POLICY EVOLUTION FOR LARGE SCALE ELECTRIC VEHICLE CHARGING CONTROL

Transcription

1 POLICY EVOLUTION FOR LARGE SCALE ELECTRIC VEHICLE CHARGING CONTROL Stephan Hutterer (a), Mchael Affenzeller (b), Franz Aunger (a) (a) Unversty of Appled Scences Upper Austra, School of Engneerng and Envronmental Scences, Stelzhamerstraße 23, 4600 Wels, AUSTRIA; (b) Unversty of Appled Scences Upper Austra, School of Informatcs / Communcaton / Meda, Softwarepark 11, 4232 Hagenberg, AUSTRIA; (a) {stephan.hutterer, franz.aunger}@fh-wels.at, (b) mchael.affenzeller@heurstclab.com ABSTRACT In future smart electrc grds, the control of electrc vehcles chargng processes wll be a central am of demand sde management. Whle ths control enables the avodance of possble crtcal peak-load values, the optmal coordnaton wth supply from fluctuatng renewables offers promsng possbltes for power grd operaton. Wthn ths work, an optmzaton approach wll be proposed that uses evolutonary optmzaton for computng performant control-polces for all EVs wthn a complex system. These polces are able to satsfy the EV users energy demand on the one hand, whle guaranteeng secure operaton of the power grd on the other hand. Consderng a hgh amount of EVs allows further the optmal ntegraton of e-moblty nto large-scale dstrbuton networks. Keywords: Electrc Vehcle Chargng Control, Probablstc Power Flow, Evolutonary Optmzaton, Smulaton Optmzaton 1. INTRODUCTION Optmal ntegraton of electrc vehcles (EVs) nto modern power grds plays an essental role n future power system operaton and control. Numerous nvestgatons have been performed n order to dentfy optmal chargng polces for meetng objectves lke peak-shavng, optmzaton of power qualty metrcs or maxmal usage of power from renewable sources. Especally ths nteracton of zero-emsson supply plants and electrfed vehcles s seen as central concern, snce the usage of energy from renewables drectly nfluences the reachable envronmental beneft of electrc vehcles. Here, both the supply as well as the demand sde show nondetermnstc behavor whch has to be tackled n some way. Therefore, a smulatonbased optmzaton approach wll be demonstrated, that uses metaheurstc algorthms for fndng optmal chargng schedules of an electrc car fleet wthn a gven system. Ths approach s capable of consderng both, the physcal power grd as well as the ndvdual electrfed traffc through probablstc smulaton models, where all nondetermnstc nfluences can be ncorporated dynamcally nto the heurstc search process. Each soluton canddate wll be evaluated a suffcent number of tmes through smulaton n order to ncrease the accuracy of the performance estmaton wthn an uncertan envronment. 2. OPTIMAL CHARGING CONTROL Varous researchers examne the problem of ntegratng electrc vehcles optmally nto power grds, where drect control of chargng power s seen as advantageous for reachng optmal load characterstcs (Clement, 2008; Clement, 2009; Sortomme, 2011). Central challenge besde the formulaton and computaton of the optmzaton problem tself s the consderaton of the ndvdual behavor that manly characterzes electrc vehcle chargng load. Dfferent approaches try to tackle ths task usng statc load profles (Clement, 2008), representatons of behavor usng Queung Theory (Vlachoganns, 2009) or smulaton va Monte Carlo methods (Sortomme, 2011). All these approaches generally have n common that they try to compute statc load profles that are later used wthn certan optmzaton methods. Thus, there s no nterrelated process that ncorporates probablstc behavor durng the search for optmal solutons. Especally when talkng about optmzaton n uncertan systems, smulaton-based optmzaton wth heurstc algorthms has been appled to varous felds of applcatons and wll be the central approach wthn ths work. Here, wth probablstc smulaton models, the uncertan system can be modeled holstcally consstng of traffc smulaton, probablstc models of renewable supply as well as the power grd smulaton model for the computaton of resultng load flows. 3. SIMULATION-BASED POLICY EVOLUTION The complete system archtecture s shown n Fgure 1: ISBN ; Bruzzone, Gronalt, Merkuryev, Pera, Talley Eds. 59

