  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.

Systems and Control