Tractable Convex Approximations for Distributionally Robust Joint Chance-Constrained Optimal Power Flow Under Uncertainty

Uncertainty arising from renewable energy results in considerable challenges in optimal power flow (OPF) analysis. Various chance-constrained approaches are proposed to address the uncertainty within OPF models. However, most existing approaches either assume that the uncertainty distributions are known
a priori
or consider individual chance constraint modeling. This paper proposes a distributionally robust (DR) joint chance-constrained OPF model, which ensures that the operational constraints are simultaneously satisfied with a given probability and does not require an assumption of specific probability distributions. An ambiguity set built on the first two moments is used to model the uncertainty. An optimized Bonferroni approximation (OBA) is first introduced to decompose the DR joint chance constraint into DR individual chance constraints. The resulting OBA formulation is strongly nonconvex. Different convex approximations are then proposed to formulate the OBA formulation as tractable forms. The proposed convex approximations can be easily extended to incorporate the structural information associated with uncertainty, and correlations among reserve chance constraints. Case studies demonstrate the effectiveness of the proposed convex approximation methods and their extensions.