The wind turbine model is controlled by its own dedicated real-time modular Bachmann M1 system, implementing supervisory control functions, pitch-torque-yaw control algorithms, and all necessary safety, calibration and data logging functions. Demanded values (e.g., pitch or yaw angle references) are computed by the control algorithms and then sent to the actuators control boards, where low level control functions are performed and executed. Measurements from the sensors and commands to the actuators are transmitted via analogue and digital (mostly through CAN) communication. The Bachmann M1 system is capable of acquiring data with a sample rate of 2.5 kHz, which is used for acquiring aerodynamic torque, shaft bending moments and rotor azimuth position. All other measurements are acquired with a sample rate of 250 Hz.

The Bachmann M1 system executes the control algorithms with a sampling time of 4 ms and implements a standard power controller based on Bossanyi (2000), with two distinct control regions. Below rated wind speed, the collective blade pitch is kept constant, while the torque reference is scheduled as function of rotor speed in order to maximize power extraction. Above rated wind speed, the torque reference is kept constant, while a proportional-integral (PI) controller is used to collectively pitch the rotor blades in order to keep the generated power at the desired level. In order to accurately track the reference torque, the closed-loop torque controller based on Bottasso et al. (2014) is implemented. This torque controller computes the necessary generator current by using measurements of the shaft torsional load T _S as feed-back. In this way, it is possible to guarantee that the torque at the rotor shaft matches the desired reference value, even in case of friction-induced mechanical losses caused by the nacelle bearings and the slip-ring.

Besides collective pitch control, the model is also capable of individually pitching each blade, enabling additional control actions for influencing loading and/or wakes (Campagnolo et al., 2016), or for implementing yaw-by-IPC. These control goals often come at the cost of a slight power loss below rated wind speed, depending on the pitch amplitude (Bossanyi, 2005).

On board the G1, two yaw control strategies have been been implemented to achieve a desired orientation γ _Dem of the wind turbine rotor, which is defined positive for a counterclockwise rotation viewed from the top, and null when the turbine is perfectly aligned with the wind tunnel inflow.

Both yaw control strategies use, as feedback, measurements of the nacelle orientation provided by an optical incremental encoder (N _e = 10,000 count per revolution). Moreover, both strategies can be employed to operate the G1 either aligned or misaligned with respect to the incoming wind vector, as well as to track steady or dynamically varying yaw references. Since the wind direction in the wind tunnel is constant, a rotation of the nacelle corresponds to a misalignment of the same magnitude with respect to the incoming wind vector.

The first control strategy makes use of the yaw actuator located within the hollow tower of the G1. The actuator, which consists of a brushed motor coupled to a gear head with reduction ratio 246, allows to rotate the entire rotor-nacelle assembly with a maximum yaw rate γ ̇ max = 10 ° /sec, which corresponds to 0.125°/sec at full scale (Campagnolo et al., 2020). This value, despite being lower than the 0.3°/sec at full scale used in other publications (Jonkman et al., 2009; Bak et al., 2013), is expected to be realistic for very large wind turbines (Yang et al., 2021). A PI controller, implemented on the actuator control board, is used for controlling the yaw motor, while the yaw reference value is externally provided. An additional control logic is implemented that engages the yaw brake once the nacelle reaches a desired position. Whenever the yaw reference is changed, the brake and the motor are simultaneously released and activated; successively, the PI controller ensures that the nacelle is yawed to the new position. Besides constant yaw references, the yaw controller is also capable of continuous yaw motions, like tracking for example a harmonic function with adjustable amplitude and frequency.

The yaw-by-IPC exploits the yaw moment induced by an appropriate pitch control of each blades. In this regard, it is important to consider the eventual cross-coupling between the fixed-frame axes due to the blade and pitch actuator dynamics (Mulders et al., 2019). As the blades of the G1 are fairly stiff, it is solely necessary to account for the effects of the eventual lag between demanded and realized pitch (Bossanyi and Witcher, 2009; Houtzager et al., 2013). Dedicated tests were therefore performed on a single G1 blade by prescribing a sinusoidal pitch reference β Dem = 2 ° cos ω t , with ω varying from 2π to 40π rad/s. The observed phase lag Δϕ between the realized and reference pitch is depicted in Figure 2A, together with the phase lag of the best fitting fourth-order transfer function (TF). This TF was derived using a Matlab algorithm based on Levy, (1959), while fixing the numerator order to null.

