Statistical Analysis and Modeling of Plug-in Electric Vehicle Charging Demand in Distribution Systems

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1 Saisica Anaysis and Modeing o Pug-in Eecric Vehice Charging Demand in Disribuion Sysems Qin Yan, Suden Member, IEEE, Cheng Qian, Suden Member, IEEE, Bei Zhang, Suden Member, IEEE, Maden Kezunovic, Feow, IEEE Deparmen o Eecrica and Compuer Engineering Texas A&M Universiy Coege Saion, TX, U.S.A Absrac This paper esabishes sochasic mode o pug-in eecric vehice (P) charging and derives he probabiisic descripion o he eecriciy needs rom charging or one charging saion a any hour o a day. Three key variabes are used o characerize he sochasic behavior o charging: saring ime o charging, sae o charge (SOC), and oa number o charging s. The eecriciy needs o an charging saion is a uncion o ime, which can be depiced by he expecaion o charging needs a a cerain ime o day. Numerica simuaions are impemened o vaidae he proposed anaysis approach and iusrae he impac o s charging demand on he disribuion sysems. Keywords charging saions; pug-in eecric vehices; saisica anaysis d PDF d k λ τ NOMENCLATURE Mies driven daa Probabiiy densiy uncion PDF o mies driven vaue Shaping parameer o a Weibu disribuion Scaing parameer o a Weibu disribuion Time index (coninuousy) or uncion ST ST ( τ ) PDF o sar ime o charging vaue α Shaping parameer o a og-ogisic disribuion β Scaing parameer o a og-ogisic disribuion γ Locaion parameer o a og-ogisic disribuion SOC Sae o Charge,, percenage e in he baery μ Percenage o disance driven in eecric mode AER A-eecric range s Index o SOC Time index (hour) r Percenage o baery can be charged per hour η charging eiciency i index i, charging power demand or i, wih remaining SOC s, a P ime i, SOC Iniia SOC beore charging SOC Fina SOC aer charging C Usabe baery aciy P charging power demand or one charging saion a ime N Toa number o s in he arge area ρ Percenage o each ype o vehices () This pubicaion was made possibe by NPRP award rom he Qaar Naiona Research Fund (a member o Qaar Foundaion). The saemens made herein are soey he responsibiiy o he auhors. ψ δ ε θ n Popuaion in he arge area Average peope amoun per residen Average number o s per residen peneraion raio Charger number I. INTRODUCTION Eecric Vehices (s) are we-known as an aernaive means o ransporaion due o he environmena advanages compared o he radiiona gas-powered vehices. Due o he reaivey arge amoun o eecriciy ha s consume, he charging o s can cause undesirabe arge peak demand, and hereore, has a remendous impac on he disribuion sysem, wih unconroed and cenraized charging []. The impac o peneraion on disribuion nework are discussed a engh in he ieraure [2-9]. To evauae he impac o s and opimay coordinae heir energy consumpion, i is necessary o expore he characerisics, anayze charging/discharging proies and esabish ypica modes [0-]. s pose chaenges and inroduce compexiy in he anaysis o he impac mainy because o he randomness o charging and driving behavior o owners. Baery characerisics, ypica driving behaviors, and drivers preerences are essenia eemens o be considered [2]. Thus, sochasic modes need o be bui o ake ino consideraion he uncerainies in regard o he charging demand proies, incuding charging ocaions, charging sar ime, aciy o baery, charging eve, baery SOC whie charging [, 2-3]. Such sudies aow or no ony an esimaion o he charging demand under dieren scenarios o marke peneraion, bu aso he poenia o serve he power grid as a mobie energy sorage [3-4]. Deerminisic modes are deveoped based on average and wors case peak oad in some sudies, bu he required inormaion or sysem operaion is oen no avaiabe. In addiion, an enormous dierence beween deerminisic and sochasic anaysis is observed in [2]. Among sochasic modeing mehods, os o sudies use Mone Caro approach o simuae he randomness [5-7]. Paper [8] assume probabiiy modes o predic he charging oad under dieren charging scenarios. In some papers [, -2, 9], he parameers are derived rom acua survey daa and measuremens, such as Naiona Househod Trave Survey /7/$ IEEE

