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A LiDAR Statistical Barnes Objective Analysis (LiSBOA) for the optimal design of lidar scans and retrieval of the velocity statistical moments is proposed. LiSBOA represents an adaptation of the classical Barnes scheme for the statistical analysis of unstructured experimental data in N-dimensional space, and it is a suitable technique for the evaluation over a structured Cartesian grid of the statistics of scalar fields sampled through scanning lidars. LiSBOA is validated and characterized via a Monte Carlo approach applied to a synthetic velocity field. This revisited theoretical framework for the Barnes objective analysis enables the formulation of guidelines for the optimal design of lidar experiments and efficient application of LiSBOA for the postprocessing of lidar measurements. The optimal design of lidar scans is formulated as a two-cost-function optimization problem, including the minimization of the percentage of the measurement volume not sampled with adequate spatial resolution and the minimization of the error on the mean of the velocity field. The optimal design of the lidar scans also guides the selection of the smoothing parameter and the total number of iterations to use for the Barnes scheme. LiSBOA is assessed against a numerical data set generated using the virtual lidar technique applied to the data obtained from a large eddy simulation (LES). The optimal sampling parameters for a scanning Doppler pulsed wind lidar are retrieved through LiSBOA, and then the estimated statistics are compared with those of the original LES data set, showing a maximum error of about 4 % for both mean velocity and turbulence intensity. 

Abstract. The LiDAR Statistical Barnes Objective Analysis (LiSBOA), presented in Letizia et al. (2021), is a procedure for the optimal design of lidar scans and calculations over a Cartesian grid of the statistical moments of the velocity field. Lidar data collected during a field campaign conducted at a wind farm in complex terrain are analyzed through LiSBOA for two different tests. For both case studies, LiSBOA is leveraged for the optimization of the azimuthal step of the lidar and the retrieval of the mean equivalent velocity and turbulence intensity fields. In the first case, the wake velocity statistics of four utility-scale turbines are reconstructed on a 3D grid, showing LiSBOA's ability to capture complex flow features, such as high-speed jets around the nacelle and the wake turbulent-shear layers. For the second case, the statistics of the wakes generated by four interacting turbines are calculated over a 2D Cartesian grid and compared to the measurements provided by the nacelle-mounted anemometers. Maximum discrepancies, as low as 3 % for the mean velocity (with respect to the free stream velocity) and turbulence intensity (in absolute terms), endorse the application of LiSBOA for lidar-based wind resource assessment and diagnostic surveys for wind farms. 

Abstract. A LiDAR Statistical Barnes Objective Analysis (LiSBOA) for the optimal design of lidar scans and retrieval of the velocity statistical moments is proposed. LiSBOA represents an adaptation of the classical Barnes scheme for the statistical analysis of unstructured experimental data in N-dimensional space, and it is a suitable technique for the evaluation over a structured Cartesian grid of the statistics of scalar fields sampled through scanning lidars. LiSBOA is validated and characterized via a Monte Carlo approach applied to a synthetic velocity field. This revisited theoretical framework for the Barnes objective analysis enables the formulation of guidelines for the optimal design of lidar experiments and efficient application of LiSBOA for the postprocessing of lidar measurements. The optimal design of lidar scans is formulated as a two-cost-function optimization problem, including the minimization of the percentage of the measurement volume not sampled with adequate spatial resolution and the minimization of the error on the mean of the velocity field. The optimal design of the lidar scans also guides the selection of the smoothing parameter and the total number of iterations to use for the Barnes scheme. LiSBOA is assessed against a numerical data set generated using the virtual lidar technique applied to the data obtained from a large eddy simulation (LES). The optimal sampling parameters for a scanning Doppler pulsed wind lidar are retrieved through LiSBOA, and then the estimated statistics are compared with those of the original LES data set, showing a maximum error of about 4 % for both mean velocity and turbulence intensity. 

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. 

This work focuses on the optimization of performance and profitability of a wind farm carried out by means of an economic model and Reynolds-Averaged Navier-Stokes (RANS) simulations of wind turbine wakes. Axisymmetric RANS simulations of isolated wind turbine wakes are leveraged with a quadratic super-positioning model to estimate wake interactions within wind farms. The resulting velocity field is used with an actuator disk model to predict power production from each turbine in the wind farm. Design optimization is performed by considering a site in North Texas, whose wind resource statistics are obtained from a meteorological tower. The RANS solver provides capabilities to simulate different incoming wind turbulence intensities and, hence, the wind farm optimization is performed by taking the daily cycle of the atmospheric stability into account. The objective functional of the optimization problem is the levelized cost of energy (LCoE) encompassing capital cost, operation and maintenance costs, land cost and annual power production. At the first level of the optimization problem, the wind farm gross capacity is determined by considering three potential turbine types with different rated power. Subsequently, the optimal wind farm layout is estimated by varying the uniform spacing between consecutive turbine rows. It is found that increasing turbine rated power, the wind farm profitability is enhanced. Substituting a wind farm of 24 turbines of 2.3-MW rated power with 18, 3-MW turbines could reduce the LCoE of about 1.56 $/MWh, while maintaining a similar gross capacity factor. The optimization of the spacing between turbine rows was found to be sensitive to the land cost. For a land cost of 0.05 $/m2, the layout could be designed with a spacing between 6 to 15 rotor diameters without any significant effect on the LCoE, while an increased land cost of 0.1 $/m2 leads to an optimal spacing of about 6 rotor diameters. 

One‐way nested mesoscale to microscale simulations of an onshore wind farm have been performed nesting the Weather Research and Forecasting (WRF) model and our in‐house high‐resolution large‐eddy simulation code (UTD‐WF). Each simulation contains five nested WRF domains, with the largest domain spanning the north Texas Panhandle region with a 4 km resolution, while the highest resolution (50 m) nest simulates microscale wind fluctuations and turbine wakes within a single wind farm. The finest WRF domain in turn drives the UTD‐WF LES higher‐resolution domain for a subset of six turbines at a resolution of ∼5 m. The wind speed, direction, and boundary layer profiles from WRF are compared against measurements obtained with a met‐tower and a scanning Doppler wind LiDAR located within the wind farm. Additionally, power production obtained from WRF and UTD‐WF are assessed against supervisory control and data acquisition (SCADA) system data. Numerical results agree well with the experimental measurements of the wind speed, direction, and power production of the turbines. UTD‐WF high‐resolution domain improves significantly the agreement of the turbulence intensity at the turbines location compared with that of WRF. Velocity spectra have been computed to assess how the nesting allows resolving a wide range of scales at a reasonable computational cost. A domain sensitivity analysis has been performed. Velocity spectra indicate that placing the inlet too close to the first row of turbines results in an unrealistic peak of energy at the rotational frequency of the turbines. Spectra of the power production of a single turbine and of the cumulative power of the array have been compared with analytical models.