Towards Stochastic Optimization-Based Electric Vehicle Penetration in a Novel Archipelago ...

22 Pages·2016·0.53 MB·English

sensors
Article
Towards Stochastic Optimization-Based Electric
Vehicle Penetration in a Novel Archipelago Microgrid
QingyuYang1,*,†,DouAn2,†,WeiYu3,*,†,ZhenganTan2,† andXinyuYang2
1 SKLMSELab,SchoolofElectronic&InformationEngineering,Xi’anJiaotongUniversity,
Xi’an710049,China
2 SchoolofElectronic&InformationEngineering,Xi’anJiaotongUniversity,Xi’an710049,China;
[email protected](D.A.);[email protected](Z.T.);[email protected](X.Y.)
3 DepartmentofComputerandInformationSciences,TowsonUniversity,Towson,MD21252,USA
* Correspondence:[email protected](Q.Y.);[email protected](W.Y.);
Tel.:[phone](Q.Y.);[phone](W.Y.)
† Theseauthorscontributedequallytothiswork.
AcademicEditors:DongkyunKim,HoubingSong,Juan-CarlosCano,WeiWang,WaleedEjazandQingheDu
Received:18April2016;Accepted:1June2016;Published:17June2016
Abstract: Due to the advantage of avoiding upstream disturbance and voltage fluctuation from
apowertransmissionsystem,IslandedMicro-Grids(IMG)haveattractedmuchattention. Inthis
paper,wefirstproposeanovelself-sufficientCyber-PhysicalSystem(CPS)supportedbyInternet
of Things (IoT) techniques, namely “archipelago micro-grid (MG)”, which integrates the power
gridandsensornetworkstomakethegridoperationeffectiveandiscomprisedofmultipleMGs
whiledisconnectedwiththeutilitygrid. TheElectricVehicles(EVs)areusedtoreplaceaportionof
ConventionalVehicles(CVs)toreduceCO emissionandoperationcost.Nonetheless,theintermittent
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natureanduncertaintyofRenewableEnergySources(RESs)remainachallengingissueinmanaging
energyresourcesinthesystem. Toaddresstheseissues,weformalizetheoptimalEVpenetration
problemasatwo-stageStochasticOptimalPenetration(SOP)model,whichaimstominimizethe
emissionandoperationcostinthesystem. UncertaintiescomingfromRESs(e.g.,wind,solar,and
load demand) are considered in the stochastic model and random parameters to represent those
uncertaintiesarecapturedbytheMonteCarlo-basedmethod. Toenablethereasonabledeployment
ofEVsineachMGs,wedeveloptwoschedulingschemes,namelyUnlimitedCoordinatedScheme
(UCS)andLimitedCoordinatedScheme(LCS),respectively. Anextensivesimulationstudybased
onamodified9bussystemwiththreeMGshasbeencarriedouttoshowtheeffectivenessofour
proposedschemes. Theevaluationdataindicatesthatourproposedstrategycanreduceboththe
environmentalpollutioncreatedbyCO emissionsandoperationcostsinUCSandLCS.
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Keywords:archipelagomicrogrid;electricvehicles(EVs);two-stagestochasticprogramming;scheduling
1. Introduction
With the development of the smart grid, microgrids (MGs) are becoming miniaturized,
independentandcommunity-basedcontinuously. Asatypicalenergy-basedCyber-PhysicalSystem
(CPS)supportedbyInternetofThings(IoT)techniques[1],MGsintegratebothphysicalelementsin
thepowergridandcyberelements(sensornetworks,communicationnetworks,andcomputation
core)tomakethepowergridoperationeffective. Suchacomplexsystemcallsfornovelapproachesfor
systemdesignandmodelingandnewtechniquestomanageenergyresourceefficiently.
Duetohighlyintermittentanduncertaintiesfrombothphysicalpowergridandcybernetwork
components,newtechniquesforMGmodelingandmanagementshouldbedevelopedtoenhance
energyefficiency[2]. Specifically,theemergedIslandedMicro-Grids(IMG)[3]havereceivedgrowing
Sensors2016,16,907;doi:10.3390/s16060907 www.mdpi.com/journal/sensors
Sensors2016,16,907 2of22
attentionduetotheself-balanceandstabilityundervoltagefluctuations. TheswitchinIMGconnected
totheutilitygridcanturnofftheconnection,incasethemalfunctionresultedfromthemaingrid,
includingupstreamdisturbances,voltagefluctuation,etc.[4].TheoperationofIMGisabletoeffectively
mitigatethedetrimentalsituationsraisedbytheutilitygrid,reducetheoperationcostandenhancethe
reliabilitywhenapowershortageoccurs.