2 (NHTS) and Eecric Power Research Insiue (EPRI) repor [20]. In his paper, he survey daa rom NHTS [2] is uiized o simuae he characerisics. This daa source provides abundan rea inormaion incuding vehice ypes, daiy rip deparure imes, as rip arriva ime, mies driven per day, driving behavior a weekdays and weekends, and ec. Paper [] describes he ype o daa rom NHTS 2009 in deai. Two main paces o recharge he baeries are eiher a home or pubic parking wih charging ocaions []. Due o he ong waiing ime or he charging o compee, i is very possibe ha he owners wi eave he vehices a he charging saion cose by heir work pace on heir way o work. Thus, in his paper, he arge ies on pubic charging saions cose by he working area and he esimaed eecriciy consumpion is or one arge charging saion. In shor, his paper is an inegraion and improvemen o he exising approaches. I uiizes he acua survey daa rom NHTS o buid he saisica mode o each key variabe or each. Dieren ypes o vehices, baery aciies, percenages o marke shares or each ype, eves o peneraion are considered. The res o he paper is organized as oows: he ramework o he proposed anaysis is described in Secion II; Secion III describes he mehodoogies and ormuaes he reaions o he variabes; case sudies are impemened in Secion IV; and conribuions o his paper are ouined in Secion V. descripions o each random variabe, he uncerainies o he variabes are inegraed and he oin sochasic mode is obained. Based on he sochasic mode, he ime-varian charging demand is esimaed wih an inpu o he peneraion. Driving behaviors Mies driven A-eecric range (AER) Baery echnoogy Charging eve peneraion Saring ime o charging Sae o Charge (SOC) Toa # o charging s Amoun o energy required o recharge Fig.. Reaion o he variabes Eecriciy consumpion o a charging saion per hour Cenraized conro II. Framework In order o generae charging schedues and mode he charging need or each charging saion a each ime poin, hree random variabes o buid he sochasic mode are sudied: Saring ime o charging SOC Toa number o charging s The charging oad o a singe charging saion is deermined by he sochasic disribuion considering he saring ime o charging, SOC, as we as AER (range o disance o a uy charged ), baery echnoogy, charging eve, and he amoun o energy required o recharge [6]. The reaion o he reaed variabes are shown in Fig.. The saring charging ime is deermined by drivers behavior and he baery aciy o he vehices. The remaining SOC in he baery when arriving a he charging pace reaes o he mies driven, he aciy ading o he baery, and cusomers driving behavior. The number o charging s in oa is deermined by marke peneraion o s in ha arge area. I aso depends on he charging sar ime, he remaining SOC and how as he charging is. Moreover, he oupu o he esimaed eecriciy consumpion o charging can be used or cenraized eedback conro in order o reduce he charging impac on power disribuion sysems. Fig. 2 shows he owchar o he proposed saisica anaysis. The irs sep is o consider he above deais on charging characerisics. Aer deveoping saisica Fig. 2. Fowchar o he Saisica Anaysis III. MATHEMATICAL METHODOLOGY A. Characerizaion o Charging Behavior Behavior o Mies Driven Mies driven daa can be obained rom survey resus o NHTS [2]. As shown in Fig. 3 wih mies driven as x axis and probabiiy as y axis, he mies driven daa bes is Weibu

3 disribuion, wih shaping parameer k =.53, and scaing parameer λ = k k d λ k d ( d; λ, k) = e, d 0 λ λ = 0, d < 0 Numerica inegra is uiized over an inerva o 5 mies o cacuae he probabiiies using he above equaion. The curve iing resu is shown in red ine, whie he probabiiies are shown in bue bars. Behavior o Sar Time o Charging I daiy arriva ime o work pace is used o esimae he charging sar ime, he daiy rave daa can be obained rom survey resus o NHTS. As shown in Fig. 4, wih hour o a day as x axis and probabiiy as y axis, he sar ime o charging daa bes is og-ogisic disribuion, wih shaping parameer α = 8.5, scaing parameer β = 6.8, and ocaion parameer γ = ST α 2 α τ τ γ γ α (; ταβγ,, ) = + β β β Numerica