Control Methods for Reducing Platform Pitching ...

Control Methods for Reducing Platform Pitching Motion of Floating Wind Turbines Hazim Namik∗and Karl Stol

Department of Mechanical Engineering, The University of Auckland, Auckland, New Zealand

Abstract Floating offshore wind turbines offer a feasible solution for water deeper than 60m. Consequently, they experience additional motion in six degrees of freedom. These additional motions can significantly affect turbine loads and power production, especially the pitch motion (fore-aft rocking). Therefore, the onboard control system has to be used to mitigate the pitching motion. Three types of controllers were implemented and compared to each other relative to a standard baseline controller. The controllers include a collective blade pitch state space (SS) controller, and individual blade pitch (IBP) SS controller, and an IBP SS controller with disturbance accommodating control. It was found that the IBP controllers, applied on a 5MW floating barge wind turbine system, achieved significant reduction in platform pitching motion as they create asymmetric aerodynamic loads to restore platform pitch motion. Simulation results show that platform pitching rate was reduced by up to 45% due to using individual blade pitching without severely affecting power regulation and turbine loads. The platform pitch restoring mechanism through individual blade pitching can be applied to any floating wind turbine system with individually operated blades.

1

Introduction

HE offshore wind energy potential is very large. For example, in 2003 the UK offshore energy potential was estimated to be 986TWh/year while demand was estimated to be 321TWh/year; i.e. more than three times the demand [1]. Therefore, utilising this offshore energy potential could increase the share of clean and renewable energy sources in the energy market. However, most of this offshore potential lies in deep water [2].

T

Floating offshore wind turbines offer a feasible solution for water depths greater than 60m [3, 4]. There are three main floating wind turbine concepts. Each concept uses a different principle to achieve stability. The three floating concepts (shown in figure 1) are: a ballast stabilized spar-buoy, a mooring line stabilized tension leg platform (TLP), and a buoyancy stabilized barge platform. Of course, each concept has its advantages and limitations. In June of 2009, the world’s first floating wind turbine, based on the spar-buoy concept, was installed off the coast of Norway in 220m deep water [5]. One drawback of having a wind turbine mounted on a floating platform is the additional motions induced by incident wind and waves. These motions can result in large loads on the turbine blades and tower as well as reduce power output. Hence, the onboard control system plays an important role at reducing platform motions while maintaining power production/regulation. One important dynamic of the floating system is the pitching motion (forward and backward rocking motion). Both Nielsen et al. [4] and Jonkman [7] found that in the above rated wind speed region (region 3) a standard onshore rotor speed controller will have reduced or even negative pitch damping resulting in large platform pitching motions and hence large turbine loads and power fluctuations. Nielsen et al. [4], working on a spar-buoy floating concept, developed an active control strategy to avoid structural resonance. That control strategy took into account the fact that as wind speed increases, the ∗ Correspondence to: H. Namik, Department of Mechanical Engineering, School of Engineering, The University of Auckland, 20 Symonds Street, Auckland, Private Bag 92019, Auckland Mail Centre, Auckland 1142, New Zealand. Telephone: +64 9 3737599 ext. 82759 Fax: +64 9 3737479 E-mail: [email protected]

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Figure 1: The three floating main floating wind turbine concepts [6] thrust force decreases which may cause negative damping of platform pitch motion in region 3. The controller achieved satisfactory results in reducing platform resonant motions in region 3 in simulation and scale model testing. Continuing on the work done by Nielsen et al. [4], Skaare et al. [8] developed an estimator based controller to avoid resonant pitch motions of the turbine and improve fatigue life. This controller was compared to a standard onshore controller applied to an offshore floating system. Results showed improvements in tower and blade fatigue life but power output was reduced. Jonkman [7] implemented several control strategies involving a torque controller with constant power algorithm and gain scheduled PI blade pitch controller for a 5MW wind turbine on a barge platform. Two of these strategies (tower top feedback and pitch to stall regulation) were not capable of reducing the pitching motion of the barge platform. The third and final strategy of detuning the speed controller gains produced the best reduction in platform pitching. Further reduction in platform pitching motion was deemed necessary by Jonkman. However, there was a limit to the improvement in performance from detuning controller gains as it approached open loop control. The focus of this study is on reducing the platform pitching motion on a barge platform floating wind turbine concept operating in region 3. The barge platform is very sensitive to incident waves thus reducing platform pitching becomes an important control objective. Three control approaches are used to mitigate platform pitching motion in region 3. These are compared to a simple and robust reference/baseline controller that is specifically designed for the barge platform (the detuned gain scheduled PI blade pitch controller developed by Jonkman [7]). In this paper, section 2 describes the simulation tools and floating wind turbine model used to obtain the results. The three control approaches as well as the baseline controller are discussed in section 3. Simulation results are discussed in section 4 followed by conclusions in section 5.

