Optimizing Operations for Large Scale Charging of Electric Vehicles

213 46th Hawaii International Conference on System Sciences Optimizing Operations for Large Scale Charging of Electric Vehicles Shiyao Chen School of ECE Cornell University Ithaca NY 14853 sc933@cornell.edu Timothy Mount School of AEM Cornell University Ithaca NY 14853 tdm2@cornell.edu Lang Tong School of ECE Cornell University Ithaca NY 14853 ltong@ece.cornell.edu Abstract The problem of operations for large scale charging of Electric Vehicles (EVs) is considered. Envisioned to be part of the future transportation infrastructure, a large scale charging facility runs on two categories of energy sources: a cheap energy source (e.g., renewable energy such as wind or solar) and an expensive energy source (e.g., grid electricity). The charging facility will be capable of charging hundreds of EVs simultaneously. In the future smart grid, charging facilities require properly designed pricing and scheduling that take into account the intermittency of renewable energy, the grid electricity cost, the arrival-departure characteristics, and customer price sensitivity. The operation of charging facilities is captured as a deadline scheduling system. On top of the scheduling system, simulations are conducted to study the impact induced by different operations of large scale charging. The monopoly pricing as well as the effect of competition in price in the presence of two charging facilities with different spatial locations when different scheduling algorithms are adopted by the charging facilities are also studied via simulations. Index Terms EV charging, deadline scheduling, renewable energy. I. INTRODUCTION The electrification of the transportation system and deep penetration of renewable energy are expected to help building a sustainable world. The advance in electrical vehicle (EV) industry is accelerating the electrification of the transportation system. However, deep penetration of renewable energy is facing the obstacle of confliction between the availability intermittency and the lack of flexibility in traditional electricity load. Therefore, crucial to the transition toward an EV based transportation powered by renewable energy is to establish charging infrastructures connecting renewable energy source with deferrable EV charging load, at public parking facilities, work places, and apartment complexes and take advantage of economies of scale, especially in densely populated urban areas, where in-home EV charging is not an option. Due to inherent fluctuation in the availability of renewable energy, electricity from the power grid is necessary for smooth charging operations. Appropriate charging operation management can take advantage of the flexibility of individual charging requests, and has the potential of significantly reducing the electricity needed from the grid, thus reducing the operating cost. The operations of large scale charging facilities are studied via simulations for the scenarios with and without competition. The operations of a charging facility is broken down to decisions in different aspects: request pricing, request scheduling and grid purchase. Customers arriving at the facility communicate their charging needs (the amount of charging required and the deadline for completion) to the facility operator, who provides a price quote for the charging request based on the amount of required charging, the deadline of completion, and the facility workload. The customer may or may not accept the offered price depending on the particular price response of the customers. The pricing, scheduling and grid purchase of charging operations are conducted in an online fashion, i.e., there is no reservation requirements for the customers, and the decisions of the operator are irrevocable and made with solely the current information. For online scheduling operating in uncertain environments with deadlines, it is often inevitable that some jobs cannot be completed by their deadlines solely with fluctuating renewable energy. The pricing can be used as a way to reduce but not eliminate such occurrences. Therefore, the operator purchases electricity from the power grid in such condition to maintain smooth operations against the fluctuation of renewable availability, at the cost of additional electricity bill. The goal of the facility operator is to maximize the profit of the charging facility. We simulate the average profit for scheduling algorithms including Charging (UC) and Threshold Assignment with Greedy Scheduling () to study the impact of different scheduling algorithms in the scenarios of monopoly and Bertrand competition model with spatial differentiation. A. Summary of Results In this paper the focus is on the comparison of different choices in the charging operations via simulation. The scheduling algorithms UC and are contrasted in monopoly as well as in the presence of competition. The profit maximizing unit price is investigated for monopoly and the equilibrium price pair for duopoly for EOU (electricity of use) pricing mechanism. The impact of competition is demonstrated in the comparison of monopoly and duopoly, in which we adopt the 153-165/12 $26. 212 IEEE DOI 1.119/HICSS.213.435 2317 2319

