A Study of a Gain-Scheduled Individual Pitch Controller for an NREL 5 MW Wind Turbine

Abstract

In order to reduce the asymmetric load acting on the blades of MW-class wind turbines, it is necessary to apply an individual pitch controller that independently adjusts the pitch angles of the three blades. This paper takes a new look at the relationship between the individual pitch controller applied to MW-class wind turbines and the vibration mode of the blades. The purpose of this study is to propose a method in which the individual pitch controller further reduces the 1P component of the bending moment in the out-of-plane direction acting on the blade, without exciting the in-plane vibration mode of the blade within the entire wind speed range, from the rated wind speed to the cut-out wind speed. To this end, a problem related to the excitation of the blade’s vibration mode that may occur when applying the individual pitch controller to an NREL 5 MW wind turbine is examined, and a method that uses gain scheduling to overcome this problem is presented. It is confirmed that it is possible to solve the problem of exciting the first-order vibration mode in the in-plane direction of the blade that can occur in the high wind speed range by applying the proposed gain scheduling method to the individual pitch controller aimed at reducing the 1P component of the out-of-plane bending moment of the blade.

1. Introduction

There are many topics related to wind turbines, including wind energy conversion systems, wind turbine performance optimization, the aerodynamics of wind turbines, wind turbine power curves, wind turbine blades, and wind turbine control [1]. Wind turbines have evolved from simple designs to complex multi-MW generation devices. The complexity of MW-class wind turbines makes control systems a key component of wind turbines [2]. The controller of an MW-class wind turbine consists of a power controller and a load controller. The power controller of an MW-class wind turbine can be mainly divided into a torque controller that adjusts the torque magnitude of the generator and a pitch controller that adjusts the pitch angle of the blades [3,4,5]. The pitch controller not only maintains the rated power above the rated wind speed, but also reduces the load acting on structures such as blades and towers. In general, the pitch controller used in MW-class wind turbines consists of a collective pitch controller (CPC) and an individual pitch controller (IPC) [5,6,7,8]. The collective pitch controller aims to maintain the rated power above the rated wind speed. For this purpose, a pitch power controller that feeds back the generator rotation speed is used to make the three blades’ pitch angles operate equally. The collective pitch controller can additionally reduce the fore–aft vibration of the tower. The individual pitch controller can reduce the dynamic load on the blades and reduce the equivalent fatigue load by independently using the pitch angles of the three blades [9,10,11]. The application of the individual pitch controller offers the advantage of reducing the mechanical loads on the wind turbine without interfering with power production [12]. The purpose of the individual pitch controller is not to control power, and the operation of the individual pitch controller has little effect on the power response.

When the rotor rotates, asymmetric loads occur on each blade due to the effects of wind shear, tower shadow, gravity, 3D turbulence, and so on. The individual pitch controller adjusts the pitch angle of each blade differently to reduce these asymmetric loads. The frequency component generated when the rotor rotates once is called 1P. When the rotor rotates, the 1P component vibration acting on each blade generates repeated loads on the blades, reducing the lifetime of the wind turbine. The main purpose of the individual pitch controller is to reduce the 1P component of the asymmetric moment load acting on the blades of the MW-class wind turbine. Among the asymmetric moment components acting on the blades, the 1P component is the largest. To this end, the pitch angles of the three blades operate independently using the tilt and yaw controllers by feeding back the out-of-plane bending moments of the blades. Proportional–integral (PI) controllers are typically used as the tilt and yaw controllers [8], and studies using optimal controllers, robust controllers, and fuzzy controllers have been conducted [13,14,15,16,17]. In addition to the 1P component of the asymmetric moment load acting on the blade, research was also conducted on using additional individual pitch control inputs to reduce higher-order harmonic components above 2P [18,19,20,21]. Just as gain scheduling is applied to compensate for the nonlinearity of the power coefficient in the collective pitch controller [3], gain scheduling can also be applied to compensate for the nonlinearity of the thrust coefficient in the individual pitch controller [21]. Previous studies related to individual pitch controllers to reduce the 1P component acting on the blade have mostly focused on the effect of applying a fixed gain. The purpose of applying gain scheduling to the individual pitch controller was to reflect the nonlinearity of the thrust coefficient. However, due to the operation of the individual pitch controller to reduce the 1P component acting on the blade, the vibration mode of the blade may be excited as the wind speed increases, so this point needs to be considered.

