The Spectrum of Wind Power Fluctuations

School of Physics Nonlinear Science and Mathematical Physics Seminar: Prof. Mahesh Bandi, Okinawa Institute of Science and Technology Graduate University

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 of atmospheric turbulence; both vary with frequency $f$ as $f^{-5/3}$. This variability decreases when aggregate power fluctuations from geographically distributed wind plants are averaged at the grid {\it via} a mechanism known as {\it geographic smoothing}. Neither the $f^{-5/3}$ wind power fluctuation spectrum nor the mechanism of geographic smoothing are understood.

In this talk, I will chart out the non-equilibrium character of wind power fluctuations, and explain the wind power fluctuation spectrum from the turbine through the 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 correlates outputs from geographically distributed wind plants over a range of frequencies that 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, which is confirmed with field data.