THE accurate estimation of electric vehicle (EV) demand

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1 Statistical Characterization of Electric Vehicle Charging in Different Locations of the Grid Kaiwen Sun, Mushfiqur R. Sarker, and Miguel A. Ortega-Vazquez University of Washington, Seattle, Washington, USA {kaiwens, sarkermu, Abstract The advent of electric vehicles (EVs) will bring forth large increases to the pre-existing demand in the power grid. Adverse impacts to the system will arise if the charging of these EVs is uncontrolled. In order to mitigate this challenge, as a first step the estimation of the additional power due to EV charging is crucial. The estimation is dependent upon the temporal (i.e. time) and spatial (i.e. location) characteristics of the EV charging process. A tool is developed in this work, which estimates the additional demand using Monte Carlo simulations performed on a large fleet of EVs over several days. The simulations include EV travel data within predefined residential, workplace, and commercial zones that are determined using traffic flow information. This tool can be used by system operators and other entities to determine the opportunities and challenges posed by additional EV demand. The results show the power consumptions at each hour of the day can be modelled by a normal distribution, thus simplifying the estimation procedure. Index Terms Electric Vehicles, Electricity Demand, Planning I. INTRODUCTION THE accurate estimation of electric vehicle (EV) demand is necessary in order to maintain optimal operation of the power system. It is expected the global EV penetration will increase to 20 million by 2020 [1], which is expected to bring forth significant challenges for the grid operators [2]. This large penetration of EVs will require energy for motion from the grid and thus the estimation of the spatial and temporal distributions, as well as the total power is required. The areas with denser spatial distribution of EV charging are expected to require upgrades to the specific locations in the grid. On the other hand, the temporal distribution and the total power of EV charging is expected to require cost/benefit analyses in order to attain optimal management of the available resources [3]. The spatial and temporal estimation can assist different entities in fixing the potential challenges and even taking advantage of the potential opportunities. The estimation of EV demand has been the focus of several works in literature [4], [5], [6]. Without any management of the charging of the EV fleets, only a small percentage of the total population can be safely accommodated in the existing grids [3]. Therefore, management techniques (e.g. [7], [8]) are to be required. However, in order for these techniques to obtain meaningful results, accurate estimation of the spatial and temporal EV charging patterns are required. This work was supported in part by the Electric Energy Industrial Consortium (EEIC) and National Science Foundation (NSF) under Grant No Authors are with the University of Washington, Seattle, WA, USA ( kaiwens@uw.edu, sarkermu@uw.edu, maov@uw.edu). The work in [4] estimates the impact of EV charging on the grid assuming the peak charging occurs at a known time of the day. This assumption is invalid because the time of the peak charging can vary on a daily and even seasonal basis. A probabilistic model is developed in [5] incorporating queuing theory. This study uses Monte Carlo simulations, which are based on assumptions on when EVs are to charge. The work in [6] considers random EV arrival times when controlling EV charging as opposed to a mathematical method of estimating arrival times. In all these works [4], [5], [6], assumptions are made on the EV temporal behavior, which may misrepresent the actual EVs charging behavior. The mobility of EVs allow them to obtain their energy needs from any location that has the required infrastructure. However, limited work is available on analyzing the impact of EV charging spatially in different locations of the grid. Majority of the work considers certain pre-defined locations, e.g. residential, as in [9] and [10]. Additionally, the results from surveys are available in [11], in which the locations for EV charging are reported. The conclusion of the surveys indicates that EV consumers are likely to charge not only at their residence, but also at their workplace. The spatial estimation of EV charging demand enables grid operators to determine which locations may require upgrades and other profit-seeking entities to develop the required infrastructure to exploit EV charging, e.g. [12]. This study quantifies the demand of a large fleet of EVs at multiple potential locations in a city where they may charge, e.g. residential, workplace, and commercial. The proposed tool uses Monte Carlo simulations where the statistical behavior of the vehicle trips is obtained from travel data, thus allowing the estimation of spatial and temporal charging over a horizon of several days. Results show the hourly demand due to charging follows a normal distribution, which passes the goodnessof-fit test with a significance level of 5%, thus simplifying the estimation procedure. The results from this tool may be applied to aid forecasts for grid operators and other work aiming to study EV charging. The remainder of the paper is organized as follows. Section II describes the methodology to estimate EV demand. Section III presents the case study as well as the results, and Section IV concludes the paper. II. METHODOLOGY The flow chart to determine the EV demand is shown in Figure 1. The process is initialized for day d = 1. Then the /15/$ IEEE

