The performance of two control strategies for floating wind turbines: lidar-assisted feedforward and multi-variable feedback

In this paper, we analyze the performances of two control strategies and their combination on a floating turbine through OpenFAST simulations. The floating wind turbine is modeled based on the demonstrative FLOATGEN, which consists of a 2MW wind turbine mounted on the Damping Pool platform designed by BW Ideol. The lidar-assisted control utilizes lidar wind preview to achieve blade pitch feedforward control. The multi-variable feedback additionally uses the platform pitch rate to determine blade pitch. By simulations with the above-rated wind and irregular wave conditions, both control strategies and their combination has the potential to reduce turbine vibrations. Especially, combining lidar-assisted control and multi-variable feedback control brings the most significant reduction in the standard deviations of rotor speed (>36%), low-speed shaft torque (>30%), and blade root moment (>15%).


Introduction
In the context of increasing demand for clean and renewable energy, offshore wind power will be a key player in the energy supply.While shallow sea areas where fixed offshore wind power can be developed are becoming saturated, Floating Offshore Wind Turbine (FOWT) technology can expand the potential deep sea areas for wind farm developments on a large scale.
Compared to conventional bottom-fixed wind turbines, one main challenge for Floating Offshore Wind Turbines (FOWT) is the additional platform pitch degree of freedom (DOF).The aerodynamic thrust from the wind and the force of waves and currents on the floating platform can excite the pitching DOF.This platform motion causes change in the relative wind speed and can significantly increase the mechanical load on the floating turbine, therefore, the design of the control system for FOWT is more demanding.Since mechanical loads are closely related to the cost of a FOWT, it becomes particularly important to analyze the performance of different control strategies against loads.
In this paper, we use the OpenFAST model of the FLOATGEN FOWT, which consists of a 2 MW wind turbine mounted on the Damping Pool platform designed by BW Ideol, and aim to analyze the potential improvements in the control performance of the FOWT using two strategies and their combination.
The first controller is the multi-variable feedback (MVFB) controller, which feeds back not only rotational speed but also tower-top or platform motion signals.In this type of controller, the motion signal is multiplied by a proportional gain and added to the conventional proportionalintegral (PI) pitch controller.This type of controller is considered has been implemented as an open-source controller, such as the Reference Open Source Controller (ROSCO) by NREL [1].The advantages of this controller, which include decreases in platform pitch variations and tower loads, have been studied by a number of publications [12,16,4].The second controller relies on lidar-assisted control (LAC), which utilizes the wind speed preview provided by a nacellemounted lidar system.Such lidar systems are installed on some of the current existing prototype FOWTs.With the LAC technology, the wind preview is used to calculate a feedforward pitch signal, which can be simply integrated into the conventional feedback PI controller.LAC has been applied to onshore commercial projects and it has been proven capable of reducing rotor speed fluctuations and loads of turbine components, e.g., tower, blades, and shaft [14,5].Because of the negative damping of platform pitch mode, LAC is expected to improve control performance outside the platform's natural frequency range.Lastly, the two control strategies mentioned above will be combined.Their combined performance will be evaluated and compared to the performance of a single strategy either using MVFB control or LAC.
The rest of this paper starts with a background section, followed by a section explaining the controller design.After presenting and discussing the simulation results, the conclusions and the outlook are provided in the end.

Backgrounds
This section illustrates the backgrounds of the simulation environments, including turbine and floater models, environmental conditions, and lidar simulation.

Floating turbine model
The floating wind turbine model is built based on the pioneering barge-based floating demo turbine: FLOATGEN, which has a 2 MW (Vestas V80) turbine mounted on a BW Ideol's Damping Pool design floater.More detail about FLOATGEN can be found in [18,11].The floating wind turbine model (applicable to OpenFAST version 3.0) was supplied by BW Ideol and the University of Stuttgart.The model includes the linear radiation and diffraction coefficients and the Morison drag model, covering the viscous effects, especially at the skirt around the barge.The structural dynamics module considers tower and blade elasticity, whereas the barge is considered rigid.The mooring dynamics are represented with the dynamic lumped-mass model MoorDyn.Aerodynamic loads are simulated with AeroDyn 15.

