Finite Action-Set Learning Automata for Economic Dispatch Considering Electric Vehicles and Renewable Energy Sources

Transcription

1 Energies 2014, 7, ; doi: /en Aricle OPEN ACCESS energies ISSN Finie Acion-Se Learning Auomaa for Economic Dispach Considering Elecric Vehicles and Renewable Energy Sources Junpeng Zhu 1, Ping Jiang 1, *, Wei Gu 1, Wanxing Sheng 2, Xiaoli Meng 2 and Jun Gao 1 1 School of Elecrical Engineering, Souheas Universiy, Nanjing , China; s: zhujp_0705@163.com (J.Z.); wgu@seu.edu.cn (W.G.); seueegj@gmail.com (J.G.) 2 China Elecric Power Research Insiue, Beijing , China; s: wxsheng@epri.sgcc.com.cn (W.S.); mengxl@epri.sgcc.com.cn (X.M.) * Auhor o whom correspondence should be addressed; jping@seu.edu.cn; Tel.: ; Fax: Received: 19 May 2014; in revised form: 10 July 2014 / Acceped: 11 July 2014 / Published: 22 July 2014 Absrac: The coming ineracion beween a growing elecrified vehicle flee and he desired growh in renewable energy provides new insighs ino he economic dispach (ED) problem. This paper presens an economic dispach model ha considers elecric vehicle charging, baery exchange saions, and wind farms. This ED model is a high-dimensional, non-linear, and sochasic problem and is soluion requires powerful mehods. A new finie acion-se learning auomaa (FALA)-based approach ha has he abiliy o adap o a sochasic environmen is proposed. The feasibiliy of he proposed approach is demonsraed in a modified IEEE 30 bus sysem. I is compared wih coninuous acion-se learning auomaa and paricle swarm opimizaion-based approaches in erms of convergence characerisics, compuaional efficiency, and soluion qualiy. Simulaion resuls show ha he proposed FALA-based approach was indeed capable of more efficienly obaining he approximaely opimal soluion. In addiion, by using an opimal dispach schedule for he ineracion beween elecric vehicle saions and power sysems, i is possible o reduce he gap beween demand and power generaion a differen imes of he day. Keywords: economic dispach; sochasic opimizaion; elecric vehicles; wind power; learning auomaa

2 Energies 2014, Inroducion Economic dispach (ED) is defined as he allocaion of generaion levels o differen elecrical generaion unis, so ha he sysem load may be supplied enirely and mos economically. To solve he ED problem, one seeks o find he opimal allocaion of he elecrical power oupu from various available generaors. Elecric vehicle (EV) flees and renewable energy sources (such as wind power) have brough wo new dimensions o his problem, along wih he challenges inroduced by heir uncerainy. EVs have he poenial o be a revoluionary invenion for boh ransporaion and he elecriciy indusry [1]. Research shows ha, if he indusry develops a medium speed, he peneraion of EVs in he USA will reach 35% by 2020, 51% by 2030, and 62% by 2050 [2]. According o he Chinese Energy saving and new energy vehicle indusry developmen plan ( ), by 2030 here will be more han 60 million EVs. If every EV simulaneously charges a 5 kw, he power demand could as large as 0.3 billion kw (13% of he projeced 2030 naional power capaciy). Meanwhile, renewable energy resources are having a significan effec on elecrical power generaion [3,4]. Wind power is a source of clean energy and is able o reduce boh he consumpion of depleing fuel reserves and emissions from polluans. In 2010, he Chinese naional insalled capaciy of wind power was 44, MW. I is widely expeced ha i will rise o 138,000 MW by 2020, which would be 10% of he expeced naional capaciy [5]. The inegraion of EVs and wind urbines ino he grid creaes new challenges for power sysem operaors. A large number of EVs will inroduce significan uncerainy ino power sysems because of he random naure of heir charging behaviors. If he EVs are disorderly when charging, an exra burden will be placed on he power sysem, which will expose vulnerabiliies. However, a fair charging schedule can significanly reduce hose negaive effecs [6 9]. In addiion, he oupu of wind farms can change rapidly hroughou a day. In mos cases, during he dayime he wind oupu is small while he power load is heavy, and he siuaion reverses during he nigh-ime. This dislocaion beween renewable resources and power demand can only be miigaed when large energy sorage faciliies are available [10 12]. The vehicle-o-grid (V2G) concep allows EVs o be regarded as such faciliies. Markel e al. [13] showed ha here will be sufficien renewable energy sources o charge a plug-in hybrid EV (PHEV) flee, based on he growh raes assumed in he analysis. Addiionally, a PHEV flee has he abiliy o serve as an energy sink for renewable power generaion. In Zhang e al. [14], a power scheduling approach was inroduced for energy managemen of micro-grids considering sochasic availabiliy of renewable energy sources and power demand of elecric vehicles. In Zhao e al. [15], he auhors developed an economic dispach model ha akes ino accoun he uncerainies of plug-in EVs (PEVs) and wind generaors. A simulaion-based approach is used o sudy he probabiliy disribuions of he charge/discharge behaviors of PEVs. Yu e al. [16] addressed he economic dispach problem for disribuion sysems ha conain wind power and mixed-mode EVs. Three ineracion modes were inroduced and compared, bu only he baery exchanger mode is schedulable. From a mahemaical poin of view, ED is an opimizaion problem. Various algorihms have been applied o solve classic ED problems. They include mixed ineger programming [17], Lagrange relaxaion [18], neural neworks [19], and paricle swarm opimizaion [20]. When sochasic variables involved, in Zhao e al. [15], he auhors used probabiliy disribuions o model wind power and he

