Time-adaptive quantile-copula for wind power probabilistic forecasting

This paper presents a novel time-adaptive quantile-copula estimator for kernel density forecast and a discussion of how to select the adequate kernels for modeling the different variables of the problem. Results are presented for different case-studies and compared with splines quantile regression (QR). The datasets used are from NREL’s Eastern Wind Integration and Transmission Study, and from a real wind farm located in the Midwest region of the United States. The new probabilistic prediction model is elegant and simple and yet displays advantages over the traditional QR approach. Especially notable is the quality of the results achieved with the time-adaptive version, namely when evaluated in terms of prediction calibration, which is a characteristic that is advantageous for both system operators and wind power producers.

[1]  T. Gneiting Quantiles as optimal point forecasts , 2011 .

[2]  Song-xi Chen,et al.  Beta kernel estimators for density functions , 1999 .

[3]  G.N. Kariniotakis,et al.  Probabilistic Short-term Wind Power Forecasting for the Optimal Management of Wind Generation , 2007, 2007 IEEE Lausanne Power Tech.

[4]  H. Madsen,et al.  From probabilistic forecasts to statistical scenarios of short-term wind power production , 2009 .

[5]  Georges Kariniotakis,et al.  Uncertainty estimation of wind power forecasts: Comparison of Probabilistic Modelling Approaches , 2008 .

[6]  Weifeng Liu,et al.  Kernel Adaptive Filtering: A Comprehensive Introduction , 2010 .

[7]  John Bjørnar Bremnes,et al.  Probabilistic wind power forecasts using local quantile regression , 2004 .

[8]  E. Parzen On Estimation of a Probability Density Function and Mode , 1962 .

[9]  Iain MacGill,et al.  Characterizing future large, rapid changes in aggregated wind power using Numerical Weather Prediction spatial fields , 2009 .

[10]  M. Brower,et al.  Development of Eastern Regional Wind Resource and Wind Plant Output Datasets: March 3, 2008 -- March 31, 2010 , 2009 .

[11]  Henrik Madsen,et al.  Skill forecasting from ensemble predictions of wind power , 2009 .

[12]  Henrik Madsen,et al.  Using quantile regression to extend an existing wind power forecasting system with probabilistic forecasts , 2006 .

[13]  M. Sklar Fonctions de repartition a n dimensions et leurs marges , 1959 .

[14]  Olivier P. Faugeras,et al.  A quantile-copula approach to conditional density estimation , 2007, J. Multivar. Anal..

[15]  P Pinson,et al.  Conditional Prediction Intervals of Wind Power Generation , 2010, IEEE Transactions on Power Systems.

[16]  Taoufik Bouezmarni,et al.  Semiparametric Multivariate Density Estimation for Positive Data Using Copulas , 2007, Comput. Stat. Data Anal..

[17]  Pierre Pinson,et al.  Non‐parametric probabilistic forecasts of wind power: required properties and evaluation , 2007 .

[18]  R. J. Bessa,et al.  Quantile-copula density forecast for wind power uncertainty modeling , 2011, 2011 IEEE Trondheim PowerTech.

[19]  Vladimiro Miranda,et al.  ‘Good’ or ‘bad’ wind power forecasts: a relative concept , 2011 .

[20]  Vladimiro Miranda,et al.  Risk management and optimal bidding for a wind power producer , 2010, IEEE PES General Meeting.

[21]  M. Rosenblatt Remarks on Some Nonparametric Estimates of a Density Function , 1956 .

[22]  Jan Kloppenborg Møller,et al.  ARTICLE IN PRESS Computational Statistics & Data Analysis ( ) – Time-adaptive quantile regression , 2022 .

[23]  C. Gouriéroux,et al.  Non) consistency of the Beta Kernel Estimator for Recovery Rate Distribution , 2006 .

[24]  Georges Kariniotakis,et al.  Advanced strategies for wind power trading in short-term electricity markets , 2008 .

[25]  Henrik Madsen,et al.  Ensemble-based Probabilistic Forecasting at Horns Rev , 2009 .

[26]  Manuel A. Matos,et al.  Comparison of probabilistic and deterministic approaches for setting operating reserve in systems with high penetration of wind power , 2010 .

[27]  Markus Junker,et al.  Elliptical copulas: applicability and limitations , 2003 .

[28]  M A Matos,et al.  Setting the Operating Reserve Using Probabilistic Wind Power Forecasts , 2011, IEEE Transactions on Power Systems.

[29]  M. Wand,et al.  Multivariate plug-in bandwidth selection , 1994 .

[30]  T. Duong,et al.  Multivariate plug-in bandwidth selection with unconstrained pilot bandwidth matrices , 2010 .

[31]  Jordan G. Powers,et al.  A Description of the Advanced Research WRF Version 2 , 2005 .

[32]  G. Powers,et al.  A Description of the Advanced Research WRF Version 3 , 2008 .

[33]  Edward J. Wegman,et al.  Remarks on Some Recursive Estimators of a Probability Density , 1979 .

[34]  David J. Marchette,et al.  On Some Techniques for Streaming Data: A Case Study of Internet Packet Headers , 2003 .

[35]  Vladimiro Miranda,et al.  Wind power forecasting : state-of-the-art 2009. , 2009 .