Branch Flow Model: Relaxations and Convexification—Part II
- Creators
- Farivar, Masoud
-
Low, Steven H.
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.
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.Attached Files
Published - 06507352.pdf
Submitted - 1204.4865v4.pdf
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Additional details
- Eprint ID
- 41349
- Resolver ID
- CaltechAUTHORS:20130916-151203881
- NSF NetSE
- CNS 0911041
- Resnick Sustainability Institute
- ARPA-E
- DE-AR0000226
- National Science Council (Taipei)
- NSC 101-3113-P-008-001
- Southern California Edison
- Cisco
- Okawa Foundation
- Created
-
2013-09-17Created from EPrint's datestamp field
- Updated
-
2021-11-10Created from EPrint's last_modified field
- Caltech groups
- Resnick Sustainability Institute
- Other Numbering System Name
- INSPEC Accession Number
- Other Numbering System Identifier
- 13686473