## Wind Turbine, Rüzgar Türbini Yunuslama Açısı Kontrolcüsü Tasarımı, Dr. Mustafa ŞAHİN. ODTÜ RÜZGEM

First of all, Hello. I am Mustafa ŞAHİN. I am working as a Dr. Instructor at Middle East Technical University… Research and Application Center for Wind Energy Technologies, shortly called as METU Center for Wind Energy. Today, I am going to mention about… how a collective blade pitch controller is designed for the horizontal axis wind turbines, which are most commonly seen in wind farms Also, we will investigate the performance analysis of the designed controller. We have realized this study… for a 5 MW turbine that belongs to the NREL Which is the National Renewable Energy Laboratory of United States In order to design the blade pitch controller… We have utilized the MS (Mustafa ŞAHİN) Bladed Wind Turbine Simulation Model… which I have developed during my PhD study. Before I go into the details of this study, I would like to mention you about the employed control systems… of horizontal axis wind turbines. Later, i will mention about turbine control regions, their control purposes and the MS Bladed Wind Turbine Simulation Model. Afterward, I will talk about the method of how modern turbines realize power regulation… by changing the blade pitch angles. We will also focus on wind turbine system linearization, blade pitch control and lastly the performance simulations of the designed controller. Modern Horizontal Axis Wind Turbines have… the proporties of variable rotor speeds and variable blade pitch angles. These turbines have three levels of controls. The highest level control, according to the wind speed information, decides… at which wind speed, and when the turbine will start generating electricity and stop generating electricity. In the mid-level control, on the other hand, we are controlling the generator torque,… blade pitch angles and nacelle yaw angle. According to the wind speed and direction data that are taken from the sensors located on top of the nacelle, … we sometimes control the generator, i.e generator torque, sometimes the blade pitch angles of the turbine … and most of the time the turbine nacelle yaw angle since the direction of the wind changes mostly. All these controllers that you have seen here are the operating controllers during the generation of electricity. Except for these control levels, we have the lowest level control. This control level is about generator internal control, blade pitch and yaw actuators’ controls of the turbine. Now, these modern variable speed variable pitch turbines have four different operating regions. These are known as Region 1, Region 2, Region 3 and

4 The figure you have seen here is drawn for a 5 MW wind turbine. Here, the vertical axis shows the power, while the horizontal axis shows the wind speed As you can see, the dashed-red line shows the rated power of this turbine. The blue one shows the available power in the wind. The green one, however, shows the controlled power curve of the turbine. Wind turbines start producing electricity at a certain wind speed. We call this wind speed as the cut-in wind speed. At a certain wind speed, it stops generating electricity. We call this wind speed as cut-out wind speed. For most of the turbines, this wind speed value is standard and corresponds to 25 m/s. The electricity generation from the wind is not carried out in Region 1, which stays below the cut-in wind speed. Because, in this region, wind level is quite low,… and the power in the wind is not enough even to operate the turbine’s own systems. For this reason, the electricity generation usually starts at a wind speed of 3, 4 or 5 m/s. Another region, where we do not get any electricity is Region 4. In this region, due to the high wind speed levels, i.e stormy wind conditions,… In order to protect the turbine from damages, we take precautions and stop the turbine for safety,… and do not take any electricity from the turbine. The electricity is generated in Region 2 and 3, which stay between cut-in and cut-out winds. There is a wind speed called rated wind speed which separates these regions. and it is the wind speed where the turbine starts producing its rated power. Now, these regions, i.e Region 2 and 3, are also known as partial and full load regions, respectively. The reason why Region 2 is called a partial load region is that… As you see here, we have a good amount of wind speed levels in this region. However, wind speed levels are not enough for the turbine to generate its rated power. Therefore, our aim in this region is to operate the turbine rotor as efficificient as or as effective as possible. In order to achieve this goal, we try to operate the turbine at the maximum power coefficient, Cpmax. Therefore, we keep the blade pitch angles of turbine blades at the optimum values. and against the increasing wind speed, we adjust the rotor shaft speed of the turbine… so that the turbine rotor can operate at the optimum tip speed ratio, TSR. In this way, in order to achieve this purpose,… we are adjusting th torque that is given by the generator to the turbine rotor. In Region 3, on the other hand, we are a kind of decreasing the performance of the turbine rotor. Because the wind speed levels in Region 3 are more than enough for the turbine to produce the rated power. Therefore, we need to prevent the turbine from damages. That is, we need to regulate the turbine power in order not to burn/damage the generator. In this way, we operate