IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 25, NO. 1, FEBRUARY 2010 371The Impact of ChargingPlug-In Hybrid ElectricVehicles on a Residential Distribution GridKristien Clement-Nyns, Edwin Haesen, Student Member, IEEE, andJohan Driesen, Member, IEEEAbstractAlternativevehicles, suchasplug-inhybridelectricvehicles, are becoming more popular. The batteries of these plug-inhybrid electric vehicles are to be charged at home from a standardoutlet or on a corporate car park. These extra electrical loads haveanimpactonthedistributiongridwhichisanalyzedintermsofpowerlossesandvoltagedeviations.Withoutcoordinationofthecharging,thevehiclesarechargedinstantaneouslywhentheyarepluggedinorafteraxedstartdelay.Thisuncoordinatedpowerconsumption on a local scale can lead to grid problems. Therefore,coordinated charging is proposed to minimize the power losses andto maximize the main gridloadfactor. The optimal charging proleoftheplug-inhybridelectricvehiclesiscomputedbyminimizingthe power losses. As the exact forecasting of household loads is notpossible, stochasticprogrammingisintroduced. Twomaintech-niques are analyzed: quadratic and dynamic programming.Index TermsCoordinated charging, distribution grid, dy-namicprogramming, plug-inhybridelectricvehicles, quadraticprogramming.I. INTRODUCTIONHYBRIDelectric vehicles (HEVs), batteryelectric ve-hicles (BEVs) and plug-in hybrid electric vehicles(PHEVs)arebecomingmorepopular.PHEVsarechargedbyeitherpluggingintoelectricoutletsorbymeansofon-boardelectricity generation. These vehicles can drive at full power inelectric-only mode over a limited range. As such, PHEVs offervaluablefuelexibility[1].PHEVsmayhavealargerbatteryand a more powerful motor compared to a HEV, but their rangeis still very limited [2].The charging of PHEVs has an impact on the distribution gridbecause these vehicles consume a large amount of electrical en-ergy and this demand of electrical power can lead to extra largeand undesirable peaks in the electrical consumption. There aretwo main places where the batteries of PHEVs can be recharged:either on a car park, corporate or public, or at home. The focusinthisarticleliesonthelatter.Theelectricalconsumptionforcharging PHEVs may take up to 5% of the total electrical con-sumption in Belgium by 2030 [3]. For a PHEV with a range of60 miles (100 km), this amount can increase to 8% taking intoaccountautilityfactorwhichdescribesthefractionofdrivingthat is electrical [4].Fromthe distributionsystemoperator point of view, thepower losses duringchargingareaneconomicconcernandManuscriptreceivedMay27, 2009;revisedJuly27, 2009. FirstpublishedDecember 18, 2009; current versionpublishedJanuary20, 2010. Paper no.TPWRS-00097-2009.TheauthorsarewiththeDepartmentofElectricalEngineering,KatholiekeUniversiteit Leuven, 3001 Heverlee, Belgium (e-mail: Kristien.Clement@esat.kuleuven.be).Digital Object Identier 10.1109/TPWRS.2009.2036481havetobeminimizedandtransformer andfeeder overloadshavetobeavoided. Not onlypower losses, but alsopowerquality(e.g., voltageprole, unbalance, harmonics, etc.) areessential tothedistributiongridoperator as well as togridcustomers. Voltage deviations are a power quality concern.Toolargevoltagedeviationscausereliabilityproblemswhichmust beavoidedtoassuregoodoperationof electricappli-ances. Overnight rechargingcanalsoincreasetheloadingofbase-load power plants and smoothen their daily cycle or avoidadditional generator start-ups which would otherwise decreasethe overall efciency [5]. From the PHEV owner point of view,thebatteriesofthePHEVhaveto bechargedovernight sothedriver can drive off in the morning with a fully-charged battery.Thisgivesopportunitiesforintelligentorsmartcharging.Thecoordinationofthechargingcouldbedoneremotelyinordertoshiftthedemandtoperiodsoflowerloadconsumptionandthus avoiding higher peaks in electricity consumption.Thisresearchtsinamoreglobalcontextwherealsoothernew technologies, such as small wind turbines and photovoltaiccells, are implemented in the distribution grid. In this optimiza-tion problem, only power losses and voltage deviations are mini-mized. Other aspects, e.g., power factor control, can be includedas well. The proposed methodology can help evaluating plannedgrid reinforcements versus PHEV ancillary services to achievethe most efcient grid operation.Thisarticlewantstoemphasizetheimprovementsinpowerquality that are possible by using coordinated charging or smartmetering. It also wants to indicate that uncoordinated chargingof PHEVs decreases the efciency of the distribution grid.II. ASSUMPTIONSAND MODELINGA. LoadScenariosFromanavailablesetofresidentialloadmeasurements[6],twolargegroupsofdailywinterandsummerloadprolesareselected. The load proles cover 24 hours and the instantaneouspower consumption is given on a 15-min time base as shown inFig. 