3 Energies 2014, behavior of EVs, and hen heoreically derived he mahemaical expecaions of he generaion coss. This mehod is effecive and convincing, bu can only be used when he mahemaical expecaions are simple. Liu e al. [21] proposed a here-and-now approach for ED problem o avoid he probabilisic infeasibiliy appearing in convenional models. In Hezer e al. [22], facors o accoun for boh overesimaion and underesimaion of available wind power are included in addiion o he classic economic dispach facors. A Mone Carlo mehod was used o generae a large number of scenarios ha represen he volailiy of wind power in [23]. The mehod required oo much compuaion o be used pracically. Inelligen algorihms ha are compuaionally efficien and have he abiliy o adap o sochasic variables need o be developed so ha he ED problem can be solved for fuure power sysems [24]. In his paper, we presen an ED model ha includes wind power and a high peneraion of EVs, which we solve using a finie acion-se learning auomaa (FALA) mehod. The organizaion of his paper is as follows. We describe he modeling of EVs, wind power and load in Secion 2, and formulae he ED problem in Secion 3. In Secion 4, we develop a FALA-based approach which can adap o a sochasic environmen o solve our ED problem. We discuss he resuls in Secion 5 and our conclusions in Secion Models of he Power Demand and Supply of EVs, Wind Power, and Load We consider he demand/supply of EVs, he oupu of wind farms, and he regular load as sochasic variables. This is because i is difficul o forecas hese variables and hey are relaed o uncerainies such as driver behavior. In his secion, we analyze and model all of hese sochasic facors Modeling of he Power Demand and Supply of EVs There are hree mainsream ineracive modes of EVs: normal ineracion (NI), fas charging (FC), and baery exchange (BE). FC mode is derimenal o he baery, and inroduces harmonic polluion o power sysems. Therefore, his mode is no likely o be widely applied in he fuure, and our ED model only considers NI mode and BE mode. The behavior characerisics of EV owners are deermined by differen uncerain facors (such as ravel habi, vehicle ype, and ineracive mode), so heir charging demand ends o be uncerain and difficul o be esimaed wih precision. Therefore, simplificaion is essenial. In his paper, we use he following condiions and assumpions. The analyses around EVs are derived from a prooype of he Nissan Leaf [25], which has a 160-km cruising radius, and a baery capaciy of 24 kwh. The energy an EV has consumed is in direc proporion o he disance i has raveled. The probabiliy disribuions of an EV s arrival ime and he disance he EV has raveled are derived from driving paern daa colleced in he Naional Household Transporaion Survey (NHTS) [26]. The peaks of baery exchange demand are during he morning rush hour, lunch ime, and afernoon rush hour. We will now discuss he ineracive modes of he EVs separaely.

