恢复交换网络中最优功率流问题的SOCP松弛可行解
Recover Feasible Solutions for SOCP Relaxation of Optimal Power Flow Problems in Mesh Networks
AI总结：
本文提出了一种替代凸优化方法，通过二次锥规划松弛的OPF结果高效恢复可行解，解决了凸松弛精确性不足时的可行解恢复问题，优于基于半正定规划的算法。
摘要：
凸松弛方法已被广泛研究和使用，以获得最优功率流（OPF）问题的最优解。同时，凸松弛的功率流方程也是高效求解电力系统中广泛问题（包括混合整数非线性规划（MINLP）和分布式优化）的前提。当凸松弛的精确性不能保证时，恢复凸松弛方法的可行解很重要。本文提出了一种替代凸优化（ACP）方法，能够高效地从交换网络中二次锥规划（SOCP）松弛的OPF结果中恢复可行解。首先将OPF问题公式化为差分凸（DC）编程问题，然后通过惩罚凸凹过程（CCP）高效求解。CCP迭代线性化功率流约束的凹部分，并求解DCP问题的凸近似。数值测试显示，所提出的方法能够找到AC OPF问题的全局或近全局最优解，并优于基于半正定规划（SDP）的算法。
英文摘要：
Convex relaxation methods have been studied and used extensively to obtain an optimal solution to the optimal power flow (OPF) problem. Meanwhile, convex relaxed power flow equations are also prerequisites for efficiently solving a wide range of problems in power systems including mixed-integer nonlinear programming (MINLP) and distributed optimization. When the exactness of convex relaxations is not guaranteed, it is important to recover a feasible solution for the convex relaxation methods. This paper presents an alternative convex optimization (ACP) approach that can efficiently recover a feasible solution from the result of second-order cone programming (SOCP) relaxed OPF in mesh networks. The OPF problem is first formulated as a difference-of-convex (DC) programming problem, then efficiently solved by a penalty convex concave procedure (CCP). CCP iteratively linearizes the concave parts of the power flow constraints and solves a convex approximation of the DCP problem. Numerical tests show that the proposed method can find a global or near-global optimal solution to the AC OPF problem, and outperforms those semidefinite programming (SDP) based algorithms.
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