  Accurately and efficiently estimating system performance under uncertainty is
paramount in power system planning and operation. Monte Carlo simulation is
often used for this purpose, but convergence may be slow, especially when
detailed models are used. Previously published methods to speed up computations
may severely constrain model complexity, limiting their real-world
effectiveness. This paper uses the recently proposed Multilevel Monte Carlo
(MLMC) framework, which combines outputs from a hierarchy of simulators to
boost computational efficiency without sacrificing accuracy. It explains which
requirements the MLMC framework imposes on the model hierarchy, and how these
naturally occur in power system adequacy assessment problems. Two adequacy
assessment examples are studied in detail: a composite system and a system with
heterogeneous storage units. An intuitive speed metric is introduced for easy
comparison of simulation setups. Depending on the problem and metric of
interest, large speedups can be obtained.
