Dynamic and Fast Electric Vehicle Charging Coordinating Scheme, Considering V2G Based Var Compensation

Transcription

1 Dynamic and Fas Elecric Vehicle Charging Coordinaing Scheme, Considering V2G Based Var Compensaion Wenjie Zhang, Hao Quan, Okoviano Gandhi, Carlos D. Rodríguez-Gallegos, Dipi Srinivasan, and Yang Weng Deparmen of Elecrical and Compuer Engineering, Naional Universiy of Singapore, Singapore, Experimenal Power Grid Cenre (EPGC), Agency for Science, Technology and Research (A*STAR), Singapore, Solar Energy Research Insiue of Singapore (SERIS), Naional Universiy of Singapore (NUS), Singapore School of Elecrical, Compuer and Energy Engineering, Arizona Sae Universiy Absrac Elecric Vehicles (EVs) are viewed as a promising soluion o reduce carbon fooprin in ransporaion. However, wihou proper coordinaion, a large scale of simulaneous EV charging aciviies can cause volage collapse and frequency insabiliy in power sysems. In lieraure, various mehods have been proposed for EV charging coordinaion. Neverheless, mos of hem only focus on acive power conrol. More recen researches have considered Vehicle-o-Grid (V2G) based var compensaion, however, hey are based on heurisic mehods, which are no compuaionally efficien and he global opimal canno be guaraneed. In his paper, a disribued EV charging coordinaing scheme is proposed for efficienly coordinaing EV charging processes and compuing V2G based var capaciy. Case sudies show ha he proposed disribued coordinaion no only has a similar performance as cenral coordinaion in erms of gaining economic benefis, bu also akes significanly less compuaional ime han he cenral coordinaion. NOMENCLATURE Variables s Sae variable SOC Sae of charge u Decision variable p Sraegy V Evaluaing funcion P Acive power charging marix of EVs Q Var supply marix of EVs I Charging inerval marix of EVs R Power raing marix of EVs Cpc ba Capaciy marix of baeries Cos k Charging cos for k h EV Parameers K The amoun of EVs T The maximum amouns of inervals Cos parameer of acive power C x /var/baery degradaion U T M Upper riangular marix RT M Marix used o calculae variaion DoD lm Deph of discharge limi Ses and indices P S EV S k EV charging periods se The se of EVs conneced o chargers Index of ime periods (1 T ), P S Index of EV(1 k K), k EV S I. INTRODUCTION Elecric Vehicles (EVs) are receiving increasing ineress as hey are viewed as a promising echnology for reducing green gas emissions [1]. However, a large deploymen of EVs no only affecs power sysem operaion and planning, bu can also induce unprecedened phenomena [2], [3], [4]. For example, uncoordinaed charging of EVs can lead o volage collapse and large charging power variaions can resul in frequency variaions. Therefore, i is necessary o coordinae complicaed EV charging processes. Moreover, as EV charger echnologies advance, EV chargers are capable of providing var o power sysems [5]. From he perspecive of power sysem operaors, Vehicle-o-Grid (V2G) based var compensaion is fasresponding due o he naure of EV chargers, which, however, is difficul o be uilized because of he mobile and uncerain behaviors of EVs. In lieraure, coordinaed charging has been performed using linear programming [6], sequenial quadraic opimizaion [3], [7], [8], dynamic programming [9], and heurisic mehods [1], [11], [12], [13], ec. However, hese previous sudies only focus on acive power coordinaion. More recen researches have been done from he perspecive of var compensaion [14], [15], [16], [17]. Neverheless, hey are no compuaionally efficien as hey are based on heurisic mehods. Moreover, charging demand of EVs is no considered in [14], [15], [16]. Noably, he aforemenioned mehods do no ake ino accoun acive charging power variaions, which can cause significan grid frequency variaions. Considering he disadvanages of exising mehods, a new coordinaion scheme is proposed in his paper. The major conribuions of his works are: 1) The proposed coordinaion scheme is compuaionally efficien as i is based on quadraically consrained programming (QCP).