Turbulence
We use the extended Mann turbulence model [6] to generate1 evolving four-dimensional turbulence fields.With this simulation method, Taylor's frozen hypothesis is avoided to simulate a more realistic lidar wind preview.
The IEC 61400-1:2019 [8] standard suggests using L =34 m and Γ = 3.9 for the turbulence length scale and the anisotropy in the Mann model [13], respectively.However, according to the analysis of the offshore FINO1 measurement site data [3], L =70 m and Γ = 3.7 are observed.Therefore, we use these parameters for stochastic turbulence generation.As for turbulence evolution-related parameters, the parameters summarized by [6] from a neutral atmosphere are chosen.As for the last energy level-related parameter αε2/3 , it is adjusted based on the hubheight mean wind speed V hub to ensure the standard deviation of longitudinal velocity component (u) equals to that specified by the IEC 61400-3-1:2019 standard [9].

Wave
Only the normal sea state parameters are considered in this work, which aims for assessing controller performances under normal operating conditions.The irregular waves are generated using the JONSWAP spectra [10] which are characterized by two parameters: the peak spectral period T p and the spectral significant wave height H s .As specified by the IEC 61400-3-1:2019 standard, the correlation between wind conditions and waves needs to be considered for the load assessment.In this work, we chose H s = 5.0 m and T p = 10 s, 12.5 s, or 15 s that are highly correlated with a mean wind speed of 20 ms −1 according to the real-time published data from SEM-REV: Centrale Nantes offshore test site 2 .The SEM-REV site is also the place where the floating turbine: FLOATGEN is installed.

Lidar simulation
Currently, a "LidarSim" module is integrated into OpenFAST (version 3.0 3 ) [7], which provides realistic lidar measurement simulations including effects such as the motion of lidar, probe volume measurement, turbine blade blockage, wind evolution, and adjustable data quality.
In the lidar simulator, the lidar line-of-sight (LOS) measurement, which is the projection of the three dimensions relative velocity into the laser beam direction, is modeled by [15]: Here, r 0 is the focused position of the measurement.n RW is the number of discrete points along the LOS direction accounting for the probe volume measurement characteristic of lidar, which should be an odd number to include the focus position r 0 .In addition, f RW (r k ) is a scalar weighting function of the probe volume at position r k , v k is the wind velocity vector at the position r k , and v lidar is the velocity vector of the lidar system.Lastly, n = [x n , y n , z n ] is the normal vector of the laser light in the inertial coordinate system.In this work, we simulate a lidar system based on the WindIris TC lidar from Leosphere, a Vaisala company.This lidar system is also installed on the nacelle of the FLOATGEN turbine [18].The simulated lidar measures four beam directions sequentially.For each beam direction, the LOS speed at ten measurement distances along the beam is recorded simultaneously.We use the measurement distance at 100m upstream only, because this range gate provides sufficient leading wind preview time for the feedforward controller, as discussed in Section 3.3.2.

Controller design
In this section, we introduce the reference single-variable feedback controller (RFB), the multivariable feedback controller (MVFB), and the lidar-assisted feedforward controller (LAC).