DuetoflexibilityofcharginganddischargingElectricVehicles(EVs)inIMG,energyefficiency
andenvironmentalfriendship,EVs,asakeycomponentinIMG,havedrawnmuchresearchattention
inrecentyears. WiththeintegrationofEVsinIMG,effectiveschedulingschemesarerequiredtohelp
smooththeloadcurveandreducetheenvironmentalemissions.Tothisend,alargenumberofresearch
effortshavebeenconductedonEVs. Forexample,anobjectiveofminimizingtheoperationcostand
maximizing the profit of IMG was studied by scheduling the EV charging and battery swapping
stationwithafuzzycontrolapproachin[5]. SaberandVenayagamoorthyin[6]investigatedtheoverall
scaleofEVsundertheobjectiveofreducingtheCO emissionandoperationcost. Nonetheless,their
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proposedschemeonlyusedEVstoreplaceallConventionalVehicles(CVs)whilethelocalunitcapacity
andtheinvestmentcostswerenotconsidered.
InanIMG,theinstalledlocalunits’generationneedtomeettheloaddemandduringthepeak
timeduration,combiningwiththegenerationofRenewableenergysources(RESs). Incomparison
withtheMGsconnectedtotheutilitygrid,alargercapacityshouldberequiredinanIMG,which
leadstoanexpensiveinvestmentcost. Inaddition,iftherearesufficientRESsinanIMG,thesurplus
energywillbewastedaftersatisfyingtheloaddemandandfillingupthestoragedevice,leadingtoan
inefficientenergyusage. Tothisend,asanessentialloadandenergystoragedevice,EVsoffergreat
flexibilitytoinfluencetheenergyefficiency,stability,andenvironmentbenefitsofIMGsignificantly.
Thus,itiscriticaltodevelopeffectiveschedulingschemesforEVsinanIMG.
Nonetheless,theintermittentandrandomnessofRESs(e.g.,windandsolar)willcreategreat
challenges to the stability and reliability of IMG operation [7]. In particular, the forecast accuracy
of the uncertain parameters are essential to the energy efficiency. For instance, a lower prediction
accuracywillleadtomorereverserequirementstocompensatetheerrorsinthecasethattheforecast
generation is more than the actual generation. In addition, the precise prediction of parameters
(electricityprices,etc.)helpstheconsumersmakerationaldecisionsofEVcharginganddischarging,
thusavoidinggeneratingnewpeakloadforthesystem. Therefore,howtotackletheuncertaintiesin
anIMGisacriticalissue.
Toaddresstheseissues,inthispaper,wefirstproposeanovelIMGsystem,named“archipelago
micro-grid(IMG)”,whichisdisconnectedfromtheutilitygridandcomposedofseveralconnected
MGs. In such a system, the energy demanded is fully satisfied by distributed energy generations.
In the proposed IMG, we formalize the optimal scheduling problem, which aims to minimize the
emissionandoperationcostbyarrangingtherationalcharging/dischargingplananddeployinga
reasonablenumberofEVswhileconsideringvariousuncertainties.
Thekeycontributionsofthispapercanbesummarizedasfollows:
• To improve the energy efficiency and ensure the stability of IMG, we propose a novel
multi-microgrid system concept named “archipelago microgrid”. In our proposed system,
the required power will be fully provided by the distributed power generation in local MGs.
ThroughtheenergytransmissioncontrolledbyaMicroGridCenterController(MGCC,aggregator)
among the MGs, the emission and operation cost created by local units can be mitigated.
Theproposedsystemishelpfulinreducingoperationcostandenhancingthestabilityofthegrid.
• WeproposeaStochasticOptimalPenetration(SOP)model,aimingtominimizethecostofthe
proposed“archipelagomicrogrid”system. ToaddresstheuncertaintiesfromRESsandelectricity
prices,theoptimizationproblemisformalizedasatwo-stagestochasticprogrammingproblem.
Intheformalizedproblem,theuncertainparameterssuchaswind,solargenerationcapacityare
capturedbytheMonteCarlo-basedmethod[8]. Forthesakeofcomparison,theDeterministic
OptimalPenetration(DOP)modelbasedonourpriorwork[9]isintroducedasabaselinescheme.
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In the optimization problem, the emission cost created by CVs and local units, the operation
costofstartup/shutdownexpenseofunits,tariffcompensation,batterycapacitydegradation,
andpowerlossesareconsideredintheoptimizationmodel. Theproposedstochasticmodeloffers
adesiredflexibilitybetweentheenvironmentalandeconomicbenefitsbyseekingtheoptimal
numberofEVswiththeconsiderationsoftheRESsandunitsgenerationlimits.
• To achieve the minimization of emission and operation cost, we propose the following two
schemes to schedule the optimized scale of EVs: (i) Unlimited Coordinated Scheme (UCS);
and (ii) Limited Coordinated Scheme (LCS). In UCS, we consider that all the surplus energy
is utilized to charge as many EVs as possible. In this ideal scenario, the mutual transmission
amongMGsisalsoallowedtoavoidenergywasted. Nonetheless,peakloadlimitsandresidence
preferenceofenergyusageshouldbeconsideredinpractice. Tothisend,weproposetheLCSto
achieveamorerealisticnumberofpenetratedEVstominimizethetotalcost.
