Convex Relaxation of OPF in Multiphase Radial Networks with Wye and Delta Connections

Changhong Zhao, Emiliano Dall-Anese, Steven Low

Research output: NRELPresentation


This panel presentation focuses on multiphase radial distribution networks with wye and delta connections, and proposes a semidefinite relaxation of the AC optimal power flow (OPF) problem. Two multiphase power flow models are developed to facilitate the integration of delta-connected loads or generation resources in the OPF problem. The first model is referred to as the extended branch flow model (EBFM). The second model leverages a linear relationship between phase-to-ground power injections and delta connections that holds under a balanced voltage approximation (BVA). Based on these models, pertinent OPF problems are formulated and relaxed to semidefinite programs (SDPs). Numerical studies on IEEE test feeders show that the proposed SDP relaxations can be solved efficiently by a generic optimization solver. Numerical evidence also indicates that solving the resultant SDP under BVA is faster than under EBFM. Moreover, both SDP solutions are numerically exact with respect to voltages and branch flows. It is further shown that the SDP solution under BVA has a small optimality gap, and the BVA model is accurate in the sense that it reproduces actual system voltages.
Original languageAmerican English
Number of pages21
StatePublished - 2017

Publication series

NamePresented at the 2017 IEEE Power & Energy Society (PES) General Meeting, 16-20 July 2017, Chicago, Illinois

NREL Publication Number

  • NREL/PR-5D00-68859


  • convex relaxation
  • multiphase distribution network
  • optimal power flow


Dive into the research topics of 'Convex Relaxation of OPF in Multiphase Radial Networks with Wye and Delta Connections'. Together they form a unique fingerprint.

Cite this