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

TL;DR

This paper develops conditions for the existence, uniqueness, and non-singularity of load-flow solutions in unbalanced multiphase distribution networks, introduces a convergent iterative algorithm, and derives linear models with accuracy analysis.

Contribution

It extends the Z-bus load-flow algorithm to generic unbalanced systems and provides explicit conditions for solution properties and convergence.

Findings

Explicit conditions for existence and uniqueness of load-flow solutions.

A convergent Z-bus iterative load-flow algorithm for complex systems.

Linear load-flow models with validated approximation accuracy.

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