy,FEh,iandFEw,i,respectively,multipliedbythe

costforthecorrespondingsourceofenergyusedbyeachsystem,

Cele,i,Cgas,iandCpel,i(electricity,gasandpellets),inagivenyeari,

forheating

ECi,h=

⎧

⎪

⎨

⎪

⎩

FEh,iık1Cele,i

FEh,iık2Cele,i

FEh,iık3Cpel,i

FEh,iık4Cgas,i

(13)

andforDHW

ECi,w=

⎧

⎪

⎨

⎪

⎩

FEw,iık1Cgas,i

FEw,iık2Cgas,i

FEw,iık3Cpel,i

FEw,iık4Cgas,i

(14)

ThenetfinalenergyneedsaftercontributionsfromRES,FEh,k

andFEw,k,areobtainedassumingtheselectedheatingandDHW

systems(Table1)andRESsystems(Table2).Considering

partic-ularitiesontherelationbetweenconventionalandRESsystems,

FEh,kandFEw,karecalculatedasfollows:

FEh,k= fh,kEh,k

h,k

−ık3Er,k (15)

FEw,k=

(fw,kEw,k)−ık1Er,k−ık2Er,k

w,k (16)

Thecostsofenergy,Cele,i,Cgas,iandCpel,i,areaffectedbyafactor forreadjustmentfCele,i(beingthesameforgasandpellets)

Cele,i=

Cele,i, i=1

Cele,ifCele,i, 1<i≤30

(17)

AccordingtothefollowingindicesbasedontheEuropean

Commis-sion’sestimatesforenergypricesdevelopmentinthenext30years

(Eurostat–EUEnergy,2013):

fCele,i=

⎧

⎪

⎨

⎪

⎩

1.0349, i<5 1.0000, 5≤i<10 1.0040, 10≤i<15 1.0000, 15≤i<20

−1.0058, 20≤i<25

−1.0020, 25≤i≤30

(18)

3.2. Amulti-objectiveapproach

ThecasestudyhasvariantswithRESsystemsembeddedinit,in

atotalof154,000possiblecombinations(packages).Thisnumber

ofcombinationscanincreasesignificantlywiththeadditionofnew

typesofcomponentsorwhenthenumber ofsystemsincreases.

Duetothelargenumberofpossiblecombinationsfortheproblem

understudy,weusedamulti-objectivegeneticalgorithm(MOGA)

speciallydevelopedtofindnon-dominatedpackages(solutions).

A non-dominated package is a feasible solution for which no

otherfeasiblepackageexistssimultaneouslyimprovingall

objec-tivefunctions,i.e.theimprovementofanobjectivefunctionvalue

canonlybeachievedbyacceptingtodegradeatleastanother

objec-tivefunction.Thatis,non-dominatedpackagesentailatrade-off

betweenthecompetingobjectivesinordertoselectacompromise

solution.Thealgorithm proposedwas calledGeneticAlgorithm

forEnergyEfficiencyinBuildings(GAEEB)anditspseudo-codeis

presentedinAlgorithm1.TheGAEEBisbasedonNSGA-II(Deb,

Pratap,Agarwal,&Meyarivan,2002),whichhasbeenusedtosolve

combinatorialproblemsinseveralareasasbuildingretrofit(Asadi

etal.,2014),optimalplacementandsizingofdistributedgeneration (Wanxing,Ke-yan,Yuan,Xiaoli,&Yunhua,2015)andgeneration expansionplanning(Kannan,Baskar,McCalley,&Murugan,2009),

amongmanyothers.

GAEEBcreatesapopulationconsistinginsetofpackages.Each

package corresponds to a random combination of the decision

variables.Packagesarethenevaluated.Thestoppingcriterionis

thenumberofevaluationsofobjectivefunctions.Thenpackage

populationevolvesusingselection,crossoverandmutation

(6)

Fig.2.Illustrationofthecrossoveroperator.

scheme(Coello,Lamont,&Veldhuizen,2007).Crossoverand

muta-tionoperatorswereespeciallydesignedfortheproblemofbuilding

retrofit.Anewpopulationwith2×npackagesiscreatedbyjoining

thepackagesofthepopandpopOffspringpopulations.

Algorithm1–GeneticAlgorithmforEnergyEfficiencyin

Build-ings(GAEEB).