inegra is uiized over an inerva o hour o cacuae he probabiiies using he above equaion. The curve iing resu is shown in red ine, whie he probabiiies are shown in bue bars. In our work, he charging saion provides wo opions or he conneced s, charging and discharging. In addiion, discharging bonus is provided as incenives o arac s o be charged a work pace, raher han a home. Thus, he arriva ime o work pace and he daiy mies driven daa are used. When NHTS survey daa is used o esimae charging sar ime, i means, uncoordinaed charging scenarios are considered. As shown in Fig., o ineigeny conro he charging consumpion, he charging sar ime can be coordinaed. Behavior o Sae o Charge (SOC) μd SOC= g = 00%, i d AER AER = 0, i d > AER For d > AER, he SOC is zero, indicaing 0% e in he baery. In his case, i wi orce he drivers o charge immediaey, in oher words eecing he sar ime o charging variabe. AER indicaes he imum mies ha percenage o disance driven in eecric mode. In (3), i is assumed ha he baery is uy charged beore he driving. Acuay, since he eecriciy demand or he rip is wha we reay considered, he SOC aer he mies driven can be adused by subsiuing o dieren iniia SOC vaues. In oher words, i is no required o uy charge he baery, bu suicien or he rip. Charging can aso be compeed aer he driving o suppemen he () (2) (3) consumed par. Zero SOC does no mean ha he baery wi be consumed compeey once, bu ha i he vehice is going o be driven d mies, a eas he whoe baery aciy need o be charged in ha day. Since our arge is one charging saion near work pace, we wi no consider he exra charge needed. Thus, or he rips exceeding AER, i is beieved ha he cusomers wish o charge he vehices o he imum as possibe or he ong rips. In ac, he SOC aso depends on he driving paern o he driver and oher acors, so i is a noninear uncion o many oher uncerain acors. Since he purpose o he paper is o buid a genera mode or charging demand, inear reaionship is uiized a his sage. More accurae reaion uncion can be considered in uure research. Given he disribuion o d, and he reaionship beween s and d, we may derive he disribuion o s. k k AER( s) AER k AER( s) μλ S() s = e, s< (4) μ λ μλ We may po he probabiiies o SOC, shown in Fig. 5, which is cacuaed using numerica inegra over an inerva o 0%. B. Join Probabiiy o SOC Based on he charging eve, SOC is assumed o increase r per hour. Thereore, i we consider he charging demand a ime, he s ha sar o charge a ime - wih iniia SOC o s-r, has he same impac or ime + as ha sar o charge a ime wih iniia SOC o s. Thereore, he probabiiy ha SOC akes he vaue s a ime is: p( s, ) = pst ps ( s r( ) ) (5) = Where p () denoes he discreized probabiiy, as compared o (), which is a coninuous disribuion uncion. I we consider a given ime, a he possibiiies o p ( s, ) a ime shoud add up o one. (, ) = ( ) p : p p s r (6) S = Fig. 3. Mies Drive Daa and Probabiiy Disribuion ST S

4 ηen N i, = η En i= ρ, s N 4,, ( min(, )) = rsoc SOC C = i= is (0) Thus, he origina probem can be simpiied as: given he oin probabiisic disribuion o (, ) vaue o En, or each hour. p s, ind he expeced Fig. 4. Sar ime o Charging Daa and Probabiiy Disribuion Fig. 5. Probabiiy Disribuion o SOC However, he righ side o he above equaion do no equa o. I is noiced ha he deiciency is due o he negec o s =. Thus, we need o consider he siuaion when no charging is required. In his case, 0.9 (, ) = s= 0 = ST S (7) p p p s r, i s = C. Coecive Behavior o s For each i, wih remaining baery eve s, a cerain ime, he charging demand needed is ormuaed as i, i, is η En = SOC SOC C, i SOC SOC,, < r r i,, s C, i SOC SOC r = (8) Where is a consan number or charging eiciency, SOC is a consan number in his sudy (in he case o i, conroed charging, SOC is no consan), SOC is a random variabe, and C is he usabe baery aciy ha depends on he ype o vehices (, see Tabe I) and corresponding AER. C ECM AER = (9) where ECM is he esimaed eecrica energy consumpion per mie proposed by Paciic Norhwes Naiona Laboraory (PNNL) [22]., The coecive behavior o N s s charging a he same charging saion can be