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RESEARCHOpenAccessConfidencemodelingwithreliability:asystemsapproachtosustainableenergyplanningXiaoshengQin1,2*,YeXu3andJianjunYu4AbstractBackground:Energysystemsplanninghasplayedastrongroleinsettinguptheframeworkfordevelopinglong-termpoliciesofenergyactivitiestohelpguidethefutureofalocal,regionalornationalenergysystem.
However,theplanningprocessiscomplicatedwithavarietyofuncertaintiesandcomplexities.
Inthisstudy,afuzzyconfidencemodelcoupledwithmixed-integerprogrammingwasproposedforregionalenergysystemsplanning.
Results:Applicationofthemodeltoahypotheticalcaseindicatedthatthemodelwascapableofhandlinguncertaintiesexpressedasfuzzysetsandtakingcapacity-expansionissuesofenergyfacilitiesintoconsideration.
Thesolutionsfromtheproposedmodelcouldmeetsystemconstraintsatdifferentconfidencelevels,whereeachconfidencelevelwasfurtherassociatedwithdifferentreliabilityscenarios.
Conclusions:Theproposedmodelcouldhelpdecisionmakersanalyzethetrade-offsbetweensystemeconomyandreliability,andexplorecost-effectiveenergysystemsplanningstrategiesunderuncertainty.
Keywords:Fuzzyprogramming,Mixed-integerprogramming,Energy,UncertaintyBackgroundIthasbeenwidelyacceptedthatthetaskofenergysystemsplanningprocessinvolvesavarietyofsocial,economic,environmental,technical,andpoliticalfactorsthatarecharacterizedwithtemporalandspatialvariabilities(Caietal.
2009).
Thesystemisfurthercomplicatedbytheexistenceofuncertaintiesthatmaybeassociatedwiththeplanningprocesses.
Previously,anumberofinexactoptimizationtechniquesweredevelopedforassistingintheformulationofenergymanagementplansandgene-rationofoptimaldecisionschemes(Liuetal.
2000;Caietal.
2009;LinandHuang,2009).
Amongvariousalterna-tives,thefuzzychance-constrainedprogramming(FCCP)wasadvantageousindealingwithoptimizationproblemssubjecttofuzzyconstraintsatprescribedconfidencelevels(LiuandIwamura,1998).
Inrecentyears,FCCPwassuccessfullyusedinmanyenvironmentalmanagementfields(Caoetal.
2009).
However,itsapplicationinenergysystemsplanningfieldwasverylimited.
Moreover,aFCCPmodelisincapableofhandlingthebinary-decision(i.
e.
yes/no)problemswhichisimportantinenergysystemsplanningforseekingsolutionstocapacity-expansionoroperation-schedulingissues.
Tofillthisgap,thisstudyaimstodevelopadouble-sidedfuzzychance-constrainedmixed-integerprogramming(DFCCMIP)modelforsupportingregionalenergysystemsplanningunderuncer-tainty.
Ahypotheticalcasewillbeusedfordemonstration.
EnergysystemsplanningmodelAregionalenergysystemplanningsystem,modifiedfromLietal.
(2010),istobeinvestigated.
Withintheenergysys-tem,multipleenergysourcesareconsideredandvariouspowerconversiontechnologiesareappliedtogeneratetheelectricityfromtheprovidedenergysources.
Generally,large-scaleconversiontechnologiesareresponsibleforcon-ventionalenergyresources,andsmall-scaleplantsarebasedonlocalavailabilityofrenewableresources(Lietal.
2010).
Thegeneratedelectricitywillbeusedtomeettherequire-mentofmultipleend-usersincludingindustrial,commer-cial,agricultural,transportationalandresidentialsectors.
Forenvironmentalprotection,thegeneratedairpollutantsfrompowerconversionplantsshouldbemitigatedbydifferenttreatmenttechnologiesinordertomeettherelatedemissionstandards.