X∗_←

GAEEB(nSol,nEval)

Input:n:numberof

packages(population

size)

Input:nEval:number

ofevaluations

Input:pc:crossover rate

Input:pm:mutation rate

Output:X*_:

non-dominated packages 1 Begin

2 pop←

InitializePop (n)

3 Evaluate(pop)

4 ori=1to

nEvaldo

5 popOffspring←

∅

6 Forj=1ton.

do

7 [parent1,parent2]←

BinaryTournament (pop)

8 [offspring1,offspring2]←

BRC (parent1,parent2,pc)

9 [offspring1,offspring2]←

BRM (offspring1,offspring2,pm)

10 Evaluate(offspring1,offspring2)

11 popOffspring[j]←offspring1

12 popOffspring[j+1]←offspring2

13 j←j+2

14 Endfor

15 pop2n←

Union (pop,popOffspring)

16 fronts←

ENSSS (pop2n)

17 pop←

FillPopulation (fronts)

18 i←i+1

19 Endfor

20 fronts←

ENSBSS (pop)

21 x*_←_{fronts [1]}

21 returnx*

22 End

GAEEBisanelitistalgorithm,wherethebestpackagesfoundare

preservedusingaprocedureknownasEfficientNon-dominated

SortwithSequentialSearchStrategy(ENS-SS)(Xingyi,Ye,Ran,& Yaochu,2015).ThefunctionFillPopulation(.) createsanew

popu-lationusingthenon-dominatedfrontsgeneratedbyENS-SS.When

packagesofafrontexceedthesizeofthepopulation,acrowding

distance(Debetal.,2002)procedureisusedtopreservediversity

andobtainawell-distributednon-dominatedfront(line17).

The crossover operator – Building Retrofit Crossover, BRC(.)

–hasbeenspeciallydesigned tocreate newpackages.TheBRC

operatorproducesapairofoffspringpackagesfromapairof

par-entpackagesselectedfromthecurrentpopulation.Thecrossover

operatorhasprobabilitypcandusesonecut-offpoint(Fig.2).In thiscase,thecut-offpointcischosenatrandom,where,1<c<7.

Theexampleshowstwopackages(parent1 andparent2)selected

bybinarytournament(c=3).Theoperatorcreatestwopackages

(offspring1 andoffspring2)thatarecomposedofpartsofparent1

andparent2.

Themutationoperatorisa“flipmutation”(Coelloetal.,2007).In

thisBuildingRetrofitMutation—BRM(.),eachpackageelementhas

aprobabilitypmofexperiencingchange.Thisoperatorisapplied

topackagesresultingfromthecrossoveroperator.Thenewvalues

foreachrandomlyselectedelementtobealteredareobtainedfrom

thesetoffeasiblealternatives.Thisensuresthatthenewgenerated

packagesarefeasible.

4. Results

Theseresultsweredividedforbetterunderstanding.First,the

resultsfromGAEEB arepresentedand discussedin Section4.1.

After,resultsofcost-optimallevels(Section4.2)andareturnon

investmentapproach(Section4.3)areshownandanalysed.

4.1. ResultsofGAEEB

ThepurposeofthissectionistoevaluatetheresultsofGAEEB,

whichwasdescribedinsection3.2.The“brute-force”algorithm

wasimplementedtocreateallpossiblepackagesfortheproblem,

totalling154,000combinations.Thenon-dominatedpackageswere

identified usingtheEfficient Non-dominatedSort with

Sequen-tialSearchStrategy(Xingyietal.,2015).Thesolutionproposedby

GAEEBwasabletogeneratetheoptimalcostcurveaccuratelywith

asignificantreductionofprocessingtime.

Alltherunsconsideredthefollowingsetofparameters:

pop-ulation size (n)=70; number of evaluations (nEval=[500, 750,

..., 3000] with step 250; crossover rate (pc)=0.9; and

muta-tionrate (pm)=0.04. Theexperimentsinvolved 33runsof the

GAEEB, usingaPCIntelCoreI7-3632,2.2GHz CPUwith8GBof

RAM.

