| dc.description.abstract | This thesis attempts to address the problems of sampling rare events in
power system operations, global optimisation studies and in higher dimensions.
Our primary algorithmic tool is the skipping sampler, an existing Metropolisclass algorithm designed to efficiently draw samples from a distribution π,
whose support C, consists of connected components. First, we apply the skipping sampler to a cyber-physical-statistical power system simulation model to
sample power injections from renewable energy sources, conditioned on the activation of frequency-related emergency responses. Such emergency responses,
designed to protect sensitive equipment from deviations in system frequency,
occur infrequently, and can be considered a rare event. We also explore how
the application of large battery energy storage systems can mitigate this risk.
Methodologically, we apply the skipping sampler to the field of global optimisation, where we present the basin hopping with skipping algorithm, which
replaces the perturbation step of the well-known basin hopping routine with
the proposal function of the skipping sampler. Results indicate that, for energy landscapes with well-separated basins, the basin hopping with skipping
algorithm is both more effective and efficient at locating the global minima
than the basin hopping routine. Finally, to address the problem of drawing
samples of rare events in higher dimensions, we propose the Sequential Monte
Carlo with skipping (SMC-S) algorithm, which use the skipping sampler as
the transition kernel of a sequential Monte Carlo framework. To address the
challenge of sampling particle paths which intersect with regions of interest
in high dimensions, the skipping sampler kernel samples the direction particle
paths from a data-driven, empirical distribution, based on the relative positions of particles. Experiments suggest that the SMC-S, using this approach,
outperforms both MCMC and other SMC routines in drawing samples of rare
events in high dimensions. | en_US |
