Citation
Socially Optimal Policies for Light-Duty Vehicle Electrification and Operations

Material Information

Title:
Socially Optimal Policies for Light-Duty Vehicle Electrification and Operations
Creator:
Kontou, Eleftheria
Publisher:
University of Florida
Publication Date:
Language:
English

Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Civil Engineering
Civil and Coastal Engineering
Committee Chair:
YIN,YAFENG
Committee Co-Chair:
ELEFTERIADOU,AGELIKI
Committee Members:
WASHBURN,SCOTT STUART
SRINIVASAN,SIVARAMAKRISHNAN
GUAN,YONGPEI
LIN,ZHENHONG
Graduation Date:
12/17/2016

Subjects

Subjects / Keywords:
bev
chargers
charging
electric
electric-driving-range
incentives
phev
plug-in-hybrid
vehicles
Uniform Resource Locators ( jstor )
Infrastructure ( jstor )
Cost estimates ( jstor )
Genre:
Unknown ( sobekcm )

Notes

General Note:
This work explores socially optimal policies for deploying plug-in electric vehicles to achieve higher energy efficiency and reduce the environmental impacts of the light-duty transportation sector. This study is motivated by four research questions: (A) what is the optimal driving range for plug-in hybrid electric vehicles (PHEVs) that minimizes the societal cost of adopting and operating this technology?; (B) can optimal control of PHEVs charging benefit the users and the government and how such control can impact the utility grid load?; (C) what is the optimal electrification pace for the household fleet yielding the greatest societal benefits?; and (D) what is the optimal investment portfolio for incentives which results in greater benefits for society during the passenger fleet electrification? This work advances our understanding on the effects of electric driving range and workplace charging infrastructure on the societal costs incurred when adopting and operating PHEVs. It evaluates the impact of cost-effective and eco-friendly PHEV charging management on the utility grid. It illustrates the socially optimal pathway from gas-fueled to battery electric vehicles (BEVs). Incentives design pinpoints government's role in promoting the adoption of BEVs. An optimization framework determining the optimal driving range of PHEVs answered the first question. The model was extended to capture the impact of workplace-charging density, as well as the optimal diversity of electric ranges on the societal cost of the PHEV operation. The second question was addressed by developing two PHEV charging management schemes. The first minimized the PHEV users' cost and the second the monetized carbon dioxide emissions from PHEV operation. The third question was answered by minimizing the societal cost of the transition through determining the annual electrification pace along with the all-electric driving range of BEVs, and the public-charging density on linear transportation corridors. The resulting electrification pathway showcased target BEV adoption goals. The last one was addressed through determining and prioritizing optimal incentives that maximize fuel consumption savings and environmental externalities reduction during the electrification timeframe. These models were applied to uncover several policy implications by leveraging datasets from the United States automobile and energy market.

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
Copyright Kontou, Eleftheria. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Embargo Date:
6/30/2017

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SOCIALLYOPTIMALPOLICIESFORLIGHT-DUTYVEHICLEELECTRIFICATIONAND OPERATIONS By ELEFTHERIAKONTOU ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF DOCTOROFPHILOSOPHY UNIVERSITYOFFLORIDA 2016

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c 2016EleftheriaKontou

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Tomyfamily

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ACKNOWLEDGMENTS Iwouldliketosincerelythankmyadvisor,Dr.YafengYin,forintroducingmetothetopic ofvehicleelectricationandforadvisingmetobecomeanexpertinthiseld.Ifeelprivileged tostudyunderhisadvisement;duringmyPhDtenurehiscontributioninmyprofessional growthwasofparamountimportance.IextendmygratitudetomyPh.D.committeemembers, Drs.AgelikiElefteriadou,YongpeiGuan,ZhenhongLin,SivaSrinivasan,andScottWashburn fortheirvaluablecommentsandsuggestionsthathelpedshapingthisdissertationdocument. IthankonceagainDr.Linwhoprovidedmetheopportunitytoworkunderhisdirection intheCenterforTransportationAnalysisattheOakRidgeNationalLaboratory.Iamalso thankfultoDr.LiuforourcollaborationandMs.DianeDavidsonforwelcomingmetoher groupofpreeminentresearchers. Iamforeverindebttomyadvisorandmentor,thelateProfessorMatthewKarlaftis,who wastheonethatmotivatedmetopursuegraduatestudiesintheUnitedStates. ShoutouttotheWomen'sTransportationSeminarFloridaGatorstudentchapter membersandMs.InesAviles-SpadoniwithwhomIsharethepassionforpromotingdiversityin academiaandparticipatinginsocialentrepreneurshipventurestocelebratetheinvolvementof womenintransportationengineering.Here,IwouldalsoliketothankMs.NancyMcIlrath,asI deeplyappreciateherassistanceduringgradschool. Iamthankfulforthefriendshipofthe"Gainesvillesquad"members:Dr.AlexKondyli, DionisisVossos,Dr.LiaMerivaki,IoannisZiogas,MariaVrachioli,Dr.AngelosDeltsidis, andIoannisPappas.IthankmyfriendsfromNTUAandmyhometownforsupportingme;I misstheirpresenceverymuch.Lastandforemost,myfamilysupportsmeimmenselyandI acknowledgethemforthat.Ithankmydad,DimitriosKontos,mymom,NtinaTiliopoulou, andmysister,ValiaKontou,fortheirloveanda! ection.ComingtoUniversityofFlorida topursuemyPhDalsoledtomeetingandhavingDr.ChrysasVogiatzisbymyside.I amgladforhavinghiminmylifeandIthankhimforhispatience,love,andnever-ending encouragement. 4

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TABLEOFCONTENTS page ACKNOWLEDGMENTS ................................... 4 LISTOFTABLES ...................................... 8 LISTOFFIGURES ..................................... 9 LISTOFSYMBOLS ..................................... 11 ABSTRACT ......................................... 12 CHAPTER 1INTRODUCTION ................................... 14 1.1Background ................................... 14 1.2ProblemStatements ............................... 18 1.2.1SociallyOptimalElectricDrivingRangeofPHEVs ........... 18 1.2.2ChargingManagementofPHEVs .................... 19 1.2.3SociallyOptimalElectricationoftheConventionalLight-dutyFleet .. 19 1.2.4IncentiveSchemeDesignforPromotingBEVAdoption ......... 20 1.3ObjectivesandContributions .......................... 20 1.4DissertationOutline ............................... 22 2LITERATUREREVIEW ................................ 25 2.1OptimalElectricDrivingRangeforPlug-inElectricVehicles .......... 25 2.2ChargingManagementStrategies ........................ 28 2.3TransitionfromConventionaltoBatteryElectricVehicles ........... 30 2.4IncentivesDesignforPlug-inElectricVehiclesAdoption ............ 34 2.5Summary ..................................... 38 3SOCIALLYOPTIMALELECTRICDRIVINGRANGEOFPLUG-INHYBRIDELECTRIC VEHICLES ....................................... 40 3.1ElectricDrivingRangeOptimizationFramework ................ 40 3.1.1InternalUserCost ............................ 41 3.1.2ExternalEnvironmentalCost ....................... 43 3.1.3ExternalChargingInfrastructureCost .................. 45 3.2Data ....................................... 45 3.3Results ...................................... 47 3.3.1BaseCase ................................ 47 3.3.2SensitivityAnalysis ............................ 49 3.4ModelExtensions ................................ 50 3.4.1DeploymentofWorkplaceChargingInfrastructure ............ 50 3.4.2DiversicationoftheElectricDrivingRange ............... 53 5

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3.5Summary ..................................... 55 4COST-EFFICIENTANDECO-FRIENDLYPLUG-INHYBRIDELECTRICVEHICLE CHARGINGMANAGEMENT ............................. 61 4.1ChargingManagementOptimizationFramework ................ 62 4.2Data ....................................... 64 4.2.1DriverTravelProles ........................... 64 4.2.2PHEVCongurationandChargingTypes ................ 66 4.2.3MarginalEmissionRates ......................... 66 4.2.4ElectricityPrices ............................. 66 4.2.5ChargingInfrastructure .......................... 67 4.2.6PHEVPenetrationRateandOtherParameters ............. 68 4.3Results ...................................... 68 4.3.1BaseCase ................................ 68 4.3.2AlternateScenarios ............................ 70 4.4Summary ..................................... 71 5SOCIALLYOPTIMALREPLACEMENTOFCONVENTIONALVEHICLESWITH BATTERYELECTRICVEHICLES .......................... 79 5.1ConventionalwithBatteryElectricVehicleReplacementOptimizationFramework 79 5.1.1ModelingFrameworkandAssumptions ................. 79 5.1.2ConventionalVehicleCosts ........................ 83 5.1.3BatteryElectricVehicleCosts ...................... 85 5.1.4P1:Distancebetweenchargerslessthanorequaltotheall-electricdriving range ................................... 86 5.1.5P2:Distancebetweenchargersgreaterthantheall-electricdrivingrange 88 5.1.6PublicCharingInfrastructureCost .................... 89 5.2Data ....................................... 89 5.3Results ...................................... 92 5.3.1BaseCase ................................ 94 5.3.2AlternativeScenarios ........................... 97 5.4Summary ..................................... 99 6INCENTIVESSCHEMESFORMAXIMIZINGTHEBENEFITSFROMBATTERY ELECTRICVEHICLEADOPTION .......................... 108 6.1IncentivesOptimizationFramework ....................... 108 6.1.1ICEVandBEVDemandFunctions .................... 110 6.1.2ModelingFramework ........................... 113 6.2Data ....................................... 115 6.3Results ...................................... 115 6.3.1BaseCaseResults ............................ 115 6.3.2AlternativeScenarioResults ....................... 117 6.4Summary ..................................... 118 6

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7CONCLUSIONSANDFUTURERESEARCH ..................... 123 7.1Contributions ................................... 123 7.2FutureResearch ................................. 124 REFERENCES ........................................ 126 BIOGRAPHICALSKETCH ................................. 138 7

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LISTOFTABLES Table page 1-1VehicleFuelEconomyCharacteristics ......................... 23 1-2ChargingE"ciencyandTime ............................. 23 1-3FuelPricing:ElectricityOn-PeakResidentialPricingvs.GasPriceperMile ..... 24 3-1CostComponentsforDailyVMTof26.2miles .................... 57 3-2BaselineandSensitivityParameters .......................... 58 4-1VehicleandChargingCharacteristics(U.S.DepartmentofEnergy,2016d) ..... 73 4-2AverageObjectiveFunctionValueResults(dollarcentsperhourperPHEV) .... 73 5-1DescriptiveStatisticsoftheNHTS2009DataSample ................ 101 5-2BaseCaseandAlternativeScenariosParameters ................... 102 6-1ParametersFunctions ................................. 119 6-2ScalarModelingParameters .............................. 120 6-3AlternateScenarioSavings,InvestmentsandBEVMarketShareDi!erencesfrom theBaseCase ..................................... 121 8

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LISTOFFIGURES Figure page 3-1Batterypackcostwithrespecttobatterycapacity. .................. 56 3-2Electricityandgasolineconsumptionrates. ...................... 56 3-3Averagecostcomponentswithrespecttotheelectricdrivingrangewithonlyhome-charging availability. ....................................... 57 3-4SensitivityoftheoptimalPHEVelectricdrivingrangeandtheminimumsocialcost. 59 3-5Averagesocialcostwithwork-chargingavailability. .................. 60 4-1AverageVMTand%ofvehiclesinsampletravelingorbeingidleperhourofday. 72 4-2Marginalelectricitygenerationemissionratesandcostsperhour(Gra!Zivinetal., 2014). ......................................... 74 4-3Percentageofpublicandworkplacechargingavailabilityfortripsdestinationsand workersrespectively. .................................. 75 4-4Optimalchargingprolespercentagesofthecost-e! ectiveandeco-friendlycharging managementschemes. ................................. 76 4-5AveragehourlypowerloadprolespereachNERCregion .............. 77 4-6DailyMileageElectricationforNERCregions. .................... 78 4-7Chargingproleswhenonlyhome-chargingandonlyhome-andworkplace-charging (all-but-public-charging)areavailablefortheWECCregion. ............. 78 5-1Expectedextendeddrivingrangeestimationwhen r w ( t ) ............. 101 5-2Expectedextendeddrivingrangeestimationwhen r < w ( t ) ............. 101 5-3Fittedequationsofthemodelparameters. ...................... 103 5-4IndicativeICEVandBEVcostcomponentvaluesfor w ( t ) =150 miles. ....... 104 5-5IndicativeBEVcostcomponentsvaryingwith w for t =1 ............. 105 5-6CumulativeBEVpenetration(a),basecasecosts(b)andVMTofICEVsreplaced andused(c). ...................................... 106 5-7Alternativescenariodecisionvariables, r and w results. ............... 107 5-8ReplacementofICEVwithBEVcumulativerateswhenaccountingfortherebound e ect. ......................................... 107 9

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6-1Theevolutionofmarketshareforvehicletechnologiesunderalternativeincentive schemeinvestments. .................................. 120 6-2Optimalincentivepoliciesunderalternativeincentiveschemeinvestments. ..... 121 6-3InitialandnalBEVmarketshareforeachU.S.CensusBureauregion,underoptimal incentivesallocation. .................................. 122 10

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LISTOFSYMBOLS,NOMENCLATURE,ORABBREVIATIONS BEVBatteryElectricVehicle DOEUnitedStatesDepartmentofEnergy GHGGreenhousegases GPSGlobalpositioningsystem HEVHybridElectricVehicle HOVHighOccupancyVehicle ICEVInternalCombustionEngineVehicle MPGMilespergallon MPGeMilespergallonequivalent NERCNorthAmericanElectricReliabilityCorporation PEVPlug-inElectricVehicle PHEVPlug-inHybridElectricVehicle TOUTimeOfUse VMTVehicleMilesTravelled 11

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AbstractofDissertationPresentedtotheGraduateSchool oftheUniversityofFloridainPartialFulllmentofthe RequirementsfortheDegreeofDoctorofPhilosophy SOCIALLYOPTIMALPOLICIESFORLIGHT-DUTYVEHICLEELECTRIFICATIONAND OPERATIONS By EleftheriaKontou December2016 Chair:YafengYin Major:CivilEngineering Thisworkexploressociallyoptimalpoliciesfordeployingplug-inelectricvehiclesto achievehigherenergye"ciencyandreducetheenvironmentalimpactsofthelight-duty transportationsector.Thisstudyismotivatedbyfourresearchquestions:(A)whatisthe optimaldrivingrangeforplug-inhybridelectricvehicles(PHEVs)thatminimizesthesocietal costofadoptingandoperatingthistechnology?;(B)canoptimalcontrolofPHEVscharging benettheusersandthegovernmentandhowsuchcontrolcanimpacttheutilitygridload?; (C)whatistheoptimalelectricationpaceforthehouseholdeetyieldingthegreatestsocietal benets?;and(D)whatistheoptimalinvestmentportfolioforincentiveswhichresultsin greaterbenetsforsocietyduringthepassengereetelectrication? Thisworkadvancesourunderstandingonthee!ectsofelectricdrivingrangeand workplacecharginginfrastructureonthesocietalcostsincurredwhenadoptingandoperating PHEVs.Itevaluatestheimpactofcost-e!ectiveandeco-friendlyPHEVchargingmanagement ontheutilitygrid.Itillustratesthesociallyoptimalpathwayfromgas-fueledtobatteryelectric vehicles(BEVs).Incentivesdesignpinpointsgovernment'sroleinpromotingtheadoptionof BEVs. AnoptimizationframeworkdeterminingtheoptimaldrivingrangeofPHEVsansweredthe rstquestion.Themodelwasextendedtocapturetheimpactofworkplace-chargingdensity,as wellastheoptimaldiversityofelectricrangesonthesocietalcostofthePHEVoperation.The secondquestionwasaddressedbydevelopingtwoPHEVchargingmanagementschemes.The 12

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rstminimizedthePHEVusers'costandthesecondthemonetizedcarbondioxideemissions fromPHEVoperation.Thethirdquestionwasansweredbyminimizingthesocietalcostofthe transitionthroughdeterminingtheannualelectricationpacealongwiththeall-electricdriving rangeofBEVs,andthepublic-chargingdensityonlineartransportationcorridors.Theresulting electricationpathwayshowcasedtargetBEVadoptiongoals.Thelastonewasaddressed throughdeterminingandprioritizingoptimalincentivesthatmaximizefuelconsumptionsavings andenvironmentalexternalitiesreductionduringtheelectricationtimeframe. Thesemodelswereappliedtouncoverseveralpolicyimplicationsbyleveragingdatasets fromtheUnitedStatesautomobileandenergymarket. 13

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CHAPTER1 INTRODUCTION 1.1Background Thepassengervehicleeetisrapidlychangingastechnologicaladvancementsimprove light-dutyvehiclesperformanceandoperation.Thelandscapeofpersonalmobilityisalso shapedbythesocialconsiderationsofthemarketforsustainabletransportation( Turrentine etal. 2007 ).Theinnovativenessandtheengineeringingenuityofthealternativefuelvehicles attractconsumerattention( Rezvanietal. 2015 );plug-inelectricvehicles(PEVs)are promotedbygovernmentsthroughincentives,duetotheirpromiseofreducingemissions andoperationalcost( MockandYang 2014 ). ThetermPEVisusedtodescribevehiclesthatoperatepartiallyorfullyusingbattery powerandchargewithelectricityfromtheutilitygrid.ThesizeofbatterythatPEVscarry determinestheirelectricdrivingrange.Plug-inhybridelectricvehicles(PHEVs)carrybothan electricmotorandaninternalcombustionengine,andthuscanelectrifyallorpartoftheir dailytrips,dependingontheelectricrangeandtheirdailytrips'mileage( U.S.Departmentof Energy 2013c ).Batteryelectricvehicles(BEVs)haveonlyabatterypackthatprovidespower totheelectricmotor,insteadofhavinganinternalcombustionengineandagastank( U.S. DepartmentofEnergy 2013b ).Whenoperatingsolelyonelectricity,PEVshavezerotailpipe emissions( U.S.DepartmentofEnergy 2016c );hence,substitutionofinternalcombustion enginevehicles(ICEVs)withPEVscanpotentiallyreducegreenhousegas(GHG)emissionsfor thepassengercartransportationsector,dependingonthesourceofelectricityusedforPEVs recharging. PEVsarepenetratingthemarketmuchfasterthanhybridelectricvehicles(HEVs)did.It onlytook36monthsforPEVstoreach160,000saleswhenintroducedin2010,whileHEVs onlycounted60,000salesafter36monthsfromtheirintroductionin1999( U.S.Department ofEnergy 2013c ).Thismarketpullisanoutcomeofresearchanddevelopmentinvestments thatledtoadvancingelectricvehiclebatterytechnologiesandaddressingclimateconcerns 14

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regardingtransportationsustainabilityandenergysecurity( U.S.DepartmentofEnergy 2013a ). PEVshavecertainadvantageswhencomparedwithICEVs.Theformeronescanachieve higherfueleconomies.Forexample,ChevyVolt2016andNissanLeaf2016bothbelongtothe U.S.best-sellingmodelseriesforPHEVsandBEVsandhave106and114MPGeratedfuel economyinchargedepletingmode( U.S.DepartmentofEnergy 2016c b ).Onthecontrary, ICEVmodels,likeHondaAccordandToyotaCamry,havecombined(highwayandcity)MPG of31and28respectively( U.S.DepartmentofEnergy 2016b ). TheextenttowhichPEVscontributetosource-to-wheelemissionsreductiondependson thegenerationsourceoftheelectricitythatisusedtorecharge.Thereisregionalandtemporal variabilityofthesource-to-wheelenvironmentalbenetsfromPEVusage.Source-to-wheel emissionsofPEVsmightnotbelowerthanthoseofICEVsingeographicregionswhere electricityislargelygeneratedfromfossilfuels( U.S.DepartmentofEnergy 2016c ).For instance,forthestateofWyomingwhere88.9%oftheelectricitygenerationsourceiscoal, byoperatingaPHEV,22%annualemissionsreductionisachievedcomparedtoanICEV operation;forthestateofVermont,thispercentageincreasesto71%becausethemajorsource ofelectricitygenerationisnuclear(71.9%).Smartandcentralizedchargingcontrolhasbeen exploredasameantominimizetheimpactsofthepotentialelectricitydemandsurgeduring theelectricationofpersonalmobility.Centralizedchargingmanagementcanenhancethe reliabilityoftheutilitygrid,decreasegenerationcosts,andcontrolemissionsassociatedwith thePEVchargingprocess( Verzijlberghetal. 2012 ). DriversofPEVsachieveoperationalsavingsbysubstitutinggasolinewithgridelectricity. Acomparisonoftheoperationalcostbetweeneachtechnologyisdemonstratedbelow.Table 1-1 showsvehiclecharacteristicsofbest-sellingICEV,PHEV,andBEVmodelsintheU.S.. Table 1-2 presentsPHEVandBEVcharginge"ciencyanddurationwhenusingdi!erent chargerlevels.Table 1-3 showcasesthecostofoperation,indollarspermile,realizedby adriver.NotethatthepricingofelectricityduringpeakdemandhoursisspecictoDTE Michiganresidentialchargingrates( DTEEnergy 2012 ),whereatime-of-usepricingschemeis 15

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e ective.Thegasolinecostisestimatedundertheassumptionofa$2pergallonpriceatthe pump,asindicatedinTable 1-3 .ThisexampleshowsthatPHEVandBEVdriversincurlower costswhentheirdailytrips'portionispoweredbyelectricity,comparedtotheonefueledwith gasoline. NotonlydoPEVsreducefuelconsumptionanddrivingcosts,butalsobolsterenergy securitybyreducingtheamountofforeignoilimports,makingacaseforinvestmentsin renewableenergyforelectricityproduction,andupgradingtheelectricitygrid( U.S.Department ofEnergy 2013c ). However,variousfactorshinderPEVadoptionbyconsumersaccordingtotheliterature. First,duetothefactthatthistechnologyisnotmatureyet,thestickerpricesofPEVsare higherthanthoseofICEVswithsimilarcharacteristics( ElectricPowerResearchInstitute 2013 ).Second,thePEVelectricdrivingrangeisamarketacceptanceconstraint,especiallyfor BEVs,duetothefearofexhaustingthebatterystateofchargebeforecompletingavehicle triporndingacharger(i.e.,rangeanxiety)( Carleyetal. 2013 ; EgbueandLong 2012 ). Third,sparsespatialdistributionofpublicandworkplacechargingstationsdiscouragesPEV ownershipdecisionsbyincreasingrangeanxiety( Rezvanietal. 2015 ; Sierzchulaetal. 2014 ). Inordertoscaleupsalesandrealizeenvironmentalbenetsfromthistechnology,charger numbersandlocationsshouldsatisfytheoperationalneedsofdriversandminimizetheir range-anxiety.Ontheotherhand,theplacementofchargersonthenetworkmayimpactthe electricitygridreliabilitythroughsurgingpowerdemandduringpeakhours( U.S.Department ofEnergy 2014c ).Fourth,thedi"cultyofinstallingchargersathomemaybeanotherobstacle ( Trautetal. 2013 ).Fifth,longdurationofrechargingisanotherdeterrentforPEVownership. Rechargingdurationdependsonthecharger'slevelandtheelectricdrivingrangeofaPEV. AsdemonstratedinTable 1-2 ,a2016NissanLEAFwith84milesofall-electricdrivingrange requiresapproximately21/5/0.5hourstofullyrechargewhenusingaLevel1/Level2/DC fastchargerrespectively( U.S.DepartmentofEnergy 2016f ).Last,lowgasolinepricesfavor ICEVs,astheperceivedoperationalsavingsofPEVsdecreaserelativelytoICEVs.Iftheprice 16

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ofgasolineatpumpis$1pergallon,thedrivingcostofaToyotaCamry,asshowninTable 1-3 ,wouldbe25%lessthanNissanLEAF's,assumingthatthelatterisrechargedbyaLevel2 charger. Despitethosebarrierstopersonalmobilityelectrication,thePEVsalescontinueto increase.Specically,thePHEVsandtheBEVsnewsalesshareshavereachedapproximately 0.25%and0.41%respectively,duringtheyearof2015intheU.S.( ElectricDriveTransportation Association 2016 ).TheU.S.DepartmentofEnergy(DOE)providesmonetaryincentivesto encouragefasteradoptionofPEVs.Onafederallevel,thefollowingsetofincentivesis currentlyavailable:ataxcreditfrom$2,500fora5kWhbatterycapacity,plus$417foreach kWhofbatterycapacityabove5kWh,uptomaximumof$7,500.Thatisine! ectuntilthe creditphasesoutwhen200,000oftax-creditqualiedPHEV/BEVsalesarereachedforeach vehiclemanufacturer( InternalRevenueService 2016 ).Residentialconsumersalsoqualifyfor upto$1,000taxcredittoalleviatehomechargingequipmentcapitalcosts( U.S.Department ofEnergy 2014b ). Chargersareessentialfortheelectricationofthedailyvehiclemilestravelled(VMT) ofPEVdrivers.Duetothishingeoncharginginfrastructure,theDOEhassetaWorkplace ChargingChallengetomotivateNorthAmericanemployerstoinvestinplacingPEVworkplace chargersontheirpremises.Participantsofthisprogrammayprovideeitherfree-of-charge orfee-basedworkplacecharging( U.S.DepartmentofEnergy 2015c ).CommercialPEV chargingprovidersinvestinplacingpubliclyaccessiblecharginginfrastructurealongthe transportationnetwork,realizingthisservice'snecessityandcompetingforitsmarketshare ( NationalRenewableEnergyLaboratory 2012 ). Thereisawealthofliteratureintheeldofmarketbehaviormodelingthatattempts todenecharacteristicsofPEVsthatmakethesevehiclesattractivetoconsumers,e.g., Carleyetal. ( 2013 )and LinandGreene ( 2010a ).PHEVsaretherststeponthepathwayto completeelectricationbecausetheydonotentirelydependonchargingfromthegridfortheir dailyoperationsanddriverscanrefueltheirvehicleswithgas.Avarietyofstudiesexamine 17