Bertrand duopoly model with spatial differentiation, i.e., two facilities with different spatial locations competing in price. B. Related Work The benefits and impact of electric vehicles on the electricity network are assessed in e.g., [1] from a regulatory or policymaking perspective, with the conclusion that argues electric vehicle technology to be promising in many aspects. There has also been economic analysis of EV charging technology. The authors of [2] has conducted an energy economic analysis of EV charging using solar photovoltaic panels at workplace parking garage with the conclusion that EV charging facility in public garage is economically beneficial to both the car owners as well as the facility operator. When it gets down to the operations level for large scale charging facilities, a variety of modeling and optimization techniques have been proposed in the literature. The authors of [3] aggregated system and operation models for the simulation of EV charging in a municipal parking lot. The EV charging for public garages (with reliable energy sources) has been considered in [4] with a heuristic optimization approach. The application of renewable energy is not addressed in [3], [4]. A recent work [5] by Subramanian et. al. addresses the application of renewable energy to EV charging and studies three different scheduling algorithms. The issues of pricing and profitability are not considered for the operator. When it comes to household electric vehicle charging, the authors of [6] propose an offline decentralized protocol for negotiating day-ahead charging prices and schedules for household EV charging between the EV owners and utility, to shift the charging load to fill the overnight demand valley. The household EV charging scheduling problem is casted into an optimal power flow (OPF) problem in [7] and the solution structure of OPF is leveraged for charging scheduling. In [8] a decentralized algorithm is proposed to coordinate the autonomous EV charging in non-cooperative game framework, which converges to a Nash equilibrium that approximately achieves the ideal solution (scheduling EV load to fill the overnight demand valley). In [9], [1] the authors consider the management of EV charging with the potential speculation in the provision of additional regulation service required by renewable energy expansion and propose a rolling horizon look-ahead stochastic dynamic programming. The authors of [11] propose the idea of using parking facility as an energy exchange station called smart garage for Vehicle-to-Grid (V2G) applications. They demonstrate the benefits of using EVs as energy storage for demand side management. The scheduling algorithm was previously proposed in our previous work [12]. The Bertrand duopoly model is one of the popular oligopoly competition model used in microeconomics [13], in which the firms compete by selecting price strategically. It differs from the other popular competition model, the Cournot model, in which the firms compete by selecting quantity strategically. II. CHARGING FACILITY AND CUSTOMER MODEL A. Energy Sources and Charging Requests The portfolio of charging energy for the facility consists of two sources, the cheap collocated renewable energy and the relatively expensive power grid. The different level of instantaneous charging power is encapsulated in the different number of standardized EV chargers, each with constant charging speed. The number of renewable chargers may vary over time, which reflects the fluctuation of renewable power. Beyond the renewable chargers, more grid chargers can be drawn from the power grid if needed, at the relatively expensive cost for electricity. In charging operations, preemption is allowed at no cost, i.e., a preempted battery can be resumed charging from the previous battery level upon preemption. Each EV charging request T =(r, p, d) is represented by a triple specified by the arrival (release) time r, charging time p (determined by the requested charging amount and the charging speed of the standardized chargers) and deadline d. For example, a customer who lives in an apartment in a highrise building without overnight charging equipment may arrive at