Ellipsoidal Prediction Regions for Multivariate Uncertainty Characterization

TL;DR

This paper introduces a systematic framework for generating and evaluating ellipsoidal prediction regions to better capture multivariate dependencies in power system forecasting, improving decision-making under uncertainty.

Contribution

It proposes a novel method to create and assess ellipsoidal prediction regions with predefined probability and minimal volume, addressing a gap in multivariate uncertainty quantification.

Findings

The proposed skill score effectively evaluates ellipsoidal prediction quality.

Application to wind, PV, and price data demonstrates improved calibration and sharpness.

The framework enhances multivariate uncertainty representation for operational decision-making.

Abstract

While substantial advances are observed in probabilistic forecasting for power system operation and electricity market applications, most approaches are still developed in a univariate framework. This prevents from informing about the interdependence structure among locations, lead times and variables of interest. Such dependencies are key in a large share of operational problems involving renewable power generation, load and electricity prices for instance. The few methods that account for dependencies translate to sampling scenarios based on given marginals and dependence structures. However, for classes of decision-making problems based on robust, interval chance-constrained optimization, necessary inputs take the form of polyhedra or ellipsoids. Consequently, we propose a systematic framework to readily generate and evaluate ellipsoidal prediction regions, with predefined probability and minimum volume. A skill score is proposed for quantitative assessment of the quality of prediction ellipsoids. A set of experiments is used to illustrate the discrimination ability of the proposed scoring rule for misspecification of ellipsoidal prediction regions. Application results based on three datasets with wind, PV power and electricity prices, allow us to assess the skill of the resulting ellipsoidal prediction regions, in terms of calibration, sharpness and overall skill.