ThequalityoftheresultsprovidedbyGAEEBwasassessedusing

thehypervolumequalityindicator (H) (Beume,Fonseca,

Lo´ıpez-Ibá ˜nez,Paquete,&Vahrenhold,2009;Zitzler&Thiele,1998),which

isameasureofthespacedominatedbyasetofnon-dominated

pointsthat are boundedbya dominatedpoint calledreference

(Pref).Tocomputethehypervolumevalue,asolution→xiinthe

non-dominatedfrontier(PFknown)fora2-dimensionalMOPdefines

arectanglearea,c(→x_i_),_bounded_by_an_origin_and_f₍_→x_i_)._The

unionofsuchrectangleareasiscalledhyperareaofPFknown:

H(PFknown)=

i

c(→x_i₎_|

_∀

_→x_i _∈_PF_known ₍₂₀₎

It is assumed that the reference point (Pref) for

assess-ing the hypervolume is the worst value for each objective

(7)

Fig.3. Thevalueofthehypervolumeindicatoristhe(hyper)volumeoftheregion

consistingofthepointsthatdominateareferencepointPref.

{c1,c2,...,c5} highlightedinFig.3 correspondstohypervolume

ofPFknown{→x1,→x2,...,→x5}consideringthereferencepoint

Pref.

Fig.4showsthehypervolumevaluescalculatedfor33runsofthe

algorithmforeachnEvaldefined.GAEEBconvergestothe

hyper-volumewithonly3000evaluationsoftheobjectivefunctions.The

blackdotsrepresentthehypervolumeobtainedbynon-dominated

packagesafterevaluationusing the“brute force”assessment of

154,000packages.Thenon-dominatedpackagesfoundthereafter

composetheoptimalParetofrontier.

Table3showsthehypervolumevaluesafter33runsofthe

algo-rithm.TheGAPcolumnshowsthepercentagedeviationfromthe

averageobtainedinrelationtohypervolumeofthenon-dominated

solutions.Notethatafter2000evaluationsoftheobjective

func-tions the algorithm has a similar behavior and converges for

hypervolumevalueswithGAPbelow1.5%.

Fig.5presentsthenon-dominatedsolutions(packages)found

byGAEEBinasinglerun.GAEEBwasabletofindalargenumberof

optimumpackages(solutions)fortheproblemunderstudy.Ofthe

27optimalpackages,i.e.,non-dominatedpackagesknowntothe

problem,theGAEEBalgorithmfoundanaverageof25.3optimal

packagesat3000evaluations.Inaddition,itshouldbenotedthat

thealgorithmrequiresaverylowcomputationtime.GAEEBdid

500evaluationsin84 milliseconds(Intel®Corei5desktopwith

Table3

Hypervolumevaluesobtainedby33roundsofGAEEBforthenumberofobjective

functionevaluations.

Numberof

evaluations

Hypervolumevalues Dev.std. GAP(%)

Best Worst Average

500 0.6961 0.5237 0.6075 0.0483 15.75

750 0.7199 0.5285 0.6484 0.0448 10.08

1000 0.7205 0.6032 0.6797 0.0358 5.76

1250 0.7207 0.6511 0.6982 0.0196 3.19

1500 0.7207 0.6572 0.7045 0.0196 2.32

1750 0.7208 0.6726 0.7091 0.0137 1.68

2000 0.7207 0.6767 0.7120 0.0106 1.28

2250 0.7208 0.6690 0.7118 0.0141 1.31

2500 0.7208 0.6723 0.7134 0.0152 1.08

2750 0.7209 0.6722 0.7106 0.0138 1.47

3000 0.7209 0.6721 0.7111 0.0154 1.40

3.30GHz),whileonly313millisecondswereneededtocalculate

3000combinations.

Inthenegativequadrant,wefindthepackagesthat

incorpo-ratephotovoltaicpanels.Theyproducemoreenergythanwhatis

consumedwithinthescopeofthisstudy(heatingof livingarea

anddomestichotwater).Table4shows4selectednon-dominated

packagesfoundbyGAEEB,includingvaluesofthermal

transmit-tance value U for roof (#1), walls (#2),ground floor (#3) and

windows(#4)andvaluesforheating(#5),DHW(#6)andRES(#7),

aswelltheresultsoftheprimaryenergyneedsandglobalcost,f1

andf2,respectively.

4.2. Cost-optimalresults

Thecost-optimalcurvebehaviourwasanalysedaccordingtothe

methodologicalframeworkproposedinDelegatedRegulation244.

Asalreadyexplainedin3.1,theprimaryenergyresultsforthecost

optimalityassessmentwerecalculatedusingtheseasonal

steady-statemethodwitha reductionfactorof0.134.Thecost-optimal

levelsinthefinancialperspective(FIN=6%)arepresentedinFig.6.