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PHEVsoperationalbenetsandassessgovernmentinterventionsthatcanestablishitsmarket success,e.g., DongandLin ( 2012 )and Michaleketal. ( 2011 ).Researchersworktowardsusing vehicleownershipdecisionmodelstoforecasttheelectricationpaceofpassengervehicles, e.g., Greeneetal. ( 2014 )and Al-AlawiandBradley ( 2013b )andexplorestrategies,suchas monetaryincentivesandworkplaceorpubliccharginginfrastructureenhancement,thatenable governmentstoacceleratethisprocess,e.g., Helvestonetal. ( 2015 )and Kangetal. ( 2015 ). Despitethethickliteraturepublishedlatelyontheaforementionedelds,thereisplenty ofroomtoposeandaddressresearchquestionswithrespecttominimizingsocietalimpactsof PEVs'penetrationandoperationinthepassengervehiclemix. 1.2ProblemStatements Themainobjectiveofthisresearchistooptimizepolicycomponents(e.g.,chargers' density,electricrangeoftheplug-inelectricvehicles,chargingpowercontrol,incentives)so astomaximizesocialbenetsfromtheelectricationanddailyoperationsofthehousehold vehicleeet.Optimizationmodelingframeworksaredevelopedtoreachthisgoal.The followingsubsectionsdescribethemotivationbehindeachresearchtaskpresentedineach chapterofthismanuscript. 1.2.1SociallyOptimalElectricDrivingRangeofPHEVs PHEVscanbedeployedimmediatelywithoutanyneedforpubliccharginginfrastructure installationsoastosupporttheirday-to-dayoperations,giventhatdrivershaveaccessto residentialcharging( NationalResearchCouncilCommitteeonAssessmentofResource NeedsforFuel,CellandHydrogen,Technologies 2010 ).Moreover,thePHEVmarketisnot constrainedbyrangeanxietybarriers,whichsignicantlydiscourageBEVscommercialization ( Lin 2014 ).Giventhepotentialofthisvehicle'stypefortailpipeemissionreduction,itis crucialforcentralplannerstoprovidesuggestionstoPHEVmanufacturersregardingoptimal electricdrivingranges.Doingsorequiresconsiderationoftheheterogeneousdailydriving patterns,ongoingdevelopmentsofbatterytechnologies,chargers'installationandotherfactors orpolicies.Non-optimaldrivingranges,ifpushedbythemanufacturers,mightimpedethe 18

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PHEVdi! usionandmisleadrelevantpolicy-making,resultingingreatersocietalcosts( Lin 2014 ).Theimpactofworkplace-chargingandtheavailabilityofdiversityofdrivingrangesis alsoexaminedinthiswork,assuchpolicysuggestionscanfurtherminimizesocietalcosts. 1.2.2ChargingManagementofPHEVs Charginginfrastructureisimperativeregardingelectrifyinggreaterportionsofthedaily householdtravel.Workplaceandpublicchargingmayincreasetheoperationalsavingsof driverswhooperatePHEVsandmaximizeemissionssavings.Ontheotherhand,denser placementofchargersmayimpacttheelectricitygridreliabilitybyincreasingpowerloads duringpeakhours( U.S.DepartmentofEnergy 2014c ).ChargingmanagementofPHEVsis aviablestrategytocontroltheimpactsoftheadditionalelectricitygeneratedtosatisfythe PHEVschargingmargin.Notethatdi!erentstakeholderdenedi!erentlye"cientrecharging; driversareinterestedinminimizingthecostsincurredfromtheirPHEVoperationandthe governmentisinvestedincontrollingtheemissionsfromthePHEVtransportationsector.This chapterinvestigatestheimpactsoftwochargingmanagementobjectives:acost-e! ectiveand aneco-friendlychargingmanagementschemearedevelopedandthee! ectsofthosestrategies ontheresultingoptimalchargingprolesforthePHEVtransportationsectorareevaluated. 1.2.3SociallyOptimalElectricationoftheConventionalLight-dutyFleet SinceBEVshaveloweroperationalcostsandtailpipeemissionsthanICEVs,their operationresultsincostssavings.Duetothisfact,autilitariangovernmentwouldbe interestedinreplacingconventionalwithbatteryelectricvehiclesforhouseholdtraveland minimizethesystem'scostsincurredduringthiseettransition.Modelsbasedonexisting data,suchaseconometricoragent-basedones,mightonlyrepresentearlyadoptersand, thus,theirresultsmaynotapplyuniversally.Marketbehaviormodelsarenotappropriate foroptimizingthehouseholdeetelectricationprocessfromasocietalperspective.In thiswork,optimalICEVsreplacementbyBEVsisinvestigated,undertheassumptionof centralized,governmentalhouseholdeetmanagement.Theproposedframeworkdetermines 19

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theupperboundofhouseholdvehicleelectricationthatmaximizessocietalbenets,and assistspolicymakerstosetBEVadoptiongoalsoveraplanninghorizon. 1.2.4IncentiveSchemeDesignforPromotingBEVAdoption Eventhoughgovernmentshaveinvestedinallocatingnancialincentivessoastosubsidize BEVsorinstallingchargingstations,thereislimitedknowledgeontheinvestmentpriorities thatshouldbesetduringthehouseholdeetelectricationtimeframe.Thelastpartof thisworkposesthefollowingquestion:whataretheoptimalBEVsubsidiesandcharging investmentvaluesthatthegovernmentshouldallocateinordertofurtherincreasethe monetizedsocialbenetsofthehouseholdpassengercarelectrication.Inthiscase,the optimalportfolioforallocatingincentivesforBEVsaimstomaximizethebenetsreceivedfrom fuelconsumptionandcarbondioxideemissionsreduction,overthegovernmentsinvestment. 1.3ObjectivesandContributions Theresearche!ortpresentedinthisdissertationfocusesonachievingthemaximum societalbenetsduringtheelectricationofthehouseholdvehicleeet.Toattainthisgoal, mathematicalprogrammingmodelsaredevelopedtoassistpolicymakersinmakinginformed decisionswhenplanningforPEVdi! usionandmanagingtheirdailyoperations.Afewprevious studieshaveinvestigatedoptimaldrivingrangesofPEVs,e.g., Lin ( 2014 2012 ); Shiauetal. ( 2010 ); Trautetal. ( 2012 ).Thosestudiesaimatminimizingoperationcostsorreducing emissions.Therstpartofthisdissertationbridgesthisliteraturegapbydeterminingthe sociallyoptimalPHEVrange.Theobjectiveistominimizesocietalcostsofhouseholdvehicles dailyoperations.Thoseareinternalandexternalcoststodrivers.Governmentsareinterested inansweringwhethertheyshouldinvestindeployingworkplacechargerstofurtherminimize thesocialcostofhouseholdPHEVoperations,andifso,determinetheoptimalchargerdensity. Thispartclosesbyinvestigatingwhetherthebatterysizediversityresultsingreatersocialcost savings.Specically,itatteststowhetherprovidingapairortripleofPHEVbatterysizesis morebenecialthandeployingworkplacecharging. 20

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Thesecondpartofthisworkpresentsoptimizationframeworksthatmanagehour-to-hour chargingforPHEVs.Twoalternateobjectivesareexploredforchargingmanagementandthe impactofsuchschemesonPHEVoperatingcosts,emissions,andtheutilitygrid'sloadis assessed.Thetargetoftherstscheme,thecost-e! ectiveone,istominimizecostsincurred bydriverswhileoperatingtheirPHEVsduringatypicalday.Wecomparetheresultingcharging proletothatofaneco-friendlyscheme,whichminimizesthesocialcostofcarbondioxide emissionsfromtheelectricitygeneratedwhilechargingandthetailpipeemissionsofthePHEV operationinthecharge-sustainingmode.Themodelingframeworkaccountsforvariation intimeandspaceofthedrivingpatternsofPHEVowners,aswellasthehourlyelectricity generationconstraintsacrosstheU.S.Thisworkenhancesourunderstandingoftheimpactof PHEVchargingmanagementontheutilitygridandontheelectricationofdailytripsforthe transportationsector. Thethirdpartfocusesonoptimizingtheelectricationpaceofthehouseholdlight-duty vehicleeet.First,thecostsassociatedwithICEVandBEVdriverownershipandoperation, infrastructureinvestment,andenvironmentalexternalitiesareanalyzed.Then,aframework thatminimizesthesocialcostofreplacingICEVswithBEVsisdeveloped.Themodelis demonstratedwithU.S.data,andtheimplicationsarediscussedwithrespecttothetimeframe neededtooptimallyelectrifythehouseholdeetandtheparametersthatsignicantlyimpact thisprocess.Thissociallyoptimaltransitionplanforthehouseholdeetmayserveasa compassforpolicymakingbecauseithighlightstheoptimalpathwaytoelectrication.Even thoughthisoptimaldi! usionpacemightnotcaptureindividualhouseholdownershipdecisions, itcanbeusedasatargetICEVreplacementrateforpolicyanalysis. Thefourthandnalpartisdevotedtodesigninge"cientincentiveschemesforBEVs adoption,whichenablegovernmentstomaximizesocietalbenetsbydetermininginvestments thatneedtobeprioritized.Anoptimizationframeworkisdevelopedtooptimallyallocate governmentinvestmentsbetweensubsidiesandcharginginfrastructure.Themodel's 21

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applicationenhancestheexistingknowledgeregardingBEVincentiveallocationandprovides policy-makinginsightsone!ectivebudgetspending. 1.4DissertationOutline Thisdissertationisorganizedintosevenchaptersaddressingtopicsinthedomainof theeconomicsandsocialbenetsofPEVsadoptionandtheirdailyoperation.Chapter2 reviewsrelatedbibliographyandnotespriorcontributions.Chapter3presentsthemodeling approachforminimizingsocialcostsofPHEVsoperationsanditsapplication.Chapter4 designsandevaluatestheoptimalchargingprolesforPHEVsundertwocentralizedcharging managementschemes,whichmeettheneedsoftheusers(cost-e! ective)andthegovernment (eco-friendly).Chapter5proposesamethodologyforminimizingthesocialcostofreplacing existingICEVswithBEVsanddemonstratesanapplication.Chapter6isdevotedtodesigning monetaryincentivesthatwouldassistpolicymakersinmaximizingsocialbenetsfromBEV salesproliferation.Chapter7concludesandpinpointspossiblepathwaystofutureresearch. 22

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Table1-1. VehicleFuelEconomyCharacteristics VehicleType Vehicles FuelTypeFuelEconomy(combined)RangeBatteryCapacity galorkWh/100miMPGemi kWh ICEV 2016ToyotaCamryGas 3.628476 n.a. 2016HondaAccordGas 3.231533 n.a. PHEV 2016ChevyVolt Electricity 31.010653 18.4 Gas 42420 n.a. BEV 2016NissanLEAFElectricity 30.011484 24 BEV 2016FordFocusElecElectricity 32.010576 22 Table1-2. ChargingE"ciencyandTime PublicChargingLevelACInputChargerate Full-rechargeduration(hours) (mi/hour)ChevyVoltNissanLeafFordFocusElec Level1 120V 4 13.0 21.0 20.0 Level2 240V 18 4.5 5.0 3.8 DCFastCharge 440V 100 n.a. 0.5 0.5 23

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Table1-3. FuelPricing:ElectricityOn-PeakResidentialPricingvs.GasPriceperMile HomeCharger Level ACInput ChargeRate (mi/hr) ResidentialChargingCost ($/mi) GasCost ($/mi) ChevyVoltNissanLeafFordFocusElec$2/gallon $1/gallon CamryAccordCamryAccord Level1 120V 4 0.064 0.051 0.0500.0720.0640.0360.032 Level2 240V 18 0.041 0.048 0.058 24

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CHAPTER2 LITERATUREREVIEW Thischapterprovidesabriefliteraturereviewonthefollowingareasofwork:published researchonassessmentandoptimizationofelectricdrivingrangeofPEVs,charging management,eetreplacementandmodelingofvehicleelectrication,charginglocation modeling,andapproachesfordesigningincentiveschemesandtheire! ectsonPEVmarket adoption. 2.1OptimalElectricDrivingRangeforPlug-inElectricVehicles PHEVsinaseriescongurationtypicallyoperateineitheroftwomodes:thecharge-depleting mode,usingonlyelectricalpower,withoutconsuminggasoline,andthecharge-sustaining mode,consumingonlygasoline.Thevehiclestartsupoperatinginthecharge-depletingmode, untilitsbatteryreachesaminimumchargethresholdatwhichtheelectricdrivingrangeis exhausted.Then,itswitchestocharge-sustainingmode( Pesaranetal. 2007 ). TheelectricdrivingrangeisacriticalparameterofthePHEVdesignandasignicant variableformakingownershipdecisions.IntheU.S.market,themajorityofPHEVsthat operateinaseriescongurationspananelectricdrivingrangeintervalfrom24to53miles ( U.S.DepartmentofEnergy 2016f ).TheU.S.AdvancedBatteryConsortiumhasproposed twosizesofbattery:a10-mileanda40-miledrivingrange( Pesaranetal. 2007 ).Thecriteria fordeterminingthoserangesinclude(a)batterypackcost,volume,weight,lifeande" ciency, (b)chargepowerandcycles,(c)energyforcharge-depletingoperations,and(d)battery concernssuchasoperatingtemperatureandvoltage( Pesaranetal. 2007 ).TheEnergyPolicy Actof1992andtheNationalHighwayTra"cSafetyAdministrationalsoestablishedthe minimumdrivingrangeforPHEVs.Thenalrule,e!ectivein1999,allowedaminimumdriving rangeof7.5milesontheEPAurbancycleand10.2milesontheEPAhighwaycycle( U.S. DepartmentofTransportationandNationalHighwayTra"cSafetyAdministration 1998 ). Therearefewstudiesintheliteraturewhichdevelopmathematicalprogramingframeworks todetermineoptimalelectricdrivingrangesofPEVs.Forexample, Lin ( 2014 )and Lin ( 2012 ) 25

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minimizethecostofbatteryandvehicleoperationsincurredbythedriverssoastodene theoptimalelectricdrivingrangeforBEVsandPHEVsrespectively.Therangeoptimization programsproposedincorporatedailyVMTvariationandaccountforchargingavailability. FocusingonPHEVs, Lin ( 2012 )minimizethesummationofbatterypurchasing C b ( r ) operation(gas C g ( r ) andelectricity C e ( r ) consumptionincluded),andrefuelinghassle C f ( r ) foralldrivers i ,asfollows: min r !" + i ( C b ( r ) +C e ( r ) +C g ( r ) +C f ( r )) (21) Theobjective( 21 )isacontinuousfunctionoftheelectricdrivingrange r .Theoperationand refuelingcostcomponentsaredecomposedinordertoaccountforthedistributionofthedaily VMTcovered.TheframeworkevaluationfortheU.S.vehicleanddrivermarketshowcasethat 10-milePHEVrangesaremorelikelytobefavorableduetotheirlowerbatterycost.However, incasegasolinepricesincreaseto$5-6pergallonandbatterypricesdropto$150-300per kWh,theoptimalPHEVdrivingrangeincreases. Shiauetal. ( 2010 )optimizethePHEVdrivingrangeandallocatePHEVs,HEVs andICEVstothedrivingpopulationsoastomeettheobjectivesofminimumpetroleum consumption,GHGemissions,andlifecyclecost.Theoptimizationframeworkforthesingle vehicleassignmentispresentedherein: min x # 0 f o (x,s)f s (s)ds (22a) s.t. g ( x ) # 0 (22b) h ( x )=0 (22c) wheretheobjectivefunctionisexpressedastheintegralofthefuelconsumedorGHGemitted perdayoftraveling f o ( x s ) ,multipliedbytheprobabilitydensityfunctionofthedailyVMT distribution f s ( s ) ; x istheelectricdrivingrangeofthevehicletechnology,whichisthedecision variable,and s arethedailyVMTofthedriver.Theconstraints( 22b )and( 22c )aretailored tomaintainvehicledesignfeasibility.Numericalexamplesofthemixedintegernon-linear 26

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programproposedaredemonstratedusingU.S.automobileandtraveldata.TheoptimalPHEV rangedesignforminimumconsumptionis87miles;theoptimalpairofelectricdrivingranges forminimumGHGemissionsare25milesforPHEVschargedevery31milesorlessand40 milesforPHEVschargedlessfrequently. Trautetal. ( 2012 )optimizethedesignofthepreviousstudy'svehiclemixinorderto minimizelifecycleGHGemissionsbyalsoinvestigatingworkplacechargingscenarios.The bi-levelframeworkofthisstudyspecicallyaimsatminimizingthevehicle,engine,motor,and batteryproductionGHGcosts,aswellasthechargerproductionandthePHEVoperational GHGcosts,whileoptimallyallocatingrangesofPEVs: min x # s=0 f o (x,s)f s (s)ds (23a) s.t. g D j ( x ) # 0, $ j % J (23b) x %& p j $ j % J (23c) where f o ( x s )= min j J | g A j ( x j s ) $ 0 f oj ( x j s ) (23d) where s denotestheannualVMT, f s ( s ) istheprobabilitydensityfunctionof s J isthe setofvehicletechnologies, f o j ( x j s ) istheannualizedGHGcostasdenedbythevehicle designvector x j g D j isthevectorofvehicledesignconstraints, g A j isthevectorofallocation constraints,and p j isthesizeofvector x j .Constraints( 23b )and( 23c )introducethe designandallocationconstraintsrespectively.NumericalresultsregardingtheU.S.vehicle marketshowthatapairofPHEVswith23and26milesofelectricdrivingrangeisoptimal whenminimizinglifecycleGHGemissionsfromtheautomobileproductionandtransportation operations. AnotherstreamofstudiesinvestigatestheroleofrechargingPHEVsonreducinggasoline consumptionanddrivercosts. PetersonandMichalek ( 2013 )evaluatethecoste!ectiveness ofincreasedbatterysizeandtheinstallationofpubliccharginginfrastructureforPHEVswith respecttoreducingfuelconsumption;theirresultsindicatethatinvestinginincreasedbattery capacityisbetterthanplacingchanginginfrastructure,whenconsideringoperationalcostsof 27

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PHEVs.Theempiricalstudyby DongandLin ( 2012 )investigatestheroleofrechargingto mileageelectricationandgasolineconsumptionreduction.TheirmodelisappliedtoAustin, TXandresultsshowthatPHEVswithsmallerbatteriesthatarechargedregularlyaremore coste"cientthanlargerdrivingrangePHEVs.Thedata-drivenstudyby Zhangetal. ( 2011 ) evaluatesaveragefuelconsumptioncostsofPHEVsforthesouthCoastCaliforniaregion, whicharecomparedtothecostsofhybridelectricvehicleandICEVoperation;itconrmsthat increasingpublicchargingdeploymentsavesfuelcomparedtojustprovidinghome-charging. Ernstetal. ( 2011 )conductPHEVcostevaluationforGermany,whichshowsthatPHEVswith smallerelectricrangesarecostcompetitivewhenchargingstationsaree! ectivelydeployed andhavethepotentialtosparktheelectricationprocessevenwhenbatterypricesare high. Shiauetal. ( 2009 )reportedtheirassessmentofconsumptionandemissionsviaPHEV simulationmodels,whichshowcasethatsmallcapacityPHEVscostandemitlesswhencharged frequently,inevery20milesorso. 2.2ChargingManagementStrategies Smartandcentralizedchargingcontrolhasbeenexploredasameantominimizethe impactsofthepotentialelectricitydemandsurgeduringtheelectricationofpersonalmobility. Centralizedchargingmanagementcanenhancethereliabilityoftheutilitygrid,decrease generationcosts,andcontrolemissionsassociatedwithPHEVcharging( Verzijlberghetal. 2012 ).Chargingscenariosandcontrollersoperationhavebeensimulatedforuncontrolledand controlledelectricvehiclechargingusingsyntheticorrealdatasets,e.g.,( DaviesandKurani 2011 ; Verzijlberghetal. 2012 ).Acoupleofsmart-chargingsystemshavebeendevelopedand testedatalocalscale( Baumanetal. 2016 ).Anon-exhaustivelistofprevalenthypotheses foruncontrolledchargingandtheobjectivesforcontrolledchargingispresentedasfollows, enhancedfromtheonein Weiller ( 2011 ): Uncontrolledchargingbehaviorhypotheses Plug-inelectricvehicle(PEV)ownerschargewheneverathome( KangandRecker 2009 ),consideringthatonlyhome-chargingisavailable; 28

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Chargewhereverandwheneverthereisachargeravailable( Weiller 2011 );this schemeisnotedas"uncoordinatedwithoutdelay"chargingscenario( Clement etal. 2009 ); Last-minutecharging,assumingthatthestartofchargingisatthelastpossible momentinordertohavemaximumbatterystateofcharge(SOC)beforebeginning thenexttrip( Kellyetal. 2012 ). Controlledchargingmodelingproceduresandobjectives UnitcommitmentmodelingtominimizepowersystemandPEVsoperationalcosts ( Clementetal. 2009 ; Sioshansi 2012 ; Weisetal. 2015 ); Valley-llingoptimization,thatminimizesthenegativeimpactsofincreased electricityloadsduringdemandpeaksfromthenon-transportationsectorby schedulingchargingduringlow-demandgridutilizationhours( Ahnetal. 2011 ); Fastcharging,whichmaximizestheelectriedmilesthatPEVdriverscoverdaily ( RoteringandIlic 2011 ); SmartchargingwithSOCmanagement,whichminimizesthechargingcostof PHEVdrivers( ZhangandMarkel 2016 ). Eachofthechargingmanagementframeworksissusceptibletoitsanalysisboundaries. Forinstance, Kellyetal. ( 2012 )focusesonlyonthee!ectsofrechargingonthetransportation sectorwithoutaccountingfortheadjustmentsthatmightberequiredforelectricitygeneration andtransmission.Onthecontrary, Sioshansi ( 2012 )jointlymodelselectricitygeneration andthePHEVtransportationoperation,duetointerdependenciesbetweenthosenetworks. Similarly, Weisetal. ( 2015 )considersthee!ectsofPHEVchargingtothepowersystem'sload anddevelopsaneconomicdispatchandunitcommitmentmodeltopinpointtheconditions underwhichcontrolledchargingisbenecialtosociety.Moreover,eachschemeproposedis tailoredtomeetingtheneedsofdi! erentstakeholdersandresultsinchargingschedulesthat varysubstantially. Sioshansi ( 2012 )ndingsindicatethatcontrolledchargingbyasystemoperatoro!ers thebestresultsistermsofminimizinggenerationcostforPHEVcharging,comparedto anyothertari!placedtoimpactthedriverschargingbehaviors.CentrallycontrolledPHEV chargingisalsofoundverye! ectiveinminimizingtotalCO2and NO x emissionsbutnotso e ectiveforminimizingSO2. Weisetal. ( 2015 )resultsshowthateventhoughcontrolled 29

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chargingofPEVscanhaveasignicantimpactinreducingelectricitygenerationcostfor thePJMinterconnection,chargingmanagementincreasestheemissionsfromgeneration duetocoal-redplantsinuse. ZhangandMarkel ( 2016 )showsthatsmart-chargingwhich minimizesthecostsincurredbythePHEVdrivercanshiftchargingtolowerTOU-rateperiods allowingtheoperatortoelectrifytheirdailytrips.However,theseresearchersconcludethat smartchargingismoree! ectivewhenpublicchargingisavailable;otherwise,thesavings mightnotbesignicant. Kellyetal. ( 2012 )simulationofPHEVchargingshowcasesthatthe averagechargingloadisexpectedtoreachitslowestfrom4:00am-10:00amanditspeakfrom 7:00-8:00pm,undertheassumptionthatdriversgettochargeimmediatelyafterreturning fromwork.Outcomesof Weiller ( 2011 )chargingbehaviorsimulationstudyaresimilartothose of Kellyetal. ( 2012 );thesealsounderlinetheimpactofworkplacechargingavailabilityin increasingtheaveragepowerloadsduringthedayfrom7:00amto11:00am. Lemoineetal. ( 2008 )indicatesthattheconjointchoiceoftypeofvehicleownership, fuelpricing,andfuelusageformulti-fuelvehiclesmighthaveasignicantimpactonthegrid utilizationthenextyears.Whenitcomestotheneedforadditionalcapacity,thesameauthors predictthishappeningonlyifPHEVownershipincreasesbymillionsastheirstudyfocuses ontheCaliforniaregion. HadleyandTsvetkova ( 2009 )analysisalsoshowsthatthePHEV penetrationisverylikelytorequireadjustmentsandadditionalelectricitycapacitygeneration, dependingonalternatescenariosfortheevolutionofthevehiclemixduringtheyearstocome. 2.3TransitionfromConventionaltoBatteryElectricVehicles Discretechoiceeconometricmodelshavebeenpopularformodelingalternativefuelvehicle ownershipchoiceandpredictingPEVsadoption.Econometricmodelsareutilizedtoforecast EVmarketpenetrationbyinvestigatingsignicantvariablesforcarownershipdecisions. Variousstudiesgothroughstatedpreferencesurveyresults.Forexample, Mustiand Kockelman ( 2011 )conductstatedpreferencessurveyinAustin,TXtomodelvehicleownership decisions;simulationresultsshowthatthePHEVmarketsharein2034canbeonly6.15%. Krauseetal. ( 2016 )alsoconductaweb-basedstatedpreferencessurveytocollectdataon 30

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electricvehiclechoicesforconsumersoflargeU.S.citiesanddevelopamultinomiallogit modelthatestimatestheprobabilityofchoosingPEVs.Theyndthatpurchasepriceparity acrossvehiclesisacrucialfactorforincreasingPEVsdi!usion. SilvaandMoura ( 2014 )usean aggregatetimeseriesmodelalongwithavehiclechoicemodel,basedonastatedpreferences survey,tocapturetheevolutionofvehicletechnologyforthePortugueseautomobilemarket. TheirresultsindicatethatBEVspenetrationpaceisnotsofastinthegreateconomygrowth scenarioduetocompetitionfromICEVswithhigherfueleconomies,butBEVsarefavored whenICEVpurchaseandgasolinetaxesareapplied. Forafewstudies,insteadofdevelopingsurveysandcollectingdata,econometricmodeling isbasedonpreviousliterature'sconsiderations. Greeneetal. ( 2014 )utilizetheLight-duty AlternativeVehicleandEnergyTransitionsModel(LAVE-Trans),whichisbasedonanested multinomiallogitmodel,inordertorepresentconsumerchoicesofalternatefuelvehicle technologies.ThebasecaseassumesthatCaliforniaandotherstateswithsimilarzeroemission vehiclemandateslead,beingintheforefrontofthevehicleeetelectrication.Findings indicatethatthemarketshareofBEVswillbeslightlyhigherthan35%by2050. Linand Greene ( 2012 )useamodelcalledMarketAcceptanceofAdvancedAutomotiveTechnologies (MA3T).Thatisanestedmultinomiallogitmodel,usedtosimulatevehicleownershipand evaluatetheimpactofchargingavailabilityonthePEVdi! usionfortheU.S.market.Their ndingsportraythatscenarioswithincreasedhome-,workplace-andpublic-chargingavailability alongwithbatteryeconomiesofscaleoutperformothersandcaninduceannually10thousands BEVsalesintheyearof2025. Agent-basedmodelssimulateconsumerdecisionsbasedonbehavioralrulesandmodeling assumptions.Forexample, Cuietal. ( 2012 )usemulti-agentsimulationfordeningthespatial distributionofvehicleshare;theirprocedureisappliedusingKnoxCounty,TNdataanda nestedmultinomiallogitmodel.ResultshighlightareasofPHEVsconcetration. Eppsteinetal. ( 2011 )alsodevelopanagent-basedmodeltopredictPHEVspatialdi!usion,accountingfor interactionsbetweenagentsandincorporatinginformationspreading. Al-AlawiandBradley 31

