Wind speed feedforward control for a wind turbine using LIDAR

Transcription

1 Wind speed feedforward control for a wind turbine using LIDAR W.V. Rietveld Delft Center for Systems and Control

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3 Wind speed feedforward control for a wind turbine using LIDAR MASTER OF SCIENCE THESIS For the degree of Master of Science in Systems and Control at Delft University of Technology W.V. Rietveld June 8, 23 Faculty of Mechanical, Maritime and Materials Engineering (3mE) Delft University of Technology

4 The work in this thesis was supported by XEMC Darwind B.V.

5 Abstract Wind energy has relatively minor environmental impact compared to traditional energy sources. It doesn t consume fuel or emits air pollution, while the land used for a wind farm can still be used mostly for other purposes such as agriculture. Some people state that wind turbines consume subsidies as a fuel, since they aren t profitable without it. They use a blurred view on the real costs of energy, since they do not consider the costs associated with the pollution of the fossil energy sources. Despite this, wind energy has to deal with the public opinion that wind energy is expensive and should look for opportunities to reduce the prices. This can be done by reducing cost, increasing the yield or by extending the lifetime of the turbine. The latter can be achieved by reducing the loads on the structure. The rotor speed of a wind turbine is the result of the balance between the aerodynamic and the generator torque. Most of the utility scale variable speed wind turbines currently use a rotor speed feedback controller to control this torque balance. They can adjust the captured aerodynamic torque by changing the angle of the blades relative to the wind. But, the effect of changes in the wind on the rotor speed is delayed due to the inertia of the rotor. Meanwhile the construction suffers from the variations in the loads. For this reason it would be advantageous to measure the wind speed and use it for control, in order to anticipate on changes in the wind earlier and reduce the loads on the structure resulting in an extended lifetime of the turbine. The wind speed is currently measured on most turbines, however this measurement is useless for control, since it is contaminated by the wake of the rotor of the turbine. LIDAR is a measurement technique, which is able to measure the upcoming wind speed in front of the turbine using a laser. This measurement technique is relatively new to the wind energy market and an optimal configuration for the measurement is yet to be defined. So are the possibilities for using these measurements in a control system. A realistic simulation environment is required to investigate this and come to a reliable conclusion. This environment is created using a coupling between the simulation software packages Bladed and Simulink. It provides the possibility to co-simulate the nonlinear model of the turbine in Bladed together with a new controller in Simulink. Bladed provides simulated line-of-sight (LOS) LIDAR wind speed measurements from the wind field used. Multiple LOS measurements are combined to determine a mean wind speed representative for the whole rotor plane. How well the reality is approximated depends on the number of LOS measurements considered, the measurement distance(s) and number of measurement points per distance. The performance of the wind turbine using various LIDAR configurations is compared. The knowledge about the upcoming wind is used in the controller by adding a wind speed feedforward loop to the existing rotor speed feedback controller. The performance of the wind turbine using two different feedforward controllers is investigated. Controller A is based on the optimal pitch action for the wind at the turbine. While controller B is based on the difference between the actual pitch angle and the optimal pitch angle related to the wind speed measured at some distance. The feedback controller parameters are relaxed while using these feedforward controllers in order to achieve load reductions without deteriorating the rotor speed control.

6 ii Abstract Feedforward controller B performs best for the load reduction, with reduced pitch rate demands, while having still sufficient disturbance rejection in the rotor speed control. This is because it takes more time to compensate for the virtual pitch error, resulting in lower pitch rate demands and thrust related loads. Filtering the measured wind speed adequately is a crucial step in the load reduction for controller A while controller B has this property by design. The filter effect of controller B changes with the wind speed as higher wind speeds provide less time to compensate for the upcoming changes in the wind. The optimal configuration of the LIDAR for the XD5 appears to be the pulsed system with four points on the azimuth at each of the three measurement distances. This configuration provides early knowledge about upcoming changes in the wind speed, while having sufficient coverage of the complete rotor plane.

7 Table of Contents Preface v Chapter Introduction. Background....2 Objective Methodology outline... 2 Chapter 2 Introduction to a wind turbine 3 2. Basic definitions and operation of a wind turbine Loads XD Dynamic model used for analysis and design Baseline rotor speed feedback controller... 8 Chapter 3 LIDAR wind speed measurements 3 3. LIDAR types LIDAR configuration... 4 Chapter 4 Wind speed feedforward controller 7 4. Gain scheduled feedforward controller A Conversion from preview distance to preview time Low pass wind speed filter Feedforward gain Result Gain scheduled feedforward controller B Chapter 5 Controller optimization Relaxing the rotor speed feedback controller Remove harmful frequencies from the wind speed measurement Result... 37

8 iv Table of Contents Chapter 6 Comparison between various LIDAR configurations Continuous wave LIDAR Pulsed LIDAR... 4 Chapter 7 Conclusions 43 Appendix A Derivations 45 A. Calculation of the rotor speed feedback controller parameters Appendix B Bladed Simulink coupling 49 Appendix C LIDAR simulation in Simulink 5 Appendix D Simulation results 53 D. Baseline controller augmented with feedforward controllers A and B D.2 Relaxed baseline controller augmented with optimized feedforward controllers A and B D.3 Number of points on the azimuth used for the LIDAR wind speed measurement D.4 Number of focal distances used in the LIDAR wind speed measurement Bibliography 57 Glossary 59 List of Acronyms List of Symbols... 59

9 Preface This research is done as a finalizing assignment for my study Systems and Control at the Delft Center for Systems and Control (DCSC) at the Technical University in Delft (TUD). It gives some insight on the functionality, usage and advantages of LIDAR technology on a wind turbine. The research was commissioned by XEMC Darwind B.V. as part of the offshore wind subsidy (EWOZ), project work package 2: Feedforward control using LIDAR. I would like to thank my employer (XEMC Darwind B.V.) for providing me the opportunity to do this research project and giving me the associated support. Especially I would like to thank Edwin Pasterkamp, for his input during our discussions. Additionally I would also like to thank my supervisor Jan-Willem van Wingerden for his support and feedback during our progress conversations. Finally I would like to express my appreciation to Ervin Bossanyi and David Schlipf, for taking the time to meet with me and providing me some suggestions for improvement. Berkel en Rodenrijs, June 23

10 vi Preface

11 Chapter Introduction. Background The EU aims to produce 2% of its used energy from renewable resources by 22. This will decrease greenhouse emissions and boost the renewables industry, which will encourage technological innovation and employment in Europe. Almost half (46%) of this energy should be generated by wind turbines [] Recent progress reports [2], [3] show that less than half of the EU member states is on track for this target. This is caused by the economic crisis, which is affecting the cost of capital resulting in delayed investments in infrastructure and changes in support schemes. Besides that, wind turbines are placed more and more offshore, where the installation, operational and maintenance costs are higher than onshore and thus are these projects harder to get financed. The higher costs for these locations are mainly due to the accessibility, since you can reach them only with an expensive boat or helicopter when the weather allows that. On the other hand, circumstances out there are attractive for a wind turbine. Not only the wind speeds are higher, which is resulting in more energy yield, but this wind also contains less turbulence such that the construction is loaded with less fluctuations. Considering this, it becomes clear that the price of wind energy is depressed and we should look for opportunities to decrease it. This can be done by minimizing the initial and operational costs of a wind turbine, maximizing the energy yield and increasing the lifetime of the turbine. The latter case can be achieved by using advanced control techniques to reduce the loads on the structure, such that it can withstand them longer. However, historical trends from installed wind turbines show increasing rotor diameters, hub heights and power output. This growth has also impact on the construction, as the loads increase with the rotor size, due to weight and aerodynamic forces. Most of the currently installed horizontal axis variable speed wind turbines have a rotor speed feedback controller. Currently applied controllers do not use the wind speed as an input, because there was no accurate method to measure it. The only available wind speed measurement is taken in the wake of the rotor and that s not useful for rotor speed control. Recent laser developments from the telecom industry have found their way to the wind energy market, and now provide a method to measure the upcoming wind sufficient accurate. This technique is called LIDAR (Light Detecting And Ranging). Ω r β Figure -: Rotor speed feedback control diagram; Wind speed measurement: Traditional (center), LIDAR (right) Now we can, use the knowledge about the upcoming changes in the wind to improve the performance of the existing controller by already compensating for these disturbances before they affect the performance. This is called wind speed feedforward control.

12 2 Introduction.2 Objective The objective of this thesis is to reduce the loads on the structure of a commercial direct drive horizontal axis wind turbine while maintaining at least the same the energy yield. To achieve that we have to improve the existing controller using wind speed feedforward control. Additionally we have to find a configuration for the LIDAR wind speed measurement in order to come to an optimal approximation of the mean wind speed on the rotor. The result will be an extended life time of the turbine in the end..3 Methodology outline An accurate mathematical description of the turbine is used to design and validate two gain scheduled wind speed feedforward controllers. These controllers are implemented in Simulink and the model of the turbine is defined in Bladed. A coupling between these simulation tools is developed to be able to co-simulate the nonlinear model of the turbine together with the developed controllers, while using reliable LIDAR wind speed measurements. The gain scheduled controller A is designed to respond on changes in the wind speed at the rotor, while controller B continuously tries to correct for the virtual pitch error. This error is defined by the actual pitch angle and the optimal future pitch angle according to the measured wind speed. The bandwidth and damping of the rotor speed feedback controller can be reduced due to the contribution of the feedforward loop. This will bring the enhanced rotor speed control back to its original level, while reducing the loads on the structure. The wind speed can now be measured on any location in the wind field that is heading to the turbine. Multiple measurements are combined to come to an average value that is approximating the mean wind speed. The performance of the wind turbine using some feasible combinations are compared. In this chapter we have tried to introduce the problem and how we will solve that. The next chapter introduces some of the terms and concepts of a wind turbine, it explains the used model and describes the baseline rotor speed feedback controller. Chapter 3 explains how we can obtain a reliable wind speed measurement form a few tens of meters in front of the turbine. Chapter 4 describes the concepts of the two feedforward controllers. Followed by a chapter where improvements for these controllers are proposed and investigated. The performance of the wind turbine using some feasible combinations for the LIDAR wind speed measurement are compared in Chapter 6. Finally we conclude on the found results in Chapter 7.

