Optimal Dispatch of Electric Vehicles and Wind Power ... - IEEE Xplore

IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS, VOL. 8, NO. 4, NOVEMBER 2012

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Optimal Dispatch of Electric Vehicles and Wind Power Using Enhanced Particle Swarm Optimization JunHua Zhao, Member, IEEE, Fushuan Wen, Zhao Yang Dong, Senior Member, IEEE, Yusheng Xue, and Kit Po Wong, Fellow, IEEE

Abstract—In this paper, an economic dispatch model, which can take into account the uncertainties of plug-in electric vehicles (PEVs) and wind generators, is developed. A simulation based approach is first employed to study the probability distributions of the charge/discharge behaviors of PEVs. The probability distribution of wind power is also derived based on the assumption that the wind speed follows the Rayleigh distribution. The mathematical expectations of the generation costs of wind power and V2G (vehicle to grid) power are then derived analytically. An optimization algorithm is developed based on the well-established particle swarm optimization (PSO) and interior point method to solve the economic dispatch model. The proposed approach is demonstrated by the IEEE 118-bus test system. Index Terms—Economic dispatch, particle swarm optimization, plug-in electric vehicle, wind power.

I. INTRODUCTION

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CONOMIC dispatch (ED) is a fundamental problem that aims at allocating available electric power generation to match load demand at the minimal possible cost while respecting security constraints [1]. Traditionally, economic dispatch mainly focuses on conventional generators using fossil fuels and hydraulic resources. However because of their damaging effects on the environment, renewable energy based generation, such as wind power generation, is rapidly expanding its market share. Given the obvious environmental benefits of wind power, its inherent and significant uncertainty can potentially cause severe difficulties to power system operation. Considering the fast expansion of wind power, in the

Manuscript received September 30, 2011; revised January 15, 2012; accepted February 22, 2012. Date of publication June 20, 2012; date of current version October 18, 2012. This work was jointly supported by National Natural Science Foundation of China (51107114, 51177145), China Postdoctoral Science Foundation (20100481406) and a Hong Kong Polytechnic University Grant (#ZV3E). Paper no. TII-11-592. J. H. Zhao is with the School of Electrical Engineering, Zhejiang University, Hangzhou 310027, Zhejiang Province, China (e-mail: [email protected]). F. S. Wen is with the School of Electrical Engineering, Zhejiang University, Hangzhou 310027, Zhejiang Province, China (corresponding author, e-mail: [email protected]). Z. Y. Dong is with the Centre for Intelligent Electricity Networks, The University of Newcastle, NSW 2308, Australia (e-mail: [email protected]. au). Y. S. Xue is with the State Grid Electric Power Research Institute, Nanjing 210003, China (e-mail: [email protected]). K. P. Wong is with the University of Western Australia, WA, Australia (e-mail: [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/TII.2012.2205398

ED problem the load should be allocated not only among conventional generators, but also among wind power generators. Moreover, it is important to appropriately model the uncertainty of wind power in the ED problem to ensure the validity of the dispatch plan. The plug-in electric vehicle (PEV) poses another new challenge to power system operation. Generally speaking, electric vehicles (EVs) are the vehicles fully or partly powered by electricity. As an effective means of reducing carbon emissions and mitigating noise pollution, EVs are becoming increasingly popular in the global motor vehicle market. To enhance the penetration of EVs, large scale electricity charging facilities are being constructed to allow EVs to be plugged into the power system and charge their batteries directly. A large number of PEVs will also introduce significant uncertainty into power system operation, because of the random nature of their charging behaviors. On the other hand, PEVs can also be used as energy storage facilities. An existing study [2] shows that most EVs are not in use for up to 96% of a day. Through V2G (vehicle to grid) technology [3], these unused EVs can discharge electricity back into the power system at peak load periods. PEVs can also act as a means of mitigating the intermittency of wind power, by providing electricity when wind power plants are unavailable. However, to fully utilize the energy storage functions of PEVs, in-depth studies on appropriate power system economic dispatch models and methods should first be conducted. From the mathematical point of view, economic dispatch is an optimization problem. Extensive studies have been carried out to apply different optimization methods on the ED problem. These methods include mathematical programming techniques such as linear programming [4] and nonlinear programming [5]. A variety of heuristic approaches have also been proven to be effective in the ED problem, such as evolutionary programming [6], genetic algorithm [7], particle swarm optimization [8], simulated annealing [9] and differential evolution [10]. Most of these studies rely on the assumption that the power system is deterministic, which is invalid when PEVs and wind power are taken into account. In the new environment, an appropriate ED method must consider the stochastic nature of plug-in EVs and wind power. Several methods have already been proposed to handle the uncertainty of wind power. A traditional approach is to maintain enough operating reserve to ensure that the available generation capacity always exceeds the load [11]. In [12], the Monte Carlo simulation is employed to formulate the feasibility constraints for wind power uncertainty. In [13], the wind power is assumed to follow the Weibull distribution. Based on the assumed distri-

