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This paper deals with the impact of linear approximations for the unknownnonconvex confidence region of chance-constrained AC optimal power flowproblems. Such approximations are required for the formulation of tractablechance constraints. In this context, we introduce the first formulation of achance-constrained second-order cone (SOC) OPF. The proposed formulationprovides convergence guarantees due to its convexity, while it demonstrateshigh computational efficiency. Combined with an AC feasibility recovery, it isable to identify better solutions than chance-constrained nonconvex AC-OPFformulations. To the best of our knowledge, this paper is the first to performa rigorous analysis of the AC feasibility recovery procedures for robustSOC-OPF problems. We identify the issues that arise from the linearapproximations, and by using a reformulation of the quadratic chanceconstraints, we introduce new parameters able to reshape the approximation ofthe confidence region. We demonstrate our method on the IEEE 118-bus system.

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