Game Theoretic Based Charging Strategy for Plug-in ... - IEEE Xplore

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IEEE TRANSACTIONS ON SMART GRID, VOL. 5, NO. 5, SEPTEMBER 2014

Game Theoretic Based Charging Strategy for Plug-in Hybrid Electric Vehicles Shahab Bahrami and Mostafa Parniani, Senior Member, IEEE

Abstract—In the future smart grids, Plug-in Hybrid Electric Vehicles (PHEVs) are seen as an important means of transportation to reduce greenhouse gas emissions. One of the main issues regarding to this sort of vehicles is managing their charging time to prevent high peak loads over time. Deploying advanced metering and automatic chargers can be a practical way not only for the vehicle owners to manage their energy consumption, but also for the utilities to manage the electricity load during the day by shifting the charging loads to the off-peak periods. Additionally, an efficient charging schedule can reduce the users’ electricity bill cost. In this paper we propose a new practical demand response (DR) program for PHEVs charging scheduling based on game theoretic approach, aiming at optimizing customers charging cost. In the proposed method, a stochastic model is given for starting time of charging, which makes the method a practical tool for simulating the vehicle owners charging behavior effectively. Index Terms—Automatic chargers, game theory, load management, peak load shaving, plug-in hybrid electric vehicles.

I. INTRODUCTION

H

IGH GASOLINE prices and environmental pollution make Electric Vehicles (EVs) and Plug-in Hybrid Electric Vehicles (PHEVs) more attractive transportation options in the future smart grids [1], [2]. PHEVs use batteries to power an electric motor and use another fuel, such as gasoline or diesel, to power an internal combustion engine [2]. PHEVs reduce the fossil fuel consumption and CO emissions compared to fossil-fueled vehicles. They can run on electricity for a certain distance after each recharge, depending on their battery’s energy storage capacity; typically between 20 km and 80 km [2], [3]. This paper mainly focuses on the electrical charging of PHEVs, and the terms EV and PHEV may be used interchangeably. The number of consumers who purchase a PHEV has been growing by 80% each year since 2000 [3], and 10% of new vehicle sales are expected to be PHEVs by year 2015 [4]. However, there still exist obstacles to the proliferation of PHEV use. When a large number of PHEVs are integrated into the grid, the total charging demand constitutes a significant load. It could add an additional 18% load to the existing power grids on average, Manuscript received June 24, 2013; revised November 13, 2013; accepted April 10, 2014. Date of publication June 27, 2014; date of current version September 05, 2014. Paper no. TSG-00469-2013. The authors are with the Department of Electrical Engineering, Sharif University of Technology, Tehran, Iran (e-mail: [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TSG.2014.2317523

and may have negative impacts on the grid reliability due to less predictable overloads [3], [4]. To overcome this drawback, a proper control mechanism of charging loads can allow shifting in times of charging from peak to off-peak, and consequently, reduce supply and customer side cost and enhance power system operating conditions [5]. In the literature, the impact of EVs’ charging load was investigated as early as 1983 with a study on the timing of EV recharging and its effect on utilities [6], and then in [7] implications of EVs on power distribution grids was studied. That paper remarked the effects of large EV fleets on the distribution grid and the effects of long charging cycles of batteries. Koyanagi et al. [8] proposed time-shifted fast charge at night time to avoid peak loads in the time intervals that already experience heavy loads. To overcome charging loads impacts on electricity power networks, several studies have been done in recent years. In [9] optimal locating of PHEVs parking lots was investigated to provide vehicle to grid (V2G) power as distribution generation. In [10], modeling micro-grids system with PHEVs and designing appropriate controllers for frequency stabilization were studied. Denholm and Short [11] published a report which provides an overview of large-scale utilization of PHEVs. In this report an analytical method was introduced by using the PHEVload tool to optimally charge and discharge the PHEV fleet. Clement et al. [12] determined the optimal charging profile to enhance the power grid operating conditions such as reducing power loss and increasing load factor. In [13], a novel algorithm was presented to maximize the advantages of utilizing EVs’ batteries as an energy storage system in power grids. Wu et al. [14] developed a smart pricing policy and designed a mechanism to achieve optimal frequency regulation performance in a distributed fashion. Mohsenian-Rad et al. [15] proposed an incentive-based energy consumption scheduling algorithm to minimize the cost of energy and also to balance the residential loads when consumers have PHEV by considering the interaction between users and utility companies. Bashash et al. [16] have derived an optimization mechanism for charging pattern of PHEVs to simultaneously minimize the total cost of fuel and electricity and the total battery health degradation over a 24-h naturalistic drive cycle. Masoum et al. [17] have investigated a smart load management strategy in a smart grid environment by considering the PHEVs charging impacts on typical daily residential load patterns. Voltage fluctuations and power losses have been included in modeling the charging pattern. Sundstrom and Binding [18] have derived two methods based on linear and quadratic approximation of the battery behavior, in order to quantify the level of detail necessary in the optimization for

