Page - 212 - in Emerging Technologies for Electric and Hybrid Vehicles

Energies 2016,9, 594 Zn, thedeterministicEVplanningalgorithmfrom[4]canbeused,and,as indicated in thispaper, this algorithmcancalculate theresult inorderofmillisecondsandhasa timecomplexityofO(M logM). Sinceweuse thisapproachforeachEVthatarrives,ourapproachhasacomplexityofO(KM logM), forKEVs. Charging the EVwithin a relatively short interval, such as the interval between 18:00 and 24:00 above, results in a relatively high charging power, especially if the charging amountCn is also relatively high. This results in a profile whereinmost intervals are used for charging (i.e., In is close to the totalnumberof intervals) and theprofile itself isflat (i.e., it precisely reachesZn). Whena longer charging interval is takenwithmultiplehigherpeaks (e.g., during thedayand/or evening), the charging is spread out and done at lower power. To illustrate this, we repeat the experimentwithachargingbetween14:00and24:00 (whenconsumption ishighest). Theachieved results areaspresented inTable2. Note that, in this table, thevalues In aremorediverse since the house consumptionplays a larger role. Note that In canbe interpretedas thenumberof intervals with lowhouseconsumptioncomparedto thefill levelZn. Sinceevenwitha longcharginghorizon, thevariation in In is small, this isanadditional indicationthatourassumptionfromthe last section that In is (almost)constant is reasonable. Theresultsalso indicate that In iseasytopredict, andthis canbedonesimilar to (andsimultaneouslywith)obtaining Zˆn, aswasdescribedabove. Tomakethisoverviewcomplete,weconsideredthehighest chargingpower (Max. power)within eachday,andpresent theminimum,medianandmaximumof thisvalueover the90days inTables1 and2,andtheresults showthat thesevaluesgrowapproximately linearlywithCn. Table2.AnalysisofZn andCn for90days forchargingbetween14:00and24:00. Cn (kWh) Zn In Max.Power √ Zˆ Z C(Zˆ) C(Z) Min Med Max Min Med Max Min Med Max Min Med Max 6 809 1057 1268 31 35 40 749 969 1184 1.25 1.00 1.06 1.18 12 1409 1721 1962 35 38 40 1349 1627 1851 1.18 1.00 1.06 1.15 18 2009 2340 2603 37 39 40 1949 2253 2468 1.14 1.00 1.05 1.12 24 2609 2943 3221 39 40 40 2549 2859 3079 1.11 1.00 1.04 1.10 6. Evaluation In this section,wecompareourworkwith thestate-of-the-art researchandseveralothercharging strategies. Thebasicvariantofourapproachaimstomakethehouse loadasflataspossiblewithout coordinationbetweenthehousesandisdenotedbyNOCOORD.Theextensionof this techniquethat shaves the neighborhoodpeakby adding coordination is referred to byCOORD. For both of our approaches,wemakepredictionsuponarrivalof theEVsusingtheapproachfromtheprevioussection with tendaysofhistoricaldataas input.Wecompareourapproacheswith thestate-of-the-art research onProfileSteering (PS) from[2]. Theprofilesteeringalgorithmisaheuristic thatpredicts the load of eachhouse,makes aplan that is asflat aspossible, and coordinates betweenhouses to further flattenthe loadpeak. Inorder tocomparewiththebestpossiblebehaviorofPS,weassumeperfect predictions forprofilesteering,whichgives thisapproachasignificantadvantage. Forcompleteness, wealsocomparetonocontrol (NC),whereEVschargeatfullpoweratarrival,andwithagridunaware peak-shaving (PEAKS),which is a simpleapproach that iteratively selectsEVsanddecreases their chargingasmuchaspossibleuntil thedesired loadat the transformer isaccomplished. Toeffectivelycompareallapproacheswith thestate-of-the-art research,wereproducethecase usedin[2]. It considers121houses,all equippedwith identicalelectricvehicles thatcharge12kWh between18:00and07:00andhaveamaximumchargingpowerof3.8kW.Weusedthesamedataset andnetworkfilesasusedin[2] tocalculate the loadflowstoobtaintheactivepowerat thetransformer (incl. losses), the lowestobservedvoltage in thegridandthehighestobservedvoltage in thegrid. For COORDandPEAKS,weneedtoseta limit for thepeak-shavingbytheneighborhoodcontroller, and 212