In addition to AFC actuators, the choice of AFC sensors is another critical aspect for the load alleviation strategies of smart rotors. give a review of the possible sensors that can be used in smart rotor control. Many of these sensors have been used in TE flap control studies over the past years. We can broadly categorize them into three groups: strain sensors, inertial sensors and inflow sensors.

Strain sensors measure the local strains on a component. These can be conventional strain gauges or optical strain sensors. Strain sensors have been widely used in TE flap control strategies. In particular, strain sensors measuring the flapwise blade root bending moment (BRBM) have received much attention. A common strategy that uses these sensors is called individual flap control (IFC). It is based on the individual pitch control (IPC) strategy and is often used in combination with the latter . Other studies have used the flapwise BRBM sensor in PID-type controllers , model-based controllers and adaptive controllers .

Strain sensors measuring the flapwise BRBM have been a popular and effective choice because the main focus of TE flap control has been fatigue load reduction of the out-of-plane loads. The frequency content of these fatigue loads is fairly low . Therefore, these sensors can be effectively used even if they measure the effect of the aerodynamic loads with a certain delay (caused by the blade inertia).

Out-of-plane fatigue loads are design driving for several turbine components. Yet if we focus on the wind turbine blade, flapwise fatigue loads are not necessarily the best objective to use TE flaps or other local AFC devices for.

Flapwise BRBM fatigue loads have a fairly low-frequency content. Most of the damage concentrates around the 1P frequency and can be addressed by the pitch controller using strategies such as IPC.

Blade optimization studies that include fatigue-oriented TE flap control as part of their optimization features did not show significant additional blade mass reduction compared to an optimized blade design without flaps. optimize the DTU 10 MW Reference Wind Turbine-blade using a multidisciplinary design, analysis and optimization tool. They find that the results of the blade optimization are comparable if the blade is optimized with a fatigue-focused flap controller or if the blade is optimized without flaps altogether. use an optimization algorithm to optimize the blade of the NREL 5 MW Reference Wind Turbine so that the levelized cost of energy is minimized. The algorithm also optimizes a model-based controller used for pitch and TE flap control . They conclude that

[t]he blade optimization problems addressed in this work are primarily driven by flapwise stiffness, with blade deflection, rotor thrust and flapwise ultimate stresses in the spar forming the design drivers (, p. 764).

point out that important load components for preliminary innovative concepts of multi-megawatt-scaled turbines include the ultimate loads of the resulting BRBM, ultimate and fatigue loads of the blade root torsional moment, fatigue loads of the edgewise BRBM, and the blade tip-to-tower clearance.

From these findings one can conclude that for modern large rotor blades, the extreme value of the resulting BRBM and the blade tip-to-tower clearance will be decisive. In the edgewise direction, the design-driving loads will be dictated by the fatigue loads arising from the blade's mass. In this direction, the blade root has to endure a load fluctuation with an amplitude equaling the blade's static moment once per revolution (1P).

Should the objective of an AFC strategy shift to reducing flapwise extreme loads and critical deflections, it would also have a positive effect on the design-driving edgewise fatigue loads of the blade. When an effective controller reduces extreme loads and deflections, the spar cap of the blade can be optimized and hence the mass of the blade reduced. This in turn reduces the edgewise fatigue loads near the blade root. These loads are mainly caused by gravitational forces. In additional optimization loops, the blade mass could be further reduced, potentially creating a virtuous cycle.

If a TE flap control strategy is used to alleviate loads with high frequency content (such as design-driving extreme loads), the choice of a sensor for controller input becomes much more relevant. Using the flapwise BRBM as an input sensor for the TE flap controller has its advantages in the implementation and maintenance of the sensor but can have negative effects on the performance of the controller. Because sensor and actuator are far apart, aerodynamic loads and deflections at the blade tip are sensed at the root with a considerable time lag. This time lag carries through to the actuation response of the controller, limiting its effectiveness . Inflow sensors would be an attractive sensor choice were it not for the practical drawbacks of cost (e.g., lidar) or susceptibility to the elements (e.g., pitot tubes and pressure sensors) in their implementation .

A possible sensor that has not received much attention from the community is the TE flap hinge moment . It has the advantage of providing local loading information of a blade section without the need of additional inflow sensors on the blade. The flap actuator is assumed to be enclosed inside the blade section. This protects the hinge moment sensor (located in the actuator) from the elements, making it a very robust sensor. The loading information from the flap hinge can be used in combination with the high actuation bandwidth of the flaps to effectively reduce extreme loads and critical deflections of the blade. This idea is attractive because it uses the robust and already available hinge moment sensor in the flap actuator system as an input for the controller, thus addressing the aforementioned drawbacks of cost and susceptibility. It is also advantageous if the TE flap system is to be designed in a modular layout.