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bution, the costs of wind power are calculated with numerical integration. In [14], a simulation method and ARMA time series model are applied to model the uncertainty of wind power, and then an economic dispatch model is formulated to investigate the impacts of wind power on power system operation. Research work on the impacts of PEVs on power system operation is still at its beginning stage. Some studies [15]–[17] focus on the cost/benefit analysis of PEVs from the economics point of view. An economic dispatch model, which takes into account the plug-in EVs with the V2G function, is proposed in [18]. This model however has two drawbacks: 1) power flow constraints are not considered; 2) it is assumed that the number of available PEVs is predictable and deterministic, and this is not realistic. In this work, a novel economic dispatch model is developed to take into account both the uncertainties of PEVs and wind power. A simulation approach is first presented to study the random behaviors of PEVs. The probability distributions of PEVs and wind power are then derived. Based on the distributions, the objective of the ED model is specified to minimize the mean of total generation cost of the system. Appropriate constraints are also formulated for PEVs and wind generators. An optimization algorithm based on particle swarm optimization (PSO) and interior point method is developed to solve the proposed ED model. The formulated ED model and optimization algorithm are finally tested with the IEEE 118-bus system to prove its validness. The rest of the paper is organized as follows: in Section II, the probability distributions of the power outputs of plug-in electric vehicles and wind generators are firstly derived. In Section III, the proposed ED model is formulated. An enhanced particle swarm optimization algorithm is developed in Section IV to solve the proposed ED model. In Section V, comprehensive case studies are performed to test the proposed approach. Section VI finally concludes the paper. II. PROBABILITY DISTRIBUTIONS OF PLUG-IN ELECTRIC VEHICLES AND WIND POWER A. Simulating the Behaviors of Plug-in Electric Vehicles Since the large-scale power charge/discharge facility for PEVs is still under construction, historical data about the behaviors of PEVs are not available. We therefore employ a simulation based approach to study the charge/discharge behaviors of PEVs in this work. The electric vehicle selected for this study is the Toyota RAV4 [19]. Its technical parameters are given in Table I[19]. We divide all the PEVs in the system into three categories: public EVs, private EVs and dispatchable EVs. Public EVs are the ones for public use. A typical example of the public EV is using EVs as taxis. The important characteristics of public EVs are that their average driving time per day is relatively long and they are usually used at the peak time of a day. Therefore, they are usually charged at off-peak time and generally cannot act as V2G power sources. Different from public EVs, private EVs are private-owned ones. Their driving pattern is relatively flexible and they are usually not in use for most of the time in a day. Private EVs are

TABLE I TECHNICAL PARAMETERS OF THE PEV

therefore suitable candidates of V2G power sources. We assume that some private EVs will voluntarily be registered as dispatchable EVs. Associate payments will be made to attract the owners to register their EVs. Once registered, the owners of dispatchable EVs should ensure that their vehicles are charged only at off-peak time. Moreover, the owners should connect their EVs with the V2G discharging facility during a certain period of each day. During this period, the system operator can then use these dispatchable EVs as power sources and dispatch them if necessary. The following assumptions are also made in the simulation: 1) The charge/discharge functionality is implemented by a DC/AC inverter from battery to the grid. 2) The charge/discharge actions of PEVs can be controlled either manually by their owners, or remotely by the system operator if the PEVs are connected with the grid. 3) Each category of PEVs has its specific charge time period and discharge time period; a PEV will charge (discharge) only in its specific charge (discharge) period. 4) Within its corresponding charge (discharge) period, the charge (discharge) behavior of a PEV follows a uniform distribution. 5) Following [20], it is assumed that the maximum charging/discharging power for the PEV is 3.6 kW. With this charging power, the battery of Toyota RAV4 can be fully charged in 6 hours. Based on the above assumptions and settings, the Monte Carlo simulation can be performed to study the charge/discharge behaviors of PEVs. For each PEV, we first determine its charge and discharge periods based on its type. We then randomly select its charge and discharge time, which should be within the charge/discharge periods. The length of the charge/discharge time is determined by its average daily mileage. It is assumed that once a PEV starts to charge, it will not stop until its battery is fully charged. Similarly, we randomly determine when a dispatchable EV will be available for discharge within the discharge period. After the charge/discharge behaviors of all PEVs have been randomly determined, we calculate the aggregate load level and V2G power capacity of PEVs for each hour in a day. This process will be repeated times to obtain the empirical probability distributions of the load level and available V2G power of PEVs for each hour. The simulation results are given in the section of case studies. The results clearly indicate that, both the aggregated load level and V2G power output of PEVs follow the normal distribution. This finding is important for the theoretical analysis in following sections.