• WecarryoutanextensivesimulationstudyonamodifiedIEEE9-bussystemtodemonstrate
theeffectivenessoftheproposedSOPmodelusingthetwoschedulingschemes. Thesimulation
resultsshowsthat,afteraddressinguncertainties,theemissionsandoperationcostarereducedin
comparisonwiththedeterministic-basedoptimizationmodel. Inaddition,withrespecttothetwo
scheduleschemesinSOP,theLCShasbeenproventobemoreeffectiveonarrangingthescaleof
EVsandrealizingtheemissionandoperationcostreductionthantheUCS.Ourexperimentaldata
showsthat,incomparisonwithabaselinenon-coordinatedaveragescheme,15.2%ofemissions
canbereducedand11.2%costcanbesavedintheLCS,weconductsensitivityanalysistovalidate
theimpactofdifferentparametersontheoptimalsolution.
Partofthisworkwaspublishedin[9]. Basedonthemuchshorterconferenceversion,wehave
madesubstantialextensionsinthisjournalsubmission. Therestofthepaperisorganizedasfollows,
wepresentsystemmodelsinSection2. InSection3,weshowtheformalizationoftheSOPproblem
andproposeour schedulingschemes. InSection 4, wegivethe performanceevaluationresultsto
demonstratetheeffectivenessofourproposedschemes. WepresenttheliteraturereviewinSection5,
andweconcludethepaperinSection6,respectively.
2. SystemModels
Inthissection,wefirstpresentthesystemmodelofourarchipelagomicrogridandthendescribe
themarketmodelusedinthepaper.
2.1. ArchipelagoMicrogridModel
In this paper, in order to refrain from the voltage fluctuations and upstream disturbances
caused by the utility grid, while increasing the reliability of local MGs, we propose the concept
of an independent and self-sufficient system, called “archipelago microgrid”. The basic structure
of“archipelagomicrogrid”isillustratedinFigure1. Asshowninthefigure,thesystemisatypical
energy-basedCyber-PhysicalSystemsupportedbyInternetofThings(IoT)techniques,whichconsists
ofbothcyberandphysicalcomponents.
(cid:48)(cid:76)(cid:70)(cid:85)(cid:82)(cid:74)(cid:85)(cid:76)(cid:71)(cid:3)(cid:21)(cid:3)
(cid:36)(cid:74)(cid:72)(cid:81)(cid:87)(cid:21)
(cid:36)(cid:74)(cid:74)(cid:85)(cid:72)(cid:74)(cid:68)(cid:87)(cid:82)(cid:85)
(cid:87)(cid:85)(cid:68)(cid:81)(cid:86)(cid:80)(cid:76)(cid:86)(cid:86)(cid:76)(cid:82)(cid:81)(cid:3)(cid:79)(cid:76)(cid:81)(cid:72)
(cid:70)(cid:82)(cid:80)(cid:80)(cid:88)(cid:81)(cid:76)(cid:70)(cid:68)(cid:87)(cid:76)(cid:82)(cid:81)(cid:3)(cid:79)(cid:76)(cid:81)(cid:72)
(cid:36)(cid:74)(cid:72)(cid:81)(cid:87)(cid:3)(cid:20) (cid:36)(cid:74)(cid:72)(cid:81)(cid:87)(cid:3)(cid:81)
(cid:48)(cid:76)(cid:70)(cid:85)(cid:82)(cid:74)(cid:85)(cid:76)(cid:71)(cid:3)(cid:20) (cid:48)(cid:76)(cid:70)(cid:85)(cid:82)(cid:74)(cid:85)(cid:76)(cid:71)(cid:3)(cid:81)
Figure1.Structureofthearchipelagomicrogrid.
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ThephysicalcomponentsarecomprisedoflocalMGs,theinterconnectiontransformerwhich
ensures the power transmission among local MGs. In each MG, the diesel unit and various RES
generationdevicesareusedtoproducetherequiredenergy. Theinstalledcapacityofalldistributed
generatorswillmeettheloaddemandofeachMGinordertoavoidtheoccurrenceofpoweroutage.
Inaddition,RESgenerators,whichconsistofsolarpanelsandwindturbines,areintegratedineachMG.
TheloadsinMGsaredividedintotwotypes: EVsandnon-EVloads. ThroughG2V(Grid-to-Vehicle)
andV2G(Vehicle-to-Grid)technologies,theEVscanbemanagedtochargeordischargeatdifferent
timeslotsaccordingtothecurrentpowerconsumption,whilethenon-EVloadsareunabletoschedule.
In addition, the cyber components guarantees the information transmission in the system,
whicharetypicalsensornetworkscomposedofAdvancedMeteringInfrastructure(AMI)—inwhich,
the data measured by sensors, including timely energy consumption, load forecasting and RES
relatedinformationwithintheMG,willbecollectedbytheMGagentsandtransmittedtotheMGCC.
The entireregionwillbemonitoredbythesystemMGCCthatcansendorreceivevariousinformation
fromortotheagentssupportedbyAMI(sensornetworks).