The goal of the present study is to explore and quantify the potential of TE flaps to mitigate design-driving extreme loads and deflections. We are also interested in exploring the possibility of using a local and robust sensor as an input choice for a controller strategy. This paper presents a novel method that allows the use of the TE flap hinge moment as an input sensor. It is a model-based observer that estimates the effective angle of attack of the blade section given the hinge moment, the accelerations and the relative wind velocity of the section (the last quantity is also estimated with our method). In addition, we use this observer as part of a simple extreme load controller for flaps and analyze its performance in a power production scenario with extreme turbulent wind. Section  summarizes our turbine and flap models as well as the aeroelastic simulation tools used in this study. In Sect. , we present the model used to calculate the unsteady flap hinge moment in aeroelastic simulations and our novel observer that estimates the local aerodynamic information based on this and other sensors. Section  presents the results of the observer under steady and turbulent wind conditions. In Sect. , we present a simple extreme load controller that uses this observer. We analyze the controller's performance in reducing extreme loads under challenging extreme turbulent wind conditions. The conclusions are drawn in Sect. .

The blade of the DTU 10 MW RWT was modified to accommodate TE flaps. The flaps are modeled via dynamic polar sets that describe the airfoil with discrete flap angles. For this study we chose a flap that covers 10 % of the chord and has maximum deflection angles of δ=±15∘. Figure a shows the polar data of the FFA-W3-241 airfoil – used in the outer part of the blade – with the modeled flap at maximum and minimum deflection. In total 15 polar sets were generated for different discrete flap positions using a Reynolds number of 1.5×107. The polars were obtained using the airfoil simulator XFLR5 integrated into QBlade . In the simulation, the polar data between the discrete states are linearly interpolated.

In total six flaps are integrated into the blade, as can be seen in Fig. b. Each section measures 3 m in the spanwise direction and is assumed to have one hinge moment sensor and one accelerometer located at the center of the section. The six sections are located between 64 and 82 m of the blade span, which corresponds to a relative location between 74.1 % and 95 % of the blade length. The flap actuators are modeled as a second-order low-pass filter. In the Laplace domain, the filter takes the form 1δLP(s)=ω2s2+2ξω⋅s+ω2⋅δ(s), where ω is the filter frequency and ξ the damping factor. For the flap actuators, we chose a frequency of 5 Hz and a damping factor of 1. The maximum and minimum flap rates are limited to ±100 ∘ s-1.

We did the development, testing and simulation of the methods presented in this study using two aeroelastic simulation tools: the first is NREL's FAST v8.15 and the second is TU Berlin's QBlade.

For this study, we used the TUB Controller . It is based on the DTU Wind Energy Controller , which features a baseline pitch and torque control. It has been extended with a supervisory control based on the report by . The supervisory control allows the controller to run a full load analysis. The controller baseline pitch and torque control parameters were taken from the report by . The controller has been extended so that it can control AFC devices such as TE flaps.

Because we use polar data to derive the aerodynamic loads on a blade section, we cannot measure the unsteady hinge moment directly in the simulations. We therefore need a model to calculate the hinge moment on a blade section. Ignoring friction, the total hinge moment on a blade section with a TE flap can be determined by the sum of the hinge moment due to gravity loads, the moment due to the flap inertial loads and the moment due to aerodynamic loads .

We can use the model presented in the previous section to estimate the effective angle of attack of the blade section by means of a linear observer. The idea is to estimate the internal states of a system based on the measured inputs and outputs. If we cannot measure the quantities α, α˙ and α¨ (because we would need an inflow sensor), we have to estimate them using the measured MHin and other available sensors.

In this study, we follow an approach used in . The observer model is comprised of three submodels: a nonlinear MH-g model, a linear hinge model (that estimates M^H-A and M^H-I) and a signal model. The latter is used to estimate the quantities we cannot measure. All three models are combined to produce an estimated hinge model M^Hin. The estimation is then compared to the measured MHin, and the error is fed back to the states of the linear hinge model and the signal model using an appropriately chosen gain L.

Figure  shows a graphical representation of the observer structure. The hinge moment model of the observer uses the same state-space matrices AHin, BHin, CHin and DHin, with the exception of DHin. The inertial loads given by Eq. () are included in the feedthrough term Dδ¨ of DHin so that the linear observer can use the state-space matrices to estimate M^H-A+M^H-I directly.

The output of the state-space representation does not include M^H-A0, the constant value of the hinge moment for α=0∘. In addition, MH-g cannot be written in state-space form due to its non-linear nature. It therefore cannot be directly included in the observer model. However, it is highly deterministic and can be estimated using Eq. () with readily available sensors. The observer uses Eq. () to estimate M^H-g. As for M^H-A0, the observer multiplies Vrel2 by a constant factor that includes Ch-0c and the dimensions of the blade section. Both quantities are subtracted from the measured MHin so that the error is calculated between (MH-A+MH-I) and (M^H-A+M^H-I).