13 Generator torque Lower generator speed set-point Rated generator speed set-point Chapter 2 Introduction to a wind turbine In this chapter we will give an explanation about the main concepts used in a wind turbine and how the wind turbine operates. More detailed explanations can be found in [4] or [5]. We will explain how we have obtained a model of the wind turbine, which is describing its dynamic behavior. Finally we will give a description of the baseline control system. 2. Basic definitions and operation of a wind turbine Most of the concepts of a wind turbine are explained in detail in the literature survey [5], that was done preceding this thesis. The most relevant definitions are repeated here shortly. A horizontal axis, variable speed, wind turbine has three main building blocks: tower, nacelle and a rotor. The tower accommodates the heavy transformer and converter at the bottom. The nacelle is the housing on top of the tower. It contains the yaw system and the generator. The yaw system is able to rotate the nacelle around its vertical axis to keep the attached rotor facing in the direction of the wind. The rotor consists of three blades that are connected to the hub. The aerodynamic force acting on the rotor can be adjusted by rotating each of the blades around its longitudinal axis (called pitching). The hub is connected to the generator, which will transform the kinetic energy from the rotor into electricity. Consuming current from the generator will result in a counter acting torque on the rotor. The speed of the rotor Ω is the result of the balance, between the aerodynamic torque Q and the electric torque Q, weighted by the inertia J of the rotor.. JΩ = Q Q (2-) The operational behavior of the turbine varies with the wind speed, three operating areas can be distinguished (see Figure 2-). At very low wind speeds () the available power in the wind is not enough to generate sufficient aerodynamic torque to get the rotor spinning at its lower speed limit. Once the rotor has reached this minimal speed (due to increase in wind speed) the generator torque is adjusted dynamically to regulate the rotor speed at its minimum setting (). When the wind speed further increases the rotor speed set-point is increased to maximize the energy capture (2). The generator torque demand is set proportional to the square of the rotor speed. This is done until the generator torque reaches the rated value, where it is kept constant. The rotor speed is now (2.5) allowed to increase up to the rated rotor speed. The generated aerodynamic torque is reduced by pitching the blades at rated rotor speed and the rotor speed is controlled by the pitch controller (3). Finally, when the wind speed increases even further, it is not responsible to keep the turbine operational and it should shut down (4). Rated generator torque set-point Rotor speed Figure 2-: Torque speed curve.

14 4 Introduction to a wind turbine 2.. Loads The wind speed in front of the tower is lower, which causes the trust force of the rotor to be affected each time a blade passes the tower. This will cause the tower to swing back and forward with the frequency of the passing blades (3P). The lower speed limit of the rotor is defined, such that the related 3P frequency is just above the Eigen frequency of the tower. Oscillations with a frequency equal to the Eigen frequency are poorly damped, causing the amplitude of the oscillation to grow with destructive result. Every material has its own behavior represented by a S-N curve showing the magnitude of cyclic stress with the number of cycles to failure. Based on this curve and time series of the loads on the construction, we can calculate the Damage Equivalent Loads (DEL). This is a figure for the number and size of oscillations of a certain frequency resulting in the same fatigue damage as the loads in the times series [6]. The DEL for the blades, calculated in this thesis, are based on the S-N slope for glass fiber reinforced plastics and for the DEL of the tower we use the S-N slope for steel. Based on statistics we know the properties of the wind to which a wind turbine will be exposed during its lifetime. This is used to define Design Load Cases (DLC) representative for some part of the life time of the turbine. A set of DLCs according to IEC64- [7] is used to calculate the size and number of cycles of the loads the wind turbine will experience during its entire lifetime. We have used DLC.3 for the simulations in this thesis to compare the DEL using the new controllers and LIDAR configurations with the DEL using the baseline controller. Ultimate loads on the structure resulting from extreme turbulence conditions are calculated this load case. The DEL of many parameters can be calculated, but only few are design driving. For this reason we will compare only the M, M, F and F of the tower base and blade roots XD5 a) In plane b) Out of plane c) Tower fore-aft Figure 2-2: Co-ordinate system of the tower (left) [6]; Mode shapes of a wind turbine [4] All calculations and simulations in this thesis are based on the XD5 wind turbine. This is a 5MW direct drive permanent magnet machine, with a hub height of m and a rotor diameter of 5m. Direct drive means that there is no gearbox between the rotor and the generator. In this case there is even not a shaft in between, since the rotor is directly connected to the bearing of the generator. The rated rotor speed of 8 rpm together with the 5.3m diameter of the generator, provides sufficient speed for the pole changes to be efficient. XEMC Darwind has two full size prototypes of this design. One is located in Wieringerwerf (NL) and the other in Fujian (CN).

15 5 Figure 2-3: XD5 prototype in Wieringerwerf (NL) 2.2 Dynamic model used for analysis and design A scheme of the model of the wind turbine is shown in Figure 2-4. The turbine has three external inputs: Generator torque demand Q, collective pitch rate demand β and the collective wind speed V. The generator torque demand is used to control the torque in the generator Q to maximize the energy capture in below rated wind speeds (), (2) and (2.5). From rated and above wind speeds (3) the generator torque is at its maximum value and the aerodynamic torque Q is limited. This is done by pitching the blades using the collective pitch rate demand input. The term collective is used to indicate that all blades receive the same set-point. We use this term for the wind speed as well. There it refers to the rotor effective wind speed representing the average wind speed acting on the three blades. The rotor speed Ω is controlled by balancing between the aerodynamic and the electrical torque, while the wind speed is disturbing this balance. Smooth control of the rotor speed has positive impact on many other system properties.

16 6 Introduction to a wind turbine V Ω r Ω r β β Q x, y Q g Q WTG z Figure 2-4: Plant model scheme. Blade root loads and the tower top and base load outputs are used as performance indicators z. Minimizing these loads is advantageous for the design and/or lifetime of the turbine. The structural damping can be increased by adding feedback loops that are mitigating the side-to-side y and fore-aft x acceleration of the nacelle, by pitching the blades accordingly. These controllers are not used in this thesis. A mathematical model governing the advanced dynamics of the turbine is required to be able to design a controller, that will maximize the energy yield over the lifetime of the turbine with minimal effort. This model is defined using Bladed, which is a commercial software package for wind turbine performance and loading calculations. All aerodynamic, electric and structural parameters of the turbine can be defined. It describes the turbine as a non-linear system, with which the response of the turbine to complicated time-varying wind conditions can be investigated [6]. The aerodynamic torque Q is calculated using the Blade Element Momentum (BEM) theory, this is a combination of two methods using different approaches. One is considering the wind turbine as a disc actuator that is extracting energy from the wind, while the other uses the approach to divide the blade into several elements and compute the flow on each of them. (see [5] and [8] for details). Equating both methods results in the non-linear relation for the aerodynamic torque, using the air density ρ, the radius R of the rotor, the wind speed V and the torque coefficient C. The latter depends on the tip speed ratio λ and the pitch angle β, see equation (2-2). Q = 2 ρπr C (λ, β)v (2-2) Where the tip speed ratio λ is defined by the ratio, between the speed of the tip of the blade and the wind speed. The tip speed of the blade is calculated using the rotational speed of the rotor and its radius. λ = Ω R V (2-3)

17 7 Figure 2-5: Torque coefficient shows some non-linearities in the system. For control design we require a linear system description. This implies that we need to linearize the nonlinear model at many operating points, defined by wind speed, blade angle and rotor speed. These linear state space models are obtained using Bladed. Model reduction is applied to reduce the number of states is these linear models from 33 to 6. The transfer functions of the three inputs to the rotor speed output can be approximated by describing only the basic dynamics. see (2-4), (2-5) and (2-6). Their Bode diagrams are shown in Figure 2-6 together with the Bode diagram of the model with all dynamics included. G = g s + p (2-4) g G = s(s + p ) (2-5) G = g (s + p )(s + p ) (2-6) Where g.22, g, g 7 for wind speed of 7 [m/s] and p = p = p. [rad/s], p 22 [rad/s].

18 Magnitude (db) ; Phase (deg) To: Rotor speed To: Rotor speed Phase (deg) Magnitude (db) 8 Introduction to a wind turbine Bode Diagram Bode Diagram From: Collective wind speed From: Collective pitch rate demand From: Generator torque demand To: Rotor speed -2 Model with dynamics Collective in plane rotor vibration (a) Simplified model -4 G G G -6 st fore-aft tower bending mode st fore-aft tower bending mode (c) (c) -8 Collective in plane rotor vibration (a) In plane rotor vibration -2 (a) Frequency (Hz) -2-2 Frequency (Hz) Figure 2-6: Open loop Bode diagram for 7 [m/s] wind speed. The mechanical properties of the tower and blades can clearly be identified by the peaks in the diagrams. The related movement of the structure is depicted in Figure 2-2. The collective in plane rotor vibration is defined as situation (a), when all blades oscillate in phase in the plane of rotation. 2.3 Baseline rotor speed feedback controller The baseline controller has a torque speed controller that is tracking the optimal C -curve in below rated wind speeds in order to maximize the energy capture. This part of the base line controller is of low interest in this study, since the load reduction and increase in energy yield using LIDAR measurements in this operating area are expected to be only marginal [9]. The rotor speed is in the (above) rated wind speeds controlled by adjusting the torque created by the wind on the rotor. This is done by altering the pitch angles of the three blades. We ll first explain this part of the baseline controller in detail and later, in the next chapter, we ll explain how we can improve it, using LIDAR wind speed measurements. An increase in wind speed will accelerate the rotor, which will be mitigated using a positive pitch rate, since the blades will capture less aerodynamic torque at larger angles (vane position is 9 deg). Positive feedback of the rotor speed is used to achieve that, as indicated in the control scheme in Figure 2-7. V WTG G d Ω ref - + C FB β G β Ω r Figure 2-7: Baseline rotor speed feedback control scheme.

