Experimental results of floating platform vibration control with mode change function using full-scale spar-type floating offshore wind turbine

Abstract

Floating offshore wind turbines have great potential for harvesting renewable energy sources since offshore wind is stronger and more stable than onshore wind. The foundations of floating offshore wind turbines are not rigidly fixed and it leads to vibration of the floating platform pitch angle. This vibration is caused by fast blade pitch angle motions of variable speed control for controlling rotor speed at rated values. This study proposes a control method to address this vibration, floating platform vibration control. This method extracts a natural frequency component of the vibration from the floating platform pitch angle signal by a band pass filter and controls the blade pitch angle on the basis of proportional–derivative control. Its key characteristic is changing control modes in accordance with electrical power. Experiments using a full-scale spar-type floating offshore wind turbine were performed, and results show that the proposed floating platform vibration control can suppress the vibration of floating platform pitch angle.

Keywords

Wind turbine floating offshore wind turbine blade pitch angle control changing control modes full-scale demonstration apparatus

Introduction

The continuous increase in electrical energy consumption for a more convenient daily life has led to concerns about global warming and a lack of fossil sources. Wind turbines show promise as a countermeasure against these concerns, and wind installations are now expanding globally. Global Wind Energy Council (GWEC) (2015) reports that cumulative wind capacity at the end of 2015 reached 432.9 GW and forecasts that it will amount to 792.1 GW in 2030.

Most wind turbines have been installed at onshore sites. GWEC (2015) reports that the cumulative capacity of offshore wind reaches 12.1 GW. The European Wind Energy Association (EWEA) (2015) reports that 91% of all offshore wind turbines were installed off the coast of European countries. Almost all these offshore wind turbines are bottom fixed type, since Europe has many shallow offshore sites suitable for them. In contrast, Japan has little shallow offshore sites suitable for wind generation, even near the coast. Therefore, floating offshore wind turbines (FOWTs) are suitable for the offshore sites like Japan.

FOWTs are not currently at the commercial stage and some demonstration projects exist. The first project of full-scale FOWT is Hywind in Norway (Hanson et al., 2011). The FOWT was built in 2010 and it has a spar-type floating platform. The second project is WindFloat installed in Portugal in 2012 (Joaogocalo, 2012). It has a semi-submersible-type floating platform. There are two national projects related to FOWTs in Japan. First, the Japanese Ministry of Environment (MOE) installed the FOWT in Nagasaki Prefecture in 2012 (Ishida et al., 2013; Utsunomiya et al., 2013, 2014a, 2014b, 2015). After one 100-kW downwind turbine on a spar-type floating platform was operated, one 2-MW wind turbine with downwind turbine on a spar-type floating platform was installed in October 2013 and then it has been in operation ever since. Second, the Japanese Ministry of Economy, Trade and Industry (METI) conducted the Fukushima FORWARD project and installed one 2-MW FOWT in 2013 (Yoshida et al., 2014). METI is also conducting the project with the aim of operational 7 and 5 MW FOWTs in 2016. When added to the 2-MW FOWT that is already being operated, the total capacity will become 14 MW.

Since the foundation of an FOWT is not rigidly fixed, it is easier to change its position than that of a fixed-type wind turbine. Larsen and Hanson (2007) have reported a negative damped low-frequency posture vibration when FOWT is in the rated operation. This vibration is caused by variable speed control (VSC). VSC adjusts the blade pitch angle to maintain the rotor speed around reference speed above rated; however, the blade pitch angle motion changes the thrust force applied to the rotor, and this change in thrust force amplifies the floating platform pitching vibration as if the damping property were changed to negative. This negative damped vibration increases the fatigue loads of system components and causes the rotor speed to fluctuate. Therefore, the vibration in FOWTs needs to be suppressed.