When the G1 operates at rated rotational speed (marked with a dashed-black line in the plot) and the pitch actuator is required to track a sinusoidal reference at 1P, the lag is significantly large (approx. 85°). To overcome this issue, an azimuth offset equal to the expected phase lag can be applied to the inverse Coleman transformation (Bossanyi and Witcher, 2009; Mulders et al., 2019), which corresponds in transforming the control-computed pitch β _q,c as follow: β d = sin Δ ϕ Ω β q , c , β q = cos Δ ϕ Ω β q , c , (4) with Δϕ the phase lag of the best fitting TF, scheduled as function of the measured rotor speed Ω, and β _q and β _d the pitch inputs to the inverse Coleman transformation. The resulting individual pitch of the ith blade is the following: β IPC , i ψ i = β d ⁡ cos ψ i + β q ⁡ sin ψ i . (5)

Even though it would be possible to coordinate the yaw-by-IPC with the brake engagement and disengagement, the yaw brake has been always kept disengaged. This approach has been preferred in spite of the fact that it requires a continuous pitch action, even when this could be avoided if the yaw reference was constant and, therefore, engaging the brake was an option. The reason lies in the desire to test the control in more severe conditions than those expected in a real application, as well as to maximize the amount of data recorded with active yaw-by-IPC. Finally, concerning the maximum achievable yaw rate, it is limited by the maximum allowed pitch input in the d-q coordinate system, set equal to ±3°.

The G1 is supported by a 2-DOFs numerical model implemented in Simulink (Documentation, 2020), whose flow chart is shown in Figure 3.

As the blades and tower of the G1 are fairly stiff, the numerical model neglects the impact of their flexibility, and thus solely solves the following simplified drive train dynamics J R Ω ̇ = T aero − T g , (6) with J _R the rotor inertia with respect to the rotor axis, T _aero and T _g the aerodynamic and generator torque, respectively. The model also solves the following dynamics of the free-yaw motion of the rotor-nacelle assembly around the tower axis (Wanke et al., 2019) J RNA γ ̈ = M yaw − M L γ ̇ , (7) where J _RNA is the inertia of the rotor-nacelle assembly with respect to the tower axis, M _yaw is the aerodynamic yaw moment around the tower axis, while M _L is the frictional moment caused by the yaw bearings. As the G1 rotor is neither tilted or coned, the yaw moment only accounts for the effects of the induction variation due to the skewed inflow, of the azimuth-dependent projection of the wind speed with the yaw angle, as well as of the cyclic pitch in the q coordinate system. To simplify the model, the aerodynamic damping induced by the yawing motion was neglected.

Both aerodynamic torque and yaw moment were computed using Blade Element Momentum (BEM) theory, as implemented in Fast v8 (Jonkman and Jonkman, 2016), making use of airfoil polars that have been properly tailored in order to have a good match between experimental and numerical performance for un-yawed operations (Wang et al., 2020b). Specifically, Fast v8 simulations were carried out for several combinations of wind speed V, yaw misalignment γ _mis, rotor speed Ω, collective blade pitch β _c and cyclic blade pitch in the q coordinate β _q . The predicted aerodynamic torque and yaw moment have been stored in 5-D Lookup tables (LUTs), which are then interpolated within Simulink during the model execution. Finally, the 2-DOFs numerical model also implements the power controller described in Section 2.2.1, as well the yaw-by-IPC described in Section 2.1.

The model described in Section 2.2.4 is used to compute the aerodynamic power coefficients C _P for a reference air density ρ _ref, and as a function of the wind speed, blade pitch and rotor speed. Following the approach of Schreiber et al. (2020), this relationship can be inverted, so as to derive LUTs (named L U T C P in the following) that return the rotor effective wind speed V _REWS given measurements of the aerodynamic torque T _aero, the collective blade pitch, the rotor speed and the air density. As the power coefficients could be reliably computed only for null yaw misalignment, the described method can provide accurate estimations of the wind speed only for moderate misaligned conditions (Schreiber et al., 2020). To overcome such a limitation, the method has been modified as following.