19 Kp Kd Pitch angle [deg] 9 The feedback controller has a proportional and a derivative action. The latter is chosen to compensate for the integral behavior of the pitch rate input. The transfer function for the PD controller C is written as (2-7). C (s) = K s + K (2-7) We will use a simplified model of the system to tune the controller for a bandwidth (ω ) of rad/s and damping (ζ) of.77. These settings are chosen to have minimal overshoot and a reasonable quick response for disturbance rejection. The optimal controller gains for these properties are calculated using (2-8) and (2-9), where the open loop system gain is defined by g, when ignoring the structural dynamics. Details on the derivation of these equations can be found in Appendix A.. The simplified model used to calculated these gains is less accurate close to the Eigen modes of the structure, so we should be cautious using the controller in those frequency ranges. K = ω g [(2ζ + ) + (2ζ + ) + ] (2-8) K = 2ζ K g (2-9) As mentioned in the previous section, the system is nonlinear, while most of our control design theory is applicable to linear systems. Therefore, we have linearized the system in several operating points and calculated the optimal controller gains using (2-8) and (2-9), for all those operating points see Figure 2-8. Additionally we have to schedule between the found parameters in order to have a smooth transition between all calculated operating points..6 Proportional gain factors 6 Derivative gain factors Steady state pitch angle vs wind speed Figure 2-8: Calculated and factors (left and center) and the steady state relation between the wind speed and the pitch angle (right) all for wind speeds between and 25 [m/s]. We could implement these gains in a look-up-table (LUT) and interpolate between them in order to obtain the optimal gains for all wind speeds. However, a reliable wind speed measurement is lacking in practice. Relating these gains to the pitch angle using the steady state relation between the optimal pitch angle and the wind speed is a more robust solution. Again we could implement this relation in a LUT, but is appears that the inverse of these gains related to the pitch angles show a linear relation for above rated wind speeds, which makes the gain scheduling rather easy. Figure 2-9 shows the comparison between the linear gain schedule and the inverse of the calculated values.

20 Phase (deg) Magnitude (db) /Kp /Kd Introduction to a wind turbine Inverse proportional gain factors 8 Calculated 7 Gain schedule Inverse derivative gain factors Calculated Gain schedule Pitch angle [Deg] Pitch angle [Deg] Figure 2-9: Inverse gain schedules for the rotor speed feedback controller. The controller proposed in (2-7) contains a differential action, which will amplify high frequency content in the input signal, resulting in unnecessary high frequent pitch activity. We can prevent this by filtering the input signal or by adding some high frequent poles to the controller. We choose to use a second order low pass Butterworth filter on the rotor speed signal. The Bode diagram of the rotor speed filter combined with the feedback compensator using the above gain schedule is depicted in Figure 2- for some above rated wind speeds. Bode Diagram From: Rotor speed To: Collective pitch rate demand Wind speed Frequency (Hz) Figure 2-: Bode diagram of the feedback compensator for wind speeds [m/s]. The Bode diagram of the resulting closed loop system using this controller, is shown in the figure below for both collective wind speed V and collective pitch rate demand β to rotor speed Ω r. It also shows a Bode diagram of the open loop system. One can clearly see that the low frequency disturbance in the wind is suppressed by the controller.

21 Rotor speed [rpm] Pitch rate [deg/s] Figure 2-: Open and closed loop Bode diagrams for wind speed of 7 [m/s]. A simulation is done using above controller together with the non-linear model of the turbine as defined in Bladed. A wind gust with the so called Mexican hat -shape, according to IEC64- standard [7], is applied to the system. This gust has impact on the rotor speed, while the controller is demanding a pitch rate to mitigate this disturbance (see Figure 2-2). Nominal wind speed at hub position Blade demanded pitch rate Measured generator speed Time [s] Figure 2-2: Simulation output for the pitch rate demand and the resulting rotor speed, when applying a wind gust of 7.5 [m/s] during.5 [s] The pitch rate is limited between 6 /s and -2 /s. The negative rate is smaller since, pitching to vane (9 ), with positive pitch rate, can be done at maximum speed without any safety issues, while pitching to fine position ( ) will speed up the rotor and one should be cautious with that. During normal operation this limit will not be reached, only under extreme circumstances, like in this situation, it might be beneficial to relax this restriction.

22 2 Introduction to a wind turbine

23 Chapter 3 LIDAR wind speed measurements The baseline controller does not use the wind speed measurement as an input. This is because the available wind speed measurement is disturbed by the wake of the rotor (as mentioned in Chapter ). However, a reliable wind speed measurement has potential for improving the performance of the turbine as we will show in Chapter 4. In this chapter we will explain how we can obtain a reliable wind speed measurement from a few tens of meters in front of the turbine. Placing a sensor in front of the turbine is not feasible, since the wind direction will change over time and so should the position of this sensor. Mounting it on a beam, which is connected to the nacelle, would solve that issue, but that s also not feasible due to the required length of such a beam and not to mention the passing blades. Recent developments in the telecom industry provide a solution by using a laser beam, which is able to determine the speed of particles in air using the Doppler shift effect. This technology is called LIDAR (Light Detection And Ranging). 3. LIDAR types Currently two types of nacelle based LIDAR systems are available on the market: pulsed systems and continuous wave (CW) systems. The pulsed LIDAR systems shoot pulses of light of one particular wave length to the atmosphere. All particles in the atmosphere, along the line of sight (LOS) of the beam, will reflect some of this light. The wave length of the reflected light is changed according to the speed of the reflecting particle (Doppler shift effect). The reflected light is captured by a receiver and its wave length is compared with that of the source light. Any measurement distance can be chosen by only using the related time slot after the pulse was sent away. The signal to noise ratio of the measurement can be improved by increasing the time slot, which will result in a measurement that is averaged over a larger range. The light pulse has some length, which will cause that the reflection will convolve with the tail of the pulse. This will affect the intensity along the pulse resulting in a triangle shape with its peak intensity at the center of the pulse (and thus range). Measurements from several distances can be taken from each light pulse, by considering multiple time slots. The continuous wave systems shoot a continuous beam of light to the atmosphere and again all particles in the atmosphere, along the LOS of the beam will reflect some of this light. These systems use the same frequency shift in the reflection, to determine the velocity of the particles. The information about a particular distance is here obtained by focusing the beam of light at the area of interest. This will cause the intensity of the light to increase there and the majority of the reflected light will thus originate from there. The focus of the beam spreads with the distance, resulting in larger measurement ranges at larger distances. The intensity Γ of the laser beam at any distance x can be calculated using (3-), using the focus distance x, radius r of the cross section of the beam at the lens and wave length λ of the laser. Γ = (x + ( x x ) ( πr λ ) ) (3-) The resulting weighting functions of some focus distances are shown in Figure 3-. Recent versions of Bladed have this implemented and facilitate to simulate the evolution of the wind over time while providing range weighted LOS wind speed measurements. This is a reliable simulation environment for comparing the performance of various LIDAR configurations.

24 Preview distance [m] Preview distance Time Normalized range weighting Normalized range weighting 4 LIDAR wind speed measurements Distance [m] m 5m 75m m 5m 3m Distance [m] Figure 3-: Range weighting functions for: CW LIDAR using various focus distances (left); pulsed LIDAR for all measurement distances (right). 3.2 LIDAR configuration We are able to simulate the measurement of the wind speed at any location in front of the turbine using either of the LIDAR technologies, by pointing a laser beam there. In order to obtain a representative measurement for the rotor average wind speed we will need to measure at several points in front of the rotor plane. A circular distribution of points equally distributed over the azimuth will provide that. The distance and the cone angle should be chosen such that the radius of the virtual circle of the focal points matches approximately with 75% of the rotor radius. This is because the correlation between the wind speed and the generated torque is maximal in this area Mean Figure 3-2: Measurement configurations for the pulsed LIDAR. Ten focus points using one laser beam, where the cone angle periodically changes between +5 and -5 (left); Two possible configurations (red and blue), for measuring at a certain percentage of the rotor span, each using three focus points, but different cone angles (right).

25 5 The LIDAR measures the wind speed along the line of sight of the laser beam, providing information about the wind direction, shear and speed. Larger angles, between the laser beam and the rotor plane, cause that less information is used for the speed component and more for the direction or shear component. Since our main interest is the wind speed, we should keep this half cone angle small (<3 ) Measuring at larger distance will result in a less accurate instantaneous wind speed due to the wider focus, on the other hand this may be advantageous, since we are only interested in the low frequency component of the wind. Another point of attention for an increased measurement distance is the increase in the evolution of the wind, before it arrives at the turbine (you may not get what you have measured). The laser beam is only focused at one location at a time, so in order to get an average of the wind speed on the whole rotor plane, we should focus at multiple points sequentially or use multiple laser beams in order to get information from these points simultaneously. Multiple laser beams make the LIDAR expensive, while the expected advantages are low. Sequential measurements describe a helix, since the air of the first points of the circle have already moved forward to the turbine (Figure 3-3). The measurements of the last full circle are averaged in order to obtain a mean wind speed at the measurement distance. Measuring at more points on the azimuth, while maintaining the measurement time per point, will stretch the helix. This will also happen when the measurement time per point is increased, while maintaining the number of measurement points per circle. Figure 3-3: Sequential measurement of circular distributed measurement points Some combinations between the measurement time per point, the number of measurements per full circle and the total time per circle, are not possible. This is because the number of samples per azimuth angle must be an integer value. sample freq. [Hz] #azi\dsr Table 3-: Number of samples per azimuth angle, based on a scanning period of 8ms per full circle and a number of measurement points on the azimuth. The minimal measurement time per point is considered as 2ms, while the sampling frequency can be influenced by using only one out of dsr samples per location (down sample rate, dsr).

