Study Method of Pitch-Angle Control on Load and the Performance of a Floating Offshore Wind Turbine by Experiments

Abstract

Offshore wind energy is a renewable energy source that is developing fast. It is considered to be the most promising energy source in the next decade. Besides, the expanding trend for this technology requires the consideration of diversified seabeds. In deep seabeds, floating offshore wind technology (FOWT) is needed. For this latter technology, such as for conventional WT, we need to consider aspects related to performance, aerodynamic force, and forces during operation. In this paper, a two-bladed downwind wind turbine model is utilized to conduct experiments. The collective pitch and cyclic pitch angle are adjusted using swashplated equipment. The fluid forces and moments acting on the rotor surface are measured by a six-component balancing system. By changing the pitch angle of the wind turbine blades, attempts are made to manage the fluid forces generated on the rotor surface. Under varied uniform wind velocities of 7, 8, 9, and 10 m/s, the effect of collective pitch control and cyclic pitch control on the power coefficient and thrust coefficient of FOWT is then discussed. Furthermore, at a wind speed of 10 m/s, both the power coefficient and loads are investigated as the pitch angle and yaw angle change. Experimental results indicate that the combined moment magnitude can be controlled by changing the pitch-angle amplitude. The power coefficient is adjusted by the cyclic pitch-angle controller when the pitch-angle phase changes. In addition, the thrust coefficient fluctuated when the pitch angle changed in the oblique inflow wind condition.

1. Introduction

The demand for using energy to develop economic, production, and other sectors in the world has been increasing at high speed in recent decades. Therefore, providing enough energy for growing the demand for energy consumption is a challenge for power generation development. Besides, renewable energy has many advantages such as the rapid decline in capital costs, air quality improvements, and reduction of carbon emissions [1]. Among renewable energies, wind energy is the one showing a continuous and accelerated growth. For onshore wind power, the installed capacity has reached about 72.5 GW, and the offshore wind power installed capacity has gone beyond 21 GW [2]. Until recent times, offshore wind energy has been deployed near shore (at depths below 60 m) using the traditional fixed bottom substructures or conventional concrete gravity foundation. Additionally, floating technology is used for deep-water areas (from 60 m to 200 m), and it is a promising technology for the future because of technical improvements and possible larger scale developments. For these reasons, the investment costs of offshore wind power projects will reduce in the coming years [3].

Because the size of the offshore wind turbine (comprising tower, blade, generator) increases rapidly, dynamic loads of the blade and wind turbine are larger when the floating offshore wind turbine operates [4,5,6]. The fluctuations of these dynamic loads can be divided into three groups: the tower vibration, blades or rotor loads, and the variation of aerodynamic torque and output power. To limit the tower vibration, the pitch angle is increased. In this way, tower fore-aft fluctuations [7,8] are reduced. For blades or rotors, the individual blade pitch control is used to smooth the blade load fluctuation or reduce the main periodic load components [9,10]. Multivariable linear parameter-varying control techniques are applied to decrease the structural loads [11]. Additionally, a fuzzy-logic proportional control method is exhibited to decrease the moment load on the rotor and tower with fixed output power [12]. For the aerodynamic torque and output power control, a multivariable disturbance observer is introduced [13] to decrease the output power vibration, tower oscillation, and drive-train torsion. The individual pitch-control method reduces the 3P fluctuating component of the output power under different wind speed conditions [14]. Therefore, in the latter work, loads are mitigated as possible solution and suitable control methods have been selected.

For increasing the cost effectiveness of the floating offshore wind power projects, the capital cost of the wind turbine needs to be limited as it strongly affects the total investment capital. The structure of a 2-bladed wind turbine will reduce the cost of the material for less than one blade, while showing a quicker installation [15]. Hence, a 2-bladed wind turbine is considered for the experimental part of this research. In the past, this wind turbine technology was not fully considered because of its asymmetrical rotation, visual, and noise impact [16]. However, the effect of noise on the installation and operation phase of offshore wind turbines (pile-driving noise or vessel noise) was considered [17,18,19]. Moreover, the asymmetry issue is investigated. The loads are caused by the asymmetry, depending strongly on the azimuth angle. A teeter hinge and active mechanisms are used to reduce loads of the wind turbine [20,21,22]. As compared with 3-bladed upwind or downwind wind turbines, the 2-bladed downwind has higher power, large tip speed ratio, and a lighter rotor [23,24].

