The maximum-reserve APC used in this work has been extensively described in , so here we only summarize its main features. The core of the wind farm control architecture is an open-loop model-based set-point optimal scheduler that determines the yaw misalignment and power demand of each turbine, given the power demand required by the TSO and the ambient conditions. Furthermore, a feedback loop serves the purpose of correcting tracking errors that may arise from the open loop in real time. A sketch of the controller is shown in Fig. .

The closed and open loops are executed at two distinct time rates, since their outputs involve physical phenomena characterized by different time scales. Specifically, the open loop updates the yaw set-points γi and the power demand PD at a slow pace, due to the time required by wakes to propagate downstream, whereas the closed-loop corrector acts at a rate that is 2 orders of magnitude faster.

We rely on three reference wind farm APC controllers to compare the performance of the maximum-reserve method, namely:

Open-loop (OL). This simple approach assigns predetermined set-points αi to each turbine, as fractions of the power demanded by the TSO, so that ∑i=1Nαi=1. The set-points αi are scheduled with the instantaneous wind direction, so that αi=αi(ψ) to account for different local power availabilities induced by wake impingements. The values αi are computed with the FLORIS model , as described in Sect. .

It is important to mention that the set-points for CL+MR are computed using the same FLORIS version adopted for OL, CL, and CL+LB. This ensures that any discrepancy deriving from the steady-state model is present in each compared control approach. Furthermore, CL, CL+LB, and CL+MR feature the same PI control block described in Sect. , ensuring that the closed-loop element is also the same.

The wind turbine controller is based on two regimes, namely below rated and rated. In below-rated conditions, blades lie at the optimal pitch angle, while the generator torque is scheduled with the rotor speed Ω to ensure that the tip speed ratio λ yields the maximum CP. The rated condition occurs when Ω exceeds its rated value ΩR. In this case, torque is fixed while pitch angle increases from its optimal value to limit the power output to PR. Turbines can track a given power demand PD (where PD≤PR) by adjusting ΩR and by setting QR=PD/ΩR.

In this control strategy, the blade pitch angle θ serves as an indicator of the operating reserve – or margin – for a curtailed wind turbine . Typically, larger values of θ suggest a greater margin, as the turbine is functioning below its optimal power coefficient. The minimum (so called “fine”) value for θ corresponds to the optimal pitch angle θopt, which achieves the maximum CP.

This controller was selected here because it directly accepts a power-demand input and uses the blade pitch angle to accurately follow it. Alternative control strategies could also be implemented, although they might lead to different APC performance.

Saturations are detected on one turbine when the blade pitch lies at its optimal value plus a tolerance, and the tracking error exceeds a given threshold as specified in Sect. . When a wind turbine enters saturation, its power demand is set to PD,i*, which is the last value recorded before saturation, and its power share is computed as 7αi=PiPref+PrefPI. Then its local tracking error is equally redistributed to non-saturated turbines in the form of an additional power demand, in order to ensure that ∑i=1Nαi=1. Notice that local isolated persistent saturation events do not necessarily introduce significant tracking errors as long as other turbines have enough margin to compensate.

Clearly, conditions in which all wind turbines are close to saturation are particularly harmful to the tracking accuracy, as a cascading effect can be triggered that may lead to all turbines being saturated. In this case, all wind turbines operate in greedy mode, and if the TSO demand drops, a large negative ΔP will result. To avoid this situation, when the wind farm produces more than the instantaneous demand (with a threshold, as explained earlier), every saturation condition is forcibly reset.

The wind tunnel experimental campaign is performed with a cluster of three G1 wind turbines – labeled WT1 (upstream), WT2 (center), and WT3 (downstream) – longitudinally spaced by 5D, where D=1.1 m is the rotor diameter. The G1 scaled machine has a rated rotor speed ΩR of 850 rpm, a rated power PR of 46 W, an optimal collective blade pitch angle θOPT of 0.43°, and zero tilt. The time compression ratio is equal to about 80, which means that time flows much faster in the experiment than at full scale . Each G1 is controlled in real time by a dedicated Bachmann M1 PLC , which executes the turbine-level controller described in Sect.  every Δt=4 ms. The maximum yaw rate is equal to 20°s-1, corresponding to approximately 0.25°s-1 at full scale, which is a realistic value .