2.2. MarketModelandAggregator
InordertopenetratethereasonablenumberofEVswhileminimizingtheoperationandemission
cost(accordingtothetimelysupplyanddemandinformation),weconsiderthatwhenthereexists
energysurplusinsomeMGs,inordertoreducetheCO emissionoperationcost,wecandevelop
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aneffectivepowerschedulingschemeforthelocalunitandarrangethemostchargedEVstofully
utilizethedistributedpowergeneration. Then,theremainingpowercanbedeliveredtootherMGsfor
thepurposeofloadoffsetandEVcharging. Inaddition,weneedtodischargeEVswhenthepower
shortage occurs. The discharged power can not only address the need of supply, but also reduce
substantialgenerationcost.
Asthe“centralnervous”ofthewholesystem,theresponsibilityoftheMGCC(MicroGridCenter
Controller)istominimizetheCO emissionandoperationcost. WeassumethatallMGsarehave
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the same interests and the surplus power transport among them is free. Nonetheless, because of
thetransmissionvoltageandresistanceofthelinebetweentheMGs,powerlossesareunavoidable
whentransmittingpowerinMV(MotorVehicle)networks[10]. Obviously,theaggregatorisableto
preferentiallyallocatethetransportedpowerbetweentheMGswithlesspowerlosses.Accordingtothe
collectedinformationassociatedwiththeelectricalquantityandRESgenerationfromMGs,theMGCC
cancomputetheoptimizedschedulingplanfortheEVsanddeployanumberofEVsforcharging.
When the RES generation in some MGs is not enough for the load demand (including EVs),
they will first send a request signal to the MGCC to ask for help. If there is any surplus energy
providedbyotherMGs,theMGCCwilldispatchtheremainingpowertotherequesterautomatically
tomeettheloaddemandandEVchargingactivities. Ifthereisnoremainingenergyleft,theMGCC
willfirstexploitthefullychargedEVtodischargewithoutaffectingitsnormaloperation,andthen,
startupthelocalunittomeetthepowershortage. WeconsiderEVsasthestoragedeviceinthesystem,
thustheunusedenergyafterschedulingwillnotaffectthescheduleinthenexttimeslot. Inaddition,
weassumethatEVsonlychargeanddischargeonceaday. Therefore,theschedulingateachperiod
willbeindependent,meaningthattheschedulingresultsattimeslottwillnotaffecttheresultatany
other time slot. Once the schedule is complete, the historical data will be stored. The MGCC will
monitortheoperationofthesystemagainandpreparefortheschedulingatthenexttimeslot.
3. OurApproach
In this section, we first present the basic idea of our approach. We then give the formulated
optimizationmodelandintroducetheproposedschedulingschemes. Table1showallkeynotations
usedinthepaper.
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Table1.Notations.
NG,NM,NT,NS: Thenumberoflocalunits,MGs,timeslots,andscenarios
φ : TheminimumbatteryenergystoredforhandlingEV’snormaldrivingactivities
min
ω: Weightingfactor
µ: Compensationfactorofpricegaps
λ ,λ : Penaltyfactorofbatterycapacitydegradationandpowerlosses
1 2
η ,η : Charging/dischargingefficiencyofstoragebattery
cha dis
a ,b : FuelconsumptioncoefficientsofDGjinMGi
i,j i,j
α ,β : TheoperationcostcoefficientsofDGjinMGi
i,j i,j
E(P ): CostofunitrtocompensateRESpredictionerrorsinMGiattimet
i,r,t
ncha,ndis: ThenumberofEVscharged/dischargedattimetinMGi
i,t i,t
r ,r : Minimumandreal-timeelectricitypriceduringtheday($/kWh)
min it
R : LineresistancebetweenMGiandl(Ω)
i,l
V: TransmissionvoltageamongMGs(kV)
Q : TransportedpowerbetweenMGiandl(kW)
i,l
N ,N ,N : ThenumberofEVs,CVsandtotalvehiclesinMGi
EV,i CV,i V,i
P : Thepowerlossesduringpowertransmission(kW)
loss
P : Powergenerationoflocalunitj(kW)
i,j,t
P : Non-EVloadinMGiattimet(kW)
load,i,t
P ,P : PowergenerationofPVandwind(kW)
Pv,i,t Wind,i,t
SU ,SD : Startupandshutdowncostofunitj($)
i,j i,j
Ru ,Rd : Ramp-up/downlimitofunitj(kW)
i,j i,j
Pcha ,Pdis : Charging/dischargingpowerofthekthEV(kWh)
EV,i,t,k EV,i,t,k
Pmin,Pmax: Minimum/maximumpowergenerationofunitj(kW)inMGi
i,j i,j
Pmax,Pmin: ThemaximumandminimumcapacityofEV’sbattery(kWh)
EV EV
Charging/dischargingstatusofEV,where0indicateschargingand1indicates
I ,U :
i,t i,t discharging,respectively
Operationstatusofunitj,where0meanstheunit’sstopstatusand1indicates
x
i,j,t: itsoperationstatus,respectively
Startupandshutdownstatusofunitj,where0and1meansstartupand
y ,z :
i,j,t i,j,t shutdown,respectively
SlopeCoefficientandInterceptCoefficientoffuelconsumptionper
SC,IC:
unitgeneration
3.1. BasicIdea
ToimprovetheenergyefficiencyandreducethecostofIMG,inthispaper,weproposeanovel
system,named“archipelagomicrogrid”structure. Theproposedsystemhastheabilityofenabling
theinteractionamongMGsandisolatingthemfromtheutilitygird,aswellastheconstantandlow
electricitypriceoftransportedpoweramonglocalMGs.
