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Cascades of failures are among the biggest threats to supply networks such as power grids: An initially failing element may trigger the failure of other elements, thereby eventually causing the entire network to collapse. Here, we analyse the statistics of Line Outage Distribution Factors (LODFs), which describe the rerouting of electric power flows after a line failure. In particular, we demonstrate that absolute LODFs are approximately log-normally distributed throughout network topologies. We then illustrate that this log-normal distribution of redistribution factors results in a heavy tailed distribution of outage sizes in a simplified, stochastic cascade model over a certain range of parameters. This cascade model extends previous stochastic cascade models by adding more realistic redistribution mechanisms as well as including more realistic initial trigger events. Our results demonstrate that the statistics of redistribution factors is a fundamental trait throughout different networks and presents a possible explanation for the vast occurrence of heavy tailed distributions in real-world reanalyses of power outage sizes.

Universal Statistics of Redistribution Factors and Large Scale Cascades in Power Grids