There has recently been a lot of focus on FOWTs as the number of offshore wind turbines increases, and various solutions for the floating platform pitching vibration mentioned above have been proposed. For example, Guo et al. (2012) researched the application of individual pitch control technology for FOWT in order to suppress the floating platform pitching vibration. They designed an expert proportional–integral–derivative (PID) controller on the basis of non-linear wind turbine characteristics with control quantity distributed to three blades by means of a d-q coordinate transformation technique. Christiansen et al. (2012) proposed a minimum thrust load control strategy for FOWT that operates both blade pitch angle and generator torque and then reduces generator speed so as to minimize thrust coefficient of the rotor. Betti et al. (2012) have developed a simplified, control-oriented mathematical model of an FOWT with a spar buoy platform and proposed the synthesis of an H∞ controller working at above-rated operations. Luo (2012) also proposed an H∞ output feedback control technique for formulating the semi-active control law, which is implemented using a tuned liquid column damper.

Although these methods are effective in terms of suppressing the floating platform pitching vibration of FOWT under above-rated conditions, all validations have been performed using simulations or experiments conducted at test facilities. In this work, we propose a floating platform vibration control (FVC) with a function, which changes control modes on the basis of output power in order to stabilize the floating platform pitching vibration under not only above-rated conditions but also low wind speed conditions. The aim of this function is to suppress the floating platform pitching vibration that occurs when an FOWT alternately operates between above-rated and below-rated conditions as soon as possible. Moreover, the validity of this method using a full-scale FOWT was investigated.

In section “Posture vibration of FOWT” of this article, we clarify the reason for the low-frequency and negative damped posture vibration. In section “FVC with mode change function,” we propose FVC along with its schematic control algorithm and mode change function, and then show some simulation results relating to the mode change. Additional results using a full-scale FOWT are given in section “Experimental results.” The FOWT was constructed as part of the MOE project mentioned above. The FVC performance is compared to the performance without FVC under a 200-kW output restricted condition. Finally, we present experimental results demonstrating that the proposed FVC can stabilize FOWT operations under the 550-kW output restricted and above-rated conditions.

Posture vibration of FOWT

In this section, we clarify the reason for the floating platform pitching vibration of FOWTs. A schematic of an FOWT with a downwind turbine and defined floating platform pitch angle is shown in Figure 1. The floating platform pitch angle is the fore-aft rotating angle of a floating platform around a rotating center. As discussed above, the floating platform pitching vibration occurs because of blade pitch angle motion under above-rated conditions. Hereafter, we assume that VSC controls the blade pitch angle to maintain a generator speed rated value under that condition.

Figure 1.

Floating offshore wind turbine (FOWT) with downwind turbine.

First, we assume a case where the floating platform pitch angle changes to the positive direction. When the floating platform pitch angle changes to positive side, input rotor torque decreases as relative wind speed decreases and then the rotor speed decreases. VSC reactively operates the blade pitch angle to fine (fine means the windward direction). However, this operation makes the rotor thrust increase, and the floating platform pitch angle changes to further positive.

Next, we assume a situation where the floating platform pitch angle changes to the negative direction. When floating platform pitch angle changes to negative, input rotor torque increases because relative wind speed increases and the rotor speed is accelerated. VSC reactively operates blade pitch angle to feather. However, this operation makes the rotor thrust decrease, and the decreased thrust force pushes the floating platform pitch angle further forward.

As stated above, blade pitch angle motion operated by VSC is a driving force behind the floating platform pitch angle vibration. Larsen and Hanson (2007) reported that the floating platform pitch angle vibration occurs in cases where the blade pitch angle changes faster than the resonance frequency of the floating platform and the floating platform pitch angle vibration is suppressed by making the control cycle for blade pitch angle motion get close to the resonance frequency of the floating platform. Although a long control cycle for blade pitch angle motion is effective as a countermeasure against the floating platform pitch angle vibration, this long control cycle degrades VSC performance.