Tests are performed in the atmospheric test section of the wind tunnel of the Politecnico di Milano in moderate turbulence conditions, with a power-law shear exponent k=0.14, a TI=6% at hub height, and an integral length scale of turbulence of 0.79D. These ambient conditions are representative of offshore scenarios under neutral atmospheric boundary-layer conditions. It is important to recall that even a fairly mild freestream turbulence intensity results in very large turbulent fluctuations at downstream turbines, especially in such closely spaced configurations; for example, Fig. 11 of shows wake-affected turbines experiencing TI values exceeding 30 % for a freestream TI of 5.7 %. Such high turbulence intensities create very challenging conditions for power tracking at downstream turbines.

The blockage ratio considering one G1 rotor is 1.8 %, which is significantly smaller than previous APC wind tunnel studies . The three turbines are installed on a large turntable. The rotational speed of the wind tunnel fans is kept constant during the experiments. The resulting wind speed U∞, measured by a pitot tube placed 4D upstream of WT1, is approximately equal to 5.5 ms-1.

Two sets of experiments are conducted, respectively referred to in the following as “static” and “dynamic”.

In the static tests, the turntable is fixed at an angle ψ to reproduce a specific wind direction. Two angles are considered, corresponding to partial rotor overlaps of 75 % (ψ=2.8°) and 50 % (ψ=5.7°), respectively. We define rotor overlap as the fraction (in percentage) of the diameter that two wind turbine rotors share when looking downstream. An overlap of 100% corresponds to perfectly aligned rotors (center-to-center), while 50% overlap means that the downstream rotor is laterally displaced by half a rotor diameter. In the static wind direction scenarios, each test has a duration of approximately 30 s, corresponding to about 4 h at full scale. Six repetitions are performed to reduce the uncertainties caused by the turbulent fluctuations of the flow.

In the dynamic tests, the turntable is rotated according to a predetermined time series, in order to dynamically vary the wind direction over the cluster of turbines. In this case, each test has a duration of 180 s, to match the overall duration of the static tests.

Figure  shows the wind tunnel set-up, while Fig.  shows the vertical profiles of the mean streamwise velocity and turbulence intensity measured at the location of the upstream turbine WT1 for ψ=0°.

The APC algorithms are implemented in MATLAB Simulink , from which C++ codes are exported, and later compiled and loaded onto a Bachmann M1 PLC . At every time step, the APC controller receives information on the current power demand and, for each wind turbine, on its instantaneous power production, blade pitch angle, and tower-base fore-aft bending moment. Furthermore, the APC controller is also informed in real time about the current wind farm power demand Pref and the current wind direction ψ. In one sampling period, the set-points of demanded power and nacelle yaw are computed by the APC controller and dispatched to each wind turbine. The direction of the wind relative to the farm is read from the turntable encoder. Therefore, its measurement can be considered exact up to the accuracy of this sensor. In the field, the knowledge of ψ is definitively more uncertain, due to the typically limited accuracy of the onboard anemometry system and the yaw encoder. The effects of wind direction uncertainties on wake steering performance were experimentally investigated by , using a very similar set-up as the one considered here.

The control cabinets executing the wind turbine and APC controllers are connected to a PC in the control room via the Ethernet. This PC is used to monitor the wind turbine sensors through a graphical user interface, to install and uninstall applications, to activate the wind farm controller, and to modify its settings as necessary. The Modbus communication protocol is used to start simultaneous data acquisitions, due to its compatibility with MATLAB. Communication between the APC and the wind turbine controllers is instead accomplished with Ethernet cables through the Profinet protocol . This system was chosen due to its relatively fast communication capabilities and integration with the existing set-up. The APC algorithms are executed with a time step of 4 ms (equivalent to approximately 0.3 s at full scale) to match the time step of the wind turbine controllers. In CL+MR, the open-loop scheduler is updated 100 times slower, i.e., every 0.4 s, corresponding to approximately 30 s at full scale. A sketch of the connections among the various components of the system is shown in Fig. .

Local saturation conditions are indicated by a flag that is raised when both of the following conditions are simultaneously verified:

The tracking error of a turbine exceeds 1 % of the rated power PR, i.e., 0.46 W, and

Saturation conditions are also used to control the integral part of the APC PI controller. As discussed in Sect. , the integrator in the APC loop includes an anti-windup element that is activated when all turbines in the wind farm become saturated. This mechanism quickly reduces the integral term by applying to it a gain of 0.99 at each time step.

