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

Type of publication Peer-reviewed
Publikationsform Original article (peer-reviewed)
Author Bernstein Andrey, Wang Cong, Dall'Anese Emiliano, Le Boudec Jean-Yves, Zhao Changhong,
Project Integration of Intermittent Widespread Energy Sources in Distribution Networks: Scalable and Reliable Real Time Control of Power Flows
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Original article (peer-reviewed)

Journal IEEE Transactions on Power Systems
Volume (Issue) 33(6)
Page(s) 5832 - 5843
Title of proceedings IEEE Transactions on Power Systems
DOI 10.1109/tpwrs.2018.2823277

Open Access

Type of Open Access Website


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 nonsingularity of the load-flow Jacobian is proposed. Finally, linear load-flow models are derived, and their approximation accuracy is analyzed. Theoretical results are corroborated through experiments on IEEE test feeders.