Space-Time Trajectories of Wind Power Generation: Parametrized Precision Matrices Under a Gaussian Copula Approach
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.
KeywordsLead Time Wind Power Dependence Structure Copula Function Conditional Correlation
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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