Optimal tuning of engineering wake models through LiDAR measurements

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 not sufficiently 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 to evolve 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.