  It is of growing concern to ensure the resilience in electricity
infrastructure systems to extreme weather events with the help of appropriate
hardening measures and new operational procedures. An effective mitigation
strategy requires a quantitative metric for resilience that can not only model
the impacts of the unseen catastrophic events for complex electric power
distribution networks but also evaluate the potential improvements offered by
different planning measures. In this paper, we propose probabilistic metrics to
quantify the operational resilience of the electric power distribution systems
to high-impact low-probability (HILP) events. Specifically, we define two
risk-based measures: Value-at-Risk ($VaR_\alpha$) and Conditional Value-at-Risk
($CVaR_\alpha $) that measure resilience as the maximum loss of energy and
conditional expectation of a loss of energy, respectively for the events beyond
a prespecified risk threshold, $\alpha$. Next, we present a simulation-based
framework to evaluate the proposed resilience metrics for different weather
scenarios with the help of modified IEEE 37-bus and IEEE 123-bus system. The
simulation approach is also extended to evaluate the impacts of different
planning measures on the proposed resilience metrics.
