Reliable Confidence Intervals for Monte Carlo-Based Resource Adequacy Studies

Abstract

Quantitative risk analysis is essential for power system planning and operation. Monte Carlo methods are frequently employed for this purpose, but their inherent sampling uncertainty means that accurate estimation of this uncertainty is essential. Basic Monte Carlo procedures are unbiased and, in the limit of large sample counts, have a well-characterised error distribution. However, for small time budgets and ill-behaved distributions (such as those for rare event risks), we may not always operate in this limit. Moreover, multilevel Monte Carlo was recently proposed as a computationally efficient alternative to regular Monte Carlo. In this approach, great asymptotic speedups are achieved by reducing the number of full model evaluations. This further challenges the assumption that normally distributed errors can be used. This paper investigates the sampling error distributions for a practical resource adequacy case study, in combination with the Multilevel Monte Carlo method. It further proposes a practical test for validating error estimates, based on a bootstrap approach.