2 2) The proposed disribued algorihm performs beer han oher exising disribued algorihms in he lieraure. 3) V2G based var compensaion is aken ino consideraion and is capaciy can be compued efficienly. 4) Uncerainies of EVs are simulaed o validae he performance of he proposed coordinaing scheme in a more realisic manner. The res of he paper is organized as follows. Problem formulaion is presened in Secion II, followed by he descripion of he case sudies in Secion III. Finally, conclusions are drawn in Secion IV. II. PROBLEM FORMULATION In he proposed EV charging coordinaing scheme, wo agens are included, which are EV agen (EVA) and parking lo coordinaing agen (PLCA). The objecive of EVA is o minimize charging coss for he corresponding EV. However, wihou coordinaing he charging power of EV flees, he aggregaed charging discharging power can become oo high in he peak and nadir price periods, respecively. Considering he capaciy of ransformers locaed in buildings (parking los), i is necessary o conrol he peak charging and discharging power. This ask is done by PLCA in he proposed EV coordinaing scheme. Moreover, large charging power variaions may lead o significan grid frequency variaions. Therefore, conrolling charging power variaions is anoher objecive of PLCA. A. Behavior and Objecive Modeling for EVA Before proceeding o he descripion of he EVAs behaviors, a preliminary sep is o model he sae of EVAs. This is because he acion aken by he EVAs is dependen upon heir sae, he sae of local environmen and he messages received. The local environmen of EVAs is nondeerminisic and so is he sae of EVAs. The nondeerminism originaes from he fac ha fuure load variaion and grid nework opology are uncerain, and ha he ime he EVs are conneced o or disconneced from chargers is uncerain. Considering he uncerain naure of EVs, i is necessary o model he EVA under uncerain decision-making process. Moreover, in order o reduce he required compuaional memory of EVAs and o simplify heir behaviors, an appropriae choice of sae variables saisfying he Markov propery is necessary. The model where he Markov propery applies indicaes ha pas acions aken by agens have an impac on he fuure only via he curren saus, in which case i is no necessary for agens o memorize acions aken before [any reference]. The model formulaion of EVA under uncerain decision making is shown below. The sae variable is defined as shown in Eq. (1). s = (SOC ) (1) where SOC is he sae of charge a ime slo, which is a measure of he remaining energy in he baeries of EVs. The decision variable is defined as shown in Eq. (2). u = P (2) where P is he acive power charging rae a ime slo. Hence, sraegies are defined as shown in Eq. (3). p,n (s ) = (u (s ), u +1 (s +1 ),..., u +n (s +n )) (3) Summarizing all above, he sae ransforming funcion is shown in Eq. (4). s +1 = T (s, u ) = s + u I (4) Considering ha economic benefis are wha cusomers concern mos, he charging cos for a single EV is adoped as an evaluaing funcion, which is shown in Eq. (5). V,n (s, u, s +1, u +1,..., s +n, u +n ) = i=+n i= u i I i C i (5) As menioned previously, economic benefi is he main prioriy of he EV owners and i direcly moivaes hem o paricipae in EV coordinaion. Hence, he objecive of EVAs is formulaed o minimize charging coss for he corresponding EV, as shown in Eq. (6). min V,n (6) To be specific, he explici objecive funcion for k h EV is shown in Eq. (7). min Cos k = T P k I k CP + T Q k I k CQ =1 =1 + T (7) min (P k, ) I k C d =1 This opimizaion is subjec o he following consrains. P 2 k, + Q 2 k, R 2 k, he maximal raing of charger for P S, k EV S (8) Q k, for P S, k EV S (9) P I UT M + SOC ini < Cpc ba baery capaciy limiaion P I UT M + SOC ini > DoD lim Cpc ba deph of discharge limiaion P I 1 N 1 SOC arge SOC arge (1) (11) (12) Wihou loss of generaliy, consrain (15) can be added o se var compensaion o be capaciive because inducive loads are mosly seen in power sysems. Q k, can also be consrained o be posiive o provide inducive var according

