ARIMA-based Demand Forecasting Method Considering...

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1 ARIMA-based Demand Forecasting Method Considering Probabilistic Model of Electric Vehicles’ Parking Lots M.H. Amini, Student Member, IEEE, O. Karabasoglu, Marija D. Ili´ c, Fellow, IEEE, Kianoosh G. Boroojeni Student Member, IEEE and S. S. Iyengar, Fellow, IEEE Abstract—In recent years, increasing fossil fuel prices, environ- mental concerns and rising electricity demand motivate the power system to evolve toward the Smart Grid. Modern transportation is one of the key elements of future power system. In this context, utilization of electric vehicles (EV) should be taken into account in a systematic way to avoid unpredictable effects on power system. Additionally, an accurate and efficient demand forecasting method is required to perform a feasible scheduling in order to supply the predicted load sufficiently. This paper presents an accurate method for the demand forecasting based on historical load data. The method is based on auto-regressive integrated moving average (ARIMA) model for medium-term demand forecasting. The proposed method inmproves the forecasting accuracy. Additionally, probabilistic hierarchical EVs’ parking lot demand modeling is used to calculate the expected load for each parking lots’ daily charging demand. Finally, to evaluate the effectiveness of the proposed approach, it is implemented on PJM historical load data. The simulation results show the high accuracy of proposed method for PJM load data by reaching 0.41% root mean square error for demand forecast. I. I NTRODUCTION In recent years, the power system is experiencing one of the most influential evolutions ever, the transition toward smart grid (SG) because of major motivations from the increasing cost of energy to climate change [1]. SG has been proposed to achieve a more sustainable, secure and environmentally- friendly power system. Future power system deployment involves several studies, such as stability, reliability, power quality, and sustainability [2]. According to [3], SG will improve power system reliability by using novel equipments and methods at supply side and demand side. In addition, real time control, self-decision making, and distributed energy management are two features of future power system [4], [5], [6]. Several technologies, including advanced metering infras- tructure, distributed renewable resources, phasor measurement units, home area network, energy storage and electric vehicles (EVs) are utilized to achieve a fast, distributed, secure and intelligent power grid [7], [8]. Recently, SG customers and EVs motivated power system to utilize accurate demand forecasting which plays a pivotal role in terms of portraying a general scope for power system studies, such as the power flow problem, energy dispatch and adequacy analysis [9]. In [10], a model predictive control is e-mails: [email protected], [email protected], [email protected], kghol002@fiu.edu, iyengar@cis.fiu.edu applied to solve the economic dispatch problem in the presence of intermittent resources. Furthermore, this study provides a framework to consider the trade-off between economic and en- vironmental effects. According to [9], there have been several efforts about demand forecasting in different time horizons using various techniques in the literature, including linear regression, fuzzy logic approach and artificial neural network, support vector machines, transfer functions, and grey dynamic model. The aim of this paper is to forecast demand in the medium-term time horizon based on historical load data using auto-regressive integrated moving average (ARIMA) model. However, a mathematical ARIMA model is introduced[11], in this paper, we calculate the optimal parameters of ARIMA model based on the historical data, which is more accurate in comparison with ARIMA implementation independent from the nature of input raw data. Electric vehicles demand modeling is another aspect of SG which is addressed in this paper. U.S. government plans to utilize more EVs in the near future [12]. From the EVs’ parking lot load modeling perspective, there have been studies to extract a model of EVs charging profile. In [13] EV parking lots are utilized to enhance the reliability of distri- bution network. According to [14], a decentralized method was proposed to motivate vehicles’ customers to use EV instead of conventional cars by minimizing cost of energy. In [15], a stochastic formulation of EV charging and ancillary services is introduced. An effective way to simulate EV energy consumption is to collect transportation survey data based on a dynamic vehicle model [16]. In [17] a simplified model is utilized for calculating the output of EV parking lots. Recent studies focused on optimal charging of EVs and try to shift the EV charging time to off-peak periods [18]. According to [19] authors proposed a model for EV charging demand and assumed that the electricity demand curve for the distribution network is known. However, our method forecasts the load and calculates the probabilistic charging demand of EVs’ parking lots to estimate total demand. Moreover, we evaluate the effect of charging rate and probabilistic parameters of drivers’ arrival and departure time on the predicted demand. In this paper, at the first step, demand forecasting is implemented in medium-term time horizon based on initial parameters for ARIMA model. The input of this step is historical hourly load data. Then, relative error of expected hourly load is calculated by comparing the real load data using

