Frequency violations from random disturbances: an MCMC approach

Abstract

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.

A rare-event study of frequency regulation and contingency services from grid-scale batteries

“…This paper continues recent work based on MCMC random sampling which was begun in [25,26]. While the latter papers also made strong simplifications, our goal in the present work is to demonstrate the incorporation of a power system model which is both detailed and adaptable.…”

“…Rare event sampling is performed using the skipping sampler, an MCMC algorithm developed for this purpose. The sampler belongs to the class of Metropolis-Hastings (MH) algorithms and, as proved in [30] and demonstrated in the case study of §4., improves performance relative to the random walk Metropolis algorithm. Starting from any state (in the present context, a vector italicu_0∈double-struckRN+L of power disturbances), a proposed new state u_false~∈double-struckRN+L is sampled from a so-called proposal density.…”

“…In [25], a simpler MCMC rare-event sampler was used to build conditional distributions of random disturbances leading to excessive RoCoF at any bus. One limitation in that work was the use of dynamics which neglect system voltage transients and are valid only for small disturbances.…”

A Metropolis-class sampler for targets with non-convex support

“…While also designed for targets with non-convex support, the ghost sampler introduced by the present authors in Moriarty et al (2018) is not general-purpose since it uses knowledge of the geometry of the set A, assuming it is polyhedral.…”

Large fluctuations in locational marginal prices

“…An alternative approach to deal with non-Gaussian fluctuations and more involved price spike structures could be to efficiently sample conditionally on a price spike to have occurred, a problem for which specific Markov chain Monte Carlo (MCMC) methods have been developed, e.g. the Skipping Sampler [42]. In the case of a complicated multi-modal conditional distribution, the large deviations results derived in this paper can be of great help in identifying all the relevant price spikes modes, thus speeding up the MCMC procedure.…”