Periodic dynamic induction control of wind farms: proving the potential in simulations and wind tunnel experiments

. In this paper, the potential of Dynamic Induction Control (DIC), which has shown promising results in recent simulation studies, is further investigated. When this control strategy is implemented, a turbine varies its induction factor dynamically over time. In this paper, only periodic variation, where the input is a sinusoid, are studied. A proof of concept for this periodic DIC approach will be given by execution of scaled wind tunnel experiments, showing for the ﬁrst time that this approach can yield power gains in real-world wind farms. Furthermore, the effects on the Damage Equivalent Loads (DEL) of 5 the turbine are evaluated in a simulation environment. These indicate that the increase in DEL on the excited turbine is limited.


Introduction
The interaction between wind turbines in a wind farm through their wake is a field of research as old as wind farms itself. The wake of an upstream turbine has a wind field with a lower velocity and a higher Turbulence Intensity (TI), resulting in a lower power production and higher relative loads for downstream turbines. To exploit this interaction between turbines, induction 10 control has been a popular research topic in recent years. The concept of this control approach is schematically shown in Figure 1a. Despite initial promising results (Marden et al., 2013;Gebraad et al., 2013), recent studies indicate that the power gain that can be achieved with this steady-state axial induction control is limited to non-existing (Campagnolo et al., 2016a;Nilsson et al., 2015;Annoni et al., 2016).
Meanwhile, recent simulation studies (Goit and Meyers, 2015;Munters and Meyers, 2017) have shown that so-called Dy- 15 namic Induction Control (DIC) improves the power production in small to medium-sized wind farms. This approach, where the induction factor is varied over time, induces a turbulent wind flow that enables enhanced wake recovery. Consequently, downstream turbines will compensate for the power loss of the upstream turbine, leading to a higher overall power production of the wind farm. The optimal dynamic control inputs are found using a computationally expensive adjoint-based Model Predictive Control (MPC) approach. 20 In Munters and Meyers (2018), a simpler approach is suggested: the induction variation is limited to a sinusoidal signal implemented on an actuator disk. This approach is here dubbed "periodic DIC". A grid search with different amplitudes and 1 (a) Static induction control with different induction settings.  frequencies is performed to find the optimal dynamic signal in a high-fidelity simulation environment. The effect of this approach on the streamtube and downstream wind velocity is shown in Figure 1b. It should be noted that the applied excitation is very low-frequent. An optimal Strouhal number St = 0.25 is found, which corresponds to a period of approximately 56 seconds for a DTU 5 MW turbine (Jonkman et al., 2009). 5 However, no experiments have yet been executed that validate this approach on actual, either scaled or full-sized, wind turbines. Furthermore, the effects of DIC on the loads of the turbines are yet to be evaluated. This paper aims to bridge this knowledge gap by executing a thorough evaluation of DIC both in simulation environments and in wind tunnel experiments.
The effects of DIC on the wake of a turbine will be investigated. Simulations will be executed using the high-fidelity Computational Fluid Dynamics (CFD) environment SOWFA (Churchfield and Lee, 2012). The effects of DIC on the loads on turbine 10 level are evaluated using the aeroelastic tool CP-LAMBDA Croce, 2009-2018;Bottasso et al., 2006). For the wind tunnel experiments, the Atmospheric Boundary Layer (ABL) wind tunnel of the Politecnico di Milano (Polimi) is used (Bottasso et al., 2014). Three G1 models, which have a rotor diameter of 1.1 m and are developed by the Technical University of Munich (TUM) (Campagnolo et al., 2016a, b, c) will be used as turbine models.
To verify the validity of the periodic dynamic induction approach for fast wake recovery in a wind farm, a number of wind 15 tunnel experiments in both low and high Turbulence Intensity (TI) conditions are executed. The effect of varying the amplitude and frequency of the signals is studied, and the performance of this approach is compared with other state-of-the-art wind farm control strategies. A positive result in these experiments would be an important step towards proving the validity of this approach in real wind farms.
The structure of this paper will be as follows: in Section 2, the DIC strategy will be explained. Sections 3 and 4 will elaborate on the simulation environment and the experimental setup, respectively. In Section 5, the simulation results will be presented, followed by the experimental results obtained in the wind tunnel in Section 6. Finally, the conclusions will be drawn in Section 7.