a EV charging facility near his office building around 8 am on the way to work. The customer may intend to catch a flight for a conference at 2 pm and plan to leave for the airport at 12 pm. The current battery level may be good for 1 miles and in order to make the round trip to the airport the desired battery level after charging should be able to travel 5 miles. In this example the release time is 8 am, the deadline is 12 pm and the charging time is determined by the 4 miles desired battery level as well as the charging speed of the charging plug. Over a certain period of time, e.g., one day, all the customer requests submitted constitute the arrival sequence to be priced and scheduled by the facility operator. B. Interaction between Customers and Operator The interaction between the customers and the facility operator is captured in the price quote offered by the operator. After the facility operator is given the charging request parameters r, p and d, the facility operator offers a price v for the charging request. The objective of the operator is to maximize his profit. Therefore the quoted price should not be too low. On the other hand, if the quoted price turns out too high and exceeds the utility associated with battery charging for the customer, the customer may decline the offer, since the objective of the customer is to obtain battery charging at a reasonable price. Beyond the customer turning down the operator s offer, the operator also has the option to raise the quoted price to cover any expected grid purchase cost and protect the profit, e.g., when the facility is currently heavily loaded and it is necessary to resort heavily to grid electricity for new arrivals. Once the offered price quote is accepted by the customer, a binding contract is established; the accepted charging request has to be completed by its deadline as promised. The profit obtained by the operator will be the total quoted price of all completed charging requests, less the operating cost of grid electricity bill. 2318 232

We quantify the bar for the customers perception of offered prices being reasonable by the customer response curve θ(u), where u is the unit price offered. The customer response curve dictates the probability a customer will accept a certain price quote v with unit price u = v/p offered by the operator, and should be decreasing with u. C. Bertrand Duopoly Model with Spatial Differentiation The customer response curve will determine the monopoly pricing of a charging facility. In order to study the effect of competition in the electric vehicle charging business, we adopt the simple but yet realistic Bertrand duopoly competition model with spatial differentiation. We assume there are many customers in need of battery charging while there are two competing charging facilities. There exist in literature the Cournot model and the Bertrand model for oligopoly, in which the Cournot model assumes that the competitors compete with each other in setting the individual production quantity and the market price depends on the collective production quantity, while the Bertrand model assumes that the competitors compete with each other in setting the individual price and the market share captured by each competitor depends on the individual price. For the specific application of electric vehicle charging, the Bertrand model is more suitable. This can be explained with the analogy to the gas stations. The gas stations never submit quantities and there is no universal market price of fueling a car that is honored everywhere (although one does note that the named prices tend to be similar in gas stations close to each other due to competition in price). In Bertrand duopoly model with homogeneous product or service, the competitors set price for the homogeneous product or service simultaneously in a non-cooperative manner. Homogeneity implies that customers will purchase charging from the lower-priced facility. Any facility charging a higher price than its rival will lose all customer, which leads to a very steep change in market share upon tiny price adjustment. We therefore introduce spatial differentiation; the two charging facilities in the Bertrand duopoly model, denoted by A and B, are located in the two ends ( and 1) of a street of length one, respectively. The customers are uniformly distributed on the street (the interval [, 1]). Transportation cost is involved for customers to obtain battery charging, at k dollars per unit distance. Except for location, the service in the two facilities are identical. A consumer located at location x incurs a transportation cost of kx to charge at facility A, and k(1 x) to charge at facility B. The consumers care about both