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Geostatistical analysis of installed wind power production data

Gafa Panagiota

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Summary

In recent years, an increasing number of countries are attempting to reduce their reliance on fossil fuels and enhance the contribution of renewable energy sources in their energy production plans. Renewable energy sources include wind, sun, geothermal sources and tidal energy. Wind is the most common renewable energy source, both for domestic and industrial use. Hence, the prediction of wind speed and aeolian energy potential is an important topic of research. This thesis focuses on the investigation of the variability of aeolian energy production in the Netherlands. Spatial and temporal models for aeolian energy are defined and estimated using geostatistical and time-series forecasting methods respectively. The available data are average daily measurements of aeolian power produced by 46 stations distributed across the Netherlands. The data are recorded during the six-year time time period from 2001 until 2006. Most of the available studies in the literature analyse wind speed data. In this approach, the wind speed is first predicted at unmeasured points in space or time. Then, the respective aeolian power is estimated using a standard ``power curve'', which relates the wind speed to power production. In contrast, the models investigated herein (both the geostatistical models for spatial prediction and the time series models for forecasting) are directly based on data of aeolian power production. Wind speed typically depends on altitude. However, in the spatial model used herein a topographic trend is not necessary, due to the flat topography of the Netherlands. In order to investigate the spatial variability of aeolian power production, the empirical variogram is calculated from the annual mean installed power production. Then, the empirical variogram is fitted to three theoretical models (Gaussian, exponential, and spherical). The spherical variogram is selected as the optimal model because it produces the minimum sum of weighted squared errors. Ordinary kriging is then applied to the aeolian power production data, in order to generate an interpolated map of aeolian power potential over the entire country and a respective variance map for each year studied. To validate the performance of the spatial model, the method of leave-one-out cross-validation is used. The spatial model performs well, as evidenced by the high values of Pearson’s correlation coefficient (85%) between the data and the predictions. The kriging-generated map gives a visual representation of aeolian power potential and its uncertainty over the Netherlands. The highest wind power predictions are in the West area of Netherlands (near the North Sea), while the lowest power estimates are in the Eastern part of the country. In addition, the uncertainty of the predictions is lower in the West and higher in the East. These spatial patterns are consistently observed for all the years (2001--2006) in the study. In the temporal analysis we focus on the time series of average monthly wind power production at each station. The methodology is illustrated for two stations, one onshore and one in the North Sea, off the Netherlands' coast. The temporal variation of wind power production exhibits seasonal behavior with an annual cycle. We follow two different modeling approaches: In the first approach, we fit an explicit periodic function to the data and then apply a SARIMA time series model to the stochastic residuals. In the second approach, a SARIMA model is directly fitted to the average monthly wind power data. The optimal parameters are used to predict wind power production for the following 12 months. Thus, the prediction involves the monthly average power production for the year 2007. To validate the performance of the models, cross-validation using the method of one-step-ahead forecast is used. The temporal models show good performance with respect to the root mean square error (RMSE)---the RMSE is in the range 0.04--0.22 MW (about 21%--43% of the average monthly wind power) at each station.

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