Multiscale Markov models with random transitions for energy demand management

Abstract

A stochastic model is proposed for fluctuations in electricity demand that are associated with individual user's consumption choices. Electricity consumption is modeled as a function of social activities of consumers. The dynamics of these activities are modeled as a Markov chain. Markov models are simplified models that capture the stochasticity to the unmodeled dynamics typically attributed to white noise disturbances. Additional uncertainties are also accrued in the process of calibrating the transition rates of these chains from finite samples. In this paper, these uncertainties are accounted for by considering random transition matrices. Such formalism can also reflect the fluctuations in the environment in which the chain evolves. We also discuss a third interpretation where uncertain transitions, in a multiscale setting, reflect the fine-resolution information that is lost in the process of state aggregation. As numerical demonstration, we study the activity modeling of a heterogeneous population. Activity uncertainties are propagated onto the energy demand. Demand uncertainties, in turn, are propagated onto a global performance metric. Such uncertainty management framework bridges between the actual drivers of the energy consumption and the system health. Subsequent decisions can be robustly supported based on the results of the quantitative model proposed in this paper.