4 Energies 2014, Power Demand and Supply of NI EVs NI EVs are widely disribued in he dayime, making i difficul for hem o follow scheduling insrucions, so his model only considers nigh-ime dispach. Suppose some EV owners (proporion τ) sign he user agreemen so ha heir car is conneced o he power grid as soon as hey finish he las rip in a day. In addiion, suppose ha hey obey he dispach plan so ha he baery will be fully charged a 6:00 a.m. The NI EVs dispach is a bi-level model: he upper dispacher gives he plan o he NI saions, and he saions conrol he charging (or discharging), of he EVs. The saions communicae he condiion of he EV o he upper dispacher, such as unsaisfied demand of baery charging. The dispach ime is beween 20:00 and 6:00 he nex day, indicaed as NI schedulable period. To simplify our model, we assume ha each EV charges/discharges in one specified NI saion. For he EVs ha sign he agreemen wih he NI saion conneced wih bus k (indicaed as NI saion k ), consider he penaly funcion a ime as: f Cpower min{0,(( PN s k ( )) Pk, NI ( ))} C min{0,( T P ( j) Qk( i))} NI schedulable period () 0 NIschedulable period energy k,ni k,ni i20:00 i20:00 Qk() i Ql (2) la( k, i) where P k,ni () is he ineracive power beween he sysem and he NI EVs signing he user agreemen in bus k a ime. P k,ni () is posiive when he NI saion is regarded as a load, negaive when he NI saion is regarded as a generaor, and 0 if is no a schedulable ime. The penaly funcion is an approximae measure of he degree of non-saisfiabiliy of he dispach schedule. The firs par represens he power dissaisfy, and he second par represens he energy dissaisfy. The penaly of all NI saions is: f NI,penaly () fk,ni () (3) The EVs no signing he agreemen are regarded as normal load. They sar o charge as soon as finishing he las rip in a day, and coninue unil he baery is full. When conneced o he power faciliies, hese EVs charge a power P s Power Demand/Supply of BE EVs In his mode, ineracion beween he EVs and he power sysem is implemened by baery exchange saions. A a given ime, he sae of he BE saion conneced wih bus m (indicaed as BE saion m ) is described in Equaion (4) [16], and he unme demand of baery exchange can be calculaed by Equaion (5): Em( 1) PmBE, ( T ) Nmex, ( E ) s ifem( 1) Pm,BE ( T ) Nmex, ( E ) s Em() 0 if Em( 1) Pm,BE () T Nm, ex() E (4) s k NI (1)

5 Energies 2014, E mun, N () E E ( 1) P () T if E ( 1) P () T N () E () 0 if E ( 1) P () T N () E m, ex s m m,be m m,be m, ex s m m,be m, ex s (5) In Equaions (4) and (5), P m,be () is posiive when he BE saion is regarded as a load and negaive when he NI saion is regarded as a generaion. The penaly funcion for all BE saions is: fbe,penaly () CBE Emun, () (6) mbe A a given ime, he baery exchange demand is expeced o follow a Poisson disribuion: P( N ) ex λ N ex ex λ e (7) Nex! We do no discuss he reacive demand and supply of EVs in his paper, as i is close o zero Modeling of Regular Load We consider all oher ypes of demand o be regular load and follow a random disribuion. Therefore, a single probabiliy disribuion funcion can be used o describe his acive/reacive demand a each bus. This disribuion can be eiher derived from measuremens or simply assumed o be he normal disribuion N(μ l,σ l ). We use he laer in his model Modeling of Wind Power The oupu of a wind farm is considered o be in proporion o he hird power of he wind speed: 2 3 PR Nw CpR vr 2 0 v v or v v P v v P v v v 3 ci PR 3 vci w() R ci R vr vci vr vci vr vvco PR where P w (v) is he oupu of a wind farm when he wind speed is v. In Hezer e al. [22] i was shown ha wind speed follows a Weibull disribuion: co (8) Vw fv ( w) 1 V w e (9) The wind speed curve is given in Secion 5. Assuming he power facor of a wind farm is consan, we can calculae he reacive power of wind farm using: Pw Qw sin w cos (10) w