2 arrves at an arbtrary locaton whch s equpped wth chargng nfrastructure. Fgure 1: Smulaton Optmzaton Here, the problem represented by smulaton conssts of the dstrbuton grd load flow smulaton tself, probablstc models for fluctuatng supply from renewable plants as well as the smulaton of the EV fleet. The soluton canddate represented by a chargng polcy for all EVs s passed to the smulaton for evaluaton, returnng ts resultng ftness value to the optmzaton algorthm. In the end, the fnally best found chargng polcy should satsfy end-users energy demand whle consderng probablstc drvng behavor of EVs (traffc smulaton), guaranteeng secure dstrbuton grd operaton (power grd smulaton) as well as maxmzng usage of power from fluctuatng renewables (probablstc power supply models) Polcy Optmzaton In exstng research lterature on ntegratng EV fleets nto dstrbuton grds, the common approach s to mplement an optmzaton procedure that computes optmal chargng schedules based on exstng knowledge and forecasted system behavor n advance. But n an uncertan and volatle system such as the underlyng one consstng of probablstcally behavng agents and ntermttent power supply from renewable plants, t would be more approprate to make chargng decsons on the fly, reactng to dynamc stuatons quckly and n a flexble manner. Therefore, a polcy-based approach s the central am of ths work. Here, each agent (EV) receves a flexble polcy rather than a statc schedule that makes t react to ts envronment dynamcally durng operaton, but n a globally optmal manner when decdng about the agent s chargng. Ths polcy s prncpally the same for all agents, but usng ndvdual data from agent s envronment, t leads to agent-specfc chargng behavor. The basc concept s ndcated n Fgure 2, where the polcy evaluaton s ndcated for a gven EV that Fgure 2: Polcy Control. Prncpally, the optmzed polcy whch fnally decdes the EV s chargng power at a gven tme step s syntheszed from atomc rules that consder agentspecfc parameters from ts envronment. Out of these parameters, atomc rules are used to compute nformaton out of them for evaluatng EVs power demand as well as the state of ts envronment. Here, three dfferent parameter classes can be dstngushed from each other: Agent-specfc parameters concern the EV s drvng behavor, lke ts resdence tme at the actual chargng staton or ts lkelhood of gettng parked at another chargng spot later on. Local parameters consder other EVs mmedately affectng the local stuaton n the power grd. For example, f the power grd s stressed locally because of a hgh amount of EVs chargng at the same bus, ther chargng power has to be reduced n the next tme step n order to avod crtcal power flow condtons. Global parameters consder nformaton descrbng the whole system s state, lke the total load to the dstrbuton grd, totally expected supply from renewables or fnancal aspects consderng costs of electrcal power supply. Usng these parameters as nput for the atomc rules, each rule delvers a numerc result n the nterval [0,1] that defnes the agent s prorty for chargng. 0 would ndcate that the correspondng EV should not charge at the actual tme step, 1 advses t to charge wth maxmum power. Snce a varety of crtera has to be taken nto account for computng the optmal chargng power of an EV, as can be estmated from the parameter ISBN ; Bruzzone, Gronalt, Merkuryev, Pera, Talley Eds. 60

3 classes defned above, multple rules have to be defned that fnally have to be merged n some way. Table 1 gves an overvew of all defned atomc rules. Tabelle 1: Atomc Rules Rule Total Resdence Tme so Far Estmated Tme to Departure Passed Resdence Tme at Locaton Actual Irradance Past Irradance Durng PRT Estmated Irradance to ETTD Actual Wnd Speed Past Wnd Speed Durng PRT Estmated Wnd Speed to ETTD Actual Base Load Past Base Load Durng PRT Estmated Base Load to ETTD Actual Prce Past Prce Durng PRT Estmated Prce to ETTD Dstance to Peak Load Mean MVA Ratng Number of EVs Same Locaton Mean number EVs Same Locaton Durng PRT Number of EVs Chargng Globally Number of EVs chargng, Same Locaton Mean Chargng Rate per EV Globally Mean Chargng Rate, Same Locaton Agent s Already Charged Energy Acronym RT ETTD PRT AI PI EI AWS PWS EWS ABL PBL EBL AP PP EP DTB MMVA NREVL MNREVL NREVC NREVCL MCR MCRL ACE More detaled nformaton about the atomc rules can be obtaned from (Hutterer, 2012). Summng up, all these rules combned are capable of consderng not only the sngle EV s needs, but also descrbe the global system s state concernng power grd operaton and behavor of the total EV fleet. These rules now have to be combned n an approprate way n order to compute the fnal chargng power of an affected EV Rule Synthess Wthn ths work, two approaches wll be compared for constructng the fnal polcy out of atomc rules. The