CWI researchers develop new mathematical framework to explain the emergence of large blackouts

The new framework combines the physics of power flow with rare event analysis for heavy-tailed distributions. The study shows that the statistical distribution of blackout sizes can be linked to city sizes. The researchers indicate that it might be more effective to help consumers react to a blackout instead of performing network upgrades.

Large blackouts are rare, fortunately. But when they do appear, the societal and economic impact they have is significant. Therefore, the possibility of such large power outages taking place cannot be ignored. Solid scientific information about the chances of the occurrence of large power outages and the context in which they manifest themselves, is very valuable. A fundamental understanding of the emergence of large blackouts is lacking, however. This hinders the development of focused prevention and/or mitigation policies.

In particular, it has been established empirically for 25 years that the statistical distribution of blackouts follows the so-called Pareto law, a law that is also observed in data on income, returns on the stock market, and sizes of pandemics. A key question is to explain the origin of this Pareto law in a power grid context.

Until recently, researchers have mainly focused on investigating internal mechanisms and characteristics of the power grid that might cause large blackouts, like physical processes. CWI researcher Bert Zwart and his colleagues of CWI’s Stochastics group have now provided evidence that a main cause of this statistical law is a similar Pareto distribution of city sizes. For the creation of this radically different and much simpler insight, they combined the physics of power flow with extreme value theory.

Blackout size linked to city size

The results of this research shed a light on the connection between blackouts and city sizes. It appears that the large blackout is most likely to occur when a large city is being cut off from the power grid. “Our explanation says the output is heavy-tailed not because of the mechanism within the system but because the input, namely the city sizes were already heavy tailed,” Zwart says in this article (link). The conclusion is that performing network upgrades will only lead to a modest decrease in the likelihood of big blackouts. The researchers suggest that it might be more effective to help consumers to react to blackouts, for example by using local energy generation and storage.

The researchers substantiated their findings using historical data for the United States and validate their new framework through simulations of the German transmission grid. They support the new model with an extensive mathematical analysis. Zwart et al. published the results in Physical Review Letters on 31 July 2020.

This research was executed in the context of the NWO Vici grant Bert Zwart received in 2015 and the NWO Gravitation grant Networks.

About Bert Zwart

Bert Zwart is group leader of CWI's Stochastics research group and professor at Eindhoven University of Technology (TU/e). His research expertise is in applied probability and stochastic networks, in particular rare event analysis and simulation, scaling limits, scheduling under uncertainty, dynamic pricing and applications in communication and energy networks.

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