For this study we use a simple signal model. It basically assumes that α and its derivatives do not change with time. The choice of this signal model is based on the fact that the source of change of α – the incoming wind speed VOP – is turbulent and therefore difficult to predict. The downside is that the estimated signal will always have a lag compared to the actual signal. The signal model has the following state-space matrices: 14ASig=010001000,15CSig=I3×3. We note that other signal models can be used, such as, e.g., a bank of independent harmonic oscillators , if the wind conditions for a particular site are known with a certain degree of accuracy.

If we combine the signal and hinge moment models, we get a state space whose input vector is uS+H=δδ˙δ¨h˙h¨T and its output is yS+H=(M^H-A+M^H-I). The state-space matrices for this combined system are as follows. 16AS+H=ASig03×4BHinαAHin17BS+H=03×5BHinRes18CS+H=DαDα˙Dα¨CHin19DS+H=DδDδ˙Dδ¨Dh˙Dh¨ In these equations, BHinα corresponds to the sub-matrix of BHin that relates to α and its derivatives. BHinRes corresponds to the rest of BHin. The entries of these matrices are written out explicitly in Appendix .

The final state-space representation of our observer has the form 20Aobs=AS+H-LCS+H,21Bobs=BS+H-LDS+HL,22Cobs=1000000,23Dobs=01×6. Its input vector is given by uobs=δδ˙δ¨h˙h¨MHin-M^H-g-M^H-A0T and its output is yobs=α^.

The gain matrix L is obtained using a standard Kalman filter design. In order to tune our estimator, we use the covariance matrices for process noise QL and for measurement noise RL.

The derivation of the linear estimator above is only valid for one fixed value of Vrel. This is not the case for a wind turbine blade in normal operation. In order to extend the estimator so that it can be used for varying Vrel, a linear parameter varying (LPV) model was built using the observer matrices for different values of Vrel. This way, the nonlinear aerodynamic behavior of the flap hinge moment is parameterized with a set of linear observers, allowing for a fast and optimal estimation for each value of Vrel. If Vrel is used for the LPV model, it needs to be measured or estimated. The former option is not available, since we chose not to use inflow sensors. This leaves us with the estimation option, presented in the next section.

To estimate Vrel, we decompose the velocity into in-plane and out-of-plane components. The in-plane component of the rigid blade can be readily estimated using the rotor speed Ω and the distance between the hub center and spanwise center of the flapped blade section rflap: 24VIP=Ω⋅rflap. For the out-of-plane component, we use a simple estimator based on the anemometer wind speed VAne, the rotor azimuth angle φ and the normal velocities of the flapped blade sections of the three blades that share the same spanwise distance from the rotor hub (h˙1–h˙3). The latter can be obtained by integrating the signal of accelerometers measuring the local accelerations of the sections of each blade: 25VOP=VAne+ΔVoph˙1,h˙2,h˙3,φ. ΔVop(h˙1, h˙2, h˙3, φ) is a function that accounts for the vertical variation in VOP dependent on the azimuthal position of the blade due to, e.g., wind shear. It comprises two parts: a vertical variation part and a tower shadow model.

The vertical variation part uses the once-per-revolution Coleman transform of the velocities of the blade sections normal to the chord to get an equivalent amplitude of the vertically varying velocity normal to the chord of the rotor annulus at the spanwise position of the flapped blade section. 26vsin=23⋅sin⁡(φ)⋅h˙1+sin⁡φ+2π3⋅h˙2+sin⁡φ+4π3⋅h˙3 We then use a linear transform of this quantity to estimate the vertical variation in the out-of-plane wind velocity at different azimuthal positions of the blade. 27ΔVop-v=c1⋅cos⁡(φ)⋅vsin+c2for-π2≤φ≤π2c3⋅cos⁡(φ)⋅vsin+c4forπ2<φ<3π2 The two cases in the above equation are necessary because of the non-linear effect of wind shear on the vertical wind velocity. Because we are approximating the out-of-plane variation with a simple cosine function, we use two amplitudes to account for the variation at the lower and upper half planes of the rotor. The constants c1–c4 were obtained by fitting the results of the values of ΔVop-v and vsin from aeroelastic constant wind simulations of the turbine. In addition, vsin is low-passed and notch filtered to filter out the higher-frequency contributions to the normal velocity of the rotor annulus.

The tower shadow variation part uses a simplified approximation of the tower shadow model from . We simplified this model by assuming a constant x distance (out of plane) between blade and tower. It was taken as the average distance between the blade section and the tower surface in constant wind aeroelastic simulations. That is one constant value that is used for all wind speeds. The tower shadow variation is added to ΔVop-v to get ΔVop.

