Fractal geometry for distribution grid topologies

This paper presents an application of fractal geometry in the design, development and expansion of distribution networks. In order to prove that electrical grids are fractal in form, the fractal dimension of distribution networks is measured using the box-counting algorithm. Then a two dimensional stochastic dielectric breakdown model (DBM) is utilized in order to generate virtual distribution networks. The fractal dimension of the simulated growth patterns varied depending on η which is the exponent of the breakdown probability distribution. By controlling the value of η, growth patterns similar to the actual distribution networks could be produced. Finally, some electrical characteristics (maximum voltage drop, total power losses) of the fractal generated networks are measured and compared with the real distribution networks.