The spectral characteristics of wind-farm power output

Over time-scales short enough that wind is relatively steady (.10 minutes), wind-power variability is due to atmospheric turbulence. Power fluctuations at time scales such as these are important for maintaining frequency regulation on the power grid. This thesis presents a holistic, physics-based approach to modeling the spatio-temporal structures of the atmospheric boundary layer, and the ways in which these structures impart themselves in wind-power variability. The following primary findings are presented. Field and laboratory experiments were performed to unravel the structure of the power output fluctuations of horizontal-axis wind turbines based on incoming flow turbulence. The study considers the power data of three wind turbines of rotor sizes 0.12 m, 3.2 m and 96 m, with rated power spanning 6 decades from the order of 100 to 106 W. The 0.12 m wind turbine was tested in a wind tunnel while the 3.2 and 96 m wind turbines were operated in open fields under approximately neutrally-stratified thermal conditions. Incoming flow turbulence was characterized by hotwire and sonic anemometers for the wind tunnel and field setups. While previous works have observed a filtering behavior in wind turbine power output, this exact behavior has not, to date, been properly characterized. Based on the spectral structure of the incoming flow turbulence at hub height, and the mechanical and structural properties of the turbines, a physical basis for the behavior of temporal power fluctuations and their spectral structure is found with potential applications in turbine control and numerical simulations. Consistent results are observed across the geometrical scales of the wind turbines investigated, suggesting no Reynolds number dependence in the tested range. The structure of the turbulence-driven power fluctuations in a wind farm is fundamentally described from basic concepts. A derived tuning-free model, supported with experiments, reveals the underlying spectral content of the power fluctuations of a wind farm. It contains two power-law trends and oscillations in the relatively low- and high-frequency ranges. The former is mostly due to the turbulent interaction between the flow and the turbine properties; whereas the latter is due to the advection between turbine pairs. The spectral wind-farm scale power fluctuations ΦP exhibits a power-law decay proportional to f−5/3−2 in the region corresponding to the turbulence inertial subrange and at relatively large scales, ΦP ∼ f−2. Due to the advection and turbulent diffusion of large-scale structures, a spectral oscillation exists with the product of a sinusoidal behavior and an exponential decay in the frequency domain. Simultaneous power measurements from a model wind farm are presented to investigate the spectral correlation of their power output. Application of a random-sweeping hypothesis to the turbulent flow in a wind farm uncovers distinctive correlations, characterized by advection and turbulent diffusion of coherent motions. This correlation is most evident in the cross-spectra of power output between turbine pairs, which contributes to peaks and troughs in the power spectra of the combined signals. These peaks and troughs occur at frequencies corresponding to the advection time between turbines, and diminish in magnitude at high frequencies due to turbulent decoherence. Experimental results support the results from the random-sweeping hypothesis in predicting characteristic advection and decoherence frequencies. The presence of turbine wakes leads to coherence magnitudes smaller than expected. This difference appears to be a function of the flow approaching the first turbine in a pair. The impact of lateral displacement is unclear from the data. Wind-farm large-eddy simulations are used to uncover the dependence of temporal correlations in the power output of turbine pairs on atmospheric stability. For this purpose, a range of five distinct stability regimes are investigated with the same aligned wind-farm layout used among simulations. The coherence spectrum between turbine pairs in each simulation is compared to theoretical predictions. We found that higher levels of atmospheric instability lead to higher coherence between turbines. This is attributed to higher dominance of atmospheric motions over wakes in highly unstable flows. An empirical model for wake-added turbulence is shown to adequately predict the variation of coherence with ambient turbulence intensity. The modulation of boundary-layer turbulence across scales by passage through the rotor of a model wind turbine is assessed experimentally using synchronous upwind and downwind hotwire anemometers. Consistent with literature, results show that the rotor simultaneously eliminates large-scale motions, and introduces comparatively small-scale flow structures. The synchronous data allows for the distinct quantification of added and dampened turbulence by considering the temporal correlation between upwind and downwind time series. The destroyed turbulence is of a larger characteristic length scale than the created turbulence, but both scales increase with downwind distance. The intensity of the destroyed turbulence does not change substantially with downwind distance, suggesting that the turbine has a much stronger effect on turbulence destruction than simple natural evolution. The cross spectra between upwind and downwind velocity measurements suggest a dispersion relation for different time scales. In the near wake, lower-frequency components appear to be advected at velocity lower than the local wake velocity, and this advection velocity asymptotically approaches the local velocity at high frequency. This trend diminishes in magnitude with downwind distance.LimitedAuthor requested closed access (OA after 2yrs) in Vireo ETD syste