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 τ2/3. Yet, this scaling has not been explained through turbulence theory. Using turbines as probes of turbulence, we show the τ2/3 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 τ2/3→τ4/3, beyond which further smoothing is not possible. Our analysis demonstrates grids have already reached this τ4/3 spectral limit to geographic smoothing.