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On the exactness of convex relaxation for optimal power flow in tree networks

Gan, Lingwen and Li, Na and Topcu, Ufuk and Low, Steven (2012) On the exactness of convex relaxation for optimal power flow in tree networks. In: 51st IEEE Conference on Decision and Control. IEEE , Piscataway, NJ, pp. 465-471. ISBN 978-1-4673-2065-8.

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The optimal power flow problem is nonconvex, and a convex relaxation has been proposed to solve it. We prove that the relaxation is exact, if there are no upper bounds on the voltage, and any one of some conditions holds. One of these conditions requires that there is no reverse real power flow, and that the resistance to reactance ratio is non-decreasing as transmission lines spread out from the substation to the branch buses. This condition is likely to hold if there are no distributed generators. Besides, avoiding reverse real power flow can be used as rule of thumb for placing distributed generators.

Item Type:Book Section
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URLURL TypeDescription DOIArticle
Low, Steven0000-0001-6476-3048
Additional Information:© 2012 IEEE. This work was supported by Bell Labs of Alcatel-Lucent, 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, Boeing Corporation, Cisco, and AFOSR award number FA9550-12-1-0302.
Group:Resnick Sustainability Institute
Funding AgencyGrant Number
Bell Labs of Alcatel-LucentUNSPECIFIED
Southern California EdisonUNSPECIFIED
National Science Council (Taipei)NSC 101-3113-P-008-001
Resnick Sustainability InstituteUNSPECIFIED
Okawa FoundationUNSPECIFIED
Boeing CorporationUNSPECIFIED
Air Force Office of Scientific Research (AFOSR)FA9550-12-1-0302
Record Number:CaltechAUTHORS:20131220-094526108
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Official Citation:Lingwen Gan; Na Li; Topcu, U.; Low, S., "On the exactness of convex relaxation for optimal power flow in tree networks," Decision and Control (CDC), 2012 IEEE 51st Annual Conference on , vol., no., pp.465,471, 10-13 Dec. 2012 doi: 10.1109/CDC.2012.6426045 URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:43112
Deposited By: Tony Diaz
Deposited On:23 Dec 2013 19:53
Last Modified:10 Nov 2021 16:32

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