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.
Highlights
All renewables fluctuate with the natural variability in their energy sources [1,2]
The power generated by a wind turbine fluctuates with varying wind speed and its spectrum is widely believed to reflect the Kolmogorov spectrum [9] of atmospheric turbulence; both vary with frequency f as f−5=3 [10,11,12] or with time scale τ as τ2=3 [13]
This variability decreases when fluctuations are averaged in the aggregate power feeding the grid from geographically distributed wind plants [14], a mechanism referred to as geographic smoothing
Summary
All renewables fluctuate with the natural variability in their energy sources [1,2]. Wind [3] and solar photovoltaics [4], in particular, exhibit fluctuations over a range of magnitudes and time scales (from milliseconds up to a day). The power generated by a wind turbine fluctuates with varying wind speed and its spectrum is widely believed to reflect the Kolmogorov spectrum [9] of atmospheric turbulence; both vary with frequency f as f−5=3 [10,11,12] or with time scale τ as τ2=3 [13]. We provide a minimal description of the wind power fluctuation spectrum from the turbine through grid scales from a turbulence theory standpoint and experimentally
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