Thedecisionmakeris*Correspondence:xsqin@ntu.
edu.
sg1SchoolofCivil&EnvironmentalEngineering,NanyangTechnologicalUniversity,50NanyangAvenue639798Singapore2EarthObservatoryofSingapore(EOS),NanyangTechnologicalUniversity,50NanyangAvenue639798SingaporeFulllistofauthorinformationisavailableattheendofthearticle2012Qinetal.
;licenseeSpringer.
ThisisanOpenAccessarticledistributedunderthetermsoftheCreativeCommonsAttributionLicense(http://creativecommons.
org/licenses/by/2.
0),whichpermitsunrestricteduse,distribution,andreproductioninanymedium,providedtheoriginalworkisproperlycited.
Qinetal.
EnvironmentalSystemsResearch2012,1:6http://www.
environmentalsystemsresearch.
com/content/1/1/6responsibleforallocatingenergyresources/servicesfrommultiplefacilitiestomultipleend-usersataminimumsys-temcostwithinamulti-periodtimehorizoninlightofen-vironmentalconstraintsanduncertainties.
Itisassumedthattheend-users'electricitydemandscanbedescribedastriangularfuzzysets.
Overthethreeplan-ningperiods(eachonehas5years),thedemandamountsare(50,70,96),(85,112,147)and(135,170,200)*103GWh,respectively.
Thepeakloaddemandsareconsideredasdeterministic,being1.
5,2.
0,2.
5GWinthreeperiods,respectively.
Totally,fiveenergysources(i.
e.
,coal,naturalgas,hydropower,wind,solarandnuclear)areusedforpowergeneration.
Overthreeplanningperiods,thesuppliedcostsofcoalare2.
5,3and3.
5(*103$/TJ),re-spectively;thosefornaturalgasare5,5.
5and6(*103$/TJ),respectively;thoseforelectricityare900,1000and1100(*103$/GWh),respectively.
Inordertomeettheincreasingenergydemandfromtheend-users,capacityexpansionsofenergy-supplyfacilitiesarenecessary.
BasedonLietal.
(2010),theexistingcapacitiesofthecoal-fired,gas-fired,hydropower,windpower,solarpowerandnuclearpowerconversiontechnologiesaresetas10,2.
2,2.
8,0,0,0(GW),respectively.
OtherrelatedparametersassociatedwiththeexpansionoptionsarelistedinTable1.
Sulfurdioxide(SO2),nitrogenoxides(NOx)andparticu-latematter(PM)arethemainpollutantsemittedfrompowerplants.
Toachievetherelatedenvironmentaltargets,eachemissionsourcehasinstalledvariousmitigationmea-surestoavoidpenaltiesfromgovernment.
Theappliedcon-troltechniquesmainlyinclude:(i)sodaashscrubber(SAS),wetlimestonescrubber(WLS)andlimespraydryer(LSD)forreducingtheSO2amounts;(ii)Selectivecatalyticreduc-tion(SCR)andselectivenon-catalyticreduction(SNCR)forcontrollingNOxemissions;(iii)Fabricfiliter/baghouse(BH),electrostaticprecipitator(ESP)andwetcollector(WC)formitigatingthePMemissions(Lietal.
2010).
Thetreatmentefficienciesofvarioustechnologies,theallowableemissionamountsofpowerplants,anddesignsafetycoeffi-cientsforenergysupplyarealsodescribedbytriangularfuzzysets(seeTable2).
ModelFormulationDouble-sidedfuzzychance-constrainedprogramming(DFCCP)wasfirstlyproposedbyFiedleretal.
(2006).
InaDFCCPmodel,constraintswithfuzzyvariablescanbesatisfiedataseriesofpredeterminedconfi-dencelevelswithtworeliabilityscenarios,i.
e.
theminimumandmaximumreliabilities.
Themodelcouldeventuallybeconvertedintotwocrispequivalentsforsolution.
Therelatedsolutionalgorithmscouldbere-ferredtoFiedleretal.
