Study on TMD Control on Stability Improvement of Barge-Supported Floating Offshore Wind Turbine Based on the Multi-Island Genetic Algorithm

A floating offshore wind turbine (FOWT) has a great potential in producing renewable energy as offshore wind resource is rich in deep sea area (water deeper than 60 m) where fixed foundations are cost-effective or deployable. However, compared with a fixed-bottom installation, FOWT has to suffer more extreme loads due to its extra degrees of freedom. Therefore, the stability of an FOWT is a key challenge in exploiting offshore deep-water wind. Focusing on the stability of barge-type FOWT, this paper is to investigate the effect of passive structural control by equipping a tuned mass damper (TMD) on the nacelle. The turbulent wind with sharp fluctuations is established both in velocity and inflow direction based on standard Kaimal turbulence spectrum as suggested in the standard IEC61400-2. The irregular wave is generated according to the Pierson-Moskowitz spectrum. The dynamic structural characteristics of FOWT are calculated based on the fully coupled aero-hydro-servo-elastic solver FAST. Evidence has shown that the proposed method of the nacelle-based TMD is effective in controlling stability of an FOWT, as the sway and roll motions of barge and the side-side displacement of tower top decreased significantly. With the increase of mass, the side-side displacement of tower-top and the amplitude of roll motion of barge reveal a trend of increasing first and then decreasing. The stiffness and damping have little effect. Furthermore, the multi-island genetic optimization algorithm (MIGA) is employed to find globally optimum structural parameters (mass, stiffness and damping) of the TMD. The optimum structure parameters of TMD are achieved when the mass is 21393 kg, damping is 13635 N/(m/s) and stiffness is 6828 N/m. By adopting the optimized TMD, stability of roll motion of barge and side-side displacement of tower-top increase up to 53% and 50% respectively when compared with the normal TMD. The simulation results verify the validity and reliability of the proposed TMD control and the optimization methods.


