Spectrum of Wind Power Fluctuations

Abstract

Wind power fluctuations for an individual turbine and plant have been widely reported to follow the Kolmogorov spectrum of atmospheric turbulence; both vary with a fluctuation time scale τ as τ^{2/3}. Yet, this scaling has not been explained through turbulence theory. Using turbines as probes of turbulence, we show the τ^{2/3} scaling results from a large scale influence of atmospheric turbulence. Owing to this long-range influence spanning 100s of kilometers, when power from geographically distributed wind plants is summed into aggregate power at the grid, fluctuations average (geographic smoothing) and their scaling steepens from τ^{2/3}→τ^{4/3}, beyond which further smoothing is not possible. Our analysis demonstrates grids have already reached this τ^{4/3} spectral limit to geographic smoothing.