(2006).
Inaddition,expansionoffacilitycapacityinenergysystemsplanningisneces-saryinordertomeettheincreasingenergydemandovertheplanninghorizons.
Mixedintegerlinearprogramming(MILP)isausefultool(throughusing0–1integervariables)tohelpdeterminewhetherornotaparticularfacilitydevelopmentoranexpansionoptionneedstobeundertaken(Huangetal.
1995).
CouplingDFCCPandMILPintoageneralframework,adouble-sidedfuzzychance-constrainedmixed-integerTable1ParametersrelatedtopowerconversiontechnologiesConversiontechnologyTimeperiodt=1t=2t=3Powergenerationcost($103/GWh)andoperatingtime(h)ofconversiontechnologyCoal-firedpower5.
0(24900*)5.
5(24900)6.
0(24900)Gas-firedpower4.
5(24600)5.
0(24600)5.
5(24600)Hydropower4.
0(21000)4.
5(21000)5.
0(21000)Windpower2.
5(15000)3.
0(15000)3.
5(15000)Solarpower2.
0(15000)2.
5(15000)3.
0(15000)Nuclearpower10.
0(24600)11.
012.
0(24600)Fixed($106)andvariable($106/GW)costsforcapacityexpansionCoal-firedpower325(700**)385(750)445(800)Gas-firedpower300(650)350(700)400(750)Hydropower700(1800)770(1900)840(2000)Windpower800(1900)880(1950)960(2000)Solarpower900(2000)990(2100)1080(2200)Nuclearpower1000(1950)1100(2100)1200(2250)Variableupperboundsforcapacityexpansion(GW)Coal-firedpower6.
54.
52.
5Gas-firedpower4.
85.
86.
8Hydropower2.
53.
54.
5Windpower0.
81.
82.
8Solarpower1.
82.
83.
8Nuclearpower2.
53.
54.
5Energyconsumptionperunitsofelectricityproduction(TJ/GWh)Coal-firedpower12.
512.
412.
3Gas-firedpower11.
511.
411.
3Hydropower4.
03.
953.
9Windpower0.
130.
120.
11Solarpower5.
04.
94.
8Nuclearpower13.
012.
812.
6Availableamountsofrenewableenergy(103TJ)Hydropower900009000090000Windpower150001500015000Solarpower200002000020000Nuclearpower150000150000150000Notes:dataaremodifiedfromLietal.
(2010);*istheoperatingtimeforconversiontechnology;**isthevariablecostsforcapacityexpansion.
Qinetal.
EnvironmentalSystemsResearch2012,1:6Page2of7http://www.
environmentalsystemsresearch.
com/content/1/1/6programming(DFCCMIP)modelcanbeformulatedasfollows(Lietal.
2010):MinfXTt1CECtXCtCENtXGtXTt1CIEtXEtXIi1XTt1CVitXWitXIi1XTt1YitAitBitXitXIi1XOo1XTt1CSotXSiotXIi1XPp1XTt1CNptXNiptXIi1XQq1XTt1CPqtXPiqt1aSubjectto:(1)Constraintsformassbalanceoffossilfuels:XW1tFE1t≤XCt;8t1bXW2tFE2t≤XGt;8t1c(2)Constraintsforavailabilitiesofenergyresources:XWitFEit≤UPit;8tfori≥31d(3)Constraintsforelectricitysupplyanddemandbalance:Pos~αl;~dt~αlXIi1XWitXEt≥~dt)≥βl;8t(1e(4)Constraintsforelectricitygenerationofeverypowerconversiontechnology:Xtt01Xit0RCi!