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ARIMA-based Demand Forecasting MethodConsidering Probabilistic Model of Electric

Vehicles’ Parking LotsM.H. Amini, Student Member, IEEE, O. Karabasoglu, Marija D. Ilic, Fellow, IEEE, Kianoosh G. Boroojeni

Student Member, IEEE and S. S. Iyengar, Fellow, IEEE

Abstract—In recent years, increasing fossil fuel prices, environ-mental concerns and rising electricity demand motivate the powersystem to evolve toward the Smart Grid. Modern transportationis one of the key elements of future power system. In thiscontext, utilization of electric vehicles (EV) should be taken intoaccount in a systematic way to avoid unpredictable effects onpower system. Additionally, an accurate and efficient demandforecasting method is required to perform a feasible schedulingin order to supply the predicted load sufficiently.

This paper presents an accurate method for the demandforecasting based on historical load data. The method is basedon auto-regressive integrated moving average (ARIMA) modelfor medium-term demand forecasting. The proposed methodinmproves the forecasting accuracy. Additionally, probabilistichierarchical EVs’ parking lot demand modeling is used tocalculate the expected load for each parking lots’ daily chargingdemand. Finally, to evaluate the effectiveness of the proposedapproach, it is implemented on PJM historical load data. Thesimulation results show the high accuracy of proposed methodfor PJM load data by reaching 0.41% root mean square errorfor demand forecast.

I. INTRODUCTION

In recent years, the power system is experiencing one of themost influential evolutions ever, the transition toward smartgrid (SG) because of major motivations from the increasingcost of energy to climate change [1]. SG has been proposedto achieve a more sustainable, secure and environmentally-friendly power system. Future power system deploymentinvolves several studies, such as stability, reliability, powerquality, and sustainability [2]. According to [3], SG willimprove power system reliability by using novel equipmentsand methods at supply side and demand side. In addition,real time control, self-decision making, and distributed energymanagement are two features of future power system [4], [5],[6]. Several technologies, including advanced metering infras-tructure, distributed renewable resources, phasor measurementunits, home area network, energy storage and electric vehicles(EVs) are utilized to achieve a fast, distributed, secure andintelligent power grid [7], [8].

Recently, SG customers and EVs motivated power systemto utilize accurate demand forecasting which plays a pivotalrole in terms of portraying a general scope for power systemstudies, such as the power flow problem, energy dispatch andadequacy analysis [9]. In [10], a model predictive control is

e-mails: [email protected], [email protected], [email protected],[email protected], [email protected]

applied to solve the economic dispatch problem in the presenceof intermittent resources. Furthermore, this study provides aframework to consider the trade-off between economic and en-vironmental effects. According to [9], there have been severalefforts about demand forecasting in different time horizonsusing various techniques in the literature, including linearregression, fuzzy logic approach and artificial neural network,support vector machines, transfer functions, and grey dynamicmodel. The aim of this paper is to forecast demand in themedium-term time horizon based on historical load data usingauto-regressive integrated moving average (ARIMA) model.However, a mathematical ARIMA model is introduced[11],in this paper, we calculate the optimal parameters of ARIMAmodel based on the historical data, which is more accurate incomparison with ARIMA implementation independent fromthe nature of input raw data.