FVC with mode change function

Control algorithm

Figure 2 shows the control block diagram of a blade pitch angle controller proposed in this research, which has a function to change control modes on the basis of electrical power in order to suppress the floating platform pitching vibration that occurs when an FOWT alternately operates between above-rated and below-rated conditions as soon as possible. The reason why the floating platform pitching vibration should be suppressed as soon as possible is that the pitching vibration increases fatigue loads of components, especially tower part. Hereafter, we assume that VSC parameters are tuned for onshore wind turbine so that it can control output power according to wind turbulence and gusts.

Figure 2.

Control block diagram of blade pitch angle controller.

FVC calculates the blade pitch angle demand θ_FVC on the basis of floating platform pitch angle ϕ. After the blade pitch angle demand based on FVC θ_FVC is added to the blade pitch angle demand based on VSC θ_VSC, the blade pitch angle demand for the blade pitch actuators is determined.

Figure 3 shows a control block diagram of the proposed FVC, which comprises a second-order band pass filter (BPF) and PD controller. The BPF extracts a natural frequency component of the floating platform pitch angle vibration ϕ_BFP from input signal ϕ. The reason why the second-order BPF is selected is that the property can be clearly set by choosing only two parameters, the frequency and the damping ratio. The PD controller then responds to the blade pitch angle demand of FVC θ_FVC on the basis of the floating platform pitch angle vibration ϕ_BFP. The blade pitch angle demand of FVC θ_FVC generates torque in order to suppress the floating platform pitch angle vibration. Their transfer function is as follows

G_{B P F} (s) = \frac{φ_{B P F} (s)}{φ (s)} = \frac{2 ζ_{F V C} ω_{T V C} s}{s^{2} + 2 ζ_{F V C} ω_{T V C} s + {ω_{F V C}}^{2}}

(1)

G_{P D} (s) = \frac{θ_{F V C} (s)}{φ_{B P F} (s)} = K_{F V C}^{P} (1 + τ_{F V C} s)

(2)

where s is the Laplace operator, ζ_FVC is the damping ratio of the BPF, ω_FVC is the frequency of the BPF, $K_{F V C}^{P}$ is the proportional gain of the PD controller, and τ_FVC is the derivative time of the PD controller.

Figure 3.

Control block diagram of proposed FVC.

As the aim of BPF is to extract a natural frequency component of floating platform pitching vibration, ω_FVC needs to be set to near the frequency of floating platform. From simulation and experimental results, it is appropriate that ω_FVC is larger than the natural frequency of floating platform. ζ_FVC is useful to determine the effective frequency width of FVC. Therefore, it should be selected according to the type of floating platform and mooring. τ_FVC and $K_{F V C}^{P}$ of PD control can adjust the response and the strength of FVC, respectively. These parameters should be determined according to the aerodynamics of blade and the characteristics of blade pitch actuator.

In addition, the proposed FVC has a function to change modes of both the BPF and PD controller in accordance with electrical power. Figure 4 shows the mode change function. Specifically, Figure 4(a) shows the relation between electrical power and frequency of BPF and Figure 4(b) shows the relation between electrical power and the gain of the PD controller. The proposed FVC keeps these values constant in the case where electrical power is less than P_L and over P_rated, where P_rated is the rated power and P_L is the electrical power less than P_rated. The value of P_L needs to be selected according to the system property. The value of P_L should be determined so that the difference between P_L and P_rated is larger than the electrical fluctuation level above rated conditions. An example value of P_L is 95% of P_rated. These values change with increasing electrical power in the middle range between P_L and P_rated so as to let these values sequentially change. This function is useful to suppress the floating platform pitch angle vibration that occurs when an FOWT alternately operates between above-rated and below-rated conditions, thus stabilizing the floating platform pitching posture of FVC under all operational conditions. As a result, this function contributes to reduce fatigue loads caused by the floating platform pitching vibration.

Figure 4.

Proposed FVC has a function to change control modes of BPF and PD control: (a) frequency of BPF and (b) gain of PD control.