am of ths so called rule synthess s to compute a fnal value that descrbes the chargng decson out of the set of atomc rules that are needed n order to consder all needed nformaton from the agent s envronment Synthess wth Lnear Combnaton The frst approach uses a fxed mathematcal structure gven n Equaton 1. Here, the agent s chargng rate (CR) at tme step s computed usng a lnear combnaton of all rules r, each rule multpled by a specfc weght w, dvded by the amount of rules j. Ths knd of rule synthess s a common approach from producton logstcs as used n (Vonolfen, 2011) and (Beham, 2009). Here, the control varables that are manpulated durng the heurstc search process are the weghts w j that descrbe the mpact of each rule. For ths knd of real-valued optmzaton, evoluton strateges accordng to (Beyer, 2002) are appled. CR J rj, * w j = j= 1 j (1) Even f the rule synthess usng a lnear combnaton s qute ntutve and leads to compettve results, t seems to be nflexble, dsregardng the possblty of dentfyng potental nonlnear relatonshps between atomc rules. Therefore, a second approach s ntroduced that allows a more flexble, nonlnear combnaton of atomc rules, namely genetc programmng (GP) (Affenzeller, 2009) Synthess wth Genetc Programmng Extendng the prncple concept of genetc algorthms, GP uses evolutonary-nspred concepts for the heurstc search process, but s able to evolve computer programs. Wthn the heren descrbed work, these computer programs take the appearance of structured trees, where leafs represent rules as defned before, that are combned by arbtrary mathematcal operators whch are ncorporated by nner nodes. Ths knd of soluton representaton allows arbtrary mathematcal combnatons of atomc rules. To gve some overvew on GP, fndng frst research actvtes n the 1980s, the computatonally expensve concept of GP was pushed majorly by the steady ncrease of computatonal power n the last two decades. One of the most mportant publcatons n ths feld was (Koza, 1992), statng GP as automated nventon machne for numerous practcal applcatons lke the artfcal ant problem or later applcatons of symbolc regresson (Affenzeller, 2009), to name the most popular ones, whle (Langdon 2002) fnally provdes profound analyss n the context of GA schema analyss. Ths ablty of GP to automatcally construct new solutons (programs) to a gven problem s enabled by ts specal knd of soluton representaton, that s not restrcted to a fxed structure (lke fxed-length onedmensonal array as n standard GA), but forms a herarchcal computer program of varable length, consstng of functons and termnals. In the heren presented applcaton, functons are nner nodes of the structured tree, whle termnals can be constants or atomc rules. Fgure 3 gves an exemplary tree that could represent a polcy for the addressed problem. Here, nner nodes that represent functons are ndcated n dotted style, whle termnal nodes are plotted n sold style. In ths case, the polcy would consder the estmated tme to departure of the approprate EV, the actual rradance and thus the supply from photovoltacs, as well as the mean chargng ISBN ; Bruzzone, Gronalt, Merkuryev, Pera, Talley Eds. 61

4 rate of all other EVs n order to not stress the dstrbuton grd wth peak chargng load. Out of ths mathematcal combnaton, fnally a numercal value s derved that represents a chargng decson. Fgure 3: Exemplary GP Soluton The great advantage of ths knd of flexble soluton representaton compared to the applcaton of a fxed-structure lnear combnaton s that GP s able to fnd nonlnear coherences between atomc rules wth varable length. Usng any arbtrary combnaton of mathematcal operators as nner nodes, the degree of freedom for fndng performant polces gets ncreased drastcally. Further, snce GP s not constraned to use the hole set of atomc rules for soluton creaton, smpler polces can be found too. In the end, ts dsadvantage s that the possble soluton space s ncreased drastcally. For overcomng ths problem and prunng the soluton space, the possble grammar s restrcted to the followng operators n Table 2. The grammar n ths case defnes the set of functons (nner nodes) that s appled for evolvng soluton canddates durng the genetc search process. Further nformaton on usable grammar can be obtaned n the approprate lterature (Affenzeller, 2009) as well as n HeurstcLab ( whch s used as heurstc optmzaton framework. multpled by the maxmum possble chargng power per EV. Thus, when usng rule synthess wth lnear combnaton, no