A statistical analysis of the reduction of the wind power prediction error by spatial smoothing effects

We discuss the accuracy of the prediction of the aggregated power output of wind farms distributed over given regions. Our forecasting procedure provides the expected power output for a time horizon up to 48 hours ahead. It is based on the large scale wind field prediction which is generated operationally by the German weather service. Our investigation focuses on the statistical analysis of the power prediction error of an ensemble of wind farms compared to single sites. Due to spatial smoothing effects the relative prediction error decreases considerably. Using measurements of the power output of 30 wind farms in Germany we find that this reduction depends on the size of the region. To generalize these findings an analytical model based on the spatial correlation function of the prediction error is derived to describe the statistical characteristics of arbitrary configurations of wind farms. This analysis shows that the magnitude of the error reduction only weakly depends on the number of sites and is mainly determined by the size of the region. Towards a correction of systematic prediction errors an analysis of the temporal structure of the forecast error is performed. For this purpose the correlation of the errors for consecutive forecasts is analyzed for single sites and ensembles.