Motion Analysis of International Energy Agency Wind 15 MW Floating Offshore Wind Turbine under Extreme Conditions

Abstract

In recent years, ultra-large-scale offshore wind turbines have attracted widespread attention. However, accurately evaluating the motion responses of offshore wind turbines under extreme conditions, especially for semisubmersible floating off-shore wind turbines, is often challenging. In order to assess the operational behavior of wind turbines under wind and wave loads, this paper adopted a numerical analysis method to solve the motion responses under extreme conditions. It specifically examines the motion responses of the IEA 15 MW wind turbine in terms of surge, heave, and pitch direction, focusing on environmental loads that occur once every 50 years. The results show that the wind turbine can still operate normally under the Ultimate condition. However, the average amplitude increased by 7% in the pitch direction and decreased by 4% in the heave direction compared to the rated condition. Under extreme conditions (occurring once every 50 years), with the wind turbine parked, the average amplitude in the surge direction reduced by 33%, while the average amplitude in the pitch direction reduced by 106%. Thus, it is essential to pitch the blades and brake the generator in extreme environmental conditions to ensure the safety of the wind turbine.

1. Introduction

At the 80th Marine Environment Protection Committee (MEPC 80), governments adopted the IMO’s revised greenhouse gas (GHG) strategy [1]. And the objective is to reach net-zero GHG emissions from international shipping close to 2050. Offshore wind energy, especially offshore wind turbines, has attracted considerable attention in power and renewables [2]. According to DNV’s Energy Transition Outlook 2023, the installed global floating offshore wind capacity will have grown from today’s 200 MW to almost 270 GW by 2050. The floating offshore wind turbine (FOWT) has a large structure and size, and the structural motion response is complex. In order to study the dynamic responses of the wind turbine, researchers have conducted a series of studies using coupling analysis software, aiming to accurately assess the characteristics of the structure.

In as early as 2005, the National Renewable Energy Laboratory (NREL) developed the popular 5 MW Reference Wind Turbine (RWT) [3], followed by the Technical University of Denmark’s (DTU) 10 MW RWT [4]. The NREL, using numerical simulation and model experiment methods, developed the OC3-Monopile and OC4-DeepC platforms to support the 5 MW RWT [5,6]. Meanwhile, a braceless steel platform was designed by the Norwegian Research Centre for Offshore Wind Technology to support the 5 MW Reference Wind Turbine (RWT) [7]. It consists of a central column, three side columns, and three pontoons; it was developed using numerical analysis methods. Additionally, the NAUTILUS-10 floating substructure [8] was provided by the LIFE 50+ project to support the DTU 10 MW RWT. In Japan, the FORWARD Semi-Sub 2 MW FOWT and V-shape Semi-Sub 7 MW FOWT have been developed and installed on a four-column floating platform [9,10]. An 8.4 MW wind turbine has been designed for installation on the WindFloat platform as part of the WindFloat Atlantic (WFA) project [11]. A concrete multi-column floating platform has been conceptually designed by Yokohama National University [12]. Moreover, several barge-type platforms have been designed and experimented with to support wind turbines [13,14]. With the development of deep water turbines and large turbines, elevated requirements are put forward for the stabilization of the floating wind turbines. When the wind turbines are operated under extreme conditions, they are a highly nonlinear system under floating body motions and extreme wave–structure interactions. The motion characteristics of the whole offshore wind structures are crucial for the generation of power, as well as their safety.

