Affine Arithmetic-Based Reliable Estimation of Transition State Boundaries for Uncertain Markov Chains

Abstract

Markov Chain-based models have been extensively used in numerous power system applications, ranging from decision support systems, to reliability and resilience analysis. The state transition probabilities, which determine the overall model dynamics, have been traditionally described by deterministic values. This common assumption might not be suitable for analyzing modern power systems, where large number of complex and correlated uncertainties could significantly affect the correct evaluation and estimation of both model parameters and model outputs. In addressing that problem, this paper advocates the role of affine arithmetic, by proposing a reliable framework for Markov Chain transient analysis in the presence of data uncertainties. The main idea is to represent the uncertainties in state transition probabilities through affine forms, which then allow to apply affine arithmetic-based operators and to identify the corresponding transient state probabilities. Two case studies are presented and discussed, in order to demonstrate the effectiveness of the proposed methodology in practical power system problems and applications.