Researchers and authors have introduced controlled methods for increasing the power and reducing loads of wind turbines. For blades, methods can be divided into two types: modifying the blades, and eliminating the reforming ones. The first type, blade-modified methods, comprise the use of trailing edge flaps, micro tabs, and synthetic jet actuators [25,26]. On the other hand, still working on the blades without changing their structure is listed in what follows: collective pitch control, individual pitch control, pitch-to-stall, and pitch-to-feather [27,28]. The rotational torque is controlled by the collective pitch angle in full load conditions [29]. A PID controller gets the signal from the generator speed to control the collective pitch angle. Using this method, the collective pitch control cannot reduce the harmonic loads due to the asymmetric loads on the rotor plane [30]. In other studies, authors used light detection and ranging (LIDAR) technology to decrease the 1P frequency harmonic loads based on wind measurement. Simple collective pitch controllers can reduce loads of the wind turbine structures when receiving feedback signs from the LIDAR system [31,32]. An individual pitch control (IPC) is applied to reduce the load of the wind turbine. One advantage over commercial turbines is that the braking systems are independent, getting rid of a high-capacity shaft brake [33]. Therefore, the pitch angle of each blade can be controlled individually [34]. Specifically, the measured blade loads are transformed to a single-input, single-output (SISO) controller; then, the control command is set up and the demand pitch angle is obtained [22,33].

FOWTs are mounted on platforms that must bear the complex dynamic load. Stochastic loads of the tower (and rotor blades) deriving from wind and waves are the main factors that need to be reduced for stabilizing the power production and load mitigation. The blade pitch controller of FOWTs is a key method under above-rated wind speeds. It can generate negative damping of the floating foundation [28,35,36,37]. The cyclic pitch-control method significantly reduces the teeter angle when operating in normal and extreme gust conditions [38]. The performance and aerodynamic forces are controlled by the cyclic pitch-control method in the diagonal inflow wind [39]. However, the wave forces are difficult to eliminate by the feedback control method [40,41]. In [42], a multi-input multi-output (MIMO) system estimates the importance of the control inputs generator torque and blade pitch angle for the rejection of wind and wave loads.

In this paper, the purpose of this work is to investigate the force under the collective pitch angle and cyclic pitch-angle control on the power coefficient, thrust coefficient, and the aerodynamic load of the 2-bladed downwind wind turbine. The pitch-angle control includes the collective pitch angle and the cyclic pitch-angle control. In these experiments, the wind speed variation and misalignment are taken into consideration. The results of this study can help researchers to better understand these control methods on the rotational rotor plane of the wind turbine.

The structure of the paper is organized in four sections: Section 1 presents the introduction. Section 2 shows the experimental types of equipment used, wind conditions, and calculation equations. Section 3 discusses the output experimental data, and the conclusion, Section 4, is reported at the end.

2. Experimental Conditions and Method

This section contains a detailed description of the experiment including an opened wind tunnel of the Mie University in Japan and key devices such as a 2-bladed downwind wind turbine, a pitch-angle control system, and Avistar blades. A brief description of the wind tunnel, the model wind turbine, a swash plate device, the overall setup, and measurement system are also given.

2.1. Experimental Method

2.1.1. Opened Wind Tunnel

Experiments for the pitch-angle control have been carried out in the opened wind tunnel. A sketch of the wind tunnel is reported in Figure 1.

The opened circular wind tunnel has an outlet diameter of 3.6 m, and the air collector size is 4.5 m × 4.5 m. A model of a 2-bladed downwind wind turbine is located in the Open Test Section. The wind turbine has blades with the length of 0.8 m.

