Ellipsoidal prediction regions for multivariate uncertainty characterization

Faranak Golestaneh*, Pierre Pinson, Rasoul Azizipanah-Abarghooee , Hoay Beng Gooi

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

84 Downloads (Pure)

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 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 multivariate prediction regions rather than scenarios. The current literature is at very primitive stage of characterizing multivariate prediction regions to be employed in these classes of optimization problems. To address this issue, we introduce a new class of multivariate forecasts which form as multivariate ellipsoids for non-Gaussian variables. We propose a data-driven systematic framework to readily generate and evaluate ellipsoidal prediction regions, with predefined probability guarantees and minimum conservativeness. 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 potential 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.
Original languageEnglish
JournalI E E E Transactions on Power Systems
Volume33
Issue number4
Pages (from-to)4519-4530
Number of pages12
ISSN0885-8950
DOIs
Publication statusPublished - 2018

Keywords

  • Probabilistic forecasting
  • Uncertainty sets
  • Ellipsoids
  • Robust optimization
  • Chance-constrained optimization

Fingerprint Dive into the research topics of 'Ellipsoidal prediction regions for multivariate uncertainty characterization'. Together they form a unique fingerprint.

Cite this