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Branch flow model: Relaxations and convexification

Farivar, Masoud and Low, Steven H. (2012) Branch flow model: Relaxations and convexification. In: 51st IEEE Conference on Decision and Control. IEEE , Piscataway, NJ, pp. 3672-3679. ISBN 978-1-4673-2065-8.

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We propose a branch flow model for the analysis and optimization of mesh as well as radial networks. The model leads to a new approach to solving optimal power flow (OPF) problems that consists of two relaxation steps. The first step eliminates the voltage and current angles and the second step approximates the resulting problem by a conic program that can be solved efficiently. For radial networks, we prove that both relaxation steps are always exact, provided there are no upper bounds on loads. For mesh networks, the conic relaxation is always exact and we characterize when the angle relaxation may fail. We propose a simple method to convexify a mesh network using phase shifters so that both relaxation steps are always exact and OPF for the convexified network can always be solved efficiently for a globally optimal solution. We prove that convexification requires phase shifters only outside a spanning tree of the network graph and their placement depends only on network topology, not on power flows, generation, loads, or operating constraints. Since power networks are sparse, the number of required phase shifters may be relatively small.

Item Type:Book Section
Related URLs:
URLURL TypeDescription DOIArticle
Low, Steven H.0000-0001-6476-3048
Additional Information:© 2012 IEEE. We are grateful to Mani Chandy, Lingwen Gan, and Javad Lavaei of Caltech, and Christopher Clarke, Michael Montoya, and Robert Sherick of the Southern California Edison for helpful discussions. We acknowledge the support of the Resnick Sustainability Institute at Caltech, NSF through NetSE grant CNS 0911041, DoE’s ARPA-E through grant DE-AR0000226, the National Science Council of Taiwan (R. O. C.) through grant NSC 101-3113-P-008-001, Southern California Edison, Cisco, and the Okawa Foundation.
Group:Resnick Sustainability Institute
Funding AgencyGrant Number
Caltech Resnick Sustainability InstituteUNSPECIFIED
NSF NetSECNS 0911041
Department of Energy (DOE) ARPA-EDE-AR0000226
National Science Council of TaiwanNSC 101-3113-P-008-001
Southern California EdisonUNSPECIFIED
Okawa FoundationUNSPECIFIED
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Other Numbering System NameOther Numbering System ID
INSPEC Accession Number13288515
Record Number:CaltechAUTHORS:20131220-084709018
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Official Citation:Farivar, M.; Low, S.H., "Branch flow model: Relaxations and convexification," Decision and Control (CDC), 2012 IEEE 51st Annual Conference on , vol., no., pp.3672,3679, 10-13 Dec. 2012 doi: 10.1109/CDC.2012.6425870 URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:43108
Deposited By: Tony Diaz
Deposited On:23 Dec 2013 19:55
Last Modified:10 Nov 2021 16:32

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