2

Simulation Tools and Model

The floating system is simulated using MATLAB Simulink and FAST [9]. In this study the same wind turbine developed by Jonkman [7] is used. The wind turbine is a fictitious 5MW machine with its properties based on a collection of existing wind turbines of similar rating since not all turbine properties are published 2

by manufacturers; the model is commonly known as the “NREL Offshore 5-MW Baseline Wind Turbine”. The wind turbine has three blades that are 61.5m long. The floating barge is a rectangular platform with 8 catenary mooring lines – 2 at each corner. The basic turbine and barge platform properties are listed in table 1.

3

Implemented Controllers

Wind turbine systems from a control point of view are severely under-actuated; the Table 1: Floating system properties system has many more degrees of freedom (DOFs) than available actuators. On Wind Turbine a typical large wind turbine, the maxi5MW mum number of actuators is four: three Power rating Upwind blade pitch actuators and applied genera- Rotor orientation Variable speed and pitch, active yaw tor torque. Having a floating platform only Control Rotor, hub diameter 126m, 3m makes it more difficult to control due to the Hub height 90m additional six DOFs (surge, sway, heave, Rated rotor, generator speed 12.1 rpm, 1173.7 rpm roll, pitch, and yaw) and no additional acBlade operation Pitch to feather tuators. Maximum blade pitch rate 8 deg/s All the controllers that are implemented Rated generator torque 43,093 Nm except for the baseline controller are lin- Maximum generator torque 47,402 Nm ear controllers. However, the floating wind turbine dynamics are nonlinear. Therefore, Barge Platform the controllers are designed based on a lin- Width 40m earised model about an operating point in Length 40m region 3. The main control objectives are Height 10m to regulate power extraction and reduce Draft 4m platform pitching motion and turbine fa- Water depth 150m tigue loads. As discussed in section 1, three controllers are implemented to reduce platform pitching; each using slightly different mechanisms. The controllers are: Baseline, collective blade pitch (CBP) state space (SS) controller, individual blade pitch (IBP) SS controller, and IBP SS controller with disturbance accommodating controller (DAC). Table 2 summarises the differences between the implemented controllers. Further description is provided in subsequent sections. Table 2: Basic comparison of implemented controllers Controller

Baseline

CBP SS

IBP SS

IBP SS with DAC

Blade pitching Gain calculation

Collective Gain scheduled

Collective LQR

Individual Periodic LQR

Individual Periodic LQR + DAC

Pros

Simple Robust

MIMO Multi-objective

MIMO Multi-objective IBP

MIMO Multi-objective IBP Disturbance rejection

Cons

SISO Single objective CBP

Additional sensors Complicated CBP

3.1

Most complicated Requires disturbance estimator

Baseline Controller

The Baseline controller used for this study is the best controller developed by Jonkman in his preliminary study to reduce platform pitch motion [7]. The Baseline controller consists of two independent controllers; a generator torque controller and a gains scheduled collective blade pitch controller. The relationship between the generator torque and generator speed is region dependent. In region 3 where the objective is to regulate power to the rated, the applied generator torque is inversely proportional to the 3

generator speed [10]. The gain scheduled PI controller is in the form given by equation 1 where θ(t) is the commanded collective blade pitch angle, KP (θ) and KI (θ) are the scheduled proportional and integral gains respectively, and e(t) is the error signal [7]. The gains are scheduled as a function of blade pitch θ to account for the change in turbine sensitivity at different wind speeds. This is a form of nonlinear control. ˆt θ(t) = KP (θ)e(t) + KI (θ)

e(τ )dτ

where

e(t) = ωGen − ωGen,Rated

(1)