the turbine rotor at the rated speed. Therefore, the turbine rotor operates at rated rotor speed. Since the generator torque is constant at its rated value as well,… In this region, we are getting the rated electrical power. The study we have realized is about Region 3. That is, soon, I am going to mention about how to design the blade pitch controller. Now, during my PhD thesis study, i have developed a wind turbine simulation model that is called MS Bladed. This model, in fact, takes an actual turbine in the field and puts its similar one into a computer environment. And this model is developed for horizontal axis wind turbine simulations. It utilizes the Blade Element Momentum Theory. However, the Blade Element Momentum Theory cannot predict… the aerodynamic performance of wind turbines for all operations in the field. Because, sometimes, wind turbines operates with a yaw angle towards the wind speed. Modern turbines have a certain nacelle tilt angle etc. etc. For these reasons, except the Blade Element Throey, i have to use some aerodynamic correction formulas. These are aerodynamic correction formulas for skewed wake rotation, turbulent wake state. Besides, i added the effect of blade hub and tip losses to the model due to… the vortices shed from corresponding portions of the turbine blades. To a large extent, the aerodynamic calculations of the MS bladed Model is similar to… those of Aerodyn and Wt_perf programs given in the literature. Now, in modern large-scale wind turbines, blades are attached to the rotor hub with a certain precone angle… In addition, nacelle/rotor is tilted with a certain angle. i.e having a certain slope. Blades can be pitched collectively or individually. Nacelle can yaw towards the wind speed. In order to realize all of these capabilities, MS Bladed Model includes particular coordinate systems. These are, for instance, inertial coordinate system, yaw-aligned coordinate system,… azimuth coordinate system and so on. In the current version, the MS Bladed Model considers the turbine to be consisting of rigid turbine structures and… as if it were an actual turbine, it consists of a turbine aerodynamic rotor,… a simple variable torque electrical generator and a gearbox between these components. In the MS Bladed Model, we have represented the turbine with this equation you see here. Here, the total turbine inertia times the derivative of rotor speed is equal to… rotor aerodynamic torque minus the electromagnetic torque from the generator. So, what can we do with the MS Bladed Model? We can construct turbine rotors with already designed turbine blades, We can increase or decrease the blade number. In addition, by defining the rotor precone angle, blade pitch angle, or nacelle yaw/tilt angle… we investigate the effects of these variables on the perfomance of turbine rotor. Besides, under normal or extreme turbulant wind conditions,… We can investigate the behaviour of the tubine in time. We can design new tubine controlers, and develop new controller algorithms. And then, we can simulate these controllers. If we get promising performance results,… Then, we can apply/test the controller algorithm on the actual wind turbine. If you would like to get more information about the MS Bladed Model,… you may read one of my papers that i presented at Ankara International Aerospace Conference… and benefit from my PhD thesis. Now, in modern wind turbines, for the design of blade pitch controller… we are using a method called pitch to feather control. That is, in Region 3, when the wind speed increases, we increase the pitch angles of the turbine blades. In this way, the angle of attack seen by each blade, i.e sections, is reduced… Therefore, all the turbine blades operates with low lift and drag coefficients. Hence, the turbine power is regulated in this way. Now, here, if we take a look at the block diagram of the blade pitch angle controller. We are feeding the rotor or generator speed information back via a sensor and then,… comparing it with the reference rotor speed, which we desire the turbine rotor to operate, i.e the rated rotor speed. When we are feed the error between the reference and rotor speed to the controller,… The controller decides how much blade pitch angles is required… for the turbine to produce the rated electrical power. A while ago, we said that we represented the turbine in the MS Bladed Model by this first order equation. Even if this equation seems to be a linear equation, it is, actually, a nonlinear equation… since both aerodynamic torque and generator torque are nonlinear. However, since the generator torque in Region 3 is kept constant at it rated value,.. The nonlinearity in this region comes only from the aerodynamic torque. This aerodynamic torque changes depending on the rotor speed, wind speed and blade pitch angles. If i linearize this equation, as you see here, and writing it as a Taylor series,… I obtain this formulation. In linear controller designs, we are neglecting the higher order terms. As you see here, there are some aerodynamic partial derivative terms. These are the derivatives of aerodynamic torque with respect to wind speed, rotor speed… and blade pitch angle. If i define these terms by gamma, eta and mu,… And then, if i linearize the whole turbine system as you see here,… I obtain this formulation. When the turbine system operates at steady-state, the aerodynamic torque… and the generator torque will cancel each other. So, i will