Introduction
With the decrease of onshore wind resources, offshore wind energy is increasingly concerned by countries all over the world due to its high energy density and low turbulence. According to the published GWEC report (GWEC, 2016), 2219 MW of new offshore wind power has been installed globally in 2016 with promising outlooks. And focus has been gradually shifted from land to ocean in the development of the future wind farms (Li et al., 2012;Ding et al., 2017b). At present, offshore wind farms are mainly in-stalled in shallow water zones but often being blamed for its visual and noise impacts. In contrast, deep water areas are more promising with less space constraints and more consistent wind.
Rather than fixed-bottom installations, floating offshore wind turbines (FOWT) have promising potential in terms of feasibility and lower costs when water depth exceeds 60 m. However, further development is urgently needed to facilitate the commercialization of FOWT. One of the key challenges is that FOWT is subjected to wind and wave loads throughout its service life. The coupled wind-wave induced nonlinear platform motion will heavily increase the loads on FOWT due to its high inertial and gravitational forces. Therefore, it is significant to improve the stability of FOWT. So far, different methods have been proposed which can be classified into three different categories.
One approach to improve the stability of FOWT is to adopt the blade pitch control strategy for aerodynamic load reduction. For example, Larsen and Hanson (2007) developed a collective pitch control system for a spar-type FOWT, ensuring the desired natural frequency of control structure lower than the lowest critical tower frequency. Jonkman (2008) proposed several modified collective blade pitch control strategies for a barge-type FOWT, including tower top feedback and controller gain detuning. Namik and Stol (2010) proposed an independent blade pitch strategy for FOWT and investigated its control performance on the platform motion. Fischer et al. (2012) proposed a nonlinear control method based on the acceleration feedback method and theoretically analyzed the stability improvement of FOWT. However, all methods mentioned above requires more blade pitch employment and more complicated control strategies which inevitably increase the fatigue loads of blade-root.
The second method to obtain stability is to improve the structural design of supporting structures. For example, Kim et al. (2014) investigated the effects of interlinked mooring line system on the improvement of hydrodynamic performance of spar-type FOWT. Subbulakshmi and Sundaravadivelu (2016) conducted a numerical study on the effects of heave plate on the heave response of spar-type FOWT. Ding et al. (2017a) proposed application of the helical strakes to the structural design of spar-type FOWT and then investigated the motion reduction effects of helical strakes on the spar-type FOWT. However, those investigations are usually evaluated in terms of rigid body motions, which would generally simplify the upper part, including rotor, hub and nacelle, as a lumped mass. The rigid hypothesis, however, is impossible to reveal the nonlinear dynamic characteristic of the deformation, buckling or even damage of the whole FOWT system under the wind-wave excitation.
Another approach to improve the stability of floating wind turbines (OWT) is structural control, which has been an active research area in civil engineering structures for over two decades (Spencer and Sain, 1997). Because of the successful and wide application of structural control in civil engineering structures, such as skyscrapers and bridges (Stewart andLackner, 2014, Yan et al., 2016), it is also expected to be a promising solution for stability control of OWT. For example, Murtagh et al. (2008) investigated the use of a TMD placed at the tower top of a simplified wind turbine model for vibration mitigation. Colwell and Basu (2009) explored the structural responses of a fixed-bottom OWT with a tuned liquid column damper. Mensah and Dueñas-Osorio (2012) assessed the reliability of this idea. However, those discussions are all about vibration mitigation of fixed-foundation OWT, while their motion characteristics are quite different from that of FOWT. Therefore, some scholars investigated the effects of structural vibration control devices on the FOWT stability improvement. For example, Sethuraman and Venugopal (2013) investigated the efficiency of TMD on the stability improvement of a spar-type FOWT, but it does not consider the external load and its work is only free vibration analysis. Mu et al. (2013) conducted the research on the effects of the TMD on six degrees of freedom motions of a spar-type FOWT. In Yang et al. (2014), a TMD was installed in the tower-top of FOWT and then the vibration characteristic of the tower was explored with the FEM method. Fan (2015) established the motion equation of an active structural control system for a spar-type FOWT under the combined effects of wind, wave, and realized the active control on surge motion of the FOWT by adopting the optimal control linear quadratic methods. Stewart and Lackner (2014) demonstrated that passive control technique is the most suitable method for structure control of FOWT.
From the above review, we can conclude that although plenty of studies aiming at the stability improvement of FOWT have made great achievements either in aspects of aerodynamic load reduction, structural design of platform and mooring line system or structural control devices application, there still exist many deficiencies (1) most of the investigations are based on the structural simplification or the rigid hypothesis which cannot reflect the complex nonlinear structural characteristic of the FOWT system; (2) the effectiveness of structural control is related to the mass system, spring system and damper system, but few studies have paid attention to the optimization of structural parameters, therefore the dynamics inhibition and the stability improvement are unapparent; and (3) much attention, both academically and industrially, has been drawn to fixed-bottom OWT or spar-type FOWT, but little to barge-supported FOWT.
Motivated by those problems and the research potentials, the current study aims to investigate the performance of a passive TMD applied on the barge-supported FOWT to wind-wave induced excitation to improve stability. The turbulent wind is generated by using the standard Kaimal spectrum, and the irregular wave is generated based on P-M spectrum. Considering the coupling effect of aerodynamic and hydrodynamic loads, dynamic structural characteristic of a barge-supported FOWT is then done on the basis of the fully coupled aero-hydro-servo-elastic solver FAST. At last, the Multi-Island Genetic Algorithm (MIGA) is employed to optimize the structural parameters of the TMD system in the hope of providing theoretical references for the research of stability improvement of FOWT.

Research object
In this paper, a barge-supported FOWT is chosen as the research object. Wind turbine is the NREL 5MW wind turbine, whose parameters, including definitions of the aerodynamic, structural, and control-system properties are listed in Table 1. More details can be seen in Jonkman et al. (2009). The platform is ITI Energy barge, of which the properties are summarized in Table 2 and more specifications can be seen in Jonkman (2007). The whole system is shown in Fig. 1.

