Machine-learning identification of the variability of mean velocity and turbulence intensity for wakes generated by onshore wind turbines: Cluster analysis of wind LiDAR measurements

Wind turbine wakes are the result of the extraction of kinetic energy from the incoming atmospheric wind exerted from a wind turbine rotor. Therefore, the reduced mean velocity and enhanced turbulence intensity within the wake are affected by the characteristics of the incoming wind, turbine blade aerodynamics, and the turbine control settings. In this work, LiDAR measurements of isolated wakes generated by wind turbines installed at an onshore wind farm are leveraged to characterize the variability of the wake mean velocity and turbulence intensity during typical operations encompassing a breadth of atmospheric stability regimes, levels of power capture, and, in turn, rotor thrust coefficients. For the statistical analysis of the wake velocity fields, the LiDAR measurements are clustered through a k-means algorithm, which enables to identify of the most representative realizations of the wind turbine wakes while avoiding the imposition of thresholds for the various wind and turbine parameters, which can be biased by preconceived, and potentially incorrect, notions. Considering the large number of LiDAR samples collected to probe the wake velocity field over the horizontal plane at hub height, the dimensionality of the experimental dataset is reduced by projecting the LiDAR data on an intelligently-truncated basis obtained with the proper orthogonal decomposition (POD). The coefficients of only five physics-informed POD modes, which are considered sufficient to reproduce the observed wake variability, are then injected in the k-means algorithm for clustering the LiDAR dataset. The analysis of the clustered LiDAR data, and the associated SCADA and meteorological data, enables the study of the variability of the wake velocity deficit, wake extent, and wake-added turbulence intensity for different thrust coefficients of the turbine rotor and regimes of atmospheric stability.