All saturation flags are reset when the wind farm power output exceeds Pref by more than 3%PR=1.38 W. This mechanism addresses the situation in which all turbines become saturated. In such cases, the rotors are commanded to follow PD,i=PD,i*, i.e., the last demanded power value prior to saturation, as described in Sect. . However, when all turbines are saturated, the system is unable to detect changes in Pref. Consequently, the machines would continue tracking PD,i* even if Pref decreases. To avoid this situation, the APC integrator and all saturations are reset whenever ΔP<-3%PR. In the CLD PI controller, the integrator is reset either when all turbines become saturated or when this condition ends.

The control algorithms rely on multiple first-order filters. Cut-off frequencies are normalized using the rated rotor speed ΩR, which allows for a straightforward conversion to the full-scale case. For all controllers described in Sect. , the power generated by each turbine is low-pass filtered using a first-order transfer function with a cut-off frequency of 5 Hz (=0.35ΩR), before inputting it in the farm-level controller. A first-order filter is chosen here to limit the time delay associated with higher-order filters, which would hinder tracking accuracy. A cut-off frequency of 1.57 Hz (=0.11,ΩR) is used to update the power set-points, while a lower cut-off of 0.72 Hz (=0.05ΩR) is employed for the power demand. These different cut-off frequencies are selected to ensure that the power-demand signal remains smooth while minimizing delays in the set-points.

For CL+LB, fore-aft bending moments are filtered using a moving average with a fundamental frequency of 1 Hz (=0.07ΩR). This value is 1 order of magnitude smaller than the turbine first fore-aft mode at 16 Hz, thereby ensuring that the controller detects only mean loads and does not react to structural vibrations.

The wind tunnel turntable has a diameter of 13 m, and it can be rotated to follow a prescribed time history . The time series has been sampled at 1 Hz at an onshore test site in northern Germany and scaled by the speed-up factor of the experiment. have extensively discussed this set-up, showing a good agreement between the wind direction dynamics in the field and in the lab. Figure  reports the tunnel-scaled direction time history ψ(t).

The figure shows that the scaled time history mainly consists of fluctuations characterized by slow frequencies fψ≤0.05 Hz. These correspond to time scales longer than 20 s, which are 1 order of magnitude larger than the 1–2 s characterizing the propagation time of wake effects. Clearly, the same conclusions would apply at full scale. This also justifies the adoption of a steady-state wake model for the synthesis of the controller.

Throughout the experiment, the wind direction changes sign five times. This condition is particularly challenging when performing double-sided wake steering since it requires a sudden, large yaw angle variation to change the side where wakes are deflected.

Figure a presents the measured available farm power as a function of wind direction ψ, while Fig. b shows the measured variation of local power share as a function of ψ in the absence of wind farm control (i.e., in standard greedy mode).

Figure a highlights the strong effect of wake impingement on power production. The minimum available power is visible in correspondence with ψ≈0°. The lack of symmetry with respect to ψ is due to a lateral inhomogeneity of the flow within the wind tunnel . Overall, WT2 appears to be suffering the most significant power losses, as in fact it produces only 15 % of the wind farm power when ψ=0°. WT3 presents a slightly higher power due to the high turbulence in the two wakes that impinge on it, which speeds up their recovery.

A dynamic reference power signal typical of automatic generation control (AGC) is used as an input signal to the farm-level tracking controllers. AGC is the secondary response regime of grid frequency control, and it consists of dynamically adjusting the power output of a plant according to the request of the TSO . A similar signal has been considered by other authors . The signal is defined as 8P(t,ψ)=Pgreedy(ψ)b+cnkAGC(t), where nkAGC(t) is a normalized time-dependent test signal, Pgreedy(ψ) is the available power of the wind farm in greedy aligned conditions at a specific wind direction ψ, and b and c are two parameters that respectively shift and scale nkAGC.

Due to the small size of the models, the original signal is accelerated in time by a factor of 81.73 . Figure a shows nkAGC as a function of time. In the tests with the dynamic turntable, the reference power signal in Fig. a is looped multiple times for a total length of 3 min. In this case, the instantaneous available wind farm power Pgreedy(ψ) depends on the instantaneous wind direction ψ as shown in Fig. a. Figure b shows the time history of nkAGC(t)Pgreedy(ψ)/Pgreedy(0°), where both the full-scale (top x axis) and wind tunnel (bottom x axis) time scales are reported.