1 for an arbitrary day during winter.B. SpecicationsofPHEVsEachofthePHEVshasabatterywithamaximumstoragecapacity of 11 kWh [5]. Only 80% of the capacity of the batterycanbeusedtooptimizelifeexpectancy. Thisgivesanavail-ablecapacityof8.8kWh;10kWhisrequiredfromtheutilitygrid,assumingan88%energyconversionefciencyfromACenergyabsorbedfromtheutilitygridtoDCenergystoredinthe battery of the vehicle [4]. The batteries can only be charged0885-8950/$26.00 2009IEEE 372 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 25, NO. 1, FEBRUARY 2010Fig. 1. Household load during winter [6].Fig. 2. Percentage of trips by vehicle each hour [8].andnotdischarged, meaningthattheenergyowisunidirec-tional and the vehicle-to-grid concept is not considered yet. Thecharger has a maximum output power of 4 kW. The charger of 4kW is chosen because the maximum power output of a standardsingle phase 230 Voutlet is 4.6 kW. Therefore, this is the largestchargerthatcanbeusedforastandardoutletathomewithoutreinforcing the wiring. Fast charging is not considered becauseit requires a higher short-circuit power which is not available atstandardelectric outletsin households.For fastcharging, con-nectionsatahighervoltagelevelareindispensable. Ahighervoltageconnectioncouldbeinstalled, but thisisanextrain-vestmentforthePHEVowner.Themaximumpenetrationde-gree of PHEVs is 30% by 2030 for Belgium as predicted by theTremove model [7].C. ChargingPeriodsIt is not realistic to assume that PHEVs could be charged anyplaceastandardoutletispresent.Thereforeinthisarticle,thebatteriesofthevehiclesareassumedtobechargedat home.Fig. 2showsthepercentageofalltripsbyvehicleeachhour.Atthatmoment,theyarenotavailableforcharging.BasedonFig. 3. IEEE 34-node test feeder [9].this gure, three important charging periods are proposed. Therstchargingperiodisduringtheeveningandnight. Mostofthe vehicles are at home from21h00 until 06h00 in the morning.Some PHEVs are immediately plugged in on return from workinordertobereadytousethroughout theevening. Thusthesecond charging period takes place between 18h00 and 21h00.Thischargingperiodcoincideswiththepeakloadduringtheevening. Thenumberofvehiclesthat will bechargedduringthis period will probably be smaller. One other charging periodis considered, that is charging during the day between 10h00 and16h00. The charging will occur in small ofces in urban areas.It is assumed that only one vehicle per household or ofce canbecharged. Thechargingofmultiplevehiclesatahouseholdorofceisnotconsideredbecauseitisnotfeasibletoreectall possible scenarios. However, the proposed methods are alsovalidforotherperiodsandscenarios.Inthisarticle,thefocuslies on charging at home, in weaker non-dedicated distributiongrids.D. GridTopologyThe radial network used for this analysis is the IEEE 34-nodetest feeder [9] shown in Fig. 3. The network is downscaled from24.9kVto230Vsothisgridtopologyrepresentsaresiden-tial radial network. The line impedances are adapted to achievetolerablevoltagedeviationsandpowerlosses. Eachnodeisaconnection with a residential load and some, randomly chosen,nodes will have PHEVs charging.E. AssumptionsThe exact advantage of coordinated charging depends on theassumptionsmadeinthissection.Thehouseholdloadprolesare typical for Belgium. Other regions may have other load pro-les because of different weather conditions, such as an air con-ditioning peak in the afternoon for warm regions. Some regionswill also have other grid voltages, such as 120 V. The IEEE gridis an example of a distribution grid, so the obtained results areonly valid for this grid. The maximum power of the charger isdetermined by the maximum power of a standard electric outlet.Other parameters which affect the obtained results are the utilityload cycle of the base-load power plants, incentives and the useof smartmeters.III. UNCOORDINATED CHARGINGAt themoment,thereisno smartmeteringsystem availableforPHEVs,sothevehicleswillbechargedwithoutcoordina- CLEMENT-NYNS et al.: IMPACT OF CHARGING PLUG-IN HYBRID ELECTRIC VEHICLES ON A RESIDENTIAL DISTRIBUTION GRID 373tion. Uncoordinated charging indicates that the batteries of thevehicles are either start charging immediately when plugged in,or after a user-adjustable xed startdelay. The vehicle ownerscurrently do not have the incentive nor the essential informationto schedule the charging of the batteries to optimize the grid uti-lization.Thexed startdelayisintroducedtogivethevehicleowner the possibility to start charging using off-peak