Branch Flow Model:  Relaxations, Convexification, Equivalence


Steven H. Low



Computing and Mathematical Sciences

and Electrical Engineering Departments

Friday, March 29, 2013

3:30 – 4:30 pm

1500 EECS (Open to the Public)



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  an second-order conic program (SOCP) that can be solved efficiently.  For radial networks, we prove that both relaxation steps are always exact provided some mild conditions are satisfied.  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.  Finally, we prove that our branch flow model is equivalent to the traditional bus injection model and its associated semidefinite relaxations.  (Joint work with Masoud Farivar, Lingwen Gan, Lina Li, Subhonmesh BoseLijun Chen, Ufuk Topcu, Mani Chandy, Caltech)


Bio:  Steven H. Low is a Professor of the Computing & Mathematical Sciences and Electrical Engineering Departments at Caltech, and an adjunct professor of both the Swinburne University, Australia and the Shanghai Jiao Tong University, China.  He was a co-receipient of IEEE best paper awards, the R&D 100 Award, an Okawa Foundation Research Grant, and was on the editorial board of major networking, control, and communications journals.  He is an IEEE Fellow, and received his B.S. from Cornell and PhD from Berkeley, both in EE.