characerized as: D. Expeced Vaue o Iniia SOC or one i, Based on saisic heory, he expeced vaue o SOC can be ormuaed as: Where sp( s, ) E s = () s= (, ) = s= 0 = ST S (7) p p p s r, i s = p( s, ) = pst ps ( s r( ) ), i s (2) = E. Expeced Vaue o Eecriciy Consumpion or one Charging Saion Taking he expecaion or boh sides o Eq. (0), we have Where, s C ρ N E En E r s η = i= C N E r s 4 ( ) = ( min(, )) 4, s = ρ = η N ( ( min(, ))) (3) ψ = ε θ (4) δ The oa amoun o charging s is a random variabe. However, i we regard each as a sochasic arge, here wi be one more redundancy i he number o charging s is considered as an individua random variabe. Thereore, we ony need o consider he oa amoun o s in he arge area, which is N, and marke shares or each vehice ype. Las, he aciy o a charging saion may be imied due o he charging imiaion o he speciic disribuion eeder where he charging saion is ocaed, e.g. imied marke peneraion, imied charger number n. Thus, he consrains are as oows, En / P (5), θ θ (6) n n (7)

5 Where P is deermined by he aciy o he speciic eeder; θ and n are aso aeced by how he charging can be coordinaed. In acor, since he imum charging rae or each charger is ixed in a charging saion, n is decided by P. Thus, as ong as (7) is saisied, a he hree consrains are saisied. I he simuaion resu a shows ha i requires more han n chargers, i.e. n> n, he En, a shoud be adused o En = P. *, IV. CASE STUDY Avaiabe daa are survey resus o daiy rave daa and mie driven daa, which can be obain rom NHTS. The probabiiy disribuions o SOC and Sar ime o charging are derived by curving iing he probabiiy disribuions o given daa and survey resus, and hen discreized in accepabe resouions. Oupu daa shoud be he eecriciy demand rom charging or one charging saion a each hour. Based on experiences, η = 83.33%, SOC = 00%. The vaue o ECM and marke shares or each vehice ype are shown in Tabe I [, 2]. Since he charging rae is assumed o be 7.2 kw/h, he SOC is assumed o increase 20% per hour. The inerva o index is assumed o be an hour. Thus, r = 0.2 and he esimaed vaue wi be eecriciy demand wihin he hour. The arge area is assumed o have a popuaion o 5000 wih 50% peneraion. Through MATLAB simuaion, he expeced vaue o SOC can be i, cacuaed, shown in Tabe II and demonsraed in Fig. 6. Subsiuing Eq. (3) wih acua vaues, we have,, ( ) 4 s s ECM AER ρ E En = N E min( r, s) (8) Fina resus o eecriciy consumpion or a charging saion are shown in Tabe III and demonsraed in Fig. 7. The expeced number o charging s are cacuaed based on he expecaion o he eecriciy consumpion, as shown in Fig. 8. I he imiaion o he charger number is 200 as an exampe, he expeced number o charging s and eecriciy consumpion need o be adused accordingy, as shown in Fig. 7 and 8. By adusing he vaue o parameers used in he agorihm, he expeced resus can be obained or dieren cases. schedues can be assumed or each case sudy by making i mach he expeced consumpion resus, i a genera TABLE I. = EXPECTATION OF SOC Vehice ype () Compac sedan Mid-size sedan Mid-size SUV Fu-size SUV ECM (kwh/mie) Percenage (%) 5.48% 0.35% 23% 5.7% Baery aciy (kwh) or PH TABLE II. EXPECTATION OF SOC Hours(h) Expecaion Hours(h) Expecaion TABLE III. Fig. 6. Expecaion o SOC a ime (-24h) ELECTRICITY CONSUMPTION OF A CHARGING STATION Hours (h) Expecaion (kwh) Hours (h) Expecaion (kwh) Fig. 7. Expecaion o eecriciy demand a ime (-24h) assumpion or orecas o charging scenarios is needed. Furher sudies o how o use he resus wi be invesigaed.

