Convergence analysis of implicit Z‐bus power flow method for general distribution networks with distributed generators

Implicit Z‐bus distribution power flow method may encounter divergence problems when applied to distribution systems with distributed generators modelled as P‐V nodes. In this study, analysis of divergence problems associated with the implicit Z‐bus method is performed. Physical insights toward the divergence problem are also provided. To this end, the iterative map of the implicit Z‐bus method is first derived. Then the fix‐point theorem and the non‐linear discrete stability theorem are applied to perform convergence/divergence analysis of the implicit Z‐bus power flow method. The authors apply the derived analytical results to conduct divergence analysis of the IEEE 13‐bus, and a practical 1101‐node distribution networks.