Online electric vehicle charging control with multistage stochastic programming

To integrate the plug-in electric vehicles (PEVs) into the power grid, it is critical to develop efficient charging coordination mechanisms that minimize the cost and impact of PEV integration. Ideally, the optimal charging decision depends on not only the existing charging demand, but also the incoming charging demand in the future. In practice, however, the future PEV changing demand is unknown. In this paper, we formulate the optimal PEV charging problem as a multistage stochastic program (MSP), assuming that only the statistical distribution of the future charging demand is known. By skillfully transforming the variables, an efficient online approximate algorithm is presented to calculate the charging decision at each time. Comparing with the traditional sample average approximate (SAA) method for solving MSPs, the proposed method greatly reduces the computational complexity from O(∈^T) to O(T³), where T is total number of time slots under consideration, and ∈ is a constant. In special cases when the charging demand follows a first-order stationary stochastic process, the computational complexity of the approximate online algorithm can be further reduced to O(1). Through extensive simulations, we show that the proposed algorithm performs very closely to the offline optimal solution that is obtained assuming that the future charging demand is known non-causally. On average, the performance gap is only 7%.