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Space-Time Trajectories of Wind Power Generation: Parametrized Precision Matrices Under a Gaussian Copula Approach

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Modeling and Stochastic Learning for Forecasting in High Dimensions

Part of the book series: Lecture Notes in Statistics ((LNSP,volume 217))

Abstract

Emphasis is placed on generating space-time trajectories of wind power generation, consisting of paths sampled from high-dimensional joint predictive densities, describing wind power generation at a number of contiguous locations and successive lead times. A modelling approach taking advantage of the sparsity of precision matrices is introduced for the description of the underlying space-time dependence structure. The proposed parametrization of the dependence structure accounts for important process characteristics such as lead-time-dependent conditional precisions and direction-dependent cross-correlations. Estimation is performed in a maximum likelihood framework. Based on a test case application in Denmark, with spatial dependencies over 15 areas and temporal ones for 43 hourly lead times (hence, for a dimension of n = 645), it is shown that accounting for space-time effects is crucial for generating skilful trajectories.

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Acknowledgements

The authors were partly supported by the EU Commission through the project SafeWind (ENK7-CT2008-213740), which is hereby acknowledged. Pierre Pinson was additionally supported by the Danish Strategic Research Council under ‘5s’–Future Electricity Markets (12-132636/DSF). The authors are grateful to Energinet.dk, the transmission system operator in Denmark, for providing the observed power data used in this paper, and to ENFOR A/S for generating the point forecasts of wind power generation used as input. Finally, reviewers and editors are acknowledged for their comments and suggestions on an earlier version of the manuscript.

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Authors and Affiliations

  1. Siemens Wind Power, Borupvang 9, 2750, Ballerup, Danmark

    Julija Tastu

  2. Technical University of Denmark, Elektrovej 325-058, 2800 Kgs., Lyngby, Danmark

    Pierre Pinson

  3. Technical University of Denmark, Matematiktorvet 322-218, 2800 Kgs., Lyngby, Danmark

    Henrik Madsen

Authors
  1. Julija Tastu
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  2. Pierre Pinson
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  3. Henrik Madsen
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Corresponding author

Correspondence to Julija Tastu .

Editor information

Editors and Affiliations

  1. Department of Statistics, University Joseph Fourier, Grenoble, France

    Anestis Antoniadis

  2. Laboratoire de Mathématiques, Université Paris-Sud, Orsay Cedex, France

    Jean-Michel Poggi

  3. Electricité de France R & D, OSIRIS, Clamart Cedex, France

    Xavier Brossat

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Tastu, J., Pinson, P., Madsen, H. (2015). Space-Time Trajectories of Wind Power Generation: Parametrized Precision Matrices Under a Gaussian Copula Approach. In: Antoniadis, A., Poggi, JM., Brossat, X. (eds) Modeling and Stochastic Learning for Forecasting in High Dimensions. Lecture Notes in Statistics(), vol 217. Springer, Cham. https://doi.org/10.1007/978-3-319-18732-7_14

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