distance and price; they will select the facility with lower overall cost: transportation cost plus the charging cost, in which the the charging cost depends on the price selected by the facilities. Spatial differentiation indicates that the customers do not just all go to the cheaper facility as in Bertrand Competition with homogenous products; lowering price below your rival s will not result in capturing the entire market, nor will raising price lead to losing the entire market. III. PRICING MECHANISM The pricing mechanism has two effects for the charging operations: customer trimming and territory definition. The customer trimming summarizes the effect that the pricing mechanism together with the customer response curve shapes the fraction of customers that accepts the offered price. This in turn determines the overall charging load for the charging facility, and further affects the portfolio of charging energy consumed, i.e., the percentage of the cheap renewable energy and the relatively expensive grid electricity consumed. The impact on the portfolio of charging energy consumed is directly related to the marginal cost of the charging facility, since more renewable energy implies lower cost, and vice versa. Specifically, if the renewable energy availability is fixed, when the overall charging load is small, with proper scheduling the majority of the charging can be fulfilled by the cheap renewable energy and the marginal cost is low. When the overall charging load increases, the component of the relatively expensive grid electricity inevitably expands and the marginal cost will increase as a result. The pricing mechanism has to justify the marginal cost, although there is no explicit formula for the marginal cost available for the charging facility with deadlines. Along this line, the pricing mechanism has to strike reasonable balance, since a price too high may turn away too much customers while a price too low will push up the overall charging load and cause unfavorable marginal cost increase. The customer trimming effect can be used to determine the monopoly pricing. The territory definition summarizes that in the Bertrand competition model with spatial differentiation selecting price is equivalent to making the strategic choice of defining the target market on the street [, 1]. Specifically, when the unit prices selected by facility A and B are c A and c B, respectively, the customer at location x with charging requirement p will be indifferent between the two facilities if pc A + kx = pc B + k(1 x), which gives x = 1 2 + p(cb ca) 2k. From the formula for indifferent (x, p) pair, we observe that a facility can expand its target market by lowering its unit price, and the expansion effect will be more dramatic for smaller unit transportation cost k, and for larger customer charging requirement p. We choose the pricing mechanism energy of use (EOU) pricing. As the name suggests, the price of a request with parameter r, d and p is simply given by the formula v(r, d, p) = cp, where c is the unit charging price. The appropriate unit price will be studied via profitability simulations. IV. SCHEDULING ALGORITHMS Similar to other problems associated with scheduling with limited resource, the resolution of conflictions is the difficulty for the scheduling of electric vehicle charging. The scheduling tend to be easy for the operator if the overall charging load from the customer requests is well below the average renewable power available. In this favorable scenario, the operator can finish the majority of charging requests with negligible electricity purchased from the power grid. However, if overwhelmingly many charging requests arrive in a short 2319 2321

period of time, the scheduling will be more challenging since the operator would like to keep the electricity bill under control, and thus has to resolve the confliction of overwhelming requests and limited renewable energy resource. A choice of scheduling, Charging (UC) mimics the operations in self-service gas stations, in which electric vehicle owners arrive at the charging facility at the release time and then immediately starts to charge his vehicle until the required charging amount is fulfilled. Under UC scheduling, there is no active scheduling from the operator involved and every customer gets charged at the earliest time possible. However, on the other hand, due to the ignorance of the time flexibility of the customers the disadvantages of unnecessary grid energy purchase and excessive peak power drawn from the power grid lead to higher operating cost. Described below is an online scheduling algorithm Threshold Assignment with Greedy Scheduling () which weighs the profitability of each