Impact of Turbulence Coherence on Wind-Farm Power Fluctuations and Effect of Atmospheric Stability*

Using a physics-based approach, we infer the impact of the turbulence coherence on wind-farm power fluctuations. Application of the random-sweeping hypothesis RSH reveals correlations characterized by advection and turbulent diffusion of coherent motions. Those contribute to peaks and troughs in the power spectrum of the combined units, which diminish at high frequencies. Experiments support the results from RSH in predicting spectral features, though the coherence spectrum is overpredicted. This deviation may be due to the presence of wakes, and appears to be function of the turbulence approaching the first turbine in a pair. Additional large-eddy simulations are used to uncover the effects of atmospheric stability. The coherence spectrum between turbine pairs in each simulation is compared to theoretical predictions for a range of stability regimes. We found that higher levels of atmospheric instability lead to higher coherence between turbines. This is attributed to higher dominance of atmospheric turbulence coherence and motions over wakes in non-neutral regimes. An empirical model for wake-added turbulence is shown to adequately predict the variation of coherence with ambient turbulence intensity.