A Caltech Library Service

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

Zhou, Fengyu and Zamzam, Ahmed S. and Low, Steven H. and Sidiropoulos, Nicholas D. (2021) Exactness of OPF Relaxation on Three-phase Radial Networks with Delta Connections. IEEE Transactions on Smart Grid . ISSN 1949-3053. doi:10.1109/TSG.2021.3066530. (In Press)

[img] PDF - Accepted Version
See Usage Policy.

[img] PDF - Submitted Version
See Usage Policy.


Use this Persistent URL to link to this item:


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 paper 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.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Zhou, Fengyu0000-0002-2639-6491
Zamzam, Ahmed S.0000-0002-1175-2801
Low, Steven H.0000-0001-6476-3048
Sidiropoulos, Nicholas D.0000-0002-3385-7911
Additional Information:© 2021 IEEE. This work was funded in part by NSF through grants CCF 1637598 and ECCS 1931662. This work was authored 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 No. DE-AC36-08GO28308. The work of A. S. Zamzam was supported by the Laboratory Directed Research and Development (LDRD) Program at the National Renewable Energy Laboratory. 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.
Funding AgencyGrant Number
Department of Energy (DOE)DE-AC36-08GO28308
National Renewable Energy LaboratoryUNSPECIFIED
Subject Keywords:Optimal power flow, semi-definite relaxation, distribution networks, delta-connected devices
Record Number:CaltechAUTHORS:20210412-095431267
Persistent URL:
Official Citation:F. Zhou, A. S. Zamzam, S. H. Low and N. D. Sidiropoulos, "Exactness of OPF Relaxation on Three-phase Radial Networks with Delta Connections," in IEEE Transactions on Smart Grid, doi: 10.1109/TSG.2021.3066530
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:108691
Deposited By: Tony Diaz
Deposited On:13 Apr 2021 23:19
Last Modified:19 Apr 2021 18:08

Repository Staff Only: item control page