Notice that the diesel generators used in the archipelago microgrid will lead to lots of CO
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emissions.TheexistenceofCVsareasourceofpollutionaswell.Withmoreattentiontoenvironmental
issues, emission cost has become an essential aspect in MGs. In addition, the startup/shutdown
associatedcost,thelifelossoflithiumbatteries,andtheamountoffuelutilizedforpowergeneration
leadtoagreateroperationcost. Thus,itisrequiredforanoptimizedpenetrationofEVstoprotectthe
Sensors2016,16,907 6of22
environmentandrealizeagreatreductiononCO emission. Inaddition,asthestoragedeviceisinthe
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archipelagomicrogrid,wecanmakeabetterresponsetothetimelyloadlevelsbyregulatingthenumber
of EVs to be charged at low demand intervals or discharged during the power shortage intervals.
Bydoingso,areductionofemissionsandgenerationcostcanbeachieved. Nonetheless,anincrease
ofothercostssuchasbatterycapacitydegradationandpowerlosseswillbeintroduced. Tothisend,
anoptimizationproblemaimstominimizetheemissionandoperationcostassociatedwiththescale
(number)ofEVsisproposedinthepaper. Theobjectivecontainstwoaspectsofcosts: emissionand
operation. Inordertoincreasetheflexibilityintheschedulingprocess,wesetthedifferentweighted
ratiosfortheenvironmentalandeconomicbenefits. Thelargerweightedfactorofemissioncostset,
themoreattentionisfocusedonenvironmentalissues,andviceversa.
Nonetheless,variabilitiesanduncertaintiesraisedbyRESsmaketheenergyresourcemanagement
inthesystemwithMGsremainachallengingissue. Onthesupplyside,unlikethetraditionalenergy
resources,windandsolarpoweroutputarehighlyuncertainandunpredictable. Evenasmallerrorin
thepredictioncanresultingreaterrorsinreal-timeoperations. Onthedemandside,factors(natural
disasters,plug-invehicles,personalhabitsofusingenergy,weatherandtemperature,etc.) makeit
difficulttoaccuratelypredicttheusageofenergy. TheeffectivenessofintegratingMGscanbeaffected
by those uncertainties, including the local generator output, reverse requirement, etc. To this end,
inthispaper,weformalizetheoptimalEVpenetrationproblemasatwo-stagestochasticprogramming
problem. Intheformalizedproblem, wefirstconsidertheparametersthatcouldcapturedifferent
uncertainties,includingtherandomnessofrenewableenergyresourcepredictionsuchaswindandPV.
WethenleveragetheMonteCarlo-basedmethodtoconstructscenariosaccordingtothedistribution
functionsofthoseparameterstocaptureuncertainties.
Tominimizetheexpectedcost,weproposetwoschemestoarrangethenumberofEVchargingor
discharging,whicharedenotedasUnlimitedCoordinatedScheme(UCS)andLimitedCoordinated
Scheme(LCS),respectively. Inourschemes,thesurplusenergyisallowedtobetransportedamong
the local MGs and the power can be used for charging the EVs and offsetting the non-EV load.
Particularly,intheUCS,allthesurplusenergyisallowedtochargeasmanyEVsaspossible,while tariff
compensationfortheresidentialuserswhocannotchargeEVsintheirpreferenceintervalsandthe
systempeakloadlimitsareconsideredinLCS.
3.2. ProblemFormulation
Wenowformalizetheoptimalemissionandoperationcostproblemasatwo-stagestochastic
programming problem. We first present the objective function and then introduce the constraints.
Generallyspeaking,thestochasticprogrammingprocessisamethodthataimstominimizethecostina
numberofscenariosconstructedbyMonteCarlo-basedmethod,whilebeingobligatedtouncertainties
intheproblem. Thebasicideaofthetwo-stageprogrammingprocessistoconductarecursionprocess
tomakeacorrectivedecisionaftertheoccurrenceofrandomevents.
