Exactness of OPF Relaxation on Three-Phase Radial Networks with Delta Connections

Fengyu Zhou, Ahmed Zamzam, Steven Low, Nicholas Sidiropoulos

Research output: Contribution to journalArticlepeer-review

6 Scopus Citations


Simulations have shown that while semi-definite relaxations of AC optimal power flow (AC-OPF) on three-phase radial networks with only wye connections tend to be exact, the presence of delta connections seem to render them inexact. This article shows that such inexactness originates from the non-uniqueness of relaxation solutions and numerical errors amplified by the non-uniqueness. This finding motivates two algorithms to recover the exact solution of AC-OPF in unbalanced distribution networks featuring both wye and delta connections. In simulations using IEEE 13, 37 and 123-bus systems, the proposed algorithms provide exact optimal solutions up to numerical precision.

Original languageAmerican English
Article number9380663
Pages (from-to)3232-3241
Number of pages10
JournalIEEE Transactions on Smart Grid
Issue number4
StatePublished - Jul 2021

Bibliographical note

Publisher Copyright:
© 2010-2012 IEEE.

NREL Publication Number

  • NREL/JA-5D00-79429


  • delta-connected devices
  • distribution networks
  • Optimal power flow
  • semi-definite relaxation


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