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The size distribution of planned and forced outages and following restorationtimes in power systems have been studied for almost two decades and has drawngreat interest as they display heavy tails. Understanding of this phenomenonhas been done by various threshold models, which are self-tuned at theircritical points, but as many papers pointed out, explanations are intuitive,and more empirical data is needed to support hypotheses. In this paper, theauthors analyze outage data collected from various public sources to calculatethe outage energy and outage duration exponents of possible power-law fits.Temporal thresholds are applied to identify crossovers from initial short-timebehavior to power-law tails. We revisit and add to the possible explanations ofthe uniformness of these exponents. By performing power spectral analyses onthe outage event time series and the outage duration time series, it is foundthat, on the one hand, while being overwhelmed by white noise, outage eventsshow traits of self-organized criticality (SOC), which may be modeled by acrossover from random percolation to directed percolation branching processwith dissipation, coupled to a conserved density. On the other hand, inresponses to outages, the heavy tails in outage duration distributions could bea consequence of the highly optimized tolerance (HOT) mechanism, based on theoptimized allocation of maintenance resources.

Revisiting and modeling power-law distributions in empirical outage data of power systems