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

Zhou, Fengyu; Zamzam, Ahmed S.; Low, Steven H.; Sidiropoulos, Nicholas D.

doi:10.1109/tsg.2021.3066530

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

Journal Article · Wed Mar 17 00:00:00 EDT 2021 · IEEE Transactions on Smart Grid

DOI:https://doi.org/10.1109/tsg.2021.3066530· OSTI ID:1774835

Zhou, Fengyu ^[1]; Zamzam, Ahmed S. ^[2]; Low, Steven H. ^[1]; Sidiropoulos, Nicholas D. ^[3]

California Institute of Technology (CalTech), Pasadena, CA (United States)
National Renewable Energy Lab. (NREL), Golden, CO (United States)
Univ. of Virginia, Charlottesville, VA (United States)

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.

View Accepted Manuscript (DOE)

Research Organization:: National Renewable Energy Laboratory (NREL), Golden, CO (United States)

Sponsoring Organization:: USDOE National Renewable Energy Laboratory (NREL), Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: AC36-08GO28308

OSTI ID:: 1774835

Report Number(s):: NREL/JA-5D00-79429; MainId:33655; UUID:65ee2f45-5c7d-4fec-8b7f-f84dffb80697; MainAdminID:21115

Journal Information:: IEEE Transactions on Smart Grid, Journal Name: IEEE Transactions on Smart Grid Journal Issue: 4 Vol. 12; ISSN 1949-3053

Publisher:: IEEECopyright Statement

Country of Publication:: United States

Language:: English

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24 POWER TRANSMISSION AND DISTRIBUTION
delta-connected devices
distribution networks
optimal power flow
semi-definite relaxation

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

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