request and leverages the time flexibility. In scheduling the operator maintains a request queue and a tentative schedule for each charger at all times according to earliest deadline first manner. The requested charging amount of every request in the request queue is divided into two parts, fulfilled by the renewable energy and grid electricity respectively. The relative percentage of the two parts is determined by the operator upon the request release. Therefore the operator can project the operating cost of each request, i.e., the grid electricity bill incurred for the request upon arrival. If the operating cost is reasonable, the operator offers the routine unit price quote. Otherwise, if the operating cost turns out to be too high (this may be a result of low renewable availability, overwhelming charging workload already in facility, or tight deadline of the request), the operator quotes a premium price to protect the profit. The determination of the price quote for follows a threshold assignment procedure explained below. When a customer request arrives and finds the facility lightly loaded (i.e., the request can be finished with other requests already in the queue without additional grid electricity), the operator offers a price quote according to the routine unit price and once the offered quote is accepted, the operator adds the request to the request queue, and dispatches the request to one of the lightly loaded chargers to be finished according to the greedy rule, i.e., in earliest deadline first manner. When a customer request arrives to a heavily occupied facility (i.e., the request cannot be finished together with other requests already in the queue without additional grid electricity purchase), the operator has to be cautious when offering price quote according to the routine unit price, since in the lightly loaded regime very cheap renewable energy is used in charging, resulting in a very small marginal cost, while expensive grid electricity may be necessary in the current situation when the facility is already heavily loaded. Therefore the operator has to weigh the potential grid electricity bill incurred to determine the offered price for the arriving request. Specifically, the operator enumerates the potential chargers to host the customer request in consideration. For each charger the potential grid electricity bill is computed by the minimum amount of the portion of the request to be finished by grid electricity without affecting previous requests in the tentative schedule in earliest deadline first manner. The charger assuming the minimum potential grid electricity bill is selected and evaluated with a threshold test; if the ratio of the potential profit associated with the request in consideration (computed with the routinely quoted price as well as the projected grid electricity bill) and the profit of the requests already in the tentative schedule of this charger is over a prescribed threshold, the operator will tag this request as worthy or profitable, and follow the routine unit price; otherwise, the operator will treat the request as an unprofitable request and provide a price quote of the electricity price plus a certain profit margin (in this way, the operating cost can be safely covered with a profit margin, although with the premium price the customer has a more significant chance of declining the offered price). The increasing trend of the marginal cost with the overall charging workload is the reason behind the tagging of requests to be unprofitable when the facility is highly congested. The projection of the potential grid purchase the operator relies on for decision making is subject to change because of the fluctuation of the renewable sources. Therefore the grid electricity also serves the purpose of reliability backup when the renewable power availability declines in time, leaving the requests already in facility risky. V. SIMULATION RESULTS In this section we simulate the average performance of scheduling algorithms and UC under the scenarios with only one facility operating as monopoly and with two facilities forming a duopoly competing in price. The monopoly pricing and duopoly equilibrium price pairs are investigated for EOU pricing mechanism via simulation. The impact of competition and the benefit of appropriate scheduling are demonstrated from the profitability in the various scenarios. A. Simulation Setup The traffic parameters in the simulation are adopted as follows: the customer arrival process is assumed to be Poisson process with mean inter-arrival time λ 1 {1, 2, 3} minutes, the charging time requirements assumed to be i.i.d. uniform in the interval [, 3] minutes, and the relative deadlines assumed to be i.i.d exponential with mean 4 minutes. The pricing function simulated is EOU pricing with unit price c [.3:.1:.27] $/kwh. The transportation cost k is.5$ per unit length. The fluctuation of the renewable availability (the number of renewable chargers) is assumed to follow random walk on {1, 2, 3,...} starting from the average number of renewable chargers m with symmetric transition probabilities with respect to m. We conduct Monte Carlo runs with time duration of 8 hours. The grid electricity price is set to be constant during the eight hour time frame with unit grid purchase price.16 $/kwh (we raise the grid electricity price from the data entry.1132 $/kwh in EIA Monthly Energy 232 2322