2 Fig. 1. Flow chart of the MC procedure processed for each EV v in day d. first step (A) consists in defining the EV characteristics, which include the charge power, efficiencies, energy capacity, and energy consumption per mile of each vehicle v. Monte Carlo (MC) simulations are performed for each day d in the total set of days D. In each MC trial, each EV v is assigned random daily trips from the dataset, as shown in step (B), and then the power consumption for the trips are calculated, as shown in step (C). This process is repeated for each EV v. In step (D), the total demand for all EVs for the day d is calculated and the simulations repeat for the remainder of the days. When the total number of days have been simulated, i.e. d = N, the simulations are complete. Each step in Figure 1 is discussed in the following subsections. A. Assigning characteristics to EVs Each EV v in the set of EVs V has different characteristics. Each EV is assigned a battery capacity γ v and an energy consumption per mile β v depending on the type of vehicle. Each EV is also assigned to belong to a specific residential and work place location. It is assumed each EV always leaves at the start and returns at the end of the day to a specific residential zone, as well as arrives and leaves during the day from a specific workplace. B. Assignment of daily trips For every day d, each EV v is randomly assigned the number and distance of the daily trips of a vehicle in the dataset. The EV mimics these trips using its battery capacity and the energy consumption per mile characteristics. C. Simulate daily trips While a given EV v is making trips, the simulation tracks the energy consumption, which is calculated by the capacity of its battery, state of charge, and the distance that the EV traveled. For each trip the EV embarks, the simulation subtracts the energy consumption from battery s state-of-charge. After each individual trip is complete, the simulator tracks which zonal location the EV is residing in. According to the vehicle s trips, if the vehicle went to its home, the simulated EV goes to its assigned residential zone. This same rationale applies to the workplace zone. For other trip purposes, the EV goes to the commercial zones. While performing the trips, if an EV s state-of-charge drops below a certain percentage θ of its capacity, it is assumed that the EV owner opts to charge at the location where the trip ended. The EV remains at that specific zone charging until either the battery reaches its maximum state-of-charge or until the charging is interrupted by another trip. D. Calculating the total demand After each EV is simulated for day d, the total charging power at each zone is determined. The next day, d + 1, the EVs are assigned new trips randomly and the process repeats until all days are simulated, i.e. d = N. E. Assumptions This work has two major assumptions. First, the distribution grid constraints and imbalances were not considered in order to primarily study EV charging behavior. Second, the zonal locations were determined using traffic flow maps. III. CASE STUDY A. Data generation for Monte Carlo simulations To characterize EV travel behavior, the 2009 National Household Travel Survey (NHTS) is used [13]. This dataset includes the surveyed information of 150,147 households with 309,163 combustion vehicles. The survey includes data such as the start and end times, distance, and purpose of each trip taken by the vehicles. In this work, it is assumed the typical behavior of EV drivers is approximately similar to combustion vehicles. The dataset includes files household (HHV2PUB.csv), person (PERV2PUB.csv), vehicle (VEHV2PUB.csv), and daily trip (DAYV2PUB.csv) in comma-separated format [13]. The household file includes information such as the size of the home, among others. The person file includes information about each member such as their age and gender. The vehicle file includes characteristic information about each vehicle such as the type, miles per gallon, among others and the trip file includes the trips taken daily by each vehicle. Each household, person, and vehicle has unique identification numbers, which are constant throughout the dataset. A combination of the household, vehicle, and trip files are used in this work. By using each vehicle s miles per gallon (MPG) information present in column EIADMPG, the vehicle size is determined. The vehicle size is then translated to an energy consumption

