Two-stage robust optimization of unified power quality conditioner (UPQC) siting and sizing in active distribution networks considering uncertainty of loads and renewable generators

This paper proposes a robust optimization siting and sizing strategy for the unified power quality conditioner (UPQC) in the active distribution network (ADN) integrated with renewable energy generators. The optimization objectives including investment cost, line loss, and voltage deviation are integrated into an overall cost for both the planning and operating stages. A novel UPQC equivalent power injection model is proposed based on the auxiliary branch method. A set of linear and second-order conic (SOC) constraints are employed to accurately describe the steady-state operation of UPQC. An improved branch current flow model is developed to incorporate radial distribution networks with UPQCs. The UPQC siting and sizing planning is formulated as a mixed integer second-order conic programming (MISOCP) problem. Accounting for the uncertainty in loads and distributed generators, a two-stage robust optimization model is established to address worst-case operational scenarios. A solving strategy is developed based on the strong duality theory and the column-and-constraint generation (C&CG) algorithm, and then commercial solvers can solve the problem accurately and efficiently. Case studies on an IEEE 33-node distribution network demonstrate this strategy's robustness in dealing with loads and renewable energy uncertainties, making it applicable across different UPQC topologies and operation modes. The proposed method has superior performance over the representative meta-heuristic approaches in terms of global optimality as well as an over 7.5 times faster computation speed. This work has significance in enhancing the quality and efficiency of modern power systems highly integrated with renewable energy.