Assessment of Impacts of PHEV Charging Patterns on ... - IEEE Xplore

IEEE TRANSACTIONS ON SMART GRID, VOL. 3, NO. 2, JUNE 2012

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Assessment of Impacts of PHEV Charging Patterns on Wind-Thermal Scheduling by Stochastic Unit Commitment Cong Liu, Member, IEEE, Jianhui Wang, Member, IEEE, Audun Botterud, Member, IEEE, Yan Zhou, and Anantray Vyas

Abstract—Light duty plug-in hybrid electric vehicle (PHEV) technology holds a promising future due to its “friendliness” to the environment and potential to reduce dependence on fossil fuels. However, the likely significant growth of PHEVs will bring new challenges and opportunities for power system infrastructures. This paper studies the impacts of PHEV charging patterns on power system operations and scheduling. The stochastic unit commitment model described in this paper considers coordination of thermal generating units and PHEV charging loads, as well as the penetration of large-scale wind power. The proposed model also addresses ancillary services provided by vehicle-to-grid techniques. Daily electricity demands by various types of PHEVs are estimated on the basis of a PHEV population projection and transportation survey. The stochastic unit commitment model is used to simulate power system scheduling with different charging patterns for PHEVs. The results show that a smart charging pattern can reduce the operating costs of a power system and compensate for the fluctuation in wind power. The proposed model also can serve as a foundation and tool to perform long-term cost-benefit analysis and to assist policy making.

B. Variables and Functions Status indicator of generating units. ,

Start-up/shut-down indicator of units. Generation dispatch of a unit (MW). Maximal generation of a unit considering the ramping limit (MW). Estimated power loss at time. Probability of each scenario. Load dispatch (MW). Wind power (MW). Spinning reserve of unit (MW). Operating reserve of unit (MW). ,

Index Terms—Mixed integer programming, plug-in hybrid electric vehicle, stochastic, unit commitment, wind power.

Start-up and shut-down cost of a unit ($). Generation cost curve ($).

C. Constants

I. NOMENCLATURE

,

A. Index

Minimum and maximum power generation if the unit is on (MW).

Index of generating unit.

Maximum wind power (MW).

Index of electricity load.

Penalty price for unserved load ($/MW).

Index of scenarios.

,

Maximum ramp up/down (MW/hour).

,

Step constant in the start-up and shut-down cost curve of a unit ($).

Index of hour. Index of segment in stepwise start-up curves. Index of wind farm.

,

Manuscript received December 20, 2010; revised June 23, 2011; accepted February 04, 2012. Date of publication April 12, 2012; date of current version May 21, 2012. This work was created by UChicago Argonne, LLC, Operator of Argonne National Laboratory (“Argonne”). Argonne, a U.S. Department of Energy Office of Science laboratory, is operated under Contract No. DE-AC02–06CH11357. Paper no. TSG-00402-2010. The authors are with the Decision and Information Sciences Division and Energy Systems Division of Argonne National Laboratory, Argonne, IL 60439 USA (e-mail: [email protected]; [email protected]; [email protected]; [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.2012.2187687

Start-up/shut-down ramp rate (MW/hour). Ramp rate of generation units (MW/minute). Quick start capacity of unit (MW). Electric energy requirement (MWh). Spinning reserve requirement (MW). Operating reserve requirement (MW).

,

1949-3053/$31.00 © 2012 IEEE

Minimum on/off time of units (hour).

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Set of charging period. Charging speed ((MWh/hour). Set of electricity load from PHEV charging. II. INTRODUCTION