3 per mile rating which is used to approximate the electrical energy the vehicle would consume on a trip. By repeating this process for each vehicle in each day, the total energy consumption can be estimated. The MC simulations, as explained in Figure 1, are performed for the city of Seattle, Washington, USA. The city s traffic flow map is used to determine zonal locations and allocation of EVs as shown in Figure 2 [14]. In Figure 2, the thickness of the dark-colored lines depict the traffic flow, which ranges from an average of [5,000 75,000] annual weekday traffic, and gives an indication of the population distributions [14]. This is used to pre-define four zones: residential zone A, residential zone B, workplace zone, and commercial zone. According to Figure 2, 60% (i.e EVs) of the total EVs were allocated to residential zone A and the remainder (i.e EVs) to residential zone B. Therefore, each EV must then begin and end its daily trips at its assigned residential zone. The MC studied the impact of 15,000 EVs (V ) over N MC trials. The number of trials is calculated by Equation 1 [15]: ( z σ ) 2 N (1) e where e is the maximum allowable error, σ is the initial estimate of the process standard deviation, and z is the (1 α 2 )100 percent point of the standard normal distribution. For example, if the desired confidence is 1 α = 95, then α = 0.05 resulting in z = 1.96 from the normal distribution [15]. The number of trials was set to N = 365 which satisfies (1). Each EV in the MC simulations are randomly assigned the characteristics of a vehicle in the NHTS dataset. Depending on the type of the vehicle assigned for an EV, it is also assigned an energy rating per mile (β v ). A small vehicle (30 MPG or more) is calculated to require 0.33 kwh/mi, a medium size vehicle (20 to 30 MPG) requires 0.37 kwh/mi, and a large vehicle (less than 20 MPG) requires 0.4 kwh/mi [16]. All EVs have a battery capacity γ v of 24 kwh and are assumed to plug in to the nearest zone for charging when the stateof-charge drops below θ = 60% of its battery capacity. The maximum charging rate is assumed to be Level II charging at 3.3 kw [17]. The MC occurs for every 15 minute period in a 24-hour day. The simulations were implemented in MATLAB 2012a [18]. B. Probability distributions of EV travel The departure, arrival, and time of travel estimations are needed to determine the time when EVs connect and disconnect from the grid. The departure and arrival locations are assumed to be from or to one of the residential zones for each EV, respectively. To determine the time of arrival and departure, the trip file is used and specifically columns ST RT T IM E and EN DT IM E in the file. The time of the trip is determined via the same file but with column T RV LCMIN. Figure 3 shows the probability distribution function (PDF) of the departure in (a), arrival in (b), and trip times in (c). From Figure 3a, it can be seen the time of departure is random Fig. 2. Seattle, Washington, USA traffic flow map with zonal locations. Zonal locations are pre-defined depending on traffic flow density. Fig. 3. PDF of EV departure (a) and arrival (b) to one of the residential zones, and the typical trip time (c). with EVs departing the residential zone throughout the day. However, there is a larger probability of departure between 0600 and 0900 hrs. On the other hand, the arrival times are skewed towards the latter hours of the day as shown in Figure 3b. In general, after each EV arrives at their last destination the owners tend to plug their vehicle into their residential power outlets for charging [19], [20]. According to Figure 3b, the greatest probabilities of arrival occur during 1600 to 1800

4 hours, which already correspond with the large demand peaks in the grid. This increases the peak demand even further and consequently causes challenges for the grid. As for the trip times in Figure 3c, most trips taken by vehicles tend to be less than one hour. The departure (Figure 3a) and travel time (Figure 3c) can be characterized by a Rayleigh Distribution. The arrival times, however, do not follow any parametric distribution. These PDFs are used in subsequent sections to estimate the zonal demand in the power grid. C. Estimation of total EV demand The MC simulations are performed to obtain the power consumption at the specific zones, and then used to obtain the total power consumption in the system. By creating a histogram of the total demand at each hour of the day, the hourly probability distribution can be analyzed. Figure 4 shows a histogram in which the x-axis represents the demand separated into 20 bins and the y-axis represents the number of days each demand bin occurs in the MC simulations. In addition, the normal distribution for the histogram is also shown in the figure. This process is performed for all hours of the day, however, only hours 0600 in (a), 1200 in (b), 1800 in (c), and 2400 in (d), are shown for simplicity in Figure 4. To test for normality, each hour was run through the Kolmogorov- Smirnov test performed at the 5% significance level [21], [22]. As a result, each hour passed the normality test and thus the hourly power consumption over the N days follows a normal distribution, which can be characterized by two parameters: the mean and standard deviation. This finding is used in the subsequent