0

3.2

Collective Blade Pitch State Space Controller

The first controller to be implemented to reduce the platform pitching motion is a multi-objective collective blade pitch state space (CBP SS) controller. The CBP SS controller is designed with two control objectives: rotor speed and platform pitch regulation. It is thought that by adding the platform pitching dynamics in the control design and as an explicit control objective using an optimal controller, platform pitching motions can be reduced. The CBP SS controller is implemented using linear quadratic regulator (LQR) theory to calculate the optimal gain matrix. The CBP SS controller uses full state feedback (FSFB) where all system states are assumed to be directly measured. The selected design states (for all the state space controllers designed in this paper) can be easily measured by readily available sensors. Furthermore, improvement in sensor measurement quality means that they can be used directly without significantly affecting the dynamic response of the system. This means that signal processing (e.g. filtering) dynamics are becoming faster and embedded within the sensor unit. Therefore, a state estimator is not necessary. However, in practice, it is desirable to reduce the number of sensors required by implementing a state estimator. Since a state estimator can be designed separately, it is considered outside the scope of this paper.

3.3

Individual Blade Pitch State Space Controller

The CBP SS controller uses collective blade pitching. This means that the controller can only influence the platform pitching through changing the rotor collective thrust. Individual blade pitching allows the controller to command blade individually to create asymmetric aerodynamic loads to create additional platform pitch resorting moment. It works by commanding the blades that are located at the top half of the rotor to increase or decrease thrust while doing the opposite for the lower half of the rotor. This creates the asymmetric loading and additional restoring moment [11]. There are many ways to achieve Individual Blade Pitch (IBP) control depending on the control objectives. Multi-blade coordinate (MBC) transformation can be used to facilitate individual blade pitching [12, 13]. MBC transformation captures periodic properties of a system in a linear time-invariant (LTI) model - useful for control design. Although MBC transformation does not capture all the periodic effects, it has been shown that the residual periodic effects are negligible for analysis and control design for three bladed onshore wind turbines [13]. Bossanyi [14] implemented IBP control using PI controllers to mitigate blade loads. He used a direct and quadrature (d-q) axis representation (a form of MBC) to be able to allow for MIMO control using PI controllers. Wright [15] achieved IBP control using disturbance accommodating control. He used an internal model for the wind disturbance and the effect of wind shear to drive the individual blade pitching. Another form of IBP is to use direct periodic control. Periodic control allows the controller gains to change depending on the rotor azimuth position and control objectives [16, 17]. Periodic control is used to implement IBP control on the floating wind turbine system as it captures all the periodicity of the floating wind turbine system. It is uncertain at this stage whether MBC captures all the important periodic elements of the floating system. To design a periodic SS controller, a periodic state-space model of the floating system must be extracted from FAST. During linearisation, FAST generates the periodic state-space matrices required for this controller design for a specified number of azimuth positions [9]; usually these matrices are averaged to design constant gain controllers (the same method used to design the CBP SS controller). The optimal periodic gain matrix is calculated by solving the periodic Riccati equation instead of the algebraic Riccati equation used by the LQR design process.

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Initial implementation of IBP SS controller showed that it sequentially 1 destabilised the platform roll, tower side-side and drive train degrees of freedom. To stabilise the system, all these DOFs were included in the design of the controller. Although the yaw DOF was not destabilised (at least around the linearisation point) it was added to the control design to improve power and load regulation. Therefore, the final controller is designed based on a 6 DOF periodic model.