Electric vehicles demand modeling is another aspect of SGwhich is addressed in this paper. U.S. government plans toutilize more EVs in the near future [12]. From the EVs’parking lot load modeling perspective, there have been studiesto extract a model of EVs charging profile. In [13] EVparking lots are utilized to enhance the reliability of distri-bution network. According to [14], a decentralized methodwas proposed to motivate vehicles’ customers to use EVinstead of conventional cars by minimizing cost of energy.In [15], a stochastic formulation of EV charging and ancillaryservices is introduced. An effective way to simulate EV energyconsumption is to collect transportation survey data based ona dynamic vehicle model [16]. In [17] a simplified model isutilized for calculating the output of EV parking lots. Recentstudies focused on optimal charging of EVs and try to shiftthe EV charging time to off-peak periods [18]. According to[19] authors proposed a model for EV charging demand andassumed that the electricity demand curve for the distributionnetwork is known. However, our method forecasts the load andcalculates the probabilistic charging demand of EVs’ parkinglots to estimate total demand. Moreover, we evaluate the effectof charging rate and probabilistic parameters of drivers’ arrivaland departure time on the predicted demand.

In this paper, at the first step, demand forecasting isimplemented in medium-term time horizon based on initialparameters for ARIMA model. The input of this step ishistorical hourly load data. Then, relative error of expectedhourly load is calculated by comparing the real load data using

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Fig. 1: General framework of the proposed method

(1).

Relative Errorj(%) =Dj −Dj

Dj× 100 (1)

where Dj represents the expected value of demand at the jth

hour of day.The ARIMA model parameters will be updated based on

the relative error and we will repeat forecasting process toachieve more accurate hourly load profile. At the second step,considering total number of EVs, the hourly expected demandof parking lots is calculated. Finally, the results of parking lotdemand profile and expected load is integrated to obtain thedaily demand taking EVs into account. Figure 1 represents thegeneral framework of the proposed method.

The rest of the paper is organized as follows. SectionII specifies the ARIMA-based load forecaster. Section IIIdevoted to EV parking lot modeling. Section IV evaluates theeffectiveness of our proposed scheme by implementing it onPJM historical load data. Finally, In Section V conclusions aregiven.

II. FORECASTING METHOD

In this section, we construct a medium-term forecaster forpower demand based on the ARIMA model and the historicalload data. Equation 2, D(i)

j specifies the average value of ith

customer’s demand in the jth day respectively. Note that ourproposed scheme is not restricted to any specific quantizationstep size (24 hours) and it can be any other value. Now, weconstruct a forecaster for the aforementioned times series ofith customer’s demand using ARIMA (N, d, 0) :

(1−N∑q=1

aqLq)(1− L)dD(i)

j = ε(i,D)j

∀i = 1, 2, , . . . , n t = N + d,N + d+ 1, . . .(2)

where N and d are the auto-regressive (AR) and integrated(I)orders of ARIMA model, the aq’s are the parameters of theautoregressive part of the ARIMA model, and L is the lagoperator on arbitrary time series ft such that Lrft = ft−r.

Equation 2 implies the following form for the demand valueD

(i)t :

D(i)t = D

(i)t + ε

(i,D)t (3)

Fig. 2: Relative error of demand forecasting considering d = 1

Fig. 3: Relative error of demand forecasting considering d = 3

where D(i)t and ε(i,D)

t specify the expected demand value andestimation error corresponding to ith customer in hour t.

By constructing the medium-term ARIMA(N ′, d′, 0) fore-caster (mentioned in Equation 3) based on real historical loaddata from PJM and computing the absolute relative error fordifferent values of N ′ and d′, we obtain the plots shown inFigures 2 and 3.

Considering Figures 2 and 3, and Table I, as the AR order(N ) increases, the average relative error of the forecasterdoesn’t converge to a constant value for the integrated orderequal to two and three. We define εt = 0.6% as the acceptableerror threshold. The acceptable error values are highlighted intable II. By defining this error limit, we guarantee that theobtained value for N is sufficient and reliable. However, inthe case that d = 1, as the AR order increases, the estimatesgenerally improve and the error decays gradually. The relativeerror stays constant for large AR orders, regarding the χ2

test, we conclude that the error values in different days areuncorrelated and since the error is a white noise. Hence,by considering N = 60 and d = 1, the average relativeerror percentage reaches its minimum (%0.3257). Assumingthat ARIMA(60, 1, 0) is utilized to forecast the demand andthe error is Gaussian white noise (Random process ft is a

TABLE I: Average Relative Error (%)