The reference power signal is initialized with a rising ramp to reduce the effects of initial transients. Notice how a 4 h long test in the field is replicated in the significantly shorter time of 180 s in the wind tunnel. It is important to notice that the test time of 3 min covers 24 full-scale 10 min turbulent realizations, which ensures the statistical convergence of results .

The gains used in the APC controllers and the cut-off frequencies of the filters are tuned using a digital twin of the wind tunnel set-up. This model of the experiment is implemented in Simulink and includes three blocks representing the wind turbines, each running the same controller used in the wind tunnel tests. The drivetrain dynamics are modeled as described in , while rotor aerodynamics are represented using LUTs computed offline with a blade element momentum (BEM) model of the G1 . The LUTs schedule rotor thrust and torque as functions of turbine operating conditions. Tower dynamics are modeled with a second-order system.

The Jensen wake model , combined with the instantaneous thrust coefficient CT, is used to estimate the wake deficit for downstream turbines. A delay is used to simulate the time required for wake effects to propagate downstream. The same CL and CL+LB controllers used in the wind tunnel experiments are included in the digital twin. To improve the robustness of gain tuning, zero-mean white noise with a variance of 0.25 W2 is added to the measured input power.

Gain optimization is performed with the goal of reducing the influence of saturation events, using a gradient-based interior-point algorithm with a power-demand signal characterized by Pgreedy=55 W, b=0.8, and c=0.1.

For the CL+LB controller, the cost function is defined as 9J=0.75Δ‾P+0.25∑i=1NΔ‾L,i, which represents a weighted sum of the non-dimensional tracking error Δ‾P and the non-dimensional load-balancing error Δ‾L,i. Both quantities are scaled to lie in the interval [0,1].

The resulting gains for the APC loop are KAPCP=1.3127 [–] ,KAPCI=14.9253s-1=1.05ΩR. For the CLD loop, the gains are KCLDP=0.03427Nm-1=0.52LR-1,KCLDI=0.07959Nm-1s-1=0.09LR-1ΩR, where LR=15.2 Nm is the tower-base fore-aft bending moment of the G1 turbine at rated wind speed.

In CL+MR, wind turbines are subjected to induction control and simultaneously perform wake steering. To model this combined off-rated and misaligned operation, LUTs of power coefficient CP and thrust coefficient CT are computed via an analytical model . The adoption of such a model is motivated by the fact that off-rated operation spans a wide range of CT values – and misaligned operation is strongly dependent on CT .

Another important aspect typical of scaled wind turbine models is the effect of the chord-based Reynolds number on the aerodynamic performance of the rotor . This is relevant since with the controller described in Sect. , turbines operating in off-rated conditions experience low rotational speeds. These effects were taken into account by using a BEM model of the G1 that includes a dependency on the chord-based Reynolds number . Figures  and  show examples of LUTs for CP and CT, where the auxiliary factor ϵ has been introduced to quantify the level of derating, with ϵ=1 corresponding to the greedy power mode.

Since both power demand and wind direction vary, the LUTs for γi(PD,ψ) and αi(PD,ψ) are two-dimensional. Other model inputs, such as TI and inflow shear, are fixed as described in Sect. . To generate the LUTs, different optimizations are solved for each wind direction and wind farm power demand. When the optimization converges, the resulting power share set-points are computed as αi=Pi/∑i=1NPi, and they are stored together with the yaw set-points. The optimization problem is solved with the gradient-based sequential quadratic programming (SQP) method . With the aim of avoiding entrapment in local minima, the optimization for the first power-demand level is carried out using various random perturbations of the power-boosting solution as initial guesses. After this first solution, the wind farm power demand is progressively lowered and the result of the previous optimization is used as a starting guess for the next curtailment level. The minimum curtailment levels is limited to 40 % of the maximum wind farm power, which is sufficient to cover the APC scenarios described in Sect. . Results are shown in Figs.  and  for the yaw and power set-points, respectively.

In the figures, ψ=0° represents a condition of precise alignment and therefore full wake impingement. Conversely, when 0°<|ψ|≤11.3°, partial wake impingement occurs. The yaw set-points present, in fact, a maximum absolute value in full waking, where steering is heavily used to increase power reserves. As ψ increases, the power set-points start converging toward an equal power dispatch, i.e., αi=1/N, while the yaw misalignment is progressively reduced. In fact, as ψ deviates away from 0°, wake impingement is less prominent, and all turbines perceive similar local inflow conditions.

