Electricity Case: Statistical Analysis of Electric Power Outages

Publication Type: 
Authors: 
Jeffrey S. Simonoff
Carlos E. Restrepo
Rae Zimmerman
Wendy Remington
Lester Lave
Richard E. Schuler
Nicole Dooskin
Description/Abstract: 
This report analyses electricity outages over the period January 1990-August 2004. A database was constructed using U.S. data from the DAWG database, which is maintained by the North American Electric Reliability Council (NERC). The data includes information about the date of the outage, geographical location, utilities affected, customers lost, duration of the outage in hours, and megawatts lost. Information found the DAWG database was also used to code the primary cause of the outage. Categories that included weather, equipment failure, human error, fires, and others were added to the database. In addition, information about the total number of customers served by the affected utilities, as well as total population and population density of the state affected in each incident, was incorporated to the database. The resulting database included information about 400 incidents over this period. The database was used to carry out two sets of analyses. The first is a set of analyses over time using three-, six-, or twelve-month averages for number of incidents, average outage duration, customers lost and megawatts lost. Negative binomial regression models, which account for overdispersion in the data, were used. For the number of incidents over time a seasonal analysis suggests there is a 9.7% annual increase in incident rate given season (that is, “holding season constant”) over this period. Given the year, summer is estimated to have 65-85% more incidents than the other seasons. The duration data suggest a more complicated trend; an analysis of duration per incident over time using a loess nonparametric regression “scatterplot smoother” suggests that between 1990-93 durations were getting shorter on average but this trend changed in the mid-1990s when average duration started to increase, and this increase became more pronounced after 2002. When looking at average customer losses by season there is weak evidence of an upward trend in the average customer loss per incident, with an estimated increase of a bit more than 10,000 customers per incident per year. Similar analyses of MW lost per incident over time showed no evidence of any time or seasonal patterns for this variable. The second part of the report includes a number of event-level analyses. The data in these analyses are modeled in two parts. First, the different characteristics related to whether an incident has zero or nonzero customers lost are determined. Then, given that the number lost is nonzero, the characteristics that help to predict the customers lost are analyzed. Unlike the first set of models described, in this section a number of predictors such as primary cause of the outage (including variables such as weather, equipment failure, system protection, human error and others), total number of customers served by the affected utilities, and the population density of the states where the outages occurred were used in the analyses to gain a better understanding of the three key outcome variables: customers lost, megawatts lost and duration of electric outages. Logistic regression was used in these analyses. For logged customers lost, the only predictor showing much of a relationship was logged MW lost. The total number of customers served by the utility was found to be a marginally significant predictor of customers lost per incident. Customer losses were higher for events caused by natural disaster, crime, unknown causes, and third party, and lower for incidents resulting from capacity shortage, demand reduction, and equipment failure, holding all else in the model fixed. The analyses for duration at the event level find that the two most causes of outages were equipment failure and weather, are very different, with the former associated with shorter events and the latter associated with longer ones. When the primary cause of the events is included in the regression models, the time trend for the average duration per incident found in earlier analyses disappears. According to the data, weather related incidents are becoming more common in later years and equipment failures less common, and this change in the relative frequency of primary cause of the events accounts for much of the overall pattern of increasing average durations by season. Holding all else in the model constant, these analyses also suggest that winter events have an expected duration that is 2.25 times the duration of summer events, with autumn and spring in between. The event-level models can be used to construct predictions for outage outcomes based on different scenarios. We look at scenarios for New York, Chicago, San Francisco, and Seattle. Using the characteristics of the utilities in these four cities, the estimated expected duration and estimated expected customer loss (given nonzero loss) of an incident, separated by season and cause, can be determined for each city. We also construct 50% prediction intervals for duration and for customer loss (given that the loss is nonzero) for any cause and season for the four cities.