5
In this section, the strategy behind dynamic induction control will be discussed shortly. As mentioned in the introduction the approach presented in Munters and Meyers (2018) is used as a basis for this paper. However, there are some fundamental differences between this work and the work presented here, which are summarized in Table 1. Due to the size of the wind tunnel (see Section 4), a 3-turbine wind farm is the deepest possible array configuration. The amplitude and frequency ranges where slightly reduced due to time constraints. Finally, to allow for practical implementation on a turbine model, the collective 10 pitch angle β of the model was excited periodically. This results in a slightly different thrust signal, as shown in Figure 2, but simulations show that the difference in output for these input signals is limited.  Since the internal torque controller of the G1 model is also active, the amplitudes and offsets of the pitch signals are tuned manually such that the resulting thrust coefficient matches the desired thrust coefficient in amplitude and frequency. To achieve this, the thrust force on the turbine is measured, which, together with knowledge about the wind conditions, is used to calculate the thrust coefficient over time.
In Munters and Meyers (2018), it is shown that the amplitude and frequency of a sinusoid determine the overall power pro-5 duction. The optimum found in here is a Strouhal number of St = 0.25, with an amplitude of the disk-based thrust coefficient The Strouhal number is defined as St = f D/U ∞ for a given frequency f , rotor diameter D and inflow velocity U ∞ , , with a the axial induction factor (Goit and Meyers, 2015). For the G1 models and an inflow velocity of 5.65 m/s, this Strouhal number would result in an excitation frequency of approximately 1.3 Hz.
Finally, a comparison will be made with wind farm control approaches that have already been investigated more extensively 10 in literature: static induction control (also called derating control) and wake redirection control (also called yaw control). The optimal control settings are found using the static FLORIS model . This parametric model is calibrated with wind tunnel measurements, as described in Schreiber et al. (2017). The control settings are then implemented on the same wind farm set-up in the wind tunnel such that a fair comparison can be made. In Section 6, the results of these experiments will be evaluated.

Simulation environment
In order to evaluate the effect of DIC on turbine level, the aeroelastic tool Cp-Lambda (Code for Performance, Loads, Aeroelasticity by Multi-Body Dynamics Analysis) Croce, 2009-2018;Bottasso et al., 2006) has been used. This software is an aeroelastic code based on finite element multibody formulation, which implements a geometrically exact non-linear beam formulation (Bauchau, 2011) (Jonkman and Buhl, 2006), were given as input to the aeroelastic solver.

Experimental Setup
The experimental results presented in this paper were gathered by performing dedicated tests within the wind tunnel of the Politecnico di Milano, which is a closed-return configuration facility arranged in a vertical layout and equipped with two test rooms. A detailed description of the facility can be found in (Bottasso et al., 2014). The tests were performed within the boundary layer test section, which has been conceived for civil, environmental and wind energy applications. This section has 5 a large cross-sectional area of 13.84 × 3.84 m, which allows for low blockage effects even with several relatively large turbine models installed within the test section.
Roughness elements located on the floor and turbulence generators placed at the chamber inlet are commonly used to mimic to scale the atmospheric boundary layer in terms of vertical shear and turbulence spectrum. During the experiments described later on, two boundary layer configurations were used: one generating low turbulent (Low-TI) and one generating 10 highly turbulent (High-TI) flow conditions. These conditions roughly correspond to off-and onshore operation respectively.
The flow characteristics are shown in Figure 3 together with the extension of the model's rotor disk along the vertical axis. The coefficients of the vertical-shear exponential law, shown in the same picture, that best fit the experimental data are 0.144 and 0.214 for the Low-TI and High-TI cases respectively.

