A stabilized Benders decomposition approach for solving the multi-period secure stochastic AC optimal power flow for energy, reserves, and storage scheduling

Abstract

The growing penetration of renewable energy sources and the increasing complexity of modern power systems demand more accurate and computationally efficient operational planning tools, as the associated optimization problems are inherently high-dimensional and computationally intensive. Traditional optimization approaches often rely on simplified DC or convex formulations, which limit their ability to capture the nonlinear behavior of AC network model. This study addresses this gap by proposing a scalable solution framework for the Multi-Period Secure Stochastic AC Optimal Power Flow (MPSSOPF-AC). The proposed approach is based on Generalized Benders Decomposition (GBD) with reformulated AC subproblems that incorporate reserve and storage scheduling. Algorithmic performance is further enhanced through a bundle–trust-region stabilization technique and the parallel solution of subproblems that exploit the problem structure. The proposed methodology is validated on the real-size Colombian 96-bus power system under several wind generation scenarios and N-1 contingencies. Results demonstrate that the proposed GBD-based framework preserves modeling accuracy while reducing computational time by up to 94.8% compared with conventional methods. The outcomes highlight the potential of decomposition-based strategies to enable realistic large-scale stochastic AC-OPF applications in modern power system operation and planning.