26 Phase Response (mod(8deg)) Magnitude Response 6 LIDAR wind speed measurements The wind speed is measured using a circular distribution of the measurement points, this together with the fact that the wind speed increases with altitude (called shear), results in a sine wave pattern (see Figure 3-4). Averaging over the last full circle will remove this sine wave and result in a mean wind speed V for the rotor plane LOS wind speed data measured at 8m in front of the turbine LOS wind speed Wind speed at x[m] before the turbine f (Hz) Frequency response of the LIDAR moving average filter Time [s] f (Hz) Figure 3-4: Calculation of the mean wind speed by averaging over several measurements (left). Frequency response of the LIDAR moving average filter using 8 samples per 8ms (right). V = N V(n k) (3-2) Where N is defined by the number of measurement in a full circle, which is calculated by dividing the time per measurement t by the period P of a full circle scan. In the next two chapters we will introduce and compare two wind speed feedforward controllers. All simulations done in these chapters will use circular distributed points focused at 8m LOS distance using the CW technology for the LIDAR wind speed measurement. In Chapter 6 we will investigate various LIDAR configurations in order to find an optimum. We will compare the performance based on the rotor speed fluctuations, the required pitch activity and the related loads, using the optimal controller found in Chapter 5.

27 Chapter 4 Wind speed feedforward controller As mentioned before the wind is a disturbance input to the rotor speed feedback controller, which can, in theory, perfectly be compensated for by a feedforward controller C, see (4-). However in practice the impact of the wind on the rotor speed G is complicated to model. Besides that, the wind speed at the rotor cannot be measured exact and the transfer function from the pitch angle to the rotor speed G contains non-minimum phase zeros, causing an unstable controller if inverted. V C FF WTG G d Ω ref - + C FB β FB β FF G β + + β Ω r Figure 4-: Combined wind speed feedforward and rotor speed feedback control scheme. Using (2-4) and (2-5) we get (4-2), since p = p C = s(s + p ) g C = G G (4-) g s + p = g s (4-2) g Ideally we are interested in the rotor average wind speed at the turbine as an input for this feedforward controller. However the pitch system needs some time to respond to given commands and the measured wind speed contains high frequent dynamics to which the pitch system is not able to respond. Filtering the wind speed with a low pass filter can remove this frequency content, but will introduce a delay as well. These delays can be compensated for, by using the wind speed just before it arrives at the turbine. Recent studies like [], [], [2] and [9] have shown promising results on load reduction using LIDAR wind speed measurements for (above) rated wind speeds. In the literature survey, which was done preceding this thesis, was concluded that the method described by [] was a preferred candidate to be investigated further in this thesis. This controller is proposed, because of its simplicity and easy combination with the existing feedback controller. Here it will be referred to as Gain scheduled feedforward controller A. During a discussion with the authors of [9] and [2] about the performance of controller A I got better understanding of the approach used in [9]. A similar controller will be investigated here as well, it will be referred to as Gain scheduled feedforward controller B. The similarities and differences between both controllers are explained according to their performance.

28 Feedforward controller 8 Wind speed feedforward controller 4. Gain scheduled feedforward controller A This controller is designed to reject disturbances caused by the wind. A constant wind speed is not disturbing the performance of the rotor speed feedback loop, while changes in the wind speed are. That s why the changes in the wind speed are calculated. They are amplified according to a gain schedule in order to match the non-linearities in the system. The measured wind speed contains relatively high frequency components which need to be suppressed. This is done by a low pass filter. The processing of the measured wind speed and the response time of the pitch system introduce a phase lag. The related delay is calculated to determine the required preview time to compensate for this delay. Using this approach we obtain the desired pitch rate that relates to the wind speed changes at the turbine. The transitions that the measured wind speed signal undergoes, in the process to obtain a feedforward pitch rate demand, are shown in Figure 4-2. An explanation of each of the transitions will follow in the course of this chapter, the related sub section numbers are indicated in the circles. V x V LIDAR LPF (.3Hz) Butterworth V t d dt dv t dt δ t + τ(v) 4..3 K(V) Gain schedule dβ ss dv ss β fb C fb_ω + β ff β WTG Ω Figure 4-2: Control diagram of the gain scheduled feedforward controller A. 4.. Conversion from preview distance to preview time The wind is measured at a (fixed) distance x in front of the turbine. The delay Δt between the moment of measurement and the moment that this wind arrives at the turbine, varies with the wind speed V (the higher the wind speed the shorter the preview time, see Figure 4-3). Δt = x (4-3) V This controller requires information about the wind speed at some constant time before it reaches the turbine, since the system delays are constant for all wind speeds. For this reason a conversion from the available preview distance information to the wind speed at a constant preview time is required. In order to accomplish that, we have to measure the wind sufficient far away, such that there remains enough time to compensate the phase lag in the system.

29 wind speed [m/s] 9 There are several methods to obtain the wind speed at a constant preview time. Three of them will be described and compared here. Method All measured wind speeds are stored in a shift register, which will shift all measurements one position each sample period. The location where the measurement is stored in this buffer, is based on the related preview time, which is calculated according to (4-3). Only wind speeds above some level are relevant for the controller and will be stored in the buffer, which will limit its length. When the wind speed increases, and the related preview time shortens, it is theoretically possible that earlier measurements are overtaken and become irrelevant. They will be removed from the buffer, because we assume that the latest information is valid. The result is a buffer of wind speeds ordered by preview time, which also contains unfilled fields for which we have to calculate a value. The most straight forward method is, by interpolating between the last and next known values. Method 2 This time a buffer is maintaining the chronological sequence of wind speeds measured at a fixed distance. Each of the values in this buffer, starting with the most recent values, is compared with the curve in Figure 4-3. The curve will function as a look-up-table (LUT) to calculate the preview time related to a particular wind speed measured a some distance. 3 Wind speed vs preview time while measuring at 8m preview time [s] Figure 4-3: Wind speed vs. preview time while measuring at 8m. We know how long ago each of the measurements in the buffer were taken. So, when the time that the measurement is in the buffer, becomes larger than its, from the LUT requested, preview time, then this wind must have reached the turbine. This wind speed matches the intersection between the buffered values and the curve as shown in Figure 4-4.

30 wind speed [m/s] wind speed [m/s] wind speed [m/s] 2 Wind speed feedforward controller 2 Wind speed at 8m distance (t=6.3s) Measured wind speed buffer Preview time vs wind speed 2 Wind speed at 8m distance (t=8.3s) 2 Wind speed at 8m distance (t=.3s) Time [s] Time [s] Figure 4-4: Determination of the preview wind speed Time [s] Theoretically it could be possible that there are more intersections between the lines, but it is most likely that the first (and largest) occurrence is the actual wind speed. The exact value can be found by interpolating between the four points around the intersection. Method 3 Again a buffer is maintaining the chronological sequence of wind speeds measured at a fixed distance. Here the wind speed measurements are delayed according to the mean wind speed and the measurement distance. [] The mean wind speed of the wind field is used according to Taylors frozen turbulence hypothesis [3]. This is useful in simulations where the mean wind speed of the wind field is defined, but not very useful in practice. It is also not the most accurate solution, since the actual wind speed could temporarily differ a lot from the minute mean. Calculating the mean wind speed during the simulation based on a the measurements of the last few seconds may be a better solution, but that will introduce similar issues as encountered in method. The changing mean wind speed will change the index in the buffer for the values to be used. This causes that some values will be skipped while others are duplicated. All tree methods describe how we can obtain the wind speed at the turbine, but we are interested in the wind speed a few seconds (t ) before it arrives at the wind turbine. This can be achieved with all methods. In the first method we can simply look at another index/time in the buffer. In the second method we can move the wind speed preview time curve to the left, using (4-4) and in the third method we can change the delay accordingly. x V = (4-4) Δt t

31 wind speed [m/s] wind speed [m/s] wind speed [m/s] wind speed [m/s] 2 5 Wind speed at 8m distance Wind speed at second preview time using method Method (interpolated) Method 2 (interpolated) Method 3 Wind speed at second preview time Method -2 Method time [s] Figure 4-5: Comparison between the three methods for translating preview distance wind speeds to preview time wind speeds. The difference between methods and 2 is only marginal and can be ignored, since the measurement accuracy is approximately 4 times larger. The difference between these methods and the third is larger but still acceptable, since the mean of the differences between these signals is negligible small (. and.35 [m/s] respectively). Moreover, all these signals will be low pass filtered, which is reducing the instantaneous accuracy substantially. We conclude that all three methods are suitable, but the second is preferred, since it is mathematically more robust and physically most realistic Low pass wind speed filter. Differences The LIDAR wind speed measurement contains high frequency components, to which the turbine cannot respond adequately due to the maximum pitch rates. It is useless and even harmful for the pitch system to feed these frequencies into the control system. We can remove these frequencies by applying a low pass filter. We decided to select a second order low pass Butterworth filter, with a flat pass band and a smooth roll off with -4 db per decade (see Figure 4-6). Such a filter will introduce some phase shift, which, in this case, can be compensated for, by using the wind speed just before it arrives at the turbine as an input. Larger cut-off frequency of the filter reduces the phase lag, but allows more frequency content of the wind to enter the control system. (resulting in more pitch actions). A match in the settings for the preview time and the cut-off frequency needs to be found, such that the combined delay is zero (and the measured wind enters the control system at the optimal moment).