This study is about a control method that further reduces the 1P component of the blade’s bending moment in the out-of-plane direction by operating the individual pitch controller stably in the entire wind speed range without an excitation of the vibration mode of the blade in the in-plane direction. One of the important considerations in the individual pitch controller of an MW-class wind turbine is that changes in pitch angle should not excite the vibration mode of the blade. For this purpose, it is important to use different gain values of the individual pitch controller according to the magnitude of the wind speed between the rated wind speed and the cut-off wind speed. Therefore, in this paper, the necessity and effectiveness of a gain scheduling method that appropriately adjusts the gain values of the individual pitch controller is examined for the purpose of further reducing the 1P component of the bending moment in the out-of-plane direction acting on the blade without exciting the blade’s vibration mode in the in-plane direction.

2. NREL 5 MW Wind Turbine

In this paper, the wind turbine used for simulation is an onshore wind turbine with a rated power of 5 MW, designed by the National Renewable Energy Laboratory (NREL) for use in research. The brief specifications of the wind turbine are shown in

Table 1. General specifications of an NREL 5 MW wind turbine.

Specification	Value	Unit
Rated power	5	MW
Rotor diameter	126	m
Blade length	61.5	m
Hub height	90	m
Number of blade	3
Gearbox ratio	97
Rated rotor speed	12.1	rpm
Rated wind speed	11.4	m/s
Cut-out wind speed	25	m/s
Fine pitch angle	0	rad

. Bladed, a type of specialized commercial software dedicated to wind turbines, was used to model the NREL 5 MW wind turbine and examine its output power and load responses. Based on the aerodynamic and structural values of the blades, tower structural values, and drivetrain and nacelle values presented in the NREL report [22], the NREL 5 MW wind turbine was modeled as shown in Figure 1 using the Bladed software [23]. Numerical simulations were performed, applying the specifications of the NREL 5 MW wind turbine. Wind shear, tower shadow, gravity, and 3D turbulence, which cause asymmetric loads on each blade, were all considered in the numerical simulations. The torque power controller and the pitch power controller were designed by reflecting the characteristics of the power coefficient. The torque power controller operates below the rated wind speed and the pitch power controller operates above the rated wind speed. To reduce the shaft vibration, a drivetrain damper was designed and added to the torque power controller. In addition, an individual pitch controller was added to the pitch power controller to reduce the load of the blade for this study. In the numerical simulations, 10 min turbulent wind speeds corresponding to Class A of the IEC-61400-1 regulation were used [24]. Turbulence intensity varies depending on the mean wind speed. When the mean wind speeds are 12 m/s, 16 m/s, 20 m/s, and 24 m/s, the values of turbulence intensity are 19.47%, 17.6%, 16.48%, and 15.73%, respectively. Figure 2a,b show the turbulent wind speeds at the hub height used in the numerical simulations, with mean wind speeds of 16 m/s and 24 m/s, respectively.

The NREL 5 MW wind turbine has a rated wind speed of 11.4 m/s and a cut-off wind speed of 24 m/s. Since the rated rotational speed of the rotor is 12.1 rpm and there are three blades, a 1P component of 0.2 Hz and a 3P component of 0.6 Hz appear in the load and power responses of the NREL 5 MW wind turbine. The first-order natural frequency of the blade in the out-of-plane direction is 0.85 Hz, and the first-order natural frequency of the blade in the in-plane direction is 1.1 Hz. The first-order natural frequencies of the tower in the fore–aft and side–side directions are the same at 0.33 Hz. The structural damping ratios for both the first-order vibration modes in the out-of-plane and in-plane directions of the blade are very small at 0.5% [22]. The aerodynamic damping of the blade due to interaction with the wind varies depending on the magnitude of the wind speed. In the case of aerodynamic damping above the rated wind speed, the damping ratio of the first-order vibration mode in the out-of-plane direction is very large at 50~60%, but that in the in-plane direction is very small at 0.5~1% [25]. The out-of-plane vibration of the blade is not a problem due to the large aerodynamic damping effect. However, vibration in the in-plane direction of the blade can have a significant impact on the dynamic load because the damping ratio is very small, even considering aerodynamic damping.

