A data-driven uncertainty modelling and reduction approach for energy optimisation problems

TL;DR

This paper presents a data-driven method for modeling and reducing uncertainty in energy optimization problems by leveraging historical data, PCA, clustering, and kernel density estimation to improve decision-making under uncertainty.

Contribution

It introduces a novel approach combining PCA, clustering, and KDE to generate structured uncertainty sets from limited data for energy optimization.

Findings

Effective reduction of uncertainty dimensionality

Identification of typical uncertainty patterns

Generation of polyhedral uncertainty sets

Abstract

Taking uncertainty into account is crucial when making strategic decisions. To guard against the risk of adverse scenarios, traditional optimisation techniques incorporate uncertainty on the basis of prior knowledge on its distribution. In this paper, we show how, based on a limited amount of historical data, we can generate from a low-dimensional space the underlying structure of uncertainty that could then be used in such optimisation frameworks. To this end, we first exploit the correlation between the sources of uncertainty through a principal component analysis to reduce dimensionality. Next, we perform clustering to reveal the typical uncertainty patterns, and finally we generate polyhedral uncertainty sets based on a kernel density estimation (KDE) of marginal probability functions.