The treatment of the ψ=0° condition is particularly relevant: under dynamic wind direction variations, when ψ switches sign, the upstream wind turbines must change their yaw set-point by more than ±40°. Delays in following this demand – which are expected due to the necessarily limited speed of the yaw actuation system – could result in relevant power losses, since the wake may be temporarily deflected toward downstream rotors, instead of away from them. To avoid this situation, no optimal wake steering is performed between -2°<ψ<2°, but instead, the set-points are interpolated from the values at ±2° to ensure a smooth transition when ψ switches sign. This solution should not result in a hindrance to the overall effectiveness of wake steering, since deflecting wakes is more effective in partial than in full impingement .

During operation, αi and γi are linearly interpolated from the LUTs in Figs.  and  based on the average power demand and wind direction computed over the previous 0.4 s. Clipping to the last available value of the LUT is used to avoid extrapolating.

The power reserves for CL+MR are compared to those of OL in steady-state conditions, using the simulation environment described earlier. The comparison considers the difference between the power-produced Pi and the available power Pa,i for each turbine. Figure  shows the locally available power and the minimum power (last column) in the farm for two wind directions, i.e., ψ=2.8 and 5.7°, corresponding to partial rotor overlaps of 75 % and 50 %, respectively.

Results show that the largest wind farm power gain is obtained for ψ=2.8° (≈+18%), followed by ψ=5.7° (≈+14%), confirming that wake steering is particularly beneficial in partial wake impingement conditions . As a result of the higher wind farm power, a significant gain in power reserve is achieved with CL+MR relative to OL, in particular for the front turbine WT1. This is favorable, since WT1 is often required to compensate for the saturations that may affect waked rotors. For these downstream turbines, the benefit of CL+MR becomes evident at severe power demands, i.e., ∑i=1NPi,OL≈95%, and it gradually decreases as ∑iPi,OL is reduced because of the loss of effectiveness of wake steering due to the lower operational CT of upstream rotors. This, in fact, implies a lower velocity deficit in the wake and a less prominent deflection. Overall, CL+MR yields a distribution of power reserves across the turbines that is more uniform than when using the OL method, consistently with the goal of the optimization.

The last two plots on the right in Fig.  show the worst power reserve in each cluster across the range of wind farm power demands for the two considered wind directions. For OL, WT1 is the most critical rotor. Under curtailment, its power reserve increases linearly, albeit at a slower rate than that of the downstream rotors, which exhibit a non-linear increase (as shown in the corresponding plots, appearing in the second and third column of the figure), likely due to wake effects. In contrast, for CL+MR, the worst power reserve shifts from WT1 to WT2 as the rotors adjust their yaw alignment, in turn resulting in consistently larger margins than in the OL case.

To quantify the mean power reserve of each turbine, we analyze the average collective blade pitch angle θ‾. With the controller described in Sect. , the closer θ‾ is to the optimal pitch θOPT, the less power reserve is available. Figures  and  show the local mean collective blade pitch angle for ψ=2.8° and ψ=5.7°, respectively.

Consistently with the tracking error analysis, θ‾ appears to decrease as the power demand increases. OL and CL+LB present a power reserve distribution that is significantly unbalanced toward WT1. In particular, CL+LB presents the highest values of θ‾ for WT1, but at the same time it also always yields low values of θ‾ for waked rotors. CL remarkably improves the balancing of power reserves compared to OL, especially for ψ=2.8° and for low values of b. CL+MR presents a rather uniform distribution of the power reserves, favoring especially the most waked rotor, i.e., WT3. This directly confirms the effectiveness of wake steering, which, by laterally moving upstream wakes, improves the power reserve of the most downstream rotor.

In the following loads and fatigue analysis, we only display data for the 75 % rotor overlap scenario, since results for ψ=5.7° (50 % rotor overlap) are similar (and reported, for completeness, in Appendix ).

The mean local load-balancing error of each rotor is shown in Fig. .

Results show that for OL and CL, loading is maximum on WT1 and decreases when moving downstream. CL+LB effectively balances loads in the wind farm, with remarkable effectiveness for b<0.9. When b=0.9, the significant increase in saturation events is such that loads cannot be balanced anymore, since power tracking accuracy is prioritized. This shows the limit of the load-balancing strategy that, in some cases, is unable to achieve the goals for which it has been formulated.

