New modeling of electrical power networks using fractal geometry

Abstract

The aim of this paper is to introduce a new approach for electrical power network modeling. It is based on fractal geometry. Over a wide range of frequency, power systems exhibit capacitive, inductive and resonant behaviors. In the resonant range, the authors show that it is possible to model the average behavior of the resonances by a power law. Its exponent is measured by a box counting method applied to a fractal analogous to the network. The resulting model is both accurate and of reduced order.