nvald chargng power can occur from the polcy, as long as the decson varables are kept wthn [0,1]. When usng rule synthess wth GP, the polcy drectly outputs the desred chargng power. Here, possbly nvald values may result from the soluton canddate (negatve chargng power, too hgh chargng power) because of the hgh degree of freedom when buldng the structured tree, whch has to be managed n some way. A reason could be for example the addton of a constant or a multplcaton of rules wth some value. In ths work, ths s consdered the followng way: f the resultng value s less than 0 or greater than the maxmum chargng power, the value s set to 0 or the maxmum value respectvely and a penalty s added to the ftness term accordng to the degree of the volaton. Snce power-flow smulaton may not converge n exceptonal condtons (for example f the resultng chargng load takes unmanageable values), ths penalty s turned nto a so called death penalty for the respectve soluton. Thus, f a soluton canddate leads to non-convergence of the load-flow smulaton, t s assumed to be useless Soluton Evaluaton The evaluaton procedure of a soluton canddate s ndcated n Fgure 4. Table 2: GP Grammar Arthmetc Operators {+, -, x, /} Condtonal Operators Condtons {IfThenElse} Comparsons {<,>} 3.3. Polcy Evaluaton The prncpal process of the polcy evaluaton can be obtaned from Fgure 4: n each tme step of the smulaton, f the agent remans at a chargng staton, the polcy evaluaton s ntated n order to compute the resultng chargng power. After gatherng all the nformaton the agent needs (global, local as well as agent-specfc parameters), the respectve outcome of the atomc rules s computed. Combnng these results accordng to the rule synthess method, the fnal chargng power can be derved. The atomc rules are generally constructed such that each rule as well as ts respectve weght results n a numerc value n the nterval [0,1]. Thus, for the lnear combnaton, the fnal results exsts n the nterval [0,1] as well. Ths value therefore s nterpreted as chargng rate and s Fgure 4: Soluton Evaluaton ISBN ; Bruzzone, Gronalt, Merkuryev, Pera, Talley Eds. 62

5 When evaluatng a soluton canddate n smulaton, frst of all the traffc smulaton s performed over the whole tme nterval, n order to descrbe the expected EV behavor. Havng ths behavor n form of computed drvng profles for each agent, ts resultng chargng power s computed for each tme step that follows from the evaluaton of the respectve polcy. Wth the chargng load caused by all agents, further the power flow smulaton s executed for each tme step consderng probablstc njecton from renewable sources, n order to compute the actually occurrng load flow n the physcal dstrbuton grd. Wth the fnal power flow soluton, all constrants as well as the objectve functon can be evaluated n order to derve the ftness of the soluton Evaluaton under Uncertanty When evaluatng a soluton canddate n an uncertan envronment, estmatng ts real performance s a ubqutous as well as challengng task whch mght be computatonally expensve. Ths s due to the stochastc nature of the evaluaton as well as the slow convergence of a performance measure estmator relatve to the number of runs performed. The obtaned ftness from a smulaton run can be formulzed as ~ f = f + ε, where the obtaned ftness value f ~ devates from the real ftness caused by some probablstc nose ε. Ths nose s manly defned n lterature as beng normally dstrbuted (Stagge, 1998; Fu 2002) by Ν ( μ, σ ) wth zero mean. Whle the evolutonary search proceeds rapdly t may happen that some other ndvdual than the best s chosen as parent for the next generaton, caused by an naccurate estmate of f. Ths may lead to a decrease n progress velocty and may also lead the evolutonary search nto unpromsng regons of the search space. Thus, dong multple evaluaton runs and averagng over the obtaned values of ~ f s mportant for estmatng the canddates real performance. Snce The accuracy of ths estmate cannot mprove faster than 1 / N, where N s the number of computed samples as ndcated n Fgure 4, choosng an approprate value of N s essental when addressng computatonal costs of evaluaton. Dfferent approaches have been nvestgated both n lterature as well as by the authors of ths paper (Hutterer, 2012) for nferrng N n an adaptve way durng the search process. Wthn ths paper, t s seen as suffcent to expermentally derve a performant value for N and fx t. 4. SETTING UP EXPERIMENTS As hghlghted n the ntroductory