On the Solution of the Three-Phase Load-Flow in Distribution Networks

This paper is concerned with the Z-Bus method to solve the load-flow problem in three-phase distribution networks with wye and delta constant-power, constant-current, and constant-impedance loads (ZIP loads). The Z-Bus method is viewed as a fixed-point iteration. By leveraging the contraction mapping theorem, a set of sufficient conditions is then presented that guarantees a) the existence of a unique solution over a region that can be computed from the network parameters, and b) the convergence of the Z-Bus method to the unique solution. It is numerically illustrated that the new set of sufficient conditions holds for practical distribution networks and improves the previously reported results on the convergence of the Z-Bus method in three-phase networks.