Convex Relaxation of Optimal Power Flow — Part I: Formulations and Equivalence

Creators: Low, Steven H.

Abstract

This tutorial summarizes recent advances in the convex relaxation of the optimal power flow (OPF) problem, focusing on structural properties rather than algorithms. Part I presents two power flow models, formulates OPF and their relaxations in each model, and proves equivalence relationships among them. Part II presents sufficient conditions under which the convex relaxations are exact.

Additional Information

© 2014 IEEE. Manuscript received September 23, 2013; revised February 5, 2014; February 19, 2014; accepted February 28, 2014. Date of publication March 5, 2014; date of current version April 9, 2014. This work was supported in part by NSF under Grant NetSE CNS 0911041, in part by ARPA-E under Grant GENI DE-AR0000226, in part by the National Science Council of Taiwan under Grant NSC 103-3113-P-008-001, in part by Southern California Edison, in part by the Los Alamos National Lab,and in part by Caltech's Resnick Institute. A preliminary and abridged version has appeared in [S. H. Low, "Convex relaxation of optimal power flow: A tutorial," in Proc. IREP Symp. Bulk Power Syst. Dyn. Control(IREP), Rethymnon, Greece, Aug. 2013.]. Recommended by Associate Editor M. Chertkov. We thank the anonymous reviewers for their helpful suggestions.

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