Wind turbine models 15
Up to three G1 wind turbine models developed at TUM were used to perform the experiments reported in this paper. This model type was widely employed and described in detail in previous research (Campagnolo et al., 2016a, b, c) and is shown within the boundary layer test section of the Polimi wind tunnel in Figure 4. With a rotor diameter of 1.1 m and a rated rotor speed of 850 rpm, the model was designed to have a realistic energy conversion process and wake behavior: it exhibits a power coefficient C P ≈ 0.41 and a thrust coefficient C T ≈ 0.81 for a tip speed ratio λ ≈ 8.2 and a blade pitch β ≈ 0.4 • .
The turbine is actively controlled with individual pitch, torque and yaw actuators and features comprehensive on-board sensorization. Three individual pitch actuators and connected positioning controllers allow for an overall accuracy of the pitch system of 0.1 degrees for each blade and the ability to oscillate the blade pitch with an amplitude of 5 degrees at 15 Hz around any desired pitch angle. Strain gauges are installed on the shaft to measure bending and aerodynamic torsional loads, as well 5 as at the tower foot to measure fore-aft and side-side bending moments. A pitot tube, placed three rotor diameters upstream of the first turbine model, provides measurements of the undisturbed wind speed at hub height. Finally, air pressure, temperature and humidity transducers allow for measurements of the air density within the test section. The measurements of these sensors are used to determine the performance of the turbine models. The thrust coefficient is obtained using measurements of the pitot tube wind speed measurement and fore-aft bending moment, while correcting for the effects of the tower and nacelle drag.

Control system
For each wind turbine model, control algorithms are implemented on a real-time modular Bachmann M1 system. Demanded values (e.g. pitch angle or yaw angle references) are then sent to the actuators, where the low level control is performed.
Torque signals, shaft bending moments and rotor azimuth position are recorded with a sampling rate of 2.5 kH, while all other measurements are acquired with a sampling rate of 250 Hz. A standard power controller is implemented on each M1 system 15 based on Bossanyi (2000), with two distinct control regions. Below rated wind speed, blade pitch angles are kept constant, while Table 2. AverageCT and amplitude CT,DIC of the three different thrust coefficient oscillations whose results are discussed in Section 6 .C the generator torque reference follows a function of the rotor speed with the goal of maximizing the energy extraction. Above rated wind speed, the generator torque is kept constant and a proportional-integral (PI) controller adjusts the collective pitch of the blades in order to keep the generated power at the desired level. All experiments presented in this work are performed below rated wind speed.
For the tests performed within the research described in this paper, the standard power controller was augmented in order to enable the rotor thrust coefficients following a specific sine wave function. However, there is not a unique way of achieving this 5 goal, since a specific thrust coefficient C T (λ, β) can be obtained by operating at different combinations of tip-speed-ratio λ and blade pitch β. In turn, the tip speed ratio can be varied either by changing the reference followed by the generator torque or changing the blade pitch. In this paper, a strategy that only changes the blade collective pitch is adopted. The implementation of this strategy simply requires changing the collective fine pitch at which the model blades are set when the machine operates in partial load conditions (region II). The fine pitch was tuned experimentally, by means of a trial and error procedure conducted 10 with a stand-alone model, to achieving the desired meanC T and amplitude A as reported in Table 2. The effects of these control actions in terms of impacts on the power output of the 3-turbine wind farm will be discussed in Section 6.

