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

We define Poisson process models for outage and restore processes in power system resilience events in terms of their rates. These outage and restore processes easily yield the performance curves that track the evolution of resilience events, and their area, nadir and duration are standard resilience metrics. We derive explicit and intuitive formulas for these metrics for mean performance curves in terms of the model parameters; these parameters can be estimated from utility data. This clarifies the calculation of metrics of typical resilience events, and shows what they depend on. We give examples of the metric formulas using a typical model of transmission system outages with lognormal rate restoration, and also for constant rate and exponential rate restorations. We give similarly nice formulas for the area metric for empirical power system data.