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

TL;DR

This paper introduces a stochastic growth model for power grids that captures key structural features like degree distribution and redundancy, providing insights into their evolution and design.

Contribution

The model combines cost-efficient tree growth with a trade-off growth phase, including line splitting, to replicate real-world power grid properties.

Findings

Degree distribution has an exponential tail and can peak at degree two.

Mean degree and decay slope are controllable and somewhat independent.

Statistical tests confirm the exponential tail hypothesis fits the model data.

Abstract

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.