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( 2013a )provideacomprehensivereviewofvehicleownershipmodelingandconcludethat realisticmodelsshouldaccountforconsumerpreferences,productionstrategies,automobile marketcompetitionandpoliciesinplace. DuetothepresentlylowshareofPEVsinthepassengercarmarket,modelsbasedon existingdatasetsmayrepresentearlyadopters,sotheirresultsmaynotapplytotherestof thepopulation.Eventhoughsuchstudiesmaycaptureconsumerpreferences,noneofthose attempttominimizethesocietalcostoftransitioningfromconventionaltoelectricvehicle technologies. Light-dutyeettechnologytransitionsaremostcommonlymodeledthrougheet replacementoptimizationframeworks.Generallythoseprovideinsightstomanagersinorder tomakeinformedreplacementdecisionsforprivatelyownedcommercialandtransiteets.In thisdomain, FengandFigliozzi ( 2013 ), FengandFigliozzi ( 2014 ),and Figliozzietal. ( 2012 ) proposedmixedintegernon-linearprogrammingframeworkstoreplaceconventionalvehicles, trucksandbuseswithelectricones,underalternativescenariosofvariationsofeconomicand technologicalfactors. Morespecically,thevehiclereplacementobjectiveof Figliozzietal. ( 2012 )isthe minimizationoftheeetoperator'scostwhilereplacingacommercialeetofICEVs withnewBEVassets,duringaplanningtimeframe.Theobjectivefunctionconsistsof discountedpurchaseprices,operationalprices,trade-incosts,maintenanceandemission costcomponentsofeithertypeofvehicles.Constraintsthatdictateeetconservationand oldvehicleretirementandensureintegralityandnon-negativityofthedecisionvariablesare added.Suchaframeworkallowsforinvestigatingvariousscenarios,suchasfuelpriceschanges, vehicleutilizationchanges,andtaxcreditadditions. StaskoandGao ( 2012 )useastochastic dynamicprogrammingformulationtomodeleetmanagementdecisionsunderenvironmental regulations. SuzukiandPautsch ( 2005 )useadeterministicmixedintegernon-linear programmingframeworktoexaminecommercialeetreplacementmodelingadaptationsunder unstableeconomies. Kimetal. ( 2004 )developanoptimizationframeworkforascrappage 32

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program,or"eet-conversionpolicy",inordertoachieveold-vehiclereplacementwithnewer onesandmeettheobjectiveoflife-cyclecostminimizationfromgovernment'sperspective. Optimizationoftheall-electricdrivingrangeofthemarketBEVsispivotalformaximizing socialbenetsfromthisvehicletechnologybecausemostofBEVcostcomponentsarea functionofit. Lin ( 2014 )developsaframeworktominimizethecostofpurchasingand operatingBEVsinordertodeterminetheiroptimalrange,whichispresentedherein: min r !" + i (C b (r)+C e (r)+C l (r)) (24) whereristheall-electricdrivingrangeofBEVsanddecisionvariableand C b ( r ) isthebattery purchasecost.Assumingthat,duringdaysthattheelectricrangeislessthanthedailyVMT,a driverusesaback-upICEV,theelectricity C e ( r ) andtherangelimitation C l ( r ) dailycostsof BEVoperationareexpressedasfollows: C e (r)=a n e (r) rd 0 xp(x)dx (25a) C l ( r )= x m rd ( l 0 + l 1 ) p ( x ) dx (25b) where a istheparameterin$perkWhtoconvertthekWhperdaytoamortizedcost, n e ( r ) is theelectricityusagerate, x istherandomdailyVMT, p ( x ) istheprobabilitydensityfunction of x d isthepercentofmaximumrangeutilization(indicativeforchargingopportunities), is theannualdiscountparameter, x m isthemaximumdailyVMT, l 0 representsthexedcostof obtainingaback-upICEVand l 1 denotesthe$perdayduetotheICEVsoperation.Numerical results,usingasampledatasetthatpertainstotheU.S.market,suggestthatthemeanofthe optimalrangesforBEVsis85mileswithastandarddeviationof40miles. ThedensityofpublicchargersonthenetworksignicantlyimpactsthecostlevelofBEV operationsbecausedensechargingplacementcanincreasetheelectriedVMT.Charging infrastructuredeploymentapproacheshavearichbodyofliterature;indicativestudiesare mentionedhere.Thestate-of-the-artchargingplacementcanbedividedintothefollowing categories:(a)studiesthatuseheuristicstodeploychargers,(b)studiesthatoptimizethe 33

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locationofchargingstationsinordertomeetacost-associatedobjectiveand(c)studies thatmaximizethedemandservedbychargers.Incategory(a), Liuetal. ( 2016 )investigate chargingopportunitiesforthePugetSound,WAmetropolitanareabyassigningchargersto theparkinglotswiththegreatestdailydemand,usingasortingalgorithm.Incategory(b), He etal. ( 2015 )optimallylocatethechargersonurbannetworksbymaximizingthesocialwelfare andconsideringcompletedailytoursofdrivers. Ghamamietal. ( 2015 )developaframework tooptimallylocatechargersbyjointlyminimizingthetotalinvestmentforfacilitydeployment anduserexpenditures. Chenetal. ( 2013 )minimizethecostofwalkingfromthechargertothe actualtripdestinationwhenoptimallyplacingchargersonSeattle,WAparkinglotnetwork.In category(c), Heetal. ( 2016b )formulatemaximumcoverageandp-medianfacilitylocation modelsandcomparetheirpublicchargingplacementresultsforthecityofBeijing,China. 2.4IncentivesDesignforPlug-inElectricVehiclesAdoption PEVswererecentlyaddedinthemassproductionlinesofautomobilemanufacturersand thosevehicleswerecommercializedbeginning2010( U.S.DepartmentofEnergy 2014d ).Due tothisfact,thisvehicletechnologyisstillnotmaturewhencomparedtoICEVproducts.There isevidencethatthebatteryproductioneconomiesofscalearequicklyexhausted( Saktietal. 2015 ),sopricesofPEVsmayremainhigherthanthoseofICEVswithsimilarspecications. HopingtoboosttheearlymarketshareofPEVs,nancialandtechnologysupport,aswell ascharginginfrastructureincentivesaredistributedbygovernmentstoPEVsadopters( Plug-In America 2016 ).TheU.S.incentivestrategiesinclude,butarenotlimitedto,federalmonetary taxcredits,staterebatesortaxcredits,HOVlanesfreeaccess,freeparkingaccessinpublic garages( NationalConferenceofStateLegislators 2015 ),andlowerresidentialelectricityrates toaccommodaterecharging Althoughacoupleofliteraturestudieshaveexaminedthee"cacyofsuchgovernment incentiveprograms,thereisnoclearconsensusintermsofwhichpolicyhasgreaterimpacton increasingthemarketshareofPEVs.Forexample,statedpreferencessurvey-basedstudies, suchas Krupaetal. ( 2014 ),supportthatrebatesandrechargingfacilitiespositivelyinuence 34

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PEVsales.However,thisworkalsostatesthatthee"cacyoftheU.S.monetaryincentives cannotsignicantlyovercomethehighpurchasepricesofPEVs. Sierzchulaetal. ( 2014 ) runparametricregressiontopredictBEVsalesandshowcasethatnancialincentivesand charginginfrastructuredeploymentlevelshaveasignicantimpactonincreasingtheU.S.BEV marketdi! usion. Helvestonetal. ( 2015 ),throughananalysisoftheU.S.marketbehavior indicatethat,inordertoachievea50%automobilemarketshareofPEVs,subsidiesof $9,000forsmall-rangePHEVsarerequired;PHEVsandBEVswithlargerbatterieswould requiremorethan$20,000.Thoseindicativeresearchndingsconrmtheimportanceofboth incentivemechanisms;however,thesestudiesdonotfurtherproposeappropriateincentive allocationorprioritization. Lieven ( 2015 ),throughmarketsimulation,revealsthatthecharging infrastructureisessentiallythe"bottleneckfortheuniversaladoptionofPEVs";incentive optionsincludinglargesubsidiesarenotnecessarilymoresuccessfulthanacombinationof lowerrebatesontopofinvestmentforpublicchargers. Recently,researche! ortshavebeenfocusingonoptimalincentivedesign,workingtowards determiningtheallocationportfolioofgovernment'sinvestmentsforacceleratingelectrication overaplanningtimeframe.SuchstrategiesshouldeventuallyresultingreaterearlyBEVsales inordertoachievegreatersocialbenets. Kangetal. ( 2015 )proposeagametheoreticapproach,whichincorporatesvarious stakeholders'goalsinthedecision-makingprocessforsubsidiesthatpromotevehicle electrication.Variouspoliciesareoptimizedlikeelectricitypricecuts,chargingdensity, andPEVrangeanddesign.Morespecically,theframeworkexaminesthreebusinessscenarios brieypresentedbelow: Threestakeholders'cooperation:government,manufacturersandchargeroperator;the goalistomaximizetotalprotsminusthemonetizedemissionexternalitysubjectto budget,engineeringandPEVproductionandchargingstationprotconstraints, Two-stakeholderscenariowithsequentialdecisions:themanufacturerrstandthen governmentwhoactsasthechargeroperator;thermmaximizesPEVprotsubject toengineeringconstraintsandthenthegovernmentminimizestheemissionssubjectto budgetandnon-negativeprotconstraintsuntilequilibriumisreached, 35

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Three-stakeholderscenariowithsequentialdecisions:themanufacturerrst,thenthe chargingoperator,andlastthegovernment:thermmaximizestheprotsubjectto engineeringconstraints,theoperatormaximizestheprotfromthechargingstation placementandutilization,andthegovernmentminimizesemissionssubjecttobudget constraintsandcontrollingforrmandchargeroperatornon-negativeprots,until equilibriumisreached. ThedemonstrationoftheframeworkwithdatafromAnnArbor,MIsuggeststhatwhen theavailablebudgetisbelowacertainthreshold,governmentshouldinvestinallocating rebates;incasebudgetsgreaterthanadeterminedboundarybecomeavailable,charging infrastructureinvestmentsareessentialforincreasingenvironmentalbenets,whichjustify greaterexpenditures. Cohenetal. ( 2015 )considertherebatedesignproblemasatwo-stageStackelberg game.Thegovernmentleadsandminimizessubsidiesinvestmentsubjecttomeetingspecic adoptiontargetgoals,andthePEVautomobilemanufactureristhefollower,aimingto protmaximization.Theyregardtheinvestmentallocationasacentralizedcontrolproblem, consideringthesubsidiesasacoordinationmechanismthatstrivesforoptimizingallthe players'surplusinthissupplychain.Further,theyshowhowdemanduncertaintyimpactsthe optimalrebatesandtheirnumericalexperimentspresentalternatescenariospinpointingthe playerswhobeartheriskofthisdemanduncertainty. Nieetal. ( 2016 )determineoptimalincentiveschemesbyincorporatingdynamicevolution ofthePEVsinthemarketoveradiscretetimeframe,alogisticvehicleownershipdecision model,andamacroscopictravelandchargingmodel.Theoptimizationframeworkisbriey 36

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presentedbelow: min s y j u y l g G+ t T+ c C (26a) s.t. x y l = x y % 1 l + u y l $ l y (26b) Q y ij = Q y % 1 ij V y % l j ij + V y ij $ i j y (26c) V y ij =( q y i + j V y % l j +1 ij ) P y ij $ i j y (26d) x y l # k l $ l (26e) M + I # B (26f) s y j 0, $ j (26g) x y l 0, $ l y (26h) wheretheobjectivefunctionisaweightedsummationoffuel G ,chargingtime T ,andcarbon dioxideemission C costs.Thedecisionvariablesaretherebate s y j fortechnology j atyear y andthenumberofchargers u y l tobeplacedinlanduse l atyear y .Constraint( 26b )isthe statetransitionfunctionforthenumberofchargers,where x y l denotesthecumulativenumber ofchargersonthetransportationnetworkinyear y .Constraint( 26c )tracksthevehiclestock evolutionacrosstime,where Q y ij isthetotalnumberofdrivers i ofvehiclestype j atyear y V y ij isthenumberofvehiclesthatareobtainedinyear y and V y % l j ij isthenumberofvehicles whoselifeexpectance l j hasbeenreachedandarereadyforreplacement.Constraint( 26d ) dictatesthatthenumberofvehiclesobtainedatyearyareestimatedbasedonathenumberof newcustomers q y i inyear y andthenumberofthosewhosevehiclewassalvaged # j V y % l j +1 ij atyear y ,multipliedbytheprobability P y ij ofclassofconsumers i topurchasevehicle j in year y .Constraint( 26e )imposesthatthenumberofchargersplacedatthenetworkeach yearcannotexceedthenumberofchargersneededtoachievemaximumnetworkcoverage k l .Constraint( 26f )ensuresthatthegovernment'sinvestmentforrebatesallocation M and chargingplacement I doesnotexceedtheavailablebudget B .Last,constraints( 26g )and 37

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( 26h )ensurethenon-negativityofthedecisionvariables.Thenumericalexamplesarebased onU.S.marketdata.Thosehighlightthattheoptimalstrategyistheprioritizationofcharging placementandthatthemajorityofthechargersshouldbeinstalledfromtherstyearofthe planninghorizononthenetwork. 2.5Summary ThisbriefreviewpresentssomeofthemajorcontributionsofthePEV-relatedliterature, whichgenerallyenhancestheunderstandingofthePEVsuserandenvironmentalsavings.The literaturepresentedalsooptimizesPEV-relatedpolicycomponentssoastoensuresmooth transitionfromconventionaltoelectriedpersonalmobility.Thisworkaimstobridgeliterature gapsasthosearebrieysummarizedbelow. Literaturerelatedtopoliciesandtheircomparisonintermsoftheire!ectivenessfor societalcostminimizationandPHEVdesignisquitethin.Chapter3buildsonprevious worktoproposeframeworksthatminimizethesocietalcostofPHEVsoperation.Thedirect comparisonofthee! ectsofworkplace-charging,ontopofhome-charging,onthesocietalcost isalsoconducted.Thispartofmydissertationassessestheimpactoftheavailabilityofbattery sizediversitytotheminimizationofthesocietalcost. InChapter4,IexploretheimpactofPHEVchargingmanagementstrategiesonthe utilitygridbycontrollingPHEVchargingproles.Thee! ectsoftwochargingmanagement schemesareevaluated:acost-e! ectiveandaneco-friendlyschemeareconsidered.Theformer isdesignedtomeettheobjectivesoftheusersofthePHEVtechnologyandthelateristailored tominimizeenvironmentalexternalities,whichmightbeagovernment'sgoalforthePHEV transportationsector. Chapter5presentsanapproachforoptimizingthetransitionfromgas-toelectricity-powered passengermobilitybyminimizingthecostofadoptionandoperationoveraplanninghorizon. Chapter6aimsatenhancingthethinliteratureontheelectricvehicleincentives'optimal design,byinvestigatinginvestmentprioritization,andpinpointingthetrade-o! sbetween 38

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charginginfrastructureexpendituresandsubsidiesallocationforoptimizingthegovernment portfolio. 39

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CHAPTER3 SOCIALLYOPTIMALELECTRICDRIVINGRANGEOFPLUG-INHYBRIDELECTRIC VEHICLES ThePHEVtechnologydiversiesthechoiceofenergyforpoweringpersonaltransportation and,atthesametime,hasthepotentialforachievinghigherenergye"ciencyanddecreasing environmentalimpactsofdailycommutes.Inordertoachievethemaximumbenetforsociety whileoperatingthisvehicletechnology,anoptimizationframeworkisdevelopedtodetermine anoptimaldrivingrangethatminimizesthesocietalcost.Thisframeworkisfurtherenhanced andmodeledasabi-levelmathematicalprogramingsoastooptimizethedeploymentof workplacecharginginfrastructureandexamineitsimpactsonthesocialcostandbatterysize; anddeterminetheoptimaldiversicationofelectricdrivingranges. Thecontributionsoftheworkaretwofold.First,modelingframeworksarepresented thatdeterminetherange(s)ofPHEVsundertheassumptionof(a)onlyhome-charging capabilities,(b)bothhome-andworkplace-chargingavailabilityand(c)batterydiversication andonlyhome-chargingcapability;thoseallowforevaluationofworkplaceinfrastructureand batterydiversicationstrategiesimpacttothesocietalcostofPHEVsoperation.Second, theframeworkdemonstrationwithsampledatarepresentingU.S.marketuncoversinteresting resultsfordiscussion,suchthattheoptimalelectricrangeofPHEVsincreasesascharging infrastructureisdeployedinordertoelectrifygreaterdailymileages. 3.1ElectricDrivingRangeOptimizationFramework Thissectionpresentsamodelingframeworktooptimizetheelectricdrivingrangeof PHEVs.Theframeworkaimsatminimizingtherelevantsocialcostofusingthetechnology, whichconsistsofthreedistinctivecomponents:therstoneisaninternalusercost, accountingforthecapitalcostofbatterypacksandtheenergycostofoperatingaPHEV; thesecondisanexternalenvironmentalcost,incorporatingthecostofGHGemissionsfrom themanufacturingprocessofbatterypacksandtheoperationprocessofthevehicle;andthe thirdcomponentrepresentstheexpenditureofinstallingworkplacechargers.Notethatonly costitemsthataredependentontheelectricdrivingrangeareconsidered.Althoughsomecost 40

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itemsmaybeperceiveddi! erentlybydi! erentusers( Stephens 2013 ),suchheterogeneityis notaddressedinthisframework. Theoptimizationmodeliswrittenasfollows: min r C ( r )= j $ C u j ( r ) + C e j ( r ) % + C g (31a) s.t. 0 # r # r u (31b) wherethedecisionvariable r istheelectricdrivingrangeinmiles; C ( r ) isthedailysocialcost relatedtotheelectricdrivingrange; C u j ( r ) isthedailycostinternaltouser j C e j ( r ) isthe dailycostexternaltouser j ,i.e.,theenvironmentalcostand C g istheexpenditureassociated withtheinstallationofworkplacechargers.Constraint( 31b )dictatesthelowerandupper boundoftheelectricdrivingrange,whichis0and r u respectively. Thethreecostcomponentsoftheobjectivefunctionarediscussedhereinafterindetail. Forsimplicity j thatpertainstoeachindividualuserisdroppedfromtherelatedvariables. 3.1.1InternalUserCost Asshowninequation( 32 ),theusercostconsistsoftwomajorcomponents:thecostof batterypacksandtheoperatingcost,bothin$/day. C u ( r )= C b ( r ) + C o ( r ) (32) where C b ( r ) isthecostofbatterypacksand C o ( r ) isthecostofconsumingelectricityand gasolineinoperatingaPHEV.Notethatthecostoftheotherpartsofthevehicleisnottaken intoaccountasitisassumedtolargelyindependentofthedecisionvariable r ,theelectric drivingrange. Thecostofbatterypacksisafunctionofelectricdrivingrange r asexpressedinequation ( 33 ).Theequationisadoptedfrom Lin ( 2014 )withminormodication. C b ( r ) = r n e ( r ) k B a ( r ) / h b (33) 41

PAGE 42

where n e ( r ) istheonboardelectricityuserateinthecharge-depletingmodeinkWh/mile; k isthemarkupfactorthatcaststhemarketinganddistributioncostsofthebatterypacks; B a ( r ) istheamortizedbatterycostin$/kWh/dayand h b isthebatteryutilizationfactor, i.e.,theratioofusablecapacityoverthetotalbatterycapacity.Asthetotalbatterycapacity increases,thesizeofbatterypacksincreasesandthePHEVcancoveragreaterelectric drivingdistance r .However,theelectricityonboardusageratewillincreasewith r duetothe additionalweightofthebatterypacksaddedtothevehicle.Theamortizedbatterypackcostis calculatedasfollows: B a ( r )= B ( r ) a CRF (34) where CRF = & i ( 1+ i ) n ( 1+ i ) n % 1 isthecapitalrecoveryfactorrepresentingtheratioofaconstant annuitytothepresentvalueofreceivingthatannuityover n years; i isthediscountrate; a isthenumberofdrivingdaysperyear;and B ( r ) isthebatterypackcostin$/kWh,whichis expectedtodecreaseasthebatterycapacityincreasesduetotheeconomyofscaleassumption ( Lin 2014 ).Thenumberofyears n intothefuturedependsonthelifespansofthebattery andthevehicle.Forthelatter,drivingagreaterdistanceeverydayleadstoashorterlifespan ofthevehicle( Pearreetal. 2011 ).Assumingthatthedesignedmileageofavehicletobe m ,wehave n =min( n u $ m d % / a ) ,where d isthedailydrivingdistanceofauserand n u the batterylifespan. Modiedfromtheonein Shiauetal. ( 2010 ),thesecondaddendoftheusercost representstheexpenseofconsumingelectricityandgasolinewhenauseroperatesthevehicle eachday,asshownbelow: C o ( r ) = ( d e ( r ) e n e ( r ) ( 1 n c )) + ( d g ( r ) g n g ( r ) ) (35) where e isthepriceofelectricityin$/kWh; n c isthebatterycharginge" ciency,i.e.,the amountofelectricityconsumedonboardperunitofelectricitytransferredfromthegrid( Lin 2014 ); g isthepriceofgasolinein$/gallonand n g ( r ) isthegasolinefueleconomyofthe PHEVsinmilepergallonwhenthevehicleoperatesinthecharge-sustainingmode.The 42

PAGE 43

e ciencydecreasesastheelectricdrivingrangeincreasesduetoheavierbatterypacks.Let d e ( r ) and d g ( r ) representthedailydistancetravelledinmilesbyauserusingelectricityin thecharge-depletingmodeandgasolineinthecharge-sustainingmoderespectively.Assuming homechargingisavailableandeachPHEVisfullychargedinthemorning,thesedistancesare estimatedasperequations( 36 )-( 37 ): d e ( r )=min( r d ) (36) d g ( r )=max(0, d r ) (37) Inequations( 36 )-( 37 ), d isthedistancethataparticularusertravelseverydayonaverage. Inthebasecase,itisassumedthatthereisscarcepubliccharginginfrastructureandPHEVs areexclusivelychargedathome.Basedonresultsfrom Trautetal. ( 2013 ),homecharging isnotalwaysanoptiontotheU.S.households.Thus,equation( 36 )mayoverestimatethe electrieddistancewhileequation( 37 )mayunderestimatethefueleddistance. OthercostcomponentsassociatedwiththemaintenanceofthePHEVenginecould havebeenconsidered.ThemaintenancecostofaPHEVengineisrelatedtothecyclesofthe charging-dischargingbatteryprocessandmaydependontheelectricdrivingrange r ,because therangedeterminesthemilesthatwillbecoveredinthecharge-sustainingmode.However, duetotheunavailabilityofempiricaldatatottherelationship,wedonotincorporatethis costcomponentinourframework.Lastly,previousstudies,whileassessingthesocialcostsof thehybridvehicles,incorporatedintheusercostspecicationregistrationfees,insurancecosts, tollsandfederal/statefuelexcisetaxes(e.g., LipmanandDelucchi ( 2006 )).Thesecostsare consideredastransfersandthusarenotincorporatedinthisframework. 3.1.2ExternalEnvironmentalCost ThePHEV'sexternalcostcontainsthecostsoftheGHGemissionsfrommanufacturing thebatteryandoperatingthevehicle,asdescribedinequation( 38 ): C e ( r ) = G m ( r ) + G o ( r ) (38) 43

PAGE 44

where G m ( r ) istheemissionscostassociatedwiththebatterymanufacturingprocess,and G o ( r ) caststheoperation-relatedGHGemissioncost.Bothcostsarein$/day. TheemissionscostassociatedwiththeGHGofbatterymanufacturingispresentedin equation( 39 ),adoptedfrom Shiauetal. ( 2010 ). G m ( r ) = ( b c ( r ) v b k c 1 a CRF ) SCC (39) where b c ( r ) isthenumberofbatterycells,dependingonthebatterysize; v b isthebattery packmanufacturingemissions,estimatedinkgCO2-equivalentperkWh; k c istheenergy capacityperbatterycellinkWh/celland SCC isthesocialcostofGHGin$/kgCO2-equivalent forthebaseyearofouranalysis,whichquantiesthe"monetizeddamagesassociatedwithan incrementalincreaseincarbonemissionsinagivenyear"( EnvironmentalProtectionAgency 2013 ). ThedailyGHGemissionscostassociatedwithoperatingthevehicleisestimatedby equation( 310 ),whichismodiedfromwhatproposedin Shiauetal. ( 2009 ): G o ( r ) = ( d e ( r ) v e n e ( r ) ( 1 n c ) + d g ( r ) v g n g ( r ) ) SCC (310) where v e istheaveragekgCO2-equivalentperkWhofelectricityconsumedinthecharge-depleting modewhile v g istheaveragekgCO2-equivalentpergallonofgasolineconsumedinthe charge-sustainingmode. Theenvironmentalcostassociatedwiththedisposalorrecyclingofabatteryattheend ofitslifecycleisanotherimportantcomponenttoconsider.However,thereuseofPHEV batteriesisnotexpectedtobecost-e! ectiveinthenearfuture,assumingthatthebattery pricescontinuetodecrease( NeubauerandPesaran 2011 ).Moreover,theliteratureassociated withreusingbatteriesofPHEVsisthin.Sinceempiricaldataarenotavailabletosupporta drivingrangedependentdisposalcost,wedonotincludethiscomponentinouranalysis.Social costsrelatedtoaccidentsandcongestiondonotdependontheelectricdrivingrangeofPHEVs and,therefore,arenotincorporatedinthisstudy.Ontheotherhand,airpollutionandhealth 44

PAGE 45

externalitiescouldbepotentiallyassessedwithlife-cyclescenarioanalysis( Delucchi 2000 ; Tessumetal. 2014 ). 3.1.3ExternalChargingInfrastructureCost InadditiontothedrivingrangeofPHEVs,theavailabilityofchargingopportunitiesalso playvitalrolesindeterminingthestatesofchargeofPHEVbatteries.Whenthedeploymentof workplacechargersonthetransportationnetworkisconsidered,therequiredcapitalinvestment canbeapproximatelyestimatedbyequation( 311 ): C g = c g CRF m a v (311) where c g isthecostofinstallingonechargerin$; CRF m iscapitalrecoveryfactorassociated withthelifecycleofacharger,and v isthetotalnumberofinstalledchargers.Notethatthe basecasemodeldoesnotconsiderworkplacecharging,thus C g =0 .Thiscostcomponent playsacriticalrolewhenconsideringdeployingworkplacechargers,whichispartofthe modelingframeworkextension. 3.2Data TheproposedoptimizationframeworkisappliedtotheU.S.PHEVmarketusingdata fromrecentstudiesthatpertaintothismarket.Hereinafter,onlylithium-ionbatteriesfor PHEVsareconsidered.Lithium-ionbatterytechnologyhashigherenergydensities,making itmoreappropriateforPHEVoperations( SamarasandMeisterling 2008 ).However,storing su cientelectricitystillrequiresbulkybatteries( Pearreetal. 2011 ).Forbatteryprices,we usethegoalsthattheU.S.AdvancedBatteryConsortiumassumingthatthoseareachieved inthebaseyearof2020( Pesaranetal. 2007 ).Therelationshipbetweenthebatterycost B ( r ) andbatterycapacityisdepictedatFigure 3-1 .Thefunctionthatrelatesthecostwith theelectricdrivingrange r is B ( r ) =450 r % 0.292 Itisassumedthatthebatteryutilizationfactor h b is90%;thebatterycharginge" ciency n c is90%;themarkupfactor k is150% Lin ( 2014 );thenumberofworking/drivingdays peryearare a =250;thedesignedmileageofavehicleis m = 150,000milesandthebattery 45

