Statistical modelling of wind energy using Principal Component Analysis

Abstract

The statistical method of Principal Component Analysis (PCA) is developed here from a time-series analysis method used in nonlinear dynamical systems to a forecasting tool and a Measure-Correlate-Predict (MCP) and then applied to wind speed data from a set of Met.Office stations from Scotland. PCA for time-series analysis is a method to separate coherent information from noise of measurements arising from some underlying dynamics and can then be used to describe the underlying dynamics. In the first step, this thesis shows that wind speed measurements from one or more weather stations can be interpreted as measurements originating from some coherent underlying dynamics, amenable to PCA time series analysis. In a second step, the PCA method was used to capture the underlying time-invariant short-term dynamics from an anemometer. These were then used to predict or forecast the wind speeds from some hours ahead to a day ahead. Benchmarking the PCA prediction against persistence, it could be shown that PCA outperforms persistence consistently for forecasting horizons longer than around 8 hours ahead. In the third stage, the PCA method was extended to the MCP problem (PCA-MCP) by which a short set of concurrent data from two sites is used to build a transfer function for the wind speed and direction from one (reference) site to the other (target) site, and then apply that transfer function for a longer period of data from the reference site to predict the expected wind speed and direction at the target site. Different to currently used MCP methods which treat the target site wind speed as the independent variable and the reference site wind speed as the dependent variable, the PCA-MCP does not impose that link but treats the two sites as joint observables from the same underlying coherent dynamics plus some independent variability for each site. PCA then extracts the joint coherent dynamics. A key development step was then to extend the identification of the joint dynamics description into a transfer function in which the expected values at the target site could be inferred from the available measurements at the reference site using the joint dynamics. This extended PCA-MCP was applied to a set of Met.Office data from Scotland and benchmarked a standard linear regression MCP method. For the majority of cases, the error of the resource prediction in terms of wind speed and wind direction distributions at the target site was found to be between 10% and 50% of that made using the standard linear regression. The target mean absolute error was also found to be only the 29% of the linear regression one.