Once we have calculated VIP and VOP, we use both quantities to obtain the relative velocity of the flapped blade section. In uniform aligned inflow, Vrel would be the resulting velocity from the previous quantities. This is almost never the case. To account for the oblique inflow, we use the trigonometric correction presented in : 28Vrel=VOP⋅cos⁡(γ)⋅cos⁡(τ)-x˙2+VIP-y˙-VOP⋅(cos⁡(γ)⋅sin⁡(τ)⋅sin⁡(φ)+sin⁡(γ)⋅cos⁡(φ))212. For this correction, we need to know the shaft tilt angle τ and the current yaw-misalignment angle γ. The latter can be obtained via the hub-mounted anemometers. In Eq. (), we also included the in-plane (y˙) and out-of-plane (x˙) velocities of the flapped blade section due to blade elasticity. These can be obtained by rotating the chordwise and normal velocities of the section by the current blade pitch angle and the twist angle (see Fig. ): 29x˙=h˙⋅cos⁡(180∘-(β+θ))+f˙⋅sin⁡(180∘-(β+θ)),30y˙=-h˙⋅sin⁡(180∘-(β+θ))+f˙⋅cos⁡(180∘-(β+θ)).

We note that the expression for VOP is a relative simple estimation of the out-of-plane velocity. This is not exact since there is significant variation in VOP along the rotor disc due to the non-linear wind shear and turbulence. This error can be tolerated because VIP2 dominates in the right-hand side of Eq. (). This is specially so for large rotor blades with high tip speed ratios, which is the current industry trend. So an error in VOP will only have a small contribution towards Vrel and hence towards α^. There have been several studies that include more accurate estimations of the rotor effective wind speed, and being two examples. Such methods could be used to further increase the accuracy of the current wind speed estimator. Additional improvements could also be achieved if we include the effect of tower top displacements on the estimated local Vrel.

Combining the Vrel estimator with the estimator for α gives us the final LPV observer based on the flap hinge moment sensor.

The derivation of the model and observer presented in this section is based on several assumptions. The first is the 2D airfoil analysis assumption. It is therefore only correct for an infinitely thin blade station. Changes in the wind distribution and angle of attack along the span of the blade section will have an integrated effect on the hinge moment and potentially deviate from the pure 2D analysis. In this study we assume that the aerodynamic conditions do not change significantly within a flapped blade section and therefore can be treated as effective quantities for the section.

To have an idea of the error made with this assumption, we take the innermost 3 m flapped section with the aforementioned sensors located at the center of the section span. The center of this section is situated at a blade radius of 65.5 m. For turbine operation at rated rotor speed, the difference of local in-plane wind speeds between the center of the blade section and the inner part of the section span is about 2 % of the in-plane velocity at the section center. For the outer flapped sections, the relative error decreases due to the increased wind speed used for reference. For the out-of-plane wind speed we can estimate the error by looking at the coherence function of the spatial distribution of the turbulence. Assuming a Kaimal wind model, the spatial coherence function of two points that are 1.5 m apart is 0.75 for a frequency corresponding to 1P and an average out-of-plane velocity of 10 m s-1 .

Ultimately the validity of this assumption is reflected in the controller performance and has to be assessed experimentally or in simulations. also assume a correlation between the lift forces occurring at nearby blade stations and the lift force of the blade station where a pitot tube is installed. With this assumption they are able to enhance the performance of an IPC controller based on the information of one inflow sensor per blade. In , the authors successfully control a 2 m flapped blade section using a feed-forward controller based on the local information of one pitot tube. These are encouraging results suggesting the aforementioned assumption is valid.

The observer presented in this section is based on a thin airfoil model and does not correspond to physical airfoils used in wind turbines. As we saw in Sect. , our model only partially captures the viscous effects of flow separation that greatly influence the behavior of Ch as a function of α. We approximated this effect with the use of flap effectiveness coefficients. Nonetheless, the nonlinear behavior for larger absolute values of α was not captured. To improve our modeling, we could determine the complete state-space models of the flap hinge moment at different wind speeds experimentally. This could be done for example in wind tunnel tests with the help of system identification techniques .

Both the hinge moment model and the observer are included in the TUB Controller . The inputs for the model (u=αα˙α¨δδ˙δ¨h˙h¨T and Vrel) and for the observer (uS+H=δδ˙δ¨h˙h¨T and the inputs for the velocity estimator) are calculated by the aeroelastic code and passed to the controller via an appropriate interface. For the FAST simulations the interface occurred within a Simulink environment. For the QBlade simulations, a special interface was developed between the software and the controller to be able to pass the required inputs.