Effect of the proposed FVC

The characteristics described in equation (3) are assumed to appear around the floating platform pitch angle vibration shown in Figure 1. Floating platform pitch angle ϕ_BFP indicates a natural frequency component below the floating platform pitch angle vibration

T_{T h r u s t} = J {\overset{\cdot\cdot}{φ}}_{B P F} + D {\overset{\cdot}{φ}}_{B P F} + K φ_{B P F}

(3)

where F_Thrust is the torque that generates floating platform pitch vibration, J is the modal inertia of floating platform pitch angle vibration mode, D is the modal damping coefficient of floating platform pitch angle vibration mode, and K is the modal stiffness of floating platform pitch angle vibration mode.

If the proposed FVC is applied to an FOWT, the floating platform pitch angle vibration mode changes as follows

T_{T h r u s t} + T_{T h r u s t}^{F V C} = J {\overset{\cdot\cdot}{φ}}_{B P F} + D {\overset{\cdot}{φ}}_{B P F} + K φ_{B P F}

(4)

where $T_{T h r u s t}^{F V C}$ is the torque generated by the blade pitch angle motion of the proposed FVC.

The torque $T_{T h r u s t}^{F V C}$ has the following characteristics based on equation (2)

T_{T h r u s t}^{F V C} = - K_{P i t c h}^{T h r u s t} θ_{F V C}

(5)

T_{T h r u s t}^{F V C} = - K_{P i t c h}^{T h r u s t} K_{F V C}^{P} φ_{B P F} - K_{P i t c h}^{T h r u s t} K_{F V C}^{P} τ_{F V C} {\overset{\cdot}{φ}}_{B P F}

(6)

where $K_{P i t c h}^{T h r u s t}$ is the linear coefficient which converts blade pitch angle into torque with the assumption that torque is linear to blade pitch angle.

Equation (7) is given by substituting equation (4) for equation (6)

T_{T h r u s t} = J {\overset{\cdot\cdot}{φ}}_{B P F} + (D + K_{P i t c h}^{T h r u s t} K_{F V C}^{P} τ_{T V C}) {\overset{\cdot}{φ}}_{B P F} + (K + K_{P i t c h}^{T h r u s t} K_{F V C}^{P}) φ_{B P F}

(7)

Comparing equations (3) to (7), we can see that the modal damping and the modal stiffness of the floating platform pitch angle vibration mode both increase. The proposed FVC suppresses floating platform pitch angle vibration by controlling blade pitch angle motion in accordance with floating platform pitch angle.

Simulation results

In this section, we investigate the mode change function of the proposed FVC in simulation. Specifically, the effects of $ω_{F V C}^{L}$ and $K_{F V C}^{L}$ described in Figure 4 are investigated. The specification of FOWT and the simulation conditions are, respectively, listed in Tables 1 and 2. The FOWT has a downwind turbine and a spar-type floating platform and its rated power is 2000 kW, and its specifications are the same as the demonstration FOWT (Utsunomiya et al., 2015). Bladed® version 4.6 is used for simulation. Wind speed is changed from 8 to 14 m/s because those wind speed conditions contain below-rated operation for the simulation period. Turbulence intensity and wave conditions are kept constant. A frequency ratio C₁ and gain ratio C₂ satisfy the following equations

ω_{F V C}^{L} = C_{1} ω_{F V C}^{r a t e d}

(8)

K_{F V C}^{L} = C_{2} K_{F V C}^{r a t e d}

(9)

Table 1.

Specifications of FOWT (Utsunomiya, 2015).

Rated power	2000 kW
Rotor position	Downwind
Rotor diameter	80 m
Floating platform	Spar-type
Mooring	Catenary, three chains
Hub height	56 m
Rated wind speed	12 m/s
Modal inertia	30,062 kN ms²/rad
Modal damping coefficient	74 kN ms/rad
Modal stiffness coefficient	805 kN m/rad

Table 2.

Simulation conditions.