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BAHRAMI AND PARNIANI: GAME THEORETIC BASED CHARGING STRATEGY FOR PLUG-IN HYBRID ELECTRIC VEHICLES

establishing the charging plan. Bayram et al. [19] proposed a novel scheme for the PHEVs fast charging mode of operation to allocate power to them from the grid, as well as charging stations. The proposed method could serve more customers with a specific amount of power, thus enabling the station operators to increase their profitability. Pang et al. [20] modeled the aggregate overnight demand for electricity by a large community of PHEVs. The paper proposed a novel method to monitor total load of the grid, and during load overages, reduce load by signaling certain consumers to interrupt charging and defer their charging load by one unit of time. Galus and Andersson [21] modeled PHEVs in an energy hub [22], [23] to provide an agent-based energy system with an efficient PHEV charging management scheme. Game theory is an appropriate approach to model PHEVs charging interaction and to study demand response programs in power grids [24]. Couillet et al. [25] provided a game formulation for the competitive interaction between electrical vehicles or hybrid gas-electricity vehicles in a Cournot power market. Nguyen et al. [26] formulated centralized and decentralized optimization models for PHEVs charging. In the decentralized model, an energy cost sharing model was designed, and a noncooperative game was used to formulate energy charging scheduling. Fan [27] studied PHEVs charging game to propose a price-based demand response program in a smart grid where users or PHEVs’ chargers can adapt their charging rates according to their preferences. Although the above-mentioned studies have examined various aspects for PHEVs charging scheduling, it is imperative to propose a practical comprehensive algorithm that is applicable to power market with dynamic electricity pricing. In this paper, the PHEVs charging scheduling problem is examined, and a time-based DR program is developed which aims at near-optimum scheduling by taking into consideration vehicle owners charging behavior and dynamic electricity pricing. In the proposed scheduling algorithm, the electricity price can be modeled as any convex function of total load consumption. Moreover, the PHEV owners are assumed to be price anticipator, which means that they are willing to minimize their cost of charging according to the electricity price at each time. Furthermore, the PHEV charging is seen as a game among all car owners to minimize all users charging cost. The proposed method is based on probabilistic model of customers charging pattern, which is more accurate in practical applications. This algorithm can be used in DR programs to encourage customers to manage their electricity consumption by shifting their PHEVs charging times to the off-peak periods. The rest of the paper is organized as follows. Section II presents the objective function of the optimization problem for PHEV charging game. Section III contains description of the proposed scheduling program and the optimization technique. In Section IV, outputs of the technique are presented by simulation, and Section V concludes the paper.

Cost Calculation: Consider PHEVs that are going to be charged in a specific period during a day (e.g., from 10 pm to 7 am). This assumption does not affect the generality of the proposed algorithm and can be varied for the study case. The charging demand for each vehicle is calculated according to the following equation: (1) where battery charging demand for

,

maximum charge that the car owner will need for the next trip or the maximum battery packs capacity, available charging capacity when the is plugged into the charger. vehicle is

Hence, the charging duration of the

(2) where charging duration of charging rate for

. .

The charging rate depends on different factors, such as charger type, battery size, the PHEV model, etc. Generally, the charging rate is modelled as a time-dependent function . In this paper, for simplification, the charging rates are assumed to be constant during the charging time; therefore, During the charging time Otherwise

(3)

Equation (4) characterizes the total residential load by two major components: the PHEVs charging load and the base load, , representing the other residential electric appliances. The major concern of this study is to minimize the peak loads potentially caused by PHEVs charging. Consequently, it is assumed that the usage time and power consumption of the other residential appliances are not controllable; and hence, is known and fixed [21]. (4) In (4), denotes the set of all PHEVs. According to the existing practices in power markets, electricity price is an increasing convex function of the total load. For price-making customers, whose total load consumption affects the electricity price, (5) can model the electricity price [21], [28], [29].