The test section area, where the wind turbine is located, has a length of 4.5 m. The mainstream speed has maximum value of 30 m/s. Pitot tube installed at the wind tunnel outlet measures the mainstream wind speed.

The room temperature is measured by a platinum-resistance temperature detector. The experimental results are calculated based on the Cartesian coordinate with the x, y, and z-axes setting in the mainstream, the lateral, and the vertical directions.

Honeycombs installed in front of the outlet reduce the turbulence intensity. The speed deviation at the center line of the hub height is 1.5% or less, and the turbulence intensity is 0.50% or less. This data is measured by the laser Doppler and the heat ray velocimeter. Maeda et al. [43] and Li et al. [44] presented the effect of the blockage on the downwind wind turbine in previous studies.

2.1.2. The 2-Bladed Downwind Wind Turbine Model

The 2-bladed downwind wind turbine model used in this experiment is a horizontal axis-type and installed at the test section with a distance from the outlet of 3084 mm (from the rotor of the wind turbine to the outlet) (seen in Figure 2a).

The diameter of the rotor is D = 1600 mm, and the hub height is 1.535 m. The rotor speed is controlled by a variable speed generator installed in the nacelle. The rotor speed is controlled via the changeable speed-generator driver, and variable speed-generator amplifier, sending the command value from a personal computer as a digital value. The rotational speed of the generator is 880 rpm. The wind speeds in this experiment are 7, 8, 9, and 10 m/s. The blades are manufactured by Avistar airfoil. The chord length and twist angle of the blade are reported in Figure 2b.

In order to consider the stability of the Avistar blade, experiments affected by the low Reynolds numbers of Re = 0.5 × 10⁵, 1.0 × 10⁵, 1.5 × 10⁵, and 2.0 × 10⁵ on the airfoil performance were carried out and there is no significant effect on the aerodynamic performance of the blades [45]. Therefore, the data of the experiment is correct and reliable.

A six-component balance device is set up between the nacelle and the tower of the wind turbine model. The forces and moments are measured by this device following the three directions of x, y, and z-axes. The digital measurement values are collected and treated by the personal computer. In addition, the load measuring point location in this experiment is the center of the rotor; it is the origin coordinate in the measurement.

2.1.3. Pitch-Angle Control Device

Actuators installed inside the nacelle control the pitch angle of the blade of the wind turbine. These actuators are linear drive actuators that incorporate a ball screw into stepping motors with built-in rotor position sensors. The pitch angle of the blade is changed when the operator sets up commands from a personal computer to control the actuator driver. Besides, a swash plate adjusts the pitch angle following the azimuth angle as exhibited in Figure 3a. This equipment is organized by a non-rotating disc, a rotating disc, and a bearing. Three actuators are installed at three positions with the azimuth angles of ψ = 0°, 120°, and 240° as exhibited in Figure 3b.

The swashplate includes a non-rotating part and a rotating part. The swashplate can adjust the collective pitch angle and the cyclic pitch angle.

For this experiment, both the collective pitch and the cyclic pitch angle are changed to estimate the phenomena of the power coefficient. The swashplate moving parallel with the rotor surface will make the collective pitch angle. Further, the cyclic pitch control followed by the azimuth angle is performed when the swashplate moves title with the rotor surface. The angle between the chord line and the rotor’s plane is called the pitch angle. The yaw angle is the angle between the wind direction and the wind turbine axis.

2.2. Input Data for the Experiment

Two pitch-angle control methods are used to estimate the change of the power and thrust coefficient in the steady and diagonal inflow wind conditions. Besides, the effect of the change of the pitch angle and yaw angle on the power coefficient and moments on the wind turbine are also investigated. The power and thrust coefficient are considered with the mainstream wind velocity of 7, 8, 9, and 10 m/s. In the collective pitch-control experiment, the power and thrust coefficient are consider in the conditions of the pitch angle of θ = −1, 0, +1 [°], the mainstream speed of U = 10 [m/s], and the maximum tip speed ratio of λ = 7.4. The load of the wind turbine is estimate based on the pitch moment and yaw moment. In another experiment, the cyclic pitch-angle control is studied in the diagonal wind condition, with the yaw angles of φ = −5, 0, +5 [°]. The experimental conditions are summarized in

Table 1. Input data of the experiment.