6 Energies 2014, Economic Dispach Formulaion 3.1. Objecive Funcion By using an appropriae scheduling sraegy, EVs can miigae problems caused by he difference beween power generaion and demand a differen imes of he day, wih minimized operaional cos. We also need o mee he demand of EV charging. Thus, he objecive funcion is: Coal T ( fg( ) fm( ) fp( )) (11) The expressions of f G, f M, and f P are as follows: 2 2 fg() ( jpj, g() jpj, g() j) jg fm() CwPi, w() CNI ( Pk,NI () Pk, sev()) CBE Pm, BE() iw k NI mbe fp () fni,penaly() fbe,penaly() (12) 3.2. Consrains We mus minimize he objecive funcion subjec o a number of consrains. Power balance consrain: PW PGPloss PEV PL (13) Generaion limiaion consrain: P P () P j min jg, jg, jg, G min P P BE m,be() P m BE BE (14) Power line ransmission limiaion consrain: P i() P j() Pij i j (15) i j indicaes ha bus i and bus j are conneced by a power line. Local volage limiaion consrain: min Ui Ui() Ui (16) Normal ineracion saion operaional consrain: (17) T P, () Q () N Q kni k k ev This consrain ensures ha he dispach schedule saisfies he EV owners requiremens. Baery exchange saion operaional consrain: Em() Em m BE (18)

7 Energies 2014, E E E m () () m 0:00 m 24:00 m BE (19) Equaion (19) ensures ha he baery exchange saion will operae susainably. I is assumed ha, o achieve a susainable operaion, he baery in BE saions should be full a he sar and end of each day ED Problem Formulaion We can wrie he objecive funcion in Equaion (11) as: Coal fobj ( x, ) (20) where x represens he conrol variables (P j,g (), P k,ni () and P m,be (), j 1 because he convenional generaor conneced wih Bus 1 is se as he balancing bus), and ξ represens he random variables (P i,w (), Q k (), and P k,sev ()). We can hen formulae he economic dispach problem as: min x C oal s. g( x, ) 0 hx (,) 0 where g(x,ξ) is he equaliy consrain funcion and h(x,ξ) is he inequaliy consrain funcion. 4. Descripion of he Proposed Approach We can conclude from Secion 3 ha his ED problem can be described as a high-dimensional, nonlinear, and sochasic model. Two classes of mehods have been used in inelligen opimizaion algorihms o obain he deerminisic soluion of a sochasic problem. The firs is o esablish an evaluaion sysem of a soluion in he sochasic environmen, so ha he sochasic problem can be ransformed ino a definie problem. Examples of his ype of mehod include expecaion derivaion, sochasic simulaion, and chance consrained programming (CCP) [27 29]. The oher mehods generae he curren environmen a each ieraion using he mahemaical descripion of he sochasic variables. One example is he coninuous acion-se learning auomaa (CALA) mehod [16]. This sudy proposes a FALA-based approach o address he ED problem The FALA Mehod Learning auomaa (LA) are adapive decision makers ha learn o choose he opimal acion from a se of available acions by using noisy reinforcemen feedback from heir environmen [30]. LA can be divided ino CALA and FALA according o wheher he acion is coninuous or discree. Only FALA is discussed in deail in his secion. Some definiions are given as follows: x is defined as a se of possible acions, f obj (x,ξ) is defined as he response o he se of acions x obained from he sochasic environmen, he funcion F is defined as a reward funcion for he auomaion, which also is defined as he expecaion of f obj : F( x) E[ fobj ( x, )] (22) The goal of FALA is o find x where F(x) is (locally) minimized. I is difficul o calculae F analyically, as he underlying probabiliy disribuion ha governs he reinforcemen, f obj, is unknown. (21)