II. OBJECTIVE FUNCTION This section presents a game theoretic based PHEV charging model that results in near-optimum electricity cost.

vehicle

(5) in which

is an increasing convex function.

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The total charging cost of customer in time interval as follows [28], [30], [31].


is

Subjected to constraints (1), (2) and (10) (10)

(6) Stochastic Modeling: The drivers’ arrival times in a certain day are random variables. If we assume that charging will start when the car owner arrives at home, the starting time of charging for each PHEV can be considered as a random variable with probability density function (pdf) of ; and the cumulative density function of starting time of charging, , will be the integral of in time domain [32]–[34]. For all PHEVs, these probability functions can be estimated based on a statistical data from different data bases such as the 2009 National Household Survey [35]. Suppose that represents the probability that is being charged in time . According to definition of and the law of total probability [34], we get that (7)

Solving the above stochastic and nonlinear optimization problem is quite complex [40]–[42]. However, we propose an effective algorithm to approximate NE in each iteration according to the following steps. Step a) List the vehicles randomly. This game will be run in an asynchronous fashion, and this step model the uncertainty of the order of players in each iteration. Step b) Start from the beginning of the list. Determine the appropriate function (or ) for each vehicle assuming that none of the other PHEV owners have incentive to change its , i.e., the others are assumed to be unchanged (NE definition). The following section elaborates this step. III. SCHEDULING ALGORITHM The expected cost for each PHEV can be expressed as follows.

According to (3), if is on charge with probability of at time , then the charging rate will be ; and otherwise, it will be zero. Consequently, the probability density function of charging rate for in a specific time is [25]:

(11)

(8) From (4), we have in which is impulse function . Strategic PHEVs charging: Suppose that all car owners are price anticipator, i.e., they know that the electricity price is calculated according to (5); besides, each user wishes to locally and selfishly choose its action to minimize its own bill cost. The strategy chosen by a user affects the performance of other users through affecting the electricity price value given in (5). Consequently, the game theory provides a natural framework for analyzing and developing proper DR mechanisms for scheduling the charging times [37]. For a PHEV and its smart charger, obtaining individual information on the charging rate and time of other PHEVs is practically impossible due to the excessive communication and processing overhead required [38], [39]. Therefore, in a distributed charging set, each user attempts to minimize its own cost (or maximize its own utility) in response to the aggregate information on the actions of other users. This makes use of non-cooperative game theory most appropriate, with the relevant solution concept which is the Nash equilibrium (NE) [37], [40]. In other words, if every user in the network picks its cost-minimizing strategy selfishly and locally, there will be a stable state at which no user can decrease its cost unilaterally. It is shown in the Appendix A that the charging game is a strictly convex N-person game (based on cost functions), and there is a Nash equilibrium for this game. In the NE, the CDF function for is the solution of the following optimization problem when other users are assumed to be fixed: (9)

(12) where the random variable is the aggregated charging load of other PHEVs at time . From (7) and (8), then, the term inside the integral in (11) can be written as (13).

(13) The term in (13) is the expected value of a function of . To approximate this term, by applying the lemma mentioned in Appendix B we have,

(14) is the second derivative of and are where the mean and variance of at time . The smart charger of can estimate the mean and variance of total charging load of all PHEVs by gathering the total load data samples (e.g., the data center can gather the data in the last 6 months and send it to each PHEV) and subtracting it from the mean and variance of charging load to calculate and . Consequently, the charger needs only the aggregate data form other chargers, and a simple communication from data center to


each smart charger can provide the necessary data for decision making process. In Appendix C it is proved that (9) is equivalent to minimize defined as follows. (15) where (16) and

(17) According to (17), the function depends only on the price function , fixed parameter , and known parameters and ; and thus, is independent of . By applying integration by parts formula, (15) becomes

(18) is the derivative function of . Since the first in which term of (18) is constant, minimizing (15) or (18) is equivalent to maximizing the following function. (19) For any probability distribution function

we have (20)

Hence, we get

(21) The equality holds when , where is the time at which the function becomes maximum. This distribution function results in step function for , i.e., . To return to the point, the above calculations show that to achieve NE, the smart charger should start charging the corresponding PHEV at time which depends on the function . According to (16) and (17), is a function of charging rate of , charging duration, base load, and the mean and variance of charging load caused by all other PHEVs. These data can be accessible for the smart charger by using appropriate communication infrastructures [35], [36]. Finally, by finding the optimum time for other PHEVs in a similar way, the near-optimum charging schedule will be obtained for that day. The flow chart for each iteration of the algorithm is shown in Fig. 1. Recall that playing the best response for each car owner would be equivalent to solving optimization problem (9). Therefore, if the users play the best responses se-