32 Pitch rate [deg/s] Rotor speed [rpm] Phase (deg) Delay [s] Magnitude (db) 22 Wind speed feedforward controller Bode Diagram From: Collective wind speed To: Collective wind speed Delay caused by the filter c =. [Hz] c =.2 [Hz] c =.3 [Hz] Frequency (Hz) Frequency [Hz] Figure 4-6: Bode diagram of three low-pass Butterworth wind speed filters and the delay they are introducing. The controller is implemented in Simulink and some simulations were done using various combinations for the preview time and the cut-off frequency of the filter. A wind gust, with the so called Mexican hat shape, was defined in Bladed and applied to the model of the turbine. The response of the rotor speed, together with the required pitch rate were used as a metric to choose the optimal settings. Some of these simulation results are shown in Figure 4-7 From these results we may conclude that the optimal setting for the relation between the preview time and the cut-off frequency of the wind speed filter, is near a preview time of 2s and a cut-off frequency of.3hz (red lines in the middle column). Measured wind speed using.5s preview time -2.5 Measured wind speed using 2s preview time c =. [Hz] c =.2 [Hz] c =.3 [Hz] Measured wind speed using 3s preview time 2 8 Wc =. Hz Wc =.2 Hz Wc =.3 Hz hub wind speed Rotor speed response to a wind gust using.5s preview time 2 Wc =. Hz 9 Wc =.2 Hz Wc =.3 Hz 8 Baseline Rotor speed response to a wind gust using 2s preview time Rotor speed response to a wind gust using 3s preview time Pitch rates caused by the wind gust using.5s preview time Wc =. Hz Wc =.2 Hz Wc =.3 Hz Baseline Pitch rates caused by the wind gust using 2s preview time Pitch rates caused by the wind gust using 3s preview time Time [s] Time [s] Time [s] Figure 4-7: Response of the system to a wind gust, which was measured using combinations of three different settings for the preview time (.5s, 2s and 3s left to right) and three settings for the cut-off frequency of the wind speed filter (.Hz,.2Hz and.3hz in each plot). The pitch rate and the resulting rotor speed of the base line feedback controller are plotted for reference. The wind speed at hub height, provided by Bladed, is given as reference for the measured wind speed. -2

33 Gain [(deg/s)/(m/s 2 )] Steady state pitch angle ( ss ) [deg] d ss /dv ss [deg/m/s] Feedforward gain A solution to overcome the issue of modeling the response of the rotor speed to the wind is by defining a look-up-table (LUT). The values in this LUT match the gain of the ideal feedforward controller, as in (4-), for above rated wind speeds Steady state wind speed (V ) [m/s] ss Figure 4-8: Steady state pitch angle per wind speed (left); Steady state pitch rate per wind speed (right). The values in the LUT are obtained by calculating the relation between the steady state collective wind speed V and a steady state pitch angle β, see Figure 4-8 (left). For each wind speed there exists a balance between the aerodynamic torque Q and the generator torque Q. For above rated wind speeds Q is constant while Q depends on the wind speed, pitch angle and tip-speed-ratio λ,see(2-) The latter is defined for each wind speed by the rated rotor speed, leaving only the pitch angle as unknown parameter. However our pitch actuator requires a setpoint for the pitch rate rather than the angle. We can obtain this pitch rate demand β by taking the derivative dβ /dv of the found relation and multiply that with the changes in the wind speed, see (4-5). This implies that we need to calculate the changes of the wind speed to use as an input for the controller. dv dβ dt dv = dβ dt Another method for obtaining this gain schedule is by calculating the magnitude of the transfer function G from wind speed disturbance to rotor speed response, for various above rated wind speeds. The same is done for the transfer function G from the demanded pitch rate to the rotor speed response. The ratio between these magnitudes is equal to the required feedforward gain. 6 (4-5) 5 d ss /dv ss Model gain Figure 4-9: Feedforward gain per wind speed.

34 Pitch rate [deg/s] Rotor speed [rpm] 24 Wind speed feedforward controller Both methods come to the same result for above rated wind speeds (V > 2.5 [m/s]) as can be seen in Figure 4-9. The resulting feedforward controller contains a pure differentiator amplified by a gain schedule. The differentiator is there to obtain the wind speed change from the measured wind speed and the gain schedule will compensate for the non-linearities of the system. The input for this controller is filtered by a low pass filter, so the high frequency components are already suppressed and thus the differential action in the controller will not amplify that (see Figure 4-). C (s) = Ks (4-6) The gain schedule is validated by applying a Mexican hat shaped wind gust to the turbine model, while scaling the above gain schedule in the range between.5 and.25. From the simulation results shown in Figure 4- we can see that disturbance in the rotor speed is minimal using a scaling factor of, while using lower pitch rates compared to the baseline controller Nominal wind speed at hub position Measured generator speed Gain =.5 Gain =.75 Gain =. Gain =.25 BaseLine Blade demanded pitch rate Time from start of simulation [s] Figure 4-: Response of the system to a wind gust, while using scaling factors for the feedforward gain schedule ranging between.5 and.25.

35 Phase (deg) Magnitude (db) Result We have found optimal settings for the preview time, cut-off frequency of the wind speed filter and a gain schedule to compensate for the non-linearities of the system. A Bode diagram of the feedforward compensator combined with the wind speed filter is shown Figure 4-. The Bode diagram of the inverse model is shown for comparison. 2 Bode Diagram From: Collective wind speed To: Collective pitch rate demand Filter Compensator Compensator with filter Inverse model -2 - Frequency (Hz) Figure 4-: Bode plot of the wind speed feedforward controller for wind speeds = 7 [m/s]. Bode magnitude diagram of the closed loop system with and without the feedforward loop are shown in Figure 4-2. The feedforward loop is suppressing the low frequent disturbances to the rotor speed. This is done with some extra effort of the pitch system in the frequency range above.7hz, except for the frequencies related to the first fore-aft tower mode and the collective in plane rotor mode. The blade root moments have marginal improvement below.5 Hz. The tower base moments show similar behavior. The transfer function between the pitch rate demand and the various outputs remains unaffected by the feedforward control loop.

36 To: Tower base My Magnitude (db) To: Blade root My To: Blade demanded pitch rate To: Rotor speed 26 Wind speed feedforward controller 2 From: Measured wind speed Bode Diagram From: Collective pitch rate demand Baseline FB Baseline FB + FF Frequency (Hz) -2 Figure 4-2: Closed loop Bode diagrams from the wind speed disturbance to various system outputs for wind speed of 7 [m/s]. The baseline rotor speed feedback controller is shown in blue and the same controller augmented with wind speed feedforward control loop in green. Some minute simulations according to DLC.3 were done using these settings for the feedforward controller. Their results are shown in Figure 4-3. These simulations show less fluctuations in the rotor speed compared to the baseline feedback controller. The standard deviation of the rotor speed was even reduced by 46% in the 9 [m/s] simulation. The penalty paid for this improvement is an increase in pitch rate demand, since the RMS value of the pitch rate demand has increased by 5% in that simulation. The DEL of the tower top thrust force F and the tower base fore-aft bending moment M show equal trends, which makes sense since they are physical related. They have drastically increased for all wind speeds, which is caused by the increased pitch activity. The increased pitch activity is mainly in the range between.2 and 2 Hz, see Figure 4-4.

37 Spectra of the rotor speed [db] Spectra of the pitch rate demands [db] Normalized tower base loads Normalized tower top loads Normalized blade root loads std rotor speed [%] rms pitch rate [%] 27. Normalized std rotor speed 2.5 Normalized rms pitch rate Baseline FB + FF Baseline FB + FF Baseline FB + FF A Mx My Mz Fx Fy Fz Mx My Mz Fx Fy Fz Mx My Mz Fx Fy Fz Mx My Mz Fx Fy Fz Mx My Mz Fx Fy Fz.6 Baseline FB + FF A Mx My Mz Fx Fy Fz Mx My Mz Fx Fy Fz Mx My Mz Fx Fy Fz Mx My Mz Fx Fy Fz Mx My Mz Fx Fy Fz.6 Baseline FB + FF A [m/s] 3 [m/s] 5 [m/s] 7 [m/s] Figure 4-3: Normalized standard deviation of the rotor speed (top left); Normalized root-mean-square (RMS) pitch rate demand (top right). Normalized tower and blade DEL based on a min. simulation using the feedforward controller A. All results are normalized with the results of the baseline feedback controller. 9 [m/s] 2-2 Collective in plane rotor mode 2-2 9P Eigen mode pitch system P 9P Hz P -2 Baseline FB Baseline FB + FF Frequency [Hz] - -2 Baseline FB Baseline FB + FF Frequency [Hz] Figure 4-4: Spectra of the rotor speed (left) and the pitch rate demands (right).