Average wind speed	8–14 m/s
Turbulence intensity	IEC C
Initial yaw error	0°
Wave height	2.16 m
Wave period	6.21 s
Wave type	Regular wave
Current	0 m/s
Simulation period	600 s
Frequency ratio $C_{1}$	0.8–2.0
Gain ratio $C_{2}$	0.2–1.8

Note that the ranges of these ratios are selected to be as wide as possible.

The simulation results are shown in Figure 5, where the horizontal axes of (a) and (b) are frequency ratio C₁ and gain ratio C₂, respectively, and the vertical axes are the normalized standard deviation of electrical power and floating platform pitch angle. Simulation results in case both the frequency ratio and gain ratio are set to 1.0 are used for the reference values of the normalization.

Figure 5.

Simulation results of normalized standard deviation: the reference values for the normalization are results in case both frequency ratio and gain ratio are set to 1.0. (a) Frequency ratio and (b) gain ratio need to be designed to satisfy low variation in electrical power and floating platform pitch angle.

As shown in Figure 5, the results of 8 m/s are constant and are not affected by changing the frequency and gain ratios. This indicates that the mode change function is effective for conditions where the FOWT alternately operates in below-rated and above-rated. We focus below on the results of over 10 m/s.

As shown in Figure 5(a), the normalized standard deviation of electrical power decreases with increasing the frequency ratio and the normalized standard deviation of floating platform pitch angle increases. In contrast, Figure 5(b) shows that the normalized standard deviation of electrical power increases with increasing the gain ratio, although the normalized standard deviation of floating platform pitch angle decreases. The characteristics shown in Figure 5(b) are present because VSC and FVC control the blade pitch angle, and so increasing the gain ratio of FVC can reduce the variation in floating platform pitch angle and deteriorate the variation in electrical power and thereby the performance of VSC.

These results indicate that a balance between gain ratio and frequency ratio needs to be designed to ensure low variation in both electrical power and floating platform pitch angle. For example, frequency ratio is set to a little larger value than above-rated in order to reduce electrical power variation, and gain ratio is also set to a little larger to prevent the floating platform pitch angle vibration from increasing. An example of optimal combination in this simulation case is as follows: C₁ is 1.1, C₂ is 1.1, $ω_{F V C}^{r a t e d}$ is 0.7 rad/s, and $K_{F V C}^{r a t e d}$ is 2.94.

Experimental results

In this section, we report experimental results that demonstrate the validity of the proposed FVC using a full-scale FOWT.

Experimental apparatus

Figure 6 shows the specifications of the experimental apparatus we used. This apparatus was originally constructed for the MOE FOWT project. Its specifications are already shown in Table 1. The spar-type floating platform has a hybrid structure: the top side is steel and the bottom is pre-stressed concrete.

Figure 6.

FOWT demonstration apparatus, originally part of MOE project (Utsunomiya, 2015).

Evaluation performances

We evaluated the suppression of floating platform pitch angle vibration under three conditions:

200-kW power restriction;

550-kW power restriction;

Above-rated conditions.

The power conditions are restricted because above-rated operations have risks of large loads if inclination angle of FOWT changes significantly. Table 3 shows the parameters of the proposed FVC for demonstration operations. These parameters have been adjusted on the basis of experimental results.

Table 3.

Parameters of FVC for demonstration operations.