N d=1 d = 2 d = 3

30 0.4402 0.4349 0.8333

40 3.7506 4.4578 1.3252

50 0.9177 0.8114 2.0219

60 0.3275 0.3284 11.1388

70 1.3457 1.3408 2.1550

80 0.6225 0.6891 9.6412

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TABLE II: Root Mean Square Error for d = 1 (%)

N 30 40 50 60 70 80

RMS error 0.5799 4.1547 1.2169 0.4181 2.3314 0.8312

Gaussian white noise of variance σ2 or ft ∼ GWN(σ2), if itis a white noise and for every t, ft ∼ N(0, σ2))(GWN), weobtain the following equation:

D(i)j = D(i)

j + ε(i,D)j ∀i = 1, . . . , n j = 61, 62, . . .

where ε(i,D)j ∼ GWN(σ2

D)(4)

Figures 2 and 3 imply that the best-fit AR and I orders ofARIMA-based medium-term forecaster are N ′ = 60days ×24hours = 1440hours and d′ = 1 respectively. Addition-ally, since the relative error of the forecaster converges to aconstant value in large AR orders, regarding the χ2 test, theestimation error is a white noise. Subsequently, assuming thatARIMA(1440, 1, 0) is utilized for medium-term forecasting,we obtain that ε(i,D)

t ∼ GWN(σ2D), where σ2

D = (0.4181)2 =1.748076 × 10−1. Note that the minimum RMS error repre-sents the standard deviation. Table II represents the value ofroot mean square (RMS) error for the optimum d parameter(d = 1).

III. ELECTRIC VEHICLE PARKING LOT MODELING

In this section, a probabilistic model of EVs is used to obtainthe daily charging demand. First, we will use the model whichis introduced in [20]. This model considered probabilisticdriven distance (Md), battery capacity (Cbat), initial state ofcharge (SOCinit), expected charging demand (Edemand), andcharging rate ( Rch). Edemand is calculated based on (5).

Edemand =

{Cbat; Md =Mdmax

MdEm; Md < Mdmax

(5)

where Mdmax and Em represent maximum drivable distance(with 100 % state of charge) and electricity consumption rateof EV respectively. Mdmax can be calculated as shown in (6).

Mdmax =Cbat

Em(6)

Expected charging duration is obtained using Cbat, Rch,and the probabilistic arrival and departure times (based onhistorical EV drivers data from [21]). Consequently, as it hasbeen derived in [20], final state of charge that is calculatedbased on the probabilistic arrival/departure times, (SOCfinal),can be calculated using (7).

SOCfinal = Min{[SOCinit +

Edemand

Cbat

],

[SOCinit +

tdurationRch

Cbat

]} (7)

Figure 4 shows the general framework of single EV model.After calculation of final SOC for each single EV, the results

TABLE III: EV parameters

EV class Cbat (kWh) Em (kWh/mile) η (%)

1 10 0.3790 20

2 12 0.4288 30

3 16 0.5740 30

4 21 0.8180 20

Fig. 4: Single Elecric Vehicle model [20]

are integrated in order to calculate the total demand of avail-able EVs at the parking lot. The number of EVs in the testsystem was calculated based on (8).

Ntotal = bEVpenetration × 1000 (kW/MW )×Loadavg × 24

η1Cbat1 + η2Cbat2 + η3Cbat3 + η4Cbat4

c(8)

where ηi represent the market share for each EV class andCbati shows the battery capacity of the ith class vehicles.Coefficient EVpenetration is the total percentage of EVs com-pared to the total demand.Table III represents four commonly used EVs based on batterycapacity and consumption [22], [23]. Figure 5 is the generalframework of charging demand of the parking lot utilizingsingle vehicle model. In this model, three different chargingmodes were considered to evaluate the effect of Rch onelectricity demand; slow, quick and fast charging rates areconsidered as 0.1, 0.3 and 1.0 Cbat/hour respectively. Finaloutput of the parking lots model gives us the hourly chargingof total EVs for one day.

