求解最优潮流问题的内点半定规划法

基于内点半定规划(semi-definite programming，SDP)，提出一种求解最优潮流(optimal power flow，OPF)的新方法--SDP-OPF法。该方法将非凸OPF问题等价转换为半定规划问题，然后应用原始-对偶内点法求解。根据OPF半定规划模型的特点，采用基于半定规划的稀疏技术，使存储效率和计算性能得以大幅度提高。以4节点的简单电力系统为例，展示模型等价转换的过程及如何获取原OPF问题的解。IEEE-300节点等6个标准系统的仿真计算表明：所提算法具有超线性收敛性，其计算结果与内点非线性规划的结果一致，且能保证解的全局最优性，可在多项式时间内完成，是一种应用前景广阔的方法。

Solution of Optimal Power Flow Problems by Semi-definite Programming

A new method using semi-definite programming (SDP) to solve optimal power flow (OPF) problems was presented. Named as SDP-OPF, the proposed method involves reformulating the OPF problem into a SDP model, which is a convex problem, and developing an interior point method (IPM) for SDP. Furthermore, the SDP sparsity technique can greatly improve the efficiency of storage and computing. A simple 4-bus power system was employed to explain the implementation process, which includes converting the OPF problem to the SDP model and mapping the results of SDP's to the OPF solutions. Extensive numerical simulations show that the results by SDP-OPF are the same as by NLP-OPF. SDP-OPF has the super-linear convergence, and it can guarantee the global optimal solutions within the polynomial times. Therefore, the study for SDP-OPF offers a good prospect.