Promises of Conic Relaxation for Contingency-Constrained Optimal Power Flow Problem
Promises of Conic Relaxation for Contingency-Constrained Optimal Power Flow Problem
复制标题
DOI：
10.1109/allerton.2014.7028573
复制
发表时间：
2014-09
影响因子：
6.6
通讯作者：
Ramtin Madani;Morteza Ashraphijuo;J. Lavaei
中科院分区：
文献类型：
--
作者：
Ramtin Madani;Morteza Ashraphijuo;J. Lavaei
本文研究了安全约束最优潮流问题，其中每一个事故对应于任意数量的线路和发电机的停运。利用凸松弛方法研究了该问题，称之为半定规划（SDP）。秩1 SDP解的存在保证了SCOPF的全局解的恢复。我们证明了SDP解决方案的秩的上限由电力网络的树宽加一，这是认为在实践中是小的。然后，我们提出了一种分解方法，以减少松弛的计算复杂度。在松弛不精确的情况下，我们开发了一个图论凸程序来识别网络的问题线，并将这些线上的损失作为惩罚（正则化）项纳入目标，从而导致惩罚SDP问题。我们进行了几次模拟大规模的基准系统，并验证了全球最小值是最多1%的可行的解决方案，从建议的惩罚放松。
This paper is concerned with the security-constrained optimal power flow (SCOPF) problem, where each contingency corresponds to the outage of an arbitrary number of lines and generators. The problem is studied by means of a convex relaxation, named semidefinite program (SDP). The existence of a rank-1 SDP solution guarantees the recovery of a global solution of SCOPF. We prove that the rank of the SDP solution is upper bounded by the treewidth of the power network plus one, which is perceived to be small in practice. We then propose a decomposition method to reduce the computational complexity of the relaxation. In the case where the relaxation is not exact, we develop a graph-theoretic convex program to identify the problematic lines of the network and incorporate the loss over those lines into the objective as a penalization (regularization) term, leading to a penalized SDP problem. We perform several simulations on large-scale benchmark systems and verify that the global minima are at most 1% away from the feasible solutions obtained from the proposed penalized relaxation.