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

Abstract

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.