PAGE 46

life n u is10years( NationalResearchCouncilCommitteeonAssessmentofResourceNeeds forFuel,CellandHydrogen,Technologies 2010 ).Moreover,themaximumelectricdriving rangeconsideredisan r u =100-mile;thebatterypackemissionsinkgCO 2 -equivalentper kWhparameteris v b =0.0216andtheenergycapacityinbatterycellis k c =120kWh/cell NormanShiau2011a. Thedatafrom2009U.S.NationalHouseholdTravelSurveyareutilizedtodenethedaily drivingdistanceofvehicles/driverswithaworkingpurpose( U.S.DepartmentofTransportation andFederalHighwayAdministration 2009 ).Inthisstudy,weareparticularlyinterestedinthe deploymentofworkplacechargingandthuswedonotlookintotripchaindatasets.Forsample generation,datalteringisperformedbasedonthefollowingvecriteriabasedon Lin ( 2014 ): Maindriverofthehousehold; Thevehicledrivenisacar,van,sportutilityvehicleorpick-uptruck; Themaindriverworksfromhomeatmost5dayspermonth; Thevehicleisnotcarryingacommercialplate; Thedailyvehiclemilestravelled(VMT)forworkingpurposesdonotexceed200miles. Applyingthesecriterialeadstoatotalsampleof40,161entries.Theaveragedailytravel distanceinthesampleis26.2miles.Thedailydrivingdistanceinthesampleisassumedto berepresentativeanditsday-to-dayvariationsarenotconsidered.Itisfurtherassumedthat thetravelpatterninthebaseyear2020oftheanalysisisthesameasthatreectedinNHTS 2009data.Notethat U.S.FederalHighwayAdministration ( 2015 )reportsadecreaseinthe totalgrowthofVMTintheU.S;e!ectsofpotentialchangestothedailycommuteVMTare examinedwhileconductingsensitivityanalysisfurtherinthischapter. Inordertodenetherelationshipoftheonboardelectricitye" ciencyrate n e ( r ) andthe gasolinee"ciencyrate n g ( r ) withthedrivingrange r ,datafromtheliteratureareutilized, particularlythosein Elgowainyetal. ( 2009 ).Theresultingttingequationsarepresentedin Figure 3-2 46

PAGE 47

Thepriceofelectricityexclusivelyforthetransportationsectorisestimatedusingthedata bystateandproviderduring1990-2012( U.S.DepartmentofEnergy 2013b ).Itisassumed thatthebasepriceofelectricityis e =0.11$/kWhforthebaseyear2020whilethegasoline pricewithouttaxis g =$4.00$/gallon. TheGHGemissionsofPHEVoperationinthecharge-depletingmodeoriginatefrom electricityproduction.Basedon Shiauetal. ( 2009 ),theGHGemissionsrateis v e =0.730 kgCO 2 -eq/kWh.Ontheotherhand,theGHGemissionsinthecharge-sustainingmodeare estimatedbysummingtheamountsofCO 2 ,CH 4 andN 2 Oemissionsofcombustingagallon ofgasolinemultipliedbytheirglobalwarmingpotentials.Thesumturnsouttobe v g =8.912 kgCO 2 -equivalent/gallon( U.S.DepartmentofEnergy 2013b ; Parry 2007 ).Inaddition,the socialcostofcarbonparameter SCC ,witha3%discountrate,isestimatedtobe0.043 $/kgCO 2 -equivalent( EnvironmentalProtectionAgency 2013 ). 3.3Results Thissectiondiscussestheresultsforthebasecaseandsensitivityanalysisresultsofthe optimalelectricdrivingrangewhenonlyhomechargingopportunityiso! ered. 3.3.1BaseCase ThecompositionofthedailysocialcostofoperatingaPHEVisprovidedonTable 3-1 whichpresentseachcostcomponentassociatedwithadailyVMTof26.2milesforaselected numberofdesignsofPHEVdrivingranges(from10to60milesranges).Aspreviouslynoted, 26.2milesistheaveragedrivingdistanceforworkingpurposesinoursamples. Itcanbeobservedthattwomajorcostcomponentsarethebatterycostandthecostof consumingelectricityandgasoline.Althoughtheenvironmentalcostisnotamajorcomponent, itstillcontributestoapproximately10%ofthesocialcost.Figure 3-3 illustrateshoweach averagecostcomponentvarieswithrespecttotheelectricdrivingrange.Intuitively,thecosts ofbatteryanditsmanufacturingemissionsincreasewiththedrivingrange.Alargerbattery willalsoelectrifylongertraveldistancesandthusleadtoalowerenergycost.Thismechanism prevailssuchthattheoperatingusercostdecreaseswiththedrivingrange.Interestingly,the 47

PAGE 48

operatingemissionscostincreaseswiththedrivingrange.Thissuggeststhatifthebattery ofthePHEVisunnecessarilytoolarge,itwillleadtogreateremissionsduetotheworsefuel economycausedbytheaddedvehicleweight. TheoptimizationmodelissolvedbyusingtheKNITROsolver( Byrdetal. 2006 )in GAMS23.3( Rosenthal 2015 )andtheresultingoptimalelectricdrivingrangeis16mileswith theminimumdailysocietalcostof$3.19perPHEV.Completeenumerationforallthecost componentsovertheintegerintegral [1,100] of r inMATLABisalsoconductedtoverifythe optimalityoftheresultsobtainedbythesolver.Theoptimalvalueofdrivingrangesuggests that,ifprescribedforallconsumers,thedrivingrangesofPHEVs(inaseriesconguration)in themarket,i.e.,30-38miles,arenotsociallyoptimalandyieldhighersocialcostsascompared withtheoptimaldrivingrangeof16miles.Thisisnotsurprisingasthosedrivingrangesare notdesignedfromsociety'sstandpoint;ourindicativeresultssuggestthatalowerdrivingrange ismorebenecialtothesociety.Theseresultsarelargelyconsistentwiththeliterature,e.g., Michaleketal. ( 2011 )and Lin ( 2012 ),whichsuggestedthatPHEVswithsmallerbatterypacks aremoresociallycoste!ective.Ontheotherhand,thismightdiscourageconsumersfrom purchasingPHEVs,especiallythoselivinginruralareas,whomaydrivelongerthan16miles dailythatsuchaPHEVcanelectrify.Ingeneral,theneedtoconsiderconsumerheterogeneity andproductdiversicationshouldberecognized.SomePHEVconsumersmaybebettero! withthe30-38milesofelectricrange,whileothersmaybewisetochooseashorterelectric range.Thendingofanaverageoptimalrangemeansnocriticismoflong-rangePHEV products,butonlysuggestsapolicydirectiontoencourageadoptionofshort-rangePHEVs, forsocietallycost-e! ectivemitigationofGHG.Similarsuggestionhasbeenmadeinprevious studies( Shiauetal. 2009 ),indicatingthatpolicymakingshouldconsiderpromotingsmaller capacityPHEVs.Infact,PHEVswith10-25mileelectricrangearealreadybeingo!eredinthe marketbutthoseoperateinblendedmode,consumingbothgasolineandelectricityduringthe charge-depletingmode. 48

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Society'stotalcostisconvexover r asdemonstratedinFigure 3-3 .Theatareaofthis costcurvebetween13and18milesimpliesthatthesocialcostisnotsensitivetotheelectric drivingrangewithinthisinterval.However,thedrivingrangesinthisintervalareallshorter thanthosecurrentlyavailableinthemarketplace.Itisalsointerestingtorefertothecase oftheelectricdrivingrangeisapproachingzero( r ( 0 ),wherethevehicleisessentiallya conventionalonewithgasolinee" ciencyofapproximately35MPG.Comparedtothiscase,a universaladoptionofPHEVswiththeoptimaldrivingrangeof16milesreducestheaverage dailysocialcostbyapproximately2.42%. 3.3.2SensitivityAnalysis Inthissubsection,thevalidityoftheindicativeoptimaldrivingrangediscussedabove isexaminedagainstprimaryinputparametersofthemodel,whicharecertainlysubjectto uncertainty.Table 3-2 presentsoptimisticandpessimisticvariationsorchangesofthese parametersconsideredinoursensitivityanalyses.Figure 3-4 showshowtheoptimaldriving rangechangeswithrespecttothosevariations. Theoptimaldrivingrangeisfoundtobemostsensitivetothebatterypackcostand thegasolineprice.Morespecically,itchangesby25%inresponsetoa10%changeinthe gasolineprice,by25%withrespectto10%changeofthechargingpotentialandby0-12.5% inresponsetoeveryotherfactor.Theoptimaldrivingrangeisfoundtobeelastictothe productionsourceoftheelectricitythatbatteriesarechargedwith,e.g.,coal,naturalgas or,particularly,nuclearpower.Thefactorshavingthegreatestimpactonthevalueofthe minimumsocietalcostarethegasolinepriceandthediscountrate,witha10%increaseof therstparameterresultingin5%increaseofthecostandwitha2%increaseofthesecond parameterresultingin6.9%decreaseofthecost.Anincreaseordecreaseof1%intheVMT haslittleimpactontheoptimaldrivingrangeresult. 49

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3.4ModelExtensions 3.4.1DeploymentofWorkplaceChargingInfrastructure Thebasemodelisextendedtoconsiderthedeploymentofworkplacecharginginfrastructure. Itisofutmostimportanceforthegovernmenttoinvestigatewhetheraninvestmentfor workplacechargingdeploymentcanfurtherreducethesocietalcostofthePHEVusage;how manychargersneedtobedeployedandhowtheavailabilityofworkplacecharginga! ectsthe optimaldrivingrange. Theavailabilityofworkplacechargersprimarilyimpactstheuseroperatingcost C o ( r ) andtheoperatingenvironmentalcost G o ( r ) .Bothcostsareexpectedtodecreaseifdrivers rechargetheirPHEVsduringtheday.Inouranalysis,weassumethatdriversfollowasimple dailytripchainofhome-to-workandwork-to-home.Fordriver j ,theone-waydistanceis d j / 2 assumingthatthedriverchoosesthesameroutebothways.Consequently,thestateofcharge ofthePHEVbatteryatthedestinationofthersttrip,i.e.,workplace,isgivenasfollows: s 1 j ( r )=max ( r d j 2 ,0 ) (312) Giventhedwelltime t atthework(inhours)andthechargingpower P atthechargingstation (inkW),thebatterystateofchargebeforeheadinghomeiscalculatedbasedonequation ( 313 ). s 2 j ( x j r )= + + + + s 1 j ( r ) ,if x j =0 min & r s 1 j ( r ) + P t n e ( r ) ,if x j =1 (313) where x j isabinaryvariable,equalto1ifthePHEVrechargesatworkand0otherwise. Theelectrieddistanceandthegasoline-fueleddistanceforthersttripcanbeestimated asfollows: d e 1 j ( r )=min ( r d j 2 ) d g 1 j ( r )=max ( 0, d j 2 r ) (314) Inthiscase,thePHEVisassumedtobefullychargedbeforeleavinghomeforwork. 50

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Similarly,thedistancesforthework-to-hometriparecalculatedbasedonequations 315 and 316 d e 2 j ( x j r ) =min ( s 2 j ( x j r ) d j 2 ) (315) d g 2 j ( x j r ) =max ( 0, d j 2 s 2 j ( x j r ) ) (316) Thetotalelectriedandgasoline-fueledmilesarethesummationsofthehome-to-work andwork-to-homedistances,andarefurtherusedtoestimatetheoperationalcostsassociated withenergyconsumptionandemissions.Wedenotetheinternalusercostandtheexternal environmentalcostas C u j ( r x j ) and C e j ( r x j ) respectively.Thecostofinstallingchargersis givenbyequation( 311 ),denotedas C g ( v ) ,where v isthenumberofchargerstobedeployed attheworkplaces.Giventhenumberofdeployedchargerswillbelessthanthenumberof PHEVs,itneedstobedecidedwhowillgettousethosechargers.Themodelingframework doesnotallowustoconsideroptimallocationsofchargingstationsforPHEVsanddescribe thechargingbehaviorsofdriverslikepreviousstudiessuchas Heetal. ( 2013 ).Instead,the locationsofworkplacechargersareassumedalwaysoptimalsothatthosewhobenetthemost fromrechargingwillgettouseworkplacechargers.Inessence,itisassumedthattheworkplace chargersareoptimallylocatedtomaximizethesavingsthatdriversreceivefromrecharging theirPHEVs. Withtheaboveconsiderations,theextendedoptimizationmodeliswrittenasfollows: min r v C ( r v ) = j $ C u j $ r x & j % + C e j $ r x & j %% + C g ( v ) (317a) s.t. 0 # r # r u (317b) x & = argmax { j C u j ( r x j ) | j x j = v x j % { 0,1 } $ j } (317c) where C u j ( r x j ) = { C u j ( r ,1 ) C u j ( r ,0 ) } x j ,i.e.,thecostsavingifrechargingatworkplace foruser j 51

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Theabovemodelisabi-levelmathematicalprogrammingmodel.Theupper-levelissetto minimizethesocialcostbydecidingthedrivingrangeandnumberofworkplacechargers.The lower-levelproblemidentiesdriverswhowillbenetthemostfromrechargingtheirvehicles atworkplacesbymaximizingtheirsavingsfromtheworkplace-rechargingprocess.Notethat inconstraint( 317c ), # j x j = v impliesthatavehiclewilloccupyonechargerfortheday. Assumingonevehicleperchargermayoverestimatethenumberofchargers,sinceundermost circumstancesPHEVswillneedonlyapartialdayofcharging.Thisconstraintcanberevised toreectthis. Theabovemodelissolvedleveragingthesamedatadescribedpreviouslyandconsider deployingLevel-2chargers,whicho! erchargingat240Vwithachargingtimerangingfrom 2.5to8hoursdependingonthebatterysizeofPHEVs( YilmazandKrein 2013 ).The installationcostforaLevel-2chargervariesfrom$1,000to$3,000.Theinvestmentcostfor aworkplacechargeris c g =$1.852percharger( YilmazandKrein 2013 ).Thecapitalrecovery factorofthecharginginfrastructureisassumed CRF m =0.12,basedona3%discountrate.A heuristicprocessisutilizedtosolvethisbi-levelprogrammingmodelinMATLAB;thisinvolves asortingalgorithm,wherethedriversthatsavethemostfromworkplacechargingavailability areidentied,andabruteforceone,whereallcombinationsofintegervaluesoftheelectric drivingrangeandworkplaceallowancewithinthefeasibilityintervalsarefullyenumerated. Figure 3-5 demonstrateshowthedeploymentofworkplacechargersimpactstheoperating userandenvironmentalcosts.Specically,itshowsthescenariosofdeploying100,1,000and 20,000chargers,aswellastheoptimalnumberofchargers,i.e.,10,958.Thosescenariosare equivalenttoassuming1chargerper401.61,40.16,2.08and3.66vehiclesrespectively.It canbeobservedthatdeployingworkplacechargerswillfurtherreducethesocietalcost;the scaleofthiscostreductiondependsonthechargingdensitydeployed.Forexample,when thegovernmentdecidestodeploy1,000chargers,theoptimaldrivingrangeincreasesto18 milesandtheaveragedailysocietalcostdropsto$3.18perPHEV.Whenthegovernmentcan 52

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provideonly100chargers,perhapsduetoalimitedbudget,theoptimalelectricdrivingrange remainsa16-mileandthesocietalcostisfoundtobe$3.19perPHEV. Whendeployingtheoptimalnumberofchargers,i.e.,10,958,whichisequivalenttodeploy achargerforevery3.66vehicles,thesocietalcostdecreasesby4.54%($3.04perPHEV)while theelectricdrivingrangesurprisinglyincreasesby37.5%,from16to22miles.Thissuggests thatalargerbatterywouldallowdriverstobetterutilizetheworkplacechargerstoachieve longerelectrieddistancesandsavemoreregardingtheiroperatingcosts.Consequently,the socialcostisreducedwithalargerbatteryifthosewhowillbenetthemostfromchargingwill gettheopportunitytorecharge.Whenonechargerisavailableforevery3.66vehicles,with a22-milebatteryforthetripfromworktohome,19.94milesperchargerareelectriedon averagecomparedto14.97milesperchargerthatwouldbeelectriedifthebatterywasstill a16-mileone.Witha22-milebattery,theadditionalaverageelectriedmilesperkWhdueto chargingis0.33,whilea16-mileoneyieldsonly0.30milesperkWh.Inotherwords,thevalue perunitofbatterycapacityincreases.Theresultsshowcasethatitisintheinterestofthe societytodeployworkplacechargersinordertofurtherreducethesocialcostofdriving. 3.4.2DiversicationoftheElectricDrivingRange Thismodelingextensioninvestigatesthee!ectsofintroducingtwoorthreedi!erent electricdrivingrangesofPHEVs.PHEVs'batteriescouldbecomediversiedinthemarket inordertoappealtomoremarketsegments( Lin 2014 ).Heretheoptimalpairandtripleof electricdrivingrangesisdeterminedinordertofurtherreducethesocietalcost.Withmore thanonedrivingrangeavailable,eachPHEVuserisassumedtoselecttheonethatminimizes exclusivelytheirinternalusercost(batteryandoperatingcost).Therefore,theproblemonce againpossessesaleader-followersgamestructureandcanbeformulatedasthefollowing 53

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bi-levelprogrammingmodel(usingthecaseoftriplebatterysizesasanexample): min C ( r 1 r 2 r 3 z j ) = j $$ C u j ( r 1 ) + C e j ( r 1 ) % z & j 1 + $ C u j ( r 2 ) + C e j ( r 2 ) % z & j 2 $ C u j ( r 3 ) + C e j ( r 3 ) % z & j 3 % (318a) s.t 0 # r 1 r 2 r 3 # r u (318b) z & j =argmin + + + + C u j ( r 1 ) z j 1 + C u j ( r 2 ) z j 2 + C u j ( r 3 ) z j 3 / / / / / / / / z j 1 + z j 2 + z j 3 =1, z j % { 0,1 } 0 + + 1 + + 2 $ j (318c) where r 1 r 2 r 3 arethetripleofelectricdrivingrangesinmiles; z j 1 z j 2 z j 3 arethebinary variablesdenotingwhichdrivingrangeisselectedbyuser j ,basedontheminimizationofhisor herownusercostand z j = { z j 1 z j 2 z j 3 } T .Intheabove,theupper-levelproblemdescribesthe decisionofintroducingthreedrivingrangeswhilethelower-levelproblemdescribethedecision ofeachuseronwhichdrivingrangetouse.Clearly, z j 1 + z j 2 + z j 3 =1 ensuresthateachuser canchooseexactlyonedrivingrangetominimizehisorherinternalcost.Forthisextension, chargingisexclusivelyconsideredhome-based. Aheuristicprocessisproposedtosolvethisbi-levelmodelingframework.Thisis,aswell, basedonabruteforcealgorithmforcompleteenumerationofallthepossibleintegerpairsand triplesofPHEVranges,withinthefeasibilityintervals,thatresultintheminimumcostfor society. Theresultsindicatethattheoptimaldrivingrangepairis8and40milesandtheoptimal tripleis7,24and51milesrespectively.Theoptimalsocialcostforthebatterypairis $2.95perPHEVandforthebatterytripleis$2.82perPHEV,areductionof7.45%and 11.5%respectivelycomparedtothecaseofasingleelectricdrivingrange.Asexpected,the diversicationofthebatterysizecandecreasesubstantiallythesocialcost(aswellasthe individualusercost). Itisinterestingtonotethatdiversifyingelectricdrivingrangesappearsmoree! ective thandeployingworkplacechargersonreducingthesocialcosts.Thepolicyallowsdriverswith variousVMTstoselecttherangetobettersuittheirneeds.Specically,inthecaseofo!ering 54

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twodrivingranges,63.14%ofdriverschoosethe8-milerangewhiletherestchoosestherange of40miles.Forthecaseoftripleranges,44.82%,33.17%and22.01%ofdriverschoosethe rangeof7,24and51milesrespectively. 3.5Summary ThePHEVtechnologyallowsforsmoothtransitionfromgasolinefuelstoelectricityby diversifyingtheenergyrequiredtopowerpersonalmobilitywithouttheneedforextensive coverageofthetransportationnetworkwithchargingstationequipment. Inordertoachievethemaximumbenetforsocietywhenusingthisvehicletechnology, thischapterdeterminestheoptimalelectricdrivingrangeofPHEVsthatminimizesthe dailycostbornebythesocietywhenusingthistechnology.Themodelingframeworksare demonstratedusingempiricaldatafromtheU.S.automobileandtravelmarkets.Results indicatethattheoptimaldrivingrangetoachievetheminimumsocialcostis16miles.The optimalvalueoftheelectricdrivingrangeisfoundtobesensitivetofactorssuchasthe batterypackcostandgasolineprice.Theresultssuggestthatitisofgovernment'sinterestto encouragecarmanufacturestoproducePHEVswithalowerdrivingrange,comparedtothose availableinthemarket. Theoptimizationframeworkisextendedinordertodeterminethedrivingrangeandthe workplacechargingdensity,whenworkplacechargingequipmentareavailable.Whendeploying workplacechargers,theoptimalelectricdrivingrangesurprisinglyincreasesto22miles.With achargerforevery3.66vehicles,thedailysocialcostdropsbyapproximately4.54%.Lastly, themodelisextendedtodeterminebatterysizediversityforminimumsocialcostofPHEVs operation.ThendingsindicatethatthemarketintroductionoftwoorthreePHEVelectric drivingrangeoptionscanleadtoareductionof7.45%,and11.5%respectivelyofthecost bornebythesociety. 55

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Figure3-1. Batterypackcostwithrespecttobatterycapacity. Figure3-2. Electricityandgasolineconsumptionrates. 56

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Table3-1. CostComponentsforDailyVMTof26.2miles Costsin$/day PHEV-10PHEV-20PHEV-30PHEV-40PHEV-50PHEV-60 Drivingranger(miles)10 20 30 40 50 60 Batterycost C b ( r ) 0.52 0.86 1.16 1.44 1.71 1.97 Useroperatingcost C o ( r ) 1.92 1.10 1.02 1.05 1.07 1.10 Operatingemissionscost G o ( r ) 0.25 0.24 0.29 0.30 0.31 0.31 Batterymanufacturing emissionscost G m ( r ) 0.01 0.02 0.03 0.04 0.05 0.06 SocialCost C ( r ) 2.70 2.22 2.50 2.83 3.14 3.44 Figure3-3. Averagecostcomponentswithrespecttotheelectricdrivingrangewithonly home-chargingavailability. 57

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Table3-2. BaselineandSensitivityParameters Baseline SensitivityAnalysis Batterycostprobable estimates2020 USABCfor 2020 Optimistic:-5.00%change Pessimistic:+5.00%change Chargingpotential n c n c =90% Optimistic:+10.00% Pessimistic:-10.00% Discountrate 3%averageOptimistic: i = 5.00% Pessimistic: i = 2.50% Batteryutilization h b h b =90% Pessimistic:-10.00% Optimistic:+10.00% Gasolineprice g =$4/gallonOptimistic:-10.00% Pessimistic:+10.00% Electricityprice e =0.11$/kWhOptimistic:-10.00% Pessimistic:+10.00% Markupfactor k k =150% Optimistic:-10.00% Pessimistic:+10.00% DailycommuteVMTNHTS2009 1.00% ElectricityGHG emissionsbasedon sourceofproduction Coal:0.73 kgCO2eq/kWh Naturalgas:0.47kgCO2eq/kWh Nuclear:0.066kgCO2eq/kWh 58

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Figure3-4. SensitivityoftheoptimalPHEVelectricdrivingrangeandtheminimumsocial cost. 59

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Figure3-5. Averagesocialcostwithwork-chargingavailability. 60

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CHAPTER4 COST-EFFICIENTANDECO-FRIENDLYPLUG-INHYBRIDELECTRICVEHICLE CHARGINGMANAGEMENT TheextenttowhichPHEVscontributetototalsource-to-wheelemissionsreduction dependsonthegenerationsourceoftheelectricityusedtorecharge.Aspowerplantsharness di erentsourcesforelectricitygeneration(e.g.,fossilfuels,renewables,naturalgas,etc.),the carbonintensityofelectricityproductiontoaccommodatecharginghasspatialandtemporal variations.Thesameholdsforelectricitygenerationcosts.Basedonavailabledata( U.S. DepartmentofEnergy 2016c ),PHEVssource-to-wheelemissionsmightnotbelowerthan thoseofICEVsandenvironmentalgainscanvarysignicantlyacrossstates.Forinstance,for thestateofWyomingwhere88.9%oftheelectricitysourcesiscoal,byoperatingaPHEV 22%annualemissionsreductionisachievedcomparedtoanICEVoperation;forthestateof Vermont,thispercentageincreasesto71%becausethemajorsourceofelectricitygeneration isnuclear(71.9%).Smartandcentralizedchargingisapromisingstrategyforcontrollingthe excessivedemand,ensuringgridreliabilityandmeetingtheneedsofboththeusersofPHEV technologiesaswellasthegovernment's. Thischapterpresentsmodelingandimpactsoftwodi!erentPHEVchargingmanagement schemes;acost-e! ectiveandaneco-friendly.Thecost-e! ectiveobjectiveissettominimizethe summationofthePHEVsrechargingcostsandthegasolineconsumptioncostswhenPHEVs operateincharge-sustainingmode.Theeco-friendlyobjectiveissettominimizethesummation ofmarginalemissionsfromtheelectricitygeneratedtorechargePHEVsandtailpipeemissions fromPHEVsoperationincharge-sustainingmode. Thescopeoftheworkpresentedinthischapteristoexploretwoalternateobjectives forPHEVchargingmanagement,andthenassesstheimpactofsuchschemesonPHEV operatingcosts,emissions,andtheutilitygridload.Amixedintegerlinearprogrammingmodel isdevelopedtomeetthoseobjectives.TheframeworkisappliedtoU.S.energyandautomobile datasets,bytakingintointoaccounttheheterogeneityofdrivingpatternsofPHEVownersand thehourlyelectricitygenerationconstraintsacrosstheU.S. 61

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4.1ChargingManagementOptimizationFramework PHEVownersareinterestedinjointlyminimizingthecostofelectricitypaidfortheir dailyoperationaswellastheirconsumptionofgasoline,asshowninobjectivefunction( 41a ). Driversarenotexpectedtofavorarechargingschemethatisnotcoste" cientforthem(under theassumptionofTOUrates);however,acontrolschemethatminimizestheiroperational costscanbepubliclyacceptable.Onthecontrary,thegovernment'sobjectiveistominimize thesocialcostofemissionsfromthedailyPHEVs'operation.Thisexternalitycostconsists oftheemissionsfromtheelectricitygeneratedtosatisfyPHEVrechargingdemandandthe tailpipeemissionsfromthegasoline-fueledportionofPHEVdailyoperation,asinobjective function( 41b ).Assuminganunregulatedfreeelectricitygenerationandtransmissionmarket, thecostofPHEVschargingcanbeviewedasatransfer,redistributedtocovertheelectricity generationcost.Therefore,onlythemonetizedenvironmentalexternalitiesareincurredbythe societyinthiscase. Theconstraintsoftheframeworkareenhancedfromthosein Sioshansi ( 2012 ).A controlledchargingsystemisassumedtobeinplaceforallPHEVowners.Thistypeofcontrol allowstripsnottobeelectried,sincePHEVscanoperateevenaftertheirbatteryisdepleted. Theindicesofthemodelarepresentedhere: i signiesthedriverofaPHEVwhere i % { 1,2,..., I } and t denotesthehoursinaday t % T = { 1,2,...,24 } .Thedecision variablesarethefollowing: r t i isthenon-negativemileageadditiontotheSOCofthebattery (inmiles)whenaPHEVisrecharginganditisestimatedinconstraint( 41f ); p t i isthepower drawnfromtheutilitygridinkWhwhilethePHEVisrechargingbetweentrips.Thishasa lowerboundofzeroandanupperboundof u t i .This u t i parameteristhemaximumhourlykW ofchargethatcanbedrawnfromthegriddependingonthelevelofchargingavailableateach destinationwherethePHEVisidle(home,workplace,orpublic),asdemonstratedinconstraint ( 41l ).Therestofthedecisionvariablesare d t CD i and d t CS i ,whichrepresentthedistance portionscoveredincharge-depletingandcharge-sustainingmodeperhour,respectively.Those 62