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quentially through running the proposed algorithm in an asynchronous fashion, the total energy cost in the system either decreases or remains unchanged every time a user updates its start time of charging. Since the charging cost has a lower bound (e.g., the charging cost is always non-negative), convergence is guaranteed. When this algorithm is run in several iterations, at the settling point of the algorithm, no user can decrease its cost by deviating from this point when playing its best response. This directly indicates that the settling point is the Nash equilibrium of charging game among the PHEV owners [37]. The proposed charging method can be easily used in the realworld DR programs. For instance, assume that data center save the load information of the last 100 days for computing the mean and variance of the total load. Now consider the first day of running the game. Each smart charger will receive necessary information and will make decision for the time of charging based on the proposed method. When all the smart chargers finish making decision, the first iteration (correspond to the first day of running the game) will complete successfully. The simulation results in the next section demonstrate that the load curve will become much smoother and peak shaving will be achieved through the game is played for only one time. The achieved smoother load curve will be added to the data base of the data center. In the next day, smart chargers will play the game again, but this time the data center will send them updated information with smoother load curve achieved in the previous day. Again, the load curve after accomplishing the second iteration becomes smooth, and the data will be added to the data base. After playing this game for 100 days, the data base will contains the data for 100 smooth load curves for previous iterations of the game. In the next day, smart chargers will make decision based on the information of 100 smooth load curves. Consequently, their decision will be more accurate and the result load curve will be smother than before. This process will continue and smart chargers strategies will converge to Nash equilibrium of the game step by step. As it can be seen, this game has two main advantages. First, it is asynchronous and so it is not dependent on the order of the players in the game. Second, the iterations of the game can be done day by day which is appropriate in real-world DR programs. In fact, the smart chargers will learn the better strategy day by day. Heuristic methods such as PSO [43]–[45] may also be suggested to solve the NP hard optimization problem stated in (9). Although heuristic algorithms may be applicable to solve such problems, the proposed method of this paper is advantageous in at least two aspects. Firstly, the proposed algorithm has high convergence speed since its calculation volume is very low. In contrast, heuristic algorithms generally have low convergence speed. In fact, based on the flow chart shown in Fig. 1, it is sufficient to calculate , and the maximum of at each step; consequently, the proposed algorithm has order of N (the PHEV numbers) time complexity, and it can be easily used in large-scale networks with high penetration of PHEVs. Secondly, this paper proposed a stochastic model for PHEV charging problem, in addition to continuous modeling of cost functions. Consequently, using heuristic algorithms to solve PHEV charging problem with this formulation will be very difficult, if not impossible. Therefore, simple approaches like the one suggested in this paper are more appropriate.

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TABLE I CHEVROLET VOLT SPECIFICATIONS

Fig. 1. Flowchart of the charging scheduling algorithm for one iteration.

IV. SIMULATION This section presents a numerical example to illustrate different features of the proposed scheduling algorithm. To eval-

uate the efficiency of the method, two scenarios are considered: low and high PHEV penetration, in which 10% and 50% of 1000 sample homes are equipped with PHEV. The Chevrolet Volt specifications shown in Table I is used for modeling PHEVs [46]. For these scenarios, it is assumed that electricity price function is modeled as a cubic function of total load, i.e., . Parameter is a weighting coefficient. The generation capacity is assumed large enough to supply both base and charging load in all time slots. The charging rate of each PHEV depends on the charger type, battery capacity and PHEVs type. The amount of power in kW provided to the PHEV’s battery, determines the levels of charging equipment as follows. AC Level 1, which is a 120-volt AC plug. A full charge at Level 1 can take between 8 to 20 hours, depending on the battery capacity of the vehicle. The charging rate in AC level 1 is approximately 1 kW [47]. AC Level 2, which is a 240-volt AC plug and requires installation of home charging equipment. Level 2 charging can take between 3 to 8 hours, again depending on the battery capacity of the vehicle. The charging rate in this type falls within a range of 3 kW to 20 kW [47]. DC fast charging, which is as high as 600-volt, enables charging along heavy traffic corridors and at public stations. A DC fast charging can take less than 30 minutes to charge a battery to most of its capacity [47]. For the vehicles with characteristics mentioned in Table I, the energy that PHEV’s battery needs to be fully charged is 16 kWh. In this study, AC level 2 charging mode has been applied. Hence, it is assumed that the charging rate for all PHEVs is 8 kW to fully charge the vehicles within maximally 2 hours. For all PHEVs, the functions are assumed to be normal distribution functions with estimated variance of 15 minutes. Based on the available data, any type of probability distributed function may be considered for the simulation. In real simulation, the values of means and variances can be estimated based on previous data about car owners’ charging behavior; however, in this study, without loss of generality, it can be supposed that in the uncontrolled charging situation, PHEVs charging starts when the car owner arrives at home from a daily trip. Consequently, it can be assumed that the mean value of starting times of charging are randomly distributed over the range of 7:00 pm and 11:59 pm. It is supposed that the base load profile from 6:00 am to 6:00 am has a peak of 5000 kW from 4:00 pm to 10:00 pm, and the rest would be 2000 kW off-peak.


