MIP Reformulation for Max-Min Problems in Two-Stage Robust SCUC

Abstract

With increasing renewable penetration in power systems, considerable research efforts have been focused on how to accommodate the uncertainties from renewables in the Security-Constraint Unit Commitment (SCUC) problem. One of the candidate approaches to handling uncertainties is the two-stage Robust SCUC (RSCUC), which enables system to survive in any scenario. The survivability is guaranteed by the solution optimality of the max-min problem in the second stage. However, as the non-convex max-min problem is NP-hard, it is difficult to get the exact optimal solution in acceptable time. In this paper, we propose a new efficient formulation which recasts the max-min problem to a Mixed Integer Programming (MIP) problem using Binary Expansion (BE). The upper bound of the gap between the new MIP problem and the original max-min problem is derived. The gap, which quantifies the solution optimality of the max-min problem, is controllable. Two effective acceleration techniques are proposed to improve the performance of the MIP problem by eliminating inactive flow constraints and decomposing time-coupled uncertainty budget constraints. Accordingly, the computation burden of solving the max-min problem is reduced tremendously. The simulation results for the IEEE 118-Bus system validate and demonstrate the effectiveness of the new BE-based solution approach to the two-stage RSCUC and the acceleration techniques.