The Spectrum of Wind Power Fluctuations*

Wind is a variable energy source whose fluctuations threaten electrical grid stability and complicate dynamical load balancing. The power generated by a wind turbine fluctuates due to the variable wind speed that blows past the turbine. Indeed, the spectrum of wind power fluctuations is widely believed to reflect the Kolmogorov spectrum; both vary with frequency $f$ as $f^{-5/3}$. This variability decreases when aggregate power fluctuations from geographically distributed wind farms are averaged at the grid via a mechanism known as geographic smoothing. Neither the $f^{-5/3}$ wind power fluctuation spectrum nor the mechanism of geographic smoothing are understood. In this work, we explain the wind power fluctuation spectrum from the turbine through grid scales. The $f^{-5/3}$ wind power fluctuation spectrum results from the largest length scales of atmospheric turbulence of order 200 km influencing the small scales where individual turbines operate. This long-range influence spatially couples geographically distributed wind farms and synchronizes farm outputs over a range of frequencies and decreases with increasing inter-farm distance. Consequently, aggregate grid-scale power fluctuations remain correlated, and are smoothed until they reach a limiting $f^{-7/3}$ spectrum.