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distancesadheretoconstraint( 41g );and a t i % { 0,1 } checksthePHEVbatterySOCfor i everyhour t ,asshowninconstraint( 41i ). Themixedintegerprogrammingformulationisasfollows: min z 1= t i ( p t e n e r t i + p gi / n g d t CS i ) (41a) min z 2= # t i ( v t e n e r t i + v g / n g d t CS i ) (41b) s.t. s t +1 i = s t i + r t +1 i d t CD i $ i t (41c) S % # s t i $ i t (41d) s t i # S + $ i t (41e) r t i = P t i ( l t i p t i / n e ), $ i t (41f) d t CD i + d t CS i = d t i $ i t (41g) d t CS i # d t i (1 a t i ), $ i t (41h) a t i ( s t i S % ) ( S + S % ) $ i t (41i) i p t i # C t $ t (41j) d t CD i 0, d t CS i 0, $ i t (41k) p t i 0, p t i # v t i $ i t (41l) where p t e isthereal-timeelectricitypriceforchargingin$perkWh; n e isthevehicle's electricityconsumptionrateinkWhpermile; p g i isthepriceofgasolinein$pergallon thatdi! ersforeachPHEVowner i ; n g isthegasolinefuele" ciencyrateinmilespergallon; # isthesocialcostofcarbonin$perkgCO2-equivalent; v t e isthemarginalemissionratein kgCO2perkWhfromelectricitygeneration;and v g istheemissionrateinkgCO2pergallon ofgasolinewhendrivinginthecharge-sustainingmode.Thebattery'sSOCthatindicatesthe remainingmilestobeelectriedisdenotedas s t i andisestimatedbasedonthestatetransition functionshowninconstraint( 41c ).TheSOCisboundedaboveby S + andbelowby S % 63

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determinedbythePHEVmanufacturer,asdictatedbyconstraints( 41d )and( 41e ).The rangeincrease r t i inmilesistheproductoftheprobability P t i ofencounteringachargerat eachtripdestinationinhour t (whichisaparameter),thepercentageofthehourbeingidle l t i ,andthechargingpowerdrawnfromthegriddividedbytheelectricityconsumptionrate,as inconstraint( 41f ).Constraint( 41h )ensuresthatthecharge-sustainingdistanceportionper hourisalwayslessorequaltothetotalhourlydistancecovered,dependingontheSOCofthe battery.Constraint( 41j )dictatesthatthetotalpowerdrawnforrechargingthePHEVsdoes notexceedthereservecapacity C t .However,constraint( 41j )couldberelaxedwhenobjective functions( 41a )and( 41b )accountfortheadditionalcostandpotentialchangeofthe marginalemissionratesthatwouldbeincurredbythePHEVownerandsocietyrespectively, duetotherequiredelectricityinfrastructurenetworkupgrades. 4.2Data Datarepresentativeofhour-to-hourdrivingandactivitypatterns,PHEVvehicle characteristicsandpenetration,andspatiallyheterogeneouschargingavailabilityareused. Datasourcesanddescriptivestatisticsareanalyticallypresentedinthefollowingsubsection. ElectricitygenerationcostsandemissionsratesareconsideredandtheeightU.S.NERC regionsareusedastheanalysisgeographicalunits.Adetailedmapofthestudyareais providedby NorthAmericanElectricReliabilityCorporation ( 2016 );theinvestigationfocuses onlyonthecontiguousU.S.partsofeachNERCregion,asshowninFigure 4-3 .Theeight regionswiththeiracronymsare:FloridaReliabilityCoordinatingCouncil(FRCC);Midwest ReliabilityOrganization(MRO);NortheastPowerCoordinatingCouncil(NPCC);Reliability FirstCorporation(RFC);SERCReliabilityCorporation(SERC);SouthwestPowerPool(SPP); TexasReliabilityEntity(TRE);andWesternElectricityCoordinatingCouncil(WECC). 4.2.1DriverTravelProles Driverhourlyprolesoriginatefromthetripdataleofthe2009NationalHousehold TravelSurvey(NHTS)( U.S.DepartmentofTransportationandFederalHighwayAdministration 64

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2009 ).Thosecorrespondtoonedayofdriving(24hours).Forsamplegenerationpurposes, datalteringisperformedbasedonthefollowingcriteria: Onlytripsconductedbyautomobile. Onlytripsthatwerecompletedwithinthestateofthedriver'sresidence. Tripsthatlastlessthan24hoursanddonotheadtoanout-of-statedestination. Thevehicleshouldnotcarryacommerciallicenseplate. Allentriescontaincompleteinformation. Theresultingsamplecorrespondsto476,504tripsand139,132vehicleownersforthe contiguousU.S.ThosearegroupedandanalyzedforeachNERCgeographicentity. TheNHTSdata,includetriptimestampsandvehiclemilestraveled(VMT),aswellasthe purposeofeachtravelingactivity.Assumptionsrelatedtoinfrastructureusagearenotedas follows.Whenatripdestinationishome,thevehicleiseligibleforhome-charging;similarly,for workingorshopping/recreationaldestinationsworkplace-orpublic-chargingcouldbeavailable. Nodescorrespondingtootherdestinationsdonothavechargingavailability,suchasnational parksandplacesforoutdooractivities.TheaveragehourlyVMTperPHEVandthehourly% ofvehiclestravelingorbeingidleathome,work,forshoppingorrecreationorotherdestination ateachNERCregionarepresentedinFigure 4-1 .Theleftaxiscorrespondstobarpercentages (0-1scale)andtherightonetoaverageVMTperPHEV.Eachsubgraphcorrespondstoeach region. Figure 4-1 showsthat75%to83%ofthevehiclesforeachregionareidleathomeby 10:00pmuntil5:00aminthemorning,asexpected.Foreveryregionapproximately20%ofits sampleislocatedatworkplaceby9:00amandspendsbetween4-10hoursparkedatworking premises.Themajorityofdrivingisconductedduringdaytime,from9:00amto8:00pm.The sameholdsforshopping/recreationaltrips,butthoseareevenlydistributedacrosstheday comparedtotheothertripcategories.Morethan71%oftheshopping/recreationaltripsare parkedattheirdestinationforlessthananhour.Acrosstheregions,averageVMTarehigher 65

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veryearlyinthemorningastripsthatareconductedthentendtolastlongerandcorrespond toasmallerpercentageofitsregion'ssamplesize. 4.2.2PHEVCongurationandChargingTypes Forthebasecase,oneprevalentPHEVtypeisassumedtobewidelyadopted;its characteristicsarethoseofthebest-sellingPHEVmodelintheU.S.ChevroletVolt2016is consideredrepresentativeofallPHEVs;itsspecicationsareshowninTable 4-1 ,basedon U.S. DepartmentofEnergy ( 2016d ).Dependingontheelectricityandemissioncostparametersof eachNERCregion,agreaterPHEVrangecaninducegreatercostsavingsandenvironmental benets.ThechargingequipmentcharacteristicsarealsopresentedinTable 4-1 4.2.3MarginalEmissionRates Marginal,insteadofaverage,hour-to-hourcarbonratesforeachNERCregionelectricity generationmixareutilized,soastocalculatetheenvironmentalexternalitiesforthePHEVs charging,assuggestedby Tamayaoetal. ( 2015 ).Thoseratesstemfrom Gra!Zivinetal. ( 2014 ),accountfortheimpactofhourlyconsumptionchangesonemissionsfromelectricity generation,andarepresentedinFigure 4-2 4.2.4ElectricityPrices PresentedinFigure 4-2 ,hourlyelectricitygenerationcostsareadoptedfrom Gra!Zivin etal. ( 2014 );thosearemultipliedbyamarkupfactor(1.5)inordertoreectthecostincurred bythePHEVoperator.Duetotemporalvariationsofelectricitygenerationsources,areal-time ratecanbepromotedbyutilitycompaniestoincentivizePHEVoperation,withoutrevenue loss.Theseratescanalsoserveasanincentivetoinduceparticipationinsuchacontrolled chargingprogram.Infact,TOUratesarealreadyavailablefromsomeU.S.utilitycompanies, e.g., CenterforClimateandEnergySolutions ( 2012 ).Thoseratesareassumedtoapplyonly tohome-andworkplace-charging.Thepublicchargingelectricitycostisconstantat$3.6/hour. Otherstudies,suchas Heetal. ( 2016a )and Sioshansi ( 2012 ),haveproposedpublic-and home-chargingoptimizedprices,asaninstrumenttomanageincreasedelectricityloadsfrom recharging,withouttheneedforcentralizedchargingcontrol. 66

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ItcanbeobservedfromFigure 4-2 thatthehourlyemissionratesandproductioncostsdo notfollowthesametrend.However,ingeneral,electricitygenerationcostsarelowerearlyin themorning;atthattimeemissionratesreachtheirpeak.Thesetrendsareexpectedtohavea pivotalimpactondeterminingtheoptimalcontrolledchargingscheduleforeachregion,since minimizingoperationalcostsormonetizedemissionsfromhour-to-hourPHEVoperationare conictingobjectives. 4.2.5ChargingInfrastructure Inourcasestudy,everyPHEVownerhasaccesstohome-charging.Thedrivermightplug thevehicleimmediatelyaftertheendoftheirtripbutacontrollingdeviceenforcescentralized managementofthevehicle'schargingschedule.Adatasetfrom U.S.DepartmentofEnergy ( 2016a )isusedtodeterminethepercentageoftripdestinationscoveredbypublicchargers foreachNERCregion.Thecurrentnetworkofgasstationsisassumedtocover100%of thetripdestinations,meaningthatvehicleshaverefuelingaccessinalltripstops.The%of publicchargingcoverageisestimatedbydividingthetotalnumberofpublicchargersbythe totalnumberofgasstationsforeveryregion.Thetextdatafrom U.S.DepartmentofEnergy ( 2016e )areusedtoinferthepercentageofworkersthathaveaccesstoworkplacechargersin eachNERCregion.Thenumberofemployeesthathavechargingaccessisdividedbythetotal employment.Thiswaythe%ofoursamplewithaccesstochargingatpublicandworkplace premisesisestimated,aspresentedinFigure 4-3 Accesstoworkplace-andpublic-chargingatthetripdestinationsofourpopulation's sampleisrandomlyassigned;thesummationoftheworkplaceandpublicdestinationsthat havechargingaccessadheretothepercentagespresentedinFigure 4-3 foreachregion.The probabilityparameter P t i is1whenaccesstoworkplace-orpublic-chargingisgrantedforeach typeofdestination;otherwiseiszero.Forevery t # P t i equalstotheportrayedpercentagein eachregion.Over1,000alternativescenariosofrandomchargerassignmentrunforeachregion andtheaverageresultsarepresentedinthefollowingsection. 67

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4.2.6PHEVPenetrationRateandOtherParameters ThepenetrationrateofPHEVsisadoptedfromthe2015data( U.S.Departmentof Energy 2015b a ).PHEVregistrationsdataforstatesthatconstituteeachregionaresummed upanddividedbythetotalvehiclepopulation.Theelectricityreservecapacitymarginis givenbythe2015projecteddatasetfrom EnergyInformationAdministration ( 2016b ). Otherparametersandscalarsare:thepriceofgas p gi in$pergallonoriginatesfrom U.S. DepartmentofTransportationandFederalHighwayAdministration ( 2009 ),the2015social costofcarbon # (3%discountrate)in$perkgCO2-equivalentfrom EnvironmentalProtection Agency ( 2013 ),andtheemissionsrateofthecharge-sustainingmodeis v g =8.912kgCO2per gallonfrom Kontouetal. ( 2015 ). 4.3Results ThemixedintegerprogramsaresolvedbythecommercialsolverCPLEX12.2inGAMS 23.3( Rosenthal 2015 ).Let t % { 1,...,72 } (threedays),assumingthattheone-daytrip isrepeatedeveryday.ThestartingSOCat t =1 israndomforeachPHEVowner.Results arereportedforthesecondday(24hrs).Discussionontheoptimalresultsforthebasecase follows.Alternativescenariosareexploredrelatedtoworkplace-orpublic-chargingavailability andalternatePHEVranges. 4.3.1BaseCase Figure 4-4 presentsthepercentageofvehicleschargingeachhourperNERCregion.The yaxiscorrespondstothecountofvehicleschargingperhourdividedbythetotalnumberof vehicleswithchargingavailabilityduringthathour(notethat0.2correspondsto20%). Theresultsindicatethatoptimalcost-e!ectiveandeco-friendlyprolesfollowthe hourlygenerationcostandemissionratetrends,aswellasthepercentageofparkedathome hourlytrends.ForalltheNERCregionschargingpercentageincreasesduringthehourswhen homeisthemostcommondestination.Also,forallregionsapartfromRFCandSPP,the daytimeout-of-homechargingpercentagesarebelow10%.Interestingly,theeco-friendly chargingproleforMROcorrespondstonotchargingatallandinsteadoperatealldayin 68

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thecharge-sustainingmode;thisresultiswell-alignedwithDOE'sindications(7)and(23), duetothehighcarbonintensityofelectricitygenerationinthatregion.Basedontheoptimal cost-e ectivechargingscheduleresults,PHEVoperatorswouldbeadvisedtodelaytheirstart ofcharginguntilveryearlyinthemorninginordertoreceivegreatercostbenetsundera real-timeelectricityrate. Cost-e!ectivecontrolresultsingreaterpercentageofPHEVschargingperhourbecause thisschemedetermineschargingforlongerperiodswithloweraveragechargingpowerinkW thanthechargingprolesresultingfromtheeco-friendlyscheme.Duetothecurrentlow PHEVdi! usionforeachNERCregion,constraint( 41j )isnotbinding. Figure 4-5 presentsthehourlyaveragechargingpowerperPHEVperregion.Theaverage chargingpowerisapproximately1.2kW(upperlevelpowerofhome-charging)foralltheregions after8:00pmuntil5:00am.Thespikesoftheaveragepowergraphsoccurduringdaytimewhen workplace-chargingopportunitiesareavailable;thosearesharperfortheeco-friendlycharging scheme.Forbothchargingcontrols,thehourlyloadtrendissimilarfortheNPCC,SERC,SPP, andWECCregions.FortheFRCCandTRE,thespikeoftheeco-friendlyschemeisshiftedto theright,laterintheafternoon,sincetheemissionratesfromelectricitygenerationarepoints oftheirdownwardslopeofFigurecurveatthattimeandgreatersocietalbenetsarereceived bychargingPHEVsthen. Table 4-2 presentstheoptimalaveragecostvaluesinU.S.dollarcentsperhourperPHEV forthetwochargingmanagementschemes.PHEVownerswhoexhibitpro-environmental behaviormightbeinterestedtoknowthetrade-o!sbetweenacost-minimizingcharging managementandaneco-friendlyone.InTable 4-2 ,regionswherethelatterleadstogreater percentageofmonetizedemissionsavingsthanthepercentofoperationalcostincreaseare pinpointed.ResultsindicatethatfortheFRCCregionthisisnotthecasesinceadriver wouldincuronaveragea4.85%increaseoftheircostfortheirdailyPHEVoperationto achieve4.63%reductioninemissions.Onthecontrary,fortheNPCCregiontheaverage operationalcostwouldincreaseby2.80%andcausemonetizedemissionsreductionby4.23%. 69

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Aneco-friendlyschemeismoree"cientinreducingemissionsthanincreasingoperationalcost attheNPCC,RFC,SPP,andWECCregions. 4.3.2AlternateScenarios Alternatescenarios,asshowninTable 4-1 ,areproposedtoexploretheimpactofthe rangeofthePHEVonthemileageelectrication.Asetofrangesthatarerepresentativeofthe marketareused.Scenariosarealsoevaluatedwhenonlyhome-chargingorall-but-public-charging areviableoptions.Inthefuture,boththepercentagesofworkplace-andpublic-chargingare expectedtoincreaseasPHEVsalesrise.However,duetouncertainties,predictingthe%of increasetoevaluatesuchcasesforeachregionisnotinvestigated. Figure 4-6 presentsthepercentageoftotaldailydistanceelectriedforeachNERCregion, comparingthebasecasetoPHEV-10and20.Figure 4-7 portraystheresultingcharging prolesassumingonlyhome-orall-but-public-chargingavailability,focusingontheregionwith thehighestpercentageofout-of-homechargingavailability,i.e.,WECC. Asexpected,thelargertheelectricrange,thegreaterportionsofdailytravelare electried.AsportrayedinFigure 4-6 ,aPHEV-10cancoverusingelectricityapproximately 1/3ofthetotaldailydistancesthataPHEV-50can;aPHEV-20covers2/3ofthat.Even thoughtheoptimalchargingprolesforeachmanagementscheme(seeFigure 4-4 forthebase case)varysignicantly,thetotaldailyelectriedmileagedoesnot.Bothcontroltypesresultin electrifying57%-80%ofthedailyVMTforPHEV-50,17-32%forPHEV-10,and33-50%for PHEV-20.ThegreatestelectriedpercentagesareachievedfortheFRCCandWECCregions andthelowestfortheSERCregion.Chargingmanagementismoree"cientforPHEVswith greaterranges;forexample,theaveragecostsoftheoperatorandsocietyarerespectively 189%and168%lowerwhenthePHEV-50isuniversallyadoptedcomparedtoaPHEV-10for theWECCregion. TheupperpanelofFigure 4-7 showsthattheabsenceofworkplaceandpublicchargers resultsindecreaseintheoptimalchargingpercentageafter5:00am.Thisreductionreaches morethan3%at9:00amwhilePHEVoperatorsareworking.Absenceofstationsatworkleads 70

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toanincreaseofthepercentagechargingathomeafter8:00pm.Whentherearenopublic chargers,thereductionofthechargingpercentageisstillevidentafter9:00ambutcorresponds onlytolessthan0.5%.Inthatcasethough,anincreaseofthepercentagechargingafter 5:00amisobserved,possiblybecausethedriversarebettero!havingmaximumSOC beforeleavinghomefortheday.ThelowerpanelofFigure 4-7 showsthattheeco-friendly managementschemeisgreatlyimpactedbythecompleteabsenceofpublicchargers,andthus bothscenariosresultinsimilarchanges.Bothscenariosshiftthechargingprolesclosertothe beginningoftheworkingday.SimilartrendsareobservedfortherestoftheNERCregions. 4.4Summary InthischaptertwoschemesforcentralizedchargingmanagementofPHEVsareconceived andcompared;acost-e! ectiveandaneco-friendly.Theirimpactonthehourlychargingproles isassessed,aswellasthecostsincurredbythePHEVoperators,themonetizedenvironmental externalitiesincurredbythesociety,andtheelectricityloads.Datasetsrepresentativeof eachNERCregionregardingelectricitygenerationandtravelingpatternsareutilized.The ndingsindicatethattheproposedchargingmanagementschemesresultinconictingcharging schedules;optimalcost-e! ectivechargingshouldoccurveryearlyinthemorningandoptimal eco-friendlychargingshouldoccurearlyintheafternoon.Eco-friendlychargingleadstogreater powerloadspikesduringthedayanditsoptimalchargingproleissignicantlyimpacted bytheabsenceofpublic-chargingavailability.Unavailabilityofworkplace-chargingresults inincreasingthechargingpercentageatnightforthecost-e! ectivemanagementscheme. Chargingcontrolismorecost-e!ectiveandenvironmentally-friendlyastherangeofPHEVs increases. 71

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Figure4-1. AverageVMTand%ofvehiclesinsampletravelingorbeingidleperhourofday. 72

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Table4-1. VehicleandChargingCharacteristics( U.S.DepartmentofEnergy 2016d ) VehicleSpecications Type Model BatteryCapacity (kWh) MaxSOC (mi) MinSOC (mi) ElectricityE" ciency (kWh/miles) GasolineEconomy (MPG) Base PHEV-50 ChevroletVolt2016 18.4 53 10.6 0.3 42 Scenario1 PHEV-10 n.a. 6.7 6 1.0 0.3 42 Scenario2 PHEV-20 n.a. 7.6 19 6.0 0.3 42 ChargingCharacteristics DestinationTypeofChargeACInput ChargeRate (kWh) ChargeRate (avg.mi) Home Level1 120V/10A 1.2 4 Work Level2 240V/40A 7.2 24 Public Level2 208V/80A 19.2 64 Table4-2. AverageObjectiveFunctionValueResults(dollarcentsperhourperPHEV) ChargingSchemeMeasure FRCCMRONPCCRFCSERCSPPTREWECC Cost-E!ectiveOperationalcost3.332.463.083.042.763.175.643.89 Emissionscost0.480.510.430.460.390.790.740.45 Eco-Friendly Operationalcost3.503.513.163.222.843.205.873.93 Emissionscost0.460.410.410.420.360.440.730.45 73

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Figure4-2. Marginalelectricitygenerationemissionratesandcostsperhour( Gra!Zivinetal. 2014 ). 74

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Figure4-3. Percentageofpublicandworkplacechargingavailabilityfortripsdestinationsand workersrespectively. 75

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Figure4-4. Optimalchargingprolespercentagesofthecost-e! ectiveandeco-friendly chargingmanagementschemes. 76

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Figure4-5. AveragehourlypowerloadprolespereachNERCregion 77

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Figure4-6. DailyMileageElectricationforNERCregions. Figure4-7. Chargingproleswhenonlyhome-chargingandonlyhome-andworkplace-charging (all-but-public-charging)areavailablefortheWECCregion. 78

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CHAPTER5 SOCIALLYOPTIMALREPLACEMENTOFCONVENTIONALVEHICLESWITHBATTERY ELECTRICVEHICLES ThegoaloftheresearchendeavorpresentedinthischapteristosolvetheICEVwithBEV replacementfromasocietalpointofview,whichmayserveasacompassforpolicymaking. TheresultingelectricationtimelineisusefultosetBEVadoptiontargetgoalsforachieving maximumsocietalbenetsandcanassistcentralplannersindesigninge! ectivesubsidiesso astomeetthosegoals.Specically,thescopeoftheworkistoanswerthefollowingsetof researchquestions: 1. Howlongwillittaketoelectrify80%ofthehouseholdvehicleswhileminimizingthe societalcostofthistransitionprocess,undervariousscenarios? 2. Whatistheoptimalall-electricdrivingrangeoftheBEVs? 3. Whatistheoptimaldensityofchargingstations,deployedbythegovernmentoverthe planninghorizon? Theoptimizationofthedescribedelectricationprocessfromasocietalperspectivehas notbeenaddressedintheliterature.Costcomponentsrelatedtovehicleoperationcapturethe heterogeneityamongdriversandareestimateddynamically.Thetotalsocialcostaccountsfor society'sspendingrequiredtosupportthetravelofhouseholds.Itconsistsofcostsincurred byroadnetworkuserswhileconductingtrips,monetizedenvironmentalexternalitiesforthe light-dutytransportationsector,andthegovernmentinvestmentforinstallingpublicchargers. Thebasecaseresultsprovideapolicymakingbenchmarktoplanforasustainablefutureof electriedpersonalmobility.Byexploringalternativescenarios,policydialogueisnurtured. 5.1ConventionalwithBatteryElectricVehicleReplacementOptimization Framework Thefollowingsubsectionspresentthemathematicalprogrammingmodelandthesocial costdecompositionforICEVsandBEVs. 5.1.1ModelingFrameworkandAssumptions Theformulationoftheprogrammingmodelisbasedonthefollowingconsiderations.The centralplannerfacesthedecisiontoreplaceICEVswithBEVsannually.Thereisnomarket 79

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fornewICEVsduringtheplanninghorizonofthetransition,soonlyBEVscanbepurchased. EveryhouseholdownsanICEVatthebeginningofthetransitiontimeframe.Thehousehold mightownmorethanoneICEVs,buttheICEVthathasagreaterannualmileageisconsidered themainhouseholdvehicle.Whenthecentralplannerdeterminesthereplacementofthe household'smainICEVwithaBEV,theBEVbecomesthemainhouseholdautomobile.When thisoccurs,eachhouseholdusesapreowned,leases,oracquiresaback-upICEVexclusivelyfor range-limiteddays(i.e.,dayswhentheall-electricdrivingrangeoftheBEVissmallerthanthe dailyVMT). Theindicesanddecisionvariablesoftheoptimizationframeworkarepresentedhere.The driverofthehousehold'smainvehicleis i % I= { 1,2,..., I } ,andthetimeperiodisdenoted by t % T= { 0,1,..., T } .Thenumberofhouseholds I isassumedtobeconstantduring theplanninghorizon.Shouldaplanninghorizonthatissmallisselected,thereplacement decisionsareseverelya! ected.Therefore,anadequatelylongplanninghorizonisallowed inordertoaccommodateatleastthe80%targetlevelofhouseholdICEVreplacement.All householdsusepassengercarsastheirmainmodeoftransport.Thecentralplanneratthe endofeachyear t makesthedecisionofreplacingorkeepingtheoldvehicleforeachdriver i ThereplacementoftheICEVforeach i canoccuratmostonceduringtheplanninghorizon; whenthisdecisionismade,theICEVretiresanditsresidualvalueisconsidered.Then,aBEV becomesthemainhouseholdvehicle.However,thecentralplannermaymakethedecisionto replacethehousehold'sBEVwithanewBEV,ifthisresultsincostsavings.Iftheoldvehicle iskeptatyear t ,thecentralplannerfacesasimilarreplacementdecisionatyear t +1 .If household i attime t operatesaBEV X ( t ) i =1 holds,otherwise X ( t ) i =0 .Whenhousehold i purchasesaBEVattheendofyear t then Y ( t ) i =1 .Also, Y ( t ) i canbe 1 morethanonce, inordertoenabletheplannertoreplaceaBEVwithanewerBEV.Whenenteringperiod t thevehiclein-usedepreciatesbasedonanexogenousdepreciatingprocess.Theall-electric drivingrangedenotedby r isdeterminedbythesocialplannerandisassumedconstantduring theplanningperiod.Thetransportationnetworkhereinisassumedtoresemblealinearcity 80

