Alternating Direction Method of Multipliers for Solving Joint Chance Constrained Optimal Power Flow Under Uncertainties

Abstract

The increasing penetration of renewable energy sources in power systems introduces additional load fluctuations. Lack of awareness of them may lead to a high risk of system failure. Many existing approaches mitigate this issue by considering individual chance constraints (CCs) for the physical limitation of the system. To guarantee that all the operational constraints are satisfied with a predetermined probability, this paper uses joint chance constraints to formulate the optimal power flow (OPF) problem. Additionally, to ensure the scalability, this paper presents an alternating direction method of multipliers (ADMM) with convex optimization subproblems to solve the joint chance-constrained (JCC) OPF, where the computational burden is reduced. At last, to avoid making assumptions about the uncertainties, the CCs are approximated with a sample-based approach.