8 Energies 2014, In FALA, he feasible region is divided ino limied areas. Suppose he amoun of areas is r. In he beginning, he decision variable should obey a discree probabiliy disribuion in he feasible region. During he ieraive process, he algorihm updaes his discree probabiliy disribuion according o he response of he environmen, unil he probabiliy ha he decision variable lies in an area is close o 1. Each area can be represened by one variable (usually he inermediae poins of he area, denoed by a i for area i, i = 1,, r). The discree probabiliy disribuion can be represened by a vecor, P() (he acion probabiliy vecor ), defined as: P () [ p(), p()] 1 r (23) where p i ()(i = 1,...,r) is he probabiliy ha he auomaon will selec he acion a i a ime, defined: p i () saisfies: p () [ () i i Pr x x ], i 1,, r (24) r pi () 1,forall (25) i1 The FALA algorihm T: [0,1] r A B [0,1] r is an updaing scheme where A = {x 1, x 2, x r }, is he se of oupu acions of he auomaon, and B is he response of he environmen. Thus, he updae is: P ( 1) T( P ( ), x ( ), ( )) (26) where x() is he curren value of he conrol variables a h ieraion, generaed based on he acion probabiliy vecor P(). β() is he response of he environmen o x(). β() is generally expressed as: () B( fobj ( x(), ()), flag, bes()) (27) where ξ() is he curren value of he generaed random variables, flag indicaes if he consrains are saisfied, and bes() is he hisorical minimum of he objecive funcion FALA-Based Approach for he ED Problem Our FALA approach is described as follows. Sep 1: The variables are iniialized. The decision variable has n-dimensions (x = (x 1,, x n )) and each dimension is divided ino M inervals, so he feasible region is divided ino M n areas (r = M n ). The acion probabiliy vecor can be expressed by an n M marix, P n,m (), a he h ieraion, where: 1 pi, j(0), i 1,2,3,, n, j 1,2,3,, M (28) M and p i,j () represens he probabiliy ha x i is seleced for he j h inerval a ime. As menioned, when seleced from an inerval, x i willed be assigned as he midpoin of he inerval. Calculae he iniial opimal value in he following way: all he sochasic variables are se o heir expeced value, and he ineracive power beween EV faciliies is equal o he expeced power demand of EVs. Then, calculae he oupu of he convenional generaors using he opimal power flow mehod. The opimal value (bes) is iniialized o be he objecive funcion (indicaed as C oal (0)), i.e.: bes(0) (0) C oal (29)

9 Energies 2014, Sep 2: A se of random variables ξ() is generaed using heir respecive probabiliy disribuions. The curren values of P i,w (), Q k (), and P k,sev () esablish he curren environmen of he ED problem. Sep 3: A se of conrol acions x() is seleced randomly based on he marix P n,m (). Sep 4: The consrains are checked and he value of he objecive funcion, f obj (x(),ξ()), is calculaed. The variable flag is a symbol of wheher he consrains are saisfied, defined as: 0 when no consrain is violaed flag (30) 1 oherwise Sep 5: Calculae he response of he environmen using: 0 if flag( x( )) 0 and bes( ) fobj ( x( ), ( )) () 1 if flag( x( )) 1 or bes( ) fobj ( x( ), ( )) (31) The response of he environmen is 0 when he curren conrol variables are beer (consrains are saisfied and he oal cos is small), he response is 1 when he curren conrol variables are worse. Sep 6: Updae he probabiliy disribuions of he acions. For he inervals ha x i (i = 1,, n) are seleced from, he probabiliies are updaed using: p i, j pi, j() c if () 0 ( 1) pi, j() d if () 1 (32) For he oher inervals, he probabiliies are updaed using: p i, j c pi, j() if () 0 ( 1) M 1 d pi, j() if () 1 M 1 (33) In Equaions (34) and (35), c is a consan represening he sep size. These updaes are derived from an inuiive idea: when he curren conrol variables are beer we increase he possibiliy ha conrol variables are se as curren values, oherwise he curren conrol variables are worse and we increase he possibiliy ha oher values are used for he conrol variables. Sep 7: Updae he curren opimal value of objecive funcion: fobj ( x( ), ( )) if ( ) 0 bes( 1) bes() if () 1 (34) Sep 8: Decide if he algorihm should erminae using: min{{ p ( )}} b i j i, j (35) where b is consan. If he inequaliy in Equaion (35) is saisfied, he probabiliy of he variable lying in an area is greaer han b i and he algorihm sops. If i is no saisfied, Seps 2 7 are repeaed unil he imum number of ieraions is reached. The flow char of he FALA-based approach is shown in Figure 1.

10 Energies 2014, Figure 1. Flow char of he FALA-based approach. 5. Case Sudies A es sysem was developed based on he sandard IEEE-30 bus sysem [31]. Bus 2 was conneced wih baery exchange saions, which had a oal daily capaciy of 2000 EVs. Bus 8 was conneced wih baery exchange saions, which has a oal daily capaciy of 1200 EVs. Buses 7, 21 were conneced wih 2000 EVs respecively using he NI mode, and he proporion of owners, τ, signing he user agreemen was 50%. Two wind farms (wih raed power of 10 MW) were conneced o bus 2 and bus 13. As previously menioned, he number of cars arriving a he NI saions a each ime inerval and he driving disance of a day has been esimaed using he driving paern daa colleced in he NHTS [26]. The daa are shown in Figures 2 and 3. Our examples assume ha he energy consumed by an EV is proporional o he disance i has driven. The predicive probabiliy of he baery exchange demand curve, convenional load demand curve, and predicaive wind speed curve are shown in Figure 4. The raed wind speed is 14 m/s. Oher parameers used for hese examples are: T = 1 h, C w = 500 Ұ/MWh, C NI = 1250 Ұ/MWh, C BE = 1000 Ұ/MWh, C un1 = C un2 = C un3 = 3000 Ұ/MWh, v ci = 3 m/s, v co = 22 m/s, P R = 10 MW, P 2 emin = 10 MW, P 2 e = 10 MW, P 8 emin = 5 MW, P 8 e = 5 MW, E = 24 MWh, U i min = 0.95, and U i = The parameers of he convenional generaors are lised in Table 1, and include he parameers of fuel cos and lower and upper limis of generaion.

