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

Bernstein, Andrey; Wang, Cong; Dall'Anese, Emiliano; Le Boudec, Jean -Yves; Zhao, Changhong

doi:10.1109/TPWRS.2018.2823277

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

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Abstract

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:

Bernstein, Andrey ^[1]; Wang, Cong ^[2]; Dall'Anese, Emiliano ^[1]; Le Boudec, Jean -Yves ^[3]; Zhao, Changhong ^[1]

National Renewable Energy Lab. (NREL), Golden, CO (United States)
EPFL, Lausanne (Switzerland)
Ecole Polytechnique Federale Lausanne (Switzlerland)

Publication Date:: Fri Apr 06 00:00:00 EDT 2018

Research Org.:: National Renewable Energy Lab. (NREL), Golden, CO (United States)

Sponsoring Org.:: USDOE Advanced Research Projects Agency - Energy (ARPA-E)

OSTI Identifier:: 1435700

Report Number(s):: NREL/JA-5D00-67920
Journal ID: ISSN 0885-8950

Grant/Contract Number:: AC36-08GO28308

Resource 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

Country of Publication:: United States

Language:: English

Subject:: 24 POWER TRANSMISSION AND DISTRIBUTION; load flow; distribution network; Wye; Delta; linear model

Citation Formats


                    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., 2018. 
Web.  doi:10.1109/TPWRS.2018.2823277.

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                    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.  https://doi.org/10.1109/TPWRS.2018.2823277

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                    Bernstein, Andrey, Wang, Cong, Dall'Anese, Emiliano, Le Boudec, Jean -Yves, and Zhao, Changhong. Fri .  
"Load-Flow in Multiphase Distribution Networks: Existence, Uniqueness, Non-Singularity, and Linear Models".  United States.  https://doi.org/10.1109/TPWRS.2018.2823277.  https://www.osti.gov/servlets/purl/1435700.

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@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         = {Fri Apr 06 00:00:00 EDT 2018},

  month        = {Fri Apr 06 00:00:00 EDT 2018}

}

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