FAST solver and TMD model
The simulation tool in this paper is NREL FAST (Fatigue, aerodynamics, structures and turbulence), which is a fully coupled aero-hydro-servo-elastic open source solver, which can simulate the loads and performance of horizontalaxis wind turbines (Ding et al., 2016;Yang et al., 2016). The motion equations of FAST are derived by adopting Kane's dynamics. Detailed information could be found in Jonkman (2008). The simulation process of NREL FAST is presented in Fig. 2.
In order to conduct structural control techniques in FOWT, this paper develops the capability to execute structural control techniques by incorporating the TMD system into the FAST. In order to model a TMD system in the wind turbine system, the equations of motion of the TMD system must be derived. It is critical that the additional dynamics of the TMD system are coupled with the original equations of motion of the wind turbine. Dynamic interactions between the TMD system and the wind turbine system are therefore captured. Some assumptions are given as below during the derivation process: (1) the TMD system is located in the na-  celle and translated in the nacelle frame of reference.
(2) position of the TMD as well as the neutral position of the spring is defined relatively to the center line of the tower top.
(3) rotational effect of the TMD system is neglected.
With the above-mentioned assumptions, the equations of the TMD system are derived, coupled with those of the original FAST. Detailed steps to derive the TMD equations of motion are given as follows: (1) Derive the kinematic expressions for the position, velocity and acceleration of the TMD system in the nacelle frame of reference.
(2) Derive the partial velocity vectors for the TMD system, which are used in Kane's dynamics.
(3) Based on the aforementioned steps, derive the kinetics of the TMD system. (4) At last, derive the full time-domain motion equations of the whole wind turbine system with TMD system equipment by adopting the kinetic expressions for the TMD. All the above-mentioned motion equations take the same general form as the original FAST, but the only difference is the additional DOFs due to the equipment of the TMD system. Because the general form is preserved, the same time marching solving technique that FAST adopts could be used to calculate the newly developed set of motion equations. The schematic of TMD equipped in the nacelle is presented in Fig. 3.
The TMD system is at the bottom of the nacelle, which consists of a mass system, a spring system and a damping system. The whole system can be seen in the picture. By changing its own mass or stiffness, the TMD achieves the purpose of adjusting the natural vibration frequency, so that it approaches the natural frequency or external excitation frequency of the vibration-damped structure when the structure is external. When the vibration is generated under excitation, the TMD will be driven, and the tuned inertia force generated by the TMD will react to the structure, and the energy will be dissipated through the damping system to achieve the purpose of structural stability control. Fig. 4 presents the structure and principle of the TMD. The principle of the equation of motion of the TMD system takes the following form: (1) where, X is the displacement of the support system, x is the displacement of the TMD, d is the damping of the TMD, k is the stiffness of the TMD, K is stiffness of the support system, M is the mass of the support system, m is the mass of the TMD, and f(t) is the external load.

Turbulent wind and irregular wave
4.1 Establishment of the turbulent wind In order to investigate the structural dynamics of FOWT under the effect of turbulent wind, establishment of the turbulent wind with fluctuations both in time and space is the first problem to be solved. The three-dimensional turbulent wind is established based on the stochastic, full-field turbulent wind simulator -Turbsim, which allows the user to select a turbulence spectra model from default models or apply a numerical user-defined turbulence spectrum and produces a 3D wind flow field with wind fluctuations governed by the spectra model. Referring to Fig. 5, the fixed, two-dimensional vertical rectangle wind field is set to 195 m (in horizontal direction) ×195 m (in vertical direction), with the hub center as the reference center. The wind field is discretized by setting the grid node to 15×15. Considering both spatial coherence and wind shear (IEC, 2005), wind speed distribution of every grid is generated by applying inverse Fourier transform to Kaimal turbulent spectrum. The IEC turbulence intensity is level A and the Kaimal spectrum is shown in Eq. (3): where f is the frequency (Hz), V represents the mean wind speed at hub height (m/s), is the standard deviation, and is the integral scale parameter of each velocity compon-ent, according to IEC 61400-3 standard. The reference average wind speed at hub center is 11.4 m/s, the whole simulation time is 600 s. The established three-dimensional turbulent wind field at the hub height is presented in Fig. 6. Besides, three components, namely u, v, w, of wind speed in the hub center are also shown in Fig. 6.

