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We propose a model to create synthetic networks that may also serve as anarrative of a certain kind of infrastructure network evolution. It consists ofan initialization phase with the network extending tree-like for minimum costand a growth phase with an attachment rule giving a trade-off betweencost-optimization and redundancy. Furthermore, we implement the feature of somelines being split during the grid's evolution. We show that the resultingdegree distribution has an exponential tail and may show a maximum at degreetwo, suitable to observations of real-world power grid networks. In particular,the mean degree and the slope of the exponential decay can be controlled inpartial independence. To verify to which extent the degree distribution isdescribed by our analytic form, we conduct statistical tests, showing that thehypothesis of an exponential tail is well-accepted for our model data.

A Random Growth Model for Power Grids and Other Spatially Embedded Infrastructure Networks