DocumentCode :
2041147
Title :
Convex relaxation for optimal power flow problem: Mesh networks
Author :
Madani, Ramtin ; Sojoudi, Samira ; Lavaei, Javad
Author_Institution :
Electr. Eng. Dept., Columbia Univ., New York, NY, USA
fYear :
2013
fDate :
3-6 Nov. 2013
Firstpage :
1375
Lastpage :
1382
Abstract :
This paper is concerned with a fundamental resource allocation problem for electrical power networks. This problem, named optimal power flow (OPF), is nonconvex due to the nonlinearities imposed by the laws of physics, and has been studied since 1962. We have recently shown that a convex relaxation based on semidefinite programming (SDP) is able to find a global solution of OPF for IEEE benchmark systems, and moreover this technique is guaranteed to work over acyclic (distribution) networks. The present work studies the potential of the SDP relaxation for OPF over cyclic (transmission) networks. Given an arbitrary weakly-cyclic network with cycles of size 3, it is shown that the injection region is convex in the lossless case and that the Pareto front of the injection region is convex in the lossy case. It is also proved that the SDP relaxation of OPF is exact for this type of network. Moreover, it is shown that if the SDP relaxation is not exact for a general mesh network, it would still have a low-rank solution whose rank depends on the structure of the network. Finally, a heuristic method is proposed to recover a rank-1 solution for the SDP relaxation whenever the relaxation is not exact.
Keywords :
Pareto optimisation; concave programming; convex programming; load flow; wireless mesh networks; IEEE benchmark system; OPF; Pareto front; SDP relaxation; acyclic network; arbitrary weakly cyclic network; convex relaxation; electrical power network; global solution; heuristic method; injection region; mesh network; nonconvex problem; optimal power flow problem; resource allocation problem; semidefinite programming; Generators; Mathematical model; Mesh networks; Power system stability; Symmetric matrices; Upper bound; Vectors;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Signals, Systems and Computers, 2013 Asilomar Conference on
Conference_Location :
Pacific Grove, CA
Print_ISBN :
978-1-4799-2388-5
Type :
conf
DOI :
10.1109/ACSSC.2013.6810520
Filename :
6810520
Link To Document :
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