Whether to Charge or Discharge an Electric Vehicle? An Optimal Approach in Polynomial Time

Under the dynamic pricing environment, electric vehicle (EV) owners are faced with the EV charging and discharging scheduling problem to minimize the electricity cost. On one hand, in existing literatures that only consider the EV charging scenario, the solution cannot be trivially extended to the EV discharging scenario. On the other hand, existing approaches for solving integer programming either have the exponential computational complexity or cannot guarantee the optimal solution. In this paper, instead of focusing on the action selection at each time slot, we traverse all possible states within the state transition process, since the total number of states is much smaller than that of action schedules. Then, the computational complexity of the problem solving can be reduced from an exponential order to a polynomial one. Algorithms with both certain and uncertain future electricity prices are developed. It is demonstrated with real price data from Commonwealth Edison Company that our proposed algorithms can facilitate the optimization solution.