Fractal images have been discovered in many areas of science and engineering in the past two decades, so it is not surprising that they have also appeared in power system literature. This article provides a brief introduction to fractals and presents some fractal patterns produced by Newton-Raphson load-flow calculations for a small power system. If we imagine performing load-flow calculations from a dense grid of initial conditions, the region of initial conditions that converge to a particular equilibrium point using the Newton-Raphson method is seen to have a fractal boundary.
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Thorp et al. (1997) studied this question.