As discussed in Sect. , the hinge moment model and observer are inherently 2D models that require the input at one specific location. We chose this location to be the center of each flapped blade section and assume that this location is representative for the whole section. For the FAST simulations, the blade is discretized into 46 aerodynamic and 57 structural nodes, with nodes specially chosen at the center of each flapped blade section. In QBlade, the blade is discretized into 25 aerodynamic and 20 structural nodes. The aerodynamic nodes are spaced sinusoidally along the blade span. The aerodynamic and structural information at the center of the flapped blade sections is obtained by linearly interpolating the information from neighboring nodes.

The performance of our observer is evaluated by its ability to estimate the representative aerodynamic quantities at the center of each flapped blade section.

This modeling approach could be improved if we consider more aerodynamic blade elements so that several of them lie within a flapped blade section. These elements would be used to calculate the lift force acting on the whole section. Using a representative airfoil polar for the blade section, we could calculate the effective angle of attack at the center location of the section and use this as an input for our hinge model. It would also be this effective angle of attack that would be estimated by our observer.

The parameters of the steady wind simulations are listed in Table  under the column “Steady calculations”.

Figure  shows three key variables for our estimator in simulations with two different hub height wind speeds. One wind speed around rated wind and one above rated where the influence of the pitch angle increases. The simulations were performed with steady wind speeds and a constant nacelle yaw angle of -8∘. We can see in Fig. a the behavior of MHin as a function of φ. In both the 11 and the 17 m s-1 wind speed simulations MHin is mostly determined by MH-A. The larger azimuthal variation in MHin in the 17 m s-1 wind speed simulations comes from the higher relative wind speed variations due to wind shear.

Figure b and c show the estimated and real values of Vrel and α as a function of φ. We can see that the observer is able to estimate the relative velocity and angle of attack at this blade section well. There is a slight delay of α^ compared to α, but it is small at the timescale of one rotor revolution. For both wind speeds, there is a clear difference at an azimuth angle of φ=180∘. The velocity drop of Vrel is due to the tower shadow, which was only approximated in our velocity estimator. This tower shadow effect on α is also not captured correctly by our estimator (Fig. c). We can also see in these figures the variation due to wind shear of Vrel and α. Our approximation captures this variation well but there are still some small differences between the real and the estimated quantities.

Figure  shows the results of steady wind calculations for all wind speeds relevant to power production and for three different yaw angles of the nacelle. The markers represent the mean of the steady simulations, and the error bars represent the extrema of the simulations. Figure a, c and e show the estimated and real relative velocities at the blade section. Our velocity estimator is able to capture these differences and keeps the relative error of the mean velocities at below 0.4 %.

Figure b, d and f show the corresponding estimated and real values of α at the blade section. We see that the observer manages to estimate the mean angle of attack with an error below 0.2∘ for all simulations. The differences in the extrema of α are more marked, especially for higher values of Vhub. The differences in the minima can be explained by the approximation of the tower shadow, which fails to capture the dip in α at azimuth values of φ=180∘ (Fig. c). If we look at the range of Vhub between 8 and 14 m s-1, we can see that the differences between real and estimated maxima of α are small. This is of importance if we want to use the observer as part of a load alleviation controller targeting extreme loads. This is the wind speed range where the turbine sees the highest out-of-plane loading in power production .

We also analyzed the performance of our estimator in fully turbulent wind load calculations. These situations are especially challenging for the observer because our relative velocity estimator does not model turbulent out-of-plane wind speeds. The setup for the turbulent calculations is shown in Table  in the column “Turbulent calculations”.

Because the observer lacks the turbulent variation in the out-of-plane wind speed in the relative velocity estimator, the estimated α^ will have a significantly larger variation than the actual α. This is because the observer will attribute the changes in MHin to the unmeasured α, since it can only assume a correct parametrization coming from V^rel. In order to limit the variations in α^, an additional first-order low-pass filter was added to the output of the α^ observer.

Figure  shows time series that illustrate the performance of the observer in turbulent wind conditions. The simulations are for mean Vhub values of 7 and 15 m s-1, representing scenarios below and above rated wind conditions. The simulations were done using the IEC NTM turbulent wind model.

We can see in Fig.  that the estimator is able to capture the low-frequency variation in α and Vrel well. The differences arise from the effect of the turbulent wind speed. Depending on the wind speed, the magnitude of the differences between V^rel and Vrel can be small or large. Figure b shows the example of 7 m s-1 mean Vhub simulations where the differences between V^rel and Vrel are small. The differences can also be more significant, especially for larger wind speeds. In the 15 m s-1 example (Fig. d), we can see large differences in the 1P variation in Vrel in the simulation time between 550 and 600 s. These variations arise from the repeated passing of the rotating blade through large-scale, slowly varying turbulent wind gusts and hence are not accounted for in V^rel. Due to the low-pass filtering of α^, the abovementioned differences in Vrel do not lead to large oscillations of the former, and we can see that α^ follows α well in the low-frequency regime.