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problem to approximate the Nash equilibrium point. The stochastic approach used in the paper makes it feasible for smart chargers to do scheduling for all PHEVs according to the vehicle owners charging data history. Simulation results show that the proposed method yields acceptable results from various standpoints: near-optimum scheduling with high convergence speed, acceptable distribution of load for different penetration levels of PHEVs, and at the same time, considering the probabilistic charging characteristic of the customers. The results reveal the benefits and potentials of the algorithm for developing load management strategies in power markets. APPENDIX

Fig. 2. Scenario 1: load curve before and after scheduling for 100 PHEVs.

N- Person Game Theorem:

Fig. 3. Scenario 2: load curve before and after scheduling for 500 PHEVs.

Fig. 2 shows the load curves in the first scenario before and after load scheduling. 100 PHEVs exist in this case. Obviously, the imposed charging load is much lower than the base load. This figure shows that before scheduling, charging load increases the peak load about 8% (400 kW). However, after scheduling, the PHEVs charging periods are shifted to the off-peak time slots. It can be seen that starting times of charging are shifted to the after-midnight hours when the electricity consumption is in its lower level. The load curve in the second scenario is shown in Fig. 3. In this scenario, 500 PHEVs exist. Therefore, the charging load is considerable, and increases the peak load about 40% (2000 kW). By applying the proposed strategic charging method, not only the PHEVs charging are shifted to the off-peak periods, but also the load profile becomes considerably smooth, both of which clarifies the efficiency of the scheduling algorithm. Furthermore, the convergence time for this case is acceptable and is about one minute. The high convergence speed is expected since the calculation of , and the maximum of is straight forward. Hence, the proposed algorithm can be used for large scale networks with high penetration of PHEVs. V. CONCLUSION This paper introduces a new load management strategy for plug-in hybrid electric vehicle charging to reduce peak load, regarding any convex electricity price function. PHEVs charging is seen as a game among all users, the purpose of which is to minimize all car owners cost of charging. A fast algorithm is presented to solve the proposed optimization

We first notice that since electricity price function is strictly convex, the cost function for each PHEV with respect to the consumed load is strictly convex, too. By defining the pay-off function as the opposite of cost function, this function will be strictly concave. Therefore, the charging game is a strictly convex N-person game. In this case, existence of Nash equilibrium directly results from [48, Theorem 1]. Moreover, the Nash equilibrium is unique due to [48, Theorem 3]. In fact, in the Nash equilibrium, functions are the solution of the optimization problem (9). One can see the distributed probability function as the mixed-strategy of player , and the equilibrium of the game as the mixed-strategy Nash equilibrium which is always exist. We have shown in Section III, that is a delta function which means that the mixed-strategy Nash equilibrium is indeed a pure Nash equilibrium. Lemma: Approximate Evaluation of Expected Value: If is a random variable with mean value of and is a function of , then is also a random variable with mean value of . If is sufficiently smooth around , then by approximating it by a parabola we have [34]: (22) Since conclude that

and

, we can

(23) Proof of the Proposed Algorithm: In this part, the mathematical formulation to minimize the following function is given. According to (13) and (14), (11) can be calculated approximately as follows.

(24)

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For simplification define


as follows.

(25)

The integral in (34) is independent of , and can be eliminated from (33) to minimize (27). Thus, only the first term of (33) should be considered. By substituting (33) in (29), minimizing (29) becomes equivalent to minimizing the following equation.