.5 1 1.5 2 2.5 Accept probability 1.9.8.7.6.5.4.3.2.1 Figure 1. Customer response curve Normalized unit price (by grid price.16 $/kwh) Customer response curve Review for July 211 1, since there is concern on the high peak powered needed by the charging facilities, thus an incentive to raise the grid purchase price for charging facilities to mitigate the impact of the spiky peak power needed). The customer response curve θ(u) is assumed to be a sigmoid function exp( 45(u.17)) θ(u) = (1+exp( 45(u.17))), the shape of which is shown in Fig. 1. B. Operations Impact: Monopoly with EOU Pricing The monopoly profit is plotted in Fig. 2 versus the normalized unit charging price under EOU pricing mechanism. Several observations can be made from Fig. 2: 1) there exists a unique unit price which corresponds to the maximum monopoly profit 2) outperforms UC in terms of the maximum monopoly profit 3) the best unit price decreases with the arrival rate (with a smaller arrival rate there are less customers, and the unit price has to be reduced to attract more business) 4) for the same unit price the profit per vehicle decreases when the arrival rate increases, which again reveals the increasing trend of the marginal cost with the overall charging workload. C. Impact of Renewable Energy Availability The performance measures of interest, including best monopoly price, maximum monopoly profit, overall charging energy delivered, total revenue, number of completed requests, grid electricity purchase amount and peak power needed from the grid, are plotted versus the average number of renewable chargers available (which indicates the level of renewable energy available for charging operations) in Fig. 3. One can observe that except the plot for the profit (Fig. 3(g)), there is zigzag shape in other curves. This is because the simulation is conducted by selecting the best monopoly unit price from the predetermined candidate set [.3:.1:.27] $/kwh, and the best price is chosen with respect to the associated profit. Consequently the plot for profit is indeed monotone, because the price selection metric is profit. On the other hand, for other plots since the price is chosen 1 Table 9.9, Transportation sector, Monthly Energy Review, United States Energy Information Administration (EIA), May 212. only from the predetermined candidate set [.3:.1:.27] $/kwh, there will be zigzags. We explain with an example, when the number of renewable charger increases from 2 to 3, the best price changes from.18 $/kwh to.17 $/kwh, and we observe an increase in the grid energy purchased, in spite of a general decreasing trend with increasing number of renewable chargers. This is because the price.18 $/kwh and.17 $/kwh are not the true best price, they are the best in the set [.3:.1:.27] $/kwh (the truly best price is lower than.18 $/kwh for 2 chargers and higher than.17 $/kwh for 3 chargers). As the price goes from.18 $/kwh to.17 $/kwh, the number of customers who accept the offered price increases, therefore leading to a zigzag increase in the grid energy purchased. Despite the zigzag shape in Fig. 3, the qualitative trend coincides with the prediction, i.e.,. the maximum monopoly profit, overall charging energy delivered, total revenue, and number of completed requests increase with the renewable energy availability, and finally level off when there is excessive renewable energy available, while the best monopoly price, grid electricity purchase amount and peak power needed from the grid decreases with the renewable energy availability. It can also be observed from Fig. 3 that is superior to UC with respect to all the performance measures plotted. D. Operations Impact: Duopoly Competition Under the Bertrand competition model with spatial differentiation, we simulate different price pairs when Facility A and Facility B choose price from the predetermined candidate set [.7:.2:.23] $/kwh separately. The two prices chosen by the two facilities divide the street (the line segment [,1]) into two territories for the two