38 28 Wind speed feedforward controller 4.2 Gain scheduled feedforward controller B This controller calculates the feedforward pitch rate demand based on the available time to compensate for the difference between the actual pitch angle and the required pitch angle (see Figure 4-5). The required pitch angle β, is derived from the mean wind speed V and the steady state relation between the pitch angle and the wind speed at some distance. The available time Δt to correct the pitch angle difference β is calculated using the average wind speed and the measurement distance. Feedforward Controller B V x Mean 2 (4s) IIR LIDAR V - β Δt + x m V x 3 δ t + τ(v) β ε x Δt C fb_ω β fb + β ff β WTG β Ω Figure 4-5: Control scheme of the gain scheduled feedforward controller B. This is not a pure feedforward controller, since the actual pitch angle is fed back to the controller to determine the pitch rate demand. When assuming a perfect pitch actuator, such that all pitch rate demands are executed as demanded, one could use the pitch rate demand to derive the actual pitch angle. V x _x β(v x ) β Δt + β - s Δt(V x ) β FF Figure 4-6: Feedforward control loop. The transfer function between the measured wind speed at distance x pitch rate demand β is derived below: β (t) = β V (t) β(t) Δt V (t) and the related feedforward (4-7)

39 Phase (deg) Magnitude (db) 29 The optimal pitch angle β at t + Δt is defined according to the steady state relation with the wind speed, shown in the left graph in Figure 4-8 and described by equation (4-8). β (t + Δt) = β V (t) (4-8) The preview time Δt is calculated according to (4-9) using the measurement distance x and the mean wind speed, that is based on the measurements of the last few seconds.. Δt = x V When using equations (4-8) and (4-9) in (4-7) we come to the following relation for the demanded feedforward pitch rate β (4-9) β (t) = β (t + Δt) β (t)dt Δt After rearranging and taking the Laplace transform we find: (4-) ΔtΒ (s) = e Β (s) Β (s) (4-) The resulting transfer function between the desired (future) pitch angle and the demanded pitch rate is then: C (s) = sβ (s) Β (s) = e (4-2) Δts + For higher wind speeds the bandwidth of this controller increases, due to the fact that the preview time Δt decreases. This matches with the derivative of the steady state wind speed pitch angle curve, which is decreasing there, indicating that fluctuations in the wind speed have less effect for higher wind speeds and thus allowing to amplify them more. The power spectrum of the wind speed together with the this controller have the effect of a low pass filter Bode Diagram Wind speed Frequency (rad/s) Figure 4-7: Bode diagram of the transfer function between the wind speed measured at 8m and the feedforward pitch rate demand for wind speeds between and 25 [m/s]. This controller is implemented in Simulink and similar simulations as with the feedforward controller A are performed. Some results are shown in Figure 4-8. The control performance of the rotor speed is comparable. We can clearly see that the pitch rate demand has improved even below the baseline results. However for the and 3 [m/s] simulations we see still an increased demand. This is caused by the fact

40 Normalized tower base loads Normalized blade root loads std rotor speed [%] rms pitch rate [%] 3 Wind speed feedforward controller that these simulations are performed with around rated wind speed. They include some periods where the wind is too low, such that the pitch angle is limited. The slope of the steady state pitch angle versus the steady state wind speed is steeper in this area. This together with the fact that the feedforward controller is responding already on upcoming changes in the wind result in a higher pitch rate demand for those simulations. The peaks in the tower thrust force F and for-aft bending moment M have been significantly reduced compared to controller A, however most of the loads are still higher than with the baseline controller.. Normalized std rotor speed 2.5 Normalized rms pitch rate Baseline FB + FF A Baseline FB + FF B Baseline FB + FF A Baseline FB + FF B Blade root Mx Blade root My Blade root Fx Blade root Fy.5 Baseline FB + FF A Baseline FB + FF B Tower base Mx Tower base My Tower base Fx Tower base Fy.6 Baseline FB + FF A Baseline FB + FF B Figure 4-8: Normalized standard deviation of the rotor speed (top left) and RMS value of the pitch rate demand (top right). Tower and blade DEL based on a min. simulation using the feedforward controllers A and B. All results are normalized with the results of the baseline feedback controller. Feedforward controller B performs best for the load reduction, while having still sufficient disturbance rejection in the rotor speed control. This is because it takes more time to compensate for the virtual pitch error, resulting in lower pitch rate demands and thrust related loads. Filtering the measured wind speed

41 Phase (deg) Magnitude (db) Pitch rate demand [deg/s] 3 adequately is a crucial step in the load reduction for controller A, while controller B has this property by design. Both controllers are mitigating low frequent changes in the wind where any DC error in the rotor speed is compensated by the feedback loop. When we compare a time series of the pitch rate demands of both controllers see Figure 4-9 we can see that controller B is acting earlier on changes than controller A. This results in lower pitch rates overall. 3 2 Gain scheduled feedforward controller A Gain scheduled feedforward controller B Time [s] Figure 4-9: Comparison between the feedforward pitch rate demands of both controllers The settings of controller A for the preview time and the cut-off frequency of the low pass filter were chosen to optimize the disturbance rejection of the rotor speed controller. A better choice for load reduction might be by using a lower cutoff frequency (e.g..2 Hz) for the wind speed filter and a larger preview time (e.g. 3s). - Bode Diagram From: Collective wind speed To: Collective pitch rate demand Feedforward controller A ( _c =.3 Hz) Feedforward controller B Feedforward controller A ( _c =.2 Hz) Frequency (rad/s) Figure 4-2: Comparison of Bode diagrams of controllers A and B for V=7 [m/s]. The dotted red line shows the bode diagram of controller A with modified cut-off frequency for the wind speed filter.

42 32 Wind speed feedforward controller

43 Spectra of the rotor speed [db] Chapter 5 Controller optimization Both controllers we have designed in the previous chapter are controlling the rotor speed very well, however they have some unexpected side effects. It was expected that the improved rotor speed control would also cause the loads to reduce. Unfortunately this is not the case and we have to look for other ways to achieve that, because a perfect controlled rotor speed is not worth much for a wind turbine manufacturer, while load reductions are! It is assumed that the load reduction can be achieved by reducing the pitch activity, since the rotor thrust is highly affected by changes in the pitch angles of the blades. 5. Relaxing the rotor speed feedback controller We will investigate the contribution of the pitch rate demand for both the feedback and the feedforward paths. In Figure 5- we can see that the feedback loop has a larger contribution when used in combination with the feedforward loop Feedback pitch rate demand -2 Feedforward pitch rate demand Total pitch rate demand Baseline pitch rate demand -4 - Frequency [Hz] Figure 5-: Demanded pitch rate separated for feedback and feedforward demand. The time series (left) of a min simulation and the related power spectra (right) are shown Reducing the bandwidth of the feedback controller will make it less aggressive to changes in the rotor speed. This will reduce the related pitch rate demand while the improved rotor speed control remains due to the contribution of the feedforward controller. New feedback controller parameters are calculated, using the same inverse gain scheduling technique as the baseline parameters were calculated with (see Appendix A.). The only differences are the design requirements for the bandwidth ω and damping ζ. Figure 5-2 and Figure 5-3 show the step responses of the turbine for various different settings for ω and ζ. As expected from theory, we can see that the overshoot increases, when the bandwidth decreases and that the settling time increases, when the damping decreases. We are looking for relaxed feedback controller parameters, where the disturbance rejection with the feedforward loop active is comparable to the baseline controller, while the setpoint tracking is almost not affected. Bandwidth ω = rad/s and damping ζ =.5 seem to be an appropriate choice. A more complete overview of step responses for various feedback controller settings is shown in Appendix A..

44 Amplitude Amplitude Amplitude Amplitude Amplitude Amplitude Amplitude Amplitude 34 Controller optimization b = [rad/s]; =.5 From: Collective wind speed To: Rotor speed.4 b = [rad/s]; =.7 From: Collective wind speed To: Rotor speed Time (seconds) b =.9 [rad/s]; =.5 From: Collective wind speed To: Rotor speed Time (seconds) b =.9 [rad/s]; =.7 From: Collective wind speed To: Rotor speed.4 baseline FB new FB new FFB Time (seconds) Time (seconds) Figure 5-2: Step responses of the collective wind speed to the rotor speed for the closed loop systems using the baseline feedback controller (blue), the relaxed feedback controller (green) and the feedforward +feedback controller with relaxed feedback parameters (red) are plotted for four sets of Kp and Kd values b = [rad/s]; =.5 From: Collective pitch rate demand To: Rotor speed - -2 b = [rad/s]; =.7 From: Collective pitch rate demand To: Rotor speed Time (seconds) Time (seconds) b =.9 [rad/s]; =.5 From: Collective pitch rate demand To: Rotor speed b =.9 [rad/s]; =.7 From: Collective pitch rate demand To: Rotor speed baseline FB new FB new FFB Time (seconds) Time (seconds) Figure 5-3: Step responses of the collective pitch rate demand to the rotor speed for the closed loop systems using the baseline feedback controller (blue), the relaxed feedback controller (green) and the feedforward +feedback controller with relaxed feedback parameters (red) are plotted for four sets of and values.

45 Spectra of the rotor speed [db] Spectra of the rotor speed [db] 35 The resulting demanded pitch rates for both the feedback and feedforward controllers, using these adjusted settings in the feedback controller, are shown in Figure 5-4. From the time series we can clearly see that the amplitude of the feedback pitch rate demand has reduced, compared to the previous situation Feedback pitch rate demand -2 Feedforward pitch rate demand Total pitch rate demand Baseline pitch rate demand -4 - Frequency [Hz] Figure 5-4: Demanded pitch rate contributions for the gain scheduled feedforward controller A, using relaxed feedback controller settings. 5.2 Remove harmful frequencies from the wind speed measurement An additional possibility for reducing the loads (and the pitch activity) is by removing the frequency content, related to the first fore-aft tower mode, from the measured wind speed, such that this mode is not excited by the feedforward path. This is done using a notch filter, with transfer function as in (5-) and coefficients ζ =., ζ = and ω = ω = 2.9 [rad/s]. H(s) = s + 2ζ ω s + ω s + 2ζ ω s + ω (5-) Feedback pitch rate demand -2 Feedforward pitch rate demand Total pitch rate demand Baseline pitch rate demand -4 - Frequency [Hz] Figure 5-5: Demanded pitch rate contributions for the gain scheduled feedforward controller A, using relaxed feedback controller settings and a notch filter applied to the measured wind speed This reduces the pitch rate demand for both the feedback and the feedforward controllers (compare with the spectrum in Figure 5-4). The spectrum of the pitch rate demand of the baseline controller is shown for comparison (black). An overview of some performance indicators of the various controller configurations is given in Table 5-.

