Min-max-min Robust optimization for Adaptivity-Constrained Economic Dispatch

With large-scale penetration of renewable energy generators, the prediction uncertainty of power demand has highly increased in recent years. In this paper, we propose a new approach for economic dispatch to obtain the tolerance interval of electric facilities' operations, which minimizes the worst-case dispatch cost while guaranteeing the adaptivity of actual dispatch schedule to any realization of net power demand predicted. Representing the dispatch cost as a quadratic function of the power outputs by fuel-based generators and the charginydischarging power of batteries, we formulate this problem as a min-max-min robust optimization problem. To solve it, we first show that the worst-case dispatch schedule consists of either maximum or minimum values in the tolerance intervals at each time slot. Then, we reduce the problem to a minimax problem and solve it using Benders decomposition to deal with the high computational cost. Finally, we verify the effectiveness of our proposed method by numerical simulations.