Revisiting and Modeling Power-Law Distributions in Empirical Outage Data of Power Systems

Hartmann, Bálint and Deng, Shengfeng and Ódor, Géza and Kelling, Jeffrey (2023) Revisiting and Modeling Power-Law Distributions in Empirical Outage Data of Power Systems. PRX Energy, 2 (3). No-033007. ISSN 2768-5608

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Abstract

The size distributions of planned and forced outages and their restoration times in power systems have been studied for almost two decades and have drawn great interest as they display heavy tails. Understanding heavy tails has been provided by various threshold models, which are self-tuned at their critical points, but as many papers pointed out, explanations are intuitive, and more empirical data are needed to support hypotheses. In this paper, we analyze outage data collected from various public sources to calculate the outage energy and outage duration exponents of possible power-law fits. Temporal thresholds are applied to identify crossovers from initial short-time behavior to power-law tails. We revisit and add to the possible explanations of the uniformness of these exponents. By performing power spectral analyses on the outage event time series and the outage duration time series, we find that, on the one hand, while being overwhelmed by white noise, outage events show traits of self-organized criticality, which may be modeled by a crossover from random percolation to a directed percolation branching process with dissipation, coupled to a conserved density. On the other hand, in response to outages, the heavy tails in outage duration distributions could be a consequence of the highly optimized tolerance mechanism, based on the optimized allocation of maintenance resources.

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