Wind Velocity [m/s]	Pitch Angle θ [o]	Pitch-Angle Amplitude [o]	Pitch-Angle Phase [o]	Yaw Angle [o]
7, 8, 9, 10	−1°, 0° and 1°	a = −1°~1°	ξ = 0°, 45°, 90°, 135° and ξ = 30°, 60°, 120°, 150°	−5°, 0°, 5°

.

The angle created by the chord line and the relative wind direction is called the angle of attack. The angle of attack changes over the entire rotor surface due to the twist angle. The fluid force on the blades is also expected to change. Therefore, the fluid force appearing on the rotor surface can change. The pitch angle is constant at all azimuth angle positions during the experimental process.

2.3. Calculation Formulas

The pitch angle is calculated as follows:

$$\theta (\psi )=a\cos (\psi -\xi )+b$$

(1)

Here, ψ is the azimuth angle; ξ is the phase angle of the pitch angle θ with respect to the azimuth angle ψ; a is the pitch-angle amplitude; and b is the average pitch angle.

The power coefficient, thrust coefficient, and the tip speed ratio are calculated as follows:

$$\lambda =\frac{R\omega }{U}$$

(2)

$$C_P=\frac{P}{0.5\rho A{U}^3}$$

(3)

$$C_T=\frac{T}{0.5\rho A{U}^2}$$

(4)

Regarding Equations (2)–(4), P and T denote the rotor performance and the rotor thrust force; R represents the rotor radius [m]; ρ the density of air [kg/m³]; A is the swept area of the rotor [m²]; U is mainstream wind speed [m/s]; and ω is the angular velocity [rad/s].

The pitching moment coefficient, C_Mx, and the yaw moment coefficient, C_Mz, are calculated:

$$C_{M\mathrm{x}}=\frac{M\mathrm{x}}{0.5\rho U^{2}AR}$$

(5)

$$C_{M\mathrm{z}}=\frac{M\mathrm{z}}{0.5\rho U^{2}AR}$$

(6)

Here, Mx is the pitching moment, and Mz is the yaw moment.

When the pitch angle changes, the angle of attack also changes on all the rotor’s span. Therefore, the fluid force acting on the blades also changes.

The angle of attack at each airfoil can be obtained through the following equation:

$$\alpha =\varphi -(\beta +{\theta }_{\mathrm{twist}})$$

(7)

Calculate the angle of attack as follows [46]:

$$\alpha ={\tan }^{-1}\left[\frac{(1-a)U_0}{(1+\mathrm{a}\prime )\mathsf{\Omega }r}\right]-({\theta }_{\mathrm{twist}}+\beta )$$

(8)

3. Results and Discussion

The stability of the offshore wind turbine is an important issue when it operates on the sea. However, more improvement is required to expand the installation in deep water offshore areas. Therefore, in this study, the flow force acting on the rotor’s area of the wind turbine was focused on, and the experiment was conducted by trying to suppress the shaking of the floating offshore wind turbine. The aerodynamic characteristics of the wind turbine are described under the front inflow wind and oblique wind conditions. The experiment to deduce the wind turbine performance is conducted to acquire basic data about the wind turbine. The pitch-angle control experiment is also carried out to measure the fluid force on the rotor’s area when the pitch angle is adjusted.

The pitch-angle control experiment includes the collective pitch-control test that keeps the pitch angle constant concerning the azimuth angle. Besides, the cyclic pitch-control test adjusts the pitch angle followed the azimuth angle according to Equation (1). The flow force on the blade element is indicated in Figure 4.

In the figure, the flow force impacting the blade element surface increases since the lift force rises and the drag force degrades. The inflow angle acting on the low wind speed region is large. When the angle of attack obtains the optimum value, the power coefficient is also at a high level. The inflow angle acting on the high wind speed region is small, the pitch angle is small, and the angle of attack is sufficiently large to generate the lift force.