chapter, many researchers are nvestgatng ths optmal ntegraton of EVs nto dstrbuton grds nowadays. When consderng the treated power grd levels, these researchers manly focus on qute low-level ntegratons n mostly radal dstrbuton feeders or even lower. The specal advantage of the heren used polcy-based control approach, as dscussed extensvely n (Hutterer, 2012), s that t enables the consderaton of huge EV fleets and thus consder ther ntegraton from a hgher level pont of vew. Hence, n ths work, larger dstrbuton networks are consdered that wll be dscussed as follows Large-Scale Dstrbuton Grd Testcases In order to guarantee unversalty for the consderatons wthn ths work, the well known IEEE dstrbuton grd testcases 1 wll be used and modfed for representng vald test nstances. Throughout the grd, a huge EV fleet s modeled, where each sngle agent can produce a chargng load of maxmum 11kW, related to a three-phase chargng process wth 400V and 16A, as exemplarly possble when usng a Mennekes VDE (Type 2) plug connector. Ths confguraton, as exstng for example when chargng the well known Tesla Roadstar, s certanly one of the most mportant techncal specfcatons n ths feld n actual developments and s seen to get a common standard throughout EV-manufacturers. The power grd smulaton model s beng downscaled such that the cumulated chargng power of all agents sums up to 20% of the daly peak load maxmally n each consdered case. For representng ndvdual electrfed traffc from a power grd pont of vew, the relevant behavor that has to be modeled descrbes tme nterval and locaton of each EV when beng parked to a chargng staton and thus beng ready for chargng. Based on real-world traffc data from an Austran survey 2, two most relevant drvng patterns can be extracted for a week day, namely the pattern of fulltme and half-tme workers. Wthn each pattern, three dfferent locatons are modeled for parkng at home, at work and at any locaton n free tme (shoppng, educaton, entertanment). For each locaton, dfferent probabltes for the exstence of a chargng nfrastructure are modeled, descrbng a possble future nfrastructure scenaro from an actual pont of vew: at home, each EV user has an own chargng staton. At work, there s a probablty of 50% that an approprate nfrastructure s avalable. For locatons where potental users reman n free tme, ths probablty s assumed to be 25%. The resultng chargng load at a specfc locaton s than beng correlated to a correspondng bus wthn the dstrbuton grd model. Wthn each smulaton run, synthetc drvng profles are computed from prototype- 1 Testcases provded by Unversty of Washngton, UW Electrcal Engneerng. (1999). 2 Federal Mnstry for Transport, Innovaton and Technology, Verkehr n Zahlen 2007, downloads/vz07gesamt.pdf, Retreved ISBN ; Bruzzone, Gronalt, Merkuryev, Pera, Talley Eds. 63

6 profles, beng randomzed n terms of drvng tme and resdence tme at specfc locatons. Thus, the probablstc behavor of ndvdual traffc can be modeled based on real-world data and ncorporated nto the evolutonary optmzaton process enabled by the smulaton-based approach. For modelng the power output of renewable sources, wnd power plants as well as large-scale photovoltac plants are added to the dstrbuton network. For wnd power modelng, the correspondng wnd speed values at the plant stes are sampled from a Webull-dstrbuton as descrbed n (Vlachoganns, 2011), where ther power curves are assumed such that each plant reaches ts maxmum output at cut-off wndspeed. Usng the sampled wnd speed value, wth the plant s power curve the resultng power output of the plant can be modeled. Photovoltac-plants follow a typcal daly generaton profle that s randomzed n each tme step wth a standard devaton of 10%, consderng a typcal uncertanty n photovoltac-generaton forecastng. All renewable supply models are desgned such that they cumulated produce n average 50% of the energy needed for all EVs n the system. In order to consder realstc power grd condtons, the base load s modeled as descrbed n the IEEE testcases, but randomzed too for smulatng a probablstc demand sde wth a standard devaton of 4%. A thorough dscusson of the used modelng approach can be obtaned from (Hutterer, 2012). The confguratons for both test cases are shown n Tabelle 13, where the dstrbuton of renewable plants throughout the grd model as well as the EV fleet are defned. Table 3: Test Cases Confguratons 14-Bus Testcase # EVs 960 # Photovoltac Plants 3 # Wnd Plants 2 Bus # wth Photovoltac 6,8,10 Injecton Bus # wth Wnd Power 3,12 Injecton Bus # wth fxed 2 Generaton Slack Bus # Bus Testcase # EVs 4366 # Photovoltac Plants 9 # Wnd Plants 3 Bus # wth Photovoltac Injecton 12,31,46,54,59,61,87,103,1 11 Bus # wth Wnd Power 25,49,100 Injecton Bus # wth fxed 10,26,65,66,69,80,89 Generaton Slack Bus # 1 5. PROBLEM FORMULATION A formal descrpton of the optmzaton problem shall now be stated n order to underlne the applcaton: gven a fleet of EVs wthn a dstrbuton grd, a vector Pc = [Pc 1,1,...,Pc,n ] descrbes the actve chargng power of each EV n at tme step over a gven tme nterval. At the end of ths consdered plannng frame, each EV must have receved a specfc amount of energy for I satsfyng ts daly demand: Emn, n Pc, n * Δt =1 Ths constrant s vald assumng that batteres are bg enough and the one-way dstance of an EV does not lead to a low state of charge. Snce addtonal load caused by related chargng of electrc vehcles can endanger power grd securty, constrants have to be satsfed that ensure secure dstrbuton grd operaton. Thus, wthn each tme step, power flow constrants have to be consdered. Steady-state securty constrants can be formulated (Wood, 1996) for ensurng lower and upper bounds for generator real and reactve power output Pg and Qg, Pg Pg Pg j, mn j j,max Qg j, mn Qg j Qg j,max maxmal power flows over transmsson lnes Pf, Pf k Pf k,max as well as admssble voltage devatons Δ V, ΔVk, ΔV mn k ΔVk, max, for all buses j=1 J and all transmsson lnes k=1 K. Whle satsfyng all formulated constrants, the objectve functon shall be defned of mnmzng fnancal costs of power supply. Snce chargng power s restrcted to a maxmum value, an addtonal constrant has to be formulated when usng the GP-based polcy synthess as dscussed n secton 3.2, beng formulzed as: Pc, n Pc,max. What s mportant to menton at ths pont s that the vector Pc as ntroduced above contanng the chargng power of each EV at each tme step s never present n a statc manner. Each value Pc,n results from a sngle evaluaton of the polcy wthn the smulaton of a certan tme step. Therefore, as ndcated n Fgure 4, the load flow n the system s computed wthn each tme step n order to check the constrants. The fnally obtaned ftness functon s stated n Equaton 2, where CV ( Pc) s a vector contanng the quadratc volatons of each constrant, multpled by k beng a vector wth fxed weghts of the constrant volaton value relatve to the fnancal cost functon value. 24 = 1 [ Cf ( Pc) + k * CV ( Pc) ] (2) ISBN ; Bruzzone, Gronalt, Merkuryev, Pera, Talley Eds. 64

7 Snce the objectve concerns fnancal costs of energy supply for chargng electrc vehcles, a daly prce profle s assumed that s taken from the European energy exchange as used n (Hutterer, 2012). 6. EXPERIMENTAL RESULTS For the experments performed wthn ths work, evolutonary algorthms are used, dependng on the appled polcy synthess approach. For optmzng the weghts for the fxed-structure lnear combnaton, Evoluton Strateges (ES) are appled accordng to (Beyer, 2002). ES are generally performant metaheurstcs for real-valued optmzaton problems and proven to be sutable for smulaton-based optmzaton (Hutterer, 2012). For the GP-based evoluton of polces, Genetc Algorthms (GA) are appled. Both classes of algorthms are executed n HeurstcLab based on ther standard mplementatons. The fnally used confguratons can be obtaned from Table 4 and Table 5. Table 4: Algorthm Confguratons 14-Bus Testcase Type (5+15)-ES Manpulator SelfAdaptveNormalAllPostons- Manpulator Recombnator Average Crossover Parents per Chld 2 Stoppng 5000 Generatons Crterum Samplng Sample Each Soluton 3 Tmes Type GA Manpulator MultSymbolcExpressonTree- Manpulator Recombnator SubtreeCrossover Populaton Sze 250 Mutaton 15% Probablty Stoppng 200 Generatons Crterum Samplng Sample Each Soluton 3 Tmes Table 5: Algorthm Confguraton 118-Bus Testcase Type (5+10)-ES Manpulator SelfAdaptveNormalAllPostons- Manpulator Recombnator Average Crossover Parents per Chld 2 Stoppng 5000 Generatons Crterum Samplng Sample Each Soluton 6 Tmes Type GA Manpulator MultSymbolcExpressonTree- Manpulator Recombnator SubtreeCrossover Populaton Sze 150 Mutaton 15% Probablty Stoppng 200 Generatons Crterum Samplng Sample Each Soluton 6 Tmes Further detals on the used confguratons can be obtaned from HeurstcLab and from the approprate lterature respectvely (Affenzeller, 2009) Results for the 14 Bus Testcase The obtaned best soluton s shown n Table 6, showng the obtaned