Wave spectrum and establishment of irregular wave
At present, the common wave spectrums include P-M spectrum, Jonswap spectrum and Brinell spectrum etc. . As one of the simplest spectra which are widely used, the P-M spectrum is an empirical relationship between the energy distribution and the frequency of the irregular wave. The energy density of wave in the P-M spectrum is defined by Eq. (4) where, S(ω) is the wave density (m 2 /Hz), ω is the wave frequency (Hz), T z is the cross zero period (s), and H s is the significant wave height (m). Fig. 7 represents a typical energy density distribution when the significant wave height is 5 m and the cross zero period is 12.4 s, respectively. For a certain spectrum, the time history of irregular wave can be generated by line su-perposition of harmonic wave components, which can be seen in Fig. 8.

Effects of TMD on 6-DOFs motions of platform
According to the Den Hartog principle (Den Hartog, 1956), structural parameters of the TMD, including mass, spring stiffness and damping, are 20000 kg, 10000 N/m and 50000 N/(m/s), respectively. The 6-DOFs motion time series of platform is presented in Fig. 9. Dynamics of original platform are also shown here for comparison. It can be seen from Fig. 9 that platform motions in sway, roll and yaw DOFs are inhibited significantly under the structural control of TMD, while platform motions in surge, heave and pitch DOFs can be neglected. Range of sway motion is inhibited from -1.03~1.12 m to -0.65~0.85 m, the fluctuation range is reduced by around 30%. In pitch DOF, motion  range is inhibited from -1.11°~1.38° to -0.54° ~0.88°, the fluctuation range is reduced by about 40%. Although the trend of roll motion has been changed greatly after configuration of TMD, changes of motion amplitude can be neglected. Furthermore, it can be concluded from the calculation that the standard deviation of sway motion of the platform is 0.477 and 0.352 respectively before and after the configuration of TMD, therefore the stability of platform in sway DOF is improved by around 25%, while for yaw DOF, the standard deviation is 0.492 and 0.289 respectively and the stability of platform increases about 40%. According to above analysis of the 6-DOFs motions of the platform in time domain, we can conclude that motion inhibition effects of TMD in surge, heave, pitch and yaw DOFs are not obvious. Therefore, we here only present the frequency analysis results of yaw and roll motion by way of fast Fourier transform for its time series, which can be seen from Fig.  10, where the x-axis and y-axis represent the frequency and the motion amplitude respectively. Referring to Fig. 10, peak frequency of the platform in sway and yaw DOFs is 0.01 Hz and 0.09 Hz respectively. And inhibition of TMD to the sway and yaw motions is more remarkable when it is around the peak frequency than in the rests frequency section, which cannot be neglected.

Effects of TMD the dynamics of the tower top
Under the structural control of TMD, the time histories of tower top displacements in the fore-aft and side-side directions are shown in Fig. 11, where x-axis and y-axis represent the time and displacement of tower top respectively. Similar to the platform motion case, the dynamics of tower top without TMD configuration are also presented here for better comparison. It can be observed from Fig. 11 that the range of tower top fore-aft displacements keeps lying between -0.8~1 m before and after the configuration of TMD, which indicates that TMD has little effects on the  fore-aft displacement. Contrary to the fore-aft case, both range and amplitude of the side-side displacement of tower top are inhibited by TMD significantly. The standard deviation calculation results of the time series of tower top sideside displacements are 0.066 and 0.041 respectively, from which we can conclude that the stability of the tower in side-side direction is improved by almost 38%. Besides, tower top displacements characteristic in frequency domain are obtained by fast Fourier transform, which can be seen in Fig. 12, of which the x-axis and y-axis represent the fre-quency and the displacements respectively. As can be seen from Fig. 12, the peak frequency of fore-aft displacement is around 0.75 Hz, while it is 0.08 Hz for side-side displacement. Both the fore-aft and side-side displacements are inhibited under the structural control of TMD. However, the inhibition effect of TMD for the side-side displacement is more significant than that of fore-aft displacement, which can be neglected when compared with the former. Besides, it also can be found that TMD would change neither the peak frequency nor the trend of tower top displacement in frequency domain.

