基于内点半定规划法的含UPFC的最优潮流

传统最优潮流(OPF)问题是一个非凸优化问题，统一潮流控制器(UPFC)的引入进一步增加了OPF问题的非凸程度，因此传统内点法无法有效保证所得解的全局最优性。基于此，将对初值选取不敏感、具有全局收敛能力的内点半定规划(SDP)算法推广至计及UPFC的电力系统OPF问题中，将UPFC变量添加至系统状态变量中，并对增广变量进行优化重组，利用直角坐标的二次形态将含UPFC的OPF问题映射到SDP空间。对IEEE 30、57、118、300节点系统和一个实际系统进行算例测试，结果表明所提算法有效保证了所得解的全局最优性，对增广变量的优化重组有效提高了算法的计算效率和数值稳定性。

Optimal power flow with UPFC based on semi-definite programming method

The traditional OPF(Optimal Power Flow) problem is a non-convex optimization problem, and the introduction of UPFC(Unified Power Flow Controller) further increases the non-convexity degree of the OPF problem, so the traditional interior point method is unable to guarantee the global optimality of the solutions effectively. On this basis, the interior point SDP(Semi-Definite Programming) algorithm, which is insensitive to the initial value and has the ability to find the global optima, is extended to the OPF problem of power system with UPFC. The UPFC variables are added to the system state variables to form the augmented variables for optimal reorganization, and the OPF problem with UPFC is mapped into SDP space based on the quadratic form in rectangular coordinates. IEEE 30-,57-,118-,300-bus systems and a practical system are tested, and the results show that the proposed algorithm effectively guarantee the global optimality of the obtained solutions, and the optimal reorganization of the augmented variables effectively improves the computational efficiency and numerical stability of the algorithm.