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Branch Flow Model: Relaxations and Convexification—Part II

Farivar, Masoud and Low, Steven H. (2013) Branch Flow Model: Relaxations and Convexification—Part II. IEEE Transactions on Power Systems, 28 (3). pp. 2565-2572. ISSN 0885-8950. http://resolver.caltech.edu/CaltechAUTHORS:20130916-151203881

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Abstract

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) 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 but the angle relaxation may not be exact, and we provide a simple way to determine if a relaxed solution is globally optimal. We propose convexification of mesh networks using phase shifters so that OPF for the convexified network can always be solved efficiently for an optimal solution. We prove that convexification requires phase shifters only outside a spanning tree of the network and their placement depends only on network topology, not on power flows, generation, loads, or operating constraints. Part I introduces our branch flow model, explains the two relaxation steps, and proves the conditions for exact relaxation. Part II describes convexification of mesh networks, and presents simulation results.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1109/TPWRS.2013.2255318 DOIArticle
http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6507352PublisherArticle
http://arxiv.org/abs/1204.4865arXivDiscussion Paper
Additional Information:© 2013 IEEE. An IEEE Open Access article. Manuscript received May 11, 2012; revised July 22, 2012, November 18, 2012, January 04, 2013, and March 01, 2013; accepted March 03, 2013. Date of publication April 23, 2013; date of current version July 18, 2013. The work was supported by NSF through NetSE grant CNS 0911041, Resnick Institute of Caltech through grant DE-AR0000226, the 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, the Resnick Institute of Caltech, Cisco, and the Okawa Foundation. A preliminary and abridged version has appeared in [1]. Paper no. TPWRS-00425-2012. The authors would like to thank S. Bose, K. M. Chandy, L. Gan, and B. Hassibi of Caltech, and C. Clarke, M. Montoya, and R. Sherick of the Southern California Edison.
Group:Resnick Sustainability Institute
Funders:
Funding AgencyGrant Number
NSF NetSECNS 0911041
Resnick Sustainability InstituteUNSPECIFIED
ARPA-EDE-AR0000226
National Science Council (Taipei)NSC 101-3113-P-008-001
Southern California EdisonUNSPECIFIED
CiscoUNSPECIFIED
Okawa FoundationUNSPECIFIED
Subject Keywords:Convex relaxation, load flow control, optimal power flow, phase control, power system management
Other Numbering System:
Other Numbering System NameOther Numbering System ID
INSPEC Accession Number13686473
Record Number:CaltechAUTHORS:20130916-151203881
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20130916-151203881
Official Citation:Farivar, M.; Low, S.H., "Branch Flow Model: Relaxations and Convexification—Part II," Power Systems, IEEE Transactions on , vol.28, no.3, pp.2565,2572, Aug. 2013 doi: 10.1109/TPWRS.2013.2255318
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:41349
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:17 Sep 2013 00:00
Last Modified:22 Sep 2015 22:55

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