STit≥XWit;8i;t1f(5)Constraintsforelectricitypeakloaddemand:XIi1RCiXIi1Xtt01Xit0≥Vt;8t1g(6)Constraintsforcapacityexpansionofelectricity-generationfacilities:Yit1;ifcapacityexpansionisundertaken0;ifotherwise;8i;t&1hXit≤MitYit;8i;t1iTable2ParametersrelatedtopollutioncontroltechnologiesPollutioncontroltechnologyTimeperiodt=1t=2t=3TreatmentcostofSO2emission($/tonne)SAS555759WLS454851LSD303336TreatmentcostofNOxemission($/tonne)SCR555962SNCR353840TreatmentcostofPMemission($/tonne)BH135140145ESP125133140WC115125135Allowableemissionamountsofpollutants(tonne)SO2(40,44,50)*(61,72,81)(69,82,93)NOx(20,32,45)(31,47,61)(35,57,80)PM(0.
3,0.
52,0.
7)(0.
45,0.
8,1.
1)(0.
49,0.
89,1.
2)Treatmentefficiencyofpollutants(%)SAS(0.
85,0.
91,0.
99)WLS(0.
76,0.
82,0.
9)LSD(0.
7,0.
77,0.
85)SCR(0.
8,0.
86,0.
9)SNCR(0.
5,0.
62,0.
7)BH(0.
96,0.
975,0.
99)ESP(0.
95,0.
964,0.
98)WC(0.
94,0.
958,0.
97)Notes:dataaremodifiedfromLietal.
(2010);*(a,b,c)representsatriangularfuzzyset,whereaandcaretheminimumandthemaximumpossiblevalues,andbisthemostlikelyvalue.
Qinetal.
EnvironmentalSystemsResearch2012,1:6Page3of7http://www.
environmentalsystemsresearch.
com/content/1/1/6(7)Constraintsforairpollutioncontroldemand:XOo1XSiotWitINSit;8i;t1jXPp1XNiptWitINNit;8i;t1kXQq1XPiqtWitINPit;8i;t1l(8)Constraintsforairpollutantsemissions:Pos~ηo;ESteXIi1XOo11~ηoXSiot≤ESte)≥βl;8t(1mPos~ηP;ENteXIi1XPp11~ηpXNipt≤ENte)≥βl;8t(1nPos~ηq;EPteXIi1XQq11~ηqXPiqt≤EPte)≥βl;8t(1o(9)Non-negativeconstraints:XCt;XGt;XEt;XWit;Xit≥0;8i;t1pwherefisexpectedsystemcostforenergysystemmanagementovertheplanninghorizon($109);iistypeofpowerconversiontechnology,i=1,2,.
.
,I(inthisstudy,Iisconsideredas6,wherei=1,2,.
.
.
,6meansthecoal,naturalgas,hydropower,windpower,solarpowerandnuclearpower,respectively);oistypeofSO2controlmeasure,o=1,2,.
.
.
,O;pistypeofNOxcontrolmeasure,p=1,2,.
.
.
,P;qistypeofPMcontrolmeasure,q=1,2,.
.
.
,Q;O,PandQarenumbersofcontrolmeasureofthepollutants,respec-tively;tistimeperiod,t=1,2,.
.
