Abstract
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.
Highlights
In our daily lives, we depend on a reliable supply with electrical power
The distribution of Line Outage Distribution Factors (LODFs) is purely based on the network topology and may be considered as a network observable, to the degree distribution or betweenness measures that have been considered in previous analyses of power grids [26], [31], [32]
We analysed how this distribution changes throughout different synthetic and real-world topologies: We found that the distribution of the magnitude of LODFs is approximately log-normal, but shows heavy tails throughout the topologies analysed here
Summary
We depend on a reliable supply with electrical power. Large scale power outages can have a catastrophic impact on society, economy and other infrastructure networks as recent examples demonstrate [1], [2]. Empirical reanalyses of historic power grid blackouts have revealed the scale-free nature of outage sizes: large scale outages are not rare, but the size of outage sizes decays algebraically [3], [4]. The reason for this scaling is still not fully understood, but different possible explanations have been put forward [5]–[8]. A single step in a cascade is essentially governed by two variables: The initial flows in the network and the flow rerouting in the network after a failure The latter may be compactly summarised in terms of the Line Outage Distribution Factors (LODFs) which arise. The distribution of LODFs is purely based on the network topology and may be considered as a network observable, to the degree distribution or betweenness measures that have been considered in previous analyses of power grids [26], [31], [32]
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