Load Coincidence Factors for Robust Optimal Power Flow in Radial Distribution Networks

This paper presents an analytically tractable method to solve a robust optimal power flow (OPF) problem in radial distribution networks considering uncertainty in solar photo-voltaic (PV) generation and load demand. The proposed method optimizes PV curtailment limits and set-points of dispatchable distributed energy resources that are feasible for any realization of unknown-but-bounded uncertainty in available PV generation and load demand. A well-motivated set representation enabled by load coincidence factors bounds uncertainty in load demand. Subsequently, closed-form expressions derived for worst-case voltage deviations arising from uncertainty in available PV generation and load demand help to bypass the need to solve inner optimization problems typical of a robust OPF problem. It can then be reformulated into a single deterministic optimization problem that can be solved efficiently. Numerical case studies involving a modified CIGRE low-voltage test system demonstrate the effectiveness of the proposed method and the validity of the closed-form expressions for worst-case voltage deviations.