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wherethedensityofchargingstationscanberepresentedasthedistancebetweenstations, denotedas w ( t ) inmiles.NotethatpublicchargingisconsideredasacrucialfactorforBEV adoptiondecisions,asnotedby Lieven ( 2015 ).Giventhatworkplacechargersarefoundtobe ane! ectivemethodforreducingsocietalcostinsimilarstudies,e.g., Kontouetal. ( 2015 ), itisdeemedworthwhiletoinvestigatethebenetsofpublic-charginginstallationforthe electricationprocess.Asthenumberofpublicchargersonthenetworkisexpectedtoincrease everyyearofourplanninghorizon,thecapitalcostannuityofthechargingdeploymentcanbe receivedoverthelifetimeofthepublicchargers.Thecostcomponentparametersincludedin thisstudyareeitherextrapolatedbasedonhistoricaldata,orassumedtobeconstantwhere appropriate. Themixedintegernon-linearprogrammingformulationispresentedhere: min z = t T ( i I ( B ( t ) ( r ) ( t ) i (1 X ( t ) i )) Y ( t ) i +( O ( t ) EV i ( r )+ E ( t ) EV i ( r )+ + A ( t ) o i ( r )+ A ( t ) e i ( r )+ I ( t ) i ( r )+ H ) X ( t ) i +( M ( t ) i + O ( t ) CV i ( r )+ (51a) + E ( t ) CV i ( r )+ F ( t ) i ) (1 X ( t ) i )) (1+ $ ) % t + P ( t ) (1+ $ ) % t s.t. X ( t +1) i # X ( t ) i + Y ( t ) i $ i % I t % T (51b) X ( t +1) i Y ( t ) i $ i % I t % T (51c) X ( t +1) i X ( t ) i $ i % I t % T (51d) X (1) i =0, $ i % I (51e) r l # r # r u (51f) X ( t ) i Y ( t ) i % { 0,1 } $ i % I t % T (51g) w ( t +1) # w ( t ) $ t % T (51h) where B ( t ) ( r ) isthecostofpurchasingaBEV; ( t ) i isthecostoftradingintheoldICEV; O ( t ) EV i ( r ) istheoperationalcostoftheBEV; E ( t ) EV i ( r ) denotestheenvironmentalcostassociated 81

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withBEVoperation; A ( t ) o i ( r ) isthecostoftheuserassociatedwiththeoperationofa back-upconventionalvehiclewhileowningaBEV; A ( t ) e i ( r ) isthecostassociatedwiththe environmentalexternalitieswhenoperatingtheback-upICEV; I ( t ) i ( r ) istheinconvenience costassociatedwiththetimespentwhilecharging,and H isthehome-chargerinstallation cost.ForICEVs, M ( t ) i isthemaintenancecostfortheuser i ; O ( t ) CV i and E ( t ) CV i aretheoperating andenvironmentalcosts,respectively,and F ( t ) i istheyearlycostofrefuelingtheICEV'stank. P ( t ) isthecapitalandinstallationcostofdeployingpublicchargingonthelinearcity,whichis incurredbythegovernment.Thepresentworth(discount)factoris (1+ $ ) % t ,with $ asthe discountrate.MostofthecostsassociatedwithBEVsareafunctionoftheall-electricdriving range,whichisoneofourdecisionvariables. Theobjectivefunction( 51a )isthetotalsocialcostofthedescribedreplacingprocess thatisminimized.TheoptimizationframeworkdeterminesthereplacementofICEVswith BEVsforeach i eachyear t ,thebatterysizerthatthemarketshouldprovideduringthe planningperiod,andtheannualspacingbetweenpublicchargers w ( t ) thatthegovernment shoulddeployonthelinearcitynetwork.Constraints( 51b ),( 51c ),and( 51d )ensurevehicle preservation.Whenthesocialplannerdeterminesthatahouseholdaattheendofyear t 1 purchasesaBEV,then Y ( t 1 ) a =1 holdsandaoperatesaBEVinyear t 1 +1 as X ( t 1 +1) a =1 holds.IfhouseholdahasnotpurchasedaBEVinyear t 1 asdenotedby Y ( t 1 ) i =0 ,oritdoes notuseaBEVat t 1 denotedby X ( t 1 ) a =0 ,thenthehouseholddoesnotoperateaBEVinyear t 1 +1 andthus X ( t 1 +1) a =0 .However,thisconstraintcombinationallowsthehouseholdtoown aBEVatyear t 2 with X ( t 2 ) a =1 ,andthecentralplannertodecidetoreplaceitwithanew BEV,hence Y ( t 2 ) a =1 ,yielding X ( t 2 +1) a =1 .Constraint( 51e )demonstratesthatinyear t =1 allhouseholdvehiclesareconventionalones.Constraint( 51f )setsthelower r l andupper r u boundsof r tobe40and300miles,basedonthesmallestandlargestrangeofthelatest BEVtechnologymarketavailable(U.S.DepartmentofEnergy2014).Constraint( 51g )sets X ( t ) i and Y ( t ) i decisionvariablestobebinary.Constraint( 51h )ensuresthatpubliccharging infrastructureisbeingplacedmoredenselyonthelinearcityovertheplanninghorizon.The 82

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relativerelationshipbetweentheall-electricdrivingrangeandthespacingofthechargers denestheexpectedextendeddrivingrangeofeachvehicleafterrecharging.Therefore, additionalconstraintsshouldbeaddedtothemodelinordertoaccountfortheextended drivingrange,asthosearepresentedontheBatteryElectricVehicleCostssubsections. 5.1.2ConventionalVehicleCosts CostcomponentsintroducedintheobjectivefunctionarerelatedtoICEVandBEV purchaseandoperation.TheICEVcostindollarsperyearconsistsofamaintenance componentasinEq.( 52 ),operationasinEq.( 53 ),emissionsasinEq.( 54 ),refuelingas inEq.( 55 ),andtrade-incomponentasinEq.( 56 ).Thesecostsareafunctionoftheannual VMTandtheageofthehouseholdICEV.Thedrivingpatternsofeachhouseholdareassumed tobethesameovertheplanningtimeframe,duetotheunavailabilityoftimeseriesdataatthe householdlevel. Themaintenancecostisestimatedby: M ( t ) i = d i m g (1+ % m ) j i + t (52) where d istheannualVMT, m g istheaverageyearlymaintenancecostin$permilefora mediumsedanvehicleconsideringengineissues,braking,anduids, % m istheaverageincrease rateofthemaintenancecostperyearand j i istheageofthevehicleatthebeginningof theplanninghorizon.DuetothewearandtearoftheICEVcomponentsovertheyears, maintenancecostincreasesatarateof (1+ % m ) j i + t .Anupperboundforthevehicledriving yearsisnotconsidered. TheoperationalcostoftheconventionalvehicleisalsorelatedtotheannualVMT,as shownin Kontouetal. ( 2015 ): O ( t ) CV i = d i p g ( t ) 1 n g (53) where p g ( t ) isthepre-taxpriceofgasolinein$/gallon,undertheassumptionthatthepre-tax priceequalsthecost,and n g isthegasolinee" ciencyinmilespergallon,undertheassumption 83

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thattheimpactofavehicle'sageonmpgisnegligible.TheICEVoperationalcostisan increasingfunctionofgasolinecost,andisthusincreasingovertime. Themonetizedenvironmentalexternalityin$/yearisestimatedas: E ( t ) CV i = d i v g 1 n g SCC ( t ), (54) where v g isthewell-to-wheelsgasolineemissionfactorinaveragekgCO2-equivalentpergallon and SCC ( t ) isthesocialcostofcarbonin$perkgCO2-equivalent.Thesocialcostofcarbon ismonetizing"thedamagesofincreasingthelevelsofCO2emissions,consideringtheeconomic costsoftheclimatechange"( EnvironmentalProtectionAgency 2013 ).TheICEVemissions areattributedtogasolineconsumptionandupstreamprocesses(e.g.,oilrenement,etc.).The EnvironmentalProtectionAgencyprojectsanincreaseinthesocialcostofcarbon,sothiscost componentisanincreasingfunctionoftime. Therefuelingtimecostin$/yearisestimatedas: F i = d i 1 n g 1 cap & f c idle (55) where cap istheaveragecapacityofanICEV'sfueltankingallons; & f istheaveragerate ofrefuelinginhourspergallonbasedonthemaximumallowablefueldispensinglimit ( EnvironmentalProtectionAgency 1996 )and c idle isthecostofwaitingwhilerefueling in$perhour( Ayala 2014 ).Thereisnoliteratureprojectingthatcost,henceisassumed constantovertheyears.Notethatthevalueofthiscostcomponentismarginalcomparedto therestoftheICEVcostvalues. Thesocietalcostaccountsalsoforthevehicle'send-of-liferesidualvalue.Atthe end-of-life,scrappedICEVsmightbeusedasmaintenancepartsfortherestoftheeet. Therefore,theresidualvehiclevalue(ifany,duetovehicledepreciation)issubtractedfrom theBEVpurchasecost.Thevehicleresidualvalueisassumedtobeapproximatelycaptured bythetrade-incost.Hence,itisafunctionoftheICEV'sage( FengandFigliozzi 2013 ).All conventionalvehiclesareconsideredeligiblefortrade-in.Thecostofthetradinginprocessis 84

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estimatedforallICEVsas: ( t ) i = p c i (1 % tr ) j i + t (56) where p c i istheICEVcostofpurchaseinpre-taxdollarsand % tr istheratethatthiscost decreasesasafunctionof j i + t .Thecostdi!ersforeachuserdependingonthevehicle'sage andtheyearsofowningthevehicle.TheuserswhohaveacquiredusedICEVsareidentied and p c i costisreducedforthoseaccordingly.DuetothedepreciationoftheownedICEVsover time,theresidualvalueofeachvehicleisadecreasingfunctionoftime. 5.1.3BatteryElectricVehicleCosts TheBEVcostconsistsofthepurchasecostinEq.( 57 ),theoperationalcost,and theenvironmentalcost.AdditionalBEVcostsassociatedwithdriverrange-anxietyandthe rechargingprocessisintroducedinthefollowingsubsections. TheBEVpurchasecostisthesummationofthebatterypackcost,modiedfrom Lin ( 2014 ),andthevehiclebodycost c b : B ( t ) ( r )= r n e ( r ) B ( r ) (1 % br ) t 1 h b + c b (57) where n e ( r ) istheon-boardelectricityusagerateinkWh/mile; B ( r ) isthebatterypackcost in$/kWh,whichisexpectedtodecreasebyarateof % br asthebatterycapacityincreases undertheassumptionofeconomiesofscale,and h b isthebatteryutilizationfactor,i.e.,the ratioofusablecapacityoverthetotalbatterycapacity.Asthetotalbatterycapacityincreases, thesizeofthebatterypackincreasesandtheBEVhasagreater r .However,theon-board electricityusageratewillincreasewith r duetothevehicle'sheavierbatterypack. Thevehiclebodycost c b isnotafunctionof r .Thevehiclebodymaterialsandpartsare susceptibletochangesovertheyears.Hence,soisthecost.However,duetotheunavailability ofrelateddata, c b isassumedtoremainconstantovertheplanninghorizon. Financingoptionsregardingvehicleownershiparenotconsidered;suchoptionsmight bebasedonvariousexogenousfactors,suchasthedealershipoptionsortheincomeofthe consumer.Inaddition,theBEVmaintenancecostisnotintroducedhereduetotheabsence 85

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ofsu"cientdatasetsthatcoulddescribetherelationshipbetweenthiscostcomponentandthe drivingrange r .Giventhatthemajorityofthebatteriesinthemarkethavean8-yearbattery packwarranty,thecostofbatteryswapping(ifneededduringthatperiod)willbeincurredby themanufacturer( O ceofEnergyE" ciencyandRenewableEnergy 2016 ). Thehomecharginginstallationcost H isnotafunctionof r .Thisremainsconstant duringtheplanninghorizon,eventhoughthecostisexpectedtodecreasewithtimedueto economiesofscale.Homechargingcapitalandinstallationcostannuityoverthelifetimeof thechargersisincurredbytheBEVownersandthussociety.Therefore, H = c hch CRF where c hch isthecostin$perhomechargingequipment(purchaseandinstallation)and CRF = (1+ ) n (1+ ) n 1 ,where n denotesthechargerlifecycleand signalstheinterestrate. TheannualBEVoperational,environmental,andrange-anxietycostsareafunctionof theavailabilityofpublicchargingandalsodependontheVMTofthehouseholds.Public chargingplacementallowsforgreaterVMTelectricationandreducestherange-anxietycost forrangelimiteddays.Inordertocapturethise! ect,bothpublicchargersandtraveldemand areassumeduniformlydistributedalongalinearcity,anassumptionthatwasalsomadein thestudiesof Heetal. ( 2013 )and Heetal. ( 2015 ).Thisassumptionisquitecommonin transportation/urbanplanningandeconomicselds,e.g., Kitamura ( 1985 )andtheseminal paperby Hotelling ( 1929 ).Acircularcityassumption( Nieetal. 2016 )wouldincrease thecomplexityofthemodelingframeworkandthedi"cultyofsolvingit.Twocasesare investigated,whichresultintheadditionalconstraintspresentedbelow. 5.1.4P1:Distancebetweenchargerslessthanorequaltotheall-electricdriving range Whenthespacingdistance w betweentwopublicchargersforacertainyear t ( y ) ,isless thanorequaltotheall-electricdrivingrange r ,BEVdriverscanalwaysrechargetheirbatteries beforedepletion.Thisimpliesthattheycandriveonelectricityasfarastheywant,with extendedall-electricdrivingrange r equaltothemaximumdailydistancecovered x m ( r = x m ) asshowninFigure 5-1 .However,driverswouldavoidrechargingconstantlyduetothehigh 86

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inconveniencecostassociatedwiththeidletimeduringrecharging.Hence,driverssetcritical ranges r i ;whenthedailydrivingmiles x i exceed r i ,theyusetheirback-upICEV.Thelower boundof r r i ,signiesthiscriticalrange. FortheP1case,additionalconstraintsareimposedontheoptimizationframework,which arepresentedbelow: w ( t ) # r (58) x i r ( t ) i (59) TheannualBEVoperatingcost,modiedfrom Lin ( 2014 ),ispresentedasinEq.( 510 ): O ( t ) EV i ( r i )=365 p e ( t ) n e ( r ) 1 n c r i ( t ) 0 x p i ( x ; k i % i ) dx (510) where p e ( t ) istheelectricitypre-taxpricein$/kWhasafunctionoftime; n c isthecharging e ciency,and p i ( x ; k i % i ) istheprobabilitydensityfunctionoftherandomdailyVMTdenoted as x ,with k i astheshapeand % i asthescaleparameterofthedistribution. TheannualenvironmentalcostofaBEV,associatedwiththeproductionoftheelectricity thatpowersit,isestimatedbyEq.( 511 ).NotethatBEVsdonotproducetailpipeemissions likeICEVs. E ( t ) EV i ( r i )=365 SCC ( t ) v e n e ( r ) 1 / n c r i ( t ) 0 x p i ( x ; k i % i ) dx (511) v e istheaveragekgCO2-equivalent/kWhofelectricityconsumed. Range-anxietyisidentiedasamajordeterrentinBEVadoptione.g., Carleyetal. ( 2013 ) and EgbueandLong ( 2012 ).Itisdenedasthefearofexhaustingtheall-electricdrivingrange ontheroadbeforereachingachargingstation.Range-anxietyiscapturedastheadditional costneededtoaccommodatetravelneedsonrange-limiteddays( Lin 2014 ).Theusercost ofoperatingaback-upICEVduringthosedaysisnotedinthispaperasrange-anxietycost. Eq.( 512 )estimatestheoperationalcostofusageofaback-upICEV.Therstaddend capturesthexedcostofobtaininganICEVasaback-upandthesecondthecostofoperating it.Eq.( 513 )capturesthemonetizedenvironmentalexternalityofoperatingtheback-up 87

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vehicle.Eq.( 514 )presentstheinconveniencecostofrechargingtheBEV.Therefuelingtime isusedtocapturetheinconveniencecostofrecharging;thiscostcomponenthasbeenalso consideredin Nieetal. ( 2016 ).TimeofrechargingisconsideredacostfortheBEVoperator. Itisassumedthatthistimeisspentwaitinginsteadofparticipatinginanotheractivity. However,thismightnotbethecasesincerechargingtimecanmeanadditionaltaxrevenuefor thestateifthedriverusesthattimeto,forexample,eatatarestaurant. A ( t ) o i ( r i )=365 i x m r i ( t ) p i ( x ; k i % i ) dx +365 p g ( t ) 1 n g x m r i ( t ) p i ( x ; k i % i ) dx (512) A ( t ) e i ( r i )=365 SCC ( t ) v g 1 n g x m r i ( t ) p i ( x ; k i % i ) dx (513) I ( t ) i ( r r i )=365 r i ( t ) r ( x r ) p i ( x ; k i % i ) dx (514) where i istherangelimitationcostassociatedwithhouseholdvehicleexibilityindaily$per mile; x m arethemaximumdailyvehiclemilestraveled,and ( x r ) isthepotentialrecharging cost,with asthecostoftimewhilerechargingin$permile. 5.1.5P2:Distancebetweenchargersgreaterthantheall-electricdrivingrange When w r theBEVrangeislessthanthedistancebetweenchargers;thus,the expectedextendeddrivingrange r iscalculatedbasedonFigure 5-2 .Theexpectedextended all-electricdrivingrangeisestimatedasthesummationofthestrippedareaofFigure 5-2 ( 3 r 0 ( x + r ) 1 w dx ) andthedottedarea ( 3 w r r 1 w dx ) as r = r 2 2 w + r ,foraspecicyear t ( y ) .Theformerintegraldenotestheportionoftheaverageextendedrangecontributedwhile conductingatripshorterthantheall-electricdrivingrange,consideringencounteringacharger withintheall-electricdrivingrangeofthevehicle,muchlikethepreviouscaseinFigure 5-1 Thelatterintegralcapturestheportionoftheaverageextendedrangethataccountsforthe casewhenadriver,whilecoveringherorhisdailyVMT,mightencounterachargerafterthe batteryhasbeendepleted. Hereanadditionalconstraintthatneedstobeaddedis r # w ( t ) .Thestrictinequality needstoberelaxedinorderforthefeasibleregiontobeclosed.RegardingP2,theconstraints 88

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addedtothesetofEqs.( 51a )-( 51h )tocompletethedescribedframeworkare: w ( t ) r (515) r ( t ) = r 2 2 w ( t ) + r (516) Inthiscase,theBEVoperational,environmental,range-anxietyandinconveniencecosts areestimatedbyEqs.( 510 ),( 511 ),( 512 )-( 513 ),( 514 )respectively,butexpected extendedrange r replaces r i 5.1.6PublicCharingInfrastructureCost Theobjectivefunctionincorporatesthecapitalcostofthepublicchargingstations P .A linearcityisconsidered.Thesizeofitisestimatedasthemaximumdrivingdistance x m ofthe samplemultipliedbythesizeofthedatasample N .Therefore,thenumberofchargersonthe networkcanbecalculatedas N x m w ( t ) .Thisnumberisexpectedtoincreaseannually.Society paystheannuityoverthelifetimeofthechargers.Eq.( 517 )introducesthegovernment's investment: P ( t ) = N x m w ( t ) c l CRF (517) where c l isthecostoftheappropriatelevelpubliccharginginfrastructurein$perchargerand CRF isthecapitalrecoveryfactor. 5.2Data TheproposedframeworkisappliedtoasampledatasetthatpertainstotheNational HouseholdTravelSurvey2009data( U.S.DepartmentofTransportationandFederalHighway Administration 2009 ).Inordertogenerateasample,datalteringisperformed,basedonthe followingcriteria: Themainvehicleofthehouseholdisidentied;usersfromthesamehouseholdarenot includedinthestudyduetopotentialcorrelationoftheirdrivingpatterns. Thehouseholdvehicleisapassengercarsuchasacompact,sedan,orstationwagon; pick-uptrucks,SUVs,andlargervehiclesareexcludedfromthisstudy. Thevehicleisnotcarryingacommerciallicenseplate. 89

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Thehouseholddriverisaworkerandthenumberofdaysworkedfromhomelastmonth areequaltoorlessthanve. Theworkingtripisconductedbythemainautomobileandnotwithothermeansof transport,suchastransit,bike,etc. Theworkplacelocationisnotthesamelocationasthelocationofresidence. Allentriescontaincompleteinformation. Eachhousehold'sVMTfollowagammadistributioninthiscasestudy.Variousliterature sourcessupportthisassumption,e.g., Greene ( 1985 )and Linetal. ( 2012 ).However,some studiestalog-normaldistribution( Plotz 2014 ),whileothersproposethesuperpositionofa broadexponentialdistributionandanarrowGaussianthatrequiremorethantwoparameters ( Tamoretal. 2013 ). Duetotheabsenceoftripchaindata,thecircledistancefromhometoworkandwork tohomeisassumedtobethemostcommontripofeachhouseholdand,thus,themode ofgammadistribution.ThemeanofgammadistributionisassumedtobethedailyVMT, denotedby x i = d i / 365 .BysolvingthesystemofEqs.( 518 ),( 519 ),and( 520 ),we calculatetheshape k i andscale % i parametersforeachhousehold i : mode i =( k i 1) % i $ i (518) x i = k i % i $ i (519) k i > 0, % i > 0, $ i (520) ThexeddailyrangelimitationcostinEq.( 521 )isassociatedwiththevehicleexibility ofeachhousehold.Thevehicleexibility H vf inEq.( 522 )capturestheeaseofobtaininga back-upICEV.The H vf notionstemsfromthestudyof Lin ( 2014 ). i = + + + + + + + + + + + + 1 H vf # 1 2 +( 1 2 ) (2 H vfi ),1 < H vf < 2, 2 H vf 2 (521) 90

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where 1 istheupperboundand 2 isthelowerboundofthedailyxedrangelimitationcost. H vf = H vnoi min ( H wnoi H dnoi ) (522) where H vnoi isthenumberofvehicles, H wno i isthenumberofworkers,and H dno i isthenumber ofdriversinthehousehold.Asthenumberofworkersordriversinahouseholdincreases, itishardertoobtainaback-upvehiclewithinthehouseholdand,since H vf # 1 ,thexed limitationcostisthecostofarentalICEV,denotedas 1 .Asthenumberofvehiclesowned inahouseholdincreases,theindicatorvalueincreases.When H vf 2 i equals 2 ,denoted astheamortizeddiscountedcostofapurchasedback-upICEV.Descriptivestatisticsofthe samplehouseholddatasetarepresentedinTable 5-1 Figure 5-3 presentsthecostparametertrendsttedondataprojections.Allinputsare "valuedine"ciencyandnotinmarketprices,"ascostsandnotpricesarecaptured( Newbery andStrbac 2014 ).Figure 5-3 ashowsthatasthebatterysizeincreases,thebatterypackcost isexpectedtodecreasein$perkWh.Figure 5-3 bportraysthatthebiggerthebattery,the heavierthevehicleandthelowerthee" ciencyinkWhpermiles.ParametersonFigure 5-3 a and 5-3 barefromthe EnvironmentalProtectionAgencyetal. ( 2010 ).Figure 5-3 cdepicts thetrendofthebatterycost,correspondingtoan80-miledrivingrange,overtime.Asthe % br rateincreases,thebatterypackcostdecreasesatafasterpaceovertheyearsoftheplanning horizonduetoeconomiesofscale.Figure 5-3 dand 5-3 eportraytheelectricityandthegasoline pre-taxpricesevolution,respectively.Thebasecaseutilizes2015EnergyOutlookdata( U.S. DepartmentofEnergy 2013b )andthelowandhighvaluescenarioscomefrom Newberyand Strbac ( 2014 )projections.Figure 5-3 fshowsthetrajectoryofthesocialcostofcarbonfrom the EnvironmentalProtectionAgency ( 2013 ).Inthatgraph,ahigherdiscountrateleadstoa decreasednetpresentsocialcostofcarbonvalue.Overall,anoptimisticcaseistheonethat leadstolowersocialcosts;otherwise,theprojectionisconsideredpessimistic. 91

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Notethatthesocialcostofelectricitydependsonthetimeandlocationofrecharging, e.g., Heetal. ( 2015 )and Heetal. ( 2013 );however,addressingthisisbeyondthescopeofthis study. Theaveragecostoftheelectricvehiclebodyistheaveragestickerpriceofthe2015BEV modelsfromthe U.S.DepartmentofEnergy ( 2016f )minustheaveragestatetax,multiplied bythepercentagecorrespondingtothevehiclebodywithoutthebatterypackcost.The purchasepriceoftheconventionalvehicle pc i isestimatedthroughtimeseriesdataofaverage pre-taxneworusedICEVmarketpricesforeachyear( KelleyBlueBook 2015 ).Allhouseholds havethecapabilityofinstallinghomechargers,althoughthismightnothold( Trautetal. 2013 ).Residentialcharginginfrastructureisassumedtoberesidentiallevel2,andthepublic charginginfrastructureisassumedtobepubliclevel2.Therearesignicantdi! erencesinthe installationandcapitalcostsforthosechargingequipment( IdahoNationalLaboratory 2015 ). Thecapitalrecoveryfactorforreceivingtheannuityofchargersisestimatedwith =7% interestrateandacompoundperiodof n =25 years,whichisessentiallytheprojected lifecycleofthechargingequipment.Table 5-2 presentstheparametersofthebasecaseandthe alternativescenarios. 5.3Results Figure 5-4 portraysthecostcurves,consideringanannualVMTvalueof12,422fora mediumsedanconventionalvehicle.ForFigures 5-4 (b,c,d,e,f,g), r % [1,300] andthe distancebetweenchargersonthelinearcitynetworkisassumedtobe w ( t ) =150 miles $ t Figure 5-4 (b,c,d,e,f,g)portraythecostcurvesforyears1,10,20and30.Figure 5-4 costs areestimatedusingtheaveragedatavaluesofoursample,asthosearepresentedinTable 5-1 Theenvironmentalexternalitiesandtherefuelingcostareatamaximum5%and3% oftheoperationalcostoftheICEV,whichisportrayedinFigure 5-4 a.Thesecostsare notexpectedtoplayavitalroleinICEVreplacementdecisions.ICEVmaintenanceand trade-incostsincreaseanddecreaserespectivelywithtimeduetovehicledepreciation.The 92

