Distributions of large-scale power outages: Extreme values and the effect of truncation

In this study, we examine the distribution of large-scale power outages using a very current database of outage events reported to the Department of Energy. Recent theoretical studies applying complex systems theory to the study of power outages have predicted that the magnitude of such events should follow a power law distribution of form l/x"+1 over certain time scales. The high probability of large events under this distribution leads to serious risk management consequences. We directly analyze outage events over the period 1984-2006 and find that the behaviour of actual outage events is actually much closer to that of a log-normal distribution. Various distributions are used to fit the data using modern statistical methodologies. The statistical theory of extremes is introduced to take into account the truncation of small values due to reporting criteria. Risk management consequences of various tail behaviours of the outage distribution are also examined.