Next, damage equivalent loads (DELs) at tower base are presented in Fig. .

Results show that waked turbines generally suffer more damage than those operating in freestream conditions, with WT3 being consistently the most damaged. This is likely due to the highly turbulent local inflow and the partial wake impingement that introduce numerous load cycles on these machines. OL generally presents a rather low level of fatigue, which is due to the limited pitch actuation deriving from the lack of a closed-loop correction. At the same time, CL+LB yields the highest damage for WT1. In contrast to OL, this is caused by the more frequent blade pitch actuation that follows the occurrence of saturation events happening downstream. CL+MR reduces the fatigue of WT3 in almost all instances, because wake steering applied to WT2 mitigates partial wake overlap effects. CL+MR also reduces the fatigue of WT1, likely because fewer saturation events occur at downstream rotors, which WT1 would otherwise have to compensate for through additional blade pitch activity. The analysis of blade pitch actuator duty cycle is reported in Appendix .

Overall, the results shown here are consistent with the numerical findings by , but they differ from those reported by , who observed significant fatigue reductions for downstream rotors when applying a load-balancing APC strategy. One possible explanation for this discrepancy is the substantially larger wind farm considered by . A larger array facilitates spatial averaging of power and load fluctuations across multiple turbines, which may enhance the effectiveness of CL+LB. In contrast, the present study considers a limited number of turbines, where farm-level averaging effects are inherently reduced. While this difference may influence the achievable fatigue mitigation, particularly for downstream machines that are generally more prone to saturations, the analysis of small clusters appears to be less forgiving and hence can more clearly highlight the effects of difficult situations on tracking performance.

The RMS of the tracking error is shown in Fig. .

Consistently with the static wind direction results, OL shows the worst performance of all APC methods. At moderate power demands, for b≤0.85, CL and CL+MR exhibit the best performance. For b=0.9, CL+MR provides the lowest RMS ΔP. The relative improvements achieved by CL+MR are less pronounced in the dynamic tests than in the static ones, as the effects of wake steering are less beneficial at large turntable misalignments where wake interactions are much reduced.

Figure  shows how the errors are distributed across the three turbines. It is important to mention that saturated turbines will display extreme error values ΔP,i, although this does not necessarily imply a large wind farm tracking error ΔP, since (except than for OL) non-saturated rotors can compensate for their error.

The figure shows relatively large tracking errors for OL, because of a lack of feedback capable of handling saturation conditions. Significant tracking errors can be observed for waked rotors in the case CL+LB, indicating persistent saturations, as seen in the zoomed regions of Fig. .

Figure  supports this analysis by presenting the mean collective blade pitch angles of the turbines during the experiment. As mentioned in the static direction study, θ‾i can be seen as an indirect measure of the power reserve for the ith turbine.

Results show that CL+LB presents a significantly unbalanced power reserve distribution, shifted toward the upstream rotor, possibly as a result of the CLD loop. This is in agreement with the other quantities presented and discussed earlier in this section. As expected, CL+MR presents a rather large power reserve for all rotors, especially for WT3, thanks to wake steering, but also for WT1, which is remarkable since this upstream turbine is often misaligned.

Figure  presents the mean load-balancing error for the dynamic turntable experiment.

For OL and CL, the front turbine WT1 exhibits the highest loading, which progressively diminishes for rotors located further downstream. As seen already in the static cases, CL+LB effectively balances the loads. Its effectiveness is excellent at b=0.8 but – importantly – gradually deteriorates as b increases since more saturation events arise that modify the power share distribution to prioritize tracking accuracy. CL+MR displays the second-best performance for the lower b values but ultimately outperforms CL+LB for b=0.9. This shows the importance of controlling saturations and the limits of a purely load-balancing strategy.

Figure  reports the normalized tower-base fore-aft DELs.

These results generally indicate a higher fatigue for WT2, followed by WT3 and WT1, which is the least-affected turbine. WT2 is also the rotor that generally has the smallest power margin in the farm, as shown in Fig. . This result is consistent with the findings of , which showed that fatigue is driven by the low-frequency load cycles that occur because of saturation events. OL generally exhibits the lowest fatigue, due to the smoother control of the rotors. The proposed CL+MR method reduces DEL(L)‾ for WT1 and WT3 compared to other methods featuring a closed loop, while it increases it for WT2, possibly due to a lower power margin deriving from the αi and γi LUTs.