Yang et al. [15] developed a coupling framework based on FAST and AQWA through modifications on source codes of the user_force.dll of AQWA, obtaining the motion of multi-body platforms under the action of wind and waves. The framework has the ability to simulate multi-body platforms and to observe unique results, which contrasts with traditional tools. Guo et al. [16] developed a multibody modeling framework, namely TorqTwin. The framework can predict the motion response of the floating platform by calling on the source code of OpenFAST through Python library. However, the portability of the code is limited. Domene et al. [17] incorporated a direct air capture (DAC) system into the IEA 15 MW Reference Wind Turbine, analyzed the motion response, and compared it to the initial design. Chen et al. [18] used a coupling analysis software based on OrcaFlex to conduct a time domain simulation for 15 MW RWTs. The analysis considered three frequency regions (low frequency, wave frequency, and high frequency) and revealed that the tension response of the mooring line would be significantly affected by high-frequency motions originating from the superstructure. Using the computational fluid dynamics (CFD) method, Xue et al. [19] utilized the FOWT-UALM-SJTU solver to calculate the motion response of OC4 FOWT under different wave conditions and found that wind turbines with larger initial inclination angle recovered faster. Tran et al. [20] used CFD to analyze the motion responses of the OC4 semisubmersible FOWT based on an overset grid technique, and found that the motion of the floating platform has good consistency compared with the calculation results of FAST. Xu et al. [21] conducted a secondary development based on OpenFAST, analyzed the dynamic response of an FOWT in different stages of typhoon transit, and found that yaw errors would lead to an increased mooring load. Guo et al. [22] conducted an experimental study based on a 12 MW semisubmersible floating wind turbine, obtaining its motion and mooring response, and found that the motion response and mooring tension in the 60° and 90° directions were greater than those in the 0° direction. Xiang et al. [23] discussed the influence of different mooring lengths and counterweights on the motion response of semisubmersible wind turbines, and found that the motion of the floating platform in the pitch direction was affected. Zhang et al. [24] used different mooring models to compare the motion performances and mooring tension of FOWTs, and found that the quasi-static method still has a better calculation accuracy in most cases, but the finite element method is more suitable for fatigue calculations. Lozon et al. [25] conducted a dynamic analysis of shared mooring for floating wind farms and found that shared mooring does not cause an increase in dynamic response. Gao et al. [26] discussed the differences in the dynamic responses of FWOTs when the platform is considered as either rigid or flexible. The results show that accounting for the flexibility of the tower and platform leads to a significant increase in both the motions in the pitch direction and the tower-base force. Huang [27] constructed a shell-based Finite Element Model (FEM) to simulate motion responses under seismic loads, and demonstrated the flexible foundation of FOWTs presents a lower stress. Rinker et al. [28] compared the aeroelastic responses from HAWC2 and OpenFAST for the IEA 15 MW RWT and found that the aerodynamic loads agree quite well. Most recently, the IEA 22 MW ultra-large-scale RWT and a floating platform have been designed in IEA Wind TCP Task 55 [29]. While some significant and useful conclusions have been obtained, these studies are inadequate for understanding the motion responses of ultra-large-scale floating wind offshore turbines (FWOTs) under extreme conditions. Therefore, it is necessary to conduct a more in-depth analysis of wind turbine motion responses in extreme conditions.

In the present work, a classical semisubmersible floating offshore wind turbine, which consists of four columns, a heave plate, and three catenary chain mooring lines, developed by the International Energy Agency is studied. The hydrodynamic and motion characteristics under extreme conditions are crucial. The main focus is to utilize a software tool to predict the motion characteristics of floating offshore wind turbines and the hydrodynamic forces excited by highly nonlinear environmental loads.

The remainder of this paper is organized as follows: Section 2 describes the methodology, while Section 3 presents the model data of the FOWTs. In Section 4, the wind and wave loads utilized in the simulation are discussed, and a comparison with the results of the free decay is made to demonstrate the accuracy of the model. The results are presented in Section 5. Finally, the conclusions are drawn in Section 6.

2. Methodology

2.1. Dynamical Equation of FOWTs

Influenced by aerodynamic load, hydrodynamic load, and mooring load, the FOWT is a complex rigid–flexible coupled dynamic system. When coupled with wind and waves, its equation of motion in the time domain can be expressed as follows:

$$\left(M+M_A\right)\ddot{x}+\left(B_R+B_V\right)\dot{x}+\left(K_S+K_M\right)x=F_{Wave}+F_{Wind}+F_{Mooring}$$

(1)

where $M$ is the mass matrix of the structure; $M_A$ is the added mass matrix of the platform at infinite frequency; $B_R$ is the radiation damping matrix; $B_V$ is the viscous damping matrix; $K_S$ is the hydrostatic stiffness matrix; $K_M$ is the mooring stiffness matrix; $x$, $\dot{x}$, and $\ddot{x}$ are, respectively, the displacement, velocity, and acceleration of each DOF; $F_{Wave}$ is the wave load; $F_{Wind}$ is the aerodynamic load; and $F_{Mooring}$ is the mooring load.