MIGA and optimization of structural parameters of TMD
6.1 MIGA From the above analysis, we can conclude that configuration of TMD would inhibit the dynamics and thereby improve the stability of the FOWT. However, a typical TMD system contains mass system, stiffness system and the damper system, which indicates that the change of the structural parameters, namely mass, stiffness and damping, would all influence its inhibition effect on the dynamics of the FOWT. Besides, the Den Hartog principle, which is widely used in the civil engineering, may not be suitable for the definition of the structural parameters of TMD in this paper, because the dynamics of modern wind turbine are rather different from those of the civil engineering structures. Therefore, it is of great importance to investigate the optimal combination of TMD structural parameters for safe operation of FOWT. The Multi-Island Genetic Algorithm (MIGA) (Zhou and Sun, 1999) was chosen as the optimization method. Since it is highly versatile in handling the optimization of multi-modal functions, in MIGA, the population is divided into several subpopulations staying on isol-ated "islands", whereas traditional genetic algorithm operations are performed on each subpopulation separately. A certain number of individuals between the islands migrate after a certain number of generations. Hence, MIGA can prevent the problem of "prematurity" by maintaining the diversity of the population. In addition, the calculation speed of MIGA can be higher than that of traditional genetic algorithm. The calculation flow chart of MIGA is shown in   In this paper, the objective function of MIGA is to minimize the sum of the standard deviation of the tower top side-side displacement and the platform sway motion . Besides, the constraints condition is shown as follows: It can be seen from Figs. 14 and 15 that the standard deviation increases initially and decreases afterwards with the increasing mass of TMD, and it is small when the mass of TMD is in the range of 15000 -25000 kg. Thus, the sectional view of Fig. 15 having a mass range of 15000-25000 kg is partially refined, as being represented in Fig. 16. It can be observed from Fig. 16, the standard deviation exceeds the minimum when the mass is in the range of 18695-22935 kg. Besides, the variation of standard deviation to the stiffness k of TMD is not obvious when the damping d keeps constant, which may indicate that stiffness changes have little impact on the standard deviation . Furthermore, when the stiffness is constant, standard deviation changes obviously only when the damping d is in the range of 12000-17000 N/(m/s). 17 and 18 that the standard deviation first increases and then decreases with the growth of the mass of TMD, and it is small when the mass of TMD is in the range of 20000 -30000 kg. Therefore, we refine the sectional view of Fig.  17 having a mass range of 15000-25000 kg, as shown in Fig. 19. It can be observed from Fig. 19, the standard deviation reaches the minimum when the mass is in the range of 18315-25905 kg. Besides, the variation of standard deviation to the stiffness k of TMD is not obvious when the damping d keeps constant, which may indicate that stiffness changes have little effect on the standard deviation . Furthermore, when the stiffness is constant, standard deviation changes obviously only when the damping d is in the range of 12000-17000 N/(m/s). The best combination of TMD structural design parameters obtained by the calculation based on the MIGA is shown in Table 3, which is consistent with the above analysis. The mass of the TMD system is about 21393 kg, according to Table 1 and Jonkman et al. (2009), parameters of the NREL 5MW wind turbine. The mass of the nacelle is about 240000 kg, and the mass of the rotor is about 110000 kg, so the mass of the TMD system only accounts for 5% of the nacelle system. Besides, the TMD is normally made of iron, so its volume is about 2.7 m 3 , and dimensions of nacelle of the DOWEC 6MW wind turbine is about 22.8 m (length)×2.28 m (width)×3.5 m (height) (Kooijman et al., 2003). Therefore, its volume is about 114 m 3 . We assume the volume of nacelle of the NREL 5MW wind turbine is about 80 m 3 , so the volume of TMD only accounts for 3.3% of the nacelle system. Therefore, enough space is available DING Qin-wei et al. China Ocean Eng., 2019, Vol. 33, No. 3, P. 309-321 317 to the installation of the TMD.
6.3 Verification of optimized results of TMD In order to verify the reliability of the MIGA as well as the accuracy of optimization results, we here reconfigure the structural parameters according to the optimized results above. The dynamics of FOWT are then recalculated, with the results shown in Fig. 20, where the x-axis represents time, and y-axis represents roll motion and tower top sideside displacement. Besides, we only show the results between 300 s and 600 s for a better and clearer display.
For the platform roll motion, it can be seen from Fig. 20 that roll motion is inhibited obviously under control of TMD, and the inhibition effect is better than the original TMD control which is defined according to the Den Hartog principle.
Under control of the optimized TMD, the range of roll motion is reduced to -0.49°~0 85°. The standard deviation of the roll motion time series under control of the optimized TMD is about 0.23, which is smaller than 0.289 of original TMD control and 0.492 without TMD configuration. There-fore, it can be concluded that the stability of roll motion is improved by about 53%.
In view of the tower top side-side displacement, according to Fig. 20, it is suppressed significantly under the control of optimized TMD, which is similar to the platform roll motion case, and its range is reduced to -0.153~0.071 m. The standard deviation of the tower top displacement series is about 0.034, which is also smaller than 0.041 of the original TMD control and 0.0662 without TMD configuration. The stability of tower top side-side displacement increases by about 50%. Thus, it can be concluded that the optimized TMD has a more remarkable control effect on the stability improvement of the platform roll motion and the tower top side-side displacement. To sum up, the calculation results and the analysis verify the effectiveness of the optimization method, the optimization algorithm and the accuracy of the calculation result presented in this paper.

