In very large wind farms, the vertical interaction with the atmospheric boundary layer plays an important role, i.e. the total energy extraction is governed by the vertical transport of kinetic energy from higher regions in the boundary layer towards the turbine level. In the current study, we investigate optimal control of wind-farm boundary layers, considering the individual wind turbines as flow actuators, whose energy extraction can be dynamically regulated in time so as to optimally influence the flow field and the vertical energy transport. To this end, we use large-eddy simulations of a fully developed pressure-driven wind-farm boundary layer in a receding-horizon optimal control framework. For the optimization of the wind-turbine controls, a conjugate-gradient optimization method is used in combination with adjoint large-eddy simulations for the determination of the gradients of the cost functional. In a first control study, wind-farm energy extraction is optimized in an aligned wind farm. Results are accumulated over one hour of operation. We find that the energy extraction is increased by 16 % compared to the uncontrolled reference. This is directly related to an increase of the vertical fluxes of energy towards the wind turbines, and vertical shear stresses increase considerably. A further analysis, decomposing the total stresses into dispersive and Reynolds stresses, shows that the dispersive stresses increase drastically, and that the Reynolds stresses decrease on average, but increase in the wake region, leading to better wake recovery. We further observe also that turbulent dissipation levels in the boundary layer increase, and overall the outer layer of the boundary layer enters into a transient decelerating regime, while the inner layer and the turbine region attain a new statistically steady equilibrium within approximately one wind-farm through-flow time. Two additional optimal control cases study penalization of turbulent dissipation. For the current wind-farm geometry, it is found that the ratio between wind-farm energy extraction and turbulent boundary-layer dissipation remains roughly around 70 %, but can be slightly increased by a few per cent by penalizing the dissipation in the optimization objective. For a pressure-driven boundary layer in equilibrium, we estimate that such a shift can lead to an increase in wind-farm energy extraction of 6 %.

Abstract:We investigate the use of optimal coordinated control techniques in large eddy simulations of wind farm boundary layer interaction with the aim of increasing the total energy extraction in wind farms. The individual wind turbines are considered as flow actuators, and their energy extraction is dynamically regulated in time, so as to optimally influence the flow field. We extend earlier work on wind farm optimal control in the fully-developed regime (Goit and Meyers 2015, J. Fluid Mech. 768, 5-50) to a 'finite' wind farm case, in which entrance effects play an important role. For the optimal control, a receding horizon framework is employed in which turbine thrust coefficients are optimized in time and per turbine. Optimization is performed with a conjugate gradient method, where gradients of the cost functional are obtained using adjoint large eddy simulations. Overall, the energy extraction is increased 7% by the optimal control. This increase in energy extraction is related to faster wake recovery throughout the farm. For the first row of turbines, the optimal control increases turbulence levels and Reynolds stresses in the wake, leading to better wake mixing and an inflow velocity for the second row that is significantly higher than in the uncontrolled case. For downstream rows, the optimal control mainly enhances the sideways mean transport of momentum. This is different from earlier observations by Goit and Meyers (2015) in the fully-developed regime, where mainly vertical transport was enhanced.

A wind measurement campaign using a single scanning light detection and ranging (LiDAR) device was conducted at the Hazaki Oceanographical Research Station (HORS) on the Hazaki coast of Japan to evaluate the performance of the device for coastal wind measurements. The scanning LiDAR was deployed on the landward end of the HORS pier. We compared the wind speed and direction data recorded by the scanning LiDAR to the observations obtained from a vertical profiling LiDAR installed at the opposite end of the pier, 400 m from the scanning LiDAR. The best practice for offshore wind measurements using a single scanning LiDAR was evaluated by comparing results from a total of nine experiments using several different scanning settings. A two-parameter velocity volume processing (VVP) method was employed to retrieve the horizontal wind speed and direction from the radial wind speed. Our experiment showed that, at the current offshore site with a negligibly small vertical wind speed component, the accuracy of the scanning LiDAR wind speeds and directions was sensitive to the azimuth angle setting, but not to the elevation angle setting. In addition to the validations for the 10-minute mean wind speeds and directions, the application of LiDARs for the measurement of the turbulence intensity (TI) was also discussed by comparing the results with observations obtained from a sonic anemometer, mounted at the seaward end of the HORS pier, 400 m from the scanning LiDAR. The standard deviation obtained from the scanning LiDAR measurement showed a greater fluctuation than that obtained from the sonic anemometer measurement. However, the difference between the scanning LiDAR and sonic measurements appeared to be within an acceptable range for the wind turbine design. We discuss the variations in data availability and accuracy based on an analysis of the carrier-to-noise ratio (CNR) distribution and the goodness of fit for curve fitting via the VVP method.

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