46 To: Tower base My Magnitude (db) Magnitude (db) To: Blade root My To: Blade demanded pitch rate Magnitude (db) To: Rotor speed 36 Controller optimization RMS(β ) RMS(β ) RMS(β ) Std(Ω) Max(Ω) [deg/s] [deg/s] [deg/s] [rpm] [rpm] Baseline feedback controller Baseline feedback with feedforward Relaxed feedback controller with feedforward Relaxed feedback controller with notch filter for wind speed in the feedforward loop Table 5-: Performance indicators of four controllers (DLC.3 5 [m/s]) When we look at the Bode diagram of the closed loop system using these adjustments (see Figure 5-6), we can see increased pitch rate demands between.5 and 2 Hz. This increase was not visible in the spectrum of the pitch rate from the simulation. This is caused by the fact that the np dynamics are not considered in the Bode diagram, while they are in the simulation (and also the scaling of the frequency axis differs). Figure 5-6 (right) shows the frequency ranges where feedforward controller A brings improvements (< db) for the loads on the tower and blades. The figure also shows that there are some frequency ranges where the loads are higher than with the baseline controller (> db). -2 Bode Diagram From: Measured wind speed Bode Diagram From: Measured wind speed To: Blade root My (FB+FF)/FB Baseline FB Relaxed FB Relaxed FB + FF Frequency Bode Diagram (Hz) From: Measured wind speed To: Tower base My (FB+FF)/FB Frequency (Hz) Frequency (Hz) Figure 5-6: Bode diagram of the optimized controller compared with the baseline rotor speed feedback controller and the relaxed equivalent.(left) Ratio between the transfer functions of the tower and blade moments using feedforward controller A and the baseline feedback controller. (right)

47 Normalized tower base loads Normalized blade root loads std rotor speed [%] rms pitch rate [%] Result The same adjustments have been applied to the gain scheduled feedforward controller B. There it appeared that the notch filter for the wind speed did not improve the results. This is probably due to the fact that the low pass filtering effect on the wind speed using this controller already removes sufficient high frequent dynamics from the wind. The simulation results using both controllers with the discussed adjustments are sown below.. Normalized std rotor speed.8 Normalized rms pitch rate Relaxed FB + notched FF A Relaxed FB + FF B Relaxed FB + notched FF A Relaxed FB + FF B Blade root Mx Blade root My Blade root Fx Blade root Fy.5 Relaxed FB + FF A Relaxed FB + FF B Tower base Mx Tower base My Tower base Fx Tower base Fy.3 Relaxed FB + FF A Relaxed FB + FF B Figure 5-7: Simulation results for the blade root and tower top and base DELs, using the gain scheduled feedforward controllers A and B together with the relaxed feedback controller. All results are normalized with the results of the baseline feedback controller. The blade load results differ per wind speed and it is hard to find a tend there. The thrust forces F on the tower top and the related for-aft bending moment M on the tower base have been reduced for the

48 power [%] 38 Controller optimization higher wind speed ( 5 [m/s]). Especially for the feedforward controller A, these figures have been reduced drastically due to the adjustments proposed in this chapter. The lower wind speed ( and 3m/s) simulation results show increased loads for these figures, which is caused by the higher sensitivity of the aerodynamic torque for low pitch angles as explained earlier. Overall we can say that the relevant loads have been reduced, while improving the rotor speed control using less pitch activity. Finally there is some increase in the energy yield for all wind speeds as well, see below...8 Normalized measured energy Relaxed FB + notched FF A Relaxed FB + FF B

49 std rotor speed [%] rms pitch rate [%] Chapter 6 Comparison between various LIDAR configurations We have many parameters, resulting in even more possible configurations for measuring the mean wind speed. Some reasonable settings for both the CW and the pulsed LIDARs have been implemented in Simulink (see Appendix C for an example). Simulations using wind speeds ranging between and 9 [m/s] with turbulence defined according to DLC.3 [7], are done. These simulations and their results are presented in this section. 6. Continuous wave LIDAR Five configurations for the CW LIDAR have been simulated. 2, 4, 8, and 5 equally distributed points on the azimuth angle, while focused at 8m with a half cone angle of 3. All distributions of the measurement points were chosen, such that there were always two measurements at each altitude. The goal of these simulations was to find an optimum for the number of points on the azimuth, while focusing on one distance. From the simulation results in Figure 6-2 we can clearly see that the rotor speed control is improved by measuring on an increasing number of azimuth angles, however we can also see that the simulation done, while measuring at 5 different azimuth angles. 2 and 5 azimuth angles have a worse rotor speed control performance than the other three. The cause of the reduced rotor speed performance in the 5 point simulation, is related to the higher period time per circular scan (s instead of 8ms), causing different filtering behavior. Normalized std rotor speed.5 Normalized rms pitch rate azimuth angles 4 azimuth angles 8 azimuth angles azimuth angles 5 azimuth angles azimuth angles 4 azimuth angles 8 azimuth angles azimuth angles 5 azimuth angles figure 6-: Comparison of normalized standard deviation of the rotor speed (top left), normalized RMS pitch rates (top right) while measuring at various number of azimuth angles.

50 Normalized tower base loads Normalized blade root loads 4 Comparison between various LIDAR configurations Blade root Mx Blade root My Blade root Fx Blade root Fy Azimuth angles 4 Azimuth angles 8 Azimuth angles Azimuth angles 5 Azimuth angles Tower base Mx Tower base My Tower base Fx Tower base Fy Azimuth angles 4 Azimuth angles 8 Azimuth angles Azimuth angles 5 Azimuth angles Figure 6-2: Comparison of normalized tower and blade DEL, while measuring at various number of azimuth angles. 6.2 Pulsed LIDAR Pulsed systems provide simultaneous LOS wind speed information from various distances, resulting in a pitch rate demand per distance. These demands are combined by weighting according to the reciprocal of their distance, such that measurements from a larger distances are used with less contribution. Figure 6-3: Feedforward control scheme with distance weighting detail for pulsed LIDARs Simulations have been done using two configurations for the pulsed LIDAR system using 3 (red) and (blue) focus distances and 4 and 2 points on the azimuth respectively. Their performance is compared with the CW simulation result using points on the azimuth on one focus distance (green).

51 Normalized tower base loads Normalized blade root loads std rotor speed [%] rms pitch rate [%] 4 Normalized std rotor speed.4 Normalized rms pitch rate Azimuth; focus 4 Azimuth; 3 focus Azimuth; focus Blade root Mx Blade root My.2 2 Azimuth; focus 4 Azimuth; 3 focus Azimuth; focus Blade root Fx Blade root Fy Azimuth; focus 4 Azimuth; 3 focus Azimuth; focus Tower base Mx Tower base My Tower base Fx Tower base Fy Azimuth; focus 4 Azimuth; 3 focus Azimuth; focus Figure 6-4: Comparison of normalized standard deviation of the rotor speed (top left), normalized RMS pitch rates (top right) and normalized tower and blade DEL, while measuring at various number of focal distances. From these simulation results we can clearly see that almost all loads have been reduced below the level of the baseline controller. Especially the tower thrust force F and for-aft bending moments M have reduced significantly compared to the -point CW measurement. We may conclude that the simulation with 4 points on the azimuth for each of the 3 focus distances, results in the optimal balance between load reduction, speed control and pitch activity, with increased energy yield for all wind speeds used.

52 power [%] 42 Comparison between various LIDAR configurations..8.6 Normalized measured energy 2 Azimuth; focus 4 Azimuth; 3 focus Azimuth; focus

53 Chapter 7 Conclusions The gain scheduled wind speed feedforward controller B performs best for the load reduction, while having still sufficient disturbance rejection in the rotor speed control. This is because it takes more time to compensate for the virtual pitch error, resulting in lower pitch rate demands and thrust related loads. Filtering the measured wind speed adequately is a crucial step in the load reduction for controller A while controller B has this property by design. Both controllers are mitigating low frequent changes in the wind where any DC error in the rotor speed is compensated by the feedback loop. Feedforward controller A is good at disturbance rejection for the rotor speed control. However the objective is to reduce the loads on the structure, while this controller deteriorates them. The increase in for example the fore-aft bending moment of the tower ranges between 25% for 3 [m/s] wind speed simulation and 7% for the 9 [m/s] simulation. This is because the measured wind speed contains relatively high frequency components. The pitch system is able to correct for them, but that will increase the pitch rate demand and thus the related tower thrust forces. The choice for the cutoff frequency (ω =.3 [Hz]) of the low pass filter together with the preview time (t = 2 [s]) was based on the optimal disturbance rejection for the rotor speed. A better approach would have been to choose values for these parameters based on the associated loads. That will probably result in a longer preview time and a lower cut-off frequency for the wind speed filter, ending up with similar performance as controller B. Feedforward controller B does accomplish load reductions. Here the for-aft bending moment of the tower has reduced for all above rated wind speeds. The reduction ranges between 8% for the 3 [m/s] simulation and 7% for the 9 [m/s]. This controller performs better, because all available time between the measurement and the moment this wind arrives at the turbine is used to correct the virtual pitch angle error. This results in a pitch angle which is smoothly following the low frequent changes in the wind speed. An attractive benefit of this controller is a small increase in the energy yield for all wind speeds used in the simulations. Even up to 5% for the [m/s] simulation, but with a small increase in the loads. Various LIDAR configurations have been simulated with the feedforward controller B. We may conclude that the pulsed LIDAR system with 4 azimuth angles and 3 focus distances is preferred. This configuration provides the measurement data from locations well spread over the rotor surface. The locations are distributed over various azimuth angles and the rotor diameter. This measurement results in the best balance between load reduction, pitch rate demand and rotor speed fluctuations, while slightly increasing the energy yield for above rated wind speeds. A LIDAR system using this configuration is not commercial available yet, but suppliers of these systems are continuously improving their products. Validating these simulation results with the developed controller and the proposed LIDAR configuration on the Darwind XD5 wind turbine, should be the next step in this research project.