3. Individual Pitch Controller and Its Problem

3.1. Individual Pitch Controller

The pitch controller applied to MW-class wind turbines consists of a collective pitch controller (CPC) and an individual pitch controller (IPC). A list of nomenclature for descriptions of the symbols used for the individual pitch controller is shown in

Table 2. List of nomenclature.

Symbol	Description	Unit
Mtilt	Tilting moment	Nm
My	Out-of-plane bending moment of the blade	Nm
Myaw	Yawing moment	Nm
θ	Rotor azimuth angles	rad
β	Pitch angle	rad
βCPC	Collective pitch angle	rad
βIPC	Individual pitch angle	rad
βtilt	Tilt angle	rad
βyaw	Yaw angle	rad

. When the wind blows and the rotor rotates, each blade has a different rotor azimuth angle. Figure 3 shows the definition of the azimuth angle of the rotor and the pitch angle of the three blades. The rotor azimuth angle is defined as 0 degrees when the blade is pointed skyward and in line with the tower. If there are three blades, the rotor azimuth angles of the three blades differ by 120 degrees. In the collective pitch controller, the same pitch angle demand (β_CPC) is used for all three blades. In contrast, in the individual pitch controller, different pitch angle demands (β₁, β₂, β₃) at different rotor azimuth angles (θ₁, θ₂, θ₃) are used for each blade.

Figure 4 shows a block diagram of how to implement a previously used individual pitch controller. Looking closely, the overall pitch controller is configured by adding the pitch demand of the individual pitch controller to that of the collective pitch controller. For the individual pitch controller, it is necessary to feed back the asymmetrical load components that occur on the three blades because each blade has a different rotor azimuth angle when the rotor rotates. Two load components of tilting moment (M_tilt) and yawing moment (M_yaw) are obtained through the Coleman transformation of Equation (1) by receiving the out-of-plane bending moment (M_y1, M_y2, M_y3) and rotor azimuth angle of each blade root from the wind turbine [5,8]. Each error component is calculated by comparing these two tilting-moment and yawing-moment load components with a control target value of 0. A tilt controller and a yaw controller are used to make each error component a control target value of 0. Proportional–integral (PI) controllers are widely used for both tilt and yaw controllers. The demands for tilt angle (β_tilt) and yaw angle (β_yaw) are determined by the tilt controller and yaw controller, respectively. Then, three individual pitch angle demands for each blade are obtained through the inverse Coleman transform of Equation (2) [5,8]. The pitch actuator of each blade is operated by adding the pitch angle demand of the individual pitch controller for each blade determined in this way to the pitch angle demand of the collective pitch controller.

$$\left[\begin{array}{c}{M}_{tilt}\\ M_{yaw}\end{array}\right]=\frac{2}{3}\left[\begin{array}{ccc}cos\theta & \mathrm{c}\mathrm{o}\mathrm{s}(\theta +\frac{2}{3}\pi )& \mathrm{c}\mathrm{o}\mathrm{s}(\theta +\frac{4}{3}\pi )\\ sin\theta & \mathrm{s}\mathrm{i}\mathrm{n}(\theta +\frac{2}{3}\pi )& \mathrm{s}\mathrm{i}\mathrm{n}(\theta +\frac{4}{3}\pi )\end{array}\right]\left[\begin{array}{c}{M}_{y1}\\ M_{y2}\\ M_{y3}\end{array}\right]$$

