A distributionally robust joint chance constraint approach to smart charging of plug-in electric vehicles

In this paper, the problem of optimal charging of plug-in electric vehicles in a parking lot is addressed. The parking time is assumed to be uncertain and characterized by a statistical distribution with fixed first and second order moments. The energy price during the day is assumed to be known on a day ahead basis. In this context, the problem of maximizing the profit of a charging station is formulated in a receding horizon framework, whose solution provides the optimal charging policy. To accommodate stochastic uncertainty affecting the parking time, a distributionally robust joint chance constraint approach is adopted when formulating the overall optimization problem. The optimal solution guarantees a customer satisfaction criterion expressed as a probabilistic confidence level. Simulation results on a case study show effectiveness and computational feasibility of the proposed approach.