,T;t'isanintermediateindexsatisfying1≤t'≤t;CECtandCENtarecostforcoalandna-turegassupplyinperiodt($103/TJ),respectively;CIEtarecostforimportedelectricitysupplyinperiodt($103/GWh),respectively;UPit(i≥3)areavailableamountsofhydropower,windpower,solarpowerandnuclearpowerinperiodt(103TJ),respectively;CVitisoperatingcostofpowerconversiontechnologyiforelectricitygenerationinperiodt($103/GWh);CSot,CNptandCPqtareunitopera-tingcostofcontrollingSO2,NOxandPMemissionsduringperiodt,($/tonne),respectively;STitisaverageservicetimeofpowerconversiontechnologyiinperiodt(h);Vtispeakloaddemandinperiodt(GW);AitandBitarefixed-chargeandvariablecostforcapacityexpansionofpowerconver-siontechnologyiinperiodt($106,$106/GW),respectively;RCiistheexistingcapacityofconversiontechnologyi(GW);FEitistheunitsofenergyconsumptionperunitsofelectricityproductionforpowerconversiontechnologyiinperiodt(TJ/GWh);Mitisvariableupperboundsforcap-acityexpansionofpowerconversiontechnologyiinperiodt(GW);INSit,INNitandINPitareunitsofSO2,NOxandPMemissionperunitofelectricityproductionforpowerconversiontechnologyiinperiodt(tonne/GWh),respect-ively;~ηo,~ηpand~ηqaretheaverageefficiencyofSO2,NOxandPMcontrolmeasure(%),whichareexpressedasthetriangularfuzzysets,respectively;ESte,ENteandEPtearetheemissionallowanceofSO2,NOxandPMinperiodt(tonne),whichareexpressedasthetriangularfuzzysets,respectively;~αlisdesignsafetyfactorsassuringtheelectri-citydemandcanbesatisfiedcompletelyduringperiodt,whichareexpressedasthetriangularfuzzysets;~dtisthetotalelectricitydemandduringperiodt(103GWh),whichareexpressedasthetriangularfuzzysets;dt~isthetotalelectricitydemandduringperiodt(103GWh),whichareexpressedasthetriangularfuzzysets;Posfgdenotespossi-bilityofeventsinfgwhereβlisapredeterminedconfidencelevelandlistypeofconfidencelevels;XCtandXGtaresup-plyamountsofthecoalandnaturalgasinperiodt(TJ),re-spectively;XEtistheimportedelectricitysupplyinperiodt(103GWh);XWitiselectricitygenerationamountsofpowerconversiontechnologyiduringperiodt(103GWh);Xitiscontinuousvariablesabouttheamountofcapacityexpan-sionofpowerconversiontechnologyiinperiodt(GW);Yitisthebinaryvariablesforidentifyingwhetherornotacapacityexpansionactionofpowerconversiontechnologyineedstobeundertakeninperiodt;XSiot,XNiptandXPiqtaretheSO2,NOxandPMamountgeneratedfrompowerconversiontechnologyitobetreatedbycontrolmeasureo,pandqinperiodt(tonne),respectively.
ResultsanddiscussionFigure1showsthemodelsolutionsforthesuppliedamountsofcoalandgas.
Itisindicatedthatthetemporalandspatialvariationsofelectricitydemandmayresultinvariedenergysupplyschemes.
Astheelectricitydemandincreases,thesuppliedamountsofthecoalandnaturalgaswouldincreaseoverthethreeplanningperiods,andthesuppliedamountsofthecoalarehigherthanthoseofthenaturalgas.
ItisalsofoundthatthereisnoneedtoimportQinetal.
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Forexample,ataconfidencelevelof0.
4withtheminimumreliability,theamountsofcoalsupplyare351.
69,851.
52and1033.
97*103TJoverthethreeplanningperiods,respectively;thesuppliedamountsofnaturalgasare0,0and471.
98*103TJ,re-spectively.
Thisisbecausethecoalownsthelowestunitsupplycost(i.
e.
31.
25,37.
20and43.
05*103$/TJ),thenaturalgasrankedinthemiddle(i.
e.
57.
50,62.
70and67.
80*103$/TJ),andtheimportedelectricityisthehigh-est(i.
e.
900,1000and1100*103$/GWh).
Figure2showsthesolutionofelectricitygenerationamounts.
Forthere-newableenergy,theelectricitygenerationamountsbythehydropowerare22.
50,22.
78and23.
08GWhoverthethreeplanningperiods,respectively.
Thosebythewind-powerare12.
00,12.
00and12.
00GWhoverthethreeplanningperiods,respectively.
Thisisduetothefactthatthehydropowerhasthehighestexistingcapacity,andthelowestfixedandvariablecostsforcapacityexpansionamongallrenewableenergysources.
FromFigures1and2,thesolutionsofdecisionvariableshavenotablevariationsatdifferentα-cutlevelswithtwore-liabilityscenarios.