T

HE interactions between renewable energy sources (e.g., wind power) and PHEVs have complicated implications on power system operations. On one hand, intermittent and volatile power generation from renewable sources has already raised significant challenges for grid management and generation scheduling for power system operators. Current industry practices must be modified to accommodate the integration of significant amounts of wind power. On the other hand, PHEVs are poised for rapid growth because of their lower environmental impacts and higher efficiency. The extensive use of PHEVs will further bring new challenges for power system infrastructures. For instance, the charging and driving patterns of PHEVs will impact the operation and scheduling of power systems. Charging a large number of PHEVs simultaneously may cause electricity shortages and price spikes in the power market [1]. Some research has been conducted to analyze the connection between wind energy sources and PHEVs. The National Renewable Energy Laboratory (NREL) examines the long-term interaction between wind energy and PHEVs [2] by assuming increasing penetration of PHEVs compared with the current vehicle fleet for future years. The NREL model focuses on probabilistic generation capacity expansion, which is determined by considering the operating and planning reserves that might be provided by PHEVs. However, this work does not consider the short-term operational impact of wind energy and PHEVs on power system operations. A study by the Rocky Mountain Institute [3] simulates the interactions among transportation, the electricity grid, and the building sector enabled by plug-in vehicles but does not address the need for new power system operational methods. Several other research efforts of PHEVs in recent years [4]–[7] examine the impact of PHEVs on the power system but do not take wind energy into account and do not propose operational methods. A study by Wang et al. [8] uses a deterministic method to address coordination of wind power and PHEV charging. Development of appropriate scheduling and simulation tools is necessary to accurately coordinate various generating resources in power systems and PHEV charging. Such tools should address uncertain wind power and general thermal units, as well as PHEV charging loads. Deterministic unit commitment traditionally deals with the unit generation schedule in a power system. The purpose of such a schedule is to minimize operating costs while satisfying prevailing constraints such as load balance, system spinning reserve, ramp rate limits, and minimum up/down time limits over a set of time periods. Compared with deterministic unit commitment and economic dispatch methods, stochastic unit commitment studies have been mostly performed in academia. Carpentier et al. [9] proposed a stochastic unit commitment model

in which random trees are used to simulate generator failures. Takriti et al. [10] presented a stochastic unit commitment model to address the mid-term fuel planning problem. Generator failures and load forecasting inaccuracies are incorporated into the model as stochastic factors. Wu et al. [11] proposed a midterm stochastic security-constrained unit commitment model by considering transmission network constraints. Monte Carlo simulation and scenario reduction techniques are used in their study. Traditional unit commitment only can dispatch generator but not load. Load dispatch can play an important role in reducing the operating cost of power systems by shaving the peak and filling in the valley of load profiles. Brooks et al. [12] presented a concept that includes the capability to precisely allocate loads on command. Clearly, electric vehicles or PHEVs could be an excellent demand dispatch resource, given their potential for rapid response and developed smart grid infrastructures. For example, wind is usually stronger at night, but the surplus wind generation may have to be curtailed because the demand and supply in electricity market must be real-time balance leading to a waste of available renewable resources. PHEVs could make use of the nighttime wind generation by charging at night. In the future, the increasing numbers of PHEVs may also benefit electric power system operation by enabling successful implementation of vehicle-to-gird technologies. By that time, PHEV loads will be able to feed back electricity like storage or provide ancillary service when the vehicle is charging its battery. For this study, we develop a short-term two-stage stochastic unit commitment model to study the impacts of PHEVs on power system operations, considering volatile and intermittent wind power. The decision variables at the first stage are the hourly unit commitment statuses of various types of generators while the second stage variables are economic dispatches and load dispatches. The wind power forecasting error is captured through generated scenarios by using quantile regression and Monte-Carlo simulation. A scenario reduction technique is applied to reduce the number of scenarios. To conduct electric power system operation and scheduling simulations, daily electricity demands from various PHEVs have to be estimated. To obtain these estimates, our study addresses four other types of information, derived from the transportation survey and other sources. 1) number of PHEVs by type; 2) battery size and all-electric range (AER); 3) vehicle driving patterns; 4) charging rate limits. The remainder of this paper is divided into the following sections: Section III introduces PHEV load estimation; Section IV briefly discusses wind forecasting; Section V describes the stochastic unit commitment model, and Sections VI and VII present case studies and conclusions, respectively. III. PHEV LOAD ESTIMATION A. PHEV Population by Type Light-duty vehicle projections from the Energy Information Administration’s (EIA’s) 2010 Annual Energy Outlook (AEO) [13] were used to estimate the number of cars and light trucks that will be on the road in the United States by 2020.