Theresultsshowthecost-optimalcurvesforeachcombinationof

insulation, windowsand theuseof differentheatingand DHW

systems,plusoptionsforRES.Theplotpresentsthedistribution

ofsolutions, andit ispossibletoseegroups ofpackageslinked

tocertainconventionalheatingsystems(electricheater—EH,air

conditioner—AC,gasboiler—GBandbiomassboiler—BM).

0,51378 0,54828 0,58278 0,61728 0,65178 0,68628 0.72124 0,73339

500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000

Number of evaluations

Hypervolume

Fig.4. Boxplotof33runsofGAEEBforeachevaluation.TheXaxisindicatesthenumberofevaluationsoftheobjectivefunctions(algorithmstoppingcriterion).Theblack

(8)

Fig.5. Non-dominatedpackages(solutions)foundinarunofGAEEB.Inlightgray,thesearchspaceoftheproblemcreatedbya“bruteforce”algorithmisdisplayed.

Table4

Selectednon-dominatedpackagesfoundbyGAEEB.

Roof(#1)

[W/(m2_.C◦_)]

Walls(#2)

[W/(m2◦_C)]

Floor(#3)

[W/(m2◦_C)]

Windows(#4)

[W/(m2◦_C)]

DHW(#5) Heating(#6) RES(#7) f1[kWh/(m2y)] f2[D/m2]

2.800a _2.000 _1.650 _5.1 _GWH_0.78 _AC _PV ₋₁₂₁ ₉₇

0.494 0.462 1.650 5.1 GWH0.78 AC PV −132 138

0.208 0.462 1.650 5.1 GWH0.78 AC PV −135 178

0.187b _0.182 _0.182 _1.87 _GWH_0.78 _AC _PV ₋₁₃₈ ₂₃₅

a_It_corresponds_to_package_13,_in_Table₅_.

b_It_corresponds_to_package_12,_in_Table₅_.

Asstatedabove,inthenegativequadrant,forexample,twoof

thatcloudsaregroupsofpackagesthatincorporatephotovoltaic

panel—PV,linkedtotwodifferentconventionalsystems:air

con-ditioner(cloudontheleft)andelectricheater(ontheright).The

valuesbecomenegativebecausethephotovoltaicpanelproduces

moreenergythanconsumedinthescopeofthisstudy(heating

oflivingareaanddomestichotwater),beingtheenergysurplus

fullytappedbyotherapplications(lighting,appliancesetc.).All

packagesthatincludebiomassboiler,BM,appearconcentratedand

pointingtozero-primaryenergyneedssincethetotalenergyneeds

aresuppliedbyRES.Bothsolarthermalsystems,thermosyphon—ST

Tandforcedcirculation—STC,reduceprimaryenergyneeds,asit

isexpectedfromRESsystems,butthesolutionofthermosyphon

hastheadvantageofreducingtheglobalcost,exceptin

combina-tionwithbiomass(BM+STT),thissystemusingthelowercostfuel

(pellets).Theverticallinesshowenergylimitsdefinedasnational

requirementsthatdependontheheatingsystemtype(AC—orange,

GB—blueandEH—gray).

Fig.6.Globalcost[D/m2_]_versus_primary_energy_needs_[kW_h/(m2_y)]_results_for_154,000_retrofit_packages,₁₅₇₀_HDD_(Amarante),_considering_a_period_of₌₃₀_years,_in_the

(9)

4.3. Returnoninvestmentapproach

Inordertodeterminetheadvantagesofinvestmentinenergy

retrofitforinvestors,regardingreturnoninvestmentanalysis,

func-tionf1isreplacedbytheadjustedvalueofadditionalinvestment,

f3,whichconsistsinthetotalamountinvestedinenergyefficiency

measuresbeyondtheBAUscenario. Theadditional investment,

AI (),referringtostartingyear,i=0,overthecalculationperiod ,resultsfromthefullinvestment costs,ICi,j,during yeari, for measureorsetofmeasuresj,lessICBAU,i,0,whichrepresentsthe

correspondingvaluesfortheBAUscenario.Thesevaluesare

dis-countedreferringtotheinitialyear,i=0,accordingadiscountfactor

Di.Forcalculationinthefinancialperspectivehavingaperiod=30 years:

f3=AI ()= J

j=1

i=0

ICi,jDi

−

i=0

ICBAU,i,0Di

(20)

Theinvestor’spointofviewisconsideredthesituationchanges

significantly,asshowninFig.7.Packagesthatincludephotovoltaic

panel,whichwouldbeconsideredbestoptionsaccordingtothe

cost-optimalapproach,arenotacceptableaccordingtoreturnon

investmentapproachduetothehighinitialinvestmentrequired.