(1)

$$\left[\begin{array}{c}{\beta }_{IPC1}\\ {\beta }_{IPC2}\\ {\beta }_{IPC3}\end{array}\right]=\frac{2}{3}\left[\begin{array}{cc}cos\theta & sin\theta \\ \mathrm{c}\mathrm{o}\mathrm{s}(\theta +\frac{2}{3}\pi )& \mathrm{s}\mathrm{i}\mathrm{n}(\theta +\frac{2}{3}\pi )\\ \mathrm{c}\mathrm{o}\mathrm{s}(\theta +\frac{4}{3}\pi )& \mathrm{s}\mathrm{i}\mathrm{n}(\theta +\frac{4}{3}\pi )\end{array}\right]\left[\begin{array}{c}{\beta }_{tilt}\\ {\beta }_{yaw}\end{array}\right]$$

(2)

3.2. Problem with Individual Pitch Controller

In the widely used individual pitch control method, the tilt controller and the yaw controller use a fixed gain in all wind speed ranges. PI controllers are widely used for both tilt and yaw controllers. Since the proportional gain and the integral gain are used in the case of the PI controller, fixed gains are used for both the proportional and integral gains of the tilt controller and the yaw controller. However, when finding and using a gain with a sufficiently good control effect in all wind speed ranges in which the wind turbine is operated, the problem of the excitation of the vibration mode of the blades may occur as the wind speed increases. This problem is explained as an example using the results of a numerical simulation for an NREL 5 MW wind turbine.

The aerodynamic torque and the thrust of a wind turbine have nonlinear characteristics with respect to changes in the blade pitch angle. As the speed increases, the variation in the aerodynamic torque and thrust for the change of the pitch angle tends to increase. Therefore, even when the individual pitch controller operates, as the wind speed increases, the pitch angle variation may affect the vibration mode of the blade. The results of the case where the PI controller of the tilt controller and the yaw controller are designed and a fixed gain is applied in the entire wind speed range are as follows. For comparison, the response results for turbulent wind speed in the cases of 1 time (1X), 5 times (5X), and 10 times (10X) the fixed gain were checked. The case of 1X is an example in which the blade load reduction effect of the individual pitch controller is sufficient, and the cases of 5X and 10X are examples in which a larger control gain is used to improve the load reduction effect. Since the bandwidth of the control loop is widened when the gain of the individual pitch controller is large, the bandwidth of the blade pitch angle is also widened so that the variation in the pitch angle could excite the vibration mode of the blade. When an individual pitch controller with a fixed gain is applied, the power spectral density (PSD) is obtained from the time response of the blade pitch angle to examine whether the pitch angle excites the vibration mode of the blade.

Figure 5a,b show the power spectral density (PSD) of the blade pitch angle when a fixed gain is used for turbulent wind speeds with mean wind speeds of 16 m/s and 24 m/s, respectively. Since the individual pitch controller aims to reduce the 1P component acting on the out-of-plane bending moment of the blade, it can be seen in both Figure 4a,b that the pitch angle mainly fluctuates with the 1P component at 0.2 Hz. It can be seen that higher-order harmonic components such as the 2P component (0.4 Hz), 3P component (0.6 Hz), and 4P component (0.8 Hz) do not appear in the pitch angle responses. At 16 m/s, it can be confirmed that 1.1 Hz, which is the first-order natural frequency of the in-plane direction of the blade, is not excited in all cases (1X, 5X, and 10X). However, at a high wind speed of 24 m/s, it can be clearly observed that the first-order natural frequency (1.1 Hz) of the in-plane direction of the blade is excited in the case of 5X and 10X. In the case of 10X, it can be confirmed that this vibration mode is more excited because the bandwidth of the pitch angle is wider than that of 5X. As a result of checking via wind speed, it was confirmed that the first-order natural frequency (1.1 Hz) in the in-plane direction of the blade was excited in the case of 5X and 10X at the mean wind speed of 18 m/s or higher. This means that when a fixed gain in the individual pitch controller is used in the entire wind speed range using a larger gain in order to increase the effect of reducing the blade load, a problem in which the vibration mode of the blade is excited in the high wind speed range may occur.

