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Published November 2014 | Published
Journal Article Open

Optimal Power Flow in Direct Current Networks


The optimal power flow (OPF) problem determines power generations/demands that minimize a certain objective such as generation cost or power loss. It is non-convex and NP-hard in general. In this paper, we study the OPF problem in direct current (DC) networks. A second-order cone programming (SOCP) relaxation is considered for solving the OPF problem. We prove that the SOCP relaxation is exact if either 1) voltage upper bounds do not bind; or 2) voltage upper bounds are uniform and power injection lower bounds are negative. Based on 1), a modified OPF problem is proposed, whose corresponding SOCP is guaranteed to be exact. We also prove that SOCP has at most one optimal solution if it is exact. Finally, we discuss how to improve numerical stability and how to include line constraints.

Additional Information

© 2014 IEEE. Open Access. Manuscript received September 09, 2013; revised January 15, 2014; accepted March 03, 2014. Date of publication April 22, 2014; date of current version October 16, 2014. Paper no. TPWRS-01160-2013.

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