IV. CASE STUDY AND DISCUSSION

In order to evaluate the effectiveness of the proposed methodPJM historical hourly load data is used [24]. As it has beenshown in section (II), in ARIMA(N, d, 0) the best choicefor parameters are N = 60 and d = 1 which means using60 days of historical load data and first order derivative in

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Fig. 5: Parking lot’s model for Ntotal EVs [20]

Fig. 6: Historical and Predicted Demand for 61th day

the forecasting process. Two scenarios are considered for thissection:

Scenario I : Impact of the number of EVs on total demand

. Case 1. NEV = 0 In this case we consider thatthere is no EV in the system. Therefore we only require toforecast the 61th day demand considering the previous 60 daysdata. Figure 6 represent the real and expected demand forthe mentioned day. As this figure represents, the accuracy offorecasting method is acceptable. RMS and average relativeerror values also proven the high accuracy of the method.

. Case 2. NEV = 100000 Here, we consider thatthe number of EVs is specified. Therefore we only requireto forecast the 61th day demand considering the previous60 days data. The average load for 60 days is Loadavg =4935.58MW . Furthermore, the value of ηi and Cbati areextracted based on Table III. Hence, by substituting thesevalues in (8), EVpenetration is 1.23%. In this scenario wehave three states for Rch; 0.1, 0.3 and 1.0 Cbat/hour.

Figure 7 represents the predicted demand for the 61th day,including three states for charging rate value when we have100000 EVs in the system. This scenario shows that, howeverutilization of the small number of EVs will increase thetotal demand at each hour, it cannot affect the peak demandconsiderably.

Fig. 7: Effect of EV utilization and charging rate on demand, Case 2

Fig. 8: Effect of EV utilization and charging rate on demand, Case 3

. Case 3. NEV = 350000 In this case, we increase thenumber of utilized EVs in order to investigate the effect ofEVs on demand. The average load for 60 days is Loadavg =4935.58MW . Furthermore, the value of ηi and Cbati areextracted based on Table III. Hence, by substituting thesevalues in (8), EVpenetration is 4.31%. Similar to previousscenario, we have three states for Rch; 0.1, 0.3 and 1.0Cbat/hour.

Figure 8 represent the predicted demand for the 61th day,including three states for charging rate value when we have350000 EVs in the system. Interestingly, this case representsthe effect of high utilization of EVs which is not onlyincrease the hourly demand but also increase the peak demandnoticeably.

Scenario II : Effect of Driven Distance on Total ChargingDemand

In the first scenario, average and standard deviation ofexpected driven distance are considered to be 40 and 20 milesrespectively. In this scenario, these values changed to 80 and30 miles respectively; we also assumed NEV = 350000.Figure 9 represent the predicted demand for the 61th day,including three states for charging rate value when we have350000 EVs in the system. Expectedly, this scenario provedif the average driven distance increase, the total predicteddemand considering EV consumption will increase in com-parison with shorter driven distances. However, based on theutilized EV parking lot model, the expected peak demand isnot increased.

V. CONCLUSION

In this paper, an accurate forecasting approach is introducedto predict demand in medium-term time horizon. The novel

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Fig. 9: Effect of the expected daily driven distance on hourly demand

feature of this method is to adjust the ARIMA model’s param-eters based on the historical load data so that the forecastingaccuracy achieves the highest possible level. Additionally, aprobabilistic model of electric vehicle parking lots is pre-sented. In order to evaluate the accuracy of the proposedmethod and investigate the effect of EV utilization on expecteddemand, two scenarios have been defined with different levelsof EV utilization and charging rate. PJM historical load datais used to implement the ARIMA-based forecasting method.Scenario I, Case 1 shows the accuracy of the forecastingmethod by reaching 0.41% RMS error for demand forecast.The results of Scenario I, case 2 represents the effect of EVutilization on total demand. Case 3 of Scenario I illustratesthe effect of high utilization of EVs which not only increasesthe hourly demand, but also increases the daily peak demandnoticeably. The second scenario is designed to investigate theeffect of expected driving cycle on the expected demand. Thisscenario shows that a longer duration of trips between parkinglots and home may deteriorate demand curve in terms of peakincreasing and total demand increase.

ACKNOWLEDGMENT

The first author would like to thank Dr. Amin KargarianMarvasti for several fruitful comments and discussions.

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