Characterizing Wind Power Forecast Error Using Extreme Value Theory and Copulas

Abstract

Wind energy is one of the fastest-growing renewable energy sources in the world. However, wind power is variable in all timescales. This variability is difficult to predict with perfect certainty, with potentially significant financial implications when rare extreme forecast errors occur. This paper focuses on three key aspects associated with the extreme errors of geographically distributed wind farms: suitable parametric distribution representation, effects of diurnality, seasonality and larger atmospheric circulations, and modeling multivariate distribution. The paper shows that some of the distributions commonly used for modeling forecast errors may be inappropriate in representing extreme errors. As the first contribution, this paper fits a Generalized Pareto distribution (GPD) from extreme value theory to achieve a better estimation of extreme errors. In the second contribution, this paper splits extreme errors by hour, month, and atmospheric states to investigate the statistical regularities of GPD parameters along diurnal and seasonal timescales and larger atmospheric circulations. In the third contribution, this paper uses copula functions to model multivariate extreme error distribution and investigates their effectiveness in providing a regional view of extreme errors. This paper tests the proposed methodology using the forecast error data obtained from 29 wind farms in South Africa. The results show that GPD outperforms commonly used distributions. Extreme errors have strong diurnal and seasonal components and vary significantly between SOM nodes. Copulas can be useful in providing a regional view of extreme errors. This paper improves the estimation of extreme errors, which is an important step toward better operating reserve allocation.