ZHAO et al.: OPTIMAL DISPATCH OF ELECTRIC VEHICLES AND WIND POWER USING ENHANCED PARTICLE SWARM OPTIMIZATION

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B. The Probability Distribution of Wind Power The probability distributions of PEVs have been discussed in Section II-A. To model the uncertainty of wind power, it is also necessary to derive the probability distribution of wind power, which can be obtained based on the wind speed distribution and the power curve to be discussed below. It is well-known that the wind speed follows the Rayleigh or the Weibull distribution [13], [21]. In this work, the wind speed is modeled with the Rayleigh distribution, which has the following probability density function (PDF): (1) where is the wind speed; is the scale parameter. The functional relationship between the wind speed and the power output of a wind turbine is usually represented by a power curve as shown in Fig. 1. The power curve can be divided into four parts. When the wind speed is lower than a threshold namely the cut-in speed, the wind turbine cannot be driven by the wind, and its power output is therefore zero. When the wind speed is higher than another threshold (cut-out speed), the power output will be zero as well. When the wind speed is between the cut-in and rated speeds, the wind power output can approximately be expressed as a linear function of the wind speed. When the wind speed is between the rated and cut-out speeds, the power output will be a constant. Thus, the power curve can be expressed mathematically as follows: (2.1) (2.2) (2.3) where , , , and are respectively the cut-in speed, the rated speed, the cut-out speed, and the power output for the rated speed. Based on (1) and (2), the wind power cumulative distribution function (CDF) can be derived as follows: When ,

Fig. 1. A typical wind turbine power curve.

From (3.2), we can then derive the PDF of the wind power as: (4.1) When

, the PDF of the wind power can be given as: (4.2)

When

, (4.3)

is the Dirac delta function, which is introduced bewhere cause the PDF of the wind power is discrete. III. THE PROPOSED ECONOMIC DISPATCH MODEL A. The Objective Function A number of uncertain factors, such as the charge/discharge actions of PEVs, the wind power output, and the system load level, are involved in the ED problem. It is therefore important to formulate a probabilistic, rather than a deterministic ED model, to handle these uncertainties. In the model to be developed here, the objective is set to minimize the mean of the total generation cost of the whole system: (5) represents the mathematical expectation operator; is the total generation cost of the system. The total generation cost consists of seven components:

where

(3.1) ,

When

(3.2) When

, (3.3)

(6.1) and are respectively the numbers of convenwhere tional generators and wind power generators; represents the number of buses with V2G facilities installed. In the developed

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model, all PEVs that are connected with an identical bus will be aggregated and considered as a single generator. The conventional generator is assumed to have a quadratic cost function:

Based on the PDF functions shown in (4.1)–(4.3), the mean of the underestimated penalty cost of the wind power can be derived as

(6.2) is the scheduled output of the conventional generator where ; , , are cost coefficients. The cost of a wind power generator could be divided into three components. The first component accounts for the direct cost paid by the system operator to the owner of the wind generator: (6.3) is the scheduled wind power output of wind generator Here ; is the direct cost coefficient. Since the wind power is highly volatile, the wind power forecast will usually have some errors. When the scheduled wind power output is lower than the available wind power output, surplus wind power will be wasted. The second component accounts for the penalty cost of underestimating the available wind power:

(7.1) where represents the Gauss error function, and can be easily calculated with numerical integration; represents a number that infinitely approaches from the left side. Similarly, the mean of the overestimated penalty cost can be derived as

