First Order Accelerated Robust Dual Dynamic Programming for Robust Economic Dispatch

Robust economic dispatch (ED) is of paramount importance for obtaining robust unit commitment when considering the uncertainty in the system, which is a typical multistage robust optimization (RO) problem. The robust dual dynamic programming (RDDP) method has been shown effective to obtain the optimal solution for the multistage RO problem, while suffering from high computational complexity for solving mixed integer linear programming (MILP) to obtain the worst case. Thus, we leverage the recent advances in the gradient based approach that allows for simple first-order updates to solve worst-case generation problems. Based on the gradient-based worst-case generations, we propose the first-order accelerated RDDP (FO-RDDP) method to solve the multistage robust ED problems, refining iteratively the upper/lower bounds of the cost-to-go functions. The finite convergence of FO-RDDP is verified by analysis and numerical tests. Comparison results on the IEEE 118-bus and 2383-bus systems have demonstrated that FO-RDDP can approach the near-optimal performance as the MILP-based RDDP with significantly improved computational efficiency.