LIU et al.: ASSESSMENT OF IMPACTS OF PHEV CHARGING PATTERNS ON WIND-THERMAL SCHEDULING BY STOCHASTIC UNIT COMMITMENT

TABLE I PHEVS ON ROAD IN ILLINOIS IN 2020 BY SIZE CLASS

The authors first allocated national vehicle projections to each region by using the population projections by age group for each region, provided by the U.S. Census Bureau [14]. However, depending on population density and transit availability, each state may have either more or fewer vehicles per driving-age person compared with the result of vehicle allocations based only on the driving age population proportion of each state. The deviation was estimated by using the 2008 state-level vehicle registration data from the Highway Statistics published by the Federal Highway Administration (FHWA) [15]. An analysis of the share of both the 2008 driving-age population and 2008 vehicle registrations yielded the propensity for each state to own either more or fewer light-duty vehicles per driving-age person. These propensity values were assumed to remain unchanged through 2020 for each state. Combined with the population projections, the authors used the estimated propensity of vehicle ownership to adjust the previous allocation for each region. The authors assume that PHEVs will be offered first in the car and sport utility vehicle (SUV) segments. Five PHEV categories—subcompact cars, compact cars, midsize cars, large cars, and small and midsize SUVs—are considered. The authors then estimate the shares of vehicles in each category in each region. The FHWA’s 2008 Highway Statistics provide the number of registrations of light trucks by state and by category (i.e., pickups, vans, SUVs, other light trucks, and farm trucks). The 2008 share of light truck by these vehicle types are computed and are assumed to remain unchanged through 2020. The authors use the SUV share of light truck registrations to arrive at 2020 state-level SUV registrations. Similarly, automobile registrations of subcompact, compact, midsize, and large cars are used to estimate the 2020 registrations in each state or region. On the basis of the assumption that 10% of registered cars and SUVs in 2020 will be PHEVs, PHEV population by type in Illinois is estimated as shown in Table I. A 10% share of on road vehicles can be achieved by a substituting technology in 10 years under a scenario of incentives and high fuel prices. This share is possible if the substituting technology’s eventual new vehicle market share of 30% is achieved in 15 years. A 10% share of on road vehicles is specified as an upper limit here. B. Charging Requirements for PHEVs PHEV can operate in either charge-depleting or charge-sustaining mode. In charge-depleting mode, the vehicle is driven by electrical motor and battery only. In charge-sustaining mode, the vehicle relies mainly on the internal combustion engine to provide power; the battery maintains a certain charge level, and the electrical motor provides ancillary power. The required AER of the vehicle is used to estimate the battery-charging requirement of the vehicle. In this paper, we as-

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TABLE II PHEV ENERGY REQUIREMENTS ON ONE CHARGE (KWH)

sume that all PHEVs with various AERs are charged once at the end of a day. The energy requirements of the four PHEV AERs (PHEV10, PHEV 20, PHEV 30, and PHEV 40) and different sizes of the vehicles are estimated by using the Powertrain System Analysis Toolkit (PSAT) [16]. The PSAT model was used to size all vehicle components such that the PHEVs would meet the minimum acceleration requirements. For example, a subcompact PHEV with a 10-mile AER and a 20-mile AER would need 2.8 kWh and 5.6 kWh respectively to be fully charged after having depleted its battery pack to the lowest allowable state of charge (SOC). The values in Table II account for charger and battery pack losses, thereby requiring more energy from the electric system than the end use energy estimated by the PSAT model. The charging efficiencies of PHEVs 10, 20, 30, and 40 are 86.4%, 86.4%, 85.5%, and 81.8% respectively. C. Traffic Data Analysis The travel day data in the 2009 National Household Travel Survey (NHTS) [17] are used to allocate total PHEVs in each geographical area by 10-, 20-, 30-, and 40-mile AER. Vehicles traveling 12–24 miles are used to compute vehicle share by PHEVs with 10-mile AER, 24–36 miles for 20-mile AER, 36–48 miles for 30-mile AER, and 48–60 miles for 40-mile AER. These distance ranges represent total daily travel by vehicles and was selected assuming that higher priced PHEVs would be purchased by those traveling at least 20% longer than a PHEV’s AER. The share of vehicles in each AER is determined and applied to PHEV estimates in each of the analysis areas. The share of PHEV 10, PHEV 20, PHEV 30 and PHEV 40 account for 38.7%, 28.0%, 19.4%, and 13.9% respectively in Illinois. Travel data from the 2009 NHTS [17] are further analyzed to determine daily driving patterns and to calculate how much of that travel can potentially rely on electricity. In other words, we examine, under different assumptions, the ending time of the last vehicle trip and the share of vehicle miles traveled that can be electrified. The NHTS files contain data on household characteristics, household member characteristics, household vehicle characteristics, and household travel characteristics. For travel data, the survey includes a one-day travel component and a long-distance travel component. Travel data from the 2009 NHTS are analyzed to develop distributions of vehicles at the time of day when vehicles finish their last trip. The