3.1. Collective Pitch Control

The wind turbine model was tested in the wind tunnel to consider the power coefficient curves in the wind speed conditions of 7, 8, 9, and 10 m/s as exhibited in Figure 5. The horizontal axis indicates the tip speed ratio λ, and the vertical axis presents the output power coefficient C_P.

From the figure, at any wind speed, the output power coefficient C_P increases as the tip speed ratio λ increases to reach the maximum value and then decreases. The angle of attack increases in the low tip speed ratio region. As a result, the blade has an excessive angle of attack, the lift force decreases, the drag force increases, and the power coefficient goes down. When the angle of attack becomes smaller in the high tip speed ratio region, the peak power coefficients are C_P = 0.3943, 0.3947, 0.403, and 0.408 at λ = 7.22, 6.74, 7.5, and 7.43 at the mainstream wind speed conditions of U = 7, 8, 9, and 10 m/s, respectively. From experimental results, the optimum power coefficient obtains C_P = 0.408 as the tip speed ratio of λ = 7.43 and the wind speed of U = 10 m/s. This issue indicates that the maximum power coefficient increases due to raising mainstream wind speed. It is considered that the relative blade inflows increase as the mainstream wind speed increases and the Reynolds number on the blade element goes up.

Similarly, the thrust coefficient curves were also experimented in the wind speed of 7, 8, 9, and 10 m/s as presented in Figure 6.

The thrust coefficient C_T increases monotonically when the tip speed ratio λ increases at any wind speed as exhibited in Figure 6. The thrust coefficient value is C_T = 0.76 at the optimum tip speed ratio of λ = 7.43 and the wind speed of U = 10 m/s. There is almost no difference in the thrust coefficient with the different wind speeds. The thrust force is generated by the lift force on the blade elements of the rotor blades. The lift coefficient depends on the angle of attack of the blade element. Therefore, the angle of attack is similar at the same tip speed ratio, and it does not depend on the mainstream wind speed. In addition, the Avistar airfoil used for this experiment did not depend on the low Reynolds number. The Reynolds number in the wind tunnel is within the range presented in Section 2.1.2.

The relationship between the thrust and the power coefficient is also considered in the next study. The thrust force can be adjusted during the collective pitch-control process, but at the same time, the power also changes secondarily. The horizontal axis indicates the power and the thrust coefficient, and the vertical axis is the amplitude of the power and the thrust coefficient. The optimum values of the power and the thrust coefficient are different when the pitch angle changes as indicated in Figure 7.

The pitch angles corresponding to the plot in Figure 7 show changes of 1 degree for the different colored bars.

The lowest thrust coefficient is C_T = 0.732 at the pitch angle of θ = 1 [°], while it increases for a pitch-angle reduction (−1°). From the figure, the power coefficient C_P becomes maximum when the thrust coefficient is C_T = 0.763 at the pitch angle θ = 0 [°] and decreases in both cases of going up and going down from the optimum pitch angle. Therefore, when controlling the thrust force by the pitch angle, the power decrease can be limited by setting the pitch angle smaller than the optimum pitch angle.

Similarly, the thrust and the power coefficient are also investigated in the oblique inflow wind of φ = −5°, 0°, 5° when the pitch angle changes. Figure 8 exhibits the relationship between the power and the thrust coefficient in the oblique inflow wind condition.

The pitch angle changes from −1° to 1° at 0.5° intervals. The yaw angles of φ = −5°, 0°, 5° are green, red, and yellow color lines, respectively. At the yaw angle declination, the thrust coefficient of C_T = 0.715 is the lowest at φ = 5 [°] and θ = 1 [°], and it is increasing in the direction of the pitch-angle reduction. From the figure, the power coefficients C_P at the yaw angles of φ = 0, ±5 [°] decrease in both cases of going up and going down from the maximum point of the power coefficient. The power coefficient and the thrust coefficient fluctuate in the oblique inflow wind. Therefore, the thrust force is adjusted by the pitch-angle change in the oblique inflow wind by setting the pitch angle smaller than the optimum pitch-angle value.

