ARIMA-based Demand Forecasting Method Considering Probabilistic Model of Electric Vehicles Parking Lots

Transcription

1 1 ARIMA-based Demand Forecasing Mehod Considering Probabilisic Model of Elecric Vehicles Parking Los M.H. Amini, Suden Member, IEEE, O. Karabasoglu, Maria D. Ilić, Fellow, IEEE, Kianoosh G. Borooeni Suden Member, IEEE and S. S. Iyengar, Fellow, IEEE Absrac In recen years, increasing fossil fuel prices, environmenal concerns and rising elecriciy demand moivae he power sysem o evolve oward he Smar Grid. Modern ransporaion is one of he key elemens of fuure power sysem. In his conex, uilizaion of elecric vehicles (EV) should be aken ino accoun in a sysemaic way o avoid unpredicable effecs on power sysem. Addiionally, an accurae and efficien demand forecasing mehod is required o perform a feasible scheduling in order o supply he prediced load sufficienly. This paper presens an accurae mehod for he demand forecasing based on hisorical load daa. The mehod is based on auo-regressive inegraed moving average (ARIMA) model for medium-erm demand forecasing. The proposed mehod inmproves he forecasing accuracy. Addiionally, probabilisic hierarchical EVs parking lo demand modeling is used o calculae he expeced load for each parking los daily charging demand. Finally, o evaluae he effeciveness of he proposed approach, i is implemened on PJM hisorical load daa. The simulaion resuls show he high accuracy of proposed mehod for PJM load daa by reaching 0.41% roo mean square error for demand forecas. I. INTRODUCTION In recen years, he power sysem is experiencing one of he mos influenial evoluions ever, he ransiion oward smar grid (SG) because of maor moivaions from he increasing cos of energy o climae change [1]. SG has been proposed o achieve a more susainable, secure and environmenallyfriendly power sysem. Fuure power sysem deploymen involves several sudies, such as sabiliy, reliabiliy, power qualiy, and susainabiliy [2]. According o [3], SG will improve power sysem reliabiliy by using novel equipmens and mehods a supply side and demand side. In addiion, real ime conrol, self-decision making, and disribued energy managemen are wo feaures of fuure power sysem [4], [5], [6]. Several echnologies, including advanced meering infrasrucure, disribued renewable resources, phasor measuremen unis, home area nework, energy sorage and elecric vehicles (EVs) are uilized o achieve a fas, disribued, secure and inelligen power grid [7], [8]. Recenly, SG cusomers and EVs moivaed power sysem o uilize accurae demand forecasing which plays a pivoal role in erms of porraying a general scope for power sysem sudies, such as he power flow problem, energy dispach and adequacy analysis [9]. In [10], a model predicive conrol is s: [email protected], [email protected], [email protected], [email protected], [email protected] applied o solve he economic dispach problem in he presence of inermien resources. Furhermore, his sudy provides a framework o consider he rade-off beween economic and environmenal effecs. According o [9], here have been several effors abou demand forecasing in differen ime horizons using various echniques in he lieraure, including linear regression, fuzzy logic approach and arificial neural nework, suppor vecor machines, ransfer funcions, and grey dynamic model. The aim of his paper is o forecas demand in he medium-erm ime horizon based on hisorical load daa using auo-regressive inegraed moving average (ARIMA) model. However, a mahemaical ARIMA model is inroduced[11], in his paper, we calculae he opimal parameers of ARIMA model based on he hisorical daa, which is more accurae in comparison wih ARIMA implemenaion independen from he naure of inpu raw daa. Elecric vehicles demand modeling is anoher aspec of SG which is addressed in his paper. U.S. governmen plans o uilize more EVs in he near fuure [12]. From he EVs parking lo load modeling perspecive, here have been sudies o exrac a model of EVs charging profile. In [13] EV parking los are uilized o enhance he reliabiliy of disribuion nework. According o [14], a decenralized mehod was