(6.4) is the underestimating penalty cost coefficient; where is the actually available wind power. On the other hand, if the actually available wind power is less than the scheduled wind power output, the deficit should be covered by calling reserve. The third component corresponds to the penalty cost of overestimating the actually available wind power: (6.5)

(7.2)

is the overestimated penalty cost coefficient. Note where that should be negative here. Similarly, the cost of V2G power also consists of three components as follows:

As stated in Section II-A, the V2G power follows a normal distribution with the following PDF:

(6.6) (6.7) (6.8) , , and are respectively the diwhere rect cost, underestimated penalty cost and overestimated penalty cost; , and are respectively the direct, underestimated penalty and overestimated penalty cost coefficients for PEVs; is the available V2G power at bus ; is the scheduled V2G power at bus .

(8) where represents the available V2G power; and are respectively the mean and standard deviation of the normal distribution. Based on (8), the underestimated penalty cost of V2G power is calculated as

B. Calculating the Means of the Generation Costs In this sub-section we derive the closed form expressions for the means of generation costs.

(9.1)

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The overestimated penalty cost of V2G power can be given as

where

represents the power flow through line is the thermal power limit of line . 3) Bus Injection Power Constraints:

;

(11.7) (11.8)

(9.2) Based on (7) and (9), (5) can be rewritten as

and are respectively the injected real power where and reactive power at bus ; and are respectively the real and imaginary parts of the admittance matrix element; is the voltage magnitude at bus ; represents the voltage angle difference between buses and ; indicates that bus is directly connected with bus . 4) Wind Turbine Constraints: It is assumed that the wind turbines studied in this work are all equipped with squirrel cage induction generators. As discussed in [22], the buses with wind turbines can then be treated as PQ buses. Moreover, the wind turbines equipped with squirrel cage induction generators should respect additional constraints [23]: (11.9) (11.10)

(10)

C. The Constraints to be Respected The following constraints are considered in the proposed ED model. 1) Generation Capacity Limits: (11.1) (11.2)

where represents the reactive power of the wind turbine and it is negative since the squirrel cage induction generator always absorbs reactive power; is the sum of the stator leakage reactance and rotor leakage reactance of the wind turbine. All the PEVs are connected with the load buses through DC-AC inverters. As discussed in [22], [23], whether the DC-AC inverter should be modeled as a PV or PQ bus is determined by its control method. In this work, it is assumed that the DC-AC inverters for PEVs are designed to control and independently [23]; the V2G power source can therefore be modeled as a PV bus. For each load bus with PEVs connected, a PV bus, which is connected with the load bus directly, will be added to represent the aggregated V2G power source.

(11.3) (11.4)

IV. INTERIOR POINT BASED PARTICLE SWARM OPTIMIZATION

(11.5)

The proposed ED model forms a highly complicated optimization problem. Because the proposed ED problem is highly nonlinear and non-convex, traditional mathematical programming methods will easily be trapped by local optima if applied directly. To tackle this difficulty, we propose an enhanced particle swarm optimization algorithm by integrating traditional PSO with the interior point method, and apply it to solve the proposed ED model. The particle swarm optimization algorithm is inspired by the sociological behaviors associated with bird flocking [8]. In the original PSO, each individual is treated as a particle in the space, with position and velocity vectors. The PSO algorithm maintains a swarm of particles, each of which represents a candidate

and are respectively the lower and where upper limits of the real power outputs of conventional generators; and are respectively the lower and upper limits of the reactive power outputs of conventional generators; and are respectively the maximum outputs of wind generators and V2G sources; and are respectively the reactive power output and reactive power limit of the V2G power source. 2) Branch flow limits: (11.6)

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Fig. 2. The aggregated load level of PEVs in 00:00–01:00.