electricitytariffs.A. LoadFlowAnalysisAloadowanalysisisperformedtoassessthevoltagede-viationsandthepowerlossesintheselecteddistributiongrid.This analysis is based on the backward-forward sweep methodtocalculatethenodecurrents,linecurrentsandnodevoltages[10]. At the initialization step, a at prole is taken for the nodevoltages. Aconstantpowerloadmodel isusedatallconnec-tionsateachtimestep.Inthebackwardstep,thecurrentsarecomputed based on the voltages of the previous iteration. In theforwardstep, thevoltagesarecomputedbasedonthevoltageat the root node and the voltage drops of the lines between thenodes. The currents and voltages are updated iteratively until thestopping criterion based on node voltages is reached.B. MethodologyAtthestartofa24-hcycle, adailyproleisrandomlyse-lectedfromtheavailableset belongingtoaspecicscenario(winter, summer) and assigned at each node. For each scenario,four cases depending on the penetration degree are selected. Therst case, with no PHEVs, is taken as a reference case. The nextcases have a PHEV penetration of, respectively, 10%, 20%, and30% representing the proportion of nodes with a PHEV present.The PHEVs are randomly placed. Separated runs are performedfor each charging period and the number of vehicles is varyingbetween 0% and 30% for each charging period.Theproleforcharging thePHEVs iskeptstraightforward.Eachindividualvehiclestartschargingatarandomtimestepwithinaspecicperiodoftimesuchthatthevehiclesarestillfullychargedattheendofthechargingperiod.Itisassumedthat the batteries of the vehicles are fully discharged at the rsttimestep.Foreveryquarterofanhour,thebackward-forwardsweep method is repeated to compute the voltage at each nodeuntil convergence is obtained.C. ResultsThe impact of uncoordinated charging on the distribution gridis illustrated by computing the power losses and the maximumvoltage deviation for the different charging periods. The numberof samples is 1000, which is large enough to achieve an accurateaverage per scenario. Taking more samples does not change theresults signicantly.The results for the 4 kW charger are shown in Tables I and II.Table I depicts the ratio of the power losses to the total load. Thetotal load includes the daily household loads and the charging ofthe PHEVs, if present. In all cases, the power losses are higherin the winter season than in the summer season due to the higherhousehold loads. The increase of the number of PHEVs leads toasignicantincreaseinpowerlosses.Thesepowerlossesareimportant for the operator of the distribution grid. The distribu-TABLEIRATIOOFPOWERLOSSESTOTOTALPOWER[%]FORTHE4kWCHARGERIN CASEOF UNCOORDINATED CHARGINGTABLE IIMAXIMUMVOLTAGEDEVIATIONS[%] FORTHE4kWCHARGERIN CASEOF UNCOORDINATED CHARGINGtionsystemoperator(DSO)willcompensatehigherlossesbyincreasing its grid tariffs.Not only the power losses, but also the voltage deviations ofthe grid voltage (230 V) which are represented in Table II, areimportantfortheDSO.AnincreaseinthenumberofPHEVsleads to a signicant increase in voltage deviations. Accordingto the mandatory EN50160 standard [11], voltage deviations upto 10% in lowvoltage grids, for 95%of the time, are acceptable.Table II shows that for a penetration of 30%, some of the voltagedeviations are close to 10%, especially during evening peak.Thepowerlossesandthevoltagedeviationsarethehighestwhilechargingduringtheeveningpeak, between18h00and21h00. The reasons are twofold. In the rst place, this chargingperiod, whereinthebatteriesmust befullychargedisrathershort, only 4 hours. Therefore, the charger output power must behigher. Secondly, the household load during the evening is thehighest of the whole day and the output power of the charger isadded to the household loads. Charging during the day is a littlemore demanding for the grid compared by charging overnight.These results are directly related to Fig. 1.Fig. 4 depicts the voltage prole in a node of the distributiongrid for a penetration degree of 0%and 30%during winter night.This gure shows two charging examples and is not the averageofseveralsamples. Clearly, thereisadecreaseofthevoltagein thepresenceofPHEVs duringthecharging periodbetween21h00 and 06h00. Between 23h00 and 04h00, most of the vehi-cles are charging and the voltage drop during these hours is thelargest and deviates the most fromthe 0%PHEVvoltage prole.Thepowerneededforchargingthesevehiclesissignicantlyhighercomparedtothehouseholdloadsduringthenight.Thesmall difference in voltage deviations during the rest of the dayis caused by the different load proles selected for both cases.IV. COORDINATED CHARGINGIntheprevioussection, thechargingofthebatteriesofthePHEVs starts randomly, either immediately when they are 374 