Optimal power flow over tree networks

Subhonmesh Bose, Dennice F. Gayme, Steven Low, K. Mani Chandy

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The optimal power flow (OPF) problem is critical to power system operation but it is generally non-convex and therefore hard to solve. Recently, a sufficient condition has been found under which OPF has zero duality gap, which means that its solution can be computed efficiently by solving the convex dual problem. In this paper we simplify this sufficient condition through a reformulation of the problem and prove that the condition is always satisfied for a tree network provided we allow over-satisfaction of load. The proof, cast as a complex semi-definite program, makes use of the fact that if the underlying graph of an n x n Hermitian positive semi-definite matrix is a tree, then the matrix has rank at least n - 1.

Original languageEnglish (US)
Title of host publication2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011
Pages1342-1348
Number of pages7
DOIs
StatePublished - Dec 1 2011
Externally publishedYes
Event2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011 - Monticello, IL, United States
Duration: Sep 28 2011Sep 30 2011

Publication series

Name2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011

Other

Other2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011
CountryUnited States
CityMonticello, IL
Period9/28/119/30/11

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Control and Systems Engineering

Cite this

Bose, S., Gayme, D. F., Low, S., & Chandy, K. M. (2011). Optimal power flow over tree networks. In 2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011 (pp. 1342-1348). [6120323] (2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011). https://doi.org/10.1109/Allerton.2011.6120323