solution to the optimization problem. The main idea of PSO is to generate new swarms by exchanging information among the velocity, global best, local best, and current particles. Theoretically, PSO can ensure the convergence to the global optimum. Its major drawback is its relatively slow convergence speed. To improve the computational efficiency of traditional PSO, we integrate PSO with the interior point method. The interior point method is highly efficient in searching local optima, and has been widely applied in power system operation and dispatch [4]. By employing the interior point method, the proposed algorithm can quickly locate local optima. On the other hand, the PSO updating procedure ensures that the proposed algorithm will not be easily trapped in local optima, which is a significant advantage compared with traditional mathematical programming techniques. The main procedure of the interior point based PSO (IPPSO) algorithm is given as follows: 1) Initialize the initial swarm of particles by employing a uniformly distributed random vector; 2) For the swarm, employ the traditional PSO updating procedure [8] to generate the swarm; 3) Select the two particles , , which respectively have the lowest and highest fitness values, from the swarm; 4) Using as the initial values, apply the interior point methods to generate two local optima, and add them into the swarm; 5) Terminate the algorithm if the stopping criterion is satisfied, otherwise go back to step 2. V. CASE STUDIES A. Simulating the Behaviors of Plug-in Electric Vehicles We first simulate the charge/discharge behaviors of PEVs using the approach discussed in Section II-A. The PEV parameters, the simulation setting and assumptions have already been given before. The normal probability plots of the load levels of PEVs in three typical time periods 00:00–01:00 (off-peak night time), 11:00–12:00 (peak day time), 19:00–20:00 (peak night time) are given in Figs. 2–4. The normal plots show that the PEV load levels in these three periods are all approximately normally distributed. Moreover, we plot the normal probability plot of the V2G capacity of PEVs in 11:00–12:00 in Fig. 5. The distribution of the V2G capacity is also similar to a normal distribution.



Fig. 5. The aggregated V2G power capacity of PEVs in 11:00–12:00.

To more strictly illustrate that the distributions of the load level and V2G capacity of PEVs are normally distributed, the simulation results are tested with the Jarque-Bera (JB) normality test, as shown in Table III. The significance level of the JB test is set as 0.05. As clearly seen, the JB statistics for all four scenarios are smaller than the critical value. Moreover, the P-values for all four scenarios are also greater than 0.05. These results clearly indicate that the aggregated load level and V2G capacity of PEVs are both normally distributed. B. Numerical Results With the IEEE 118-Bus System The proposed ED model and optimization algorithm are tested with the IEEE 118-bus system. In our study, it is assumed that 3 additional wind generators are installed at buses 24, 26, and 116, respectively. The parameters of the wind generators are given in Table IV. Then based on (2.2) and (2.3), we can


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TABLE II SIMULATION SETTING

TABLE III JB NORMALITY TEST RESULTS

Fig. 6. Load curves with and without PEVs (Bus 59).

TABLE IV WIND GENERATOR PARAMETERS

TABLE V THE COST COEFFICIENTS OF WIND AND V2G POWER Fig. 7. Optimal real power outputs of generators in 00:00–01:00.

obtain parameter values , . The parameter of the Rayleigh distribution can be estimated from the forecasted wind speed. We set the forecasted wind speed as the mean of the wind speed. It is easy to show that the mean of the Rayleigh distribution is . can then be calculated as (12) is the forecasted wind speed. In this study, the forewhere casted wind speed is set as 20 m/s, then we can approximately obtain that . It is assumed that plug-in EVs can be connected with the system at buses 59, 80, 90 and 116. It is further assumed that 90,000 PEVs will be connected at each bus. With the simulation approach discussed in Section II-A, we can obtain the means and variances of the load level and V2G capacity of PEVs in each hour. Moreover, the cost coefficients of wind and V2G power are given in Table V. The direct cost of wind power is relatively low since it is well known that wind power has a very small operational cost. On the other hand, the direct cost of V2G power is relatively high, because the high price is a necessary incentive to attract PEV owners to register as dispatchable EVs. To study the impact of PEVs on the load level, the load curve of bus 59 with PEVs connected, is compared with its original

load curve in Fig. 6. As observed, the load levels in 23:00–7:00 have been significantly increased. This is caused by the charge behaviors of a large number of PEVs in the system. As shown in Table II, most PEVs will charge power in off-peak periods, especially between 23:00–07:00. The load curve therefore is significantly reshaped. Based on the above simulation setting, the optimal dispatch plans for periods 00:00–01:00, 11:00–12:00, 19:00–20:00 are illustrated in Figs. 7–9. In these figures, W24 and P59 represent the wind generator at bus 24 and the V2G power source at bus 59, respectively. As clearly seen, the outputs of the wind generator are very close to its maximum capacity in all three periods. This is mainly because the direct cost of a wind generator is very low compared with a conventional generator and a V2G source. On the other hand, because of their high direct cost, the outputs of V2G sources are relatively low compared with their capacities. In Fig. 7, the capacities of all V2G sources are set to zero, since it is assumed that PEVs will only be dispatched during peak periods. If we reset the direct cost and underestimated cost coefficients of V2G power as 30 and 50 respectively, the V2G power outputs will significantly increase and be close to their maximum capacities, as illustrated in Fig. 10. Therefore, the output of the V2G power can be controlled by adjusting its direct cost (the payment to the PEV owner) and the underestimated penalty cost. This however shows a dilemma of V2G power: to attract more dispatchable PEVs and increase the available V2G capacity, a higher direct cost must be set; this high direct cost on the other

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Fig. 8. Optimal real power outputs of generators in 11:00–12:00.