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 25, NO. 1, FEBRUARY 2010Fig. 4. Voltageproleinanodewith30%PHEVscomparedtothevoltageprole with 0% PHEV.plugged in, or after a xed start delay. The idea of this sectionis to achieve optimal charging and grid utilization to minimizethe power losses. A direct coordination of the charging will bedone by smart metering and by sending signals to the individualvehicles.This optimization problem can be tackled with the quadraticprogramming technique (QP). This technique optimizes aquadraticfunctionofseveralvariables, inthiscasethepowerofthePHEVchargersatalltimesteps, whichissubjectedtolinearconstraints.Inthissection,theQPtechniqueisappliedto handledeterministic andstochastic householdloadproles.The objective is to minimize the power losses.A. OptimizationProblemBy minimizing the power losses, the owners of PHEVs willno longerbe ableto controlthecharging prole. The only de-greeoffreedomleftfortheownersistoindicatethepointintimewhenthebatteriesmustbefullycharged. Forthesakeofconvenience,theendoftheindicatedchargingperiodistakenasthepointintimewhenthevehiclesmustbefullycharged.Thecharging powervaries between zeroandmaximumandisno longer constant. The coordinated charging is analyzed for thesame charging periods as described in the previous section. Therange of PHEV penetration levels remains the same, and the ve-hiclesarealsoplacedrandomly.ThesameIEEE34-nodetestgridisused. Foreachchargingperiodandseason, thepowerlosses and voltage deviations are calculated and compared withthe values of uncoordinated charging.B. MethodologyTheobjectiveis tominimizethe power losses whicharetreatedasareformulationofthenonlinear powerowequa-tions. Thisnonlinearminimizationproblemcanbetackledasasequential quadraticoptimization[12]. Thechargingpowerobtainedbythequadraticprogrammingcannotbelargerthanthe maximum power of the charger . The batteries must befully charged at the end of cycle, so the energy which ows tothe batteries must equal the capacity of the batteries .is zero if there is no PHEV placed and is one if there is a PHEVFig. 5. Algorithm of coordinated charging.atnode .Thegoalistominimizepowerlosseswhiletakinginto account these constraints. The quadratic programminguses(1)and (2):(1)(2)C. Deterministic ProgrammingFig. 5 represents the outline of the algorithm of coordinatedcharging.The vehicles areplacedrandomlyafter theselectionof a daily load prole and the number of PHEVs. A at voltageproleisassumedandthenodevoltagesarecomputedwiththebackward-forwardsweepmethodassumingthat therearenoPHEVs. Thebackwardandforwardsweepareformulatedasamatrixmultiplication. Thequadraticoptimizationisper-formed in order to determine the optimal charging prole. Then,the node voltages are computed again. This process is repeateduntil the power losses based stopping criterion is reached.This paragraph describes the results of the coordinatedcharging to illustrate the impact on the distribution grid.TableIIIandTableIVrepresentrespectivelythepowerlossesand the maximumvoltage deviations for the coordinated CLEMENT-NYNS et al.: IMPACT OF CHARGING PLUG-IN HYBRID ELECTRIC VEHICLES ON A RESIDENTIAL DISTRIBUTION GRID 375TABLEIIIRATIOOFPOWERLOSSESTOTOTALPOWER[%]FORTHE4kWCHARGERIN CASEOF COORDINATED CHARGINGTABLE IVMAXIMUMVOLTAGEDEVIATIONS[%] FORTHE4kWCHARGERIN CASEOF COORDINATED CHARGINGFig. 6. Voltage prole in a node with 30% and 10% PHEVs compared to thevoltage prole with 0% PHEV for coordinated charging.chargingduringthedifferent chargingperiods. TheseresultsmustbecomparedwithTableIandTableII.Forallchargingperiods andseasons, the power losses are decreasingif thecoordinatedchargingisapplied.Thevoltagedeviationsareinaccordancewith EN50160 standard andthemaximum voltagedeviationforapenetrationdegreeof30%isnowwell below10%. IftherearenoPHEVspresent,chargingduringthedayandthenightgivesmoreorlessthesameresults.However,ifthenumberofPHEVsisincreased,thevoltagedeviationsandthe power loss increases are larger for charging during the daythan during the night.Fig. 6shows that the maximumvoltage deviationduringovernight charging when no PHEVs are involved, occurs at thebeginningof thechargingperiodwhenthehouseholdloadsare still high. Apenetrationdegree of 10%gives the samevoltagedeviations, meaningthat thevehiclesarenot chargedFig.7. Loadproleofthe4kWcharger forthechargingperiodfrom21h00until 06h00 during winter.whenthehouseholdloadpeakoccurs. Thevehiclescauseanextraloadduringtheoff-peakhourstoobtaintheobjectivetominimize the power losses. The voltage deviations during theseoff-peakhoursissmallercomparedtothevoltagedeviationsdue tothe householdloads duringthe eveningpeak. For avehicle penetrationof20%ormore,thenumberofvehicles