Tractable Convex Approximations for Distributionally Robust Joint Chance Constrained Optimal Power Flow under Uncertainties

Uncertainties arising from renewable energy bring huge challenges in optimal power flow (OPF) analysis. Various chance constrained approaches are proposed to manage the uncertainties in OPF models. However, most existing approaches assume that the probability distributions of uncertainties are known \emph{a priori}, or consider chance constraint individually. This paper proposes a distributionally robust (DR) joint chance constrained OPF model, which ensures that all the operation constraints are satisfied with a given probability and does not require the assumption on specific probability distributions. An ambiguity set built on the first and second moments is used to model the uncertainties. 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 non-convex. Different convex approximations are then proposed to formulate the OBA based DR individual chance constraints as tractable formulations. The proposed convex approximations can be easily extended to incorporate the structural information associated with uncertainties like unimodality and symmetry. Case studies demonstrate the effectiveness of the proposed convex approximation methods.