The filtering introduces a time lag which could potentially be detrimental for a controller. The effects of the filter would certainly be more marked for an extreme load controller than for a fatigue load controller. Since we are interested in the extreme load reduction potential of flaps, we will be analyzing the more critical situation in this study. The description and performance of such an extreme loads controller are presented in the next section.

The estimated V^rel and α^ from the observer can also be used for a pitch-based fatigue load controller – such as the one presented by – thereby indirectly increasing the use of the flap system beyond extreme load reduction.

The controller used in this study is based on the extreme load controller presented by . It has an attractively simple architecture and was shown to work effectively in the mentioned study. In the original controller, all three out-of-plane BRBM signals MY-iBR are compared to a maximum threshold Mthr. If 31MY-iBR≥Mthr, then all flaps of all blades are deployed to a target angle.

We expanded this controller by including additional sensors and criteria to trigger flap action. The controller logic is shown in Fig. . The subscripts of the figure correspond to the jth flap of the ith blade. Although there are six flaps per blade, the controller treats them all as a single unit. The input of the individual flaps is averaged per blade (denoted by the symbol (⋅)‾). Combinations of input sensors are compared against thresholds. If they pass the thresholds, then all flaps of all blades are set to a target value. The first condition for triggering the flap action is Eq. (). This condition is identical to the one proposed by . Here, a careful selection of Mthr has to be made in order not to influence the turbine in normal power production. The other three conditions are 32MY-iBR≥Mtr1andx˙‾i≥x˙tr1orMY-iBR≥Mtr2andx˙‾i≥x˙tr2,33MY-iBR≥Mtr1andα^‾i≥αtr1andV^‾rel-i≥Vtr1,34MY-iBR≥Mtr1andM‾Hin-i≤MHin-tr1andV^‾rel-i≥Vtr1. Here, Mtr-i, x˙tr-i, αtr1, Vtr1 and MHin-tr1 are threshold values for the respective input sensors. The idea of these conditions is to lower the threshold for MY-iBR to deploy the flaps for the cases where extreme bending moments are expected to happen. It was seen in preliminary simulations that the flap deployment had a delayed effect on the lowering of the blade root bending moment. Deploying the flaps close to a load peak would only have a small load reduction effect on MY-iBR. Yet this condition is necessary in order to limit the influence of the flap controller on the power output of the turbine.

By using the flap hinge sensor in the outer blade span (Eqs.  and ), the controller has additional aerodynamic information about the likelihood of a strong wind gust and is able to deploy the flaps at a lower threshold value of MY-iBR (Mtr1<Mthr), thus giving the flaps more time to effectively mitigate the blade root loads. We mentioned in Sect.  that our observer includes a low-pass filter for α^ which causes a delay in the signal. To enable our controller to sense sudden increases in α, we also included a condition based on M‾Hin-i directly. Assuming that the flap deployment angle will mostly be δi,j=0∘, the value of M‾Hin-i will be approximately proportional to α‾i for small reduced frequencies (Fig. b).

Preliminary simulations also revealed that blade deflection dynamics are critical for predicting extreme events of MY-iBR and were not always strongly correlated to the aerodynamic information. The controller includes Eq. () to account for extreme loads due to large values of x˙‾. We include two conditions to also account for very high velocities that occur at lower values of MY-iBR (Mtr2<Mtr1 and x˙tr2>x˙tr1).

If any of the above conditions are met for any blade, then all flaps of all blades are deployed to the target angle δtar=-14.5∘. This value is slightly lower than the maximum modeled value in the polars. This was done to still be able to model the aerodynamic effect of a flap angle overshoot when the flaps are deployed. Additionally, the flaps were kept deployed for a given time τdep before they were returned to the original position. τdep was chosen to be about a third of one rotor period. This way if a localized gust triggers the flap controller of one blade, the following blade will already have deployed flaps when encountering the local gust. Finally, the controller also returns the flaps to their 0∘ position with a reduced rate compared to the maximum flap rate. This is to have a smooth return to normal conditions and to avoid excessive oscillations of the blades by frequent on–off transitions.

The conditions explained so far are valid for cases where the strategy is used to mitigate the maxima of MY-iBR. This is the case of the considered load cases (Table ). Equivalent conditions can be defined for the controller to mitigate the minima of MY-iBR.

We note that this controller treats all flaps in one blade as a single unit. Why should we make the additional effort to include multiple flaps per blade? One reason for having several flaps per blade instead of one is that a system of multiple independent flaps will still be able to reduce the loads in the event of one flap ceasing to function. This makes the system more redundant and thus more appropriate for extreme load reduction. A second reason is that the controller will have sensorial input from multiple sources. Averaging the signals of the six flaps smooths out possible local variations that could arise from using a single set of sensors. Finally, having multiple sensors and actuators per blade opens up the possibility of using local distributed control strategies in future studies.

