Convex Relaxation of OPF in Multiphase Radial Networks with Wye and Delta Connections
Abstract
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 deltaconnected 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 phasetoground 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.
 Authors:
 National Renewable Energy Laboratory (NREL), Golden, CO (United States)
 California Institute of Technology
 Publication Date:
 Research Org.:
 National Renewable Energy Lab. (NREL), Golden, CO (United States)
 Sponsoring Org.:
 USDOE Advanced Research Projects AgencyEnergy (ARPAE)
 OSTI Identifier:
 1374123
 Report Number(s):
 NREL/PR5D0068859
 DOE Contract Number:
 AC3608GO28308
 Resource Type:
 Conference
 Resource Relation:
 Conference: Presented at the 2017 IEEE Power & Energy Society (PES) General Meeting, 1620 July 2017, Chicago, Illinois
 Country of Publication:
 United States
 Language:
 English
 Subject:
 24 POWER TRANSMISSION AND DISTRIBUTION; optimal power flow; multiphase distribution network; convex relaxation
Citation Formats
Zhao, Changhong, DallAnese, Emiliano, and Low, Steven. Convex Relaxation of OPF in Multiphase Radial Networks with Wye and Delta Connections. United States: N. p., 2017.
Web.
Zhao, Changhong, DallAnese, Emiliano, & Low, Steven. Convex Relaxation of OPF in Multiphase Radial Networks with Wye and Delta Connections. United States.
Zhao, Changhong, DallAnese, Emiliano, and Low, Steven. 2017.
"Convex Relaxation of OPF in Multiphase Radial Networks with Wye and Delta Connections". United States.
doi:. https://www.osti.gov/servlets/purl/1374123.
@article{osti_1374123,
title = {Convex Relaxation of OPF in Multiphase Radial Networks with Wye and Delta Connections},
author = {Zhao, Changhong and DallAnese, Emiliano and Low, Steven},
abstractNote = {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 deltaconnected 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 phasetoground 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.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = 2017,
month = 8
}

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