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Fig. 1. Distribution of vehicles by last trip ending time.


Fig. 3. Scenarios of wind power outputs.

begins will have to be staggered in order to avoid sudden surge of demand on the distribution system. Note that the estimates for PHEV load are deterministic and can be employed as input data for the power system scheduling program. IV. WIND POWER PROBABILISTIC FORECASTING

Fig. 2. Percentages of different types of PHEVs by last trip ending time during weekday.

travel data include important information about the household, vehicle type, travel miles, start time, and end time of each trip. These data are analyzed to develop distributions of vehicles by the last trip ending time for each area of interest, showing percent of vehicles that ended their last trip at different time of day. For instance, the state of Illinois is used as a case study in Section VI, the distributions of vehicles by last trip ending time for Illinois on weekdays and weekends is shown in Fig. 1. The same methodology can be used to form curves for each area of interest in each season. From the data in Fig. 1, Table I, and the share of vehicles in each AER, we obtain the share of different types of PHEV by last trip ending time in Illinois as shown in Fig. 2. D. Charging Rate In this paper, we assume that PHEVs with a 10-mile and a 20-mile AER can be charged easily by a 110- to 120-volt and 15-ampere (12-ampere average output) circuit drawing 1.3 kW of electricity on average. A PHEV with a 30-mile AER can be charged through a 110-volt to 120-volt and 20-ampere circuit drawing 1.75 kW of electricity, and a PHEV with a 40-mile AER can be charged through a 220- to 240-volt and 20-ampere circuit drawing 3.5 kW of electricity. Each charging circuit was selected such that a PHEV would be fully charged within a period of 6 hours. We assumed that PHEVs would be fully charged by 7 AM in the morning. However, the time when the charging

In this study, the time series of wind power generation for the 15 hypothetical sites in Illinois for 2006 were obtained from NREL’s Eastern Wind Integration and Transmission Study (EWITS) [18]. These data were produced by combining a numerical weather simulation model with a composite power curve for a number of potential sites for wind power farms. The wind power data for the 15 sites were aggregated into one time series. The accuracy of the wind power forecast varies from day to day. The forecasts error was observed forecast from real wind power plants. In this analysis, we use the day-ahead forecast from the EWITS study. A nonparametric forecast of the density function of the variable of wind power generation can be produced by gathering a set of quantile forecasts. We use a combination of quantile regression and Monte Carlo simulation [19], [20] to produce the wind power scenarios. Forecasts and realized wind power generation during a time window in the past (We use EWITS data from January to June in this study) are used to calculate the quantile regression. 1000 scenarios of wind power output are generated for each day. To simplify the computation, a scenario reduction technique was applied to reduce the 1000 scenarios to 10 scenarios by using GAMS/SCENRED [21]. Fig. 3 shows the wind power scenarios after reductions for one selected day. The horizontal axis represents time intervals. The vertical axis represents the ratio of wind power production with respect to the total installed wind power capacity. Each scenario has a probability that is used to quantify the likelihood of the scenario to unfold. V. STOCHASTIC UNIT COMMITMENT FORMULATIONS A two-stage unit commitment model is proposed to address the uncertainty in wind power output. The structures and philosophy in the two stages are different respectively. The first-stage problem corresponds directly to current decision-making, before future uncertainties are disclosed. Once the decisions in the first stage are made, they cannot be changed in the second stage.


