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

The size distribution of planned and forced outages in power systems have been studied for
almost two decades and has drawn great interest as they display heavy tails. Understanding of this
phenomenon has been done 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 is needed to
support hypotheses. In this paper, the authors 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, it is found that, on the one hand, while being overwhelmed by white noise, outage
events show traits of self-organized criticality (SOC), which may be modeled by a crossover from
random percolation to directed percolation branching process with dissipation. On the other hand,
in responses to outages, the heavy tails in outage duration distributions could be a consequence of
the highly optimized tolerance (HOT) mechanism, based on the optimized allocation of maintenance
resources.