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Published December 2012 | public
Book Section - Chapter

Branch flow model: Relaxations and convexification

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) 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.

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.

Additional details

Created:
August 19, 2023
Modified:
October 25, 2023