3.4

IBP Disturbance Accommodating Controller

In an ideal case, a disturbance accommodating controller can completely cancel the effects of persistent disturbances [15, 18]. In the case of a floating wind turbine, the disturbances are the incident wind and waves. If the effects of wind and, more importantly, waves can be cancelled or reduced, the platform motions will be significantly reduced thus reducing the additionally induced loads on the wind turbine and improve power regulation. In this study, only wind disturbances are considered into the design of the disturbance accommodating controller. To design a DAC, the effects of the disturbances on the system states have to be included in the model as shown by equation 2 where x, u, and ud are the state, control input, and disturbance vectors respectively, A, B, and Bd are the state, actuator, and disturbance gain matrices respectively. The disturbance accommodating control law (given by equation 3 where z is the disturbance states of an assumed wave form model, G is the state regulator gain matrix and Gd is the disturbance minimisation gain matrix ) consists of a state regulating part which is exactly the same for the IBP SS controller and a disturbance rejection part. The disturbance minimisation gain, Gd , is calculated using equation 4 where Θ relates ud and z . B + denotes the Moore-Penrose pseudoinverse.

x˙

= Ax + Bu + Bd ud

u = Gx + Gd z Gd

+

= −B Bd Θ

(2) (3) (4)

Wind Speed (m/sec)

A disturbance state estimator is required since direct measurement of the distur24 bance states is usually difficult or impossible. This leads to the problem that design22 ing a state estimator for the disturbances only is not possible without measuring any 20 of the disturbances states z. However, it is possible to use turbine measurements 18 to estimate the disturbance states thereby utilizing the turbine as a large anemome16 ter. A periodic disturbance state estimator was designed to estimate the incident 14 wind speed using the information from all the system states by augmenting the tur12 bine state with the disturbance states. The Actual wind disturbance wave form was modelled Estimate 10 as step disturbance about the linearisation 0 20 40 60 80 100 point. Figure 2 shows a sample wind speed Time (sec) estimator performance in turbulent wind. The estimator also acts as a low pass filter, Figure 2: Actual and estimated hub height wind speed hence the delay, which minimises the fluctuations in the wind speed estimate and thereby reducing the blade pitching since the DAC output is a direct function of wind speed. 1 Not all these three DOFs were destabilised simultaneously but one at a time as each DOF was stabilised the other was destabilised.

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4

Results and Discussions

Each of the abovementioned controllers was simulated under two different wind and wave conditions. The turbulent wind and irregular sea states were simulated to cover the entire operational range of the floating system in region 3 under normal operating conditions. Extreme conditions and events are outside the scope of this study as the control system is usually shutdown. The simulations were carried out using all the 21 DOFs that FAST models to account for the turbine nonlinearities, flexible components, and coupling in order to assess if the un-modelled DOFs significantly affect the controllers’ performance. To quantify the performance of each controller, eleven performance measures/metrics are used. These range from root mean square (RMS) of the power regulation error, blade pitch usage, platform RMS motions, and fatigue damage equivalent loads (DELs) of key turbine components. These performance metrics are then averaged across the different simulation conditions and normalised relative to the reference/baseline controller. With all the performance metrics, a value of less than 1 is desired meaning an improvement relative to the baseline controller. At this stage, determining whether the absolute values of these performance metrics are comparable to those of a monopole offshore wind turbine is outside the scope of this paper. The averaged and normalised results are shown in figure 3. Just by inspection of the figure, it can be seen that the individual blade pitch controllers (IBP SS and DAC) generally have improvements across most of the performance indices. To understand all the results presented in figure 3, the controllers will be compared sequentially. 1.80 CBP SS 1.60

