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Title: 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 power-flow models are developed to facilitate the integration of delta-connected 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 per-phase 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:
ORCiD logo [1];  [1];  [2]
  1. National Renewable Energy Laboratory (NREL), Golden, CO (United States)
  2. 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 (ARPA-E)
OSTI Identifier:
1410967
Report Number(s):
NREL/CP-5D00-67852
DOE Contract Number:
AC36-08GO28308
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, Dall-Anese, Emiliano, and Low, Steven H. Optimal Power Flow in Multiphase Radial Networks with Delta Connections: Preprint. United States: N. p., 2017. Web.
Zhao, Changhong, Dall-Anese, Emiliano, & Low, Steven H. Optimal Power Flow in Multiphase Radial Networks with Delta Connections: Preprint. United States.
Zhao, Changhong, Dall-Anese, 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 Dall-Anese, 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 power-flow models are developed to facilitate the integration of delta-connected 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 per-phase 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 =
}

Conference:
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  • This paper examines the AC Optimal Power Flow (OPF) problem for multiphase distribution networks featuring renewable energy resources (RESs). We start by outlining a power flow model for radial multiphase systems that accommodates wye-connected and delta-connected RESs and non-controllable energy assets. We then formalize an AC OPF problem that accounts for both types of connections. Similar to various AC OPF renditions, the resultant problem is a non convex quadratically-constrained quadratic program. However, the so-called Feasible Point Pursuit-Successive Convex Approximation algorithm is leveraged to obtain a feasible and yet locally-optimal solution. The merits of the proposed solution approach are demonstrated usingmore » two unbalanced multiphase distribution feeders with both wye and delta connections.« less
  • 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 delta-connected 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 phase-to-ground 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 studiesmore » 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.« less
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