Convex Relaxations and Approximations of Chance-Constrained AC-OPF Problems
For power system operators, this work provides a tractable and convergent method for chance-constrained AC-OPF, improving solution quality over nonconvex approaches.
This paper introduces the first chance-constrained second-order cone (SOC) OPF formulation, which provides convergence guarantees and high computational efficiency. It identifies better solutions than nonconvex AC-OPF formulations and performs a rigorous analysis of AC feasibility recovery procedures.
This paper deals with the impact of linear approximations for the unknown nonconvex confidence region of chance-constrained AC optimal power flow problems. Such approximations are required for the formulation of tractable chance constraints. In this context, we introduce the first formulation of a chance-constrained second-order cone (SOC) OPF. The proposed formulation provides convergence guarantees due to its convexity, while it demonstrates high computational efficiency. Combined with an AC feasibility recovery, it is able to identify better solutions than chance-constrained nonconvex AC-OPF formulations. To the best of our knowledge, this paper is the first to perform a rigorous analysis of the AC feasibility recovery procedures for robust SOC-OPF problems. We identify the issues that arise from the linear approximations, and by using a reformulation of the quadratic chance constraints, we introduce new parameters able to reshape the approximation of the confidence region. We demonstrate our method on the IEEE 118-bus system.