Modeling space-time correlations of velocity fluctuations in wind farms

Wind energy as a source of renewable energy is a field of growing importance. In order to improve power grid stability, power output fluctuations of individual wind farms need to be better understood. Power output fluctuations of wind farms are statistically related to the spatial and temporal decorrelation of wind velocity fluctuations in the atmospheric boundary layer. Consequently, simple physics-based models are needed which capture the characteristics of the velocity fluctuations. In this presentation, we discuss such a model based on the Tennekes-Kraichnan random sweeping hypothesis, in which we assume that small-scale velocity fluctuations are advected by a mean velocity and large-scale perturbations. We show that the space-time velocity correlations can be described in terms of a convolution of the pure spatial correlation and an analytical temporal decorrelation kernel. Comparing our model to a large eddy simulation of a fully developed wind turbine array boundary layer, we find good qualitative agreement.