Day-Ahead Distributionally Robust Optimization-Based Scheduling for Distribution Systems With Electric Vehicles

In this paper, a day-ahead optimal scheduling strategy for the DSO based on EV aggregation is proposed. Generally, the uncertain parameters of EVs, i.e., arrival and departure times as well as the charging demands, can be effectively modeled by a Gaussian mixture model (GMM) with historical charging records. The empirical data of net load error, i.e., mean values and covariance, can be obtained from historical data, while the explicit probability distribution function may not be fully known. Therefore, a distributionally robust optimization (DRO) model is formulated for the DSO to characterize the net load uncertainty. Then, an EV aggregation-based reservation capacity prearrangement method is proposed to specifically address the net load error. Next, with the reservation capacity from EVs, the DRO model is convexified by transforming into two subproblems with deterministic forms. Finally, simulation and comparison tests are conducted on the 33-bus distribution network to demonstrate that the proposed approach achieves a tradeoff between economic performance and computation efficiency compared with the scenario-based stochastic optimization method and achieves a tradeoff between operation costs and system reliability compared with the chance constraint method.