Inourtwo-stagestochasticprocess,theinputstotheunderlyingproblemincludethescenarios
generatedbytheMonteCarlo-basedmethod,whichrepresenttheuncertaintiesinrenewableenergy
outputs,includingwindandsolar,aswellaselectricityprices.Theoutputsoftheoptimizationproblem
arecomposedofthefirst-stagedecisionsandthesecond-stagedecisions. Thefirst-stagedecisions
includethecommitmentstatusesofallconventionalunits, powerdispatchofallgenerationunits,
andlossescreatedbythepowertransmissionamongMGs. Thesecond-stagedecisionsconsistofEV
chargingdecisionsandreversetocompensatethepredictionerrorswhentheactualRESgeneration
is lower than the predicted amount. In addition, for the purpose of comparison, a Deterministic
OptimalPenetration(DOP)modelisconsideredasabaselinescheme,inwhichtheparameterssuchas
renewableenergygenerationarebasedonthepersistforecast,andtheelectricitypricesareabletobe
predictedbytechniques(e.g.,Auto-RegressiveandMovingAverage(ARMA)[11]andSupportVector
Machines(SVM)[12]).
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3.2.1. StochasticOptimalPenetration(SOP)Model
SOPmodeling:
Inordertominimizetheemissionandoperationcostwithconsideringthevariousuncertainties,
theobjectivefunctionoftheStochasticOptimalPenetration(SOP)modelisasfollows:
(cid:40) (cid:34) (cid:35)
NMNT NG
∑ ∑ ∑ (cid:0) (cid:1)
2min w E P +E (N ) +(1−w)
i,j,t CV CV,i
i=1t=1 j=1
(cid:34)
NG NG NS NR
∑(cid:0) (cid:1) ∑ (cid:0) (cid:1) ∑ ∑
SU +SD + Cost P + ρ E(P )
i,j i,j i,j,t s i,r,t
j=1 j=1 s=1 r=1
 ndis 
i,t (1)
+λ1ηchan∑ic,htaPEchVa,i,t,kIi,t+ k∑=1PEdηVisd,iis,t,kUi,t
 k=1 
NS ni,t (cid:35)(cid:41)
+λ Ploss+ ∑ ρ µ ∑ Pcha (r −r )
2 i,t s EV,i,t,k t min
s=1 k=1
WenowexplaintheSOPmodelindetail. Theemissioncostconsistsofthelocalunitemission
andCVsemission,respectively. Thestartup/shutdownandgenerationcostoflocalunits,thepenalty
ofbatterycapacitydegradation,thepowerlosscreatedbytransmission,andtariffcompensationare
theexamplesoftheoperationcostaccordingtoEquation(1).
(cid:0) (cid:1)
The detail of the objective function is that, the first part E P and second part E (N )
i,j,t CV CV,i
inourmodelcapturetheemissioncostscausedbythelocalunitsandCVs, respectively. TheCO
2
emissionofthelocalunitsdependsontheconsumptionoffuel,andtheCVemissionsaredirectly
basedontheirnumberandtravelingdistance. BecausethePVandwindarecleanenergyresources,
therewillbenopollutioncausedduringthegenerationofsuchresources.
(cid:0) (cid:1)
The third part SU + SD and fourth part Cost P in the SOP model represent the
i,j i,j i,j,t
startup/shutdownandoperationcostoflocalunits,respectively. InourMGmodel,thedistributed
generation is composed of diesel generators, PV panels and wind turbines as shown in Figure 1.
Notice that as the installation cost for PV panels and wind turbines integration is associated with
long-termissues,weonlyconsidertheoperationcostofdieselgeneratorsinthepaper.
Inthefifthpart, E(P )isthecostassociatedwithutilizingreversestocompensatetheerrors
i,r,t
whenthepredictionoutputislargerthantheactualRESgeneration. Wedefineρ astheprobabilityof
s
scenariosanddenoteNSasthenumberofscenarios.
ThesixthpartincludestheequationonthethirdlineoftheEquation(1),whichrepresentsthe
penaltyoflithiumbatterydegradationinEVs. Theseventhpartλ Ploss presentsthepenaltyofthe
2 i,t
powerlossraisedbythepowertransmissionamongMGs. Duetothelineresistance,powerlossis
inevitablewhilethesurplusistransportedfromoneMGtoanother.Toalleviatethepowertransmission
loss,aMediumVoltage(MV)betweentwogridsisused. Accordingto[10,13],thepowertransmission
lossescanbeobtainedthrough
R Q2
P = i,l i,l,t (2)
loss V2
whereR isthelineresistancebetweenMGiandl,andV indicatesthetransfervoltagebetweenthe
i,l
interconnectedMGs. Inordertofacilitatethemanagementofthesystem,alltransfervoltagesbetween
differentMGsareconsideredtobethesamevalue.
The eighth part, which is located after the last plus sign, represents the tariff compensation,
enablingarealisticconsiderationofresidents’behaviors. Inreal-worldpractice,alltheconsumers
tendtochargeEVsatalowerelectricitypriceinterval. Nonetheless,duetothelimitationofloadand
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generation capacities, it is impossible to depose all the EVs in the same time slot. To this end, the
aggregatorcandeferaportionofEVstoothertimeslotswithmoreRESsandlowloads. Noticethat
thisbehaviorviolatestheconsumer’saspirationandincursanextracostsincethechargingoccurs
athighpriceslots. Tothisend,itisessentialtointroducetariffstomakeupfortheresidentialusers’
additionaloverheadraisedbynotbeingchargedattheirdesiredslots. Inparticular,withtheincrease
ofµ,morecompensationcanbepaidandthenumberofEVscanbesignificantlyreducedtoo.
