Abstract
Abstract. Engineering wake models provide the invaluable advantage to predict wind turbine wakes, power capture, and, in turn, annual energy production for an entire wind farm with very low computational costs compared to higher-fidelity numerical tools. However, wake and power predictions obtained with engineering wake models can be insufficiently accurate for wind farm optimization problems due to the ad hoc tuning of the model parameters, which are typically strongly dependent on the characteristics of the site and power plant under investigation. In this paper, lidar measurements collected for individual turbine wakes evolving over a flat terrain are leveraged to perform optimal tuning of the parameters of four widely used engineering wake models. The average wake velocity fields, used as a reference for the optimization problem, are obtained through a cluster analysis of lidar measurements performed under a broad range of turbine operative conditions, namely rotor thrust coefficients, and incoming wind characteristics, namely turbulence intensity at hub height. The sensitivity analysis of the optimally tuned model parameters and the respective physical interpretation are presented. The performance of the optimally tuned engineering wake models is discussed, while the results suggest that the optimally tuned Bastankhah and Ainslie wake models provide very good predictions of wind turbine wakes. Specifically, the Bastankhah wake model should be tuned only for the far-wake region, namely where the wake velocity field can be well approximated with a Gaussian profile in the radial direction. In contrast, the Ainslie model provides the advantage of using as input an arbitrary near-wake velocity profile, which can be obtained through other wake models, higher-fidelity tools, or experimental data. The good prediction capabilities of the Ainslie model indicate that the mixing-length model is a simple yet efficient turbulence closure to capture effects of incoming wind and wake-generated turbulence on the wake downstream evolution and predictions of turbine power yield.
Highlights
Once the parameters of the four considered engineering wake models have been optimally tuned based on the mean velocity fields retrieved from the lidar measurements, and their trends as functions of the normalized incoming wind speed at hub height, Uh∗ub, and turbulence intensity, TI, have been discussed, it is worth scrutinizing the predictions generated from the wake models more
The velocity field predicted through the Bastankhah wake model looks very similar to the mean velocity field measured by the lidar, especially in the far wake, indicating that the velocity profiles in the radial direction can be modeled with a good level of accuracy through a Gaussian function, which is the underlying assumption of the Bastankhah wake model
For these data clusters, which are calculated for incoming wind speed within the range 0.62 < Uh∗ub < 0.71 and different TI, it is observed that in the near wake the mean velocity field measured by the lidar is not axisymmetric, and, more importantly, it is significantly different from a Gaussian function (Zhan et al, 2020a)
Summary
Wake interactions are responsible for significant power losses of wind farms (Barthelmie, et al, 2007; El-Asha et al, 2017), and numerical tools for predicting the intra-windfarm velocity field are highly sought after for the optimal design of wind farm layout (Kusiak and Song, 2010; González et al, 2010; Santhanagopalan et al, 2018b), development of control algorithms for improving turbine operations (Lee et al, 2013; Annoni et al, 2016), and enhancement of accuracy in predictions of power capture (Tian et al, 2017). L. Zhan et al.: Optimal tuning of engineering wake models through lidar measurements between fidelity, in terms of accuracy of the predicted flow and turbine power capture, and required computational costs. Ainslie developed one of the classic field models and calculated the complete flow field numerically by solving the RANS equations with a turbulence closure based on the mixing-length assumption (Ainslie, 1988). We optimally tune parameters of four engineering wake models based on lidar measurements collected for a utility-scale wind farm. The optimal tuning of the model parameters is performed for various clusters of the lidar dataset based on the turbine thrust coefficient and incoming wind turbulence intensity at hub height.
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