Parameter names	Units	Conditions
		Power restriction		Above-rated
		200 kW	550 kW	500 kW	2000 kW
ζ_FVC	–	0.4	0.4	0.4	0.4
τ_FVC	s	0.3	0.3	0.3	0.3
$ω_{F V C}^{L}$	rad/s	0.15	0.40	0.7	1.54
$ω_{F V C}^{r a t e d}$	rad/s	0.15	0.28	0.26	0.7
$K_{F V C}^{L}$	–	2.04	2.45	2.45	4.07
$K_{F V C}^{r a t e d}$	–	2.04	2.45	2.45	3.74
P_L	kW	185	525	475	1850
P_rated	kW	200	550	500	2000

200-kW power restriction

The experimental results under the 200-kW power restriction are shown in Figure 7. Figure 7(a) shows time histories, and the vertical axes indicate wind speed measured by a wind speed sensor attached at the nacelle top (nacelle wind speed), electrical power, generator speed, floating platform pitch angle, and blade pitch angle. Figure 7(b) shows the power spectral densities (PSDs) of nacelle wind speed, electrical power, generator speed, floating platform pitch angle, and blade pitch angle. Note that a backward direction of floating platform pitching motion indicates a plus sign direction of floating platform pitch angle. In Figure 7, dotted lines are results without the proposed FVC and solid lines are results with the proposed FVC. Each period for which experiments were executed without and with the proposed FVC was close, and each environmental condition, average wind speed, turbulence intensity, and wave, was similar.

Figure 7.

Experimental results of 200-kW electrical power restriction. Proposed FVC suppresses fluctuation of wind speed, blade pitch angle, floating platform pitch angle, and blade pitch angle. Fluctuation frequency is around 0.039 Hz. (a) Time history and (b) power spectral density.

As indicated by the dotted line in Figure 7(a), without the proposed FVC, the nacelle wind speed, generator speed, floating platform pitch angle, and blade pitch angle oscillate. This oscillation of the floating platform pitch angle is generated by the blade pitch angle motion of the VSC as mentioned above. It is clear that the variation range of floating platform pitch angle (peak to peak) is over 20°. Moreover, vibrations of nacelle wind speed and generator speed synchronize the floating platform pitch angle vibration. This is because the floating platform pitch angle vibration leads to vibration of wind energy input to the rotor.

The dotted line in Figure 7(b) shows that every PSD has peaks around 0.039 Hz. This indicates that the natural frequency of floating platform pitch angle is approximately 0.039 Hz.

The solid lines in Figure 7(a) show that periodic vibrations of wind speed, generator speed, and floating platform pitch angle were suppressed. In Figure 7(b), there is no peak around 0.039 Hz. These results demonstrate that the proposed FVC can reduce the resonance vibration of floating platform pitch angle.

550-kW power restriction

Figure 8 shows the experimental results without and with the proposed FVC under 550-kW power restriction. Figure 8(a) are time histories, and the vertical axes are nacelle wind speed, electrical power, generator speed, floating platform pitch angle, and blade pitch angle, and Figure 8(b) shows PSDs. In Figure 8, dotted lines are results without the proposed FVC and solid lines are results with the proposed FVC. Each average wind speed condition in Figure 8 is approximately 8.3 and 8.7 m/s, respectively. These wind speed conditions are near the rated speed under 550-kW power restriction, and the FOWT operates alternatively above and below rated conditions. Note that each period for which experiments were executed without and with the proposed FVC was close, and each environmental condition, average wind speed, turbulence intensity, and wave, was similar.

Figure 8.

Experimental results of 550-kW electrical power restriction, rated generator speed 2098/min, average wind speed 8.3 m/s without proposed FVC, and 8.7 m/s with proposed FVC: (a) time history and (b) power spectral density.

We can deduce from Figure 8(a) that there exists vibration of floating platform pitch angle in case without the proposed FVC even though the electrical power keeps approximately 550 kW. Although the vibration amplitude decreases with wind speed decrease after 500 s, the vibration amplitude increases after wind speed rises and the vibration continues. In contrast, the proposed FVC can reduce the duration of floating platform pitch angle vibration. The peak-to-peak floating platform pitch angle is still large, but it could be reduced by adjusting FVC parameters. Looking at Figure 8(b), it is clear that the solid lines of nacelle wind speed, generator speed, floating platform pitch angle, and blade pitch angle have lower peaks than those of the dotted lines. These results demonstrate that the proposed FVC can also reduce floating platform pitch angle vibration under 550-kW power restriction.

