Promises of Conic Relaxation for Contingency-Constrained Optimal Power Flow Problem

被引:93
作者
Madani, Ramtin [1 ]
Ashraphijuo, Morteza [1 ]
Lavaei, Javad [1 ]
机构
[1] Columbia Univ, Dept Elect Engn, New York, NY 10027 USA
基金
美国国家科学基金会;
关键词
Convex relaxation; graph theory; optimal power flow; security-constrained optimal power flow; semidefinite program; EXPLOITING SPARSITY; SEMIDEFINITE RELAXATIONS; CONVEX RELAXATION;
D O I
10.1109/TPWRS.2015.2411391
中图分类号
TM [电工技术]; TN [电子技术、通信技术];
学科分类号
0808 ; 0809 ;
摘要
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.
引用
收藏
页码:1297 / 1307
页数:11
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