3.2. Cyclic Pitch Control

In this section, the experimental data are analyzed to understand the effect of this control method on the power coefficient and load. The pitch-angle amplitude changes from −1° to −1° at 0.1 intervals. The phase angle is divided into two cases of ξ = 0°, 45°, 90°, and 135°, and the ξ = 30°, 60°, 120°, and 150°.

Figure 9a,b describe the effect of the pitch-angle amplitude change on the power coefficient with the phase angle defined as above at the averaged pitch angle b = 0°.

For the cyclic pitch control as Equation (1), the pitch angle of the blade is calculated by a cosine function. When the rotor turns repeatedly in a rotation from 0^o to 360^o, it leads to the azimuth angle of the pitch angle fluctuating according to the azimuth angle rotation. The power coefficient at the phase angle of ξ = 0° has stronger fluctuation than others as exhibited in Figure 9. This can be seen as the angle phase changes, and the power coefficient oscillates following the pitch-angle amplitude. Therefore, the power coefficient of the wind turbine can be affected by the azimuth angle rotation. In addition, the maximum power coefficient depends on the azimuth angle rotation in the pitch-angle amplitude range from −1° to 1°; this happened due to the azimuth angle rotation. The value of the maximum and minimum of the pitch angles depends on each phase angle. The fluctuation of the power coefficient at the pitch angle differing from 0° is smoother than the phase angle of ξ = 0°. Therefore, it is controlled by the cyclic pitch control when the azimuth angle rotates.

3.3. Moments on the FOWT

In this study, the slope of the moments (pitching and yaw moment) is called the moment axis angle ψ_M, and the equation for deriving ψ_M from C_Mx (ξ, a), C_Mz (ξ, a) is shown in the following equation:

$${\psi }_M(\xi ,a)={\tan }^{-1}\left[\frac{-C_{M\mathrm{x}}(\xi ,a)}{C_{M\mathrm{z}}(\xi ,a)}\right]$$

(9)

where C_Mx (ξ, a) and C_Mz (ξ, a) are the results of subtraction of the pitching moment and the yaw moment at the pitch-angle amplitude of a for a = 0°.

Consider the relationship between the moment-axis azimuth and the pitch-angle amplitude as indicated in Figure 10. The fluctuation of the moment-axis angle ψ_M (ξ, a) when the pitch-angle amplitude a changes during the periodic pitch-angle control with the phase angle of ξ = 0°, 45°, 90°, and 135°, and the ξ = 30°, 60°, 120°, and 150°.

The pitch-angle amplitude of a = 0 [°] is the reference point and has no slope, so the plot is omitted. The moment-axis angle is almost constant in the same phases ξ, and unaffected by the change of the change amplitude a. Figure 11 exhibits the correlation between the phase angle ξ and the moment-axis angle ψ_M (ξ)′ and the approximate curve.

The horizontal axis of the figure is the pitch-angle phase ξ and the vertical axis presents the moment-axis angle ψ_M (ξ)′. The moment-axis angle ψ_M (ξ)′ fluctuates linearly with the phase angle ξ as indicated in Figure 11. Besides, there is a difference in ψ_M (ξ)′ concerning the pitch-angle phase ξ. It means that the azimuth angle, which indicates the difference between the flap moments on the rotor, lags behind the azimuth angle, which shows the maximum pitch-angle amplitude. The phase difference of ψ_M (ξ)′ with respect to this phase ξ is defined as ψ_dis. The approximate straight line in Figure 11 is shown in the following E = Equation (10).