Reference feedback controller
We use the NREL's Reference OpenSource Controller4 (ROSCO) as the benchmark for comparisons.ROSCO is written by FORTRAN programming language and is compiled as a Dynamic Link Library (DLL).The DLL relies on the legacy Bladed style interface [2] to exchange data with the OpenFAST executable.All exchanged data are written into a data array called "avrSWAP", following a specific sequence.
ROSCO provides several blade pitch and generator torque control options.For this study, only the above-rated operations are analyzed.A Proportional Integral (PI) controller is used for the collective blade pitch feedback control (see Figure 1) where the pitch command is determined by where k P is the proportional gain, T I is the integral time constant, Ω g,ref is the reference generator speed, and Ω g,LPF is the measured and low-pass filtered generator speed.We use constant torque mode for generator torque control where Ω g,LPF is used to determine the state of operation.If the Ω g,LPF is above the rated value, then the constant (rated) generator torque is applied.The current version of ROSCO does not provide drivetrain damping mode; therefore, the source code is modified to include a drivetrain damper in the generator torque control module.In the drivetrain damper, the generator speed signal is firstly filtered using a band-pass filter that passes frequencies within a certain range centered at the shaft's natural frequency.Then, the band-passed generator speed is multiplied with a gain constant equivalent to the gearbox ratio.The signal after multiplication is added to the output of the original generator torque controller (without the drivetrain damper).In the end, the generator command signal passes the rate limit and saturation blocks.

Multi-variable feedback controller
The MVFB aims to provide more compensation to relative wind speed change caused by platform motion or damping effect to the floating platform pitch motion.Except for the generator speed signal, the platform pitch rate βp (angular velocity) signal is feedback in the MVFB.In the current version of ROSCO (2.6.0), one can choose to feedback on the tower-top translational or rotational velocity.This implementation does not require further modification of the DLL interface module in OpenFAST [1].However, as suggested by [4], better control performance is achieved by feeding back the platform pitch signal.Thus, we modified the DLL interface module in the used OpenFAST (version 3.0) to write the platform pitch rate signal into the avrSWAP array.Also, ROSCO is modified to accept the option of feeding back the platform pitch rate and using this signal to determine the pitch signal.
The floating feedback design has been discussed in detail by [1] where the derivation is based on the feedback signal: tower-top translational velocity ẋt .In this work, the platform pitch rate is first filtered by a band pass filter, then multiplied by a gain k p,float , and lastly added to the output of the collective pitch feedback controller (see Figure 1).Then, the pitch command of the MVFB controller turns out to be where β p,BPF is the measured and band-passed platform pitch rate.The band-pass filter of the floating feedback loop needs to be designed to band-pass frequencies near the natural frequency of the platform motion, which is achieved by first low-pass filtering and then high-pass filtering the signal.The value of the floating feedback gains k p,float can affect the overall control performance considerably.If the platform pitch angle shown in Figure 2 is defined to be positive, then an increase in the platform pitch rate results in a reduction in relative wind speed v rel = v 0 − ẋt , where v 0 is the free-stream rotor effective wind speed.Following the decrease of v rel , both aerodynamic torque M a and rotor thrust force F a descent.A positive k p,float gives a higher pitch command thus reducing the aerodynamic torque and thrust force further, which eventually leads to a higher damping effect of the platform motion but also a higher rotor deceleration owing to a lower aerodynamic torque.Oppositely, a negative k p,float delivers a lower pitch command, causing increments in aerodynamic torque and rotor thrust.The raising aerodynamic torque can compensate for the reduced aerodynamic torque due to platform motion but also imposes higher thrust force.The floating feedback gains k p,float is tuned by brute force optimization later in Section 4.1.