facilities. Equivalently, with the overall customer arrival rate fixed the two prices define two thinning processes of the customer arrival sequence as the new arrival sequences for the two facilities. Since there are two facilities, we assume that the overall arrival rate is 2.5 EV/minute, and the two facilities have the same renewable availability, with 6 renewable chargers on average. The profit of each individual facility is arranged in Table I to Table IV. The (i, j)th entries in Table I stands for the profit Facility A obtains when Facility A and Facility B select the ith and jth entry in the predetermined candidate vector [.7:.2:.23] $/kwh, respectively. First observe Table I and Table II, or Table III and Table IV. This corresponds to the scenario in which two facilities adopt the same scheduling algorithm. It can be observed from Table I and Table II that in the price range from.11 $/kwh to.15 $/kwh, if the two facilities offer the same unit price, then the price pair is in equilibrium in the sense that neither facility would like to adjust the price unilaterally since this hurts its own profit. The equilibrium pairs are not stable in the sense that if one facility increases or decreases the price unilaterally, the other facility will find itself better off switching to a new price upon the opponent s change. Therefore the prices pairs may bounce around between.11 $/kwh and.15 $/kwh. Interestingly, depending on which price the two facilities settle 2321 2323

.2.4.6.8 1 1.2 1.4 1.6 1.8 6 Arrival rate 1 EV/min 45 Arrival rate 1/2 EV/min Arrival rate 1/3 EV/min 5 25 35 Profit earned ($) Profit earned ($) 25 15 Profit earned ($) 15 1 1 1 5 5 Normalized unit price (by grid price.16 $/kwh).2.4.6.8 1 1.2 1.4 1.6 1.8 Normalized unit price (by grid price.16 $/kwh).2.4.6.8 1 1.2 1.4 1.6 1.8 Normalized unit price (by grid price.16 $/kwh) (a) Arrival rate 1 EV/minute (b) Arrival rate 1/2 EV/minute (c) Arrival rate 1/3 EV/minute Figure 2. Monopoly profit versus normalized unit charging price, the average number of renewable chargers m =6 Profit maximizing unit price ($/kwh).18.17.16.15.14.13 Profit earned ($) 9 8 7 6 5 Overall charging energy delivered (kwh) 65 6 55 5 45 35 25.12 (a) Best price (in terms of profit) (b) Best profit (c) Overall energy delivered in charging 9 85 18 16 35 Total revenue ($) 8 75 7 65 6 55 Number of completed requests 25 Gird energy purchased (kwh) 1 1 1 8 6 15 5 45 1 (d) Total revenue collected (e) Number of vehicles fulfilled (f) Overall grid electricity purchased 7 6 Peak grid power needed (kw) 5 1 (g) Peak power needed from grid Figure 3. Performance measures versus the average number of renewable chargers available, arrival rate 1 EV/minute 2322 2324

down on, the individual profit with UC adopted can vary from dollars per 8 hours to more than 5 dollars per 8 hours. Applying the same analysis to Table III and Table IV leads to the equilibrium price pair range of.7 $/kwh to.15 $/kwh. Depending on the price the two facilities settle down on, the individual profit with adopted can vary from dollars per 8 hours to more than 6 dollars per 8 hours. The superior individual profit confirms that performs better than UC in the oligopoly competition setup as scheduling ingredient. Next we compare two facilities with different scheduling algorithms. Specifically, we analyze Table III and Table II, corresponding to the scenario in which Facility A adopts while Facility B UC. In this case the equilibrium price pair range is.11 $/kwh to.15 $/kwh. The individual profit with adopted can vary from 5 dollars per 8 hours to more than 6 dollars per 8 hours, while the individual profit with UC adopted only varies from 25 dollars per 8 hours to around 5 dollars per 8 hours. The superior individual profit for the facility that adopts again confirms the superiority of compared with UC. [5] A. Subramanian, M. Garcia, A. Dominguez-Garcia, D. Callaway, K. Poolla, and P. Varaiya, Real-time scheduling deferrable electric loads, in 212 American Control Conference, 212. [6] L. Gan, U. Topcu, and S. H. Low, Optimal decentralized protocol for electric vehicle charging, in Proceedings of the 5th IEEE Conference on Decision and Control, 211. [7] S. Sojoudi and S. H. Low, Optimal charging of plug-in hybrid electric vehicles in smart grids, in Proc. IEEE PES General Meeting, 211. [8] Z. Ma, D. S. Callaway, and I. A. Hiskens, Decentralized charging control of large populations of plug-in electric vehicles, IEEE Trans. Control Systems Technology, 211. [9] M. Caramanis and J. M. Foster, Management of electric vehicle charging to mitigate renewable generation intermittency and distribution network congestion, in Proceedings of the 48th IEEE Conference on Decision and