最优潮流问题的凸松弛技术综述
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摘要
求解最优潮流问题(optimal power flow, OPF)的凸松弛技术可将非凸的OPF问题转化为凸优化问题,并在精确松弛的前提下获得原问题的全局最优解。近10年来,该项技术已成为国内外电力系统优化领域的一个研究热点。首先,回顾电力系统优化领域凸松弛技术的发展过程,介绍半正定规划松弛、二阶锥规划松弛、二次凸包络松弛的基本概念与数学形式。接着,对于凸松弛技术的精确性,总结并梳理保证精确松弛的充分条件和构造更紧凸松弛的方法。最后,从技术手段与应用场景两个方面对OPF凸松弛技术未来的研究方向做出展望。
Convex relaxation for the optimal power flow(OPF) problem can transform the non-convex OPF problem into a convex one, and thereafter the global optimal solution of the original problem can be obtained when the relaxation is exact. Over the past decade, it has been a research hotspot in the field of power system optimization. In this paper, the state-of-the-art researches on convex relaxations for OPF problems were firstly reviewed. The basic concepts and mathematical forms of the semi-definite programming(SDP),second-order cone programming(SOCP) and quadratic convex(QC) relaxations were then introduced. As for the exactness of the convex relaxation, the sufficient conditions for ensuring exact relaxations and the approaches for generating tighter relaxations were summarized. Finally, the potential research topics on the technique and application of convex relaxations were proposed.
Convex relaxation for the optimal power flow(OPF) problem can transform the non-convex OPF problem into a convex one, and thereafter the global optimal solution of the original problem can be obtained when the relaxation is exact. Over the past decade, it has been a research hotspot in the field of power system optimization. In this paper, the state-of-the-art researches on convex relaxations for OPF problems were firstly reviewed. The basic concepts and mathematical forms of the semi-definite programming(SDP),second-order cone programming(SOCP) and quadratic convex(QC) relaxations were then introduced. As for the exactness of the convex relaxation, the sufficient conditions for ensuring exact relaxations and the approaches for generating tighter relaxations were summarized. Finally, the potential research topics on the technique and application of convex relaxations were proposed.
引文
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