Lidar-assisted controller
The LAC utilizes the wind speed preview signal from a nacelle-mounted lidar system and provides a feedforward blade pitch signal.Previously, a reference LAC has been developed by [5] for bottom-fixed turbines, which includes a lidar data processing module and a feedforward pitch (FFP) module.This work uses the extended version of the LAC in which a motion compensation algorithm is added to the Lidar Data Processing (LDP) module for floating turbine applications.
3.3.1.Lidar data processing Lidar only measures the LOS wind speed, a LDP module is necessary to estimate the aerodynamic-dominant longitudinal wind component from the LOS speed measurements.In addition, the lidar motion caused by platform movement contributes significantly to the measured LOS speed; therefore, a motion compensation (MC) algorithm is necessary to ensure that the measurement is primarily contributed by the wind.
This MC algorithm additionally uses the rotations (roll, pitch, yaw) of the lidar system provided by a simulated Inertial Measurement Unit (IMU).These rotations are sued to calculate the normal vector of the back-scattered light n in the inertial coordinate system.Lastly, the motion compensated LOS wind speed v los,mc is calculated using the lidar system velocity from the IMU v lidar and the lidar LOS measurement v los : After the MC, the longitudinal wind components û is estimated by the simple reconstruction algorithm: which assumes the contribution of the u component is more dominating than other velocity components.Further, the Rotor Effective Wind Speed (REWS) is calculated by taking the average value of estimated û from a full lidar scan.
The LDP module also uses the DLL interface mentioned previously.The lidar integrated OpenFAST version [7] writes the line-of-sight wind speeds, other lidar-related signals, and the IMU measurements into the avrSWAP array in every time step.This information is read by LDP and used to calculate REWS.The LDP then writes the REWS in the avrSWAP array.

Feedforward pitch
The FFP module is responsible for filtering the REWS and timing the filtered REWS.
The lidar-estimated REWS is firstly filtered by a first-order low-pass filter and then by a notch filter.The target of the low-pass filter is to avoid activating collective blade pitch at uncorrelated frequency components (see [14]).Further, a notch filter is necessary because the activation of blade pitch near the natural frequency of platform pith mode is undesired.The detailed methods of deriving the low-pass filter parameter have been discussed in [6,5].As for the notch filter, the cutoff frequency is placed at the natural frequency of the platform pith mode.
The filtered REWS is then buffered for an adjustable time to ensure the feedforward pitch is activated at a proper time.The buffer time is related to the pitch actuator delay, filter delay, lidar measurement distance, lidar full scan time, and mean wind speed.The detailed calculation has been demonstrated by [5].
After the REWS is filtered and buffered, the feedforward pitch angle is obtained by interpolating the static blade pitch curve (a function of wind speed) using the buffered REWS.Instead of using the feedforward pitch angle directly, its time derivative is calculated to obtain the feedforward pitch rate θFF .
In the last step, the feedforward pitch rate is added to the integrator of the PI feedback blade pitch controller.As a consequence, the overall collective pitch command of LAC is calculated using In the case both LAC and MVFB are considered, the last term at the right side of Equation 3 can be added to the right side of Equation 6.

Results and discussion
This section first tunes the floating feedback gain and then assesses the performance of MVFB and LAC controls.

Floating feedback gain tuning
To find a reasonable k p,float value, we perform simulations considering first turbulent wind and still water and then turbulent wind with irregular waves (See Figure 3).Six simulations are performed using different random seed numbers for both turbulence and wave.Also, the wave is assumed to be uncorrelated with turbulence and has the same direction as the wind.Each simulation is executed for 1850 s and the first 50 s of initializing duration is ignored.The simulation configurations mentioned here are applied in the rest of this paper.The mean standard deviations (STD) of the output variables are calculated from the results by different random seed numbers.A comparison of the STDs by RFB (k p,float =0) and MVFB is shown in Figure 3.In the still water case.We can see that the platform pitch is very sensitive to the k p,float .A positive value clearly reduces the platform pitch variation without impacting other turbine motions.However, in the irregular wave case.A positive k p,float value can contribute to reducing the platform pitch (PtfmPitch), while the STDs of blade pitch rate and most of the load-related variables increase significantly.On the other side, when negative k p,float is applied, variations in the rotor speed (RotSpeed), low-speed shaft torque (LSShftTq), and blade 1 root bending moment (RootMyb1) are obviously alleviated.A smaller k p,float tends to have more reductions in the STDs above but imposes more blade pitch activities and platform pitch variations compared to RFB when k p,float is smaller than -0.75.In addition, it can be seen that the tower base fore-aft bending moment (TwrBsMyt) is not sensitive to the changes in k p,float .In the later analysis, we chose the optimal k p,float to be -0.75, because it has a similar blade pitch rate STD as that by RFB control, does not increase platform pitch significantly, but reduces the variations in rotor speed and blade root moment considerably.The tuning of k p,float in this section indicates that the wave characteristic needs to be considered when optimizing the floating feedback.The wave force indirectly changes the aerodynamic forces because it results in platform pitch motion and therefore the induced (relative) wind velocity.The spectra of turbine-related variables, estimated using Welch's method [17].Both x and y axes are in logarithmic scale.The labels of the axes are not shown due to the confidentiality agreement.The peak spectral frequencies (1/T p ) are indicated by the dashed lines.

