Convex Relaxations and Approximations of Chance-Constrained AC-OPF Problems

TL;DR

This paper introduces a convex second-order cone formulation for chance-constrained AC optimal power flow, providing convergence guarantees and improved solutions through a novel feasibility recovery and approximation analysis.

Contribution

It presents the first chance-constrained SOC-OPF formulation with convergence guarantees and a rigorous analysis of AC feasibility recovery procedures.

Findings

The proposed method outperforms nonconvex formulations in solution quality.

Convex SOC-OPF demonstrates high computational efficiency.

New parameters effectively reshape the confidence region approximation.

Abstract

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.