6 Fig. 8. Expeced number o charging s a ime (-24h) V. CONCLUSION The conribuions o his work are as oows: The driving and charging characerisics are anayzed using he rea saisica daa. Baery echnoogy, charging eve, peneraion, AER, daiy rip mies, saring ime o charging, and SOC are aken ino consideraion; The saisica descripions (pd) o he key variabes are deveoped. The coninuous uncions are discreized o simuae he probabiiy disribuion; The uncerainies o he random variabes are inegraed and inerconneced; Numerica experimens are impemened o veriy he proposed anaysis and iusrae he eecriciy demand ha s conribue o he disribuion sysems. REFERENCES [] K. Cemen-Nyns, E. Haesen and J. Driesen, "The Impac o Charging Pug-In Hybrid Eecric Vehices on a Residenia Disribuion Grid," in IEEE Transacions on Power Sysems, vo. 25, no., Feb [2] Q. Yan and M. Kezunovic, "Impac anaysis o Eecric Vehice charging on disribuion sysem," Norh American Power Symposium (NAPS), 202, Champaign, IL, 202, pp. -6. [3] R. C. Green, L. Wang and M. Aam, "The impac o pug-in hybrid eecric vehices on disribuion neworks: a review and ouook," IEEE PES Genera Meeing, Minneapois, MN, 200, pp. -8. [4] R. Liu, L. Dow and E. Liu, "A survey o P impacs on eecric uiiies," Innovaive Smar Grid Technoogies (ISGT), 20 IEEE PES, Hion Anaheim, CA, 20, pp. -8. [5] A. Dubey and S. Sanoso, "Eecric Vehice Charging on Residenia Disribuion Sysems: Impacs and Miigaions," in IEEE Access, vo. 3, no., pp , 205. [6] S. Rahman and G. B. Shresha, "An invesigaion ino he impac o eecric vehice oad on he eecric uiiy disribuion sysem," in IEEE Transacions on Power Deivery, vo. 8, no. 2, pp , Apr 993. [7] X. Yan, C. Gu and F. Li, Vaue Quaniicaion o Eecric Vehice Response on Nework Invesmen in he UK, 206 IEEE PES Innovaive Smar Grid Technoogies (ISGT), Lubana, 206 [8] G. M. L. Guérin and P. R. W. G. Buckna, "High peneraion o eecric vehices in an isoaed grid: A sudy in Guadeoupe," 206 IEEE 6h Inernaiona Conerence on Environmen and Eecrica Engineering (EEEIC), Forence, 206, pp. -6. [9] S. Fukushima and K. Tanaka, "Vehice-o-grid uiizaion possibiiy based on run daa o eecric vehices," 206 IEEE 6h Inernaiona Conerence on Environmen and Eecrica Engineering (EEEIC), Forence, 206, pp. -6. [0] D.Thomas, C. S. Ioakimidis, V. Konari, F. Vaee and O. Debecker, Eec o eecric vehices opima charging-discharging schedue on a buiding s eecriciy cos demand considering ow voage nework consrains, 206 IEEE PES Innovaive Smar Grid Technoogies (ISGT), Lubana, 206 [] S. Shaiee, M. Fouhi-Firuzabad and M. Rasegar, "Invesigaing he Impacs o Pug-in Hybrid Eecric Vehices on Power Disribuion Sysems," in IEEE Transacions on Smar Grid, vo. 4, no. 3, Sep [2] R. C. Leou, C. L. Su and C. N. Lu, "Sochasic Anayses o Eecric Vehice Charging Impacs on Disribuion Nework," in IEEE Transacions on Power Sysems, vo. 29, no. 3, May 204. [3] J. Fuhr, K. H. Aher and C. Weinhard, "A Sochasic Mode or Simuaing he Avaiabiiy o Eecric Vehices or Services o he Power Grid," Sysem Sciences (HICSS), rd Hawaii Inernaiona Conerence on, Honouu, HI, 200, pp. -0. [4] Q. Yan, B. Zhang and M. Kezunovic, "The demand response suppor under weaher impacs using PV generaion and energy sorage," 206 IEEE 6h Inernaiona Conerence on Environmen and Eecrica Engineering (EEEIC), Forence, 206, pp. -6. [5] R. Scharrenberg, B. Vonk and P. H. Nguyen, " sochasic modeing and is impacs on he Duch disribuion nework," Probabiisic Mehods Appied o Power Sysems (PMAPS), 204 Inernaiona Conerence on, Durham, 204, pp. -6. [6] I. Sharma, C. Cañizares and K. Bhaacharya, "Smar Charging o Ps Peneraing Ino Residenia Disribuion Sysems," in IEEE Transacions on Smar Grid, vo. 5, no. 3, pp , May 204. [7] J. A. Orr, A. E. Emanue and K. W. Oberg, "Curren Harmonics Generaed by a Cuser o Eecric Vehice Baery Chargers," in IEEE Transacions on Power Apparaus and Sysems, vo. PAS-0, no. 3, pp , March 982. [8] K. Qian, C. Zhou, M. Aan and Y. Yuan, "Modeing o Load Demand Due o Baery Charging in Disribuion Sysems," in IEEE Transacions on Power Sysems, vo. 26, no. 2, pp , May 20. [9] S. Shey and K. Bhaacharya, "A sochasic disribuion operaions ramework o sudy he impac o P charging oads," Norh American Power Symposium (NAPS), 205, Charoe, NC, 205, pp. -6. [20] M. Duva and E. Knipping, "Environmena assessmen opug-in hybrid eecric vehices voume : Naiona wide greenhouse gas emissions," EPRI, Tech. Rep., [2] U.S. Deparmen o Transporaion, Federa Highway Adminisraion, 2009 Naiona Househod Trave Survey. URL: hp://nhs.orn.gov. [22] PNNL Rep., Nov. 2007, Impacs assessmen o pug-in hybrid vehices on eecric uiiies and regiona U.S. power grids par : Technica anaysis, [Onine]. hp://