نبذة مختصرة : Lidar systems have the potential of alleviating structural loads on wind turbines by providing a preview of the incoming wind field to the control system. For a collective pitch controller, the important quantity of interest is the rotor-effective wind speed (REWS). In this study, we present a model of the coherence between the REWS and its estimate from continuous-wave nacelle-mounted lidar systems. The model uses the spectral tensor definition of the Mann model. Model results were compared to field data gathered from a two- and four-beam nacelle lidar mounted on a wind turbine. The comparison shows close agreement for the coherence, and the data fit better to the proposed model than to a model based on the Kaimal turbulence model, which underestimates the coherence. Inflow conditions with larger length scales led to a higher coherence between REWS and lidar estimates than inflow turbulence of smaller length scale. When comparing the two lidar systems, it was shown that the four-beam lidar is able to resolve small turbulent structures with a higher degree of coherence. Further, the advection speed by which the turbulent structures are transported from measurement to rotor plane can be estimated by 10 min averages of the lidar estimation of REWS. The presented model can be used as a computationally efficient tool to optimize the position of the lidar focus points in order to maximize the coherence.
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