3 o load demands. The formulaion shown above ensures he Markov propery, which means he pas sraegy has an impac on he fuure only via he curren saus. Hence, as long as we know he curren sae, we have all informaion abou he pas and we can make a decision only based on he curren sae. One of he rigger condiions of he above opimizaion behavior is ha he respecive EVA is generaed. The condiion for generaing EVA is ha a new EV is conneced o a charger and he EVA will vanish when he EV is disconneced, in order o save memory and compuaional resources. During he periods when EVs are conneced o chargers, he opimizaion behavior is sill necessary o be aken a a consan frequency o reflec unexpeced changes in power sysems. B. Behavior and Objecive Modeling for PLCA The objecive of PLCA is o minimize he oal charging cos of a parking lo, which is shown in (13). min Cos = K + K T P k, I k, CP + K Respecive consrains are lised below. P 2 k, + Q 2 k, R 2 k, charger raing limiaion T Q k, I k, CQ T (P k,, ) I k, C d (13) for P S, k EV S (14) Q k for P S, k EV S (15) P k is he charging acive power of he k h EV a ime slo, Q 11 Q Q 1T Q = Q 21 Q Q 2T Q K1 Q K2... Q KT Q k is he charging var of he k h EV a ime slo, I 11 I I 1T I = I 21 I I 2T I K1 I K2... I KT and I k is he charging inerval of he k h EV a ime slo. RCM is a T by T 1 consan marix, as shown in Eq. (22) RCM = (22) The operaor is he enrywise produc, which is defined as (P I) mn = P mn I mn. The UT M is he upper riangular marix. DoD lim is he maximum deph of discharge, which is se o be.2 in his work. To make (13) in he sandard form of convex programming problems, he dimension of variables is augmened by adding a variable Z. P I UT M + SOC ini < Cpc ba baery capaciy limiaion (16) The new objecive funcion is: Z k = min (P k ) (23) P I UT M + SOC ini > DoD lim Cpc ba deph of discharge limiaion P I 1 K 1 SOC arge SOC arge (17) (18) Pcap low 1 1 K P Pcap high oal charging acive power is limed o he capaciy of parking los (19) Q low cap 1 1 K Q Q high cap oal charging reacive power is limed o he capaciy of parking los (2) Pramp low < P RCM < Pramp high (21) charging power variaion is limied where P 11 P P 1T P = P 21 P P 2T P K1 P K2... P KT min Cos = K T P k I k CP + K T Q k I k CQ + K (24) T Z k I k C d Two more consrains are needed o guaranee ha he modified opimizaion problem is equivalen o he original one. Z P (25) Z (26) As i can be appreciaed, he objecive funcion (24) is linear, consrains (16), (17), (18), (19), (2), and (21) are linear, and consrain (14) is quadraic. Hence, he modified opimizaion problem is a sandard QCP problem. Even hough he QCP problem can be solved efficienly by some commercial opimizers, such as MOSEK [18] and Gurobi [19], when here is a large number of EVs, he compuaional ime required for he opimizaion process is

4 Sar A new EV is conneced? Yes EVA is acivaed No PLCA is acivaed Arrival ime (hour) No Toal charging power or is variaion exceeds limis? Yes Fig. 1. Disribued EV coordinaion TABLE I DISTRIBUTION PARAMETERS OF ARRIVAL TIME AND DEPARTURE TIME Arrival Deparure Parameer weekday weekend weekday weekend µ T [h] (σ T ) 2 [h] sill exremely high. Hence, he cenral coordinaion of PLCA is ime-consuming wih a large number of EVs. k=k k=1 min Cos EV k k=k min Cos EV k (27) k=1 To furher reduce he compuaional ime, he cenral coordinaion of PLCA should be called only when i is necessary. This progressive relaionship shown in Eq. (27) indicaes ha if consrain (19) and (2) are no violaed, he PLCA is doing charging opimizaion for each EV in a EV flee, which furher indicaes ha only when consrain (19) and (2) are violaed, he PLCA should be acivaed o cenrally conrol he charging power of he EV flee, as shown in Fig. 1. Moreover, o gain some power margins o reduce he number of imes he PLCA is acivaed, he oal charging power can be reduced o be less han he maximum raing once he PLCA is acivaed. III. CASE STUDY AND DISCUSSION A. Uncerainy Modeling of EV Charging Parking Los To es he PLCA and he EVA, i is necessary o build uncerainy scenarios for EVs. Using he daa from [12], uncerainy scenarios of EV charging in parking los are creaed based on Mone-Carlo simulaion. The average and variance of arrival and deparure ime are shown in Table I. The visualizaion of he parking duraion ime disribuion during weekdays is shown in Fig. 2. The energy requiremens of EVs are shown in Fig. 3, which is ploed according o he inverse Gaussian disribuion of daily ravel disance analyzed in [12]. The visualizaion of he parking duraion ime disribuion in weekday is shown in Fig Deparure ime (hour) Fig. 2. Disribuion of arrival ime and deparure ime (5 EVs case) EV amoun Daily energy demand (KJ) B. Simulaion Seing Fig. 3. Disribuion of energy requiremens The peak charging and discharging power limi and charging power variaion limi for differen cases are lised in Table.??. Cos parameers such as acive power price and reacive power price are aken from 215 Singapore annual elecriciy price [reference o EMA websie]. The baery degradaion parameer C d is se according o [2]. The simulaion is done on a DELL 92 compuer, wih 12GB memory and i5-459 CPU insalled. C. Resuls and Discussions Four ypes of sraegies are simulaed in he case sudies, which are lised in Table II. Sraegy Average sraegy Maximum power sraegy Cenral coordinaion Disribued coordinaion TABLE II LIST OF STRATEGIES Explanaion Charge EVs a a consan power Charge EVs a he maximum power raing Charge EVs only under PLCAs Charge EVs under EVAs, PLCAs are acivaed when necessary Fig. 4 shows he charging power and SOC profile of EV No. 13 in EV case 3. In he Fig. 4, under coordinaion, EV No. 13 is charged during low price periods and discharge during high price periods. In he peak price periods or nadir price

