Statistical modelling of space-time processes with application to wind power

Short-term wind power forecasts together with a quantification of uncertainties are required for the reliable operation of power systems with significant wind power penetration. A challenge for utilizing wind power as a source of energy is the intermittent and hardly predictable nature of wind. This thesis aims at contributing to the wind power literature by building and evaluating new statistical techniques for producing forecasts at multiple locations and lead times using spatio-temporal information.

By exploring the features of a rich portfolio of wind farms in western Denmark, we investigate different types of models and provide several forms of predictions. Starting with spatial prediction, we then extend the methodology to spatio-temporal prediction of individual wind farms and aggregated wind power at monitored locations as well as at locations where recent observations are not available.

We propose spatial models for predicting wind power generation at two different time scales: for annual average wind power generation and for a high temporal resolution (typically wind power averages over 15-min time steps). In both cases, we use a spatial hierarchical statistical model in which spatial correlation is captured by a latent Gaussian field.

We explore how such models can be handled with stochastic partial differential approximations of Matérn Gaussian fields together with integrated nested Laplace approximations. We show that complex hierarchical spatial models are well suited for wind power data and provide results in reasonable computational time.

Moreover, the hierarchical approach for obtaining predictions at a high temporal resolution is found to produce accurate predictions with improved performance compared to a standard geostatistical method at a small additional computational cost. The use of the integrated nested Laplace approximations is motivated by the desire to produce forecasts on large data sets with hundreds of locations, which is critical during periods of high wind penetration.

Subsequently, the extension from spatial to spatio-temporal models is iven. Three different hierarchical models are developed for obtaining probabilistic wind power forecasts. First, a time series model consisting of an autoregressive process with a location specific intercept is considered. This approach gives satisfactory results for individual forecasts but fails to generate calibrated aggregated forecasts.

The second approach has a common intercept for all farms and a spatio-temporal model that varies in time with first order autoregressive dynamics and has spatially correlated innovations given by a zero mean Gaussian process. The third model, which also has a common intercept as well as an autoregressive process to capture the local variability and the spatio-temporal term from the second approach, is able to produce reliable individual and aggregated forecasts for multiple lead times.

Finally, very-short-term wind power forecasting is considered. Probabilistic forecasts from 15 minutes up to two hours ahead are produced by using anisotropic spatio-temporal correlation models to account for the propagation of weather fronts and a transformed latent Gaussian field is used to accommodate the probability masses that occur in wind power distribution due to chains of zero measurements.

Using what is called kriging equations, even the simplest proposed covariance model is able to produce calibrated spatio-temporal predictions of wind power production.