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A stochastic time-series model for solar irradiation

Author

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  • Larsson, Karl
  • Green, Rikard
  • Benth, Fred Espen

Abstract

We propose a novel stochastic time series model able to explain the stylized features of daily irradiation level data in 5 cities in Germany. The model is suitable for applications to risk management of photovoltaic power production in renewable energy markets. The suggested dynamics is a low-order autoregressive time series with seasonal level given by an atmospheric clear-sky model. Moreover, we detect a skewness property in the residuals which we explain by a winter–summer regime switch. The stochastic variance is modeled by a seasonally varying GARCH-dynamics. The winter and summer standardized residuals are proposed to be a Gaussian mixture model to capture the bimodal distributions. We estimate the model on the observed data, and perform a validation study. An application to energy markets studying the production at risk for a PV-producer is presented.

Suggested Citation

  • Larsson, Karl & Green, Rikard & Benth, Fred Espen, 2023. "A stochastic time-series model for solar irradiation," Energy Economics, Elsevier, vol. 117(C).
    • Handle: RePEc:eee:eneeco:v:117:y:2023:i:c:s0140988322005503
    DOI: 10.1016/j.eneco.2022.106421
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    References listed on IDEAS

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    1. Sean D. Campbell & Francis X. Diebold, 2005. "Weather Forecasting for Weather Derivatives," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 6-16, March.
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    3. Laura Casula & Guglielmo D’Amico & Giovanni Masala & Filippo Petroni, 2020. "Performance estimation of photovoltaic energy production," Letters in Spatial and Resource Sciences, Springer, vol. 13(3), pages 267-285, December.
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    6. Engle, Robert F & Gonzalez-Rivera, Gloria, 1991. "Semiparametric ARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(4), pages 345-359, October.
    7. Fred E. Benth & Troels S. Christensen & Victor Rohde, 2021. "Multivariate continuous-time modeling of wind indexes and hedging of wind risk," Quantitative Finance, Taylor & Francis Journals, vol. 21(1), pages 165-183, January.
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    9. Kaldellis, John K. & Kapsali, Marina & Kavadias, Kosmas A., 2014. "Temperature and wind speed impact on the efficiency of PV installations. Experience obtained from outdoor measurements in Greece," Renewable Energy, Elsevier, vol. 66(C), pages 612-624.
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    More about this item

    Keywords

    Solar; Time-series; Photovoltaic; Renewable; Energy; Risk;
    All these keywords.

    JEL classification:

    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • Q4 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Energy

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