Simulation Results
Once the optimal DIC parameters in terms of wake mixing have been evaluated using CFD, a full set of aeroelastic turbulent simulations (DLC 1.1) has been executed. These analyses have been conducted on the NREL 5 MW wind turbine with the 15 main goal of quantifying the effect of this DIC on the fatigue loads. The analysis focuses mainly on the main wind turbine sub-components, such as the blade root flap-and edge-wise loads, as well as the tower base fore-aft bending moments.
The DIC was assumed to be activated for wind speeds between 3 and 15 m/s, to cover the totality of regions I-1/2, II, II-1/2 and the first part of region III. Notice that 15 m/s seems a rather high speed, considering the fact that in the full power region DIC might not be necessary. In region III, the lower rotor inductions (i.e a lower in-wake speed deficit) may guarantee, together 20 with the high inflow velocity, the full power region for the downwind rotor(s). Nevertheless, in the 10-minute simulation, the high turbulence intensity (class "A") causes a relatively long period where the mean wind speed is below the rated one and Due to the relatively low excitation frequency, the baseline turbine control is able to trim the machine without a significant additional effort or detrimental performance. Moreover, a coalescence between the DIC input frequency and turbine vibratory modes is not to be expected, at least for on-shore or off-shore turbines installed on rigid foundations.  speeds, it is assumed active in the entire region III. As can be seen, the tower base fore-aft bending moment and the blade root flapwise are affected the most by this controller. As expected, the blade edge-wise bending moment is only slightly affected, since the DEL in edge-wise direction is mainly driven by gravity.

5
In order to have a more comprehensive indication about the impact of DIC on fatigue loads, one can consider the Weibullweighted DELs, i.e. the DELs weighted throughout the probability distribution of the wind as expressed by the Weibull distri- where k is the shape parameter and C = 2V av / √ π the scale factor and V av the average wind speed 10 The Weibull-weighted DEL, DEL w , is hence computed as where V CI and V C0 are respectively the cut-in and cut-out wind speed.    Considering the class "A", where the Weibull distribution has k = 2 and V av = 10 m/s, it is possible to compute the Weibullweighted DEL for the previously considered loads. To this aim, we suppose to switch off the DIC controller at wind speeds 15 higher than 15m/s, so that in region III the DELs are lower than the ones shown in the previous figures and equal to the baseline values. These results are summarized in Table 3. As can be seen, the tower base load is affected the most (about 7%), while loads on the blade root increase with about 2%. A negligible impact (+0.4%) is found in the blade edge-wise and in the hub.
Up to now, the analysis has not considered the probability of activation of the DIC-based wind farm control, which will depend on the specific farm layout and wind rose. From this point of view, the computed DEL increments seen before are to be considered as the maximum possible obtainable, as if DIC would always be implemented regardless of wind direction and 5 subsequent wake interaction. It is therefore possible to assess that the impact of DIC on turbine fatigue loads for the analyzed NREL 5 MW reference machine is small compared to the possible gains.

Experimental Results
In this section, the results of the experiments executed in the wind tunnel at Polimi, as described in Section 4, will be presented.
The effects of periodic DIC on the power production of a 3-turbine wind farm are presented for two cases, similar to onshore 10 and offshore wind conditions. The performance of DIC will be compared with the state-of-the-art wind farm control strategies: greedy control, "static" induction control and wake redirection control.

