  A key objective of the smart grid is to improve reliability of utility
services to end users. This requires strengthening resilience of distribution
networks that lie at the edge of the grid. However, distribution networks are
exposed to external disturbances such as hurricanes and snow storms where
electricity service to customers is disrupted repeatedly. External disturbances
cause large-scale power failures that are neither well-understood, nor
formulated rigorously, nor studied systematically. This work studies resilience
of power distribution networks to large-scale disturbances in three aspects.
First, a non-stationary random process is derived to characterize an entire
life cycle of large-scale failure and recovery. Second, resilience is defined
based on the non-stationary random process. Close form analytical expressions
are derived under specific large-scale failure scenarios. Third, the
non-stationary model and the resilience metric are applied to a real life
example of large-scale disruptions due to Hurricane Ike. Real data on
large-scale failures from an operational network is used to learn time-varying
model parameters and resilience metrics.
