Optimal Power Flow in Multiphase Radial Networks with Delta Connections: Preprint
Abstract
This paper focuses on multiphase radial distribution networks with mixed wye and delta connections, and proposes a semidefinite relaxation of the AC optimal power flow (OPF) problem. Two multiphase powerflow models are developed to facilitate the integration of deltaconnected generation units/loads in the OPF problem. The first model extends traditional branch flow models  and it is referred to as extended branch flow model (EBFM). The second model leverages a linear relationship between perphase power injections and delta connections, which 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 SDP relaxations can be solved efficiently by a generic optimization solver. Numerical evidences indicate 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 also shown that the SDP solution under BVA has a small optimality gap, while the BVA model is accurate in the sense that it reflects 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 Agency  Energy (ARPAE)
 OSTI Identifier:
 1410967
 Report Number(s):
 NREL/CP5D0067852
 DOE Contract Number:
 AC3608GO28308
 Resource Type:
 Conference
 Resource Relation:
 Conference: Presented at IREP 2017 Bulk Power Systems Dynamics and Control Symposium, 27 August  1 September 2017, Espinho, Portugal
 Country of Publication:
 United States
 Language:
 English
 Subject:
 24 POWER TRANSMISSION AND DISTRIBUTION; optimal power flow; multiphase distribution network; semidefinite relaxation
Citation Formats
Zhao, Changhong, DallAnese, Emiliano, and Low, Steven H. Optimal Power Flow in Multiphase Radial Networks with Delta Connections: Preprint. United States: N. p., 2017.
Web.
Zhao, Changhong, DallAnese, Emiliano, & Low, Steven H. Optimal Power Flow in Multiphase Radial Networks with Delta Connections: Preprint. United States.
Zhao, Changhong, DallAnese, Emiliano, and Low, Steven H. 2017.
"Optimal Power Flow in Multiphase Radial Networks with Delta Connections: Preprint". United States.
doi:. https://www.osti.gov/servlets/purl/1410967.
@article{osti_1410967,
title = {Optimal Power Flow in Multiphase Radial Networks with Delta Connections: Preprint},
author = {Zhao, Changhong and DallAnese, Emiliano and Low, Steven H.},
abstractNote = {This paper focuses on multiphase radial distribution networks with mixed wye and delta connections, and proposes a semidefinite relaxation of the AC optimal power flow (OPF) problem. Two multiphase powerflow models are developed to facilitate the integration of deltaconnected generation units/loads in the OPF problem. The first model extends traditional branch flow models  and it is referred to as extended branch flow model (EBFM). The second model leverages a linear relationship between perphase power injections and delta connections, which 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 SDP relaxations can be solved efficiently by a generic optimization solver. Numerical evidences indicate 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 also shown that the SDP solution under BVA has a small optimality gap, while the BVA model is accurate in the sense that it reflects actual system voltages.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = 2017,
month =
}

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