proposed o moivae vehicles cusomers o use EV insead of convenional cars by minimizing cos of energy. In [15], a sochasic formulaion of EV charging and ancillary services is inroduced. An effecive way o simulae EV energy consumpion is o collec ransporaion survey daa based on a dynamic vehicle model [16]. In [17] a simplified model is uilized for calculaing he oupu of EV parking los. Recen sudies focused on opimal charging of EVs and ry o shif he EV charging ime o off-peak periods [18]. According o [19] auhors proposed a model for EV charging demand and assumed ha he elecriciy demand curve for he disribuion nework is known. However, our mehod forecass he load and calculaes he probabilisic charging demand of EVs parking los o esimae oal demand. Moreover, we evaluae he effec of charging rae and probabilisic parameers of drivers arrival and deparure ime on he prediced demand. In his paper, a he firs sep, demand forecasing is implemened in medium-erm ime horizon based on iniial parameers for ARIMA model. The inpu of his sep is hisorical hourly load daa. Then, relaive error of expeced hourly load is calculaed by comparing he real load daa using

2 2 Fig. 1: General framework of he proposed mehod Fig. 2: Relaive error of demand forecasing considering d = 1 (1). Relaive Error (%) = ˆD D D 100 (1) where ˆD represens he expeced value of demand a he h hour of day. The ARIMA model parameers will be updaed based on he relaive error and we will repea forecasing process o achieve more accurae hourly load profile. A he second sep, considering oal number of EVs, he hourly expeced demand of parking los is calculaed. Finally, he resuls of parking lo demand profile and expeced load is inegraed o obain he daily demand aking EVs ino accoun. Figure 1 represens he general framework of he proposed mehod. The res of he paper is organized as follows. Secion II specifies he ARIMA-based load forecaser. Secion III devoed o EV parking lo modeling. Secion IV evaluaes he effeciveness of our proposed scheme by implemening i on PJM hisorical load daa. Finally, In Secion V conclusions are given. II. FORECASTING METHOD In his secion, we consruc a medium-erm forecaser for power demand based on he ARIMA model and he hisorical load daa. Equaion 2, D specifies he average value of i h cusomer s demand in he h day respecively. Noe ha our proposed scheme is no resriced o any specific quanizaion sep size (24 hours) and i can be any oher value. Now, we consruc a forecaser for he aforemenioned imes series of i h cusomer s demand using ARIMA (N, d, 0) : (1 N q=1 a q L q )(1 L) d D = ε (i,d) i = 1, 2,,..., n = N + d, N + d + 1,... (2) where N and d are he auo-regressive (AR) and inegraed(i) orders of ARIMA model, he a q s are he parameers of he auoregressive par of he ARIMA model, and L is he lag operaor on arbirary ime series f such ha L r f = f r. Equaion 2 implies he following form for he demand value D : D = + ε (i,d) (3) Fig. 3: Relaive error of demand forecasing considering d = 3 where and ε (i,d) specify he expeced demand value and esimaion error corresponding o i h cusomer in hour. By consrucing he medium-erm ARIMA(N, d, 0) forecaser (menioned in Equaion 3) based on real hisorical load daa from PJM and compuing he absolue relaive error for differen values of N and d, we obain he plos shown in Figures 2 and 3. Considering Figures 2 and 3, and Table I, as he AR order (N) increases, he average relaive error of he forecaser doesn converge o a consan value for he inegraed order equal o wo and hree. We define ɛ = 0.6% as he accepable error hreshold. The accepable error values are highlighed in able II. By defining his error limi, we guaranee ha he obained value for N is sufficien and reliable. However, in he case ha d = 1, as he AR order increases, he esimaes generally improve and he error decays gradually. The relaive error says consan for large AR orders, regarding he χ 2 es, we conclude ha he error values in differen days are uncorrelaed and since he error is a whie noise. Hence, by considering N = 60 and d = 1, he average relaive error percenage reaches is minimum (%0.3257). Assuming ha ARIMA(60, 1, 0) is uilized o forecas he demand and he error is Gaussian whie noise (Random process f is a TABLE I: Average Relaive Error (%) N d=1 d = 2 d =

