Energy Systems

, Volume 4, Issue 4, pp 393–417

An effective method for modeling wind power forecast uncertainty

  • Brandon Mauch
  • Jay Apt
  • Pedro M. S. Carvalho
  • Mitchell J. Small
Original Paper


Wind forecasts are an important tool for electric system operators. Proper use of wind power forecasts to make operating decisions must account for the uncertainty associated with the forecast. Data from different regions in the USA with forecasts made by different vendors show the forecast error distribution is strongly dependent on the forecast level of wind power. For low wind power forecast, the forecasts tend to under-predict the actual wind power produced, whereas when the forecast is for high power, the forecast tends to over-predict the actual wind power. Most of the work in this field neglects the influence of wind forecast levels on wind forecast uncertainty and analyzes wind forecast errors as a whole. The few papers that account for this dependence, group wind forecasts by the value of the forecast and fit parametric distributions to actual wind power in each bin of data. In the latter case, different parameters and possibly different distributions are estimated for each data bin. We present a method to model wind power forecast uncertainty as a single closed-form solution using a logit transformation of historical wind power forecast and actual wind power data. Once transformed, the data become close to jointly normally distributed. We show the process of calculating confidence intervals of wind power forecast errors using the jointly normally distributed logit transformed data. This method has the advantage of fitting the entire dataset with five parameters while also providing the ability to make calculations conditioned on the value of the wind power forecast.


Renewable energy Wind power forecasting Uncertainty  Logit-normal distribution 


  1. 1.
    Energy Information Administration (EIA).: Electric power annual 2012 (2012).
  2. 2.
    Wilkes, J., Moccia, J., Drangan, M.: Wind in power: 2011 European wind statistics, European Wind Energy Association Technical Report (2012) online.
  3. 3.
    Ortega-Vazquez, M.A., Kirschen, D.S.: Estimating the spinning reserve requirements in systems with significant wind power generation penetration. IEEE Trans. Power Syst. 24(1), 114–124 (2009)CrossRefGoogle Scholar
  4. 4.
    Bouffard, F., Galiana, F.D.: Stochastic security for operations planning with significant wind power generation. In: 2008 IEEE Power and Energy Society General Meeting—Conversion and Delivery of Electrical Energy in the 21st Century, pp. 1–11 (2008)Google Scholar
  5. 5.
    Doherty, R., O’Malley, M.: A new approach to quantify reserve demand in systems with significant installed wind capacity. IEEE Trans. Power Syst. 20(2), 587–595 (2005)CrossRefGoogle Scholar
  6. 6.
    Hodge, B., Milligan, M.: Wind power forecasting error distributions over multiple timescales. In: 2011 IEEE Power and Energy Society General Meeting, pp. 1–8 (2011)Google Scholar
  7. 7.
    Hodge, B., Florita, A., Orwig, K., Lew, D., Milligan, M.: A comparison of wind power and load forecasting distributions. In: 2012 World Renewable Energy Forum. NREL/CP-5500-54384 (2012).
  8. 8.
    Makarov, Y.V., Loutan, C., Ma, J., de Mello, P.: Operational impacts of wind generation on California power systems. IEEE Trans. Power Syst. 24(2), 1039–1050 (2009)CrossRefGoogle Scholar
  9. 9.
    Lange, M.: On the uncertainty of wind power predictions–analysis of the forecast accuracy and statistical distribution of errors. J. Sol. Energy Eng. 127, 177–184 (2005)CrossRefGoogle Scholar
  10. 10.
    Nielsen, H.A., Madsen, H., Nielsen, T.S.: Using quantile regression to extend an existing wind power forecasting system with probabilistic forecasts. Wind Energy 9(2006), 95–108 (2006)CrossRefGoogle Scholar
  11. 11.
    Bludszuweit, H., Dominguez-Navarro, J.A., Llombart, A.: Statistical analysis of wind power forecast error. IEEE Trans. Power Syst. 23(3), 983–991 (2008)CrossRefGoogle Scholar
  12. 12.
    Luig, A., Bofinger, S., Beyer, H.G.: Analysis of confidence intervals for the prediction of regional wind power output. In: Proceedings of the European Wind Energy Conference, Copenhagen, Denmark, 2–6 June 2001, pp. 725–728Google Scholar
  13. 13.
    Fabbri, A., Gomez San Roman, T., Rivier Abbad, J., Mendez Quezada, V.H.: Assessment of the cost associated with wind generation prediction errors in a liberalized electricity market. IEEE Trans. Power Syst. 20(3), 1440–1446 (2005)CrossRefGoogle Scholar
  14. 14.
    Al-Awami, A.T., El-Sharkawi, M.A.: Statistical characterization of wind power output for a given wind power forecast. In: North American Power Symposium (NAPS), pp. 1–4 (2009)Google Scholar
  15. 15.
    Lau, A., McSharry, P.: Approaches for multi-step density forecasts with applications to aggregated wind power. Ann. Appl. Stat. 4(3), 1311–1341 (2010)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Pinson, P.: Very-short-term probabilistic forecasting of wind power with generalized logit-normal distributions. J. R. Stat. Soc. Ser C (Applied Statistics) 61(4), 555–576 (2012)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Rogers, J., Fink, S., Porter, K.: Examples of wind energy curtailment practices. NREL Subcontract Report. NREL/SR-550-48737 (2010)Google Scholar
  18. 18.
    Wiser, R., Bolinger, M.: DOE 2010 wind technologies market report, Department of Energy. DOE/GO-102011-3322 (2011)Google Scholar
  19. 19.
  20. 20.
    Kehler, J., Ming, H., McMullen, M., Blatchford, J.: ISO perspective and experience with integrating wind power forecasts into operations. In: 2010 IEEE Power and Energy Society General Meeting, pp. 1–5 (2010)Google Scholar
  21. 21.
  22. 22.
    Makarov, Y.V., Guttromson, R.T., Huang, Z., Subbarao, K., Etingov, P.V., Chakrabarti, B.B., Ma, J.: Incorporating wind generation and load forecast uncertainties into power grid operations. Report PNNL-19189. PNNL, (2010)Google Scholar
  23. 23.
    Frederic, P., Lad, F.: Two moments of the logitnormal distribution. Commun. Stat. Simul Comput. 37(7), 1263–1269 (2008)MathSciNetCrossRefMATHGoogle Scholar
  24. 24.
    Focken, U., Lange, M., Mönnich, K., Waldl, H.P., Beyer, H.G., Luig, A.: Short-term prediction of the aggregated power output of wind farms—a statistical analysis of the reduction of the prediction error by spatial smoothing effects. J. Wind Eng. Ind. Aerodyn. 90, 231–246 (2002)CrossRefGoogle Scholar
  25. 25.
    Giebel, G., Sørensen, P., Holttinen, H.: Forecast error of aggregated wind power. TradeWind Deliverable Report. Risø-I-2567(EN) (2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Brandon Mauch
    • 1
    • 2
  • Jay Apt
    • 1
    • 4
  • Pedro M. S. Carvalho
    • 2
  • Mitchell J. Small
    • 1
    • 3
  1. 1.Department of Engineering and Public PolicyCarnegie Mellon UniversityPittsburghUSA
  2. 2.Department of Electrical and Computer Engineering, Instituto Superior TecnicoTechnical University of LisbonLisbonPortugal
  3. 3.Department of Civil and Environmental EngineeringCarnegie Mellon UniversityPittsburghUSA
  4. 4.Tepper School of BusinessCarnegie Mellon UniversityPittsburghUSA

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