SOPconstraints:
Intheoptimizationproblem,theconstraintsneedtobeconsideredaswell. Thefirstconstraint
is to balance power. For each MG in the system, the following power balance constraint needs to
be satisfied:
The first constraint is to balance the power. For each MG in the system, the following power
balanceconstraintneedstobesatisfied:
ni,t NG
P + ∑ Q + ∑ Pcha ×I = ∑ P +
load,i,t i,l,t EV,i,t,k i,t i,j,t
l(cid:54)=i k=1 j=1
Pi,r,t+PPv,i,t+PWind,i,t+ ∑ Ql,i,t− ∑ Qloss,l,i,t (3)
l(cid:54)=i l(cid:54)=i
ni,t
+ ∑ Pdis I ∀i,t
EV,i,t,k i,t
k=1
where the left parts in the equality indicate the the local units generations, RES generations
(e.g., solar and wind), the discharged power from EVs, and the transported power from other
MGs,therightpartspresenttheamountofdemand,whichconsistsofnon-EVloads,theamountof
powerchargedtotheEVs,powerlossesresultedfromlineresistance,andtheamountofthesurplus
powertransmittedtootherMGs.
Second,thelocalunitsconstraintsshouldbesatisfied. Recallthatthefuelconsumptionfeatures
ofdieselgeneratorsarevariedduetodifferentlevelsofpowerrated. Ingeneral, thefuelusedfor
theunitpowergenerationwillreduceastheincreaseoftheratedlevelofpowerusedbygenerators.
To describethecharacteristicofdieselgenerators,weusealinearmodelforthefuelconsumptionthat
considersdifferenttypesofgenerationsby[14]:
FC = a P +b P ,∀i,j,t (4)
i,j i,j i,j,t i,j rated,i,j
where FC is the fuel consumption of diesel generator j in MG i. For the operation cost of diesel
i,j
generators,weusethecostmodeldevelopedby[15]asfollows:
(cid:0) (cid:1)
Cost P = α x +β P , ∀i,j,t (5)
i,j,t i,j i,j,t i,j i,j,t
wherethe Cost(.) representstheoperationcostofdieselgenerator j inMG i. Inaddition, theunit
operationconstraintscanbeexpressedas:
Pminx ≤ P ≤ Pmaxx
i,j i,j,t i,t,j i,j i,j,t
(cid:0) (cid:1)
Pi,j,t−Pi,j,t−1 ≤ Rui,j (cid:0)1−yi,j,t (cid:1)+Pim,jinyi,j,t (6)
Pi,j,t−1−Pi,j,t ≤ R(di,j 1−zi,j,t +Pim,jinzi,j,t
yi,j,t+zi,j,t ≤1,yi,j,t−zi,j,t = xi,j,t−xi,j,t−1
where the first constraint indicates the power limit of the diesel generator, the second and third
constraintsshowtheramp-up/downlimits,andthefourthconstraintindicatestherelationshipamong
thedifferentoperationstatusesofgenerators.
In addition, notice that the unlimited integration of EVs is unrealistic. Thus, the scale of EVs
should be constrained. The number of vehicles, including CVs and EVs, can be estimated by the
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analysisbasedonthenumberofresidentsineachMG.Weleveragethemodeldevelopedin [6,16]to
conducttheestimation. Then,wehave
R Q D
N = V2G REC Total (7)
R
D
Average
whereD indicatesthetotalloaddemandineachMGperday. D istheaveragedailyelectricity
total Average
consumptionofresidents,whichisequalto2.0833kWaccordingtheresultsin[6]. Q isthevehicle
REC
ownershiprateofresidents,andR istheproportionofresidentswhoparticipateintheV2Gplan.
V2G
Apparently,withthepopularityofthevehicles,itisreasonabletoassumethatQ =1. Inthispaper,
REC
weconsiderthatalltheresidentsuseV2GtechnologysothatR = 100%. Thus,therelationship
V2G
betweenvehiclescaleandthenumberofresidentsisderivedasfollows:
NT
N = ∑ ncha
EV,i i,t (8)
t=1
N = N = N +N ,∀i
V,i R,i EV,i CV,i
wherethefirstequationindicatesthatthenumberofEVsiscomputedbythesumofEVsineachtime
slot. ThesecondequationsmeansthatthenumberofvehiclesiscomposedofCVsandEVs.
Withconsiderationofloadlimits,wealsoassumethatthesumofthenewlyaddedloadcaused
byEVchargingandnon-EVloadshouldnotbelargerthanthemaximumloadcapacity(Pmax )at
load,i
eachtimeslot. Tothisend,thefollowingconstraintisproposedtoprotectthesystemfromgenerating
newloadpeaks:
ncha
i,t
∑ Pcha I +P ≤ Pmax (9)
EV,i,t,k i,t load,i,t load,i
k=1
where the left parts in the inequality are the consumptions of EVs and non-EV loads, and Pmax
load,i
indicatesthelimitationsofloadinMGi.