Fig. 11. Wind power outputs for different scale parameter ’s.

Fig. 9. Optimal real power outputs of generators in 19:00–20:00 .

Fig. 12. V2G power outputs for different standard deviation ’s.

sources; because there is a higher probability that the reserve is called and a higher overestimated penalty cost is incurred. Therefore, to fully utilize the V2G power, it is important to design an appropriate market mechanism to ensure that the available V2G capacity is stable and predictable. C. Evaluating the Interior Point Based PSO Algorithm

Fig. 10. Optimal real power outputs of generators in 11:00–12:00 .

hand will decrease V2G power outputs and result in the waste of the available V2G power. To study the statistical properties of the ED model, we also investigate the impacts of probability distribution parameters and on the optimal dispatch plan. As shown in Fig. 11, the optimal real power outputs of wind generators increase as the scale parameter increases. Since is positively proportional to the forecasted wind speed, we can also conclude that the wind generator output is positively proportional to the forecasted wind speed. The relationship between the optimal V2G real power outputs and the standard deviation of the V2G capacity distribution is shown in Fig. 12. Generally, V2G outputs will decrease as grows. Note that measures the uncertainty of the available V2G power capacity. The results clearly show that the uncertainty of the V2G power will hinder the dispatch of V2G

To empirically demonstrate the effectiveness of the proposed IPPSO algorithm, we firstly test the IPPSO algorithm with 4 widely-used benchmark functions, which are listed in Table VI. The global minima of the 4 functions are all 0. The performance of the proposed IPPSO is compared with genetic algorithm [24], differential evolution [25], and three well-known variants of PSO, namely HPSO [26], IPSO [27] and SPSO [28]. In this study, the employed genetic algorithm is a modified GA with elitism and adaptive mutation probability control. The employed differential evolution has self-adaptive mutation control, which has been applied in electricity price forecasting. To make a fair comparison, we set the population sizes of all algorithms as 80, and select the same initial population for all 6 algorithms. All the algorithms were tested on a PC with 2.13 GHz Intel Core 2 CPU and 2G RAM. Tables VII–X show the results out of 50 runs of benchmark functions with each method. As clearly shown in Tables VII–X, the proposed IPPSO algorithm generally outperforms other 5 evolutionary algorithms on the 4 benchmark functions. Especially, the IPPSO demonstrates superior computational efficiency due to the integration of the interior point method. This is important when dealing with large-scale real-world power systems.


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TABLE VI FOUR BENCHMARK FUNCTIONS

TABLE VII PERFORMANCES OF 6 ALGORITHMS ON THE SPHERE FUNCTION

TABLE VIII PERFORMANCES OF 6 ALGORITHMS ON THE JASON FUNCTION

TABLE XI PERFORMANCES OF 4 ALGORITHMS ON IEEE 118-BUS TEST SYSTEM

We have also compared the performances of GA, DE, SPSO and IPPSO on the IEEE 118-bus system. The system parameters are set as discussed in Section V-B. As clearly shown in Table XI, IPPSO is able to locate better solutions in less computational time compared with other evolutionary algorithms. This result has again demonstrated its effectiveness. VI. CONCLUSION