Sincethediscountrateissignificantlyhigherthantheestimatesof

Fig.7.(a)Globalcost[D/m2_]_and_additional_investment_[D/m2_]_results_for_154,000_retrofit_packages,₁₅₇₀_HDD_(Amarante),_considering_a_period_of₌₃₀_years,_in_financial

(10)

theevolutionofenergypricessuggestedbyEurostat(Eurostat–EU Energy,2013),thepotentialenergycostsavingsbecome insuffi-cienttooffsettheinitialinvestment.

Fig.7 includes a grey linewhere theglobal cost of a given

package,plustheadditionalinvestment(amountinvestedbeyond

theBAUscenario),isequaltotheglobalcostoftheBAUscenario

pluscostsformaintenance,replacementandresidualvalueof

win-dowsandsystemsalreadypresentinthereferencebuilding,during

theperiodof=30years.

Astheglobalcostandtheadditionalinvestmentareshownin

netpresentvalue,packagescanbecomparedusingthisgraylineas

reference.Onlysolutionsthatarewithinthetriangleformedbythis

lineandtheaxesdeliverpositiveROIandtheadditionalinvestment

isnothigherthantheglobalcostinBAUscenario,whenconsidering

adiscountrateof6%.Inpackagesthatareonthisline,the

addi-tionalinvestmentdoesnotoffsettherelativedecreaseinglobal

cost,whencomparedwiththeBAUscenario.Theremaining

solu-tions(outsidethetriangle)canevenreducetheglobalcost(when

belowD _191.89),_but_the_ROI_is_negative.

Inthistypeofanalysis,thediscountrateof6%canalsobe

under-stoodascostofcapital,especiallywhentheinvestordoesnothave

theresourcesand needstohaveaccess tocreditlines tomake

additionalinvestment,incomparisonwiththeBAUscenario.This

analysisislimitedtothereturnoninvestmentforpackagesthat

providethesameconditionsofthermalcomfort,notconsidering

otherbenefitsthatcertainenergyretrofitmeasurescanprovide.

Concerningthisissue,theinterestofeachinvestormustbe

con-sideredintheelectionofthepackagewithhigheraddedvalue,

amongthosewithhigherreturnthan theBAUscenario,aswell

astheminimumrequirementsatnationallevel.Forexample,we

canseethatGBwithoutinsulationisthebestpackagefromthe

investor’spointofviewbutthisoptiondoesnotmeetthe

mini-mumrequirements,asshowninFig.8.AfterinstallingSTT,the

optionGB(stillwithoutinsulation)meetstheminimumnational

requirements.

ThereplacementoftheDHWsystempresentsanopportunity

forexchangeattheendoftheexistingequipment’slifecycle.When

consideringinsulation,thebestoptionisthethicknessof30mm,

onlyintheroof.Inthisreferencebuilding,roofinsulationismore

costeffectivethanintheotherelements,followedbyinsulationin

thewalls.Theinsulationofthegroundflooristheleastcosteffective

duetotheirhighcostsbecauseincreaseddifficultiesforadoption

ofthismeasureinexistingbuildings.Ingeneral,inthisreference

buildingasinothers,theinvestmentininsulationbecomesmore

cost-effectivewhenusefulenergyneedsarehigherortheheating

systemisalowefficiencyone.