DAC 1.20 1.00

1

0.80 0.60

0.99 0.45 0.46

1.06 0.55 0.59

Pitch

Yaw

Roll Rate

0.97 0.37 0.39

0.74 0.68 0.69

Roll

0.72 0.58 0.55

1.02 0.68 0.71

1.41 1.00 1.06

1.22 0.57 0.60

0.85 0.78 0.80

1.01 1.07 1.09

0.20

3.29 3.86 4.34

0.40 0.81 0.80 0.74

Normalised Performance Metric

IBP SS 1.40

0.00

0 Power Error Blade Pitch Blade Flap Rate RMS of Power

RMS of Actuator Usage

Tower Tower Side- Low Speed Fore-Aft Side Shaft Fatigue DEL

Pitch Rate Yaw Rate

RMS of Platform Motions

Figure 3: Averaged and normalised simulation results

4.1

CBP SS Controller

Comparing the performance of the Baseline controller with the CBP SS controller, the following is observed: Both controllers have a rotor speed and power regulation as control objectives yet the CBP SS controller improves speed regulation. As a direct result of that, power fluctuations are reduced by 19%. Platform pitch and pitch velocity are reduced by approximately 27% each which in turn explains the reduction in the tower fore-aft fatigue loads. This is because the controller is utilising the blades to create the collective platform pitch restoring thrust force by increasing the actuation of the blade; this explains the significant increase in blade pitching (Blade Pitch Rate performance metric). The 41% increase in the low speed shaft (LSS) fatigue loads is a direct result of increased blade pitching. Furthermore, reducing this load was not an explicit control objective for the CBP SS controller. Unfortunately, one limitation for collective blade pitching exists. Conflicting blade pitch commands are issued by each control objective. For example, assume the turbine is pitching forward. The platform pitch regulation part of the SS controller will command the blades to increase the rotor collective thrust. However, due to blade aerodynamics, increasing thrust also increases the torque produced by the rotor causing it to 6

accelerate. Simultaneously, the rotor speed regulation part of the SS controller will command the blades to reduce the torque generated by the rotor to maintain the same rotor speed and hence the conflicting blade pitch commands. This is essentially what Jonkman found when he added the tower top feedback control loop [7]; the two independent controllers were competing for blade pitch usage. However, the CBP SS controller was able to improve all of its design objectives despite the conflicting blade pitch commands imposed by the nature of the control objectives. Although the exact physical mechanism is not yet fully understood, there are two factors that may explain this improvement in performance. First, the CBP SS controller was designed with an emphasis on regulating platform pitch states. Therefore, the platform pitch regulation will take precedence due to higher gains and hence platform pitch motion is reduced. It is believed that this reduction in platform pitching actually reduces the relative wind speed perturbations induced by platform pitching and therefore improves speed regulation. Second, in terms of an optimisation problem, the Baseline controller is not optimal and therefore speed regulation may be improved by tuning. Being an optimal controller, then perhaps the CBP SS controller was able to find a collective blade pitch trajectory that improved speed and platform pitch regulation up to a point where further improvement was no longer possible due to the aforementioned conflicting blade pitch demands. Due to the increased blade pitching, the CBP SS controller causes the turbine to roll even more thus increasing tower side-side fatigue loads by 22%. To look for interaction, the effect of the blade pitching on the platform roll is studied through the B matrix. Interestingly, the blades affect the platform roll the same way it affects platform pitch and the effect is almost exactly in phase. This means that when the controller generates the platform restoring pitch moment by increasing rotor thrust it also induces a rolling moment by an asymmetric torque load. Although the rotor is symmetric and an increase in symmetric thrust should not result in torque imbalance on the rotor, the asymmetry is created by having blade pre-cone and shaft tilt angles. This rolling motion is thought to be the main contributor to the increase in tower side-side fatigue load. Taking all that into account, the CBP SS controller noticeably improves turbine power and rotor speed regulation as well as reducing platform pitching but it also significantly increases fatigue loads on some turbine components. More DOFs can be added to improve the performance of the CBP SS controller. However, since the IBP controller has better performance than the CBP SS controller, the IBP controller was chosen to further improve the turbine performance by including the aforementioned DOFs.

