Optimal charging strategies for electrical vehicles under real time pricing

We address the problem of serving plug-in hybrid electric vehicles (PHEVs) in a charging station using a local storage energy unit, with finite capacity. Our goal is to find a control policy minimizing the operational cost of the charging station. We assume that the price of the electrical power unit is determined by a Real Time Pricing scheme, in which, the price of the electrical power is continuously updated with respect to the state of the grid at each time instance. We first model the charging station as a continuous time Markov Decision Process with three control actions: the probability of blocking new arrivals, the rate of charging the battery and the proportion of cars being served by the battery. By using dynamic programming, we prove the existence of the optimal policy minimizing a discounted cost over an infinite time horizon. We also show that it is stationary and bang-bang, i.e. the admissible action set in the optimal policy assumes only the extreme values in the action set.