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This paper derives a set of sufficient conditions guaranteeing that theload-flow problem in unbalanced three-phase distribution networks with wye anddelta ZIP loads has a unique solution over a region that can be explicitlycalculated from the network parameters. It is also proved that the well-knownZ-Bus iterative method is a contraction over the defined region, and henceconverges to the unique solution.

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