Trilevel Mixed Integer Optimization for Day-Ahead Spinning Reserve Management of Electric Vehicle Aggregator with Uncertainty

Abstract

This paper studies a trilevel profit maximization problem of electric vehicle (EV) aggregator participating in the day-ahead reserve market, considering the uncertain EV connectivity to the grid. At the upper level (UL), the aggregator purchases reserve from individual EVs and trades it in the reserve market. It determines the optimal reserve purchasing price and reserve trading amount to maximize profit. Responding to the reserve purchasing price, at the middle level (ML), each EV owner maximizes his/her own utility by scheduling the battery usage for charging/discharging, reserve or transportation. As the connectivity of EV to the grid is uncertain due to transportation randomness, we characterize the worst-case connectivity at the lower level (LL) such that energy consumption for transportation tasks can be guaranteed. The proposed trilevel optimization problem is challenging because of its multi-level structure and binary variables at ML and LL. Firstly, total unimodularity property, primal-dual and value-function methods are used to convert this problem into a single-level mixed integer nonlinear program (MINLP). Then, a sample-based algorithm is developed to solve the single-level MINLP and the convergence is proved. In addition, an acceleration strategy is proposed to facilitate the computation. Case studies validate the effectiveness of our proposed solution method.