isincreased, and the charging is more distributed. Some vehiclesarechargingduringpeakhoursandthisincreasesthevoltagedeviation and thus lowers the voltage.Fig. 7 shows the load proles of the nodes 1 and 33 of Fig. 3withapenetrationdegreeof30%duringthechargingperiodfrom 21h00 until 06h00 during winter. The nodes are chosen atthe starting and end point of the grid feeder. It is clear that thepower output of the charger is not constantly 4 kW, but varies.D. Stochastic ProgrammingThe previous results are based on deterministic or historicaldataforthedailyloadproles.Sotheessentialinputparame-ters are xed. For this approach, a sufcient number of measure-mentdatamustbeavailable.Mostofthetime,however,thesemeasurements are not adequate to perform a perfect forecastingof the data. A stochastic approach in which an error in the fore-casting of the daily load proles is considered, is therefore morerealistic.The daily load proles are the essential input parameters. Theuncertaintiesoftheseparameterscanbedescribedintermsofprobabilitydensityfunctions. Inthat way, thexedinput pa-rameters are converted into random input variables with normaldistributions assumed at each node. independent samples ofthe randominput variable , the daily load prole, are selected.Equation (3) gives the estimation for the stochastic optimum. The function gives the power losses and isthe power rate of the charger for all the PHEVs and time steps.isasample-averageapproximationoftheobjectiveofthestochastic programming problem:(3) 376 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 25, NO. 1, FEBRUARY 2010The mean value of the power losses, , is a lowerbound for the real optimal value of the stochastic programmingproblem, [13], as shown in (4):(4)can be estimated by generating independent sam-ples oftherandominputvariableeachofsize . op-timizationrunsareperformedinwhichthenonlinear powerowequations are solved by using the backward-forward sweepmethod. According to (5), is the mean optimal value of theproblem for each of the samples. The optimal values of thesamples constitute a normal distribution:(5)In (6), is an unbiased estimator of . Simulationsindicate that in this type of problem, the lower bound convergesto the real optimal value when is sufciently high:(6)Aforecastingmodel forthedailyloadproleforthenext24 h is required. The daily load proles of the available set arevaried by a normal distribution function. The standard deviationis determined in such a way that 99.7% of the samples vary atmaximum 5% or 25% of the average .E. ResultsFor 2000 independent samples of thedaily load prole, oneoptimal chargingproleiscalculated. Thisoptimal chargingproleisusedtodeterminethepowerlossesforthe2000in-dividual load proles. This is the stochastic optimum. For eachof these 2000 load proles, the optimal charging prole and thecorresponding power losses are also computed, which is the de-terministic optimum.The power losses of the deterministic optimumare subtractedfrom the power losses of the stochastic optimum and divided bythe deterministic optimum, dened as . This is shown for avariation of the household loads of 5 and 25% in Figs. 8 and 9,respectively. The value of this difference is always positive. TheforecastingofthedailyloadprolesintroducesanefciencylossbecausethechargeprolesofthePHEVs arenotoptimalforthisspecicdailyloadprole.Ifthestandarddeviationofthe normal distribution and thus the variation of the householdloadisreduced, the2000chargeprolesofthedeterministicoptimumwillconvergetotheoptimalchargeprole. Theef-ciency loss will also reduce indicating that the power losses ofthe differences will go down by a factor 25 as shown in Fig. 8compared to Fig. 9.Ingeneral, thedifferencebetweenthepowerlossesofthestochasticandthedeterministicoptimumisrathersmall. Itisclear that theerror inforecastingdoes not havealargeim-pact onthepower losses. Thedailyhouseholdloadprolesduring the winter season show the same trend each day duringFig. 8. Histogram of the efciency loss of an arbitrary day during winter for avariation of5%.Fig. 9. Histogram of the efciency loss of an arbitrary day during winter for avariation of25%.Fig. 10. Deterministic optimum and optimal charger prole for node 33.winter season resulting in a optimal charge prole which resem-bles a deterministic charge prole of a specic day as shown inFig.10forthelastnodeofthetestgrid. Bothchargeproleshave the same trend. Therefore, the contrast in terms of power CLEMENT-NYNS et al.: IMPACT OF CHARGING PLUG-IN HYBRID ELECTRIC VEHICLES ON A RESIDENTIAL DISTRIBUTION GRID 377Fig. 11. Histogram of the efciency loss of an arbitrary day during winter forother household proles.losses between the