The second-stage problem considers the recourse cost and examines the viability of the decisions made in the first stage using scenarios. In two stage stochastic unit commitment problem, the first stage of the problem corresponds directly to day-ahead unit commitment which cannot be changed in real time (second stage). The second-stage problem considers the real-time generation dispatch which is based on the actual load and wind power output and the unit commitment solution from the first stage. Hence, in our model, the decision variables in the first stage are the commitment statuses of all thermal generating units considering the decision variables including generation dispatch, reserves, wind power output, and PHEV load dispatch in the second stage. The objective of this formulation is to find an optimal UC solution which takes into account all possible realizations of the underlying uncertain factor (wind power) in the second stage. This type of two-stage stochastic optimization problems is well-known and has been applied in similar problems [11], [22]. The proposed two-stage stochastic unit commitment problem is formulated by a mixed integer programming problem (1)–(22). 1) Objective Function: The objective function is to minimize expectation of the power system operating costs while satisfying some prevailing constraints. and are start-up and shut-down costs of unit at time interval . The cost curve of the generating unit in (1) is linearized in a piecewise manner so that a mixed integer linear solver (e.g., CBC or CPLEX) can be used to solve the optimization problem. Unserved PHEV load and unserved non-PHEV load for the entire planning period are incorporated as penalties into the objective function. Note that PHEV load requirement in (1) denotes electricity demand , which fits in the time set . If the set includes more than one time interval, the PHEV load can be optimally dispatched to other hours that belong to the time set .

(1)

2) Start-Up and Shut-Down Costs Constraints: The start-up cost is a function of the number of hours the generator has been turned off. The constraints (2)–(3) implicitly determine the start-up and shut-down costs of generating units in each hour during the optimization process. represents the index of time segment in stepwise start-up curves. provides a lower bound for . will be zero during optimization process if the unit does not change its status from off to on at hour .

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3) Power Balance and Reserve Constraints in the System: The essential scheduling problem of the electric power system is to balance supply with demand, so hourly generation and load dispatches in each scenario must satisfy the power balance constraint (4). However, contingencies in real-time operation may still jeopardize the security of power systems. In addition, there are spinning and operating reserves (5)–(6), which may be used to address the inaccuracies associated with load forecasting or potential failures of transmission or generation components in the power network. We assume that the some part of spinning and operating reserves can be provided by either power generators or PHEV loads.

(4) (5) (6) 4) Coupling Constraints of Individual Unit Status, Start-Up, and Shut-Down Indicators: The start-up indicator and shutdown indicator are relaxed in this study to be continuous variables in (10) in order to accelerate the computational speed of solving the Mixed Integer Programming (MIP) problem by using the Branch and Cuts strategy [23]. Formulations (7)–(9) will restrict these continuous variables to be an integer (1 or 0). (7) (8) (9) (10) 5) Individual Unit Balance and Reserve Constraints: Constraints (11)–(13) define the bounds for the generations and the reserves for each unit. Spinning Reserve is the on-line available capacity that is synchronized to the transmission grid and ready to serve additional demands within 10 minutes’ notice. Operating reserve include spinning reserve and nonspinning reserve. Only the unit which is offline and has quick start capability can provide nonspinning reserve. (11) (12) (13) 6) Individual Unit Ramping Constraints and Minimum On/Off Time: Formulations (14)–(18) represent the operational characteristics of individual thermal units, such as ramp rate, minimum on/off time, etc. [24]–[26]. Ramp rate limits restrict the difference of power generations in two adjacent hours. Minimum off time represents that the generator has to stay offline for several hours before it is committed again.