Figure 9 shows the experimental results without and with the mode change function of the proposed FVC under 550-kW power restriction. Figure 9(a) shows time histories, and the vertical axes are nacelle wind speed, electrical power, generator speed, floating platform pitch angle, and blade pitch angle, and Figure 9(b) shows PSDs. In Figure 9, dotted lines are results without the mode change function and solid lines are results with the mode change function. Each average wind speed condition in Figure 9 is approximately 6.4 and 6.6 m/s, respectively. Note that the frequency of BPF keeps 0.28 rad/s in the experiment without the mode change function, and that each period for which experiments were executed without and with the mode change function was close, and each environmental condition, average wind speed, turbulence intensity, and wave, was similar.

Figure 9.

Experimental results of 550-kW electrical power restriction with FVC, rated generator speed 2098/min, average wind speed 6.4 m/s without mode change, and 6.6 m/s with mode change: (a) time history and (b) power spectral density.

We can deduce from Figure 9(a) that vibrations of electrical power and floating platform pitch angle in case without the mode change occur and continue even though FVC function is activated. In contrast, the results with the mode change function show that electrical power, generator speed, and floating platform pitch angle vibration tend to settle. Looking at Figure 9(b), it is clear that the dotted lines of nacelle wind speed, generator speed, and floating platform pitch angle have peaks around 0.039 Hz, and the peaks around 0.039 Hz of the solid lines are lower than those of the dotted lines. These results demonstrate that the mode change function can also suppress floating platform pitch angle vibration even when an FOWT alternately operates between above-rated and below-rated conditions.

Above-rated conditions

Figures 10 and 11 show the experimental results above rated wind speed. Time histories are shown, and the vertical axes are nacelle wind speed, electrical power, generator speed, floating platform pitch angle, and blade pitch angle. The rated power conditions of Figures 10 and 11 are 500 and 2000 kW, respectively, and those rated generator speed conditions are 1600 and 2098 min⁻¹; each rated wind speed is approximately 7 and 12 m/s, respectively. The average wind speed conditions are approximately 12 and 15 m/s. Note that experiments with the proposed FVC are conducted in order to avoid large loads because the average speed conditions are relatively high and experiments without the proposed FVC may increase maximum and fatigue loads.

Figure 10.

Experimental results of 500-kW electrical power restriction, rated generator speed 1600/min, average wind speed 12 m/s, with proposed FVC.

Figure 11.

Experimental results of 2000-kW electrical power restriction, rated generator speed 2098/min, average wind speed 15 m/s, with proposed FVC.

It follows from Figure 10 that electrical power is kept to 500 kW and generator speed is held to 1600 min⁻¹ without floating platform pitch angle vibration even under the 12 m/s condition, which is higher than Figures 8 and 9. Moreover, as indicated in Figure 11, electrical power is kept to 2000 kW and the generator speed is held to 2098 min⁻¹ without floating platform pitch angle vibration, even under the 15 m/s condition. These results demonstrate that the proposed FVC can also suppress floating platform pitch angle vibration above rated conditions.

Conclusion

In this article, we proposed a mode change function for FVC, which changes control modes according to electrical power, in order to suppress floating platform pitching vibration of an FOWT by adjusting the blade pitch angle in accordance with the floating platform pitch angle signal. Simulation results demonstrated that an optimal combination between the frequency and gain of FVC related to the mode change can suppress the floating platform pitching vibration even below rated conditions. The results of experiments using a full-scale spar-type FOWT showed that the proposed FVC can stabilize the posture of FVC not only under conditions of 200 kW and 550 kW power restrictions, and above-rated but also under conditions that an FOWT alternatively operates between above-rated and below-rated.

Footnotes

Acknowledgements

The experiments in this work were performed using the commercial scale demonstration FOWT project, GOTO-FOWT, of MOE in Japan. The authors thank MOE and the participants for permitting them to use it.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

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