Convergence regions of Newton method in power flow studies: Numerical studies

Abstract

Power flow study is a fundamental task of power system operation and planning. Of the several methods developed in commercial package for power flow study, the Newton-Raphson method is the most successful one. It is however well recognized that the NR method may diverge in power flow study. In this paper, we numerically study the convergence regions of power flow solutions using Newton-Raphson(NR) method. This study of convergence region is motivated by the need to determine an initial guess which converges to one of the power flow solution. It will be numerically shown that the convergence region of NR method, if exist, has a fractal boundary and is hence sensitive to initial conditions. Several fractal features will be investigated considering the convergence regions of power flow at the base case and at various loading conditions, and with different load models. An IEEE 14-bus system will be used to illustrate the fractal boundary via numerical results.