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Exact Convex Relaxation of Optimal Power Flow in Tree Networks

Gan, Lingwen and Li, Na and Topcu, Ufuk and Low, Steven H. (2012) Exact Convex Relaxation of Optimal Power Flow in Tree Networks. . (Unpublished)

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The optimal power flow (OPF) problem seeks to control power generation/demand to optimize certain objectives such as minimizing the generation cost or power loss in the network. It is becoming increasingly important for distribution networks, which are tree networks, due to the emergence of distributed generation and controllable loads. In this paper, we study the OPF problem in tree networks. The OPF problem is nonconvex. We prove that after a "small" modification to the OPF problem, its global optimum can be recovered via a second-order cone programming (SOCP) relaxation, under a "mild" condition that can be checked apriori. Empirical studies justify that the modification to OPF is "small" and that the "mild" condition holds for the IEEE 13-bus distribution network and two real-world networks with high penetration of distributed generation.

Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription Paper
Low, Steven H.0000-0001-6476-3048
Additional Information:This work was supported by NSF NetSE grant CNS 0911041, ARPA-E grant de-ar0000226, Southern California Edison, National Science Council of Taiwan, R.O.C, grant NSC 101-3113-P-008-001, Resnick Institute, Okawa Foundation, NSF CNS 1312390, DoE grant DE-EE000289, and AFOSR award number FA9550-12-1-0302.
Group:Resnick Sustainability Institute
Funding AgencyGrant Number
Department of Energy (DOE)DE-AR0000226
Southern California EdisonUNSPECIFIED
National Science Council (Taipei)101-3113-P-008-001
Resnick Sustainability InstituteUNSPECIFIED
Okawa FoundationUNSPECIFIED
Department of Energy (DOE)DE-EE0002890
Air Force Office of Scientific Research (AFOSR)FA9550-12-1-0302
Record Number:CaltechAUTHORS:20190628-105122130
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:96823
Deposited By: Tony Diaz
Deposited On:28 Jun 2019 17:55
Last Modified:03 Oct 2019 21:25

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