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operationalcostgrowthrateis1.07%andisonlya! ectedbythegasolinecosttrajectory,which isincreasingintime. TheBEVbatterypackcostisthelargestcostcomponentinthecaseoflargebatteries. Assmallerbatteriesmaycauserange-anxiety,thecostassociatedwithoperatingaback-up ICEVbecomeslargerthanthebatterypackcost.Thisoccursduetothenecessityofowning aback-upICEVvehicleforrange-limiteddays.Theoperationalandenvironmentalcostcurves areestimatedbothfor r < w and r w .Thecurvesarecontinuousat r = w wherethe twocostbranchesmeet,estimatedfromP1andP2.Figures 5-4 eand 5-4 fshowthatsmall all-electricdrivingrangesarepenalizedcomparedtolargerones,asdriversofsuchvehiclesare moresusceptibletoexperiencingrange-anxietyandpaymoreforaback-up,gasoline-fueled, vehicle.InFigure 5-4 e,theoperationalanxietycosthaslittlevariationovertheyearssincethe xed,annual"limitation"costofobtainingaback-upICEVisthelargestaddend.InFigure 5-4 gtheinconveniencecostincreasesexponentiallywhen r # 150 miles.Thebranchthat correspondsto r 150 indicatesthatforall-electricdrivingrangeslargerthan200miles thecostdecreases,sincetheprobabilityofdrivingabovethatmileageislowduetogamma's distributionthintail. Overall,thehighcostofaBEVacquisitionindicatesthatthesavingsfromoperating theBEVforusersovertheplanninghorizonshouldbeatleastinthemagnitudeoftensof thousands.ThiswouldimplythatthosecoveringagreaterannualVMTwouldbenetsociety morewhenswitchingfromICEVstoBEVsandpotentiallydrivethemarkettoprovidehigher BEVrangestomaximizebenetsfromthetransition.However,consideringthehighcostof purchasingBEVswithgreater r inthebeginningoftheplanningphase,anestimationofthe optimal r valueisaconundrum. Figure 5-5 showstheplotsofthecostsassociatedonlywithBEVs.ComparedtoFigure 5-4 ,Figure 5-5 costcomponentsaredrawnfor w % [10,400] ,for t =1 ,andforsome indicativevaluesoftheall-electricdrivingrange r inmiles(specically50,100,150,200). 93

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Figure 5-5 costsarealsocalculatedusingtheaveragedatavalues.Thecostcomponent calculationsaredi! erentwhen r w (1) forP1and r < w (1) forP2,aspresentedinthe "ModelingFrameworkandAssumptions"sectionandalsopointedoutinFigure 5-4 .The curveschangetrajectoryatpoint r = w ,asexpected.Figure 5-5 ashowsthattheBEV operationalcostincreasesexponentiallywhentherangeislessthanthespacingdistance betweenpublicchargersanddecreasesexponentiallyasthepublicchargingspacingincreases relativetotherangeoftheBEV.Whentherangeislessthanthedistancebetweenchargers, asthespacingincreases,theprobabilityofndingachargerdecreases.Thiscausesthe operationalcosttoincrease.However,whentherangeisgreaterthanthespacing,thedriver canpotentiallyelectrifythewholetrip,inwhichcasethecostassociatedwiththeoperation decreases.TheBEVenvironmentalexternalityin5bfollowsasimilartrajectoryduetothe productionoftheelectricitythatpowerstheBEVs,andtheinconveniencecostin5edueto recharging.Asexpected,Figures 5-5 cand 5-5 dmirrorFigures 5-5 aand 5-5 bbecausethey portraythecostassociatedwithoperatingback-upICEVs. Themixedintegernon-linearP1andP2programsaresolvedusingCONOPTsolver ( Drud 1994 )inGAMS23.3 Rosenthal ( 2015 ).Theall-electricdrivingrangespaceis discretized,andtheoptimizationproblemwassolvedforeachdiscreteelectricdrivingrange r thatbelongstotheinterval [40,300] inordertoavoidrunningoutofmemory.Discussionon theresultsispresentedinthefollowingsubsections. 5.3.1BaseCase Thebasecaseresultsindicatethattheoptimalsolutionisobtainedwhen r w ( t ) from P1.Figure 5-6 aportraystheoptimalcumulativepenetrationrateofBEVsforbaseandfuel costalternativescenarios.Figure 5-6 bshowstheminimumaverageannualsocialcostsofeach householdvehicletechnologyforthebasecaseparameters.Figure 5-6 cshowstheaverage VMTsoftheICEVsbeingreplaced,aswellasthosebeingused,forthebasecasescenario. Specically,ourndingsindicatethatapproximately8yearsareneededfor80%oftheUS householdICEVsinoursampletobereplacedbyBEVs.For9,952households,thereplacement 94

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processlastsatotalof31years.Byallowingforalargeplanninghorizon,a100%ICEV replacementrateisessentiallyforced.An80%BEVpenetrationachievementischosenasa morerealisticelectricationgoal.TheBEVadoptionrateincreasesrapidlyinthebeginningof theplanningyears,asitissociallyoptimaltoreplace50%oftheICEVsbythe2ndplanning year,andthentheratedecreasesgradually,asportrayedinFigure 5-6 a.Ourndingssupport thatitisinsociety'sbestinteresttoachieveafasttransitionfromconventionalvehicle technologiestoelectricones.Ontheotherhand,behavioralstudiesthatmodelBEVmarket acceptanceshowthatsuchatransitionmightoccurslowly,e.g., Greeneetal. ( 2014 )estimates themarketshareofBEVsasonly38%by2050. Forthebasecase,theoptimalall-electricdrivingrangeoftheBEVsis r =204 miles.The optimaldistancebetweenpublicchargersis172milesatyear1andstaysconstantfortherest oftheyears ( w ( t ) =172, $ t ) .Thisresultindicatesthatalldeployedpublicchargingstations shouldbeinplaceasearlyaspossibleinordertoreceivegreatersavingslaterintheplanning horizon.Thisndingiswell-alignedwith Nieetal. ( 2016 )results,astudyalsodescribing acentral-planner'soptimizationmodelfordetermininggovernment'sinvestmentsonpublic charginginfrastructureandelectricvehiclesubsidies.Theoptimalextendedall-electricdriving rangeis r i ( t ) 290 milesforeveryyear t BEVsbecomemoreattractiveunderthescenarioofincreasedgasolinecost,whichresults inreaching80%BEVdi! usioninjust7years.Undertheassumptionofdecreasedgasoline costs,theICEVproductbecomesmoreattractiveandthereplacementprocessreaches80%in approximately9years.IncreasedelectricitycostprojectioncausesreachingthecumulativeBEV 80%penetrationgoal1yearafterthebasecase,whereasoptimisticprojectionofelectricity costresultsinfasterBEVdi! usion,reachingthegoalof80%1yearearlier. Figure 5-6 bshowcasesthebasecasescenarioannualcosts.NotethattheBEVpurchase costiscomprisedofthebatterypackandvehiclebodycostsminustheICEVtrade-incost. TheBEVoperationcostportrayedisthesummationofoperational,environmental,anxiety andinconveniencecosts,andtheICEVoperationcostaccountsformaintenance,operation, 95

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environmentalandrefuelingcosts.TheaveragecostofpurchasingaBEVisapproximately thesameduringtheyearsportrayed;thetrendslightlyvariesbecausethebatterypackcost decreaseswithtimeandthetrade-incostvariesaccordingtotheICEVpopulationreplaced. ICEVoperationalcostsincreaseovertheyearsduetothedepreciationofthevehicles,andBEV costsincreaseovertheyearsduetothecostcomponentsprojections,whichincreasewithtime. InterestinglytheaverageVMToftheICEVs,whicharenotreplacedbyBEVsinourmodel andremaininthemarket,decreasewithtime.Thisindicatesthatsocietybenetsmorefrom rstreplacinghouseholdvehiclesthatcovergreaterannualmileages,asthisresultsinlower cumulativeoperationalandenvironmentalcosts. ThesociallyoptimalBEVpenetrationratescouldbecomparedwithmarket-basedand othermodelresults,astheirndingsarepresentedintherecentliterature.Itshouldbenoted thattheassumptionsofeachmodelvarysignicantly;therefore,comparisonsdonotmean criticismandarepresentedbelowtoraisefurtherdiscussion. Theannualenergyoutlookprovidesvehiclestockprojectionsasreferencesforthe penetrationofalternativefuelvehicles,suchasbatteryelectricones,intheyearstocome. ThosearebasedontheNationalEnergyModelingSystem(NEMS),"amarket-basedapproach subjecttoregulationsandstandards"( EnergyInformationAdministration 2009 ).Findings showcasethatBEVswouldaccountfor1.33%ofthemarketina15yearspanand2.10%in 25years( EnergyInformationAdministration 2015 ).Anothermodel,theMarketAdoptionof AdvancedAutomotiveTechnologies(MA3T)isamulti-variablenested-logitmodel,whichalso aimstoprovideinsightsonthepenetrationofvariouspassengercartechnologies.Thismodel projectsthatBEVsmighttakeupapproximately15%ofthetotalmarketshareby2050( Oak RidgeNationalLaboratory 2015 ).Inasimilarmanner, Greeneetal. ( 2014 )utilizeaconsumer behaviormodelwithvariousfeedbackloopstoprojectBEVdi!usion.Theyshowcasethatin anapproximately25year-spantheBEVdi! usionwilltakeup5%ofthetotalmarketshare, reachingeventually38%by2050. Nieetal. ( 2016 )performnumericalexamples,usingamodel thatcapturesconsumerbehavior;theirndingsprojectBEVsreachingapproximately10%of 96

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themarketshareina30yearplanninghorizon.Afteroptimizingincentives,themarketshare ina30-yearsspan,fortheconsumersegmentoffrequentdrivers,isfoundtoexceed20%. Consumersstatedpreferencesresultsaremoreoptimistic;forinstance, Krauseetal. ( 2016 ) showcasethat44%ofthesampleintenttoadoptBEVsunderthescenarioofcostparity. Obviously,thereisawidegapintermsoftheBEVadoptionratesprojectedwhen comparingbehavioralandmarketresultstoourndings.Thisgapwasanticipatedbecause:(a) varioussocio-economiccharacteristicsplayanimportantroleinvehicleownershipdecisions, (b)consumersresistswitchingtoinnovativeproductsimmediately,(c)consumersmightnot havecompleteinformationonthesavingstheycanachievethroughBEVsoperation,and(d) incentivescurrentlyarenotdesignedoptimallyinordertoe! ectivelypromotethisproduct. 5.3.2AlternativeScenarios MoreresultsforalternativescenariosarepresentedonFigure 5-7 .Thedi!erencesbetween theoptimalall-electricdrivingrangesandtheoptimaldistancesbetweenchargingstations,for eachoftheparametersinTable 5-2 ,arepresentedinFigure 5-7 aand 5-7 b,respectively. Forallsensitivityanalysiscases,theoptimalapproachistoplaceallpublicchargersonthe linearnetworkfromthe1styearoftheplanninghorizon.Thus,theoptimal w ( t ) isconstant overtheyears.Moreover,inallcasesissociallyoptimaltoplacechargersindistanceshorter thantheall-electricdrivingrangeoftheBEVs. Increasedgasolinee" ciencymeansBEVusagebecomescheaperandresultsindecreasing theall-electricdrivingrangeby6.3%.Italsoplaceschargersslightlyscarcer,astheoptimal valueof w increasesby3.4%.LowerICEVmaintenancecostleadsto1.98%smalleroptimal r ,withoutsignicantlyimpacting w .FasterdepreciationofICEVs(i.e.,decreaserateof trade-incostbecomesgreater)resultsina3%decreaseoftheall-electricdrivingrangebecause purchasingaBEVbecomesmoreexpensive;societyplaceschargersmoredenselyonthelinear city.Ahigherbatteryutilizationfactorimpliesthatusershavetopaylessforlargerbatteries; r increasesby2.45%and w increasesbyapproximately1.7%inthiscase.Thevehiclebody costimpactsseverelytheoptimal r decision;a50%increasein c b resultsin8.8%decrease 97

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in r ,assmallerrangeswouldmakeBEVsmorecompetitivewithICEVinthebeginningof theplanninghorizon.Whenittakeslongertotransitiontoeconomiesofscaleforbattery packs, r decreasesbyalmost3.9%andthedistancebetweenchargersonthenetworkincreases by4.65%.Thediscountratehasasignicantimpactontherangeanddistancespacing decisionvariables.CheaperhomechargersresultinsavingsandmakelargerbatteryBEVs morea! ordable.Adramatic63%increaseofpublicchargingequipmentcostresultsin12.2% increaseofdistancebetweenchargers.Unsurprisingly, r increasesby10.7%inthiscasein ordertoo!sethighanxietycosts;theelectricationrateinthiscaseslowsdownasyearsgo by.Increasedgasolinecost,resultsindecreasedrangeandpublicchargerdistanceinorderto makeBEVsattractiveinthebeginningoftheplanningphase.Underthescenarioofoptimistic electricitycostprojection,rrisesonlybyapproximately1%.Theimpactofsocialcarboncost changeismarginalrelativelytotheaforementionede! ectsfortherestoftheparameters. Theimpactofgasolinecostprojectiononthisvehicletechnologytransitionisfurther investigatedbyaccountingfortherebounde! ect.Thise! ectreferstotheelasticityofthe VMTwithrespecttothegasolinecost.Underthebasecase,gasolinecostsareexpectedto riseduringthenextyearssoVMTareexpectedtofollowadownwardtrajectory( Greene 2012 ; HymelandSmall 2015 );.Sinceourmodelconsiderstheheterogeneityofdailydriving patternsandasthedailyVMTforeachdriverareassumedtofollowagammadistribution, Idonothavethemeansintermsofdatatoaccountfortherebounde!ectimpactsoneach individualdriver.However,ageneralizedtrendthata! ectsallthevehicledriverssimilarly isassumed,leveragingliteratureinsights.A10%increaseinthegasolinecostwillleadtoa conservativeshort-run5%decreaseintheVMT.Thisrelationshipisconsideredlinearandthe magnitudeoftherebounde! ectisbasedontheconservativevaluesofthersttablein Greene ( 2012 ).However,wenotethat HymelandSmall ( 2015 )suggestthatrebounde!ectisgreater whengasolinepricesgoupratherthanwhengoingdown,implyinganon-linearrelationship. ResultsofourndingsarepresentedinFigure 5-8 98

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TheresultsshowninFigure 5-8 suggestthattherebounde! ect,ontopofthegasoline costchanges,doesnothaveasignicantimpactontheBEVpenetrationresults.Asexpected, thise! ectleadstoshiftingthecurveright,deceleratingslightlythepenetrationunderthebase andthepessimisticscenarioofgasolinecost.Onthecontrary,undertheoptimisticscenario, wheregascostdecreasesovertimeandVMTincrease,therebounde!ectleadstoslight accelerationoftheBEVpenetrationbyshiftingthecurveleft. 5.4Summary ThischapterpresentsaframeworkthatoptimizesthereplacementofhouseholdICEVs withBEVsbyminimizingthesocialcostduringthistransitionphasewithoutmodeling consumerbehavior.Therefore,theneedforacostlybehavioralmodelingprocessiseliminated whileenablingpolicymakerstocomprehendthesocietalcostincurredovertheelectrication timeframe. Themodelingframeworkusedaccountsfortravelingpatternsheterogeneitybyintroducing operationalcostofthehouseholds'vehiclesbasedontheirdailyVMT.Theimpactofpublic charginginfrastructureonalineartransportationnetworkisalsoconsidered,asthedensity ofchargersgreatlya! ectsthemileageelectried.Theframeworkisdemonstratedempirically usingU.S.household,energy,andmarketdata. ResultsunderlinethesensitivityoftheoptimalsetofBEVs'drivingrange,publiccharging density,andtheBEVpenetrationunderalternateparameters'projections.Basecaseresults indicatethatsocietalcostisminimizedforanall-electricrangegreaterthanthedistance betweencharges;costsassociatedwithBEVoperationanddrivinganxietyareminimized thisway.Targetingtheelectricationof80%ofthehouseholdeet,thetransitionlasts approximately6to12yearsunderalternativescenarios.Fastertransitionisachievedwhen gasolinecostisprojectedtoincrease,electricityisprojectedtodecrease,discountrateis higher,batteriesarecheaperandICEVsdepreciatefaster.Decisionvariablesaremoresensitive togasolinecosts,discountrate,batterypackandvehiclebodycosts,andICEVsfueleconomy. 99

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Limitationsoftheproposedmethodologyarediscussedhere.Obviously,themodel proposedinthischaptercannotbeusedtoinferBEVmarketpenetration,whichisdriven byconsumerpreferences.Socio-economicfactorsandmarketconsiderationsimpactsuch ownershipdecisions( Krauseetal. 2016 ).Also,word-of-mouthandsocialnetworkinuences ( Eppsteinetal. 2011 ),whichmightimpactthedi!usionofinnovativeproducts,suchasBEVs, arenotaccountedforinthiswork,becauseadoptiondecisionsaremadecentrally.Inaddition, themodelingframeworkisbasedoncertainassumptionsthatsignicantlya! ecttheresulting BEVadoptiontimeline,whichisgenerallythecaseforanymodelingframework.However,this workissuccessfulinpinpointingBEVadoptiontargetgoalsbyminimizingcostsincurredby stakeholderswhocomprisesociety,suchastheusersandthegovernment.Deningsocially optimalBEVpenetrationtargetlevelsistherststeptowardsthedevelopmentofaplanfor sustainableelectricationofthevehicleeet.Therefore,theBEVpenetrationtimelineresulting fromourmodelcanbeutilizedbypolicymakerstosettargetsforBEVmarketshareover theplanninghorizonwhen,e.g.,designingsubsidiestobedistributedtoconsumerssoasto acceleratetheadoptionofBEVs. 100

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Figure5-1. Expectedextendeddrivingrangeestimationwhen r w ( t ) Figure5-2. Expectedextendeddrivingrangeestimationwhen r < w ( t ) Table5-1. DescriptiveStatisticsoftheNHTS2009DataSample d i H dno i H wno i H vno i H vfi x i mode i j Mean 124221.991.542.161.5235.4938.446.895.26 Std.Dev.77790.740.660.990.7416.1648.759.493.48 Max 900247.005.0011.009.0050.00246.64181.0015.00 Min 3691.001.001.000.3315.001.010.001.00 SampleSize 9952 101

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Table5-2. BaseCaseandAlternativeScenariosParameters Parameters BaseSensitivityAnalysisParameterReferences OptimisticPessimistic Increaserateofmaintenancecost % m 0.25 0.20 0.30 KelleyBlueBook ( 2015 ) Averageannualmaintenancecostin$permile m g 0.0492 n.a. AAA ( 2013 ) Gasolinee" ciencyinmpg n g 28 36 20 U.S.DepartmentofTransportationandFederalHighwayAdministration ( 2009 ) GHGemissionsinkgCO2-eq/gallon v g 11.8 n.a. Yawitzetal. ( 2013 ) AveragecapacityofICEVfueltankingallons cap 10.8 n.a. U.S.DepartmentofEnergy ( 2016f ) Averagerateofrefuelingingallonsperhour & f 0.0396 n.a. EnvironmentalProtectionAgency ( 1996 ) Costofwaitingwhilerefuelingin$/hour c idle 24.85 n.a. Ayala ( 2014 ) Decreaserateoftrade-incost % tr 0.16 0.1 0.2 KelleyBlueBook ( 2015 ) Batteryutilizationfactor h b 0.9 1 0.8 Lin ( 2014 ) Vehiclebodycostin$ c b 12,0008,00018,000 U.S.DepartmentofEnergy ( 2016f ) Decreaserateofbatterypackcost % br 0.0086 0.010.0005 EnvironmentalProtectionAgencyetal. ( 2010 ) Charginge"ciency n c 1 n.a. 0.9 Lin ( 2014 ) GHGemissionsinkgCO2-eq/kWh v e 0.73 n.a. EnergyInformationAdministration ( 2013 ) Upperboundofdailyxedlimitationcost 1 50 n.a. Lin ( 2014 ) Lowerboundofdailyxedlimitationcost 2 15 n.a. Lin ( 2014 ) Costoftimewhilerechargingin$/mile 1.66 n.a. Ayala ( 2014 ) Discountrate $ 0.03 0.10 0.025 EnergyInformationAdministration ( 2013 ) Maximumdistancecovereddaily x m 390 n.a. U.S.DepartmentofTransportationandFederalHighwayAdministration ( 2009 ) ResidentialLevel2chargingcostin$/charger c hch 1354 300 8,000 IdahoNationalLaboratory ( 2015 ) PublicLevel2chargingcostin$/charger c l 3,108 60012,600 IdahoNationalLaboratory ( 2015 ) 102

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Figure5-3. Fittedequationsofthemodelparameters. 103

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Figure5-4. IndicativeICEVandBEVcostcomponentvaluesfor w ( t ) =150 miles. 104

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Figure5-5. IndicativeBEVcostcomponentsvaryingwith w for t =1 105

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Figure5-6. CumulativeBEVpenetration(a),basecasecosts(b)andVMTofICEVsreplaced andused(c). 106

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Figure5-7. Alternativescenariodecisionvariables, r and w results. Figure5-8. ReplacementofICEVwithBEVcumulativerateswhenaccountingfortherebound e ect. 107

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CHAPTER6 INCENTIVESSCHEMESFORMAXIMIZINGTHEBENEFITSFROMBATTERYELECTRIC VEHICLEADOPTION DevelopinganationalorregionalpolicyroadmapforincentivizingadoptionofPEVscan potentiallyhelpmovingtowardsamoresustainable,electric-poweredtransportationfuture. Governmentallocatesincentivesforzerotailpipeemissionvehicles( Plug-InAmerica 2016 ) toinducebatteryelectricvehiclesdemand.Monetaryincentivesintheformofsubsidiescan discountthesignicantcapitalcostsassociatedwithownershipofthosevehicles.Investing inpubliccharginginfrastructureplacementcontributestoreductionoftheoperationalcosts incurredbythedriver,aswellastheenvironmentalexternalitiesassociatedwithconducting dailytripsbyelectrifyingmoremiles.Thechapter'sobjectiveistodesignandprioritizecertain investmentsformonetaryincentivesthatenablethegovernmenttomaximizethebenets returnedfromthedi!usionofBEVtechnology. Theworkproposedhereinhasnotbeenaddressedintherecentliterature.Therefore, thecontributionsofthisstudyincludetheframeworktodesignrebatesandincentivize BEVspenetration,aswellastheapplicationofthemodelusingU.S.household,energy,and automobilemarketdata.Thestudy'smethodologycanbeutilizedbypolicymakersonstate, regionalornationallevelsoastoallocateincentivesbudgete!ectivelyandmeetstrategicBEV di usiongoalsforthepassengervehicletransportationsector. 6.1IncentivesOptimizationFramework Thisstudyaimsatdesigningoptimalmonetaryincentivepolicies,i.e.,BEVsubsidiesand investmentincharginginfrastructure,forthepromotionofBEVtechnologies.Theobjective hereistomaximizesocialsavingsthatthegovernmentcanachievefromthisinvestment.It isassumedthatthebenetaccruedbysocietyduringtheperiodwhenthoseinvestmentsare allocatedarethecarbondioxideemissionsreductionaswellasthefuelconsumptionsavings achievedfromtheintroductionoftheBEVtechnology,atanationallevel.Itshouldbenoted that,accordingto SkerlosandWinebrake ( 2010 ),thenationallevelpolicyapproachshould beconsideredsub-optimal,andincentiveschemesshouldbedesignedonaregional,stateor, 108

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even,citylevel,duetoconsumers'heterogeneity.Therefore,notonlyweoptimizethisincentive portfolioatanationallevel,butapplytheproposedmodelforeachU.S.CensusBureauregion forthecontiguousU.Sandraisediscussionontheneedtoaddressspatialheterogeneity. Theoptimizationframeworkpresentedhereinafterpresentsthepolicymaker'sobjective aswellasthedemandmodelthatcapturesthedecisionsforvehicleownershipfromapoolof twovehicletechnologies;conventionalandbatteryelectricpassengercars.Theformulation followsverycloselythemodelpresentedin LobelandPerakis ( 2011 );howeveritisnowapplied todetermineBEVdi! usionandthemodelingcomponentsandconstraintsareenhancedto capturecertaincharacteristicsoftheautomobileandenergymarket.Theformulationisalso enhancedbyconsideringtheworkof Nieetal. ( 2016 ).Thefollowingmodels,usedtodesign incentivesforinnovativetechnologiespromotionin VanBenthemetal. ( 2008 )and DeShazo etal. ( 2015 )werealsoconsideredwhileshapingtheproposedapproach. Thesetofyearsforwhichtheplanningagency/governmentallocatesincentivestoinduce EVadoptionandusageis t % T = { 1,2,..., n } .Thevariable x t k isthenumberofvehicles oftechnology k % { 0: ICEV a =100: BEV } thathavebeenadoptedbytime t .We assumetwomajorvehicletechnologiessharingandcompetingforthemarket:ICEVswith noall-electricdrivingrange k =0 milesandBEVswithall-electricdrivingrange k = a miles.Theconsumers'demandforeachtechnology k foragivenyear t isdenotedas q t k .The existingvehiclestock,updatedbythenumberofvehiclesofeachtechnologysoldeachyear t isassociatedwiththediscretetimesystempresentedinEquation( 61 ).Thestatetransition functionthatportraysthedynamicnatureofthechargersplacementonthetransportation networkispresentedinEquation( 62 ). x t +1 k = x t k + q t k ( r t u t ), (61) v t +1 = v t + u t (62) Thetransitionfunctiondescribedin( 62 )showstheevolutionoftheinstallationofchargers onthetransportationnetwork.Thenumberofthechargingequipmentinplaceuptoyear t is 109

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denotedby v t ;thenumberofchargerstobeinstalledatyear t isnotedas u t .Thedecision variableinthiscaseis u t ,whichhasanupperboundof u t .Thisupperlimitconstraintis placedtoensurerealisticdensityofthechargingnetwork,e.g.,usingthenumberofpumps ofthegasstationnetworkastheupperboundof u t .Itisassumedthatwhenthenumber ofchargersisequaltothenumberofpumpsofthegasolinestationscurrentlyinplaceand whenchargingequipmentdistributionresemblesthatofthegasstationnetwork,re-charging availabilityreaches100%. 6.1.1ICEVandBEVDemandFunctions Thedemand q t k fortheICEVandBEVtechnologyarecontrolvariables.Theconsumers' demandalongwiththecostevolutiondynamicsareestimatedduringaplanningperiod T Abinarylogitmodelisproposedtocalculatethenumberofsalesofeachvehicletechnology k inyear t .Eachvehicletechnologyisassociatedwithautility U t k .Notethattheperceived utilityoftheaverageconsumerisdenedasthesummationoftheindirectutilityandanerror component: U t ( r t u t )= V t ( r t u t )+ ( t .Hereallconsumersaremaximizingtheirutility.The demandfunctionsforthealternativeandtheconventionalvehicletechnologiesarealsodriven bytheexpectedvalueofthevehiclessold.Utilizingthelogisticfunction,thesedemandsare presentedasfollows,inEquations( 63 )and( 64 ): q t a ( r t u t )=[ m ( t )] e V t a ( r t u t ) e V t 0 + e V t a ( r t u t ) (63) q t 0 ( r t u t )=[ m ( t )] e V t 0 e V t 0 + e V t a ( r t u t ) (64) where m t isthemarketsize(newvehicleregistrations)ofthesegmentofpotentialbuyers ofnewvehicles,whichisanincreasingfunctionoftime,and V t istheindirectutilityofthe averageconsumer.Theindirectutilitiescanbemodiedinordertoconsiderdi! erentaverage consumersegmentsproles,ifneeded.TheprobabilityofchoosingEVandCVisestimatedby e V t a ( r t u t ) e V t a ( r t u t ) + e V t 0 and e V t 0 e V t a ( r t u t ) + e V t 0 ,respectively.Itisassumedthat m ( t ) q t a + q t 0 q t k 0 ,and U t k > 0 110

