Convergence of the Z-Bus Method for Three-Phase Distribution Load-Flow with ZIP Loads

TL;DR

This paper establishes conditions for the unique solvability of three-phase distribution load-flow problems with ZIP loads and proves that the Z-Bus iterative method reliably converges under these conditions.

Contribution

It provides explicit sufficient conditions for solution uniqueness and demonstrates the convergence of the Z-Bus method in unbalanced three-phase networks.

Findings

Unique solution conditions derived from network parameters

Z-Bus method shown to be a contraction mapping

Guaranteed convergence of the iterative method

Abstract

This paper derives a set of sufficient conditions guaranteeing that the load-flow problem in unbalanced three-phase distribution networks with wye and delta ZIP loads has a unique solution over a region that can be explicitly calculated from the network parameters. It is also proved that the well-known Z-Bus iterative method is a contraction over the defined region, and hence converges to the unique solution.