Spectral analysis
To investigate the performance of the MVFB and LAC controls in other most possible wave conditions, we consider two more wave conditions with peak periods of 10 s and 15 s.For each simulation case characterized by V hub , T p , and H s , the simulations are performed considering four controller scenarios: the reference RFB, MVFB, RFB with LAC, and MVFB with LAC.
Figure 4 shows the spectra of turbine load-related variables.For the investigated wind turbine, the platform motion contributes significantly to the variations of other turbine-related variables, because their spectral peaks are in accordance with the spectral peaks of the platform pitch.In panels (a), (b), and (c), it can be seen that MVFB control clearly reduces the rotor speed variations at the frequency close to the spectral peak of platform motion.At lower frequency ranges, the variations are mainly contributed by the aerodynamics that is alleviated using the LAC.The MVFB+LAC control has the smallest rotor speed variations since both the contributions from aerodynamic and platform motion are reduced by the two control strategies.
As shown by panels (d), (e), and (f), RFB+LAC control reduces variations in blade pitch rate obviously which is promising for load alleviation for the pitch actuator [5].MVFB control has higher spectra compared to RFB control at the spectral peaks, while it gives lower spectra at higher frequency ranges.RFB+LAC control and MVFB+LAC control have overall similar spectra of blade pitch rate, and they both reduced the blade pitch activities at lower frequency ranges where the lidar provides reliable wind preview.
The spectra of blade 1 root bending moment are shown in Panels (g), (h), and (i).The purple lines are slightly lower than the blue lines at the first spectral peak, indicating that LAC helps to reduce the blade root moment variation slightly.More obvious benefits are brought by MVFB control.At the second spectral peak, the difference between different control strategies is marginal.
The platform pitch spectra are shown in panels (j), (k), and (l).There is no clear difference between using LAC and not.However, as expected, using MVFB slightly increases the platform pith variation, because a negative k p,float value is adopted (see the discussion in Section 4.1).
The last row shows the spectra of low-speed shaft torque.The reductions in shaft torque variation show a high correlation with that of the rotor speed.
Overall, by comparing different columns corresponding to different wave peak spectral periods.The spectra simulated with T p =15 s are generally lower than the other two columns.This is caused by the fact that less wave energy is distributed in the spectral peak where the platform motion is primarily excited.

