The intentional yaw misalignment of leading, upwind turbines in a wind farm, termed wake steering, has demonstrated potential as a collective control approach for wind farm power maximization. The optimal control strategy and the resulting effect of wake steering on wind farm power production are in part dictated by the power degradation of the upwind yaw misaligned wind turbines. In the atmospheric boundary layer, the wind speed and direction may vary significantly over the wind turbine rotor area, depending on atmospheric conditions and stability, resulting in freestream turbine power production which is asymmetric as a function of the direction of yaw misalignment and which varies during the diurnal cycle. In this study, we propose a model for the power production of a wind turbine in yaw misalignment based on aerodynamic blade elements, which incorporates the effects of wind speed and direction changes over the turbine rotor area in yaw misalignment. The proposed model can be used for the modeling of the angular velocity, aerodynamic torque, and power production of an arbitrary yaw misaligned wind turbine based on the incident velocity profile, wind turbine aerodynamic properties, and turbine control system. A field experiment is performed using multiple utility-scale wind turbines to characterize the power production of yawed freestream operating turbines depending on the wind conditions, and the model is validated using the experimental data. The resulting power production of a yaw misaligned variable speed wind turbine depends on a nonlinear interaction between the yaw misalignment, the atmospheric conditions, and the wind turbine control system.

Wind turbines located in wind farms are operated to maximize only their own power production. Individual operation results in wake losses that reduce farm energy. In this study, we operate a wind turbine array collectively to maximize total array production through wake steering. The selection of the farm control strategy relies on the optimization of computationally efficient flow models. We develop a physics-based, data-assisted flow control model to predict the optimal control strategy. In contrast to previous studies, we first design and implement a multi-month field experiment at a utility-scale wind farm to validate the model over a range of control strategies, most of which are suboptimal. The flow control model is able to predict the optimal yaw misalignment angles for the array within ±5 • for most wind directions (11-32% power gains). Using the validated model, we design a control protocol which increases the energy production of the farm in a second multi-month experiment by 2.7% and 1.0%, for the wind directions of interest and for wind speeds between 6 and 8 m/s and all wind speeds, respectively. The developed and validated predictive model can enable a wider adoption of collective wind farm operation.

Abstract. The magnitude of wake interactions between individual wind turbines depends on the atmospheric stability. We investigate strategies for wake loss mitigation through the use of closed-loop wake steering using large eddy simulations of the diurnal cycle, in which variations in the surface heat flux in time modify the atmospheric stability, wind speed and direction, shear, turbulence, and other atmospheric boundary layer (ABL) flow features. The closed-loop wake steering control methodology developed in Part 1 (Howland et al., 2020c, https://doi.org/10.5194/wes-5-1315-2020) is implemented in an example eight turbine wind farm in large eddy simulations of the diurnal cycle. The optimal yaw misalignment set points depend on the wind direction, which varies in time during the diurnal cycle. To improve the application of wake steering control in transient ABL conditions with an evolving mean flow state, we develop a regression-based wind direction forecast method. We compare the closed-loop wake steering control methodology to baseline yaw-aligned control and open-loop lookup table control for various selections of the yaw misalignment set-point update frequency, which dictates the balance between wind direction tracking and yaw activity. In our diurnal cycle simulations of a representative wind farm geometry, closed-loop wake steering with set-point optimization under uncertainty results in higher collective energy production than both baseline yaw-aligned control and open-loop lookup table control. The increase in energy production for the simulated wind farm design for closed- and open-loop wake steering control, compared to baseline yaw-aligned control, is 4.0 %–4.1 % and 3.4 %–3.8 %, respectively, with the range indicating variations in the energy increase results depending on the set-point update frequency. The primary energy increases through wake steering occur during stable ABL conditions in our present diurnal cycle simulations. Open-loop lookup table control decreases energy production in the example wind farm in the convective ABL conditions simulated, compared to baseline yaw-aligned control, while closed-loop control increases energy production in the convective conditions simulated.

Wind turbines located in wind farms are operated to maximize only their own power production. Individual operation results in wake losses that reduce farm energy. In this study, we operate a wind turbine array collectively to maximize total array production through wake steering. The selection of the farm control strategy relies on the optimization of computationally efficient flow models. We develop a physics-based, data-assisted flow control model to predict the optimal control strategy. In contrast to previous studies, we first design and implement a multi-month field experiment at a utility-scale wind farm to validate the model over a range of control strategies, most of which are suboptimal. The flow control model is able to predict the optimal yaw misalignment angles for the array within ±5 • for most wind directions (11-32% power gains). Using the validated model, we design a control protocol which increases the energy production of the farm in a second multi-month experiment by 2.7% and 1.0%, for the wind directions of interest and for wind speeds between 6 and 8 m/s and all wind speeds, respectively. The developed and validated predictive model can enable a wider adoption of collective wind farm operation.

Abstract. The magnitude of wake interactions between individual wind turbines depends on the atmospheric stability. We investigate strategies for wake loss mitigation through the use of closed-loop wake steering using large eddy simulations of the diurnal cycle, where variations in the surface heat flux in time modify the atmospheric stability, wind speed and direction, shear, turbulence, and other atmospheric boundary layer flow (ABL) features. The closed-loop wake steering control methodology developed in Part 1 (Howland et al., Wind Energy Science, 2020, 5, 1315–1338) is implemented in an eight turbine wind farm in large eddy simulations of the diurnal cycle. The optimal yaw misalignment set-points depend on the wind direction, which varies in time during the diurnal cycle. To improve the application of wake steering control in transient ABL conditions with an evolving mean flow state, we develop a regression-based wind direction forecast method. We compare the closed-loop wake steering control methodology to baseline yaw aligned control and open-loop lookup table control for various selections of the yaw misalignment set-point update frequency, which dictates the balance between wind direction tracking and yaw activity. Closed-loop wake steering with set-point optimization under uncertainty results in higher collective energy production than both baseline yaw aligned control and open-loop lookup table control. The increase in wind farm energy production for closed- and open-loop wake steering control compared to baseline yaw aligned control, is 4.0–4.1 % and 3.4–3.8 %, respectively, with the range indicating variations in the energy increase results depending on the set-point update frequency. The primary energy increases through wake steering occur during stable ABL conditions. Open-loop lookup table control decreases energy production in the convective ABL conditions simulated, compared to baseline yaw aligned control, while closed-loop control increases energy production in convective conditions.