Abstract
Instrumented small-scale porous disk models are used to study the spectrum of a surrogate for the power output in a micro wind farm with 100 models of wind turbines. The power spectra of individual porous disk models in the first row of the wind farm show the expected -5/3 power law at higher frequencies. Downstream models measure an increased variance due to wake effects. Conversely, the power spectrum of the sum of the power over the entire wind farm shows a peak at the turbine-to-turbine travel frequency between the model turbines, and a near -5/3 power law region at a much wider range of lower frequencies, confirming previous LES results. Comparison with the spectrum that would result when assuming that the signals are uncorrelated, highlights the strong effects of correlations and anti-correlations in the fluctuations at various frequencies.
Highlights
Unsteady flow properties and wind turbine wake interactions are a source of power output variability for wind turbines
Two important characteristics of the power output variability which determine the necessary amount of fill-in power and the speed over which the fill-in power units have to react are the fluctuation amplitudes and the accompanying ramp speeds. These characteristics can be studied by calculating the power spectral density (PSD) of the power output signals to find the distribution of the variance in function of the frequency or corresponding time scale
The PSD of a power output signal Pi of a porous disk model i is here calculated after
Summary
Unsteady flow properties and wind turbine wake interactions are a source of power output variability for wind turbines. Fluctuations in the power output are continuously present on scales from seconds to minutes due to turbulence, and on larger scales due to for example diurnal, synoptic and seasonal variations. The power output variability, characterized by the fluctuation amplitudes and accompanying ramp speeds, determines the necessary fill-in power required to follow a signal from the grid operator [2]. Summation over a large number of turbines reduces the power output fluctuations [10]. Field data [2] and a LES study [14] have shown that the spectrum of the aggregate power output follows a power law with a nearly -5/3 slope, similar to a Kolmogorov scaling for the inertial range of hydrodynamic turbulence
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