Fhgfhfghf

IEEE TRANSACTIONS ON SMART GRID, VOL. 3, NO. 3, SEPTEMBER 2012

1095

Optimal Scheduling for Charging and Discharging of Electric Vehicles
Yifeng He, Member, IEEE, Bala Venkatesh, Senior Member, IEEE, and Ling Guan, Fellow, IEEE
Abstract—The vehicle electrification will have a significant impact on the power grid due to the increase in electricity consumption. It is important to performintelligent scheduling for charging and discharging of electric vehicles (EVs). However, there are two major challenges in the scheduling problem. First, it is challenging to find the globally optimal scheduling solution which can minimize the total cost. Second, it is difficult to find a distributed scheduling scheme which can handle a large population and the random arrivals of the EVs. In this paper,we propose a globally optimal scheduling scheme and a locally optimal scheduling scheme for EV charging and discharging. We first formulate a global scheduling optimization problem, in which the charging powers are optimized to minimize the total cost of all EVs which perform charging and discharging during the day. The globally optimal solution provides the globally minimal total cost. However, theglobally optimal scheduling scheme is impractical since it requires the information on the future base loads and the arrival times and the charging periods of the EVs that will arrive in the future time of the day. To develop a practical scheduling scheme, we then formulate a local scheduling optimization problem, which aims to minimize the total cost of the EVs in the current ongoing EV set inthe local group. The locally optimal scheduling scheme is not only scalable to a large EV population but also resilient to the dynamic EV arrivals. Through simulations, we demonstrate that the locally optimal scheduling scheme can achieve a close performance compared to the globally optimal scheduling scheme. Index Terms—Charging and discharging, convex optimization, distributed solution, electricvehicle, optimal scheduling, smart grid, vehicle-to-grid (V2G).

Maximum charging power. Final energy ratio of EV Charging-interval matrix. Total load in interval . Real base load in interval . Forecasted base load in interval . Charging load in interval . Intercept in the real-time pricing model. Slope in the real-time pricing model. Cost for EV charging in interval . Previous-interval set ofinterval . Group set. Ongoing EV set at the beginning of interval in group . Sliding window at the beginning of interval in group . Charging-only EV set at the beginning of interval in group . V2G EV set at the beginning of interval in group . Arrival time of EV Departure time of EV . . . . .

NOMENCLATURE Interval set. Set of electric vehicles (EVs), Charging-only EV set. Vehicle-to-grid (V2G)EV set. Charging power of EV Charging period of EV Length of an interval Initial energy of EV Final energy of EV . . . Battery capacity of EV in interval . .

Start time of the charging period of EV End time of the charging period of EV I. INTRODUCTION

T

Manuscript received February 21, 2011; revised June 20, 2011, September 12, 2011; accepted October 17, 2011. Date of publication July 19,2012; date of current version August 20, 2012. Paper no. TSG-00027-2011. The authors are with the Department of Electrical and Computer Engineering, Ryerson University, Toronto, Ontario, M5B2K3, Canada (e-mail: yhe@ee.ryerson.ca; bala@ryerson.ca; lguan@ee.ryerson.ca). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital ObjectIdentifier 10.1109/TSG.2011.2173507

HE automotive industry is heavily investing in plug-in hybrid electric vehicles (PHEVs) and fully electric vehicles (EVs) mainly in order to reduce the CO emissions and oil dependency of current automotive technology. The vehicle electrification will have significant impacts on the power grid due to the increase in electricity consumption. The overall load profile of...