4. Gain Scheduling of Individual Pitch Controller

4.1. Gain Scheduling Method

It was confirmed that the gain used for the individual pitch controller can be large in the vicinity of the rated wind speed, but cannot be large in the high-wind-speed region near the cut-off wind speed (Figure 5). Therefore, a method involving scheduling the PI gains of the individual pitch controller to be large near the rated wind speed and small near the cut-off wind speed will be proposed and reviewed. That is, as the wind speed increases, the gains are scheduled by reducing the PI gain values of the tilt controller and the yaw controller. The goal of the gain scheduling of the individual pitch controller in this paper is to prevent the problem of excitation of the first-order vibration mode in the in-plane direction of the blade in the high-wind-speed region.

In real-world wind turbine control, pitch angle information may be used instead of wind speed information. When the wind speed exceeds the rated value, the pitch angle increases as the wind speed increases. Therefore, in real-world wind turbines, the gain scheduling of the individual pitch controller is applied by reducing the PI gain values of the tilt and yaw controllers as the pitch angle increases, and the effect of reducing the load is examined. Figure 6 shows a block diagram of the proposed gain scheduling method for the individual pitch controller. In addition to the widely used individual pitch controller (Figure 4), the PI gains of each tilt controller and yaw controller are scheduled separately. Each tilt gain scheduler and yaw gain scheduler use pitch angle information instead of wind speed information, and the PI gains of the tilt and yaw controllers decrease as the pitch angle increases.

4.2. Gain Scheduling Effects

Let us look at the results for the case of applying a fixed gain (1X) and the case of applying gain scheduling over the entire wind speed range when designing the PI gain values of the tilt controller and the yaw controller. The tilt gain scheduler and the yaw gain scheduler are implemented so that each PI gain is divided by the gain divisor and becomes smaller as the pitch angle increases (Figure 7). That is, for gain scheduling, a gain as large as 10 times (10X) was used near the rated wind speed and a small gain of 1 time (1X) was used near the cut-off wind speed.

The form of the gain scheduler shown in Figure 7 is similar to that of the gain scheduler used in the pitch power controller of the collective pitch controller. This is one of the methods used to demonstrate that the gain decreases nonlinearly as the pitch angle increases. The gain divisors of the tilt gain scheduler and the yaw gain scheduler can be used differently, but the same gain divisor is applied in this paper. By using such a gain scheduling method for the individual pitch controller, it is possible to obtain an optimal load reduction effect by using a large gain near the rated wind speed, and to operate without the excitation of the vibration mode of the blade near the cut-off wind speed. The frequency responses of the blade pitch angle in the case of using a fixed gain (1X) and the case of applying gain scheduling can be compared in Figure 8a and Figure 8b, respectively. Figure 8a,b show the power spectral density of the blade pitch angle for turbulent wind speeds with mean wind speeds of 16 m/s and 24 m/s, respectively. The pitch angle responses show that only the 1P component (0.2 Hz), which is the target of the individual pitch controller, appears at both wind speeds. It can be seen that at both mean wind speeds of 16 m/s and 24 m/s, the individual pitch controller with gain scheduling does not excite the 1.1 Hz in-plane direction of the first-order vibration mode of the blade. Even in the pitch angle response at a mean wind speed of 24 m/s, high-order harmonic components such as the 2P component (0.4 Hz), 3P component (0.6 Hz), and 4P component (0.8 Hz) and the first-order vibration mode component in the in-plane direction (1.1 Hz) do not appear at all. This shows that the problem of excitation of the vibration mode of the blade, which can occur in the high-wind-speed region when using a fixed gain, can be solved using gain scheduling.