deterministic and stochastic optimum is notlarge.However,thedifferencebetweenuncoordinatedandco-ordinatedchargingismuchlargerbecausethechargeprolesaremore different.Theuncoordinatedcharginghasaconstantcharge prole for a specic amount of time.In Fig. 8 and 9, a specic household load prole is assumedwhich is varied by a normal distribution function. In Fig. 11, theload proles are randomly selected out of a database of house-holdloadproles. Thisdatabasecontainsprolesthat differmoreeachdayandaremorepeakedwhichincreasestheef-ciencylosses.V. DYNAMIC PROGRAMMINGTheoptimal coordinationof chargingPHEVscanalsobetackled by the dynamic programming technique (DP). The QPand DP techniques are compared with respect to results, storagerequirementsandcomputational time. TheDPtechniquede-composestheoriginal optimizationproblemintoasequenceof subproblems which are solved backward over each stage. Aclassical implementation of the DP technique is the shortest pathproblem. For the application of this article, the model is repre-sented as a series of plug-in hybrid electric vehicles.A. MethodologyThereare vehicleswithbatterieschargingandthemax-imum value of corresponds with a penetration degree of 30%.Thebatterycontent of these vehiclesat eachstageisthestatevariable, .Thenumberofstages ,isthenumberof hours of the charging period multiplied by four because thehousehold loads are available on a 15-min time base.Thebackwardrecursiveequationsfortheconventionaldy-namic programming technique are given in (7) and (8):(7)(8)The function represents the total optimal power losses fromperiod to the last period . The vector is a Q-dimensionalvector of the possible storage levels at time . is the powerloss during period and is the battery content of the th ve-hicleattimestage .Thepowerofthechargersisrepresentedby andisalsoa -dimensionalvector.Sotherstcompo-nentofthisvectorgivesthepowerofthechargerfortherstPHEV.Theoutputofthechargerisnotcontinuous,buthasastep size of 400 W. This is relatively large, but smaller step sizeswouldleadtotoomuchcomputational timewhichispropor-tional to [14]. As such, the battery content is also discrete.The constraints of the problem remain the same and are shownin(9)(11):(9)(10)(11)The power loss is the objective function which must be min-imized. Thestoragevector isaQ-dimensional vectorandthus the curse of dimensionality [15] arises which is handledby modifying the original dynamic programming technique.The dynamic programming technique successive approxima-tion(DPSA) decomposesthemultidimensional probleminasequenceofone-dimensionalproblems whicharemucheasiertohandle[16].Theoptimizationsoccuronevariableatatimewhileholdingtheothervariablesat aconstant value. All thevariables are evaluated that way. This technique converges to aoptimum for convex problems. This method will be used for thedeterministic and stochastic programming.B. Deterministic ProgrammingA daily load prole of the selected season is chosen and thevehicles are placed randomly. The DPSAtechnique needs initialvalues ofthestatevariablesto starttheiteration.ThesevaluesaregeneratedbycalculatingtheoptimalchargetrajectoryforeachPHEVseparatelywithout consideringtheotherPHEVs.Theseoptimaltrajectoriesareputtogetherintoonetemporaryoptimal trajectory and thus one -dimensional state vector. Allthe components of the state vector are held constant, except therst one. The optimal charge trajectory for the rst componentof the state variable is dened. The new value is ascribed to therst component and the procedure continues until the last com-ponent ofthestatevectorisoptimized. Thisprocedureisre-peated until convergence is obtained. The problem is switchedfrom a multidimensional problem to a sequence of one-dimen-sional problems. The algorithm of dynamic programming suc-cessive approximation is represented in Fig. 12.C. StochasticProgrammingThe uncertainties of the household loads must also be imple-mented in the DP technique. Two thousand stochastic householdload proles are generated and the mean power losses of theseloads are used to determine the total power losses as presentedin(12):(12) 378 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 25, NO. 1, FEBRUARY 2010Fig. 12. Algorithm of DPSA charging.Thesamestochasticloadproles as producedinthesto-chastic programmingoftheQP techniqueare appliedtomakethe comparison more clear. One optimal charge prole is gener-ated for these 2000 stochastic household loads with the DPSAtechnique. Thepowerlossesarecalculatedseparatelyforthe2000householdloadproles andthe single optimal chargeprole. Thisisthestochasticoptimum. Forthedeterministicoptimum, the optimal charge prole and power losses are deter-mined for each of the 2000 stochastichousehold load proles,giving2000optimal chargeproles. Thepowerlossesofthedeterministicoptimumaresubtractedfromthepower lossesof the stochastic optimumanddividedbythe deterministicoptimum for a variation of the household loads of 5 and 25%.D. ResultsIn Fig. 13, the charge proles for the QP and DP technique arecompared. In general, the difference between the results of theDP and QP techniques is negligible, although the QP techniquegivesmoreaccurateresultsbecausethevaluesof thechargeFig. 