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Published July 2021 | Submitted
Journal Article Open

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


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.

Additional Information

© 2021 IEEE. Manuscript received August 20, 2020; revised January 30, 2021; accepted March 1, 2021. Date of publication March 17, 2021; date of current version June 21, 2021. This work was supported in part by the National Renewable Energy Laboratory, operated by Alliance for Sustainable Energy, LLC, for the U.S. Department of Energy (DOE) under Contract DE-AC36-08GO28308. The work of Fengyu Zhou and Steven H. Low was supported in part by NSF under Grant CCF#1637598 and Grant ECCS#1931662. The work of Ahmed S. Zamzam was supported by the Laboratory Directed Research and Development (LDRD) Program at NREL. Paper no. TSG-01282-2020. The views expressed in the article do not necessarily represent the views of the DOE or the U.S. Government. The U.S. Government retains and the publisher, by accepting the article for publication, acknowledges that the U.S. Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for U.S. Government purposes.

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August 20, 2023
October 20, 2023