weghts for the gven atomc rules. It can easly be seen, that most rules are weghted near to 1, n order to construct the fnal polcy out of them. The fnally best found soluton for the GP-based rule synthess cannot be vsualzed at ths pont, snce t forms a structured tree of length 28 (number of used nodes) and depth 5. Some statements can even be done: the best found tree uses only 9 out of the 24 atomc rules for syntheszng the polcy. Ths means that the rules are hghly correlated to each other (whch s obvous) and not all of them are needed for fndng vald polces. Table 7 shows same numerc results. Table 6: Best Soluton 14 Bus Testcase Rule Weght Rule Weght RT 1 AP ETTD 1 PP PRT 1 EP AI DTB PI MMVA EI NREVL AWS MNREVL PWS 1 NREVC EWS NREVCL 1 ABL 1 MCR PBL MCRL EBL 1 ACE Table 7: Numerc Results 14 Bus Testcase Ftness Standard Devaton of Ftness: 100 Replcatons Synthess wth Lnear Combnaton % GP-based Synthess % The ftness addresses the resultng costs (n Euro) for supplyng energy for chargng the EV fleet. These costs only address the energy-generaton costs, whch vary n a range of around 0.03 to 0.08 per kwh over a typcal day at the European energy exchange (EEX). The prce that a consumer would have to pay addtonally contans taxes as well as a fee to the power grd operator. Each soluton s evaluated over 100 smulaton runs for fnal results n order to obtan ts robustness wthn the uncertan envronment. Therefore, the standard devaton of the obtaned ftness over these 100 runs s used as robustness estmator. ISBN ; Bruzzone, Gronalt, Merkuryev, Pera, Talley Eds. 65

8 As can be seen n Table 7, the synthess wth fxed structure lnear combnaton outperforms GP-based synthess n both metrcs. Thus, the harder heurstc search caused by an ncreased soluton space when tryng to fnd a vald soluton wth GP domnates ts advantage of fndng nonlnear coherences between rules. Nevertheless, both approaches are capable of fndng feasble (all constrants are satsfed) solutons wth optmzed fnancal costs of energy supply Results for the 118 Bus Testcase As can be seen from the algorthm confguratons, for the second testcase, qute lower populaton szes have been used. Ths s due to the fact that ths testcase consders 4366 EVs and therefore the evaluaton of the polcy when smulatng ts performance has to be executed more than 4 tmes more often than n the smaller testcase. Thus, populaton sze has been decreased n order to keep the optmzaton computatonally tractable. Table 8: Best Soluton 118 Bus Testcase Rule Weght Rule Weght RT AP 0 ETTD PP PRT EP AI DTB PI MMVA EI NREVL AWS MNREVL PWS NREVC EWS NREVCL ABL MCR PBL MCRL EBL ACE Table 9: Numerc Results 14 Bus Testcase Ftness Standard Devaton of Ftness: 100 Replcatons Synthess wth Lnear Combnaton % GP-based Synthess % The best found soluton as vsualzed n Table 8 dffers wth respect to the smaller testcase drastcally, consderng a much hgher varaton n the sngle weghts. Takng a look at the numercal comparsons n Table 9, once more the gven fxed structure synthess outperforms the GP-based one. Comparng the reached ftness-values of both testcases, n the 14-bus case costs of result per sngle EV, whle these costs are ncreased to n the 118-bus case for the best soluton. Snce n both cases same generaton costs are assumed for the power grd smulaton, t can be stated that the soluton of the smaller testcase has better overall qualty, provng that the optmzaton task n the second case seems to be harder. CONCLUSION In ths work, a smulaton optmzaton framework has been proposed that s capable of computng optmal chargng decsons for a huge fleet of electrc vehcles for optmally ntegratng them nto dstrbuton grds. These decsons are prncpally performed usng flexble polces that enable the EVs to act ndvdually wthn a dynamc envronment. The respectve polces are evolved usng evolutonary computaton technques, where the search space s spanned through a smulaton ensemble consstng of the electrc power grd model, electrc vehcle behavor models as well as probablstc supply models. Two dfferent representatons have been formulated and compared to each other that enable the synthess of the fnal polcy usng a set of atomc rules. Snce these varants for rule synthess majorly nfluence the evolutonary search, comparsons have fnally been performed for evaluatng reachable soluton qualty based on two practcal test nstances. ACKNOWLEDGMENTS Ths project was supported by the program Regonale Wettbewerbsfähgket OÖ , whch s fnanced by