On-line quantile regression in the RKHS (Reproducing Kernel Hilbert Space) for operational probabilistic forecasting of wind power

Wind power probabilistic forecast is being used as input in several decision-making problems, such as stochastic unit commitment, operating reserve setting and electricity market bidding. This work introduces a new on-line quantile regression model based on the Reproducing Kernel Hilbert Space (RKHS) framework. Its application to the field of wind power forecasting involves a discussion on the choice of the bias term of the quantile models, and the consideration of the operational framework in order to mimic real conditions. Benchmark against linear and splines quantile regression models was performed for a real case study during a 18 months period. Model parameter selection was based on k-fold crossvalidation. Results showed a noticeable improvement in terms of calibration, a key criterion for the wind power industry. Modest improvements in terms of Continuous Ranked Probability Score (CRPS) were also observed for prediction horizons between 6 and 20 h ahead.

[1]  Ginés Rubio,et al.  Kernel Methods Applied to Time Series Forecasting , 2007, IWANN.

[2]  Pierre Pinson,et al.  Optimal Offering Strategies for Wind Power in Energy and Primary Reserve Markets , 2016, IEEE Transactions on Sustainable Energy.

[3]  Jooyoung Jeon,et al.  Using Conditional Kernel Density Estimation for Wind Power Density Forecasting , 2012 .

[4]  Bernhard Schölkopf,et al.  A tutorial on support vector regression , 2004, Stat. Comput..

[5]  Cristobal Gallego-Castillo,et al.  A review on the recent history of wind power ramp forecasting , 2015 .

[6]  Shie Mannor,et al.  The kernel recursive least-squares algorithm , 2004, IEEE Transactions on Signal Processing.

[7]  V. Miranda,et al.  Wind power forecasting uncertainty and unit commitment , 2011 .

[8]  R. Tibshirani,et al.  Generalized additive models for medical research , 1986, Statistical methods in medical research.

[9]  Ricardo J. Bessa,et al.  Wind power probabilistic forecast in the Reproducing Kernel Hilbert Space , 2016, 2016 Power Systems Computation Conference (PSCC).

[10]  R. J. Bessa,et al.  Reserve Setting and Steady-State Security Assessment Using Wind Power Uncertainty Forecast: A Case Study , 2012, IEEE Transactions on Sustainable Energy.

[11]  Gregor Giebel,et al.  The State-Of-The-Art in Short-Term Prediction of Wind Power. A Literature Overview , 2003 .

[12]  Vladimiro Miranda,et al.  Time-adaptive quantile-copula for wind power probabilistic forecasting , 2012 .

[13]  Weifeng Liu,et al.  Kernel least mean square algorithm with constrained growth , 2009, Signal Process..

[14]  Henrik Ohlsson,et al.  A multiple quantile regression approach to the wind, solar, and price tracks of GEFCom2014 , 2016 .

[15]  Patrick E. McSharry,et al.  Quantile Forecasting of Wind Power Using Variability Indices , 2013 .

[16]  Jianxue Wang,et al.  Review on probabilistic forecasting of wind power generation , 2014 .

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

[18]  Pierre Pinson,et al.  An Integrated Multiperiod OPF Model With Demand Response and Renewable Generation Uncertainty , 2016, IEEE Transactions on Smart Grid.

[19]  Yao Zhang,et al.  Probabilistic wind power forecasting based on logarithmic transformation and boundary kernel , 2015 .

[20]  Narendra Ahuja,et al.  Online learning with kernels: Overcoming the growing sum problem , 2012, 2012 IEEE International Workshop on Machine Learning for Signal Processing.

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

[22]  G. Nagy,et al.  GEFCom2014: Probabilistic solar and wind power forecasting using a generalized additive tree ensemble approach , 2016 .

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

[24]  Stefano Alessandrini,et al.  A novel application of an analog ensemble for short-term wind power forecasting , 2015 .

[25]  H. Hersbach.  Decomposition of the Continuous Ranked Probability Score for Ensemble Prediction Systems , 2000 .

[26]  Vladimiro Miranda,et al.  Wind Power Trading Under Uncertainty in LMP Markets , 2012, IEEE Transactions on Power Systems.

[27]  Alex J. Cannon.  Quantile regression neural networks: Implementation in R and application to precipitation downscaling , 2011, Comput. Geosci..

[28]  Pierre Pinson,et al.  Global Energy Forecasting Competition 2012 , 2014 .

[29]  I. González-Aparicio,et al.  Impact of wind power uncertainty forecasting on the market integration of wind energy in Spain , 2015 .

[30]  Alexander J. Smola,et al.  Online learning with kernels , 2001, IEEE Transactions on Signal Processing.

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

[32]  Kurt Hornik,et al.  kernlab - An S4 Package for Kernel Methods in R , 2004 .

[33]  Alexander J. Smola,et al.  Nonparametric Quantile Estimation , 2006, J. Mach. Learn. Res..

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

[35]  Carlos Moreira,et al.  Handling renewable energy variability and uncertainty in power systems operation , 2014 .

[36]  Alberto Prieto,et al.  Computational and ambient intelligence , 2009, Neurocomputing.

[37]  N. Menemenlis,et al.  Methodologies to Determine Operating Reserves Due to Increased Wind Power , 2012, IEEE Transactions on Sustainable Energy.

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

[39]  N. D. Hatziargyriou,et al.  Probabilistic Wind Power Forecasting Using Radial Basis Function Neural Networks , 2012, IEEE Transactions on Power Systems.

[40]  Feng Gao,et al.  Sparse online warped Gaussian process for wind power probabilistic forecasting , 2013 .

[41]  Jianxue Wang,et al.  K-nearest neighbors and a kernel density estimator for GEFCom2014 probabilistic wind power forecasting , 2016 .

[42]  P. Pinson,et al.  Very‐short‐term probabilistic forecasting of wind power with generalized logit–normal distributions , 2012 .

[43]  Badong Chen,et al.  Quantized Kernel Least Mean Square Algorithm , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[44]  H. Madsen,et al.  Influence of local wind speed and direction on wind power dynamics - Application to offshore very short-term forecasting , 2011 .