The metrics considered in this study are max(MYBR) – the extreme out-of-plane bending moment at the blade root, max(MXYBR) – the extreme resulting bending moment at the blade root – and max(DXT2T) – the maximum blade out-of-plane deflection in the region defined by 5∘ before the blade's closest azimuthal position to the tower and 5∘ after this position. For a blade whose rotor azimuth angle is defined as 0∘ when the blade is pointing vertically upward, this region would lie between the azimuth angles of 175 and 185∘. This metric gives us an estimate of the minimum blade tip-to-tower surface distance.

Because we are dealing with stochastic wind simulations, we chose to follow the averaging procedure for extreme values described in . The maximum value of MYBR, MXYBR and DXT2T (considering all three blades) is recorded for each simulation. The extreme value is then taken as the average of the six highest maxima of all simulations. For the case of MXYBR, we did this averaging analysis for 72 different angular bins. For each time step, the direction of the load vector was calculated, and the maximum of MXYBR was determined for each angular bin in each simulation. This gives a more detailed picture of the effect of the flap controller on the extreme resulting bending moments in different load directions. No safety factors were applied since all the considered load cases share the same safety factor.

A complete analysis should include other key turbine sensors to measure the overall effect of the controller on the turbine. We chose not to include these sensors in order to limit the scope of this study.

In this study we focused on the load case group that caused the highest MXYBR design loads of our selected turbine . This is the DLC load case group 1.3 which has the ETM wind model. We considered a subset of wind speed bins of this group around the rated wind speed (see Table  in the column “Turbulent calculations”). This is also the region of maximum rotor thrust and thus the expected maximum values of MXYBR and DXT2T. We considered wind speeds in a range of mean VHub between 9 and 17 m s-1 in 2 m s-1 steps. Six different simulations were done for each wind speed bin, giving us a total of 30 simulations for each controller configuration. We also included the results of simulations from the DLC load case group 1.1 without flap controller. This way we have a reference of the load increase due to the increased turbulence of the DLC 1.3 group.

Although the number of simulations is rather low to determine the overall extreme values of MXYBR and DXT2T, our selection will give us a good estimate of their maxima. By using QBlade – which has the lifting line free vortex wake (LLFVW) aerodynamic model and a multi-body based structural model – we ensure that the results of our load calculations are more accurate than with other codes that use the more common BEM aerodynamic model . In all simulations we included additional 100 s simulation time to allow the wake to develop. This time was discarded in our analysis.

Figure  shows an overview of the maxima of MYBR for the individual simulations of the different DLC groups and controller configurations.

As expected, the highest values of MYBR for the DLC 1.1 power production group occur for wind speed bins around rated wind. Although some high extreme values are also recorded for the wind speed bin of Vhub=15 m s-1. This is because of the turbulent wind conditions. The increased turbulence of the DLC 1.3 load cases leads to significantly higher values of max(MYBR) when compared to the values of the DLC 1.1 group. This is for all the considered wind speeds. Including the TE flap controller in the DLC 1.3 simulations visibly lowers the maxima of MYBR. The extremes for wind speed bins between 11 and 15 m s-1 are comparable to the extremes of the DLC 1.1 group without flap actuation. These wind speed bins also include the highest values of max(MYBR).

A numerical comparison is shown in Fig. . Here we can see the normalized values of max(MYBR), max(DXT2T) and max(MXYBR) for all simulations with and without active flaps (AFC in the figure). As explained in Sect. , these values were obtained by using the averaging procedure of extrema according to the IEC standard. We can see that by including active trailing edge flaps we can reduce the extreme out-of-plane moment MYBR by 8 %, the extreme resulting bending moment by 7.6 % and the critical deflection of the blade tip DXT2T by 7.1 %. The resulting values are comparable to the ones obtained by extrema of the DLC 1.1 group.

It is also interesting to see what effect an active flap system has on the different load directions of max(MXYBR) around the blade root. Figure  shows the averaged value of max(MXYBR) for different load directions. We can see that the largest values of max(MXYBR) occur for angular bins between 70 and 100∘. These angles are around the value of positive MYBR (90∘). Because we are only considering the DLC 1.1 and 1.3 groups, we will only have a good estimation for the extreme resulting bending moments due to the maximum thrust of the wind turbine, which happens to correspond to this region.

When we look at the effect of the active flap system, we can see that the reduction of max(MXYBR) occurs in this angular range. In the rest of the angular bins, the maximum resulting bending moments are practically identical. This can be understood if we recall that the controller input only included strain gauge information in the out-of-plane direction. Extreme resulting bending moments that arise from the combination of MYBR and MXBR cannot be captured by the controller sensors. In addition, the flaps' control authority is mainly on the lift, so flap actuation will have little effect on the variation in MXBR. Again, the reduction due to flap activity seen in Fig.  reduces the values of MXYBR to values close to the ones obtained from considering the loads from DLC 1.1 only.