Hence, (24) can be written as: (26) Consequently, the optimization problem in (9) is equivalent to minimizing (26). Parameter is fixed and has no effect in minimization problem; and therefore we can omit it from (26) and minimize the following equation:

(35) where (36)

(27)

Equations (35) and (36) are used to determine the optimum charging times in Section III.

Substituting (7) in (27) yields: (28)

ACKNOWLEDGMENT Extending the prentices, the right side becomes: (29) In the first step, the second integral will be calculated. Let us define as follows. (30) By changing the variable

, (31)

It is known that charging PHEVs start within time period ; therefore, function is zero for . Arising out of this fact, the lower limit of the second integral in (31) can be changed to . This alteration leads us to: (32) Dividing the interval of the above integral in two parts yields:

(33) For charging duration , since the charging should end up , charging would have been started before . As a result, for . Consequently, we have: by

(34)

The authors gratefully acknowledge the contributions of Elham Hokmabadi and Aras Sheikhi for their kind help and constructive comments on the original version of this paper. REFERENCES [1] “Technology roadmap electric and plug-in hybrid electric vehicles,” Int. Energy Agency, Jun. 2011. [2] B. Daehyun, G. Michailidis, and M. Devetsikiotis, “Demand response control for PHEV charging stations by dynamic price adjustments,” in Proc. Innov. Smart Grid Technol. Conf., Washington, DC, USA, Jan. 2012. [3] D. Lemoine, D. Kammen, and A. Farrell, “An innovation and policy agenda for commercially competitive plug-in hybrid electric vehicles,” Environ. Res. Lett., vol. 3, no. 1, Feb. 2008. [4] M. Duvall, E. Knipping, M. Alexander, L. Tonachel, and C. Clark, “Environmental assessment of plug-in hybrid electric vehicles. Vol. 1: nationwide greenhouse gas emissions,” Electric Power Research Institute, Technical Report, 2007. [5] S. Gao, K. T. Chau, C. C. Chan, C. Liu, and D. Wu, “Optimal control framework and scheme for integrating plug-in hybrid electric vehicles into grid,” J. Asian Elect. Veh., vol. 9, no. 1, pp. 1473–1481, Jun. 2011. [6] M. M. Collins and G. H. Mader, “The timing of EV recharging and its effect on utilities,” IEEE Trans. Veh. Technol., vol. 32, no. 1, pp. 90–97, Feb. 1983. [7] S. Rahman and G. Shrestha, “An investigation into the impact of electric vehicle load on the electric utility distribution system,” IEEE Trans. Power Del., vol. 8, no. 1, pp. 591–597, Apr. 1993. [8] F. Koyanagi and Y. Uriu, “A strategy of load leveling by charging and discharging time control of electric vehicles,” IEEE Trans. Power Syst., vol. 13, no. 3, pp. 1179–1184, Aug. 1998. [9] M. Moradijoz, M. P. Moghadam, M. R. Haghifam, and E. Alishahi, “A multi-objective optimization problem for allocating parking lots in a distribution network,” Int. J. Elect. Power Energy Syst., vol. 46, no. 1, pp. 115–122, Mar. 2013. [10] S. Vachirasricirikul and I. Ngamroo, “Robust controller design of micro turbine and electrolyzer for frequency stabilization in a micro grid system with plug-in hybrid electric vehicles,” Int. J. Elect. Power Energy Syst., vol. 43, no. 1, pp. 804–811, Dec. 2012. [11] P. Denholm and W. Short, “An evaluation of utility system impacts and benefits of optimally dispatched plug-in hybrid electric vehicles,” U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, National Renewable Energy Laboratory (NREL), Tech. Rep., 2006.


