  The frequency stability of power systems is increasingly challenged by
various types of disturbances. In particular, the increasing penetration of
renewable energy sources is increasing the variability of power generation and
at the same time reducing system inertia against disturbances. In this paper we
are particularly interested in understanding how rate of change of frequency
(RoCoF) violations could arise from unusually large power disturbances. We
devise a novel specialization, named ghost sampling, of the Metropolis-Hastings
Markov Chain Monte Carlo method that is tailored to efficiently sample rare
power disturbances leading to nodal frequency violations. Generating a
representative random sample addresses important statistical questions such as
"which generator is most likely to be disconnected due to a RoCoF violation?"
or "what is the probability of having simultaneous RoCoF violations, given that
a violation occurs?" Our method can perform conditional sampling from any joint
distribution of power disturbances including, for instance, correlated and
non-Gaussian disturbances, features which have both been recently shown to be
significant in security analyses.