According to several studies, as those by Gebraad et al. (2016) and Gao and Hong, (2021), the steady-state power of a yawed turbine can be derived as follows P = P γ = 0 cos ⁡ γ P P , (8) with P _γ=0 the power output that the turbine would produce if operated aligned, and P _P the cosine exponent that describes the power loss due to yaw misalignment. Regardless of whether the machine operates aligned or not, the relationship between rotational speed and mechanical power at the rotor shaft, equal to P = ΩT _S, is governed by the scheduled dependency between torque reference and rotor speed tracked by the power controller. Figure 2B depicts the relationship between rotational speed and mechanical power at the rotor shaft for the G1, together with the best-fitting curve based on the following equation Ω = c P n . (9) By combining Eqs 8, 9, it is possible to derive the following relationship Ω = Ω γ = 0 cos ⁡ γ n P P (10) between the rotational speed of a yawed turbine and the rotational speed Ω _γ=0 at which the turbine would rotate if operated aligned. Given that the relationship between torque and mechanical power at the rotor shaft is T S = P Ω = 1 c P 1 − n , (11) it similarly derives that T S = T S , γ = 0 cos ⁡ γ 1 − n P P , (12) with T _S,γ=0 the expected torque at the rotor shaft if the turbine was operated aligned. The rotor effective wind speed can then be estimated as V REWS = L U T C P β c , Ω γ = 0 , T aero , γ = 0 , ρ ρ ref , (13) with T _aero,γ=0 the expected aerodynamic torque if the turbine was operated aligned, computed accounting for the rotor inertia J _R as following T aero , γ = 0 = T S , γ = 0 + J R Ω ̇ (14) For the G1, values equal to 2.174 (Campagnolo et al., 2020) and 0.268 (see Figure 2B) were used for P _P and n, respectively. Finally, this formulation allows for the estimation of the rotor-effective wind speed when the machine operates in region II. An extension of the method is also possible above rated, but has not been implemented.

For the tests performed with steady yaw reference, experiments were conducted at both static wind speed and variable wind speed.

Once analyzed the performance of the control with steady yaw references, the next step aimed at assessing the response of the control with quickly varying references. Such a situation can arise, for example, when wake steering by yawing is used to boost the power produced by a wind farm exposed to unsteady inflow conditions. Under these conditions, indeed, quick variations of the wind direction may induce a rapid change of the demanded yaw offset, whose tracking would require an equally fast modification of the nacelle orientation. It was therefore decided to track, as a reference, the signal shown in Figure 10A, which comes from a recent experiment, conducted in a boundary layer wind tunnel described in Campagnolo et al. (2020). This experiment aimed at assessing the effectiveness of wake steering by yawing under realistic dynamic wind direction changes. As a consequence, also the reference yaw signal can be considered as a realistic implementation of the typical yaw settings that a full-scale wind turbine could be required to track.

The test duration was 30 min, which corresponds to 40 h once scaled back at full-scale (Campagnolo et al., 2020). Figure 10B shows a zoomed-in comparison of the reference signal and the measured yaw. As one might note, both controls allow the reference to be tracked with very good precision. Although this result is largely expected when the control is performed with the yaw actuator, the performance of yaw-by-IPC is remarkable. Indeed, the latter is able to track the reference even slightly better, as shown by the comparison of the tracking error distributions, illustrated in Figure 10C. The tracking error for yaw-by-IPC, indeed, is more frequently closer to 0° than with the control performed with the yaw actuator. This could be due to the limitation imposed on the yaw rate, applied to the control realized with the yaw actuator but not to the yaw-by-IPC, rather than to the backlash of the yaw actuator gear, which deteriorates the reference tracking. Yet overall, for both control strategies the tracking error very seldom exceeded 2°.

In order to further highlight the performance of yaw-by-IPC, Figure 11A shows the zoomed-in time histories of the yaw reference and of β _q . It may be noted that the pitch varies oppositely to the reference. To a negative value of the required yaw, in fact, tends to correspond a positive value of β _q . This is evident also in Figure 11B, which shows the mean of the pitch in d-q coordinates as a function of the demanded yaw, as well as the range of values within two standard deviations from the mean. To reduce noise, the plot depicts average values according to yaw reference bins with a width of 5°. Overall, the trend is almost similar to the one observed for the experiments performed with stationary yaw reference (see Figures 8B, 9G), but with some differences. In fact, the pitch action in the q-coordinate is slightly increased, as indicated by the higher slope of the interpolating line. This seems to indicate that an higher amount of cyclic pitch is required, on average, to keep the turbine yawed to the desired position. This could be related to the aerodynamic damping associated to yawing maneuver, which counteracts the yaw motion (Wanke et al., 2019), or even to other dynamic effects which should be further investigated. Moreover, the deviations of β _q from its mean values are far more significant that what observed for steady yaw references. This is definitely expected, as additional moment must be produced to accelerate and decelerate the entire rotor-nacelle assembly. On average, it appears that a cyclic pitch β _q approximately equal to half degree is the maximum amount of pitch actuation that is needed for this purpose, independently of the required yaw reference.

Finally, Figure 11C depicts the average values of the pitch actuator duty cycle, binned according to yaw reference bins. Differently that what observed for the steady yaw reference cases, the usage of the pitch actuator is more uniform. This can be attributed to the extra pitch demand necessary for accelerating and decelerating the entire rotor-nacelle assembly which, as discussed before, does appear to be independent from the demanded yaw reference.