ψ_M (ξ)′ = 1.01ξ + 73.5°

(10)

From Equation (8), the y-intercept is ψ_dis = 73.5 [°]. This phase difference ψ_dis is due to the changes in the moment on the rotor area because the angle of attack of the blade element fluctuates due to the oblique inflow wind and the lift generated changes. Next, the magnitude of the moment acting around the axis is combined and factorized into C_M (ξ, a). The calculation formula of C_M (ξ, a) is shown in the following:

$$C_M(\xi ,a)=\sqrt{C_{M\mathrm{x}}{(\xi ,a)}^2+C_{M\mathrm{z}}{(\xi ,a)}^2}$$

(11)

$$C_{Mmean}(\xi )=\left({\displaystyle \sum _{a=-1.0}^{1.0}{C}_M(\xi ,a)}\right)÷6$$

(12)

Figure 12 shows the correlation between the change of the pitch-angle amplitude a at the phase angles of ξ = 0, 30, 45, 60, 90, 120, 135, and 150 [°], and the combined moment coefficient C_M (ξ, a).

The combined moment largely relates to the change pitch-angle amplitude of a = −1 to 1 [°], and it is almost unaffected by the phase angle. The combined moment coefficient C_M (ξ, a) differs slightly because of the phase angle when the inflow velocity in the rotating surface is irregular. This effect happened due to the wake influence of the tower on the rotor area, and the wind blowing in the rotor changes at the different azimuth angles. Here, the average value of C_M (ξ, a) in phase ξ of a certain change amplitude a is calculated and used as C_Mmean (ξ). The averaging equation is shown in the following Equation (13).

Figure 13 indicates the relationship between the pitch-angle amplitude change and the average moment value C_Mmean (ξ) of the combined moment coefficient C_M (ξ, a).

The horizontal axis shows the pitch-angle amplitude change a, and the vertical axis presents the average value C_Mmean (ξ). From the figure, the average value C_Mmean (ξ) changes linearly with the pitch-angle change amplitude. The combined moment coefficients C_M (ξ, a) have a small difference in Figure 13. It can be considered the influence of the angle phase of the blade on the moments. In addition, the average value C_Mmean (ξ) increases or decreases at a constant rate with respect to the pitch-angle amplitude change. The approximate straight line in Figure 13 is shown in Equation (13) below:

C_Mmean (ξ) = 0.01602x − 0.00005

(13)

From Equation (13), with the pitch-angle amplitude a altered by 1°, the slope of the mean value C_Mmean (ξ) of the combined moment increases or decreases by 0.01602. From this, the combined moment changes at a constant rate. Therefore, the combined moment can be controlled by adjusting the pitch angle.

From the above results, the pitch-control method can be proved for controlling the aerodynamic load effect on the rotor area during the rotating rotor process.

4. Conclusions

In this paper, the power and thrust coefficient of FOWT were estimated under the collective pitch angle and the cyclic pitch-angle control at different wind speeds of 7, 8, 9, and 10 m/s. This experiment tested the change of the power and thrust coefficient of the two-bladed downwind wind turbine in the wind tunnel. The swashplate was installed to control the pitch angle. In addition, the moments of the wind turbine model were also analyzed when the amplitude and phase angle of the pitch angle change. Following are the study’s key findings in brief:

The wind speed significantly impacts the power coefficient. The optimum power coefficient was C_P = 0.403 at the tip speed ratio of λ = 7.43 and the wind speed of U = 10 m/s. Contrarily, there is almost no difference in the thrust coefficient for the different wind speeds under the uniform wind speed.

The thrust force is generated by the lift force acting on the blade elements, and the lift coefficient depends on the angle of attack of the blade element. Therefore, the thrust coefficient is adjusted by the pitch angle when the pitch angle and yaw angle changed.

The optimum power coefficient depends on the phase angle in the pitch-angle amplitude. The azimuth angle positions cause to change of the phase angle, leading to fluctuating power coefficients. Hence, the power coefficient is adjusted by the cyclic pitch-angle control method.

The moment-axis azimuth is almost constant in the same phases ξ in the pitch amplitude range from −1° to 1°. The magnitude of the combined moment largely depends on the change of the pitch-angle amplitude of a = −1° to 1°. And it is almost unaffected by the phase angle. Furthermore, the mean value C_Mmean (ξ) of the combined moment increases or decreases by 0.01602. The pitch-control method can be proved for controlling the aerodynamic load effect on the rotor surface.