Tower-top and tower-base shear force and bending moment
The tower-top shear force and the bending moment time series both in side-side and fore-aft direction are presented in Fig. 21. According to Fig. 21, after configuration of the TMD, tower top side-side shear force is reduced slightly, while fore-aft shear force is reduced significantly. With the optimized TMD, the standard deviation of the tower top side-side shear force is reduced by 1.57%, while the standard deviation of the tower top fore-aft shear force is reduced by 34.52%. Regarding tower top bending moment, after configuration of the optimized TMD, the tower top side-side bending moment is increased, but the increase isn't significant at all, while the tower top fore-aft bending moment is almost unchanged. The tower-base shear force and the bending moment time series in side-side and fore-aft directions are presented in Fig. 22. As shown in Fig. 22, after configuration of the TMD system, standard deviations of tower base side-side and fore-aft shear force are reduced by 5.72% and 38.5%, respectively. In view of the tower base bending moment, both the side-side and fore-aft bending moment are reduced, while the side-side bending moment is reduced significantly. The standard deviation of the side-side and fore-aft bending moments are reduced by 36.69% and 3.69%, respectively.

Platform 6-DOFs motions in time domain under the typical sea condition based on the South China Sea
In order to better understand the effect of the TMD device, another group investigation was conducted. The environmental conditions are set based on the typical South China Sea conditions (Yang, 2013). Specifically, the significant wave height is about 3 m, the cross zero wave frequency about 8.8 s, and the average wind speed around 9 m/s. Under the typical sea conditions, 6-DOFs motion time series of the platform with the optimized TMD installation is presented in Fig. 23, where x-axis and y-axis stand for time and displacement respectively. Dynamics of original barge type FOWT are also shown here for comparison. According to Fig. 23, it can be seen that under the typical sea conditions in the South China Sea, the 6-DOFs motion re-sponse of the platform is smaller than that of the previous study of the sea state when compared with the results in Fig. 9. Besides, TMD has played a different role in controlling the motion response of the platform at different degrees of freedom. Among them, it has little control over the sway and heave motions of the platform, while it plays a good role in controlling the surge, roll, pitch, and yaw motions. It can be concluded that under typical sea conditions, TMD also improves the stability of the platform.

Conclusions
In this paper, the structural control is proposed to improve the stability of barge type FOWT by equipping a TMD on the nacelle. The turbulent wind is established based on the standard Kaimal spectrum. And the irregular wave is generated by the P-M spectrum. Considering the coupled effects of wind and wave load, the dynamics of the FOWT are investigated based on the aero-hydro-servo-elastic solver FAST. Besides, the MIGA is employed to find a globally optimum structural parameters (mass, stiffness and damping) of the TMD. According to the numerical results, the following main findings are summarized.
(1) The TMD is effective on stability control of FOWT. Sway and roll motion of barge and side-side displacement of tower top decrease significantly. The stability of roll motion increases by about 40%, while the stability of tower top side-side is around 38%.
(2) With the increase of mass, both side-side displacement of tower-top and platform roll motion show a trend of first increasing and then decreasing, while the stiffness and damping have little effect.
(3) The optimum structure parameters of TMD are as follows: the mass is 21393 kg, damping is 13635 N/(m/s) and stiffness is 6828 N/m. Stability of platform roll motion and side-side displacement of tower-top increase up to 53% Fig. 22. Tower base shear force and bending moment.