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Using Conditional Kernel Density Estimation for Wind Power Density Forecasting


  • Jooyoung Jeon
  • James W. Taylor


Of the various renewable energy resources, wind power is widely recognized as one of the most promising. The management of wind farms and electricity systems can benefit greatly from the availability of estimates of the probability distribution of wind power generation. However, most research has focused on point forecasting of wind power. In this article, we develop an approach to producing density forecasts for the wind power generated at individual wind farms. Our interest is in intraday data and prediction from 1 to 72 hours ahead. We model wind power in terms of wind speed and wind direction. In this framework, there are two key uncertainties. First, there is the inherent uncertainty in wind speed and direction, and we model this using a bivariate vector autoregressive moving average-generalized autoregressive conditional heteroscedastic (VARMA-GARCH) model, with a Student t error distribution, in the Cartesian space of wind speed and direction. Second, there is the stochastic nature of the relationship of wind power to wind speed (described by the power curve), and to wind direction. We model this using conditional kernel density (CKD) estimation, which enables a nonparametric modeling of the conditional density of wind power. Using Monte Carlo simulation of the VARMA-GARCH model and CKD estimation, density forecasts of wind speed and direction are converted to wind power density forecasts. Our work is novel in several respects: previous wind power studies have not modeled a stochastic power curve; to accommodate time evolution in the power curve, we incorporate a time decay factor within the CKD method; and the CKD method is conditional on a density, rather than a single value. The new approach is evaluated using datasets from four Greek wind farms.

Suggested Citation

  • Jooyoung Jeon & James W. Taylor, 2012. "Using Conditional Kernel Density Estimation for Wind Power Density Forecasting," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 66-79, March.
  • Handle: RePEc:taf:jnlasa:v:107:y:2012:i:497:p:66-79
    DOI: 10.1080/01621459.2011.643745

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    Cited by:

    1. Zhang, Yao & Wang, Jianxue & Wang, Xifan, 2014. "Review on probabilistic forecasting of wind power generation," Renewable and Sustainable Energy Reviews, Elsevier, vol. 32(C), pages 255-270.
    2. Song, Zhe & Jiang, Yu & Zhang, Zijun, 2014. "Short-term wind speed forecasting with Markov-switching model," Applied Energy, Elsevier, vol. 130(C), pages 103-112.
    3. Kusiak, Andrew & Zhang, Zijun & Verma, Anoop, 2013. "Prediction, operations, and condition monitoring in wind energy," Energy, Elsevier, vol. 60(C), pages 1-12.
    4. Ashish Arora & Michelle Gittelman & Sarah Kaplan & John Lynch & Will Mitchell & Nicolaj Siggelkow & Mei Li & Ying Lin & Shuai Huang & Craig Crossland, 2016. "The use of sparse inverse covariance estimation for relationship detection and hypothesis generation in strategic management," Strategic Management Journal, Wiley Blackwell, vol. 37(1), pages 86-97, January.
    5. Georgios Anastasiades & Patrick McSharry, 2013. "Quantile Forecasting of Wind Power Using Variability Indices," Energies, MDPI, Open Access Journal, vol. 6(2), pages 1-34, February.
    6. Brenda López Cabrera & Franziska Schulz, 2016. "Time-Adaptive Probabilistic Forecasts of Electricity Spot Prices with Application to Risk Management," SFB 649 Discussion Papers SFB649DP2016-035, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    7. Arora, Siddharth & Taylor, James W., 2016. "Forecasting electricity smart meter data using conditional kernel density estimation," Omega, Elsevier, vol. 59(PA), pages 47-59.
    8. Xydas, Erotokritos & Qadrdan, Meysam & Marmaras, Charalampos & Cipcigan, Liana & Jenkins, Nick & Ameli, Hossein, 2017. "Probabilistic wind power forecasting and its application in the scheduling of gas-fired generators," Applied Energy, Elsevier, vol. 192(C), pages 382-394.
    9. Gallego-Castillo, Cristobal & Bessa, Ricardo & Cavalcante, Laura & Lopez-Garcia, Oscar, 2016. "On-line quantile regression in the RKHS (Reproducing Kernel Hilbert Space) for operational probabilistic forecasting of wind power," Energy, Elsevier, vol. 113(C), pages 355-365.
    10. Taylor, James W., 2017. "Probabilistic forecasting of wind power ramp events using autoregressive logit models," European Journal of Operational Research, Elsevier, vol. 259(2), pages 703-712.
    11. Fresoli, Diego E. & Ruiz, Esther, 2016. "The uncertainty of conditional returns, volatilities and correlations in DCC models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 170-185.
    12. Antonio Bracale & Pasquale De Falco, 2015. "An Advanced Bayesian Method for Short-Term Probabilistic Forecasting of the Generation of Wind Power," Energies, MDPI, Open Access Journal, vol. 8(9), pages 1-22, September.
    13. repec:eee:rensus:v:81:y:2018:i:p2:p:1953-1965 is not listed on IDEAS
    14. repec:eee:intfor:v:34:y:2018:i:1:p:45-63 is not listed on IDEAS
    15. Taylor, James W. & Jeon, Jooyoung, 2015. "Forecasting wind power quantiles using conditional kernel estimation," Renewable Energy, Elsevier, vol. 80(C), pages 370-379.
    16. Giwhyun Lee & Yu Ding & Marc G. Genton & Le Xie, 2015. "Power Curve Estimation With Multivariate Environmental Factors for Inland and Offshore Wind Farms," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 56-67, March.
    17. Xinxin Zhu & Marc Genton & Yingzhong Gu & Le Xie, 2014. "Space-time wind speed forecasting for improved power system dispatch," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(1), pages 1-25, March.
    18. Ziel, Florian & Croonenbroeck, Carsten & Ambach, Daniel, 2016. "Forecasting wind power – Modeling periodic and non-linear effects under conditional heteroscedasticity," Applied Energy, Elsevier, vol. 177(C), pages 285-297.
    19. Haben, Stephen & Giasemidis, Georgios, 2016. "A hybrid model of kernel density estimation and quantile regression for GEFCom2014 probabilistic load forecasting," International Journal of Forecasting, Elsevier, vol. 32(3), pages 1017-1022.
    20. Jeon, Jooyoung & Taylor, James W., 2016. "Short-term density forecasting of wave energy using ARMA-GARCH models and kernel density estimation," International Journal of Forecasting, Elsevier, vol. 32(3), pages 991-1004.
    21. Xinxin Zhu & Marc Genton & Yingzhong Gu & Le Xie, 2014. "Rejoinder on: Space-time wind speed forecasting for improved power system dispatch," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(1), pages 45-50, March.
    22. Arora Siddharth & Little Max A. & McSharry Patrick E., 2013. "Nonlinear and nonparametric modeling approaches for probabilistic forecasting of the US gross national product," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 17(4), pages 395-420, September.
    23. repec:eee:energy:v:135:y:2017:i:c:p:833-850 is not listed on IDEAS
    24. Soukissian, Takvor H. & Karathanasi, Flora E., 2017. "On the selection of bivariate parametric models for wind data," Applied Energy, Elsevier, vol. 188(C), pages 280-304.
    25. de Almeida, Daniel & Hotta, Luiz K. & Ruiz, Esther, 2018. "MGARCH models: Trade-off between feasibility and flexibility," International Journal of Forecasting, Elsevier, vol. 34(1), pages 45-63.

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