(2) (3)

(14)

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(15) (16) (17)

(18) 7) Wind Power Constraints: (19) Wind power is different than power generated by thermal units in term of its limited controllability. Constraint (19) represents the relationship between actual wind generation and available wind power. is the actual dispatched wind power output at time in scenario . is the forecasted hourly maximum wind power of the wind farm in one scenario. In general, it is economical to use all available wind power because there are no fuel costs for wind power generation. However, if volatile and intermittent wind power fluctuates intensely and frequently, turning on or turning off the peak thermal unit is not economical or feasible compared with reducing wind power outputs, wind power generation may have to be curtailed. As shown in [27], dispatching down wind power through control mechanisms in combination with the ramping capabilities from other conventional units can smooth out the variability of wind power to some extent. Also, some studies have concluded that wind power on the presently foreseeable scale will not require significant increases in regulation reserves for frequency response [28]. Hence, wind power curtailments are represented, but no specific constraints regarding the frequency issues with wind power are modeled in the paper. 8) PHEV Load Charging Balance: Supported by demand response mechanics and smart grid infrastructures, PHEV loads can be dispatched within the charging period and satisfy constraint (20). In this study is set before we run the stochastic unit commitment. We assume that all PHEVs have to complete charging before 7:00 a.m., the next day, whereas the start time of the charging varies. (20) 9) PHEV Load Hourly Charging Limit: Constraint (21) restricts the charging rate for each PHEV load, which is dependent on the technical parameters of charging facilities and devices we discussed in Section III-D. (21) 10) Reserve Provided by Vehicle-to-Grid: PHEVs not only consume electricity; they can also introduce some benefits to power systems. For example, aggregators of PHEVs in the future can play a storage role in the power system. Many previous vehicle-to-grid studies have focused on two-directional power

flow [29]–[31], in which PHEVs can feed back energy into the power grid. However, there are still technical challenges for this technique [32], [33], such as the life cycle of the PHEV battery. We do therefore not consider vehicle to grid power flow in this analysis. Instead, PHEVs may provide ancillary services to the power system, including reserve and regulation products. In this study, we assume that PHEVs provide 10 minutes of spinning reserve to the power system, as represented in constraint (22). Once a contingency occurs during real-time operation, power system operators can call on the reserve from PHEVs by reducing the scheduled PHEV charging amount. The mechanism of reserve provided by PHEV is not like conventional power plants through increasing their outputs, but decreasing or shifting the previous scheduled electricity demands of PHEVs. Constraint (22) represents that the reserve from a PHEV load is less than its scheduled dispatch. (22) VI. CASE STUDIES We apply two cases studies consisting of a 10-unit hypothetical power system and a 214-unit power system in the Illinois region to analyze the impacts of PHEVs on wind-thermal power system operation and to illustrate the effectiveness of our proposed methodology. In the 10-unit case study, we illustrate how stochastic unit commitment works and compare the results based on different PHEV charging patterns. For Illinois, we run 24 hours stochastic unit commitment simulations based on the generated scenarios of wind power and estimated PHEV loads in Illinois. The program is coded by AMPL, which is a kind of modeling language for mathematical programming. AMPL routes the model into mixed integer programming solver CPLEX 12.2. All case studies are solved on a 2.6-GHz personal computer with 3 GB memory. A. 10-Unit Case The generator data and cost curve can be found in [34], and we assume that there are no quick-start units. Wind power scenarios and PHEV loads are obtained by multiplying Illinois data by a coefficient. The wind power scenarios and the non-PHEV load is shown in Fig. 4. Three different charging patterns are simulated by running the two-stage stochastic unit commitment program. Case 1: Unconstrained Charging: The scenario assumes that charging begins as soon as PHEVs arrive home after the final trip of the day. Case 2: Constrained Charging: The scenario assumes that PHEVs start charging three hours after the hour when PHEVs finish final trip of the day and arrive home. Case 3: Smart Charging: The scenario assumes that PHEVs can be charged flexibly and dispatched to fill valleys in the daily utility demand period at night. For Case 1, the hourly commitments, which are the first-stage decision variables, are listed in Table III. The net peak electricity loads occur during the period from 10:01 to 17:00, when an additional unit (unit 3) is committed to balance the peak load.


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Fig. 6. Hourly non-PHEV load.

Fig. 4. Wind power scenarios and non-PHEV electricity load. TABLE III COMMITMENT OF 10 UNITS IN CASE 1

Fig. 7. Start-up cost of all generating units.

not need to be committed for certain hours. The expected daily operating cost for this case is $389 424. Hence smart charging is the most flexible and economical pattern and will benefit the system operation by reducing the overall operating cost and the commitment of more expensive gas units. B. 214-Unit Power System

Fig. 5. Hourly PHEV charging in scenario 1.