11 Energies 2014, Figure 2. Driving paern daa: rip lengh [26] Share of sampled vehicles Cumulaive frequency Las rip ending ime (h) Share of sampled vehicles Cumulaive frequency 0 Figure 3. Driving paern daa: driving disance [26] Probabiliy densiy Probabiliy disribuion Driving disance during one day (km) Probabiliy densiy Probabiliy disribuion Figure 4. Power demand and wind farm oupu predicion. Predicive value (p.u.) :00 9:00 12:00 15:00 18:00 21:00 0:00:00 3:00 Time (h) Wind speed Load Baery exchange

12 Energies 2014, Table 1. Parameers of convenional generaors. Bus Number α i (Ұ) β i (Ұ/MW) γ i (Ұ/MW 2 ) 5.1. Parameer Seings P (MW) min ig, P (MW) ig, The parameers of FALA were se as: M = 10, r = 10 24, c = 0.02 and d = The CALA-based approach is described in Yu e al. [16]. The parameers were se o: a = 0.001, b = 1000, and σ 0 = The PSO-based (paricle swarm opimizaion) approach is summarized as follows: Sep 1. The sochasic problem was ransformed ino a deerminisic problem using CCP (see [32] for deails). The parameers were se as: N = 10, N = 8. Sep 2. The ransformed problem was solved using he PSO algorihm (see Equaion (6) in [33]). The parameers were se as: Popsize = 20, φ ic = 0.5, and φ 1 = φ 2 = Resuls and Analysis All programs were wrien using MATPOWER 4.1 [34] in MATLAB 2010b, and have been run on a deskop PC wih an Iner Core i GHz CPU, and 16 GB ks 4g/1333 RAM Comparison of Convergences The convergence characerisics of he hree algorihms are shown in Figure 5. (1) The convergence crierion of he FALA algorihm is given in Equaion (35). I converged afer approximaely 150 ieraions. In he firs 30 ieraions, he acion probabiliy vecor changed rapidly because bes() was no so small ha he inequaliy consrain in Equaion (36) was easily saisfied. During ieraions he acion probabiliy vecor changed slowly as bes() became smaller. Afer 120 ieraions, he acion probabiliy vecor had changed dramaically and here was a high probabiliy ha he conrol variables were seleced in he opimal inervals, so he inequaliy in Equaion (36) was easily saisfied. These resuls show ha his algorihm is seady, and ha, once converged, he acion probabiliy vecor does no flucuae: bes() fobj ( x(), ()) (36) (2) The CALA algorihm converged afer approximaely 270 ieraions for his ED problem. The convergence crierion of he CALA algorihm flucuaed more dramaically han ha of FALA algorihm, because i had he possibiliy o increase (opposie o he converging direcion) even hough he response of he curren soluion was good enough.

13 Energies 2014, (3) The characerisic curve of he PSO algorihm shows he change of he curren global opimal value wih each ieraion. The value was ransformed using: bes( )' exp(100 ( bes( ) bes(1)) / bes(1)) (37) where bes() is he global opimal value afer ieraions. Afer approximaely 70 ieraions, he global opimal value no longer changed. Alhough he number of ieraions was less han he LA algorihms, i did need more compuing ime because each ieraion was much more complex. We will analyze his in he nex secion. 1.2 Figure 5. Convergence characerisics of hree algorihms. 1 Convergen cierion Ieraion imes FALA convergence crierion PSO curren opimal value CALA convergence crierion Comparison of Compuaion Efficiency The main compuaion work needed for hese algorihms was he power flow calculaion. To calculae he objecive funcion of one se of conrol variables in a deerminisic environmen, he compuer needs o calculae he power flow 24 imes. During each ieraion, he FALA algorihm needs one objecive funcion calculaion; he CALA needs wo, while he PSO needs 200 (he Popsize is 20, calculaing he response of he environmen of one pop using he CCP model requires N (=10) calculaions of he objecive funcion). The complexiy and compuing ime of each algorihm is shown in Table 2. Algorihm Table 2. Algorihm complexiy and compuing ime. f 0bj Calculaion Times Each Ieraion Ieraion Times Toal Times of f 0bj Calculaion Compuing Time(s) FALA CALA PSO ,000 15,872