represent the linerized open loop turbine system in this way. Later, if i solve for the derivative of rotor speed, and then, when i define these terms by A, B and Bd terms, which corresponds to… system gain, input gain and disturbance gain to the turbine system. In this way, i obtain the linearized open loop wind turbine system. In the MS Bladed Model, wind is a disturbance input to the turbine system,… while blade pitch angles appear as control inputs. A while ago, i showed you a block diagram for the pitch controller. Considering that block diagram, i can construct a relation between the rotor speed and blade pitch angles… if i design a proportional and integral based controller. Afterwards, if i put this term into the previously linearized model,… It becomes such an expression. If i take the Laplace Transform of this expression, later. I obtain the transfer function between the rotor speed and wind speed. Any system, including wind tubines to be stable, all the roots of the characteristic equation must be negative. For the roots to be negative, the terms in these brackets must be positive. But, it is not enough for the system to be stable. I must get the desired response from the controller, as well. For a second order system, what decides this response? These are damping ratio and natural frequency. If i consider this turbine system as a second order system, I can get such an expression among the natural frequency, damping ratio, system gain, and input gain. If i consider a proportional and integral strategy based controller, in order to calculate the controller gains. i can get these equations from these above equations. As you can see, the values of proportional and integral gains,… depends on system gain, input gain, natural frequency and damping ratio. Now, I linearized the turbine system at an operating point that corresponds to a wind speed of 18 m/s. And then, i designed a controller, However, in order to calculate the controller, as i said previously, we need to know… the damping ratio and natural frequency. When we check the literature, for wind turbines, the value of 0.6 is chosen for natural frequency. But, for the damping ratio, it changes from turbine to turbine. Therefore, the value of damping ratio may be decided after an investigation. In the literature, for the damping ratio, the value of 0.6-0.7 is suggested by some scientists. For instance, for the experimental NREL CART turbine with a rated power capacity of 600 KW,… during the blade pitch controller design. the control researchers at NREL decided to use a damping ratio of 1 after some investigation. Therefore, i investigated here which damping ratio value is the most suitable for the 5 MW turbine. A damping ratio value of 0.8 gave me the best response in terms of settling time. So, throughout the control design process, i used the value of 0.8 for the damping ratio,… while i took a value of 0.6 for the natural frequency. But, a while ago, i talked about one linear controller design. When i test this one linear controller at other operating points, i.e other wind speeds, The performance of the controller deteriorates as you see here. This deterioration occurs more around 13 m/s wind speed, namely while approaching to the rated wind speed. That is, the following is important. While designing a blade pitch controller for a wind turbine,… one linear controller is not enough. In any case, we have to find a method to deal with this issue. Namely, according to the turbine operating point, we have to adjust the controler gains. So, what is the reason behind this performance deterioration if you ask me? A while ago, i mentioned about the input gain. This input gain, in fact, is a function of eta. Eta, on the other hand, depends on the derivative of aerodynamc torque with respect to blade pitch angle. I obtained these curves in this figure using the MS Bladed Model. They are the aerodynamic torque versus blade pitch angle at different wind speeds. Here, this black solid line is the rated torque. The crossing points of this line and the curves are the operating points at steady-state. As you see from the figure, at these operating points, the slope of these curves changes in magnitude… i.e., increasing in magnitude but with negative sign. This effects the partial derivative here. Therefore, the input gain, B, always changes. Then, as the input gain always changes, our controller gains must be varied relying on the blade pitch angle. So, how can we realize the change of controller gains. According to the control reseachers at NREL, for this type of turbine, we first choose an operating point,… which is close to the rated wind speed. And then, i linearize the turbine system at the selected operating point. If i linearize the turbine system using MS Bladed Model,… I obtain the values of A, B and Bd terms Later on, from the formulations that i derived previously. I calculate the controller gains, i.e proportional and integral gains… I designed a controller at one operating point,… which corresponds to an operating point of 11.5 m/s wind speed. Further, i need to schedule the controller gains. For this gain scheduling process, i used a gain correction formula. This is the formula for the gain correction factor. As you see here, the gain correction factor formula is a function of blade pitch angles. In this formula, the term ‘beta’ is any blade pitch angle,… which gives the rated torque at the rated rotor speed in Region 3. You said