TABLE IX PERFORMANCES OF 6 ALGORITHMS ON THE GRIEWANK FUNCTION

TABLE X PERFORMANCES OF 6 ALGORITHMS ON THE ROSENBROCK FUNCTION

The fast penetration of wind power generation and electric vehicles have introduced severe challenges to power system operation. Moreover, a plug-in electric vehicle can act either as a load, or as a power source by employing the V2G technology. However, the impacts of V2G power on power system operation have not yet been deeply studied. In this paper, a novel economic dispatch model is formulated to take into account the uncertainties of both PEVs and wind generators. An interior point based particle swarm optimization algorithm is also developed to solve the proposed ED model. The main contributions of this paper are the following: 1) A simulation based approach is proposed to study the statistical property of the charging/discharging behaviors of electric vehicles. 2) A novel power system economic dispatch model is formulated to take into account both the impacts of electric vehicles and wind power generators. 3) By integrating the interior point method with the particle swarm optimization algorithm, a novel algorithm is proposed. Its effectiveness in solving nonlinear and non-convex optimization problems have been demonstrated by four well-known benchmark functions and the IEEE 118-bus test system. REFERENCES [1] M. E. El-Hawary and G. S. Christensen, Optimal Economic Operation of Electric Power System. New York: Academic Press, 1979.

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Jun Hua Zhao (S’04–M’07) received the Bachelor and Ph.D. degrees from Xi’an Jiaotong University, China, and University of Queensland, Australia, in 2003 and 2007, respectively. He then worked as a Postdoctoral Research Fellow at the University of Queensland, Australia, from 2007 to 2010. He is now a Lecturer in Zhejiang University, China. His research interests include power system analysis and computation, electricity market management and analysis, nonlinear optimization, statistical methods, data mining and their applications in power engineering.

Fushuan Wen received the B.E. and M.E. degrees from Tianjin University, China, in 1985 and 1988, respectively, and the Ph.D. degree from Zhejiang University, China, in 1991, all in electrical engineering. He joined the faculty of Zhejiang University in 1991, and has been a full Professor and the Director of the Institute of Power Economics and Information since 1997, and the Director of Zhejiang University–Insigma Joint Research Center for Smart Grids since 2010. He had been a University Distinguished Professor, the Deputy Dean of the School of Electrical Engineering and the Director of the Institute of Power Economics and Electricity Markets in South China University of Technology (SCUT), China, from 2005 to 2009. His current research interests lie in power industry restructuring, power system alarm processing, fault diagnosis and restoration strategies, as well as smart grids.

Zhao Yang Dong (M’99–SM’06) received the Ph.D. degree from University of Sydney, Australia in 1999. He is now Ausgrid Chair Professor and Director of the Centre for Intelligent Electricity Networks (CIEN), The University of Newcastle, Australia. He also holds academic and industrial positions with the Hong Kong Polytechnic University, the University of Queensland, Australia and Transend Networks, Tasmania, Australia. His research interest includes power system planning, power system security, stability and control, load modeling, electricity market, and computational intelligence and its application in power engineering. He is an editor of IEEE TRANSACTIONS ON SMART GRID. Yusheng Xue (M’87) received the M.Sc. (Eng) degree in electrical engineering from EPRI, China, in 1981, and the Ph.D. degree from the University of Liege, Belgium, in 1987. He was elected an academician of Chinese Academy of Engineering (CAE) in 1995. He was the Chief Engineer at the Nanjing Automation Research Institute (NARI), China during 1993–2009, and is now the Honorary President of State Grid Electric Power Research Institute (SGEPRI or NARI), China. He has authored and coauthored 400 technical papers and his research interests include power system stability control, security and economic operation.


Kit Po Wong (M’87–SM’90–F’02) received the M.Sc, Ph.D., and D.Eng. degrees from the Institute of Science and Technology, University of Manchester, U.K., in 1972, 1974, and 2001, respectively. He was with the University of Western Australia, Perth, Australia, from 1974 until 2004 and is now an Adjunct Professor there. Since 2002, he has been Chair Professor, and previously Head, of Department of Electrical Engineering, The Hong Kong Polytechnic University. His current research interests include computational intelligence applications to power system analysis, planning and operations, as well as power market analysis.

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Prof. Wong received 3 Sir John Madsen Medals (1981, 1982, and 1988) from the Institution of Engineers Australia, the 1999 Outstanding Engineer Award from IEEE Power Chapter Western Australia, and the 2000 IEEE Third Millennium Award. He was a Co-Technical Chairman of IEEE Machine Learning and Cybernetics (ICMLC) 2004 Conference and General Chairman of IEEE/CSEE PowerCon2000. He is now Editor-in-Chief of IEEE POWER ENGINEERING LETTERS and was Editor-in-Chief of IEE Proc. Generation, Transmission and Distribution and Editor (Electrical) of the Transactions of Hong Kong Institution of Engineers. He is a Fellow of IEEE, IET, HKIE, and IEAust.