Multi-Objective Mixed-Integer Convex Programming Method for the Siting and Sizing of UPFCs in a Large-Scale AC/DC Transmission System

To solve the problem of uneven distribution of power flow and limited transfer capability for the transmission section in a large-scale AC/DC transmission system, a multi-objective mixed-integer convex programming method for the siting and sizing of unified power flow controllers (UPFCs) in an AC/DC transmission system is proposed. Considering the four objectives of the annual equivalent investment and operation cost, bus voltage deviation, transfer capability of the transmission section, and renewable energy accommodation, a multi-objective optimization model is established. By using the convex relaxation method, the original mixed-integer nonlinear programming model is transformed into a mixed-integer second-order cone (SOC) programming model to improve the computational efficiency. Furthermore, a successive inscribed polygon method is proposed to tighten the relaxation gap for the SOC constraints in the optimization model and improve the calculation accuracy. In addition, a direct and fast method for solving the compromise optimal solution of the multi-objective optimization model is proposed. Finally, the effectiveness of the proposed method is demonstrated by an actual 8733-bus large-scale AC/DC transmission system and the modified IEEE-39 bus AC/DC system.