14 Energies 2014, Comparison of he Soluion Qualiy The environmen is sochasic and he goal of he LA algorihms is o opimize he expecaion of he environmen s response. Moreover, he LA algorihms do no esablish an evaluaion sysem of a soluion in he sochasic environmen. To compare he resuls of he hree algorihms, each soluion was esed in he sochasic environmen 30 imes (Table 3). Algorihm Mean Cos (Ұ) Table 3. Performance of algorihm resuls. Mean Diff (MW) Mean Diff When Charging/ Discharging Disorderly (MW) FALA 57, CALA 57, PSO 57, The resuls in Table 3 show ha he mean cos of he resuls of he PSO algorihm is a lile higher han ha of he LA algorihms. This is because he goal of PSO is no o find he opimal soluion in erms of he expeced cos. The CCP model iself has esablished an evaluaion sysem of a soluion in he sochasic environmen. If he correlaion parameer was se properly in CCP, he PSO algorihm could also achieve an equivalen resul o he LA algorihms. We define Diff as he peak-value difference of hermal power-generaing unis. The algorihms can decrease he peak value by abou 30%. The comprehensive load (including convenional load and EV load) when EVs and baery exchange saions charge/discharge orderly and disorderly are shown in Figure 6. As seen in Figure 6, he scheduling of he EV saion s charging/discharging behavior can decrease he flucuaion of he comprehensive load demand, which is supplied by convenional generaors and wind farms. Considering he dislocaion beween renewable resources and power demand ha we menioned in Secion 1, he dispach of EV saions can accommodae flucuaions in wind power in power sysems Figure 6. Change of comprehensive load. Convenional load (MW) :00 9:00 12:00 15:00 18:00 21:00 0:00 3:00 Time (h) Comprehensive load when charging/discharging disorderly Comprehensive load when charging/discharging orderly

15 Energies 2014, Conclusions In his paper, we have developed a sochasic ED model ha considers a high peneraion of EVs. Boh he NI and BE modes are assumed o be schedulable in our model. We have proposed a FALA-based approach o solve he ED problem and compared he resul wih oher wo inelligen algorihms. Our resuls show ha he FALA algorihm required less ime han he CALA algorihm o reach he opimal soluion, while PSO needed much more ime han boh. FALA can only converge o an inerval, he measure of which is deermined by he iniial values. We conclude ha he decrease in compuaion ime of he FALA algorihm is obained by sacrificing he accuracy. However, he resuls show ha he accuracy of he FALA algorihm is saisfacory in he sochasic environmen ha we esablished in his paper. We also conclude ha orderly charging of EVs can miigae he flucuaion of load, and decrease he peak-value difference of hermal power-generaing unis. However, he ED model developed in his paper should be used wih cauion. Considering he compuaion speed, he lower model of he NI saion is no opimized, and he penaly funcions (Equaion (1) and Equaion (5)) are only an approximaion of he non-saisfiabiliy of he dispach schedule. The models in his paper should be furher developed and more efficien sochasic opimizaion algorihms should be invesigaed before he echniques are applied. Acknowledgmens This work was suppored by he Sae Grid Corporaion of China (PD ), he Naional High Technology Research and Developmen Program of China (863 Program Gran 2012AA050210), he Naional Science Foundaion of China ( ), he Fundamenal Research Funds for he Cenral Universiies, he Naural Science Foundaion of Jiangsu Province of China (SBK ). Auhor Conribuions The lised auhors conribued ogeher o achieve his research paper. Junpeng Zhu designed he opimizaion algorihm, Ping Jiang conribued o economic dispach formulaion, Wei Gu conribued o he modeling of power demand and supply, Wanxing Sheng and Xiaoli Meng did he case sudies, and Jun Gao assised in ypeseing and revision work. Conflics of Ineres The auhors declare no conflic of ineres. Nomenclaure A. Nouns, Numbers, and Ses: EV NI BE Ω a Ω NI Ω W Ω G Elecrical vehicle Normal ineracion model of EVs Baery exchange model of EVs Se of EVs arriving a he NI saion Se of buses conneced wih NI saions, wind farms and convenional generaors