4.2

IBP SS Controller

Comparing the IBP SS controller with the CBP SS controller we observe the following: The IBP controller has similar power regulation but reduced platform motions which indicate that individual blade pitching is using the asymmetric aerodynamic loads to regulate platform motions while using the collective pitching for rotor speed regulation. The IBP SS controller was able to reduce platform rolling, pitching, and yawing rates/velocities by 45%, 42%, and 63% respectively. The improvement in reducing platform pitching resulted in reducing tower fore-aft fatigue loads by 22% even though it was not part of the controller objectives. With respect to turbine fatigue loads, the increase in blade fatigue loads was expected due to two factors. First, the blades had to create the platform pitch restoring moment which created thrust loads on the blades. Second, blade load reduction was not one of the control objectives and is outside the scope of this work. However, the increase in blade loads was moderate when the blade actuation has increased by at least 380%. The IBP controller significantly reduced tower side-side loads by 43%; the CBP SS controller increased tower side-side loads by 22%. Similarly, the low speed shaft loads were maintained similar to the Baseline controller by the IBP SS controller while the CBP SS controller caused a 41% increase the shaft loads. The reduction in these loads is a direct result from including their corresponding DOF in the controller design (tower side-side and drive train DOFs) coupled with further reduction in turbine platform motions.

4.3

DAC

Looking at the performance of the DAC, it can be seen that there is little difference across all performance metrics when compared to the IBP SS controller. This can be explained by the fact that the DAC is essentially an IBP SS controller with an additional disturbance rejection component. Furthermore, the barge floating system is much more sensitive to incident waves than wind. This can be seen through the further improvement in power regulation by the DAC as it is reducing the effect of wind disturbances on the system but this improvement has little impact on platform motions. 7

One limitation of DAC applied to wind turbine systems exist; collective blade pitch drifting. Assuming a linear wind turbine system, the collective blade pitch commanded by the feed-forward action of the DAC to reject wind disturbances and maintain steady state is a linear function of the wind speed described by equation 5 where uop is the collective actuators operating point. However, the collective blade pitch required to keep the floating wind turbine in steady state as the wind speed varies is a nonlinear function of wind speed as shown in figure 4. u = G∆x + Gd ∆z + uop

(5)

Blade Pitch (deg)

As illustrated in figure 4, the DAC action will force the blades away from the optimum blade 25 Optimum operating point pitch. An IBP SS controller without the DAC DAC collective pitch command component will follow the optimum blade pitch 20 Operating point but with the delay of the integral effect. If both IBP SS controller and DAC are working together, 15 then the DAC will force the operating blade pitch 10 away from the optimum but the integral action will eventually bring it back to the optimum curve. 5 One way to overcome this limitation is to limit the DAC to only command perturbation about the 0 nonlinear operating point and rewrite equation 5 8 10 12 14 16 18 20 22 24 ¯ d is the azimuth averinto equation 6 where G Wind Speed (m/s) aged gain and Gd (ψ) is the periodic gain perturbation about that average at azimuth angle ψ. Figure 4: Optimum and DAC commanded collective The first term of equation 6 is state regulation pe- blade pitch riodic blade pitch, second term is the commanded collective blade pitch perturbation by the DAC, the third term is the periodic perturbations (IBP) and the last term is the collective blade pitch operating point about the linearisation point. The second and last terms of equation 6 can be combined to give the nonlinear collective blade pitch operating point uop (v) as a function of wind speed v as shown in equation 7.

¯ d ∆z + Gd (ψ) ∆z + uop u = G∆x + G

(6)

u = G∆x + Gd (ψ) ∆z + uop (v)

(7)

Simulation results of the modified DAC using turbulent wind conditions around the operating point show little or no improvement upon the originally implemented DAC. This was expected as the modification should only improve the DAC response away from the linearisation point. The performance of the DAC with the variable operating pitch (VOP) relative to the original DAC simulated in turbulent wind conditions that are, on average, away from the linearisation point of 18m/s is listed in table 3. The table shows a consistent improvement across all performance metrics as expected. Table 3: Variable operating blade pitch DAC performance relative to IBP SS controller with DAC RMS Blade Power Pitch Error Rate -5.8%

