Stochastic coefficient of variation: Assessing the variability and forecastability of solar irradiance

Cyril Voyant (), Alan Julien, Milan Despotovic, Gilles Notton, Luis Antonio Garcia-Gutierrez (), Claudio Francesco Nicolosi, Philippe Blanc () and Jamie Bright
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Cyril Voyant: Mines Paris - PSL (École nationale supérieure des mines de Paris) - PSL - Université Paris Sciences et Lettres
Alan Julien: O.I.E. - Centre Observation, Impacts, Énergie - Mines Paris - PSL (École nationale supérieure des mines de Paris) - PSL - Université Paris Sciences et Lettres
Milan Despotovic: University of Kragujevac
Gilles Notton: SPE - Laboratoire « Sciences pour l’Environnement » (UMR CNRS 6134 SPE) - CNRS - Centre National de la Recherche Scientifique - Università di Corsica Pasquale Paoli [Université de Corse Pascal Paoli]
Luis Antonio Garcia-Gutierrez: Università di Corsica Pasquale Paoli [Université de Corse Pascal Paoli], SPE - Laboratoire « Sciences pour l’Environnement » (UMR CNRS 6134 SPE) - CNRS - Centre National de la Recherche Scientifique - Università di Corsica Pasquale Paoli [Université de Corse Pascal Paoli]
Claudio Francesco Nicolosi: Unict - Università degli studi di Catania = University of Catania, SPE - Laboratoire « Sciences pour l’Environnement » (UMR CNRS 6134 SPE) - CNRS - Centre National de la Recherche Scientifique - Università di Corsica Pasquale Paoli [Université de Corse Pascal Paoli]
Philippe Blanc: Alcatel Alenia Space [Cannes] - Alcatel Space, TAS - Thales Alenia Space [Toulouse] - THALES [France], CEP - Centre Énergétique et Procédés - Mines Paris - PSL (École nationale supérieure des mines de Paris) - PSL - Université Paris Sciences et Lettres, O.I.E. - Centre Observation, Impacts, Énergie - Mines Paris - PSL (École nationale supérieure des mines de Paris) - PSL - Université Paris Sciences et Lettres
Jamie Bright: UKPN - UK Power Networks

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Abstract: A novel methodology for short-term energy forecasting using an Extreme Learning Machine ($\mathtt{ELM}$) is proposed. Using six years of hourly data collected in Corsica (France) from multiple energy sources (solar, wind, hydro, thermal, bioenergy, and imported electricity), our approach predicts both individual energy outputs and total production (including imports, which closely follow energy demand, modulo losses) through a Multi-Input Multi-Output ($\mathtt{MIMO}$) architecture. To address non-stationarity and seasonal variability, sliding window techniques and cyclic time encoding are incorporated, enabling dynamic adaptation to fluctuations. The $\mathtt{ELM}$ model significantly outperforms persistence-based forecasting, particularly for solar and thermal energy, achieving an $\mathtt{nRMSE}$ of $17.9\%$ and $5.1\%$, respectively, with $\mathtt{R^2} > 0.98$ (1-hour horizon). The model maintains high accuracy up to five hours ahead, beyond which renewable energy sources become increasingly volatile. While $\mathtt{MIMO}$ provides marginal gains over Single-Input Single-Output ($\mathtt{SISO}$) architectures and offers key advantages over deep learning methods such as $\mathtt{LSTM}$, it provides a closed-form solution with lower computational demands, making it well-suited for real-time applications, including online learning. Beyond predictive accuracy, the proposed methodology is adaptable to various contexts and datasets, as it can be tuned to local constraints such as resource availability, grid characteristics, and market structures.

Keywords: Machine Learning (cs.LG); Data Analysis; Statistics and Probability (physics.data-an); FOS: Computer and information sciences; FOS: Physical sciences (search for similar items in EconPapers)
Date: 2026-01
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Published in Renewable Energy, 2026, 256, pp.123913. ⟨10.1016/j.renene.2025.123913⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-05296372

DOI: 10.1016/j.renene.2025.123913

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