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Title: Load-Flow in Multiphase Distribution Networks: Existence, Uniqueness, Non-Singularity, and Linear Models

This paper considers unbalanced multiphase distribution systems with generic topology and different load models, and extends the Z-bus iterative load-flow algorithm based on a fixed-point interpretation of the AC load-flow equations. Explicit conditions for existence and uniqueness of load-flow solutions are presented. These conditions also guarantee convergence of the load-flow algorithm to the unique solution. The proposed methodology is applicable to generic systems featuring (i) wye connections; (ii) ungrounded delta connections; (iii) a combination of wye-connected and delta-connected sources/loads; and, (iv) a combination of line-to-line and line-to-grounded-neutral devices at the secondary of distribution transformers. Further, a sufficient condition for the non-singularity of the load-flow Jacobian is proposed. Lastly, linear load-flow models are derived, and their approximation accuracy is analyzed. Theoretical results are corroborated through experiments on IEEE test feeders.
Authors:
 [1] ;  [2] ;  [1] ;  [3] ;  [1]
  1. National Renewable Energy Lab. (NREL), Golden, CO (United States)
  2. EPFL, Lausanne (Switzerland)
  3. Ecole Polytechnique Federale Lausanne (Switzlerland)
Publication Date:
Report Number(s):
NREL/JA-5D00-67920
Journal ID: ISSN 0885-8950
Grant/Contract Number:
AC36-08GO28308
Type:
Accepted Manuscript
Journal Name:
IEEE Transactions on Power Systems
Additional Journal Information:
Journal Volume: 33; Journal Issue: 6; Journal ID: ISSN 0885-8950
Publisher:
IEEE
Research Org:
National Renewable Energy Lab. (NREL), Golden, CO (United States)
Sponsoring Org:
USDOE Advanced Research Projects Agency - Energy (ARPA-E)
Country of Publication:
United States
Language:
English
Subject:
24 POWER TRANSMISSION AND DISTRIBUTION; load flow; distribution network; Wye; Delta; linear model
OSTI Identifier:
1435700

Bernstein, Andrey, Wang, Cong, Dall'Anese, Emiliano, Le Boudec, Jean -Yves, and Zhao, Changhong. Load-Flow in Multiphase Distribution Networks: Existence, Uniqueness, Non-Singularity, and Linear Models. United States: N. p., Web. doi:10.1109/TPWRS.2018.2823277.
Bernstein, Andrey, Wang, Cong, Dall'Anese, Emiliano, Le Boudec, Jean -Yves, & Zhao, Changhong. Load-Flow in Multiphase Distribution Networks: Existence, Uniqueness, Non-Singularity, and Linear Models. United States. doi:10.1109/TPWRS.2018.2823277.
Bernstein, Andrey, Wang, Cong, Dall'Anese, Emiliano, Le Boudec, Jean -Yves, and Zhao, Changhong. 2018. "Load-Flow in Multiphase Distribution Networks: Existence, Uniqueness, Non-Singularity, and Linear Models". United States. doi:10.1109/TPWRS.2018.2823277. https://www.osti.gov/servlets/purl/1435700.
@article{osti_1435700,
title = {Load-Flow in Multiphase Distribution Networks: Existence, Uniqueness, Non-Singularity, and Linear Models},
author = {Bernstein, Andrey and Wang, Cong and Dall'Anese, Emiliano and Le Boudec, Jean -Yves and Zhao, Changhong},
abstractNote = {This paper considers unbalanced multiphase distribution systems with generic topology and different load models, and extends the Z-bus iterative load-flow algorithm based on a fixed-point interpretation of the AC load-flow equations. Explicit conditions for existence and uniqueness of load-flow solutions are presented. These conditions also guarantee convergence of the load-flow algorithm to the unique solution. The proposed methodology is applicable to generic systems featuring (i) wye connections; (ii) ungrounded delta connections; (iii) a combination of wye-connected and delta-connected sources/loads; and, (iv) a combination of line-to-line and line-to-grounded-neutral devices at the secondary of distribution transformers. Further, a sufficient condition for the non-singularity of the load-flow Jacobian is proposed. Lastly, linear load-flow models are derived, and their approximation accuracy is analyzed. Theoretical results are corroborated through experiments on IEEE test feeders.},
doi = {10.1109/TPWRS.2018.2823277},
journal = {IEEE Transactions on Power Systems},
number = 6,
volume = 33,
place = {United States},
year = {2018},
month = {4}
}