The expected daily operating cost (over the 10 wind power scenarios) for Case 1 is $408,310. For Case 2, we postpone the charging start time by 3 hours, as illustrated by the green line in Fig. 5. PHEV charging contributes less to the peak of non-PHEV minus wind profile between 15:01 and 20:00 compared with Case 1. Because the additional unit (unit 3) is no longer required, the expected daily operating cost for Case 2 is $396 565, which is lower than that in Case 1. In Case 3, smart charging is incorporated into the stochastic unit commitment, and the optimization process optimally allocates PHEV load into nonpeak hours to fill the valley in the net load profile. Fig. 5 shows the profile of non-PHEV load minus wind power (dark line) in scenarios, as well as hourly charging amounts based on the three different charging cases in scenario 1. The figure shows that the valley of the orange line (smart charging case) just fits into the peak of the dark line. On the contrary, the peaks of the blue and the dark lines run together on the same hours. In Case 3, the expensive units (2 and 6) do

We use a 214-unit power system in an Illinois region to illustrate the effectiveness of our proposed model. The data was first prepared for the study in [35], but has been updated to reflect the historical conditions in 2007. The 24-hour scheduling problem is implemented by stochastic unit commitment with consideration of the penetration of wind power and the different charging cases for PHEV loads. The MIP gap for running cases is set at 0.5% and the maximal central processing unit (CPU) time limit for solving the 24-hour problem is set to 900 seconds. The CPLEX will record the best upper bound (feasible solution) if the 0.5% convergence gap has not been achieved. We run the 24-hour stochastic unit commitment program with 7000 MW installed wind power capacity. The simulation process is implemented day by day for a week. The peaking of non-PHEV load in the studied week is 38 749 MW on Tuesday as shown in Fig. 6. The results in Table VI clearly indicate that smart charging can potentially reduce the operating costs of the power system compared with unconstrained charging. There is no wind curtailments and load shedding in both cases. Fig. 7 shows the sum of start-up costs in different operating days, showing that smart charging leads to lower start-up costs for most of the days. VII. CONCLUSIONS This paper develops a stochastic unit commitment model to study the impacts of PHEV charging patterns on power system operation and scheduling. The uncertainty surrounding wind power availability is addressed in the proposed model by generating different wind power scenarios. By using transportation survey data and other statistical information, we estimate

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TABLE IV COMMITMENT OF 10 UNITS IN CASE 2

TABLE V COMMITMENT OF 10 UNITS IN CASE 3

TABLE VI EXPECTED OPERATING COST OF SEVEN DAYS SIMULATIONS FOR THE 214-UNIT POWER SYSTEM

electricity demand of PHEV charging in 2020. The study also includes modeling of ancillary services provided by PHEVs. The numerical examples indicate that the proposed model is effective in coordinating volatile wind power, thermal generating units and PHEV charging loads. The load shifting and shaving enabled by optimal allocation of the PHEV charging load can help flatten the system load profile. The results also show that the total operating cost of the system can be reduced by smart charging of PHEVs. Our future research will focus on how to decompose the stochastic unit commitment problem into small-scale subproblems that can be more easily addressed from a computational perspective. REFERENCES [1] C. S. W. Hadley and A. A. Tsvetkova, “Potential impacts of plug-in hybrid electric vehicles on regional power generation,” Electr. J., vol. 22, no. 10, pp. 56–68, 2009. [2] “NREL, plug-in hybrid electric vehicles and wind energy” [Online]. Available: http://www.nrel.gov/analysis/winds/pdfs/ wind_phev_poster.pdf [3] Rocky Mountain Institute, “Smart garage” [Online]. Available: http:// move.rmi.org/innovation-workshop-category/smart-garage.html

