Models, metrics, and their formulas for typical electric power system resilience events

TL;DR

This paper develops explicit formulas for resilience metrics in power systems using Poisson process models, enabling better analysis of outage and restoration events based on utility data.

Contribution

It introduces analytical formulas for resilience metrics derived from Poisson process parameters, applicable to empirical data and different restoration rate assumptions.

Findings

Formulas for area, nadir, and duration of resilience performance curves.

Application of formulas to a North American transmission event.

Validation of formulas with empirical power system data.

Abstract

Poisson process models are defined in terms of their rates for outage and restore processes in power system resilience events. These outage and restore processes easily yield the performance curves that track the evolution of resilience events, and the area, nadir, and duration of the performance curves are standard resilience metrics. This letter analyzes typical resilience events by analyzing the area, nadir, and duration of mean performance curves. Explicit and intuitive formulas for these metrics are derived in terms of the Poisson process model parameters, and these parameters can be estimated from utility data. This clarifies the calculation of metrics of typical resilience events, and shows what they depend on. The metric formulas are derived with lognormal, exponential, or constant rates of restoration. The method is illustrated with a typical North American transmission event. Similarly nice formulas are obtained for the area metric for empirical power system data.