3 3 TABLE II: Roo Mean Square Error for d = 1 (%) N RMS error TABLE III: EV parameers EV class C ba (kwh) E m (kwh/mile) η (%) Gaussian whie noise of variance σ 2 or f GW N(σ 2 ), if i is a whie noise and for every, f N(0, σ 2 ))(GWN), we obain he following equaion: D = + ε (i,d) i = 1,..., n = 61, 62,... where ε (i,d) GWN( σ 2 D) Figures 2 and 3 imply ha he bes-fi AR and I orders of ARIMA-based medium-erm forecaser are N = 60days 24hours = 1440hours and d = 1 respecively. Addiionally, since he relaive error of he forecaser converges o a consan value in large AR orders, regarding he χ 2 es, he esimaion error is a whie noise. Subsequenly, assuming ha ARIMA(1440, 1, 0) is uilized for medium-erm forecasing, we obain ha ε (i,d) GWN( σ D 2 ), where σ2 D = (0.4181)2 = Noe ha he minimum RMS error represens he sandard deviaion. Table II represens he value of roo mean square (RMS) error for he opimum d parameer (d = 1). (4) III. ELECTRIC VEHICLE PARKING LOT MODELING In his secion, a probabilisic model of EVs is used o obain he daily charging demand. Firs, we will use he model which is inroduced in [20]. This model considered probabilisic driven disance (M d ), baery capaciy (C ba ), iniial sae of charge (SOC ini ), expeced charging demand (E demand ), and charging rae ( R ch ). E demand is calculaed based on (5). E demand = { Cba ; M d = M dmax M d E m ; M d < M dmax (5) where M dmax and E m represen maximum drivable disance (wih 100 % sae of charge) and elecriciy consumpion rae of EV respecively. M dmax can be calculaed as shown in (6). M dmax = C ba E m (6) Expeced charging duraion is obained using C ba, R ch, and he probabilisic arrival and deparure imes (based on hisorical EV drivers daa from [21]). Consequenly, as i has been derived in [20], final sae of charge ha is calculaed based on he probabilisic arrival/deparure imes, (SOC final ), can be calculaed using (7). { SOC final = Min [SOCini + E demand ], C ba [ SOCini + } (7) duraionr ch ] C ba Figure 4 shows he general framework of single EV model. Afer calculaion of final SOC for each single EV, he resuls Fig. 4: Single Elecric Vehicle model [20] are inegraed in order o calculae he oal demand of available EVs a he parking lo. The number of EVs in he es sysem was calculaed based on (8). N oal = EV peneraion 1000 (kw/mw ) Load avg 24 η 1 C ba1 + η 2 C ba2 + η 3 C ba3 + η 4 C ba4 where η i represen he marke share for each EV class and C bai shows he baery capaciy of he i h class vehicles. Coefficien EV peneraion is he oal percenage of EVs compared o he oal demand. Table III represens four commonly used EVs based on baery capaciy and consumpion [22], [23]. Figure 5 is he general framework of charging demand of he parking lo uilizing single vehicle model. In his model, hree differen charging modes were considered o evaluae he effec of R ch on elecriciy demand; slow, quick and fas charging raes are considered as 0.1, 0.3 and 1.0 C ba /hour respecively. Final oupu of he parking los model gives us he hourly charging of oal EVs for one day. IV. CASE STUDY AND DISCUSSION In order o evaluae he effeciveness of he proposed mehod PJM hisorical hourly load daa is used [24]. As i has been shown in secion (II), in ARIMA(N, d, 0) he bes choice for parameers are N = 60 and d = 1 which means using 60 days of hisorical load daa and firs order derivaive in (8)

