Turbulence coherence and its impact on wind-farm power fluctuations

Abstract

Using a physics-based approach, we infer the impact of the coherence of atmospheric turbulence on the power fluctuations of wind farms. Application of the random-sweeping hypothesis reveals correlations characterized by advection and turbulent diffusion of coherent motions. Those contribute to local peaks and troughs in the power spectrum of the combined units at frequencies corresponding to the advection time between turbines, which diminish in magnitude at high frequencies. Experimental inspection supports the results from the random-sweeping hypothesis in predicting spectral characteristics, although the magnitude of the coherence spectrum appears to be over-predicted. This deviation is attributed to the presence of turbine wakes, and appears to be a function of the turbulence approaching the first turbine in a pair.

On the spectral behaviour of the turbulence-driven power fluctuations of horizontal-axis turbines

“…wind farms) (Stevens & Meneveau 2014; Bossuyt et al. 2016; Stevens, Gayme & Meneveau 2016; Bandi 2017; Bossuyt, Meneveau & Meyers 2017; Tobin & Chamorro 2018). Moreover, indirect measurements from the electrical power output for more than one wind farm (Apt 2007; Katzenstein, Fertig & Apt 2010; Vigueras-Rodríguez et al.…”

“…To explain the existence of these peaks, first Bossuyt et al. (2017) and later Tobin & Chamorro (2018) and Tobin et al. (2019) used the random-sweeping hypothesis of Kraichnan (1964) and Tennekes (1975) following previous studies that utilised the same theory to obtained spatio-temporal spectral correlations in the logarithmic layer of wall turbulence (Wilczek, Stevens & Meneveau 2015 a , b ).…”

“…To understand the effect of turbulence on wind or tidal-stream power output variability, numerous studies have attempted to quantify the impact of upstream turbulence on a single horizontal-axis turbine (Chamorro et al 2013(Chamorro et al , 2015Tobin, Zhu & Chamorro 2015;Payne et al 2018) or turbine arrays (e.g. wind farms) (Stevens & Meneveau 2014;Bossuyt et al 2016;Stevens, Gayme & Meneveau 2016;Bandi 2017;Bossuyt, Meneveau & Meyers 2017;Tobin & Chamorro 2018). Moreover, indirect measurements from the electrical power output for more than one wind farm (Apt 2007;Katzenstein, Fertig & Apt 2010;Vigueras-Rodríguez et al 2010) have also been obtained and studied.…”

“…Even more interesting, the same studies found that the aggregate power spectra exhibit characteristic peaks at integer multiples of the advective frequency f a = 2π/T a , where T a corresponds to the mean velocity-driven travel time between two adjacent in-line turbines. To explain the existence of these peaks, first Bossuyt et al (2017) and later Tobin & Chamorro (2018) and Tobin et al (2019) used the random-sweeping hypothesis of Kraichnan (1964) and Tennekes (1975) following previous studies that utilised the same theory to obtained spatio-temporal spectral correlations in the logarithmic layer of wall turbulence (Wilczek, Stevens & Meneveau 2015a,b).…”

The Influence of Winglet Pitching on the Performance of a Model Wind Turbine: Aerodynamic Loads, Rotating Speed, and Wake Statistics

“…Interestingly, the wake transport speed is in general higher than the time-averaged wake velocity at the turbine hub height (U U hub ) from Figure 8), especially under high α cases. This further highlighted that the pitching of winglet facilitates the wake mixing, where the wake transport is not barely determined by the local wind velocity but also influenced by the mixing with the surrounding background TBL, which is always higher than the local wake flow velocities [48].…”