Forecasting the intermittent solar resource: a course

Course UE14, Mines Paris – PSL, 2026 · taught in French · slides and Python/Matlab practicals

How do you forecast solar irradiance one hour ahead, and how do you know whether your forecast is any good? This course answers both questions from scratch, on ten years of real hourly measurements from Ajaccio (Corsica, 1998–2007), and ends with the methods used in current research: clear-sky index, forecastability, NICE metrics, Extreme Learning Machines, online learning and frugal AI.

Course outline

1. Why forecast solar power? Grid integration, irradiance vs irradiation vs PV output, the Ajaccio dataset.
2. Solar radiation: direct and diffuse components, attenuation in the atmosphere, sun position, the double (daily and annual) seasonality of GHI.
3. Time series and forecasting: components and decomposition, horizons and time steps, predictable part vs error, a worked AR(1) example.
4. Clear sky and clear-sky index: the Solis clear-sky model, two ways to stationarise (difference or ratio), is the CSI stationary?, site variability with the stochastic coefficient of variation (sCV) and forecastability F, step-by-step preprocessing.
5. Autoregressive models and least squares: from AR(p) to linear regression, building X and y by hand, ordinary least squares and its geometric meaning, train/validation/test split, choosing p with ACF, PACF, filter or wrapper approaches, AIC/BIC.
6. Evaluation, ELM and online learning: reference models (persistence, smart persistence), nMBE, nRMSE, skill score and NICE^Σ, day-only vs day-and-night scores, Extreme Learning Machines (principle, neurons, random draws, sin/cos time encoding), AR vs ELM, sliding-window online learning, frugality.

What students take away

• A forecast is only useful if it beats a reference: always report persistence and smart persistence.
• Remove or encode the deterministic solar cycle before learning, and state how (difference, ratio, or time encoding).
• Choose model complexity from data you have not tested on; report the protocol (day only or day and night).
• A smaller model that is refreshed often can rival a larger one: frugality is a design choice.

Research behind the course

Each chapter rests on published work by the author and colleagues: - C. Voyant et al., Machine learning methods for solar radiation forecasting: a review, Renewable Energy, 2017 · doi:10.1016/j.renene.2016.12.095 - C. Voyant et al., Benchmarks for solar radiation time series forecasting, Renewable Energy, 2022 · doi:10.1016/j.renene.2022.04.065 - C. Voyant et al., NICE^k metrics, Sustainable Energy Technologies and Assessments, 2025 · doi:10.1016/j.seta.2025.104588 · guide - C. Voyant et al., Stochastic coefficient of variation: variability and forecastability of solar irradiance, Renewable Energy, 2026 · doi:10.1016/j.renene.2025.123913 - C. Voyant et al., On the importance of clearsky model in short-term solar radiation forecasting, Solar Energy, 2025 · doi:10.1016/j.solener.2025.113490 - C. Voyant et al., Symmetry-constrained forecasting of periodically correlated energy processes, Applied Mathematical Modelling, 2026 · doi:10.1016/j.apm.2026.116988

Open code to go further: PV_ELM_pred (ELM benchmark), cyclostationary persistence, Make_Stationary.

How to cite this course

Voyant, C. (2026). Prévision de la ressource solaire intermittente [Forecasting the intermittent solar resource]. Course UE14, Mines Paris – PSL. https://cyrilvoyant.github.io/teaching/solar-forecasting-course.html

When you reuse a method from the course, please also cite the corresponding article above.

Slides are available to students of the course. For other uses, contact the author through the author profile.