Next, let us look at the blade load response and fatigue load for each wind speed when the individual pitch controller is applied to realistic turbulent wind speeds. Figure 9a,b show the power spectral density of the out-of-plane bending moment at the blade root for turbulent wind speeds of 12 m/s and 16 m/s, respectively. In the case of the bending moment in the out-of-plane direction of the blade, the component of the first-order natural frequency (0.85 Hz) is so small that it can be ignored, and the 1P component (0.2 Hz) and higher-order harmonic components above 2P (0.4 Hz) are dominant. The magnitude of the frequency component is the largest at 1P (0.2 Hz) and decreases in the order of 2P (0.4 Hz), 3P (0.6 Hz), 4P (0.8 Hz), and so on. It can be confirmed that the individual pitch controller reduces the 1P component in the out-of-plane bending moment of the blade, and that the application of gain scheduling has the effect of further reducing the 1P component. Since the reduction effect is greatest near the rated wind speed, it can be seen that the reduction effect is greater at the mean wind speed of 12 m/s than at 16 m/s. For reference, the effect of the individual pitch controller on the bending moment in the fore–aft direction of the tower is very small. Figure 10a,b show the power spectral density of the fore–aft bending moment of the tower foundation for turbulent wind speeds with mean wind speeds of 12 m/s and 16 m/s, respectively. In the case of the tower’s fore–aft bending moment, there are components of both the first-order natural frequency (0.33 Hz) and higher-order harmonic components such as 3P (0.6 Hz), 6P (1.2 Hz), and 9P (1.2 Hz). As for the magnitude of the frequency component, the first-order natural frequency component is the largest, followed by the 3P component, and the 6P and 9P components are relatively small. Since the individual pitch controller does not control the components of the first-order natural frequency and the 3P in the fore–aft direction of the tower, the influence of the individual pitch controller on the bending moment in the fore–aft direction of the tower is very small. Figure 11a and Figure 12b compare representative time responses to the out-of-plane bending moment at the blade root at mean wind speeds of 12 m/s and 16 m/s, respectively. From these time responses, it can be seen that the main frequency component of the dynamic load is 1P (0.2 Hz), and that reducing the 1P component can reduce the peak-to-peak value of the dynamic load. It can be confirmed that the peak-to-peak value can be reduced by further reducing the 1P component in the out-of-plane bending moment of the blade by applying gain scheduling. Figure 12a,b show the damage equivalent load (DEL) and its reduction ratio for the bending moment in the out-of-plane direction at the blade root when the individual pitch controller is applied in the range above the rated wind speed, respectively. When gain scheduling to prevent blade vibration mode excitation is applied, the fatigue load reduction ratio of the blade is much better—about 14 to 24% in the entire wind speed range. The fatigue load reduction ratio of the blade is almost similar at the cut-off wind speed of 24 m/s, but by applying gain scheduling, it can be confirmed that the fatigue load reduction ratio of the blade is much better at about 5 to 10% for most wind speeds.

5. Conclusions

In this paper, we take a new look at the influence of the first-order vibration mode in the in-plane direction of the blade on the individual pitch controller applied to an NREL 5 MW wind turbine. The main contributions of this paper on the individual pitch controller aimed at reducing the 1P component of the bending moment in the out-of-plane direction for the NREL 5 MW wind turbine are as follows.

First, it was determined that the individual pitch controller has a problem in that it may excite the first-order vibration mode in the in-plane direction of the blade. It was found that, if a fixed gain is applied to the entire wind speed range with a larger gain in the individual pitch controller for the purpose of further reducing the 1P component of the bending moment in the out-of-plane direction acting on the blade, the problem of the first-order vibration mode in the in-plane direction of the blade being excited in the high-wind-speed region may occur.

Second, a novel gain scheduling method was proposed to overcome the problem of the individual pitch controller exciting the first-order vibration mode in the in-plane direction of the blade. The proposed gain scheduler for use with the individual pitch controller makes the PI gain values smaller as the pitch angle increases. It was shown that the proposed gain scheduling method can solve the problem of the first-order vibration mode in the in-plane direction of the blade that can occur in the high-wind-speed region.

Third, the effect of reducing the dynamic moment load on the blade when applying the proposed gain-scheduled individual pitch controller was presented. It was shown that the 1P component of the bending moment of the blade in the out-of-plane direction can be further reduced. As a result, it was confirmed that the fatigue load reduction ratio of the blade in the out-of-plane direction was further improved by about 5 to 10% at most speeds above the rated wind speed.