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[29] W. Kempton and J. Tomic, “Vehicle-to-grid power fundamentals: Calculating capacity and net revenue,” J. Power Sources, vol. 144, no. 1, pp. 268–279, Jun. 2005. [30] J. Tomic and W. Kempton, “Using fleets of electric-drive vehicles for grid support,” J. Power Sources, vol. 168, no. 2, pp. 459–468, Jun. 2007. [31] S. Han and K. Sezaki, “Development of an optimal vehicle-to- grid aggregator for frequency regulation,” IEEE Trans. Smart Grid, vol. 1, no. 1, pp. 65–72, Jun. 2010. [32] A. Brooks and S. H. Thesen, “PG&E and tesla motors: Vehicle to grid demonstration and evaluation program,” in Proc. 23rd Electr. Veh. Symp., Dec. 2007, pp. 1–10. [33] B. K. Sovacool and R. F. Hirsh, “Beyond batteries: An examination of the benefits and barriers to plug-in hybrid electric vehicles (PHEVs) and a vehicle-to-grid (V2G) transition,” Energy Policy, vol. 37, no. 3, pp. 1095–1103, 2009. [34] S. A. Kazarlis, A. G. Bakirtzis, and V. Petridis, “A genetic algorithm solution to the unit commitment problem,” IEEE Trans. Power Syst., vol. 11, no. 1, pp. 83–92, 1996. [35] R. R. Cirillo, P. Thimmapuram, T. Veselka, V. Koritarov, G. Conzelmann, C. Macal, G. Boyd, M. North, T. Overbye, and X. Cheng, “Evaluating the potential impact of transmission constraints on the operation of a competitive electricity market in Illinois,” Argonne National Laboratory, Rep. ANL 16/06, 2006. Cong Liu (S’08–M’10) received the B.S. and M.S. degrees in electrical engineering from Xi’an Jiaotong University, China, in 2003 and 2006, respectively, and the Ph.D. degree from the Illinois Institute of Technology, Chicago, in 2010. Currently, he is working in the Decision and Information Sciences Division of Argonne National Laboratory, Argonne, IL. His research interests include numerical computation, and optimization and control of power systems and natural gas systems.

Jianhui Wang (M’07) received the Ph.D. degree in electrical engineering from Illinois Institute of Technology, Chicago, in 2007. Presently, he is a Computational Engineer with the Decision and Information Sciences Division at Argonne National Laboratory, Argonne, IL. Dr. Wang is the chair of the IEEE Power & Energy Society (PES) power system operation methods subcommittee and cochair of an IEEE task force on the integration of wind and solar power into power system operations. He is an Editor of the

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IEEE TRANSACTIONS ON SMART GRID, a Guest Editor of a Special Issue on Electrification of Transportation of the IEEE Power and Energy Magazine, and a Guest Editor of a Special Issue on Smart Grids, Renewable Energy Integration, and Climate Change Mitigation-Future Electric Energy Systems of Applied Energy. He is the Technical Program Chair of the IEEE Innovative Smart Grid Technologies conference 2012.

Audun Botterud (M’04) received the M.Sc. degree in industrial engineering and his Ph.D. in electrical power engineering from the Norwegian University of Science and Technology, Trondheim, in 1997 and 2003, respectively. He was previously with SINTEF Energy Research, Trondheim. He is currently an Energy Systems Engineer in the Center for Energy, Environmental, and Economic Systems Analysis (CEEESA) at Argonne National Laboratory, Argonne, IL. His research interests include electricity markets, renewable energy, wind power integration, forecasting, stochastic optimization, and agent-based modeling.

Yan Zhou received the Ph.D. degree in civil engineering with a concentration on transportation engineering from Clemson University, Clemson, SC, in 2010. Currently, she serves as a Postdoctorate Researcher in the Center for Transportation Research at Argonne National Laboratory, Argonne, IL. Her research interests mainly include the energy and environmental impacts associated with using advanced transportation technologies to build sustainable transportation systems.

Anantray Vyas received the B.S.E.E. degree from Gujarat University, India, in 1962 and the M.S.I.E. degree from West Virginia University, Morganton, in 1971. He conducts research on transportation demand, market potentials of transportation technologies and materials, and environmental impacts of new technologies. During his 31 years at the Argonne National Laboratory, he has developed and exercised mathematical, simulation, behavioral, and cost models for evaluation of technologies, materials, alternative fuels, policies, and regulations.