Control, Dec 9, pp. 4717 4722. [1] M. Kefayati and C. Caramanis, Efficient energy delivery management for PHEVs, in 21 First IEEE International Conference on Smart Grid Communications (SmartGridComm), Oct 21, pp. 525 53. [11] C. Pang, P. Dutta, S. Kim, M. Kezunovic, and I. Damnjanovic, PHEVs as dynamically configurable dispersed energy storage for V2B uses in the smart grid, in 7th Mediterranean Conference and Exhibition on Power Generation, Transmission, Distribution and Energy Conversion (MedPower 21), Nov 21, pp. 1 6. [12] S. Chen, Y. Ji, and L. Tong, Large scale charging of electric vehicles, in Proceedings of IEEE PES General Meeting, 212. [13] D. Kreps, A Course in Microeconomic Theory. Princeton, 199. E. versus UC We reiterate the observation from the scenarios of monopoly and duopoly that performs stronger compared with UC as the scheduling ingredient of the entire charging operation scope. This illustrates the impact of appropriate scheduling as one competitive advantage for a charging station, among others such as abundant renewable energy and lower grid purchase price. VI. CONCLUSION The problem of large scale electric vehicle charging operations management is considered where customers arrive over time with deadlines and battery charging level requirement. The operations aspects of the charging facility are investigated, and simulation studies are conducted for the impact of the operations aspects in the scenarios of monopoly and Bertrand duopoly competition. Our conclusions include the customers time flexibility will be helpful for the operator to improve profitability and build a competitive edge; the operating cost of charging facility has to be closely monitored and balanced with the pricing; the Bertrand competition with differentiation may lead to a range of equilibrium price pairs, over which the individual profit for each competitor may vary. REFERENCES [1] Electrification of the transportation system, MIT Energy Initiative Symposium, Tech. Rep., April 21. [Online]. Available: http://web. mit.edu/mitei/docs/reports/electrification-transportation-system.pdf [2] P. Tulpule, V. Marano, S. Yurkovich, and G. Rizzoni, Energy economic analysis of pv based charging station at workplace parking garage, in IEEE EnergyTech 211, Cleveland, OH, USA, May 211, pp. 1 6. [3] P. Kulshrestha, L. Wang, M.-Y. Chow, and S. Lukic, Intelligent energy management system simulator for phevs at municipal parking deck in a smart grid environment, in IEEE Power and Energy Society General Meeting 9, Calgary, AB, Canada, July 9, pp. 1 6. [4] W. Su and M.-Y. Chow, Performance evaluation of a phev parking station using particle swarm optimization, in IEEE Power and Energy Society General Meeting 211, Detroit, MI, USA, July 211. 2323 2325

.7.9.11.13.15.17.19.21.23.7-33.9-429.7-537.2-556.2-567.6-569. -571. -572.8-573.8.9 148.3 155.9-188.4-272.7-286.8-292.2-294.1-294.1-296.2.11 49.3 186.5 271.3 58.6 11.3-11.5-9.6-13.8-14.1.13 18.7 42.7 215.3 44.7 313.8 287.5 28.1 279.6 275.4.15 1.4 19.1 53.4 186.7 516.4 534.9 543.5 546.8 541.9.17 4.1 9.1 1.7 32.2 166.4 518.7 682.2 693.7 72.6.19 1.6 2.1 4.5 3.5 11.9 89.3 467.3 745.8 746.9.21.9 2.9 6. 11.5 88.8 398.7 561.2.23 1.2 1.1 1.1 36.8 26.4 Table I THE PROFIT OF FACILITY A ADOPTING UC.7.9.11.13.15.17.19.21.23.7-5.7 153.3 46.7 22.5 8.1 2.9.1.6.9-416.2 94.2 17.2 4.4 24.3 9.6 2.9.6.11-534.7-169.3 258.2 171.1 36.7 11.7 3.8.4.13-558.1-272.9 63.3 389.9 177.8 29.7 8.1 1.7.15-567.2-283.9 1.6 33.4 489.4 154.8 1.1 1.6 1.2.17-568.4-291.1-7.4 282.1 544.8 536.9 123.6 11.7 4.4.19-572.7-29.5-13.5 27.8 537.6 685.9 471.5 76.4 1..21-572.5-295.2-11.1 275. 537.4 7.6 713.8 344.1 45.7.23-573.5-297.2-15.8 275.7 544.5 78.3 719.5 561.8 181. Table II THE PROFIT OF FACILITY B ADOPTING UC.7.9.11.13.15.17.19.21.23.7 317.4 347.5 365.4 365.5 375.9 379.2 375.9 373. 372..9 166.1 45. 444.4 46.4 449.9 457.4 459.5 457. 461.8.11 51.9 213.3 55.8 535.4 551.4 554.3 562.3 555.3 559.8.13 2. 43.3 228.7 571.5 632.3 648. 645. 653.1 652.7.15 8.2 18.6 57.2 195.4 668.8 736.6 752.2 752.2 757.1.17 5.3 9.1 12.7 28.8 151.3 622.6 811.2 832.5 842.9.19 1.1 3.3 6.4 4.5 15.3 112.7 516.2 766.5 843.5.21.1.9 2.8 3.3 16.6 79.9 391.9 577.7.23 1.7.9 2.8 28.6 213.6 Table III THE PROFIT OF FACILITY A ADOPTING.7.9.11.13.15.17.19.21.23.7 311.2 157.2 45.3 23.6 6.3 2.8.8.9 361.7 417.7 19. 41.4 2.5 7. 2.5.11 357. 447.5 481.3 181.8 44.9 11.2 3.1.6.13 376.4 461.3 532. 588.5 193.1 31.4 11.7 2.1.15 379.8 456.9 546.5 627.7 646.9 129.5 14.2 3.5.7.17 37.1 465.7 557. 655.5 724.2 64.1 132.4 6.8 1.4.19 368.7 457.7 56.5 648.6 742.2 841.3 486. 7. 7.6.21 379.7 454.4 561.2 652.1 738.6 834.1 87.4 353.2 39.9.23 374.2 457.8 559.6 645.7 734.4 821.9 834.4 61.1 177.2 Table IV THE PROFIT OF FACILITY B ADOPTING 2324 2326