The energy produced by wind plants can be increased by mitigating the negative effects of turbine–wake interactions. In this context, axial-induction control and wake redirection control, obtained by intentionally yawing or tilting the rotor axis away from the mean wind direction, have been the subject of extensive research but only very few investigations have considered their combined effect. In this study we compute power gains that are obtained by operating tilted and yawed rotors at higher axial induction by means of large-eddy simulations using the realistic native National Renewable Energy Laboratory (NREL) 5 MW actuator disk model implemented in the Simulator for On/Offshore Wind Farm Applications (SOWFA). We show that, for the considered two-row wind-aligned array of wind turbines, the power gains of approximately 5

In wind farms, wind turbines shadowed by the wakes of other upwind turbines
experience a decrease in the mean available wind speed and an increase in
turbulent fluctuations, resulting in decreased extracted wind power and
increased fatigue loads (see

In axial-induction control the induction factors of selected (usually upwind)
turbines are steered away from the greedy operation mode in order to increase
the power production of other (usually downwind) turbines. While static axial-induction control has not demonstrated significant power gains in realistic
settings

In two recent studies

The results reported in these previous studies

In the second part of the study we address the case of yaw control. Indeed,
the increased power gains obtained by operating tilted turbines at higher
thrust coefficients mostly result from the increase in wake deviations
obtained without a penalization of the power production of the tilted turbine.
Overinductive wake deflection could therefore be beneficial also in the case
of yaw control, where it is known that higher thrust coefficients also result
in larger wake deviations

The second objective of the present study is therefore to ascertain if significant power gains can be obtained with a combination of static yaw control and static axial-induction control by operating yawed turbines at higher axial induction and including the effect of wake rotation in the turbine model. An affirmative answer would allow the isolation of the mean wake redirection as the most relevant physical effect at play (instead of, e.g., the dynamical adaptation to the incoming wind) and indicate that it is robust with respect to the inclusion of wake rotation effects. Furthermore, if successful, static overinductive yaw control could be easily implemented by simply updating existing yaw-control protocols with a prescription of the suitable turbine rotor-collective blade-pitch angle (controlling the axial induction and the thrust coefficient) for each accessible yaw angle.

The potential of static overinductive wake redirection is investigated by
computing power gains that can be obtained in a wind turbine array composed of
two spanwise-periodic rows of wind-aligned turbines where the same control is
applied to all upwind-row turbines, while downwind-row turbines are left in
default operation mode. This idealized configuration, which is an extension
to the spanwise-periodic case of the two-turbine configuration considered by

We anticipate that substantial enhancements (up to a factor of 3) in the power gains induced by wake redirection are found when operating the tilted or yawed turbines at higher axial induction.

The formulation of the problem at hand is introduced in
Sect.

We address the case of two spanwise-periodic rows of wind turbines immersed in a neutral atmospheric boundary layer (ABL) at latitude 41

NREL 5 MW turbines

Simulations in the presence of wind turbines are repeated in the same

Definition of the positive rotor tilt and yaw angles

Tilt control: mean (temporally averaged) streamwise velocity field in the horizontal plane at hub height obtained

In each (spanwise-periodic) row, turbines are spaced by

Tilt control: cross-stream view of the mean streamwise vorticity and velocity fields in the baseline case

In the baseline case (all turbines operated with

Effect of enforcing negative rotor-collective blade-pitch angles

We then consider the case where upwind-row turbines are tilted by

In a further step, the rotor-collective blade-pitch angle of the tilted
upwind-row turbines is changed. Enforcing increasingly negative values of

The effect of the increased thrust is twofold: (a) the downwash associated with the stronger tilt-induced streamwise vortices is reinforced (see
Fig.

This might be related to blockage effects which induce an increase with

Effect of the tilt angle

Finally, a full set of

The high enhancement in power gains obtained by combining overinduction with
tilt control with respect to those obtained by standard tilt control at
baseline induction is consistent with that found in our previous studies

We now evaluate the benefits of combining static yaw control with static
overinduction. We proceed similarly to the tilt-control case by using the
same precursor simulation and the same baseline case, where all turbines
operate at default values

Yaw control: mean streamwise velocity field in the horizontal plane at hub height obtained

We first simulate the standard yaw control where the yaw angle

Increasing the local thrust coefficient

Yaw control: cross-stream view of the mean streamwise vorticity and velocity fields with upwind turbines yawed by

Effect of changing the rotor-collective blade-pitch angle

Effect of the yaw angle

The analysis of a full range of

These results confirm the first intuition that, also in the static yaw-control case, static overinduction leads to a substantial improvement of the power gains which is based on the same mechanisms discussed for the tilt-control case confirming, that these mechanisms are quite robust.

