Modelling Wind Turbine Power Curves based on Frank’s copula

Abstract

In the study of wind turbines, one of the most relevant and useful indicators is the power curve. It has been shown to be of paramount importance in evaluating turbine performance and therefore reducing operation and maintenance (O&M) costs. Various techniques can be applied to model and obtain the shape of this curve, which relates the electrical power generated by a turbine to the wind speed. Statistical copulas are used in this paper, a tool used in other fields such as econometrics, and whose potential lies in its ability to capture the complex dependency between the variables involved. In particular, the Frank copula is applied to obtain a probabilistic model of the power curve of a wind turbine. This model is compared with the Gaussian Mixture Model, a technique widely used to obtain parametric probabilistic models. As a result of this comparison, it is observed that the Frank copula model fits the power curve of the wind turbine with greater precision and reliability, which would allow its use for prediction and fault detection.