-5.9%

Blade Flap -5.8%

Fatigue DELs Tower Tower SideFore-Aft Side -5.1%

-2.7%

RMS Platform Motions Low Speed Shaft

Roll

Pitch

Yaw

Roll Rate

Pitch Rate

Yaw Rate

-5.8%

-2.4%

-1.6%

-3.8%

-5.0%

-0.9%

-5.9%

Another limitation of implementing DAC on such a floating system is actuator saturation. The calculated DAC gain can sometimes (depending on how many DOFs are included in the DAC design) be very high resulting in blade actuator saturation [19]. Unfortunately, the gain Gd cannot be tuned as it is the result of a pseudoinverse as shown in equation 4. It may seem unfair to compare four types of controllers with differing number of control objectives (ranging from one to twelve (6DOFs)). Furthermore, the Baseline controller (gain scheduled PI) is a form of a nonlinear controller and therefore has an advantage over the other linear controllers as the turbine operates 8

away from the linearisation point. However, recall that the main objective of this work is to investigate whether performance improvement is possible for the floating wind turbine system. Adding more control objectives to the Baseline and CBP SS controllers was not justified. Both controllers (Baseline and CBP SS) suffer from the same limitation of conflicting collective blade pitch commands. While it may be possible to add more control loops to the Baseline controller and attempt to decouple the control loops, it is outside the scope of this paper. The implemented DACs were able to improve the performance even more than the IBP SS controller. The improvement was consistent but small if not even statistically insignificant. Furthermore, there are some limitations of DACs applied to this system. Therefore, it can be concluded that individual blade pitch control with 6 design DOFs noticeably improve turbine performance relative to the Baseline and the collective blade pitch state space controllers without severely affecting other main turbine components.

5

Conclusions

Floating wind turbine systems are large and flexible machines that require controllers with multiple control objectives to reduce the effects of additional motions and loads. More specifically, the platform pitching motion (fore-aft rocking motion) can directly affect power production in addition to affecting tower loads. Three control strategies were implemented to reduce platform motions with an emphasis on the platform pitching motion. The control strategies include: Collective blade pitch (CBP) state space (SS) controller, individual blade pitch (IBP) SS controller, and IBP SS controller with a disturbance accommodating controller (DAC). Simulation results using a 21 degrees of freedom (DOFs) nonlinear floating turbine model indicate that three control strategies were able to reduce platform pitching motion when compared to a gain scheduled PI controller as a baseline. The IBP controllers were more successful at reducing platform motions because they utilise asymmetric aerodynamic loading to create additional restoring moments without negatively affecting rotor speed and power regulation. Conflicting blade pitch commands were issued with the CBP SS controller when trying to regulate rotor speed and reduce platform pitch simultaneously due to turbine pitching dynamics coupled with rotor aerodynamics. The DAC was designed to minimise the influence of wind speed perturbations about an operating point. The DAC was able to consistently but only marginally improve performance relative to the IBP SS controller. The limited improvement was due to the sensitivity of the floating system to the waves dominating the response of the system. A DAC designed to minimise the effect of the waves may improve the performance subject to actuator saturation; this will be the focus of our future work. However, at this stage, the best controller that can reduce platform motions is the IBP SS controller. All of the above linear controllers were simulated in region 3 (above rated wind speed region) designed about an operating point. However, the wind conditions were simulated to cover the entire range of region 3 to assess the robustness of these linear controllers operating away from the linearisation point. Simulation results show a stable and acceptable performance from all the implemented controllers. The individual blade pitch mechanism that regulates platform motions is generic to any wind turbine with individual blade pitching blades. Therefore, the IBP SS controller can be applied to other floating concepts to reduce the floating motions. The extent of the improvement depends on the hydrodynamic properties of the floating system. Furthermore, the same IBP mechanism can be used in region 2. However, the controller formulation has to be changed as the control objectives regarding power production is different (maximise power production in region 2 and limit/regulate power capture in region 3). Since the controllers that reduce closed loop pitch damping only operate in region 3, platform pitching motion is expected to be smaller in region 2.

Acknowledgments H. Namik would like to thank the Tertiary Education Commission of New Zealand for student funding through the Top Achiever Doctoral Scholarship. We are also grateful for the support of Jason Jonkman at the National Renewable Energy Lab (NREL) for providing the simulation models and advice.

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