Load-Flow in Multiphase Distribution Networks: Existence, Uniqueness, Non-Singularity and Linear Models
For power system engineers, this work provides theoretical guarantees and linear approximations for load-flow in complex multiphase distribution networks, addressing a known bottleneck in unbalanced system analysis.
This paper extends the Z-bus iterative load-flow algorithm for unbalanced multiphase distribution networks, providing explicit conditions for existence, uniqueness, and convergence of load-flow solutions, as well as a sufficient condition for non-singularity of the Jacobian. Linear load-flow models are derived and their accuracy is validated on IEEE test feeders.
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.