results to estimate the time-series profile for the total system demand. From a grid operator s perspective, analyzing the total increase in demand in the system due to the advent of EVs is required and is shown in Figure 5. Since at each hour the power consumption follows a normal distribution, the profile is presented within specific probability bands. In Figure 5, in light grey is the 50% band (i.e of the standard deviation from the mean consumption), in red is the 90% band (i.e of the standard deviation from the mean), and lastly in dark grey is the 100% band, which represents the minimum/maximum of the data. For example at 1800 hours, with a probability of 100% the demand is in the range [ ] MW, with a probability of 90% the demand is in the range [ ] MW, and with a probability of 50% the demand is in the range [ ] MW. In this figure, the EVs tend to charge during the later periods of the day as opposed to the earlier. This is the case because EVs will charge at their own convenience, e.g. after arriving at a specific residential zone at the end of their daily trips, without considering the issues on the grid. It is evident that without proper management techniques, the city of Seattle, WA, USA will see a substantial peak demand increase. D. Estimation of zonal demand The analysis of the zonal power consumption due to EVs provides more insight as to the locations in the area of Fig. 4. Distribution of demand at 0600 (a), 1200 (b), 1800 (c), and 2400 (d) hours. Fig. 5. Total system demand of all zonal locations for each hour of the day. Seattle, WA, USA where EVs may potentially charge. The grid operator can then use this information to reinforce the system in the specific zones or apply EV management techniques. Figure 6 shows the demand profiles of EV charging for residential zone A in (a), residential zone B in (b), workplace in (c), and commercial in (d). Note that the same rationale of probability-based profiles is also used for this figure. In Figure 6a, large peaks occur from 1500 to 2400 hours because all EVs return to their residential zone for charging. The opposite holds for the earlier hours because all EVs complete their charging by then and depart for their daily trips. The same rationale applies for residential zone B in Figure 6b. However, due to the traffic flow in Figure 2, the population distribution is lower in residential zone B as compared to zone A, and thus the power consumption in zone B is also lower for all hours. For the workplace zone in Figure 6c, the peak consumption occurs from 0900 to 1200 hrs. This is the case because as soon as EVs arrive at the workplace they begin charging, if they require the energy. On the other hand, the commercial demand is more constant from 1000 to 1900 hours because majority of shopping centers are open for business during these periods, as shown in Figure 6d. The demand profiles in Figure 5 and 6 show the probabilitybands widening during the peak hours and decreasing during the off-peak hours. For example, from hours 0900 to 1500 in Figure 6c the bands are wider as compared to the other hours. This is because a large portion of EVs tend to charge

5 to these zones at the end of the day. In addition, the Monte Carlo simulations show that at each hour the power consumption can be represented by a normal distribution without loss of accuracy. This simplifies the estimation procedure, which can be implemented and studied by grid operators, entities attempting to assess the impact of EV charging, or even for those that can exploit EV flexibility. REFERENCES Fig. 6. Zonal demand for residential zone A (a), residential zone B (b), workplace (c), and commercial (d). within certain times as shown in Figure 3. However, since the MC simulations are performed over several days (N), each EV charges differently during each day depending on its energy needs. This creates the wider bands and indicates more variability during the zonal peak hours, which may potentially be more difficult to estimate. The impact of EV charging, according to Figure 6, is the largest in the residential zones, since all the EVs tend to end their daily trips there. By comparing the workplace and commercial zone, the workplace has a lower peak. This sort of analysis provides an idea as to the location where EVs are most likely to charge frequently. The grid operator or other entities can then manage this additional EV demand in the most suitable manner. IV. CONCLUSION The advent of EVs is expected to bring forth large increases to the pre-existing demand in the power grid. Hence, the analysis of the spatial and temporal estimation of EV charging must be performed in order to assess the potential future stress scenarios the system might undergo. This information is also required in order to assess whether the existing assets are sufficient to ensure the system can be operated within secure thresholds, or if improvements to the grid are required. The tool developed in this work statically characterizes the power consumption of a large fleet of EVs for multiple pre-defined residential, workplace, and commercial zones. 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