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Therearenumerousstudiesintheliteraturethatmodelalternativefuelvehicles ownershipdecisions.Forthesakeofcomputationaltractability,onlycertaincostand"wordof mouth"-relatedvariablesenterthetwoutilityfunctions,asinEqs.( 65 )-( 66 ): V t a ( r t u t )= 1 C t a ( r t u t )+ 2 lbd t a + 3 + ) t (65) V t 0 = 1 C t 0 + 4 + ) t (66) where 3 and 4 thebaselineutilitiesfortheelectricandtheconventionalvehicletechnology respectively,and ) t istherandomdemand.Theunderlyingassumptionhereisthatthe variablesthatentertheutilityfunctionarenotcorrelated. C t a and C t 0 arethesummationof thecapitalandoperationalcostsofaBEVandanICEVrespectively,incurredbytheaverage consumerwhoisconsideringtomakeanewvehicleownershipdecision.Thecapitaland operationalcostofeachvehicletechnologyispresentedasinEqs.( 67 )-( 68 ): C t a ( r t u t x t a )= O t a ( v t )+ B t a ( x t a ) r ( t ), (67) C t 0 = O t 0 + B t 0 (68) where O t a ( v t ) istheannualoperationalcostofaBEV,estimatedfortheannualVMTdriven bytheaverageU.S.driverin$pervehicle,and B t a ( x t a ) istheacquisitioncostofanaverage BEV.Duetoeconomiesofscale,themanufacturingcostofBEVsisdecreasingasthedemand increases.Hence,thecostofowningthetechnologyisassumedtobedecreasingwith x t a becauseinourcaseretailstickerpricesareapproximatedbyproductioncosts.Similarly, O t 0 accountsfortheoperationalcostoftheICEVtechnologyand B t 0 canbeestimatedby projectingavailabledata,sincetheICEVtechnologyismature. Operationalcostsareestimatedasfollowsforeachvehicletype k : O t a ( u t )= q d ( t ) p e ( t ) n e ( t ) + d ( t )(1 q ) v ( t ) v p e ( t ) n e ( t ) +(1 q )(1 v ( t ) v ) d ( t ) p g ( t ) n g ( t ) (69) O t 0 = d ( t ) p g ( t ) n g ( t ) (610) 111

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whereparameter q isthepercentageofnonrange-limiteddaysoverayear, d t theaverage annualVMT, p e ( t ) in$perkWhisthecostofelectricityrealizedwhilechargingthebattery oftheelectricvehicle, n e ( t ) istheon-boardelectricitye" ciencyinmiles/kWh, p g ( t ) isthe gasolinecostin$pergallon,and n g ( t ) isthegasolinee" ciencyinmilespergallon. ForEq.( 69 ),theyearlyoperationalcostoftheaverageBEVdriverisafunctionofthe annualVMTconducted d t .DuetothelimitedrangeofBEVs,theaverageBEVdrivercan accommodateonlycertainpercentageoftripsperyear;therestofthetripsarecharacterized asrange-limitedonesandaback-upICEVhastobeusedtosatisfythose.Parameter q accountsforthepercentageofdaysduringtheyearthattripscanbepoweredbyelectricityand isadoptedfrom Tamoretal. ( 2013 ).Duringtheyears,asmorechargersbecomeavailable,the percentageofannualVMTcoveredbyelectricityadditionallyincreasesby (1 q ) v ( t ) v andthe percentageofVMTfueledbygasolinedecreasesby (1 q ) (1 v ( t ) v ) .Theoperationalcostof anICEVfortheaverageconsumerin( 610 )isfrom Kontouetal. ( 2015 ). Thecapitalcostsforvehicles'purchaseareestimatedasfollowsfortheBEVandtheICEV technology: B t a ( x t a )= B ( x 1 a ) ( x t a x 1 a ) w 2 (611) B t 0 = + t (612) Basedon Weissetal. ( 2012 ),theBEVproductioncostisassumedasasurrogatemeasurefor itsprice.FromEq.( 611 ), B t a ( x t a )=exp( w 1 + w 2 ln( x t a )) ,with w 1 =ln( B 1 a ( x 1 a )) w 2 ln( x 1 a ) and B 1 a ( x 1 a ) and x 1 a theproductioncostandtheEVadoptioninyear1,respectively.Note that w 2 istheparameterofpower-lawbatterycostproduction,whichcanbedeterminedby utilizingtheprogressratioofthelearningbydoingprocess(presentedinthedatasectionof thischapter).ThestickerpriceofICEVsisalinearfunctionoftimeasin( 612 ). Factorsthatcapturesocialnetworkinuencearecommonlyenteredinutilitiesof innovativeproductpurchasechoices,e.g., VanBenthemetal. ( 2008 )and LobelandPerakis ( 2011 ),inordertoaccountfortheexposuretoanewtechnologyandwordofmouthe!ects. 112

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Informationspreadingbyexistingadoptersisafactorthatisaccountedforinalternative fuelvehiclechoicemodelingstudies.WithrespecttoBEVmarketpenetration, Zhangetal. ( 2011 )assumeapositivee!ectofthe"wordofmouth"variableintheiragent-basedmodeling study. Eppsteinetal. ( 2011 )accountforthee!ectofsocialinuencetowardsbuilding environmentalconcerns;researchersaddthisvariablewhenmodelingPHEVpenetration. Shepherdetal. ( 2012 )alsoconsiders"wordtomouth"e!ectsthatdriveEVsocialexposure, fortheirsystemdynamicsapproachtoprojectelectricvehiclesdemand.TheBEVindirectutility functioncapturestheimpactofinformationspreadingforBEVs,undertheassumptionthat theprobabilityofchoosingBEVsismorelikelytoincreaseasthenumbersofvehiclesadopted increaseforacertainregion.Alogarithmicfunctionisusedtocapturethise! ect,asproposed by LobelandPerakis ( 2011 ). lbd t a =log 10 ( x t a M ( t ) ), (613) where M ( t )= x t 0 + x t a denotesthetotalvehiclestock.ThisfunctionpenalizeslowBEV adoption:thisfactorwhenstockapproacheszerogoesto ') ;asthelevelofBEVstock increasesandtheratiogoesto1thenthisfactorgoestozero. 6.1.2ModelingFramework ThegovernmentisinvestedinpromotingBEVsandsubsidizetheiradoption.Thegoalis tomaximizetheratioofthefuelandemissionssavingsachievedfromthedi! usionoftheBEV technologytotheinvestmentthegovernmentallocatesfortheirpromotion.Thenon-linear programmingframeworkinpresentedhere: 113

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max z = # t T ( x t a ( E t 0 E t a ( u t ))+ x t a ( O t 0 O t a ( u t ))) / (1+ $ ) t # t T ( r t q t a ( r t u t )+ & v t CRF ) / (1+ $ ) t (614a) s.t. q t a ( r t u t )=[ m ( t )] e V t a ( r t u t ) e V t 0 + e V t a ( r t u t ) $ t % T (614b) q t 0 ( r t u t )=[ m ( t )] e V t 0 e V t 0 + e V t a ( r t u t ) $ t % T (614c) x t +1 k = x t k + q t k ( r t u t ), $ k % { 0, a } t % T (614d) v t +1 = v t + u t $ t % T (614e) r t 0, r t # r $ t % T (614f) x t k v t 0, $ k % { 0, a } t % T (614g) v 1 = # u t 0, v t # v u t # v $ t % T (614h) x 1 0 = % 1 x 1 a = % 2 $ k % { 0, a } t % T (614i) t T ( q t a ( r t u t ) r t ) # B (614j) where E t k isrepresentativeofthemonetizedcarbondioxideemissionsin$perBEV, CRF is thecapitalrecoveryfactor, $ isthediscountfactor,and & isthecapitalandinstallationcost ofalevel-2publiccharger.Non-negativityandupperboundconstraintsareadded,setting intervalsoffeasibilityforthedecisionvariables,asin( 614f )-( 614i ).Thenalconstraint ( 614j )setsanupperboundtothebudgetforsubsidyallocation.Abudgetconstraintisnot setforthecharginginfrastructureexpendituresinceupperlimitsforchargingavailabilityare alreadyinplacethroughconstraint( 614h ). Monetizedcarbondioxideemissionsarecalculatedasfollows: E t a ( u t )= ( t )( q d ( t ) v e n e ( t ) + d ( t )(1 q ) v t v v e n e ( t ) +(1 q )(1 v t v ) d ( t ) v g n g ( t ) ), (615) E t 0 = ( t ) d ( t ) v g n g ( t ) (616) 114

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where ( t ) isthesocialcostofcarbonin$perkgC02-eq, v e istheemissionfactorin kgCO2-eqperkWhrealizedduringtherechargingprocess,and v g istheemissionsfactor inkgCO2-eqpergallonforthetailpipeemissionsofICEVsorback-upICEVsduringthe range-limiteddaysoftheBEVoperation.Oncemore,socialcostofcarbonismonetizing thedamagesofincreasingthelevelsofcarbondioxideemissions( EnvironmentalProtection Agency 2013 ). 6.2Data Thenon-linearoptimizationframeworkisappliedleveragingdatasetsrepresentativeofthe U.S.travelingpatterns,theenergyandtheautomobilemarkets. Theplanninghorizonforincentivedesignandallocationisassumedtobe T =30 years. ThelinearfunctionsoftheparametersthatvaryovertimearepresentedinTable 6-1 ;their sourcesarealsonotedthere.Thescalarsthatenterthecostscomponentsandequations presentedintheprevioussectioncanbefoundinTable 6-2 ,withtheirsourcesaswellasthe methodsfordeningthose. 6.3Results Thenon-linearprogramof( 614a )-( 614j )issolvedusingKNITROsolver( Byrdetal. 2006 )inGAMS23.3( Rosenthal 2015 ).Locallyoptimalsolutionsareobtained.Thedatasets presentedintheprevioussectionareleveragedtoapplytheproposedmodelingframework foroptimizingincentivesataU.S.nationalandregionallevel.Basecaseresults,aswellas alternativescenariosndingsarepresentedinthefollowingsubsections. 6.3.1BaseCaseResults Forthebasecase,incentivesforBEVpromotionaredesignedonaU.S.nationallevel, usingtheaforementionedaggregatedatasets.Threeincentiveschemesarecompared: optimizationandallocationofgovernment'sinvestmentforbothsubsidiesandpublic charginginstallation,onlyBEVsubsidiesallocation(whichisassumedtoresemblethecurrent state-of-practice),oronlyinvestmentdistributedforpubliccharginginstallation. 115

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Therstschemeresultsingreaterreturnscomparedtotherestandleadstoadopting BEVsatafasterpace.ResultsonthemarketshareachievedbytheICEVandBEVtechnology overtheplanninghorizonsarepresentedinFigure 6-1 .Morespecically,allocatingsubsidies andinstallingchargingequipmentatthesametimeisoverallamorecost-e! ectivestrategy thantherest.Thisschemeleadstoanalyear( t =30 )marketshareofapproximately27% BEVs,whentheBEVsubsidycaseachieves21%andtheBEVchargingonly15.5%. Forapproximately400millionnewvehicles'marketoverthe30yearplanninghorizon,by investing$12.88billionsonsubsidiesand$0.52billionincharginginfrastructure,thesavings fromfuelconsumptionreach$444billionsandthesavingsfromenvironmentalexternalities reduction$2.56billions.Itisobservedthattheoptimalresultoutperformsthecurrentpractice casewhichisessentiallyonlyinvestinginsubsidies,andleadstoanincreasedratioofbenets toinvestmentbyapproximately9.5%. TheoptimalincentivepolicyforeachschemeproposedispresentedinFigure 6-2 .Note thatthepoliciesthatallowtheallocationofsubsidiesforBEVs,duringtherstyearsof theplanningtimeframedistributethemaximum$7,500incentive.Thisleadstoincreasing themarketshareofBEVsafterthe4thyearforbothschemes,whichisnotthecaseforthe charging-onlyinstallationscheme.TheoptimalsubsidyperBEVofthepreferredschemestarts atthemaximumlevelandafteryear8beginsdecreasinglinearlyuntilithits$4,500atyear 12.Then,itremainsconstantforthreeyearsandbeginslinearlydecreasingonceagain,untilit discontinuesatyear22.Ontheotherhand,fortheonlysubsidyscenario,subsidiesallocated therst10yearsare$7,500andthenlinearlydecreasinguntiltheyarediscontinuedbyyear14. Whenitcomestotheoptimalcharginginstallationpolicyforthechargers-onlycase,itturns outthatitforces100%chargingavailabilityaftertherstfewyearsinordertomaximizethe operationalsavingsfromthisinvestment.Thepreferredscheme,ontheotherhand,gradually increasesthechargingavailabilityfrom45%inyear6to100%attheendoftheplanning horizon. 116

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Theimpactofspatialheterogeneityisalsoexaminedforthebasecasescenario.The proposedoptimizationframeworkisappliedtoeachofthenineU.S.CensusBureauregions ( U.S.DepartmentofEnergy 2013b ).Spatialvariabilityofgasolineandelectricityprices, chargingavailabilitybasedonthenumberofchargersat t =1 ,variabilityoftheaverage driver'sVMTperregion,aswellasthestartingmarketshareofBEVsinaccordanceto U.S. DepartmentofEnergy ( 2015a )aretakenintoconsiderationforapplyingthemodel.The regionalspecicdatastemfrom U.S.DepartmentofEnergy ( 2013b ).Theresultsforthenal year'sBEVmarketpenetrationarepresentedinFigure 6-3 andindicatethatcertainregions, suchasPacic,startintheforefrontoftheelectricationandcontinuetobethereafter e ectiveincentiveallocation.Resultsalsoindicatethatincentiveoptimizationataregional level,takingconsiderationregionaldrivingpatternsandthelocaltransportationsector/energy marketleadstocertainregions,suchasPacic,WestSouthCentral,EastNorthCentraland NewEnglandreachingBEVmarketsharegreaterthattheU.S.nationalaverageoutcomeof thenationalleveloptimization. 6.3.2AlternativeScenarioResults Thesensitivityoftheoptimalrebatescheme,appliedatanationallevel,andthesavings thatcanbeachievedthroughgovernment'sinvestmentonBEVsisexaminedinthissubsection. Specically,thescenariosexamined,apartfromthebasecasepreferredscenario,are:(a)a scenariosimilartothebasecase,wherethegasolinecostsincreasesadditionally50%from thebasecase,(b)ascenariosimilartothebasecasebutwherethesocialcostofcarbon parameterincreases150%annually,and(c)ascenariowherethethebatterypackcost decreasesadditionallyby1%. Forscenario(a)and(b),theincreasesinthegasolinecostandsocialcostofcarbon impacttheoperationalandmonetizedemissionscostsrespectively.Eventhough,those scenarioscertainlyresultingreatercostsforsociety,thee! ectivenessoftheincentives distributedisnotedbasedonthedi! erenceinthesavingsthatthegovernmentcanachieve byinvestinginsuchschemes,presentedinTable 6-3 .Asexpected,the%ofthesavings 117

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thattheapplicationoftheincentivescanachieveisincreasedinallcases;whatismore,the investmentrequiredforsubsidyallocationisreducedsincethosescenariosresultinmakingthe BEVproductmoreattractivethattheICEVs.Thegasolinecostispinpointedonceagainasa parameterofparamountimportance,thatcanplayasignicantroleintheBEVmarketshare numbersovertheyears. 6.4Summary Thischapterpresentsaframeworkforoptimizingtheinvestmentportfolioforincentive allocationoveracertainplanninghorizonofelectricationofthehouseholdpassengervehicle eet.TheobjectiveofthisapproachistopromoteBEVswhilemaximizingthereturnsthat societyreceivesfromthisgovernmentinvestment.Benetsarerelatedtofuelconsumptionand environmentalexternalitiesreduction. Thebasecaseresultsindicatethattheoptimalsubsidydecreasesovertimeand discontinuesafteryear22.Ontheotherhand,charginginstallationincreasesgraduallytoreach 100%byyear t =30 .Publiccharginginstallationisimportanttosustainoperationalsavings overtheyearsbutaBEVrebateacceleratesthesalesshare,specicallyatthebeginningofthe planninghorizon.Designingincentivesonaregionallevelcancontributetobettercapturing marketparametersvariabilityandleadtogreatermarketBEVsharesoverall.Pessimistic gasolinecost,pessimisticsocialcostofcarbon,andreductionofthebatterypackcost,along withe!ectiveincentiveoptimization,canresultinincreasingtheshareofBEVsattheendof theplanninghorizoncomparedtothebasecase. 118

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Table6-1. ParametersFunctions Parameters BaseCaseFunction Source GasolinePrice($/gallon) p g ( t )=0.0422 t +2.5252 EnergyInformationAdministration ( 2016a ) ElectricityPrice($/kWh) p e ( t )=0.0009 t +0.1036 EnergyInformationAdministration ( 2016a ) SocialCostofCarbon($/kgCO2-eq) ( t )=0.0009 t +0.032 EnvironmentalProtectionAgency ( 2013 ) AnnualVehicleMiles d ( t )=10893+89 t Davisetal. ( 2015 ) GasFuelEconomy(mpg) n g ( t )=0.7114 t +36.746 EnergyInformationAdministration ( 2016a ) ElectricmodeFuelEconomy(mi/kWh) n e ( t )=0.0052 t +3.7501 EnergyInformationAdministration ( 2016a ) NewVehicleRegistrations(ICEVs+BEVs) m ( t )=6 10 9 +559900 Davisetal. ( 2015 ) 119

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Table6-2. ScalarModelingParameters Scalars ValueProcess DataSource EmissionFactor(gasoline)11.8n.a. Yawitzetal. ( 2013 ) EmissionFactor(electricity)0.73n.a. EnergyInformationAdministration ( 2013 ) CostofLevel-2Charger7500n.a. IdahoNationalLaboratory ( 2015 ) UpperBoundofChargers156065n.a. U.S.DepartmentofEnergy ( 2014a ) w1 6.9713Eq.( 611 ) U.S.DepartmentofEnergy ( 2016f ) w2 -0.2583Eq.( 611 ) U.S.DepartmentofEnergy ( 2016f ) bc -0.00165linearregressionn.a. b2 -0.4374linearregressionn.a. b3 0 linearregressionn.a. b4 9.64linearregressionn.a. mu 24634linearregression U.S.DepartmentofEnergy ( 2016f ) gamma 523.71linearregression U.S.DepartmentofEnergy ( 2016f ) Figure6-1. Theevolutionofmarketshareforvehicletechnologiesunderalternativeincentive schemeinvestments. 120

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Figure6-2. Optimalincentivepoliciesunderalternativeincentiveschemeinvestments. Table6-3. AlternateScenarioSavings,InvestmentsandBEVMarketShareDi!erencesfrom theBaseCase AlternateScenario:ParameterChange Savings (%di!erencefrombase) (a)GasCost(b)SocialCostofCarbon(c)BatteryPack Fuelconsumption +128% +34% +105% Emissionsreduction +420% +369% +100% Subsidyinvestment -20% -8% -24% Investmentinchargers+75% +23% +34% FinalBEVMarketShare46% 35% 32% 121

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Figure6-3. InitialandnalBEVmarketshareforeachU.S.CensusBureauregion,underoptimalincentivesallocation. 122

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CHAPTER7 CONCLUSIONSANDFUTURERESEARCH Thisdissertationdocumentpresentsresearchconductedonoptimizingvariouspolicy componentssoastomaximizethesocialbenetsfromtheprocessofhouseholdpassenger vehicleelectricationanddailyoperations.Inthisnalchapter,themajorcontributionsofthis workarerevisitedanddirectionsforfutureresearcharediscussed. 7.1Contributions Inthissectionthemostsignicantresearchcontributionsofthisworkareonceagain pointedout.ThersttworesearchinitiativesfocusonPHEVs;there,theoptimalrangedesign andchargingcontrolaredeterminedfore"cientPHEVdailyoperations.Thenexttworesearch endeavorsconcentrateonBEVs.Specically,thoseaimto(1)determineanoptimalpathway toelectrication,whichminimizesthesocietalcostofthattransition,and(2)optimizethe investmentportfolioofmonetaryincentivestoensuremaximumfuelandexternalitiessavings fromtheirallocation. AnoptimizationmodelthatdeterminestheoptimaldrivingrangeofPHEVsby minimizingthesocialcostincurredduringthePHEVsdailyoperationisdeveloped (Chapter3).Theobjectivefunctionaccountsfordriversexpenditureandenvironmental externalitiesfromdailyPHEVoperation.Themodelisextendedtocapturethee! ect ofworkplacecharginginstallationondeningtheoptimalrangeofPHEVs;inthiscase, governmentexpenditureforchargersenterstheobjectivefunction.Furthersocietal costreductionisachievedviadiversifyingthePHEVdrivingrangesavailabletodrivers. Novelbi-leveloptimizationframeworksareproposedformodelingtheseextensions.The applicationofthosemodelswithU.S.representativedatasetsallowpolicymakersto suggestone,apair,oratripleofPHEVrangesthatminimizesocialcostsforPHEV adoptionandoperations,aswellastheoptimalworkplacechargingdensity,andshowcase thetrade-o! sbetweenvariouscostcomponents. Twohourlychargingmanagementschemesforcost-e!ectiveandeco-friendlyoptimal PHEVchargingareproposed(Chapter4).Theseschemescontrolcharginginorderto minimizeoperationalcostandenvironmentalexternalitiesforthePHEVdriversand thegovernment,respectively.Theapplicationofthesemodels,leveragingdatasets representativeoftheU.S.automobileandenergymarket,showcasestheverydi!erent chargingprolesresultingfromthoseobjectives,picturesthehourlysamplecharging percentagesandtheutilitygridloads,andemphasizesthetrade-o!sbetweencostsavings andenvironmentalexternalitiesreductionofthesecontrolledchargingschemes. 123

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AnICEVwithBEVreplacementmodelisdevelopedandappliedinordertodetermine theupperlimitofhouseholdvehicleelectricationformaximumsocialbenets(Chapter 5).Thisnovelmodelingframeworknotonlydeterminestheoptimalreplacementrate ofICEVswithBEVs,butalsopinpointstheoptimalall-electricdrivingrangeandpublic chargingdensityonlineartransportationnetworks.Policymakersmaysuggestthose decisionvariablesvaluessoastominimizedrivers'andgovernment'sexpenditures,as wellasenvironmentalexternalities.Themodelingframeworkaccountsforthee!ectof publicchargersonextendingtheall-electricdrivingrangeofBEVs,whichresultsintwo distinctoptimizationframeworks.Thetrajectoriesofvarioussocialcostcomponentsare portrayedovertime,range,andpublicchargingdensity.Byapplyingthoseframeworksto U.S.pertinentdatasets,theneedforfast-pacedelectricationbecomesevidentbasedon theoptimaltransitiontimeframeresults. AmodelthatdeterminesoptimalBEVincentives,suchasBEVsubsidiesandpublic charginginfrastructureinvestments,atanationalorregionallevelisproposed(Chapter 6).ThisframeworkdenestheoptimalannualmarketshareofICEVandBEV technologies,aswellastheoptimalannualdistributionofmonetizedincentivesover aplanningtimeframe.TheICEVandBEVdemandismodeledusingalogisticfunction whichwasttedusingmarketdatasets.Apartfromoptimizingincentivesatanational aggregatelevel,anapplicationofthemodelonU.S.regionsispresented.Results showcasethatoptimizedincentivescanachievegreaterfuelconsumptionandmonetized emissionsavingsthatthecurrentstate-of-practiceincentivesavailable. TheapplicationsoftheaforementionedmodelingframeworksusingU.S.datacreatea poolofinformationofinteresttocentralplannersandgovernmentagenciesregarding thesocialbenetsgainedfromoptimizingthetransitionfromconventionaltoelectried mobilityanddailyoperations. 7.2FutureResearch Assumingthatadoptionandoperationratesofelectricvehicleswillkeepclimbinginthe nearfuture,dataofgreatersamplesizesthatreectconsumersbehaviortowardsownership, usage,andchargingofsuchvehicleswillbecomeavailable.Anaturalextensionoftheresearch workpresentedinthisdissertationemergesfromtheneedtobettercapturedriverspreferences withinoptimizationmodeling.Integrationofbehavioralmodelswithoptimizationonescanhelp towardsdevelopingincentivestoshiftthetimelineofPEVadoptiontoanoptimalonethat willresultinmaximumsocietalbenets.Anotherexampleofsuchintegrationisthedesign ofoptimalelectricitytari! stoinducedriverstofolloweco-friendlychargingproles,ifthatis necessary.Inthiscontext,availabilityofsuchdatasetsisofgreatimportanceinreinforcingthe 124

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realismofthemodels;however,suchintegrationcanhurtcomputationale"ciencyor,even, tractability. Concreteexamplesofpotentialpathwaysofextensionofthisworkarelistedherein.The basecasemodelofdrivingrangeoptimizationforPHEVscanbeextendedtoaccountfor thedistributionofdailyandannualVMT;thecostcomponentswouldneedtobeadjusted accordingly,e.g., Lin ( 2014 ),and LinandGreene ( 2012 ).Apartfromworkplacecharging,the modelcanbeextendedtoaccountfortripsseries,notonlycommutingtrips,anddeterminethe publicchargingdensityforPHEVs.Usingdatathatdescribechargingbehavior( Kellyetal. 2012 ),thedi!erencesbetweenactualchargingprolesandtheoptimalonesforcost-e!ective andeco-friendlygridmanagementcanbepinpointed.Thenextstepwouldbetodesign incentivesorelectricitychargingtari! sforinducingPHEVdriversbehaviortofollowoptimal chargingschemes.TheICEVwithBEVreplacementmodelcanbeextendedtocapture thee! ectsoftheavailabilityofapairofBEVrangestotherestofthedecisionvariables. Additionalconstraintsneedtobeincorporatedinthiscasetodenetheallocationofranges tothehouseholdeet.Theoptimizationframeworkthatdeterminesincentivescanbefurther extendedbyutilizingadetailedandvalidatedownershipdecisionmodel,suchas Linand Greene ( 2010b ).Inthatcase,simulation-basedanalysis,inordertoovercomecomputational issues,wouldbeproposedtodeterminetheoptimalincentivesforacceleratingPEVadoption. Amultinomialornestedlogitmodelforvehicleownershipdemandwouldbee!ectivefor determiningoptimalincentivesforPHEVandBEVtechnologiesatthesametime.Lastbut notleast,thecompetitionbetweenPHEVsandBEVscanbeconsideredfortherestofthe modelingframeworksthatarepresentedinthisworkandnotonlyfortheincentivedesign. 125

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BIOGRAPHICALSKETCH EleftheriaKontoureceivedherPh.D.incivilengineering,focusingontransportation systems,inDecember2016fromUniversityofFlorida.Herdissertationworkfocusedon maximizingsocialbenetsfromthelight-dutyvehicleelectricationandoperations.She holdsaM.Sc.fromVirginiaPolytechnicInstituteandStateUniversityandaDiploma(B.Sc.) fromNationalTechnicalUniversityofAthens,bothincivilengineering.Sheisfondofsolving problemsatthetransportation/energynexusandherresearchinterestslieintheeldsof emergingvehicletechnologies,transportationplanning,operationsandeconomics.Shehas conductedresearchattheCenterofTransportationAnalysisoftheOakRidgeNational LaboratoryandattheTurnerFairbankHighwayResearchCenteroftheFederalHighway Administrationduringhertenureasagraduatestudent. 138