### Abstract

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.

Original language | English |
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Title of host publication | 2015 IEEE Eindhoven PowerTech, PowerTech 2015 |

Place of Publication | Piscataway |

Publisher | Institute of Electrical and Electronics Engineers |

Number of pages | 6 |

ISBN (Electronic) | 9781479976935 |

DOIs | |

Publication status | Published - 31 Aug 2015 |

Event | IEEE Eindhoven PowerTech, PowerTech 2015 - Eindhoven, Netherlands Duration: 29 Jun 2015 → 2 Jul 2015 |

### Conference

Conference | IEEE Eindhoven PowerTech, PowerTech 2015 |
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Country | Netherlands |

City | Eindhoven |

Period | 29/06/15 → 2/07/15 |

### Keywords

- box-counting method
- Dielectric Breakdown Model
- electricity network
- fractal dimension
- fractal geometry

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## Cite this

*2015 IEEE Eindhoven PowerTech, PowerTech 2015*[7232496] Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/PTC.2015.7232496