5 Charging power (kw) Dynamic Charging Power scheduling of EV No. 13 in EV 3 cases Charging power under cenral coordinaion Charging power under disribued coordinaion Charging power under average sraegy Charging power under max power sraegy ime.65 SOC Saus.6 SOC Saus SOC Saus under cenral coordinaion SOC Saus under disribued coordinaion SOC Targe Time (h).11.1 Elecriciy Price Acive Power Price Elecriciy Price ($/kwh) Half Hour Periods Fig. 4. Dynamic acive power profile of EV No. 13 Load(kW) Var (kvar) Elecriciy Price ($/kwh) 5 EV Acive Power Charging Load Profile EV charging acive power load profile EV charging Load variaion Time V2G based Var resources profile -5-1 V2G based Var resources Time Elecriciy Price Acive Power Price Half Hour Periods Fig. 5. Charging load profile, charging power variaion, and V2G based var capaciy profile under disribued coordinaion (1 EVs) EV charging cos ($) Cos of disribued coordinaion Cos of cenral coordinaion EV number Fig. 7. Economic comparison a individual EV level (1 cases) Toal charging cos ($) EV case 1 EV case 2 EV case 3 Cos of disribued coordinaion Cos of cenral coordinaion Cos of averge sraegy Cos of max power sraegy Fig. 6. Economic benefi comparison beween four sraegies periods, EVs wan o maximize heir own profis. However, if every EVA maximizes heir own profis, he overall charging power would be oo large o be afforded by disribuion sysems. In his case, PLCA plays a role in conrolling he peak charging and discharging power and charging power variaion, as shown in Fig. 5. The maximum power of he EV case 1 is conrolled o be less han 5 kw and he charging power variaion is less han 25 kw, which coincides wih he peak charging power and charging power variaion limis. In Fig. 5,a dynamic var capaciy profile is also shown. As can be observed from Fig. 5, as he number of EVs increases, available var resouces generally increase as well. This is due o more EV chargers can be uilized for var compensaion. The overall economic benefi comparison is shown in Fig. 6. Compared wih he average charging sraegy and he maximum power sraegy, he coordinaed charging sraegies are convincingly superior. The disribued coordinaion has almos he same performance as he cenral coordinaion. The economic benefi comparison of individual EV is shown in Fig. 7. As can be seen from Fig. 7, he performance of he disribued coordinaion is mosly he same as he cenral coordinaion a he individual EV level as well.

6 TABLE III AVERAGE COMPUTATION TIME FOR EACH EV UNDER DISTRIBUTED AND CENTRAL COORDINATION Compuaional ime(sec) Case 1 Case 2 Case 3 disribued coordinaion cenral coordinaion Improvemen (%) The compuaional ime for each EV are analyzed in Table III, in which i can be observed ha he disribued coordinaion saves up o 9% compuaional ime, compared wih he cenral coordinaion. Considering ha hey have mosly he same performance in erms of economic benefis, he disribued coordinaion is superior because i akes significanly less compuaional ime. IV. CONCLUSIONS In his paper, an EV coordinaion scheme is proposed for coordinaing charging processes of EV flees. In he proposed scheme, EV coordinaion is formulaed as a dynamic programming problem and charging opimizaion is solved using quadraically consrained programming. Furher, o reduce compuaional ime coss, he cenral EV coordinaion is disribued o each EV. Case sudies show ha he disribued coordinaion no only has a similar performance as he cenral coordinaion in erms of gaining economic benefis for EV owners, bu also akes significanly less compuaional ime. Therefore, he proposed disribued EV coordinaion scheme can improve he speed of opimal Vehicle-o-Grid var dispach and EV based demand response. ACKNOWLEDGMENT This work was suppored by he Minisry of Educaion, Singapore under Gran R-263--C [8] A. Hajimiragha, C. A. Canizares, M. W. Fowler, and A. Elkamel, Opimal ransiion o plug-in hybrid elecric vehicles in onario, canada, considering he elecriciy-grid limiaions, IEEE Transacions on Indusrial Elecronics, vol. 57, no. 2, pp , 21. [9] S. Han, S. Han, and K. Sezaki, Developmen of an opimal vehicle-ogrid aggregaor for frequency regulaion, IEEE Transacions on smar grid, vol. 1, no. 1, pp , 21. [1] K. Schneider, C. Gerkensmeyer, M. Kinner-Meyer, and R. 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