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Improved Probabilistic Wind Power Forecasts with an Inverse Power Curve Transformation and Censored Regression


  • Jakob W. Messner


  • Achim Zeileis


  • Jochen Broecker


  • Georg J. Mayr



Forecasting wind power is an important part of a successful integration of wind power into the power grid. Forecasts with lead times longer than 6 hours are generally made by using statistical methods to postprocess forecasts from numerical weather prediction systems. Two major problems that complicate this approach are the nonlinear relationship between wind speed and power production and the limited range of power production between zero and nominal power of the turbine. In practice, the nonlinearity is often tackled by using nonlinear nonparametric regression methods while the limited range is typically not addressed explicitly. However, such an approach ignores valuable and readily available information: the power curve of the turbine's manufacturer. Much of the nonlinearity can be directly accounted for by transforming the observed power production into wind speed via the inverse power curve so that simpler linear regression models can be used. Furthermore, the limited range of the transformed power production can be easily exploited by adopting censored regression models. In this study, we evaluate quantile forecasts from a range of methods: (a) using parametric and nonparametric models, (b) with and without the proposed inverse power curve transformation, and (c) with and without censoring. The results show that with our inverse (power-to-wind) transformation, simpler linear regression models with censoring perform equally or better than nonlinear models with or without the frequently used wind-to-power transformation.

Suggested Citation

  • Jakob W. Messner & Achim Zeileis & Jochen Broecker & Georg J. Mayr, 2013. "Improved Probabilistic Wind Power Forecasts with an Inverse Power Curve Transformation and Censored Regression," Working Papers 2013-01, Faculty of Economics and Statistics, University of Innsbruck.
  • Handle: RePEc:inn:wpaper:2013-01

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    References listed on IDEAS

    1. Peng, Limin & Huang, Yijian, 2008. "Survival Analysis With Quantile Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 637-649, June.
    2. Thordis L. Thorarinsdottir & Tilmann Gneiting, 2010. "Probabilistic forecasts of wind speed: ensemble model output statistics by using heteroscedastic censored regression," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 173(2), pages 371-388.
    3. Powell, James L., 1986. "Censored regression quantiles," Journal of Econometrics, Elsevier, vol. 32(1), pages 143-155, June.
    4. Lin, Guixian & He, Xuming & Portnoy, Stephen, 2012. "Quantile regression with doubly censored data," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 797-812.
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    Cited by:

    1. repec:gam:jeners:v:10:y:2017:i:9:p:1402-:d:111989 is not listed on IDEAS
    2. Iversen, Emil B. & Morales, Juan M. & Møller, Jan K. & Madsen, Henrik, 2016. "Short-term probabilistic forecasting of wind speed using stochastic differential equations," International Journal of Forecasting, Elsevier, vol. 32(3), pages 981-990.

    More about this item


    wind power; probabilistic forecasting; power curve transformation; censored regression; quantile regression;

    JEL classification:

    • Q42 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Energy - - - Alternative Energy Sources
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods


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