13. Charge prole for node 1 for the QP and the DP program technique.TABLEVPOWER QUALITYAND LOSSESFORTHE TEST GRIDprolearecontinuousinthat case. TheDPtechnique, wherea step size of 400 W is introduced for the power of the charger,givesadiscretechargeprole.Reducingthesteptoaninni-tesimalvaluewouldgivethesameresultastheQPtechnique.This step size is taken rather large in order to reduce the numberof levels and thus computational time and storage requirements.The storage requirements are heavier for the DP technique com-pared to the QP technique because every possible path over eachstage must be stored. Since this leads to very large matrices andincreased computational time, the DP technique is slower.VI. IMPACTONTHE DISTRIBUTION GRIDUncoordinated charging of the batteries of PHEVs has a non-negligible impact on the performance of the distribution grid interms of power losses and power quality. Both power quality andpower losses are represented in Table V for three cases: withoutPHEVs, uncoordinatedandcoordinatedcharging. Thepowerquality is given as the average of 1000 samples of the maximumload, voltagedropandlinecurrentfortheIEEE34-nodetestfeeder during winter season for a penetration degree of 30%.The power losses are the ratio of the power losses to the totalload. Withrespect touncoordinatedcharging, the coordinationofthe charging reduces the power losses. Power qualityis improvedtoalevel whichis similar tothecasewherenoPHEVs arepresent.Because the extra loads for charging PHEVs remain in the caseof coordinated charging, additional losses are still higher.The coordination of the charging can be done by a smart me-teringsystem. Thedistributiongridmustbeenforcedtocopewith the increased loads and voltage drops caused by chargingPHEVs if this coordination systemis not applied. Both scenarioswillintroduceextracostsforthedistributionsystemoperatorsand eventually for the customers. CLEMENT-NYNS et al.: IMPACT OF CHARGING PLUG-IN HYBRID ELECTRIC VEHICLES ON A RESIDENTIAL DISTRIBUTION GRID 379A global estimation is performed in order to indicate the levelof upgrading needed for a small distribution grid. For the argu-mentation, theIEEE34-nodetestfeederisconnectedtoeachphase of a three phase transformer of 100 kVA, forming a globalgrid of 100 nodes. When no PHEVs are present, the maximumloadfor thethreegridstogether is 69kVA. ConsideringnoPHEVsinthefuture, thetransformerhasenoughreserveca-pacity for this global grid to meet additional peak load and loadgrowthforthenexttenyears, whichispredictedtobeafewpercent.A Aluminumundergroundconductor of400 V is standard. The maximum capacity of these conductorsis about 160 A [17]. For the case without PHEVs, the standardunderground conductor would be sufcient.If 30% PHEVs are introduced, the power for the global gridincreasesto108kVA, whichisoutofrangeforthe100kVAtransformer. Thistransformermustbereplacedbyastandardtransformer of 125 kVA to deal with extra PHEVs, load growthandadditionalpeakload. DuetothePHEVs, thelinecurrentincreases to 163 A. The maximum capacity of the current con-ductorisnotenoughandmustbereplacedbyaAluminum underground conductor with a capacity of 220 A.Voltage deviations up to 10% in low voltage grids are accept-ablefor95%ofthetimeaccordingtotheEN50160standardwhichismandatoryinBelgium.Inthecaseofuncoordinatedcharging, thislimit hasbeenreachedforchargingduringtheeveningandactionmustbetakentoreducethevoltagedrop.The problem of the voltage drop can be tackled by placing a ca-pacitorbankoraloadtapchangingtransformer.Althoughthelatterisnot commonat lowvoltages, it maybenecessaryinthe future, especially for the vehicle-to-grid concept. This typeof transformer can handle voltage variations of plus and minus10%byadjustingamong32tapsettingsbuilt intothewind-ings [18]. There is also another cost involved: the power losses.Theselossesincreasereasonablyinthecaseofuncoordinatedcharging. Thepowerlossesandloadsmust alsobeproducedand transported over the transmission lines.Asmart meteringsystemmust beimplementedtocontrolthe coordination and communication between the PHEVs indi-vidually,thedistributionsystemoperatorandthetransmissionsystem operator (TSO). The