the European Regonal Development Fund and the Government of Upper Austra. REFERENCES Affenzeller, M., Wagner, S., Wnkler, S., & Beham, A., Genetc algorthms and genetc programmng: Modern concepts and practcal applcatons. Chapman & Hall, London, UK. Beham, A., Kofler, M., Wagner, S., Affenzeller, M., Hess, H., & Vorderwnkler, M., 2010: Enhanced Prorty Rule Synthess wth Watng Condtons, Proceedngs of the European Modelng and Smulaton Symposum, pp , Morocco. Clement K., Haesen, E., & Dresen, J.,2008. The mpact of uncontrolled and controlled chargng of plugn hybrd electrc vehcles on the dstrbuton grd. European Ele-Drve Conference, Geneva, Swtzerland. Clement, K., Haesen, E., & Dresen, J., Stochastc analyss of the mpact of plug-n- hybrd electrc vehcles on the dstrbuton grd. 20th Internatonal Conference on Electrcty Dstrbuton CIRED, Prague, Czech Republc. Langdon, W. B. & Pol, R, Foundatons of Genetc Programmng. Sprnger, Berln Hedelberg New York. Stagge, P., Averagng effcently n the presence of nose. In A. Eben (Ed.), Parallel Problem Solvng From Nature PPSN V, Lecture Notes n Computer Scence, Vol pp Berln/Hedelberg, Germany, Sprnger. Sortomme, E., Hnd, M. M., McPherson, J., & Venkata, M., Coordnated chargng of plugn hybrd electrc vehcles to mnmze dstrbuton ISBN ; Bruzzone, Gronalt, Merkuryev, Pera, Talley Eds. 66

9 system losses. IEEE Transactons on Smart Grd, 2(1), Vlachoganns,John G., Probablstc Constraned Load Flow Consderng Integraton of Wnd Power Generaton and Electrc Vehcles, IEEE Transactons On Power Systems, 24 (4), pp Vonolfen, S., Affenzeller, M., Beham, A., Lengauer E., & Wagner, S., 2011: Smulaton-based evoluton of resupply and routng polces n rch vendormanaged nventory scenaros, Central European Journal of Operatons Research (CEJOR), Accepted (avalable onlne: DOI: /s ). Fu, M. C., Feature artcle: Optmzaton for smulaton: Theory vs. practce, INFORMS Journal on Computng, 14(3), pp Beyer, H. G. and Schwefel, H. P., Evoluton Strateges - A Comprehensve Introducton, Natural Computng, 1, pp. 3-52, Sprnger. Hutterer, S., Aunger, F., & Affenzeller, M., Metaheurstc optmzaton of electrc vehcle chargng strateges n uncertan envronment, Proceedngs of the Internatonal Conference on Probablstc Methods Appled to Power Systems (PMAPS), Istanbul Turkey. Hutterer, S. and Affenzeller, M., Probablstc Electrc Vehcle Chargng Optmzed Wth Genetc Algorthms and a Two-Stage Samplng Scheme. Internatonal Journal of Energy Optmzaton and Engneerng (accepted). IGI Global. Koza, J. R., Genetc Programmng: On the Programmng of Computers by Means of Natural Selecton. The MIT Press, Wood, A. J., & Wollenberg, B. F., Power generaton, operaton, and control. Second edton. Wley-Interscence, New York, US: receved hs habltaton n appled systems engneerng, both from the Johannes Kepler Unversty of Lnz, Austra. Mchael Affenzeller s professor at the Unversty of Appled Scences Upper Austra, Campus Hagenberg, and head of the Josef Ressel Center Heureka! at Hagenberg. Dr. Franz Aunger receved hs Dplomngeneur (Master) n electrcal engneerng at Venna Unversty of Technology. PhD thess n the feld of automaton objects and generc components for mechatronc engneerng. Untl february 2003 head of the group for ntellgent automaton and holonc at PROFACTOR. Snce February 2003 professor for ndustral nformatcs at the Unversty of Appled Scences Upper Austra at campus Wels n the feld of embedded & real-tme systems and snce July 2006 head of the department for electrcal engneerng. Dr. Aunger holds publcatons n the area of holonc and dstrbuted control systems, as well as smart electrc grds. AUTHORS BIOGRAPHY Stephan Hutterer receved hs Dplomngeneur (FH) (graduate engneer) n Automaton Engneerng at the Unversty of Appled Scences Upper Austra. Snce 2009, he s PhD canddate at the Johannes Kepler Unversty Lnz, Austra, workng n the feld of evolutonary optmzaton for ntellgent power grds. Hs specal research nterests are smulaton-based optmzaton for the ntegraton of dstrbuted renewable supply as well as electrc vehcle fleets nto power grds. He s member of the Heurstc and Evolutonary Algorthms Laboratory at the Unversty of Appled Scences Upper Austra. Mchael Affenzeller has publshed several papers, journal artcles and books dealng wth theoretcal and practcal aspects of evolutonary computaton, genetc algorthms, and meta-heurstcs n general. In 2001 he receved hs PhD n engneerng scences and n 2004 he ISBN ; Bruzzone, Gronalt, Merkuryev, Pera, Talley Eds. 67