Theanalysisof18selectedpackagesofefficiencymeasuresin

comparisonwiththereferencescenarioshowninTable5enables

usto understandtheimpactofeach action, aloneand in

com-bination.Package 0 representsthereference buildingin a BAU

scenario.Theelementsthatarechangedincomparisonwiththe

BAUscenarioareinyellow.Thevaluesthatdonotmeetminimum

requirementsonprimaryenergyneeds,globalcostorROIarein

orange,withintheirrespectivecolumns.Similarly,thebluevalues

representthebestwithinthesesamecolumns.Notethatpackage

12hasthelowestneedforprimaryenergy,package 13hasthe

lowestglobalcost,andpackage14hasthehighestROI(takingin

accountminimumrequirementsforprimaryenergy)ofall154,000

combinations.Packages1–4consistofjusttheinsulationof

com-ponents,EPSboardswithathicknessof60or80mm.InPackage5

onlythewindowsarereplaced.Packages6–11consistofreplacing

systemsorinstallationofRESsystems.Thatis,packages1–11

rep-resentindividualmeasures,highlighted,andtheirimpactonthe

primaryenergyneeds,globalcostandROI.Packages12–18

repre-sentcombinedmeasuresanditispossibletoseetheinteraction

betweenthem.Thecomparisonofthesepackagesconfirmsthat

replacementoftheheatingsystemisfarmorecosteffectivethan

theimprovementofinsulationintheopaqueenvelope,according

totheeconomiccriterionROI.Whilepackage14isthebestoption,

package12occupiesthe26123stpositionintheROIranking.

13 12

6 7

11

9 10

0 1

4 2

3 5

14 8

16 15

17 18

0 50 100 150 200 250 300 350 400

-150 -125 -100 -75 -50 -25 0 25 50 75 100 125 150

[

a

er

a

g

ni

vil

f

o

r

et

e

m

er

a

u

qs

r

e

p

ts

oc

l

a

b

ol

G€

/m²]

Primary energy needs [kWh/(m².y)]

AC + PV

AC

BM

EH + PV

EH + ST T

EH + ST C

EH

GB + ST T

GB

Limit AC

Limit EH

Limit GB

EH, without insulaƟon (BAU scenario)

GB + ST T,without insulaƟon (best ROI, following minimum naƟonal requirements) AC + PV, without insulaƟon

(cost-opƟmal, following Delegated RegulaƟon 244/2012)

(11)

Table5

BAUscenario(package0)and18selectedpackages.

Insulation Glazing Systems Renewables Energy Globalcost ROI

Roof Walls Floor Windows Panes Heating DHW Primary Financial Financial

Package t[mm] t[mm] t[mm] U[W/m2◦_C] _gˆvi _Equipment _Equipment _Equipment _[kW_h/m2_y] _[D/m2_] _[30_years]_(%)

0 – – – 5.1 0.85 EH GWH0.60 – 123 192 –

1 60 – – 5.1 0.85 EH GWH0.60 – 94 181 −59

2 – 60 – 5.1 0.85 EH GWH0.60 – 103 194 −108

3 – – 80 5.1 0.85 EH GWH0.60 – 110 216 −163

4 60 60 – 5.1 0.85 EH GWH0.60 – 74 184 −85

5 – – – 1.87 0.58 EH GWH0.60 – 121 219 −197

6 – – – 5.1 0.85 AC GWH0.78 – 49 150 −20

7 – – – 5.1 0.85 BM BM – – 156 −57

8 – – – 5.1 0.85 GB GB – 64 133 275

9 – – – 5.1 0.85 EH GWH0.60 STT 96 181 −56

10 – – – 5.1 0.85 EH GWH0.60 STC 98 201 −122

11 – – – 5.1 0.85 EH GWH0.60 PV −46 139 −67

12 180 180 180 1.87 0.58 AC GWH0.78 PV −138 235 −112

13 – – – 5.1 0.85 AC GWH0.78 PV −121 97 −56

14 – – – 5.1 0.85 GB GB STT 45 132 47

15 60 – – 5.1 0.85 GB GB – 52 143 18

16 30 – – 5.1 0.85 GB GB – 53 143 25

17 – 30 – 5.1 0.85 GB GB – 57 149 6

18 – – 30 5.1 0.85 GB GB – 60 162 −40

Package14providesaROIof47%,a15.47%IRR,asimple

pay-backof6 years and anadjusted paybackof 7years. Package 8

offersthe higher ROI over the 30 years, but does not comply

withregulations. We must stress that package 14 can only be

adoptedbecausethebuildingenvelopedoesnotundergoa“major

renovation”giventhattheregulationinforce(REH,2013)

estab-lishesminimumrequirementsforthermal transmittancevalues

in the envelope. This analysisshows the importance of

evalu-ating the return on investment in a long-term rather than in

theshort-termperspective. It alsoshows that thecost-optimal

approach is not enough to cover the information required by

investors.

Fig.8showsthecost-optimalgraphfortheselectedpackages

andregulatorylimitstobemetforprimaryenergyneeds,

depend-ingontheequipmentusedforheating.