4 4 Fig. 7: Effec of EV uilizaion and charging rae on demand, Case 2 Fig. 5: Parking lo s model for N oal EVs [20] Fig. 8: Effec of EV uilizaion and charging rae on demand, Case 3 Fig. 6: Hisorical and Prediced Demand for 61 h day he forecasing process. Two scenarios are considered for his secion: Scenario I : Impac of he number of EVs on oal demand. Case 1. N EV = 0 In his case we consider ha here is no EV in he sysem. Therefore we only require o forecas he 61 h day demand considering he previous 60 days daa. Figure 6 represen he real and expeced demand for he menioned day. As his figure represens, he accuracy of forecasing mehod is accepable. RMS and average relaive error values also proven he high accuracy of he mehod.. Case 2. N EV = Here, we consider ha he number of EVs is specified. Therefore we only require o forecas he 61 h day demand considering he previous 60 days daa. The average load for 60 days is Load avg = MW. Furhermore, he value of η i and C bai are exraced based on Table III. Hence, by subsiuing hese values in (8), EV peneraion is 1.23%. In his scenario we have hree saes for R ch ; 0.1, 0.3 and 1.0 C ba /hour. Figure 7 represens he prediced demand for he 61 h day, EVs in he sysem. This scenario shows ha, however uilizaion of he small number of EVs will increase he oal demand a each hour, i canno affec he peak demand considerably.. Case 3. N EV = In his case, we increase he number of uilized EVs in order o invesigae he effec of EVs on demand. The average load for 60 days is Load avg = MW. Furhermore, he value of η i and C bai are exraced based on Table III. Hence, by subsiuing hese values in (8), EV peneraion is 4.31%. Similar o previous scenario, we have hree saes for R ch ; 0.1, 0.3 and 1.0 C ba /hour. Figure 8 represen he prediced demand for he 61 h day, EVs in he sysem. Ineresingly, his case represens he effec of high uilizaion of EVs which is no only increase he hourly demand bu also increase he peak demand noiceably. Scenario II : Effec of Driven Disance on Toal Charging Demand In he firs scenario, average and sandard deviaion of expeced driven disance are considered o be 40 and 20 miles respecively. In his scenario, hese values changed o 80 and 30 miles respecively; we also assumed N EV = Figure 9 represen he prediced demand for he 61 h day, EVs in he sysem. Expecedly, his scenario proved if he average driven disance increase, he oal prediced demand considering EV consumpion will increase in comparison wih shorer driven disances. However, based on he uilized EV parking lo model, he expeced peak demand is no increased. V. CONCLUSION In his paper, an accurae forecasing approach is inroduced o predic demand in medium-erm ime horizon. The novel

5 5 Fig. 9: Effec of he expeced daily driven disance on hourly demand feaure of his mehod is o adus he ARIMA model s parameers based on he hisorical load daa so ha he forecasing accuracy achieves he highes possible level. Addiionally, a probabilisic model of elecric vehicle parking los is presened. In order o evaluae he accuracy of he proposed mehod and invesigae he effec of EV uilizaion on expeced demand, wo scenarios have been defined wih differen levels of EV uilizaion and charging rae. PJM hisorical load daa is used o implemen he ARIMA-based forecasing mehod. Scenario I, Case 1 shows he accuracy of he forecasing mehod by reaching 0.41% RMS error for demand forecas. The resuls of Scenario I, case 2 represens he effec of EV uilizaion on oal demand. Case 3 of Scenario I illusraes he effec of high uilizaion of EVs which no only increases he hourly demand, bu also increases he daily peak demand noiceably. The second scenario is designed o invesigae he effec of expeced driving cycle on he expeced demand. This scenario shows ha a longer duraion of rips beween parking los and home may deeriorae demand curve in erms of peak increasing and oal demand increase. ACKNOWLEDGMENT The firs auhor would like o hank Dr. Amin Kargarian Marvasi for several fruiful commens and discussions. [9] L. Hernandez, C. Baladron, J. Aguiar, B. Carro, A. Sánchez-Esguevillas, J. Llore, and J. Massana, A survey on elecric power demand forecasing: Fuure rends in smar grids, microgrids and smar buildings, IEEE Communicaion Survey & Tuorials, vol. 16, no. 3, pp , [10] L. Xie and M. D. Ilić, Model predicive economic/environmenal dispach of power sysems wih inermien resources, in Proc. IEEE Power and Energy Sociey General Meeing, 2009, pp [11] A. Swami and J. M. Mendel, Arma parameer esimaion using only oupu cumulans, IEEE Transacions on Acousics, Speech and Signal Processing, vol. 38, no. 7, pp , [12] K. Sikes, T. 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