vehicles could also be grouped andrepresentedbyaeetmanagertocommunicatewiththeDSOandTSO. Smart meteringwill leadtoopportunitiestomakePHEVs a controllable load, to apply the vehicle-to-grid conceptand to combine PHEVs and renewable energy. This technologyisavailableforimplementation,butcapitalinvestmentsbytheutilities are necessary [19]. For the implementation of smart me-tering, also other incentives, such as real-time pricing and inte-gration of renewable energy, are important.Lessgridenforcementsarenecessarywiththecoordinationsystem. Themaximumloadislowerbecausethevehiclesarenot charging if the household loads are peaking. Therefore, thevoltagedrops,linecurrentsandpowerlossesareconsiderablyreduced. The cost of upgrading the grid must be compared withthecostoftheexecutionofsmartmetering.Inbothcases,thecostfortheimplementationandthepossibleadditionalpowerproductionwill bepassedontothecustomers. Inpractice, itwouldbenodifferencefortheDSOswhichtechnologyisim-plemented, as they are allowed to have a fair rate of return in acostplusmechanism.Withthismechanism,theDSOsarenotstrongly pushed towards the use of the most efcient technolo-gies.Thetariffsandtheperformanceofthegridaremoreim-portantinapricecapmechanism.Therealizationisfavorableif the smart metering system helps a signicant deferral of gridinvestments compared to the enhancement of the grid.VII. CONCLUSIONIn general, coordinated charging of plug-in hybrid electric ve-hiclescanlowerpowerlossesandvoltagedeviationsbyat-teningout peakpower.However,whenthechoiceofchargingperiods is rather arbitrary, the impact of the PHEV penetrationlevel is large. The implementation of the coordinated chargingis not without costs.In the rst stage, historical data are used so there is a perfectknowledge of the load proles. In a second stage, stochastic pro-gramming is introduced to represent an error in the forecastingwhichincreasethepowerlosses.Thisefciencylossisrathersmallifthetrendofthehouseholdloadprolesisknown, socharging during the peak load of the evening can be avoided.Theseresultsareobtainedwiththequadraticprogrammingtechnique. The dynamic programming technique is also imple-mentedbut doesnot improvethecomputational timenortheachieved accuracy. The applied techniques and methods can beextended to other objective functions, such as voltage control byPHEV reactive power output control and grid balancing.REFERENCES[1] A. Raskin and S. Shah, The Emerge of Hybrid Electric Vehicles. NewYork:AllianceBernstein, 2006. [Online]. Available:http://www.cal-cars.org/alliance-bernstein-hybrids-june06.pdf.[2] Anderman,Thechallengetofullelectricalpowerrequirementsofadvanced vehicles, J. Power Sources, vol. 127, no. 12, pp. 27, Mar.2004.[3] K. Clement, K. VanReusel, andJ. Driesen, Theconsumptionofelectrical energyof plug-inhybridelectricvehiclesinBelgium,inProc. 2ndEur. Ele-DriveTransportationConf., Brussels, Belgium,May2007.[4] M. Duvall andE. Knipping, Environmental Assessment of Plug-InHybridElectricVehicles,Volume1:NationalWideGreenhouseGasEmissions, EPRI, 2007, Tech. Rep.[5] P.DenholmandW.Short,AnEvaluationofUtilitySystemImpactsandBenetsofOptimallyDispatchedPlug-InHybridElectricVehi-cles, Oct. 2006, Tech. 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NewYork: Marcel Dekker, 1997.[19] U.S. Departement of Energy, Summary Report: Discussion Meeting onPlug-In Hybrid Electric Vehicles, 2006, Tech. Rep.KristienClement-Nyns receivedtheM.S. degreein electro-mechanical engineering in 2004 with spe-cializationinenergy.Currently, sheispursuingthePh.D. degreeinelectrotechnical engineeringat theKatholiekeUniversiteit LeuvendivisionELECTA,Heverlee, Belgium.Herresearchinterestsincludehybridandelectricvehicles.EdwinHaesen(S05)receivedtheM.Sc.degreeinelectricalengineeringattheKatholiekeUniversiteitLeuven(KULeuven), Heverlee, Belgium, in2004.He is currently pursuing the Ph.D. degree at the KULeuven.HeisaResearchAssistant at KULeuveninthedivision ESAT-ELECTA. His research interests are inthe domain of power system analysis and distributedgeneration.Mr. HaesenreceivedtheEuropeanTalentAwardfor InnovativeEnergySystems2005for hisM.Sc.thesis on Technical aspects of congestion management.Johan Driesen (S93M97) received the M.Sc.and Ph.D. degrees in electrical engineering fromKatholieke Universiteit Leuven (KU Leuven),Heverlee, Belgium, in 1996 and 2000, respectively.Currently, heisanAssociateProfessorwithKULeuven and teaches power electronics and drives. In2000,hewaswiththeImperialCollegeofScience,TechnologyandMedicine, London, U.K. In2002,hewaswiththeUniversityofCalifornia, Berkeley.Currently, he conducts research on distributed gener-ation, power electronics, and its applications.