Finally,thecharginganddischargingconstraintsofEVsshouldbeconsideredaswell.
NT
0≤ ∑ Pcha I ≤ PMax
EV,i,t,k i,t EV
t=1
NT
0≤ ∑ Pdis U ≤ (1−φ )PMax
EV,i,t,k i,t min EV (10)
t=1
(cid:18) (cid:19)
φ PMax ≤ N∑T ηchaPcha I − PEdVis,i,t,kUi,t ≤ PMax
min EV EV,i,t,k i,t ηdis EV
t=1
I +U =1
i,t i,t
Here,thefirsttwoconstraintsillustratethecharginganddischarginglimits,andtheφ refers
min
totheminimumbatteryenergystoragefortheregulardrivingofEVs. Thethirdoneguaranteesthe
storedpowerinEVs. Thelastconstraintisusedtoavoidthesimultaneousoperationofchargingand
dischargingatthesametimeslot.
3.2.2. DeterministicOptimalPenetration(DOP)Model
IncomparisonwiththeperformanceoftheSOPmodel,aDeterministicOptimalPenetration(DOP)
modelisformulatedasabaselinescheme,inwhichtheparametersassociatedwiththeuncertainties
(ambienttemperature,windspeed,etc.) arebasedonapersistpredictionandtheelectricitypricesare
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forecastedbypredictiontechniques[11]. TheconstraintsfromEquations(2)to(10)shouldalsobe
satisfied. Tothisend,weintroducethefollowingDOPmodelasthebaselinescheme:
(cid:40) (cid:34) (cid:35)
NMNT NG
∑ ∑ ∑ (cid:0) (cid:1)
2min w E P +E (N )
i,j,t CV CV,i
i=1t=1 j=1
(cid:34)
NG NG
∑(cid:0) (cid:1) ∑ (cid:0) (cid:1)
+(1−w) SU y +SD z + Cost P
i,j i,j,t i,j i,j,t i,j,t
j=1 j=1
 ndis 
i,t (11)
+λ1ηchan∑ic,htaPEchVa,i,t,kIi,t+ k∑=1PEdηVisd,iis,t,kUi,t
 k=1 
NR ni,t (cid:35)(cid:41)
+ ∑ E(P )+λ P + µ ∑ Pcha (r −r )
i,r,t 2 loss EV,i,t,k t min
r=1 k=1
Here,thefirstandsecondpartsintheDOPmodelindicatetheemissioncostraisedbythelocalunits
andCVs. Thethirdandfourthpartsarethestartup/shutdownandoperationcostoflocalgenerators.
ThefifthandsixtharethepenaltyofbatterydegradationofEVsandthepowerlosscreatedbypower
transmission among local MGs. The seventh part part is the tariff compensation to make up the
overheadoftheusersforcharingEVsatthetimeslotswithhigherprices.
Notice that, in comparison with the SOP model, the uncertainties of the renewable energy
resources are not considered and addressed. In addition, as essential energy resources in the
"archipelago microgrids", the uncertainties raised by RESs could affect the operation of system.
Therefore, the DOP model will result in a higher operation cost than the SOP model. Because of
this,moretraditionalenergyresourcescouldbeutilizedtocompensateforthepredictionerrorsofthe
generationfromRESs(i.e.,theactualgenerationissmallerthantheprediction). Tothisend,theDOP
modelisproposedasabaselineschemetoevaluatetheeffectivenessoftheproposedSOPmodel.
3.3. ProposedSchedulingSchemes
We now present the two proposed scheduling schemes to carry out the optimal scale of EVs
effectively. Todemonstratetheeffectivenessofthetwoschemes,abaselineallocationschemeforEVs,
namedUncoordinatedAverageScheme(UAS),isalsoconsidered. Inthefollowing,wedescribethese
threeschedulingschemesindetail.
3.3.1. UncoordinatedAverageScheme(UAS)
Sincethenon-EVloadsareinflexible,theaverageallocationmethodforEVsisafeasiblewayto
reducetheemission. IntheUAS,thesurplusofpowerisusedtosupplyloadspreferentially,andthen,
theremainingpowerisusedtochargeEVs. ByaccumulatingallthesurpluspowerineachMG,the
maximumallowablenumberofEVscanbederived. Inparticular,ifthereisnotenoughRESpowerto
meettheaveragedemandofEVsatthetimeslott,theexceededEVswillbedeferredtothenexttime
slot. Byusingthisscheme,wecanplanthemaximumnumberofEVsineachMGtoreachtheupper
limitofvehiclescale. NoticethattheUASistheleastdesirablescenariosincethesurpluspoweris
unabletotransportamonglocalMGs. Itmeansthatalloftheexcessenergyafterfulfillingtheload
andEVschargingwillbedissipated. Inthisscheme,eachMGoperatesasanindependentindividual
withouttheinterconnectionwitheachother,whichwilldirectlyresultinlessaccommodatedEVsand
lowenergyefficiency.