Forthisreferencebuildingandtheelectricheater—EH,thelimit

standsat77.23[kWh/(m2_y)]._For_the_air_conditioner,_the_limit_is

50.87[kWh/(m2_y)]_and_it_is_56.72_[kW_h/(m2_y)]_for_the_gas_boiler

andthebiomassboiler.Thus,theBAUreferencescenario(package

0)andpackages1–3,5,8–10and17–18donotmeettheregulations.

13

12

6 7

11 9

10 0

1 2 ₄

3 5

14

8 16 15

17 18

0 50 100 150 200 250 300 350 400

[

a

er

a

g

ni

vil

f

o

r

et

e

m

er

a

u

qs

r

e

p

ts

oc

l

a

b

ol

G€

/m²]

Addional investment [€/m²]

AC + PV

AC

BM

EH + PV

EH + ST T

EH + ST C

EH

GB + ST T

GB

Limit FIN = 6%

AC + PV,without insulaƟon (cost-opƟmal, following Delegated RegulaƟon 244/2012) EH,without insulaƟon (BAU scenario)

GB + ST T,without insulaƟon (best ROI, following minimum naƟonal requirements)

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Table6

Summaryoftheanalysisofrealoptions.

Measure:Investmentin Lifecycle

(years)

Contributionontheglobal

cost[D/m2_.30_years]

ROIforadditional

investment

Technical uncertainty

Economic uncertainty

Risk Option

Photovoltaicpanel(self-consumption) 20 −53 −67% Middle Middle ↓ Defera

Solarthermalthermosyphon 20 −11 −56% Low Low ↓ bInvest

Solarthermalforcedcirculation 20 9 −122% Low Low ↓ Donotinvest

Airconditioner(heating),GWH(DHW) 20 −42 −20% Low High ↓ Donotinvest

Biomassboiler(heating,DHW) 20 −36 −57% Low High ↓ Donotinvest

Gasboiler(heating,DHW) 20 −59 275% Low High ↓ Investb

Newwindows 40 27 −197% Middle Low ↓ Donotinvest

Insulationoftheopaqueenvelope 50 ↓↑ ↓↑ Middle Low ↓ Defer

a_Although_still_having_a_negative_ROI,_the_price_of_the_equipment_has_fallen_rapidly,_determining_that_this_investment_option_should_be_reassessed_{periodically.}

b_As_shown_in_Table₅_,_the_investment_in_ST_T_is_necessary_to_sustain_the_investment_in_GB_and_fulfil_the_minimum_national_{requirements;}_this_package_composition_has_a

ROIof47%.

Fig.9showstheadditionalinvestmentfortheselectedpackages

andthelimitwheretheROIissimilartotheBAUscenario.

Packages1–7,9–13and18haveaworseeconomicperformance

thantheBAUscenario,althoughpackages7and11–13raisethe

buildingtotheNZEBcondition(nearlyzeroenergybuilding),with

primaryenergydemandbelow15[kWh/(m2_y)].

Regardingtherealoptionsthatareavailabletoinvestors,itis

clearthattheprofitabilitydependsontheheatingsystemthatis

adopted.Investmentinsystemswithhighefficiencyorlowprimary

energyconversionfactorcanevenallowthedeferralofinvestment

ininsulationorreplacingwindows.Theinvestmentintheenvelope

representsacapitalcommitmentforanextendedperiodoftime

duetothelonglifecyclesofthesematerials.Table6summarizes

theanalysisofrealoptions.

TheDHWsystemcouldbeexchangedattheendofthelifecycle

of existingequipment; however,this representsa small

reduc-tion in the global cost. The combination of the gasboiler and

thesolarthermal thermosyphonsystemprovidesanimmediate

investmentopportunity,sincethebuildingdoesnothave

architec-turalortechnicalrestrictions,suchasorientationofthebuilding

orshade.Thisoptionisbetterthantheinvestmentinanair

con-ditionerincombination witha gaswaterheater,for this range

of usefulenergy needs. The biomass system,heredesigned for

heatingandDHWintheentirethebuilding,offersnegativeROI,

althoughitsignificantlyreducestheprimaryenergyneeds.Possibly

itcanbeagoodalternativeinthecomingyears,supplementingthe

solarthermalsystem,sincethecostoffirewoodandpelletsshould

remain low. This type of application requires furthertechnical

research.