Statistics
The statistics collected from the simulation results by different control strategies are shown in Table 4.3.
The MVFB control, in general, is able to reduce the STDs of rotor speed, shaft torque, and blade root moment by approximately 25%, 26%, and 12%, respectively.With T p =10 s, there is a marginal increment in tower base bending moment STD and slight increments in blade pitch rate and platform pitch STDs.As for the rest two wave conditions, MVFB control method results in a slight increase in platform pitch STD, but reduces the STDs of blade pitch rate and tower base bending moment.
Compared to the RFB control, in all three wave conditions, RFB+LAC control method reduces the STDs of all variables except that of platform pitch motion.However, it can be seen that the changes in platform pitch STD are marginal, owing to the fact that a notch filter is applied to avoid LAC contributing close to the pitch form pitch natural frequency.The most objective benefit of LAC is the reduction in blade rate (13.5%) and rotor speed (11%) STD.In addition, slight reductions (about 5%) of STDs are observed in the shaft torque and blade root moment.
Combining LAC and MVFB brings the most significant reduction in STD.Overall, the STD of rotor speed, shaft torque, and blade root moment are decreased by more than 36%, 30%, and 15%, respectively.Except for the case with T p =10 s, the STDs of blade pitch rate and tower base moment are slightly reduced.With T p =10 s, there is a slight increment in blade pitch rate STD and a negligible increment in tower base moment STD.However, it can be seen that MVFB+LAC control leads to slight increases of platform pitch STD, which are more pronounced at smaller T p .
By comparing the energy production (EP), it can be observed that all three advanced control strategies produce marginally higher electricity.The increment is highest by MVFB+LAC control, medium by RFB+LAC control, and lowest by MVFB control.

Conclusions and outlook
In this work, the performance of two advanced control strategies: multi-variable feedback and lidar-assisted feedforward are evaluated using aeroelastic simulations.Under the above-rated wind speed conditions, most of the turbine vibrations are found to be related to the excitation of platform pitch motion by waves.
The multi-variable feedback is tuned to bring a damping effect to most of the turbine-related variables.With a negative feedback gain, it can provide a significant damping effect on the rotor speed fluctuation caused by the relative wind speed change owing to platform motion.And, this control strategy contributes significantly to reducing the variations in rotor speed, low-speed shaft, and blade root bending moment.The lidar-assisted feedforward pitch signal can improve the control performance at lower frequency ranges that are more dominated by turbulent wind.The most promising reductions of fluctuation by lidar-assisted turbine control are in the blade pitch rate and the rotor speed.
Combing multi-variable feedback and lidar-assisted control shows great potential in load alleviation for the investigated floating turbine.Under the three investigated wave conditions, the standard deviations of rotor speed, shaft torque, and blade root moment are decreased by more than 36%, 30%, and 15%, respectively.
In future work, the tuning of the floating feedback gain in the multi-variable feedback loop can be further improved by considering cost functions for the turbine variables.Assessment of the controllers can be extended to full design load cases.The lifetime fatigue reductions and profits brought by the advanced control strategy can be analyzed.Evaluation of the controller performances can be made on larger rotor turbines.As for larger turbines, the natural frequency of the platform pitch tend to shift to lower frequency range where the aerodynamic forces by turbulent wind become dominant.In this case, the method of combining wind preview by lidar systems and the platform pitch rate for a proper blade pitch command should be further investigated.

Figure 1 .
Figure 1.The overall control diagram.Note that the real-time pitch angle (θ) signal is also used in the generator torque control and collective blade pitch feedback control modules for controller scheduling, but the lines are omitted.

Figure 2 .
Figure 2. The trends of turbine variables by different signs of floating feedback.

Figure 3 .
Figure 3.The relative change of STDs under different floating feedback gain k p,float .The relative change refers to the change relative to the RFB case with k p,float =0.Note that LAC is not considered.(a): the sea water is assumed still (no wave).(b): the wave is modeled to be irregular and simulated using V hub =20 m −1 , H s =5 m, and T p =12.5 s.

Figure 4 .
Figure 4.The spectra of turbine-related variables, estimated using Welch's method[17].Both x and y axes are in logarithmic scale.The labels of the axes are not shown due to the confidentiality agreement.The peak spectral frequencies (1/T p ) are indicated by the dashed lines.

Table 1 .
The changes (in %) in standard deviations or energy production under different control strategies relative to the RFB controller.Note that positive values mean that the standard deviation is higher than the RFB controller.The standard deviations by different stochastic winds and waves are averaged before calculating the relative change.V hub = 20 ms −1 and H s =5 m. .40-36.90 -2.80 2.57 -32.34 -16.72 0.39