16 Energies 2014, N w N k,s X ξ Number of wind urbines in a wind farm Toal number of EVs signing he dispach agreemen in he NI saion k Se of conrol variables Se of random variables B. Consans: P s Maximum power of EV charging/discharging T Time inerval beween operaions C power, C energy Penaly parameers of unsaisfied baery charging demand C BE Penaly parameer of he unsaisfied baery exchange demand E s Baery capaciy of a single EV λ ex Predicive value of he baery exchange demand P R Raed power of a wind farm ρ Air densiy C p Energy conversion efficiency of a wind farm R Radius of he wind urbine blade v R v ci v co Raed wind speed, cu-in wind speed and cu-ou wind speed μ Prediced value of he wind speed κ Shape parameer of Weibull disribuion θ w Power facor of a wind farm α j, β j, γ j Power generaion cos parameers of a convenional generaor C w Cos of wind power generaion per MW C NI Cos of ineracion power beween NI EVs and he power sysem per MW C BE Cos of he ineracion power beween he baery exchange saions and he power sysem per MW min P ig, P ig, Lower and upper generaion limis of a convenional generaor min P BE min U i Q ev Em P BE Lower and upper limis of ineracive power of he baery exchange saions U i Lower and upper limis of he volage of bus i. C. Uncerain Quaniies: Baery capaciy of a EV Maximum energy sorage capaciy of he BE saion m Q l Q k N k E m P m,be N m,ex E m,un C oal Energy lef in he baery of EV l Toal energy in he baeries of he EVs ha arrive in he NI saion k Number of EVs ha finish he las rip in he NI saion k Salled energy of he saion m The power ransmission beween BE saion m and he power sysem Number of he EVs ha need baery exchange Unsaisfied baery exchange demand Toal operaional cos of he whole sampling period

17 Energies 2014, P i,w P k,sev P W P G P L P EV P i Pij U i E m Wind farm oupu of bus i Ineracive power beween he power sysem and he NI EVs no signing he dispach agreemen in NI saion k Oupu of he wind farms, oupu of convenional generaors and power Loss hrough he ransmission lines Toal ineracive power beween he power sysem and he EV insallaion Injecion power of bus i Maximum power ransmission of he power line ha connecs bus i and bus j Volage of bus I Salled energy of he BE saion m D. Decision Variables: P k,ni Ineracive power beween he sysem and he NI EVs signing he user agreemen in bus k P j,g Oupu of a convenional generaor of bus j, j 1. E. Funcions: f k,ni () f NI,penaly () f BE,penaly () f G () f M () f P () f obj () g(, ) h(, ) F() Penaly funcion of he NI saion of bus k Penaly funcion of all NI saions Penaly funcion of all BE saions Fuel cos, mainenance cos and penaly cos of he sysem Objecive funcion of he opimizaion model Equaliy and inequaliy consrain funcion Reward funcion for he auomaion References 1. Juul, N.; Meibom, P. Road ranspor and power sysem scenarios for Norhern Europe in Appl. Energy 2012, 92, Duvall, M.; Knipping, E.; Alexander, M. Environmenal Assessmen of Plug-in Hybrid Elecric Vehicles; Volume 1: Naionwide Greenhouse Gas Emissions; Elecric Power Research Insiue: Palo Alo, CA, USA, Liu, W.; Lund, H.; Mahiesen, B.V. Large-scale inegraion of wind power ino he exising Chinese energy sysem. Energy 2011, 36, Mahiesen, B.V.; Lund, H.; Karlsson, K. 100% Renewable energy sysems, climae miigaion and economic growh. Appl. Energy 2011, 88, Li, J.F.; Shi, P.F.; Gao, H. Wind Power Developmen Repor in China; Hainan Press: Haikou, China, Fernandez, L.P.; San Roman, T.G.; Cossen, R.; Domingo, C.M.; Frias, P. Assessmen of he impac of plug-in elecric vehicles on disribuion neworks. Power Sys. IEEE Trans. 2011, 26,

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