Regardingtheinvestmentinphotovoltaicpanels,theavailable

technologydidnotrevealitselfprofitable.Althoughitsignificantly

reducestheprimaryenergyneeds,theseequipmentdonotoffer

theattractivereturnoninvestmentthatwasprovidedintheearly

yearsofthesubsidizedscheme.Thereductionofthereferencerates

formicro generationsince2014discouragesthesale ofsurplus

productiontothegridbyencouragingself-consumption(Decreto,

2014),whichmakesitanunaffordableinvestment.Atthispoint,

itisunknownwhetherthecostofinitialinvestmentcouldfalldue

totechnologicalprogressorwhatthereferencetariffpolicyforthe

subsidizedschemewillbeinthecomingyears.

Assumingadiscountrateof3%,alargernumber ofpackages

would presenta satisfactoryROI,includingthepackage AC+PV

withoutinsulation,ascanbeseeninFig.10.Thisconfirmsthat

creditlines withlowerinterest ratescanencourageinvestment

Fig.10.Globalcost[D/m2_]_and_additional_investment_[D/m2_]_results_for_154,000_retrofit_packages,₁₅₇₀_HDD_(Amarante),_considering_a_period_of₃₀_years,_in_financial

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in energy retrofitand efficiency measureswith lower

environ-mental impact,a fact alsodetectedin previousstudies (Tadeu,

Rodrigues, Tadeu, Freire, & Simões, 2015). However, GB+STT

withoutinsulationremainsthebestinvestmentoption,sinceGB

withoutinsulationdoesnotmeettheminimumnational

require-ments.

5. Conclusions

Thisstudyassessedtherelevanceofapplyingtherealoptions

theoryandreturnoninvestmentcriteriatothecostoptimalityof

energyefficiencymeasuresintheretrofitof buildings.Eighteen

packagesleadingto154,000possiblecombinationsofmeasuresfor

areferencebuildingwereselected.Theoptimizationproblemwas

solvedusingamulti-objectiveevolutionaryalgorithm,GAEEB,

tak-ingintoaccountthemethodologicalframeworkproposedbythe

EuropeanCommission.Theresultsfromtherealoptions

perspec-tiveenabledtoconcludethat:

Regarding the profitability of the measures under analysis,

thereplacementoftheDHWsystempresentsanopportunityfor

exchangingat theendoftheexisting equipmentlifecycle.The

combinationofgasboilerwithsolarthermalsystemprovidesan

immediateinvestmentopportunity.Thisheatingand DWH

sys-temisbetterthantheinvestmentinairconditionercoupledwith

gaswaterheater,foralowrangeofusefulenergyneeds, asthe

onesconsideredinthisstudy.Thebiomasssystemoffersnegative

ROI,althoughitsignificantlyreducestheprimaryenergyneeds;the

photovoltaicpaneldidnotshowprofitability.

Reducingthecostofcapitalthroughprovisionofpubliccredit

linesatratesbelow6%mayencourageinvestmentinenergyretrofit

andefficiencymeasuresthatminimizetheprimaryenergyneeds.

Inthisscenario,alargernumberofpackageswithlower

environ-mentalimpactwouldhaveasatisfactoryROI,includingrenewables.

Regardingtheenergyretrofitofbuildings,ananalysisfromthe

perspectiveofthetheoryofrealoptionsisfundamentalbecause

thereareirreversibilityissuesandthepossibilityofdeferrallinked

totheinvestment.Mainlyinlargeinvestmentprojects,thevalue

ofoperationalflexibilityandotherstrategicfactors,inparticular thepossibilityofdeferralhastobeaddedtoNPVinthecalculation process.

Acknowledgments

The first author (Sérgio Tadeu) is grateful for the financial

supportprovidedby Ciência semFronteirasProgramand CNPq

(ConselhoNacionaldeDesenvolvimentoCientíficoeTecnológico)

inBrazil,throughthedoctoraldegreegrant237489/2012-0.The

second author would like to acknowledge the financial

sup-portfromCoordinationfortheImprovementofHigherEducation

Personnel(CAPES,grant 012322/2013-00) and theFederal

Uni-versityofOuroPreto.Thisworkhasbeenpartiallysupportedby

theR&D Project EMSURE (Energy and Mobility for Sustainable

Regions) – CENTRO 07 0224 FEDER002004 and projectgrants

UID/MULTI/00308/2013andMITP-TB/CS/0026/2013.Theauthors

are also grateful for the support of Institutefor Technological

ResearchandDevelopmentinConstructionSciences(ITeCons)and

ADENEforthedatausedinthisresearch.

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