Convergence of the Z-Bus method and existence of unique solution in single-phase distribution load-flow

For a single-phase distribution network with constant-power, constant-current, and constant-impedance loads (ZIP loads), sufficient conditions are presented that explicitly define a region where a unique load-flow solution exists. The Z-Bus method is shown to be a contraction mapping iteration, which upon initialization within this region, is guaranteed to converge to the unique load-flow solution. The sufficient conditions for convergence of the Z-Bus method are numerically verified for IEEE distribution test feeders.