Branch Flow Model: Relaxations, Convexification, Equivalence

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 Bose,
Lijun Chen, Ufuk Topcu, Mani Chandy, Caltech)

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-recipient of IEEE
best paper awards, the R&D 100 Award, an Okawa Foundation Research
Grant, and was on the editorial boards 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.