Seite - 204 - in Emerging Technologies for Electric and Hybrid Vehicles

Energies 2016,9, 594 Theexample indicates thatsumminguplocalpredictionsofeventsmaycausepredictionerrors thatwouldnothavebeenmadeatamoreglobal level. Furthermore,predictionsbasedonstatistics alonework ingeneralonly for largegroups,e.g., forneighborhoods insteadofhouses [11].Whenthis observationisusedasawork-aroundintheplanning-basedDSMapproach,detailsaboutuserbehavior andmeasurementsareaccumulatedat theneighborhoodcontroller level suchthatdecisionsmaybe madetherebasedonprobabilitiesover largegroups (insteadofwithin thehouse).However, suchan approachwouldnolongerbe (decentralized)DSM,but is, e.g., closer todemandresponse [1]andno longerdistributed. Furthermore, itwouldrequiresharingofprivacysensitive information. Thegoal of thisarticle is toavoidthementionedrestrictions. Summarizing,wemaystate that robustdemand sidemanagementshouldonlyrelyonhouse levelpredictions if thismethodology is robustagainst predictionerrors. 2.3.GroupsofElectricVehicles For the application of EV charging, the state-of-the-art research onDSM (see, e.g., [13–17]) requiresEVowners toshare information(e.g.,EVarrival)withacentralizedcontroller. Theapproach presented in thisarticledoesnot requiresuchsharingofprivacysensitive informationandhasa low communicationfootprint. TheapproachORCHARDpresentedin[14]alsoflattenstheloadprofileforagroupofEVswithout requiringknowledgeof futureEVarrivals. Ithasa timecomplexityofO(N5) forNEVsandissimilar toourwork in thesense thatwealsodonotknowaboutEVarrivalsbeforehand. Contrary to [14], ourworkrequiresO(M logM) time(forM timeintervals)whenanEVarrives (withineachhouse). Furthermore,ourresearchflattens the loadbothat thehouse levelandat theneighborhoodlevel. 3.OnlineElectricVehiclePlanning Thissectiondescribes for thecaseofcharginganElectricVehicle (EV)howahousecanfollow someprofile, forexample tomakethe loadprofileasflataspossible,byusingproperchargingsettings. Section3.1 introduces thecorrespondingEVplanningproblem. Section3.2presentsourapproach, whichis inspiredbyonlineoptimization,rollinghorizonplanning,andmodelpredictivecontrol: at the startofeverytimeinterval,weuseapredictionof thepowerfor this interval togetherwithaprediction ofasinglevalue thatcharacterizes therequirements for the future intervals todetermine thecharging power for thenext timeinterval. Bydelaying thedecision for theamountofchargingdone inan intervaluntil theverystartof this interval,wecanhopethatmoreaccuratepredictionsarepossible. Furthermore,wecancompensate forerrorsmade inprevious time intervals. Finally,Section3.3discusses the influenceofprediction errorsonthisalgorithm. 3.1. TheEVChargingProblem Wefirst introducesomenotationbeforewegivea formaldefinitionof theEVplanningproblem. Let anbe the time intervalatwhich theelectricvehiclearrivesathousen∈{1,. . . ,N}andis ready tobecharged, letdnbethe the intervalatwhichthecharginghas tobecompleted,andletCnbethe energythatneeds tobechargedin the intervals an, . . . ,dn. TheEVchargingdecisionscanbedescribed byavector xn=(xn,1, . . . ,xn,M),wherexn,m is theamountofelectricitychargedforvehiclenduring timeintervalm. Themaximumchargingpower isgivenby x¯ (inwatts), andthevector xn is feasible ifxn,m= 0 form< an andm> dn , 0≤ xn,m≤ x¯ in theremaining intervals, and∑dnm=an τxn,m=Cn, whereτ is the lengthofa timeinterval. Toease thenotation,weuseτ=1. Let thedesiredpowerprofile for thehouseandEVloadtogetherbe qn. Thegoal is todetermine achargingvector xn such that theuncontrollablehousepowerconsumption ( pn) togetherwith the charging xnmatches thisdesiredpowerprofile qn aswell aspossible. Moreprecisely,we look for avector xn thatminimizes theEuclideandistancebetweenthevectors qn and ( pn+ xn). Toexpress the differencebetweentheactualanddesired load,wedefinezn,m := pn,m+xn,m−qn,m,m∈{1,. . . ,M}. 204