[12] K. Clement, E. Haesen, and J. Driesen, “Coordinated charging of multiple plug-in hybrid electric vehicles in residential distribution grids,” in Proc. IEEE Power Syst. Conf. Exposition, Seattle, WA, USA, Mar. 2009. [13] T. Chen, T. Hsieh, N. Yang, J. Yang, and C. Liao, “Evaluation of advantages of an energy storage system using recycled EV batteries,” Int. J. Elect. Power Energy Syst., vol. 45, no. 1, pp. 264–270, Feb. 2013. [14] C. Wu, H. Mohsenian-Rad, and J. Huang, “Vehicle-to-aggregator interaction game,” IEEE Trans. Smart Grid, vol. 3, no. 1, pp. 434–442, Mar. 2012. [15] H. Mohsenian-Rad, V. W. S. Wong, J. Jatskevich, R. Schober, and A. Leon-Garcia, “Autonomous demand-side management based on gametheoretic energy consumption scheduling for the future smart grid,” IEEE Trans. Smart Grid, vol. 1, no. 3, pp. 320–331, Dec. 2010. [16] S. Bashash, S. J. Moura, J. C. Forman, and H. k. Fathy, “Plug-in hybrid electric vehicle charge pattern optimization for energy cost and battery longevity,” J. Power Sources, vol. 196, no. 1, pp. 541–546, Jan. 2011. [17] A. S. Masoum, S. Deilami, P. S. Moses, M. A. S. Masoum, and A. Abu-Siada, “Smart load management of plug-in electric vehicles in distribution and residential networks with charging stations for peak shaving and loss minimization considering voltage regulation,” IET Gener., Transm., Distrib., vol. 5, no. 8, pp. 877–888, Aug. 2011. [18] O. Sundström and C. Binding, “Optimization methods to plan the charging of electric vehicle fleets,” in Proc. Int. Conf. Control, Commun., Power Eng., Chennai, India, Jul. 2010. [19] S. Bayram, G. Michailidis, M. Devetsikiotis, and F. Granelli, “Electric power allocation in a network of fast charging stations,” IEEE J. Sel. Areas Commun., vol. 31, no. 7, pp. 1235–1245, Jul. 2013. [20] G. Pang, G. Kesidis, and T. Konstantopoulos, “Avoiding overages by deferred aggregate demand for PEV charging on the smart grid,” in Proc. IEEE Int. Conf. Commun., Ottawa, Canada, Jun. 2012. [21] M. D. Galus and G. Andersson, “Demand management of grid connected plug-in hybrid electric vehicles (PHEV),” in Proc. IEEE Energy 2030 Conf., Atlanta, GA, USA, Nov. 2008. [22] S. Bahrami and F. Safe, “A financial approach to evaluate an optimized combined cooling, heat and power system,” Energy Power Eng. J., vol. 5, no. 5, pp. 352–362, Jul. 2013. [23] A. Sheikhi, A. M. Ranjbar, and H. Oraee, “Financial analysis and optimal size and operation for a multicarrier energy system,” Energy Buildings J., vol. 48, no. 1, pp. 71–78, May 2012. [24] W. Saad, Z. Han, H. V. Poor, and T. Basar, “Game-theoretic methods for the smart grid: an overview of microgrid systems, demand-side management, and smart grid communications,” IEEE Signal Process. Mag., vol. 29, no. 5, pp. 86–105, Sep. 2012. [25] R. Couillet, S. M. Perlaza, H. Tembine, and M. Debbah, “Electrical vehicles in the smart grid: a mean field game analysis,” IEEE J. Sel. Areas Commun., vol. 30, no. 1, pp. 1086–1096, Jul. 2012. [26] H. K. Nguyen and J. B. Song, “Optimal charging and discharging for multiple PHEVs with demand side management in vehicle-to-building,” J. Commun. Netw., vol. 14, no. 6, pp. 662–671, Dec. 2012. [27] Z. Fan, “A distributed demand response algorithm and its application to PHEV charging in smart grids,” IEEE Trans. Smart Grid, vol. 3, no. 3, pp. 1280–1291, Sep. 2012. [28] S. Bahrami, M. Parniani, and A. Vafaeimehr, “A modified approach for residential load scheduling using smart meters,” in Proc. IEEE Conf. Innov. Smart Grid Technol. (ISGT Eur.), Berlin, Germany, Oct. 2012. [29] H. Bessembinder and M. L. Lemmon, “Equilibrium pricing and optimal hedging in electricity forward markets,” J. Finance, vol. 57, no. 3, pp. 1347–1382, Jun. 2002. [30] C. Wang, M. D. Groot, and P. Marendi, “A service-oriented system for optimizing residential energy use,” in Proc. IEEE Int. Conf. Web Services (ICWS), Los Angeles, CA, USA, Jul. 2009. [31] E. Inoa and J. Wang, “PHEV charging strategies for maximized energy saving,” IEEE Trans. Veh. Technol., vol. 60, no. 7, pp. 2978–2986, Sep. 2011. [32] S. M. aguilar, A. Doria-Cerezo, and F. Puleston, “Simulation of demand management and grid balancing with electric vehicles,” Int. J. Power Sources, vol. 216, no. 15, pp. 104–116, May 2012. [33] T. -K. Lee, Z. Bareket, T. Gordon, and Z. S. Filipi, “Stochastic modeling for studies of real-world PHEV usage: Driving schedule and daily temporal distributions,” IEEE Trans. Veh. Technol., vol. 61, no. 4, pp. 1493–1502, May 2012.