The wake has been sampled at several points distributed along 18 uniformly-spaced radial lines. In order to correct the measured data from the effects of wall blockage, normalized wake velocities V ̃ wake have been obtained by diving the average values of the recorded speed data with the rotor effective wind speed, estimated as in Section 2.2.5. Due to the limited probe movement allowed by the vertical traversing system, the wake was mapped by first measuring the flow in the lower part of the rotor (from near the floor to hub height), and then in the upper part (from hub height upwards). In particular, the wake velocity was measured twice along a horizontal line at hub height, and the corresponding measurements were used to correct all acquired data, as well as to estimate the measurement uncertainty. Specifically, the two profiles of the normalized velocity at hub height V ̃ wake - y H , 1 − 2 were used to identify a scaling factor s, such that V ̃ wake - y H , 1 ̄ ( 1 + s ) = V ̃ wake - y H , 2 ̄ ( 1 − s ) , where ⋅ ̄ denotes the mean value. A different scaling factor was identified for each of the six wake measurements, and was subsequently used to correct the entire corresponding data-set. The associated measurement uncertainty is instead defined as the root mean square of the difference between the two profiles at hub height.

Figure 12 shows the resulting wake mappings, derived by interpolating biharmonic splines to the normalized velocities measured at the locations marked by the black squares. The lower and upper plots show the mappings for the yaw control realized using the yaw actuator and yaw-by-IPC, respectively. Unfortunately, due to the limitations imposed by the traversing system, the wakes were not fully mapped, specially for the γ = 30° cases. However, it was deemed that the collected data were sufficient to conduct the analyses discussed in the next sections.

Figure 13 reports, for the −30° (left plot), 0° (middle plot) and 30° (right plot) yaw misalignment cases, the comparison between the wake velocity profiles at hub height without (IPC off) and with (IPC on) yaw-by-IPC. The error bars within the plot show the measurement uncertainty, estimated as in Section 3.3.1. Looking at the yawed cases, it is possible to appreciate the induced wake deflection. The wake, indeed, is shifted toward right or left (when looking upstream) if the turbine is negatively or positively misaligned, respectively.

Looking at the profiles for γ = 30°, it appears that yaw-by-IPC decelerates the flow in the wake area located downstream of the leeward side of the rotor. On the contrary, a slight acceleration of the flow is noticed downstream of the windward side. This effect is proportional to the pitch amplitudes β _q , and can be explained as follows. Without yaw-by-IPC, the leeward side of the rotor experiences lower angle of attacks, and thus lower loads, than the windward side. When the yaw-by-IPC is activated, the pitch on the leeward side decreases, as explained in Section 3.2.1, hence the wake section immediately behind decelerates as a result of the higher axial induction. This effect is partially visible also in the γ = −30° case. In fact, a slight acceleration of the flow can be seen in the area immediately behind the windward side of the rotor, while only a trace of deceleration is visible when looking at leeward side. The incomplete mapping of the left side of the wake, in fact, does not permit to fully compare the wake profiles in this area. As for γ = 0°, the observed differences are only marginal and within the range of the measurement uncertainty. In this case, in fact, the cyclic pitch required by yaw-by-IPC is rather low (just a little more than 0.1°), resulting in a very limited effect on the wake. Once more, similar observations have been also noticed by Wang et al. (2020a) while testing IPC for load reductions applied to a yawed G1.

Figure 14 shows the difference in the normalized wake speed between yaw-by-IPC and yaw by geared actuation. As shown before, yaw-by-IPC generates an acceleration close to the windward side of the rotor and a deceleration close to its leeward side. As the wake, during its propagation, swirls clockwise when looking upstream, the acceleration and deceleration regions are convected clockwise around the wake center. Such an effect is highlighted by the high-speed (blue-purple) bubbles present in the γ = ±30° plots, which indeed result clockwise rotated from the leeward side of the rotor.

The differences between the velocity fields with and without yaw-by-IPC produce changes in the available wind power at a downstream turbine. In this regard, the available wind power was calculated by assuming that another G1, aligned with the upstream machine, was placed at the location where the wake measurements were taken. The resulting variation of the available power is +0.85%, −0.5% and +1.34% for the −30°, 0° and 30° yaw cases, respectively. Based on these results, the use of yaw-by-IPC on the upstream turbine is expected to have a positive effect on the power of the downstream turbine for γ = ±30°, while it should have a negative effect for γ = 0°.

It is important to stress that these results apply to the specific environmental conditions of the tests, i.e., very low turbulence, and with the assumption of a second rotor placed only 1.82D downstream from the upper one. However, similar results were observed by Wang et al. (2020a) while testing IPC for loads reduction applied to a yawed G1 under turbulence conditions typical of offshore environments, and with a longitudinal spacing between the turbines of 5D.