Thesuppliedamountsofthecoalwiththemaximumreliabilityareinadecreasingtrendwhentheα-cutlevelisincreasing.
Comparedwiththoseofthecoal,thesuppliedamountsofthenaturalgaswouldincreasewiththeincreaseoftheα-cutlevel.
Thisisbecause,whentheconfidencelevelincreases,theelectricitydemandwouldincreaseaccordingtofuzzyalgorithmrule(Fiedleretal.
2006);meanwhile,theconstraintsoftheenvironmentalemissionstandardswouldbecomestricter.
Thiswillleadtothedecreaseofthecoalsuppliedamounts,whicharedeci-dingfactorforpollutantemissions.
Atthesametime,thesuppliedamountsofthenaturalgaswithlowpollutantemissionswouldincrease.
Thisreflectsthetrade-offbetweensystemeconomyandreliability.
Alowersystemcostwouldbeincurredifalargerquantityofpollutantemissionisallowable;meanwhile,theplanningschemewithahighercostwouldurgetheenvironmentalqualitymain-tainatahigherlevel.
Thevariationtrendofthesolutionsunderthemini-mumreliabilityisgenerallysimilartothoseunderthemaximumone,exceptforafewinconsistentpoints.
Forexample,inperiod3,thesuppliedamountsofthecoalare1520.
76,1345.
90,1173.
80,1033.
97,918.
11,820.
54,737.
25,665.
32and602.
57*103TJ,respectively;thoseofthenaturalgasare0,213.
41,423.
83,471.
98,328.
16,473.
37,606.
19,594.
80and710.
26*103TJ,respectively.
Thesuppliedamountsofthenaturalgasattheconfi-dencelevelsof0.
5and0.
8inperiod3arenotconsistentwiththegeneralchangingtrend,asarethecasesforanumberofsolutionsofcoalinperiods1and2.
Thisismainlyduetothecomplexinteractiverelationshipsamongvariouscomponentsoftheplanningsystem.
Anotherreasonmaybethelooseconstraintsincurredbythesettingofminimumreliability,makingtheeffectofconfidencelevelsbecomelesssignificant.
Inaddition,atthesameα-cutlevels,thesuppliedamountsofthecoalundertheminimumreliabilityarehigherthanthoseunderthemaximumone;fornaturalgas,thevaryingtrendisopposite.
Thisisduetothefactthatthemini-mumreliabilitypreferslooserenvironmentalemissionstandardsandlowerelectricitydemandthanthema-ximumreliabilitydoes.
Therefore,theenergysourceofcoalwouldbecomemorepopularthanthenaturalgas.
Theoptimaltreatmentamountsofpollutantscanbegeneratedfromvariousconversiontechnologiesundertworeliabilitylevels.
Thesolutionindicatesthatthein-creaseofthecoalandnaturalgasamountswouldresultinFigure1Solutionsofcoalandgassuppliedamounts.
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com/content/1/1/6anincreasedamountofpollutantreduction.
Forexample,thedisposalamountsofSO2generatedfromthecoal-firedpowerconversiontechnologybySASoverthethreeplan-ningperiodsare0,170.
25and243.
56t,respectively;theallocatedamountsofNOxtotheSCRtechnologyare0,49.
61and62.
89t,respectively;thetreatedamountsofPMtotheBHtechnologyare13.
47,55.
92and67.
25t,respect-ively.
Generally,thevaryingtrendsofthepollutanttreat-mentamountsweresimilartothoseofthesuppliedamountsfortheemissionsources.
Whentheconfidencelevelincreases,thetreatedamountsofSO2fromcoalwouldgenerallydecrease.
Forexample,underthemini-mumreliability,attheperiod3,thetreatedamountsbySASatthedifferentconfidence-levelsare459.
86,390.
28,310.
01,243.
56,186.
98,140.
01,99.
44,61.