Power production
First, the results with low turbulent wind (TI of approximately 5%) are evaluated. For this case, 5 different sets of experiments have been conducted: three experiments with different amplitudes on a sinusoidal input, one with a block signal on the input 15 and one where a sinusoid is put on both the first and the second turbine. In this last experiment, the phase difference between the two turbines is varied. Figure 9 shows the mean power of the turbines and the total wind farm. To account for the small variations in flow conditions, the power divided by the available power in the wind. As such, these values can be seen as power coefficients. Increasing the amplitude of the sinus decreases the power coefficient of turbine 1, while it increases the power coefficient of turbine 2.
However, for higher C T , the loss at turbine 1 is too significant to compensate for by the downstream turbines. As a result, the case with the lowest amplitude proves to be the most effective. The highest increase in power extraction is found with C T = 1 and St = 0.33, resulting in a 2.4 % gain. Table 4 gives an overview of the effect of different amplitudes and frequencies on the power production of the 3-turbine model wind farm. A = 2.0 -11.76% -9.89% -7.97% -6.61% -7.30% -7.41% -9.09% -8.80% Finally, the reliability of these results will be examined. To do this, the results are divided into four segments of 60 seconds.
These shorter segments of measurements, still containing 15000 measurement points and between 30 (0.5 Hz) and 138 (2.3 Hz) sine cycles, will then be used to determine the variance of the measurements. Figure 10 shows box plots of these data sets for A = 1, normalized by the steady state optimal C P of turbine 1. This figure shows that the variance becomes larger at each downstream row due to the increased turbulence. As a result, the variance is significant in the total power production: up to ±2% of the power. However, this figure also shows that the variance is lower than the power gained by using dynamic induction control: the lowest values of the box plot around the optimal frequency of 1.8 Hz are still higher than the baseline value. This analysis therefore indicates that the power increase is significant, as it is not a coincidental result of measurement errors. The same experiments were conducted in high turbulence intensity conditions. The results of all the amplitudes and frequencies that were studied are shown in Figure 11. The main conclusion that can be drawn from this figure, is that the effect of exciting the first turbine on the power production of this turbine is lower in these conditions. Due to the turbulence, the 10 power production of this turbine is already slightly lower than in low TI conditions. As a result, the power loss at turbine 1 is negligible for the A = 1 case. As the power gain at the downstream turbines is similar, the total power gain for this case is 4 %.
This gain is found with A = 1 and St = 0.29, as can be seen in Table 5 where the results are summarized.  When the amplitude of the excitation is increased, the power loss at turbine 1 is comparable with the results in low TI conditions. However, since the power gain at turbine 3 is slightly lower, the total power is also lower than in the baseline case. 15 Subsequently, it seems that the amplitude of the excitation is more important than the frequency in these conditions.

Controller comparison
To emphasize the value of the results shown in the previous subsection, a comparison of the effectiveness of the periodic DIC approach with state-of-the-art wind farm control approaches is executed in the case of full wake interaction. The optimal inputs are found using the steady-state FLORIS model , which is calibrated using measurements from the wind tunnel. Three different control strategies are investigated:

5
-Greedy control: all turbines operate at their individual optimum, disregarding interaction between turbines due to their wakes.
-Static induction control: the induction settings (i.e. collective pitch angles) that predict the highest power capture according to the calibrated FLORIS model are implemented.
-Yaw control: the yaw angles that predict the highest power capture according to the calibrated FLORIS model are The results of these experiments are shown in Figure 12. Similar to results in literature (Campagnolo et al., 2016a), static induction control is found to be unable to increase the power production of this wind farm. Yaw control on the other hand results in a benefit of 3.1 % As reported earlier, DIC was able to increase the power production with 2.4 % in these conditions.
It can therefore be concluded that the potential profit of periodic DIC is significantly higher than with static induction, while it 15 is comparable to that of yaw control when full wake interaction is present.

Conclusions
In this paper, the effect of periodic Dynamic Induction Control (DIC) on both individual wind turbines and on small wind farms is investigated. For this purpose, both high-fidelity simulation tools and scaled wind tunnel experiments are executed.
The unique wind tunnel experiments with DIC show, for the first time, that this control approach not only works in a simulation 5 environment, but also in real world experiments. A comparison between DIC and static induction control as well as wake redirection control shows that this approach works significantly better than the former and approximately as good as the latter.
This greatly strengthens the premise that DIC is an effective method to increase the power production of a wind farm as a whole.
Furthermore, by means of the aeroelastic tool CP-LAMBDA, it was shown that the effect of DIC on the Damage Equivalent In all, it can be concluded that the dynamic induction control approach shows great promise, as now both simulations and scaled experiments show that it is possible to achieve a power gain. However, significant differences are found between 15 simulation and experiments, which still need to be adressed. Future research can therefore be directed into clarifying these 15 differences, as well as executing additional experiments.
As the amplitude and frequency of the excitation are shown to be important control parameters, it would be a very interesting challenge to develop an algorithm that is able to optimize these parameters. Furthermore, additional analysis on the increased loads on the (downstream) turbines can be done to investigate the effect of these loads on the lifetime of turbines. Finally, application on full-scale wind turbines could be the last step in proving the validity of this approach.