54 44 Conclusions

55 Magnitude (db) ; Phase (deg) To: Rotor speed To: Rotor speed Appendix A Derivations A. Calculation of the rotor speed feedback controller parameters The controller will be tuned for a bandwidth (ω ) of rad/s and damping (ζ) of.77. We use a simplified model of the turbine for the frequency range of interest to calculate the control gains that satisfy the design requirements. 6 From: Collective wind speed Bode Diagram From: Collective pitch rate demand g s g s The simplified open loop transfer function from the demanded pitch rate to the rotor speed can be written as: G (s) = g (A-) s The simplified open transfer function from the wind disturbance to the rotor speed can be written as: G (s) = g (A-2) s The transfer function for the PD controller is written as: C (s) = K s + K (A-3) The rotor speed can be specified as: 9-2 Frequency (Hz) Ω = VG + β G -2 (A-4) The demanded pitch rate is obtained according to: β = Ω Ω C (A-5) Combining (A-4) and (A-5) results in: Ω = VG + Ω Ω C G (A-6)

56 46 Derivations C G Ω = VG Ω C G (A-7) Assuming the disturbance is constant Ω Ω = C G C G Using (A-) and (A-3) in the above equation and some rearranging we get: H (s) = K g s K g s K g s K g (A-8) (A-9) K g = 2ζω K g = ω (A-) When using the relations in (A-) and considering that the system gain (g ) is negative, since positive pitch rate decreases the rotor speed, we get : H (s) = 2ζω s + ω (A-) s + 2ζω s + ω The bandwidth (ω ) of the closed loop system corresponds to the natural frequency (ω ) where it s magnitude equals (= 3dB) H (jω ) = (Re (H (jω ))) + (Im (H (jω ))) = 2 (A-2) ω + 4ζ ω ω H (jω ) = ω 2ω ω = + ω + 4ζ ω ω 2 2ω + 8ζ ω ω = ω 2ω ω + ω + 4ζ ω ω ω + (2 + 4ζ )ω ω + ω = (A-3) (A-4) (A-5) a =, b = (2 + 4ζ )ω, c = ω (A-6) (2 + 4ζ )ω ± (2 + 4ζ )ω 4( )ω ω = 2( ) (A-7) ω = ω [(2ζ + ) ± (2ζ + ) + ] (A-8) Using the second term of (A-) and rearranging we get the following expression for K K = ω [(2ζ + ) + (2ζ + ) + ] (A-9) g K can be calculated using (A-), (A-8) and (A-9) K = 2ζ ω g = 2ζ K g (A-2)

57 Amplitude Amplitude Amplitude Amplitude Amplitude Amplitude Amplitude Amplitude Amplitude Amplitude Amplitude Amplitude 47 Derivations The step responses from the collective pitch rate demand to the rotor speed of the closed loop system using various settings for the feedback controller are shown here b =.7 [rad/s]; =.5 From: Collective wind speed To: Rotor speed Time (seconds) b = [rad/s]; =.5 From: Collective wind speed To: Rotor speed Time (seconds) b =.9 [rad/s]; =.5 From: Collective wind speed To: Rotor speed Time (seconds) b =. [rad/s]; =.5 From: Collective wind speed To: Rotor speed Time (seconds) b =.7 [rad/s]; =.6 From: Collective wind speed To: Rotor speed Time (seconds) b = [rad/s]; =.6 From: Collective wind speed To: Rotor speed Time (seconds) b =.9 [rad/s]; =.6 From: Collective wind speed To: Rotor speed Time (seconds) b =. [rad/s]; =.6 From: Collective wind speed To: Rotor speed Time (seconds) b =.7 [rad/s]; =.7 From: Collective wind speed To: Rotor speed Time (seconds) b = [rad/s]; =.7 From: Collective wind speed To: Rotor speed Time (seconds) b =.9 [rad/s]; =.7 From: Collective wind speed To: Rotor speed Time (seconds) b =. [rad/s]; =.7 From: Collective wind speed To: Rotor speed baseline FB new FB new FFB Time (seconds)

58 Amplitude Amplitude Amplitude Amplitude Amplitude Amplitude Amplitude Amplitude Amplitude Amplitude Amplitude Amplitude 48 Derivations The step responses from the collective pitch rate demand to the rotor speed of the closed loop system using various settings for the feedback controller are shown here b =.7 [rad/s]; =.5 From: Collective pitch rate demand To: Rotor speed Time (seconds) b = [rad/s]; =.5 From: Collective pitch rate demand To: Rotor speed Time (seconds) b =.9 [rad/s]; =.5 From: Collective pitch rate demand To: Rotor speed Time (seconds) b =. [rad/s]; =.5 From: Collective pitch rate demand To: Rotor speed Time (seconds) b =.7 [rad/s]; =.6 From: Collective pitch rate demand To: Rotor speed Time (seconds) b = [rad/s]; =.6 From: Collective pitch rate demand To: Rotor speed Time (seconds) b =.9 [rad/s]; =.6 From: Collective pitch rate demand To: Rotor speed Time (seconds) b =. [rad/s]; =.6 From: Collective pitch rate demand To: Rotor speed Time (seconds) b =.7 [rad/s]; =.7 From: Collective pitch rate demand To: Rotor speed Time (seconds) b = [rad/s]; =.7 From: Collective pitch rate demand To: Rotor speed Time (seconds) b =.9 [rad/s]; =.7 From: Collective pitch rate demand To: Rotor speed Time (seconds) b =. [rad/s]; =.7 From: Collective pitch rate demand To: Rotor speed baseline FB new FB new FFB Time (seconds)

59 Appendix B Bladed Simulink coupling A coupling between the software package Bladed, where the non-linear model of the turbine is simulated and the software package Simulink, where the model of the controller is simulated, is developed. With this coupling we can co-simulate the models of the turbine and the controller, using the same wind field. The coupling is developed in the programing language C and is implemented by means of a dll. This dll is allocating shared memory to which both models can read and write an array of data in turn. The size of this array is determined by a static and a dynamic part, which depends on the number of LIDAR laser beams and number of focal distances, defined in Bladed. Static size 2 Bladed 4 Dynamic size Shared memory 3 Simulink Figure B-7-: Scheme of the data flow in the coupling between Bladed and Simulink The dll contains five functions, two of them are used by Bladed and three of them by Simulink. A short description of the actions in each of the functions is given below. DISCON: INIT: Read discon.in-file. Create COM connection with Matlab. Start Matlab. Execute commands indiscon.in-file. MAIN: Determine size of the buffer from static part. Copy array from Bladed to shared memory. Trigger event for writing ready, such that Simulink can start reading. Wait for Simulink to finish reading and writing. Copy array from shared memory to Bladed. Reset write event from Simulink. Check if Simulink simulation has ended. Check if Bladed simulation has ended. GetSharedMem: - Wait for Bladed to finish reading and writing. - Determine size of the buffer from static part. - Copy array from shared memory to Simulink. - Reset write event from Bladed. SetSharedMem: - Determine size of the array from static part. - Copy array from Simulink to shared memory. - Trigger event for writing ready, such that Bladed can start reading. GetDisconDataSizeInfo: - Read values related to the size of the array from the static part. The Bladed Co-simulation -subsystem calls two Matlab S-functions, BusRead and BusWrite, which in their turn call the related functions from the dll. BusWrite sets the LIDAR related variables in the shared memory such that Bladed knows from which part of the wind field the LOS wind speed should be determined. BusRead gets this LOS wind speed for each configured laser beam and each focal distance. The various, on the market available, LIDAR configurations and more, can be defined in the LIDAR subsystem. Each of the outputs of this subsystem has dimensions matching, the number of

60 5 Bladed Simulink coupling simultaneous focal points (nf) for each laser beam (nl). The Bladed Co-simulation -subsystem outputs the contents of the static sized part of the shared memory in the DISCON data BUS. The LOS wind speed(s) and the values of the Torque-Speed LUT, from the dynamic sized part of the shared memory, are output as well. Figure B-7-2: Simulink block scheme of the coupling between Simulink and Bladed Challenges during the implementation were related to allocating sufficient shared memory and the sizing of the IO-channels in Simulink. This is caused by the fact that the related information is defined in Bladed and comes only available during runtime. LIDAR configuration in Bladed: File Project Info MSTART EXTRA GUSTPROPAGATION SPECTRALWIND LIDARINTERP WINDF2 'C:\Users\Walter\Documents\Walter\Memory stick\afstuderen\bladed\xd5\bladed models\windfiles\ wind_5_4.wnd' NLIDAR *No. of effectively independent Lidar beams NFOCUS *No. of focal points * CW LIDAR configuration NWEIGHT 3 ALPHA 6.354e-4 * wavelength/lens area (m-) WEIGHTS DIRCOORD *beam direction co-ordinate system: = nacelle (yaw bearing centre) ANGLESTYLE LIDARX 3.38 *\ LIDARY.6 *} GL x, y, z co-ordinates of Lidar beam origin referred to yaw bearing centre. LIDARZ */ MEND