2375

[34] At. Papoulis, Probability and Statistics. Englewood Cliffs, NJ, USA: Prentice-Hall, 1989. [35] Federal Highway Administration, National Household Travel Survey 2009. Washington, DC, USA: Department of Transportation, 2010. [36] H. Chao, “Price-Responsive demand management for a smart grid world,” Electr. J., vol. 23, no. 1, pp. 7–20, Feb. 2010. [37] A. M. Rad, V. W. S. Wong, and J. Jatskevich, “Autonomous demand side management based on game theoretic energy consumption scheduling for the future smart grids,” IEEE Trans. Smart Grid, vol. 1, no. 3, pp. 320–331, Dec. 2010. [38] L. D. Ha, S. Ploix, E. Zamai, and M. Jacomino, “Real-time dynamic optimization for demand-side load management,” Int. J. Manage. Sci. Eng. Manage., vol. 3, no. 1, pp. 243–252, Mar. 2008. [39] A. M. Rad and A. Leon-Garcia, “Optimal residential load control with price prediction in real time electricity pricing environments,” IEEE Trans. Smart Grid, vol. 1, no. 2, pp. 120–133, Nov. 2010. [40] J. Xiao, J. Y. Chung, J. Li, R. Boutaba, and J. W. Hong, “Near optimal demand-side energy management under real-time demand-response pricing,” in Proc. Int. Conf. Netw. Service Manage. (CNSM), Niagara Falls, ON, Canada, Oct. 2010. [41] E. Inoa, F. Guo, J. Wang, and W. Choi, “A full study of a PHEV charging facility based on global optimization and real-time simulation,” in Proc. Int. Conf. Power Electron. ECCE Asia, Jeju, Korea, Jun. 2011. [42] O. Asad, M. Erol-Kantarci, and H. T. Mouftah, “Management of PHEV charging from the smart grid using sensor web services,” in Proc. Can. Conf. Elect. Computer Eng., Niagara Falls, ON, Canada, May 2011. [43] B. Mozafari, T. Amraee, A. M. Ranjbar, and M. Mirjafari, “Particle swarm optimization method for optimal reactive power procurement considering voltage stability,” Scientia Iranica, vol. 14, no. 6, pp. 534–545, Dec. 2007. [44] B. Mozafari, A. M. Ranjbar, T. Amraee, M. Mirjafari, and A. R. Shirani, “A hybrid of particle swarm and ant colony optimization algorithms for reactive power market simulation,” J. Intell. Fuzzy Syst., vol. 17, no. 6, pp. 557–574, Dec. 2006. [45] M. Hajian, A. M. Ranjbar, T. Amraee, and A. R. Shirani, “Optimal placement of phasor measurement units: Particle swarm optimization approach,” in Proc. Int. Conf. Intell. Syst. Appl. Power Syst., Niigata, Japan, Nov. 2007. [46] Chevy Volt website [Online]. Available: http://www.chevyvolt.net/chevrolet-volt-specs.htm. [47] C. Botsford and A. Szczepanek, “Fast charging vs. slow charging: Pros and cons for the new age of electric vehicles,” in Proc. Elect. Veh. Symp. (EVS24), Norway, May 2009. [48] J. B. Rosen, “Existence and uniqueness of equilibrium points for concave n-person games,” Econometrica, vol. 33, pp. 347–351, 1965.

Shahab Bahrami received the B.Sc. and MSc. degrees in Electrical Engineering from Sharif University of Technology, Tehran, Iran, in 2010 and 2013, respectively. He is a Ph.D. student at the University of British Columbia (UBC), Vancouver, Canada. His research interests include load management, communication systems, renewable energy technologies, game theory, and theoretic analysis in smart power grids.

Mostafa Parniani (SM’06) received his B.Sc. degree from Amir-Kabir University of Technology, Iran, in 1987, and the M.Sc. degree from Sharif University of Technology (SUT), Tehran, Iran, in 1989, both in electrical power engineering. He obtained the Ph.D. degree in electrical engineering from the University of Toronto, Canada, in 1995. He is an Associate Professor at SUT. His research interests include power system dynamics and control, applications of power electronics in power systems, and renewable energies.