14and31.
88t,respectively;thosebytheLSDare529.
26,485.
10,453.
44,428.
94,410.
16,393.
68,380.
07,371.
59and360.
03t,respectively.
Thereasonisthat,whentheconfidencelevelgoeshigher,theconstraintsoftheenvironmentalstan-dardswouldbecomestricter;thiswouldleadtoreducedsuppliedamountsofthecoal,andconsequentlydecreasedemissionlevelsofthepollutants.
Meanwhile,overthethreeplanningperiods,thetreatedamountsofthecoalbySASarelowerthanthosebyLSD,duetoitshigheroper-ationalcost.
Similartrendscanalsobefoundforthepol-lutantsgeneratedfromthenaturalgas.
Thetotalcostsatdifferentα-cutlevelsalsovarywithreliabilities.
Astheα-cutlevelincreases,theelectricitysupplywouldincrease,leadingtobetterenvironmentalquality;however,therelatedsystemcostwouldincrease.
Thesystemcostwiththeminimumreliabilitywouldbelowerthanthatwiththemaximumone,indicatingthatalowersystemcostisrelatedtoahigherenvironmentalrisk.
Aconservativealternativeismoreeffectivetomeettheelectricityrequirementandmaintaintheenviron-mentalquality.
Atrade-offbetweenthetotalsystemcostandreliabilityofsatisfyingmodelconstraintsneedstobeanalyzedinordertogainanin-depthinsightintothecharacteristicsofenergyplanningsystems.
ConclusionsAdouble-sidedfuzzychance-constrainedmixed-integerprogramming(DFCCMIP)modelwasdevelopedinthisstudyandappliedtoaregionalenergysystemsplanningFigure2Solutionsofelectricitygenerationamounts.
Qinetal.
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com/content/1/1/6problem.
ThemodelcoupledDFCCPandMIPmodelsintoageneralframework,andcouldhelpdealwithun-certaintiesexpressedasfuzzysetsassociatedwithboththeleft-andright-hand-sidecomponentsofcon-straints,andthecapacityexpansionissueofenergy-productionfacilities.
ThestudyresultsindicatedthatDFCCMIPallowedviolationofsystemconstraintsatspecifiedconfidencelevelswithvariousreliabilityscenarios.
Thesolutionsofcontinuousandbinaryvari-ablescouldhelpdecisionmakersestablishvariousenergyproductionpatternsandcapacity-expansionplansundercomplexuncertainties,andgainin-depthinsightsintothetrade-offsbetweensystemeconomyandreliability.
CompetinginterestsTheauthorsdeclaredthattheyhavenocompetinginterest.
AcknowledgementThisresearchwassupportedbyEarthObservatoryofSingapore(EOS)Project(M4080891.
B50)andSingapore'sMinistryofEducation(MOM)AcRFTier1Project(M4010973.
030).
Authordetails1SchoolofCivil&EnvironmentalEngineering,NanyangTechnologicalUniversity,50NanyangAvenue639798Singapore.
2EarthObservatoryofSingapore(EOS),NanyangTechnologicalUniversity,50NanyangAvenue639798Singapore.
3S-CResearchAcademyofEnergy&EnvironmentalStudies,NorthChinaElectricPowerUniversity,Beijing102206,China.
4DHI-NTUWater&EnvironmentResearchCentreandEducationHub,NanyangTechnologicalUniversity,50NanyangAvenue639798,Singapore.
Authors'contributionsQXSisresponsibleforthedevelopmentoftheenergysystemsplanningmodelanddraftedthemanuscript.
XYparticipatedinmodelcomputation,andinvolvedinresultanalysis.
YJJparticipatedinthemodeldevelopment,andhelpedpolishthemanuscript.
Allauthorsreadandapprovedthefinalmanuscript.
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JPetrolSciEng26:301–309doi:10.
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:Confidencemodelingwithreliability:asystemsapproachtosustainableenergyplanning.
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