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Large-eddy simulations of the flow past an array of three aligned turbines have been performed. The study is focused on below rated (Region 2) wind speeds. The turbines are controlled through the generator torque gain, as usually done in Region 2. Two operating strategies are considered: (i) preset individual optimum torque gain based on a model for the power coefficient (baseline case) and (ii) real-time optimization of torque gain for maximizing each individual turbine power capture during operation. The real-time optimization is carried out through a model-free approach, namely, extremum-seeking control. It is shown that ESC is capable of increasing the power production of the array by 6.5% relative to the baseline case. The extremum-seeking control reduces the torque gain of the downstream turbines, thus increasing the angular speed of the blades. This results in improved aerodynamics near the tip of the blade that is the portion contributing mostly to the torque and power. In addition, an increase in angular speed leads to a larger entrainment in the wake, which also contributes to provide additional available power downstream. It is also shown that the tip speed ratio may not be a reliable performance indicator when the turbines are in waked conditions. This may be a concern when using optimal parameter settings, determined from isolated turbine models, in applications with waked turbines.

Yaw misalignment between the incoming wind and the rotor of a turbine causes a lateral displacement of the wake. This effect can be exploited to avoid or mitigate wake interactions in wind farms, so that power losses are minimized. We performed large‐eddy simulations to evaluate yaw control for a three‐turbine wind farm. We used two different turbine models to assess how the size of the turbine rotor affects the farm efficiency and the effectiveness of the control strategy. A utility‐scale wind turbine with rotor diameter of 126 m is compared with a scaled research wind turbine with rotor diameter of 27 m. In both cases, a model‐free algorithm is used to determine the turbine yaw set point, which maximizes total power production. The algorithm is the nested extremum‐seeking control (NESC), which allows for the coordinated optimization of the wind turbine operating points. The results achieved with NESC are validated by computing a static performance map for different yaw angles. NESC converges to optimal operating conditions, which are in good agreement with the static map benchmark. Numerical results show that a larger rotor diameter induces larger wake deflection, thus achieving higher power improvements. From the analysis of the turbine structural loads, an increase in damage equivalent load is observed for both the yawed turbine and the waked one. Present results suggest that there is a cost‐effective trade‐off between performance and loads for large turbines.

A numerical framework for simulations of wake interactions associated with a wind turbine column is presented. A Reynolds-averaged Navier-Stokes (RANS) solver is developed for axisymmetric wake flows using parabolic and boundary-layer approximations to reduce computational cost while capturing the essential wake physics. Turbulence effects on downstream evolution of the time-averaged wake velocity field are taken into account through Boussinesq hypothesis and a mixing length model, which is only a function of the streamwise location. The calibration of the turbulence closure model is performed through wake turbulence statistics obtained from large-eddy simulations of wind turbine wakes. This strategy ensures capturing the proper wake mixing level for a given incoming turbulence and turbine operating condition and, thus, accurately estimating the wake velocity field. The power capture from turbines is mimicked as a forcing in the RANS equations through the actuator disk model with rotation. The RANS simulations of the wake velocity field associated with an isolated 5-MW NREL wind turbine operating with different tip speed ratios and turbulence intensity of the incoming wind agree well with the analogous velocity data obtained through high-fidelity large-eddy simulations. Furthermore, different cases of columns of wind turbines operating with different tip speed ratios and downstream spacing are also simulated with great accuracy. Therefore, the proposed RANS solver is a powerful tool for simulations of wind turbine wakes tailored for optimization problems, where a good trade-off between accuracy and low-computational cost is desirable. KEYWORDSactuator disk, CFD, mixing length model, RANS, wind turbine wakes INTRODUCTIONThe US Department of Energy estimated that typical power losses for a wind power plant are about 20% of its annual production, 1 which are mainly due to wind turbine wake effects, such as complex wake interactions and shadowing due to upstream wind turbines. 2 Wake-related phenomena within wind farms affect not only power production but also the overall life cycle of wind turbines. Therefore, there is significant potential for efficiency improvement of power plant operations and reduction of wind energy costs. 3 Various strategies have been proposed to reduce detrimental wake effects on power production and turbine durability. These strategies have in common a coordinated control over the entire wind farm as a whole system, rather than control at single-turbine level. A control strategy is based on derating power capture from upstream turbines, which leads to a higher potential power for downstream turbines. An optimal trade-off between underperformance of the derated turbines and increased power production of the downstream turbines must be estimated to maximize the overall power production from the entire wind farm. [3][4][5][6][7][8][9][10][11] Another technique to inhibit, or at least reduce, wake impact on downstream turbines consists in steering or redirecting wind turbine wakes by introducin...