Matrix minor reformulation and SOCP-based spatial branch-and-cut method for the AC optimal power flow problem
Matrix minor reformulation and SOCP-based spatial branch-and-cut method for the AC optimal power flow problem
复制标题
交流最优潮流问题的矩阵次要重构和基于SOCP的空间分支割法
DOI：
10.1007/s12532-018-0150-9
复制
发表时间：
2017
影响因子：
6.3
通讯作者：
X. Sun
中科院分区：
文献类型：
--
作者：
Burak Kocuk;Santanu S. Dey;X. Sun
交流最优潮流（AC OPF）是电力系统中最基本的优化问题之一。它可以表示为具有等级约束的半定规划（SDP）。求解AC OPF，即获得接近最优的原始解以及该非凸程序的高质量对偶界限，对当今电力行业大规模电网的实时运行提出了重大的计算挑战。在本文中，我们提出了一种使用所涉及的 Hermitian 矩阵变量的主和非主 2×2 次要变量来重新表述秩约束的新技术，并将所有这些次要属性分为三种类型。我们展示了这些次要约束与电网中三个和四个周期内电压角差总和为零的物理约束的等效性。我们研究了这种次要重构的二阶圆锥规划（SOCP）松弛，并提出了强切割平面、凸包络线和边界紧缩技术来加强由此产生的 SOCP 松弛。然后，我们提出了一种基于 SOCP 的空间分支剪切方法来获得 AC OPF 的全局最优值。大量的计算实验表明，所提出的算法显着优于最先进的基于 SDP 的 OPF 求解器，并且在简单的个人计算机上能够在不超过 720 秒的时间内获得文献中最具挑战性的电力系统实例的平均最优差距。
Alternating current optimal power flow (AC OPF) is one of the most fundamental optimization problems in electrical power systems. It can be formulated as a semidefinite program (SDP) with rank constraints. Solving AC OPF, that is, obtaining near optimal primal solutions as well as high quality dual bounds for this non-convex program, presents a major computational challenge to today’s power industry for the real-time operation of large-scale power grids. In this paper, we propose a new technique for reformulation of the rank constraints using both principal and non-principal 2-by-2 minors of the involved Hermitian matrix variable and characterize all such minors into three types. We show the equivalence of these minor constraints to the physical constraints of voltage angle differences summing to zero over three- and four-cycles in the power network. We study second-order conic programming (SOCP) relaxations of this minor reformulation and propose strong cutting planes, convex envelopes, and bound tightening techniques to strengthen the resulting SOCP relaxations. We then propose an SOCP-based spatial branch-and-cut method to obtain the global optimum of AC OPF. Extensive computational experiments show that the proposed algorithm significantly outperforms the state-of-the-art SDP-based OPF solver and on a simple personal computer is able to obtain on average aoptimality gap in no more than 720 s for the most challenging power system instances in the literature.
影响因子：
6.6
作者：
Zimmerman, Ray Daniel;Edmundo Murillo-Sanchez, Carlos;Thomas, Robert John
通讯作者：
Thomas, Robert John
DOI：
--
发表时间：
2006
期刊：
Journal of Optimization Methods and Software 21
影响因子：
--
作者：
Naoya Watanabe;Takeaki Kojima;Tanemasa Asano;中田和秀;Kazuhiro Kobayashi;Tomanari kitahara;Kazuhide Nakata;Makoto Yamashita;Katsuki Fujisawa
通讯作者：
Katsuki Fujisawa