Robust Price-Based Demand Response Framework for Flexibility Provision in Distribution Systems

This paper proposes a robust optimization frame-work of price-based demand response (PBDR) programs to procure flexibility from distributed energy resources (DERs) in distribution systems. The proposed method uses an uncertain budget to accommodate worst-case scenarios of available photovoltaic (PV) generation and determines an aggregated feasible flexibility range based on flexibility requirements. To solve the robust optimization problem effectively, AC optimal power flow is formulated using DistFlow equations, which are convex relaxed by second-order cone (SOC) relaxation and further linearized by polyhedral approximation techniques. An optimal solution is found using a column-and-constraint generation (C&CG) algorithm by decomposing the multi-stage robust optimization problem. The errors resulting from the SOC relaxation of the DistFlow equations are corrected using the exactness recovering procedure. The effectiveness of the proposed method is verified by case studies using an IEEE 33-bus test system with prosumers.