The results obtained in the previous section show that active TE flaps are able to reduce extreme loads and critical deflections of the blade substantially. Given the constraint that the control strategy should not interfere with the normal power production (DLC 1.1), a reduction of 7.6 % in max(MXYBR) is significant because it almost eliminates the increased extrema in DLC 1.3 due to the extreme turbulence (Fig. ). These results are statistical and should be interpreted as an average performance of the flap system. To better understand the potentials and limitations of the proposed system, it is useful to look at some exemplary time series.

Figure  shows a selection of the time series for two simulations from the V‾hub=11 m s-1 wind speed bin, where several of the maxima occurred. Each column corresponds to one simulation. The first column shows a scenario where the average wind speed (not shown) is increasing and Ω is rising to values around rated rotor speed (Fig. d). The low value of β (Fig. c) leads to high values of rotor thrust and high values of MYBR (Fig. a) and to the activation of the flaps (Fig. b). We can see that the flaps are being deployed even if the values of MYBR do not reach an apparent peak. This is because Fig. a only shows the value of MYBR for one blade, and all flaps are activated as soon as the deployment criteria are met by any blade. Let us now consider the situation around the simulation time of 520 s. Here the blade passes a local wind gust, and it significantly increases the value of MYBR for the simulation without flaps. This also accelerates the rotor and activates the pitch system. This does not happen in the simulation with active flaps. Due to a previous activation of the flap system, the blade enters the wind gust with deployed flaps, thereby creating less lift and thus reducing the load peak by about 16 %. This is one example showing the large potential that active flap systems have in reducing the extreme loads of wind turbine blades.

The second column shows a situation where the controller does not perform as desired. At around 685 s of simulation time, there is a sudden peak in MYBR for the simulations with active flaps (Fig. e). Just before that event the flaps had just arrived at their 0∘ position, thus allowing the blade to generate normal lift (Fig. f). The flap controller reacts quickly, but the reaction is not quick enough to mitigate the high loading. Because we are trying to reduce the extreme loads, such events – although rare – are the ones that lead to the recorded maxima. In the case of this particular simulation, the extreme load reduction of the active flap system is only about 1.5 %. This example also illustrates well the necessity of having fast reactions from the flap system to sudden changes. This can only be obtained by including local sensorial information of the flap system – such as the flap hinge moment and acceleration signals – as part of the controller input.

One challenge in this particular study is that the difference in extrema between the DLC 1.1 and 1.3 groups is relatively small. Given the fact that the flap system needs a certain amount of time to have an effect on MYBR, we require the values of the different thresholds to be low. On the other hand they should not be too low in order to avoid influencing the normal power production of the turbine. The combination of these two requirements does not leave much room for threshold selection. Slightly changing the threshold values helped improve the performance of the flap system in certain scenarios but lowered the performance in others, thus giving similar results overall. If the difference in extreme conditions between the DLC 1.1 group and other DLC groups is higher (as was reported in ), then this issue becomes less critical.

Another observed issue with the proposed strategy is the unwanted mutual influence between the pitch and the flap controllers. We can see an example of this in Fig. c. The deployment of the flaps lowers the lift force but also the torque produced by the rotor and thus the rotor acceleration. This results in the pitch controller leaving the pitch angle longer at 0∘ compared to a simulation without active flaps. While the overall effect on the rotor speed and hence generator power is small, the effects on MYBR are more substantial. Lower values of β increase the values of α along the blade, leading to higher lift values and higher values of MYBR. It was observed in some simulations that there were values of max(MYBR) with fully deployed flaps comparable to values of max(MYBR) from the same simulations without active flaps. The difference lay in the respective values of β in each simulation. The influence of the flap controller led to lower values of β compared to the simulation without active flaps, indirectly reducing its effectiveness.

A possible solution would be to decrease the value of τdep or increase the flap rate when returning to the 0∘ position, thus lowering the time that the flaps influence lift production. Because of the constraints in threshold selection mentioned before, having a flap deployment cycle that is too fast could lead to an unstable behavior where the flap system amplifies the blade oscillation. Another possible solution could be to adapt the controller so that each blade uses its flap system independently. While this strategy reduces the interference between the flap and the pitch controllers, it loses the information about the inflow conditions of the preceding blade. This leads to more false negative scenarios such as the one described in Fig. e–h, again lowering the effectiveness of the strategy.

All of the limitations discussed above arise mainly from the chosen controller strategy. While being simple, robust and able to reduce extreme loads and deflections significantly, the proposed architecture shows its limits when used in such a challenging scenario. Other controller strategy types, such as, e.g., model-based or adaptive-data-driven controllers that include combined pitch and flap action, are possible candidates that could exploit the full potential of active flaps while overcoming the observed limitations in this study.