A random growth model for power grids and other spatially embedded infrastructure networks
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We propose a model to create synthetic networks that may also serve as a narrative of a certain kind of infrastructure network evolution. It consists of an initialization phase with the network extending tree-like for minimum cost and a growth phase with an attachment rule giving a trade-off between cost-optimization and redundancy. Furthermore, we implement the feature of some lines being split during the grid's evolution. We show that the resulting degree distribution has an exponential tail and may show a maximum at degree two, suitable to observations of real-world power grid networks. In particular, the mean degree and the slope of the exponential decay can be controlled in partial independence. To verify to which extent the degree distribution is described by our analytic form, we conduct statistical tests, showing that the hypothesis of an exponential tail is well-accepted for our model data.
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- 1.BDEW, Press Release, http://www.bdew.de/internet.nsf/id/20130412-pi-deutsches-stromnetz-ist-18-millionen-kilometer-lang-de (accessed: 20.01.2014)
- 4.O. Borůvka, Elektrotechnický Obz. 15, 153 (1926)Google Scholar
- 5.O. Borůvka, Elektrotechnický Obz. 15, 153 (1926)Google Scholar
- 6.C. Bracquemond, et al., Laboratoire Jean Kuntzmann, Appl. Math. Comput. Sci., Techn. Report 6 (2002)Google Scholar
- 13.E.N. Gilbert, Annals Math. Stat., 1141 (1959)Google Scholar
- 16.J. Kruskal, Proc. Am. Math. Soc. 5 (1956)Google Scholar
- 17.P. Menck, J. Kurths, Nonlinear Dyn. Electron. Syst., 144 (2012)Google Scholar
- 19.M. Molloy, B. Reed, Random Struct. Algorithms 1 (1995)Google Scholar
- 24.G. Pagani, M. Aiello, Phys. A Stat. Mech. Its Appl. 1 (2013)Google Scholar
- 26.M. Rosas-Casals, Topological Complexity of the Electricity Transmission Network (UPC, Barcelona, 2009)Google Scholar
- 27.M. Rosvall, et al., Phys. Rev. E 67, 028701 (2005)Google Scholar