The main goal of this study was to assess the magnitude of global power gains that can be obtained in wind turbine arrays by combining static wake redirection control and static axial-induction control operating tilted or yawed turbines at higher axial induction (overinduction). Results have been obtained by means of large-eddy simulations of a two-row array of NREL 5 MW turbines in a neutral atmospheric boundary layer.

In the first part of the study we consider the effect of higher induction
on tilt control by using an actuator disk model less idealized than the one
used in our previous studies of this approach. The results confirm that, also with this more realistic turbine model, power gains can be highly increased by operating tilted turbines at higher induction (power gains above 15

In the second part of the study we ascertain if similar power gain
enhancements can be obtained by combining static overinduction with static yaw control. To this end, we have first considered the standard case where yawed turbines are operated at the reference rotor-collective blade-pitch angle

The findings concerning the static overinductive yaw control are probably the
most relevant of this study for short-term applications because they show that
significant power gains can be realized with a simple static overinductive yaw
control in a realistic model (the atmospheric boundary layer with NREL 5 MW
turbines simulated with SOWFA) where wake rotation effects are fully taken
into account. They also probably isolate the main physical mechanisms
underlying the significant power gains found by

Another important result, obtained for both tilt and yaw overinductive
controls, is that while maximum power gains (

It is also to be noted that here we have considered only two rows of turbines
and a single configuration, with a small value of the

Additional investigations are, however, necessary to further refine, in many directions, the conclusions of the present study. A first important issue is to understand what the effects of overinduction are on the static and dynamic structural loads experienced by the blades of tilted and yawed turbines. A complete aeroelastic analysis based on higher-fidelity simulations making use of the actuator line method, requiring more refined grids and time steps and larger computational resources, is highly desirable, especially for the largest considered values of the yaw, tilt and pitch angles, where the near- and middle-wake structures are probably more sensitive to details of the turbine model.

Other issues are wind direction and array configuration. The present study is
limited to a two-row array in the wind-aligned case, but it is, of course,
important to evaluate power gains in arrays with many more rows also in
non-aligned configurations. This kind of analysis, where the optimal combination of tilt, yaw and pitch angles of all turbines has to be computed
for a high number of wind directions and intensities, would be too
computationally demanding if performed by means of large-eddy simulations and
is customarily based on less computationally demanding simplified sets of
equations where the accurate modeling of the controlled wakes is of primary
importance

Finally, it would be very interesting to ascertain if additional power gain enhancements could come from the simultaneous activation of tilt, yaw and axial-induction control. It might indeed be possible that, as a consequence of the symmetry breaking associated with wake rotation effects and Coriolis acceleration, optimal power gains are obtained with “hybrid” yaw–tilt rotor-axis rotations even in wind-aligned configurations. This is the subject of current intense research effort.

The large-eddy simulations presented in this study are performed with SOWFA, a set of libraries and codes able to simulate atmospheric flows over wind
turbines

Periodic boundary conditions are applied in the

The solution domain extends 1

The aerodynamic forces developing on NREL 5 MW turbines, having a

The NREL 5 MW five-region controller implemented in SOWFA is used to control
the turbine's rotational speed and axial induction. In the Region II regime,
the one accessed in the presented simulation, the turbine is driven to the
design point (tip-speed ratio and thrust coefficient corresponding to the
maximum power coefficient for an isolated non-tilted, non-yawed turbine) by
means of generator torque control at the default rotor-collective blade-pitch
angle

The local thrust coefficient is retrieved from the computed turbine thrust
magnitude and rotor-averaged normal mean wind speed

A quantitative analysis of the effect of the improved actuator disk method (ADM) model used in the present study by means of a direct comparison with the results obtained in

Tilt control: cross-stream view of the mean streamwise vorticity and velocity fields obtained by using the ADMC turbine model in the baseline case, where all turbines are operated at

First a baseline case has been simulated, with all turbines operated at the
reference values

For the two-row-array layout, therefore, the ADMC model also predicts that
power gains obtained by overinductive tilt control are much larger than those
obtained by standard tilt control (by

Data can be obtained from the author upon request.

The author declares that there is no conflict of interest.

I gratefully acknowledge the use of the Simulator for On/Offshore Wind Farm Applications (SOWFA) developed at the NREL

This paper was edited by Johan Meyers and reviewed by Wim Munters and one anonymous referee.