2.2. Aerodynamic Loading

The most widely used methods for the aerodynamic load calculation of FOWTs are Blade Element Momentum (BEM), free vortex wake (FVW), and computational fluid dynamics (CFD) methods. In OpenFAST, BEM is utilized to primarily calculate the aerodynamic loads. The basic process of BEM involves calculating the thrust and torque of the wind turbine using momentum theory and blade element theory, respectively. Then, the induction factor and the actual angle of attack of the blade can be solved. According to the blade element theory, the force on a certain blade element of the wind turbine can be solved as follows:

$$dT=B\frac{1}{2}\rho V_{total}^2(C_l\cos \phi +C_d\sin \phi )cdr$$

(2)

$$dQ=B\frac{1}{2}\rho V_{total}^2(C_l\sin \phi -C_d\cos \phi )crdr$$

(3)

where $dT$ and $dQ$ are, respectively, the thrust and torque on the unit blade element; $B$ is the number of blades; $\rho$ is the density of air; $V_{total}$ is the relative speed of air flow over the blade; $C_l$ and $C_d$ are, respectively, the lift coefficient and drag coefficient; $\phi$ is the angle of indraft; $c$ is the chord length of blade element; and $r$ is the extension radius of the blade element.

After calculating the initial aerodynamic performance through the BEM method, the Generalized Dynamic Wake (GDW) model is used to further accurately calculate the aerodynamic loads in OpenFAST. And the GDW model is based on the Pitt–Peters–He acceleration potential method.

2.3. Hydrodynamic Loading

Hydrodynamic load calculation methods of FOWTs include the potential theory and the Morison equation, and sometimes a combination of the two methods is used. The potential theory is primarily suitable for large-scale components with a structural characteristic size-to-wave wavelength ratio greater than 0.2. The Morrison equation is applicable to structures with a ratio of structural characteristic size-to-wave wavelength of less than 0.2, and it is commonly used in the calculation of slender and small-scale components such as cross bracing, diagonal bracing of floating foundations, and mooring cables.

The potential theory assumes that the fluid is an ideal fluid and defines the velocity potential of the fluid in an irrotational flow field. The Laplace equation and the corresponding boundary conditions of the velocity potential are as follows:

$$\phi (X)={\phi }_I+{\phi }_D+\sum _{j=1}^6{\phi }_R$$

(4)

$${\mathsf{\partial }}^2\phi /\mathsf{\partial }{x}^2+{\mathsf{\partial }}^2\phi /\mathsf{\partial }{y}^2+{\mathsf{\partial }}^2\phi /\mathsf{\partial }{z}^2=0$$

(5)

$$\mathsf{\partial }\phi /\mathsf{\partial }z=0$$

(6)

$$\left(\mathsf{\partial }\phi /\mathsf{\partial }\phi \right)g^2+{\mathsf{\partial }}^2\phi /\mathsf{\partial }{t}^2=0$$

(7)

$$\mathsf{\partial }\phi /\mathsf{\partial }n=0$$

(8)

where $\phi (X)$ is the velocity potential function; ${\phi }_I$ and ${\phi }_D$ are, respectively, the incident potential and the diffraction potential function; ${\phi }_R$ is the radiation potential function; $z$ is the depth of water; and n is the normal vector on the surface of a floating structure.

Morison’s equation defines the wave force on a structure as the sum of the drag force and the inertial force, as follows:

$$\mathrm{d}{F}_H=\frac{1}{2}{C}_D\rho D{u}_x|u_x|\mathrm{d}z+C_M\rho \frac{\pi D^2}{4}\frac{\mathsf{\partial }{u}_x}{\mathsf{\partial }t}\mathrm{d}z$$

(9)

where $C_D$ is the drag force coefficient, $\rho$ is the density of the fluid, $D$ is the diameter of the member, $u_x$ is the incoming flow velocity in the vertical direction of the structure axis, and $C_M$ is the inertia coefficient.

2.4. Mooring Loading

The quasi-static method, lumped-mass method, and finite element method are often used to calculate the mooring loads. In this paper, the lumped-mass method is used to calculate the mooring load.

The mooring cable is divided into a number of spring–mass–damping systems in the lumped-mass method. Parameters such as mass, gravity, and buoyancy are concentrated on the nodes. The lower end of the first segment is connected to the anchor, and the upper end of the nth segment is connected to the platform. The equilibrium equation of the mooring system can be described as follows:

$$M_i{a}_i=F_{Ti}-F_{Ti-1}+F_{Di}+F_{Ai}-W_i$$

(10)

$$F_{\mathrm{DN}i}=\frac{1}{2}\rho C_{\mathrm{DN}}D{u}_{\mathrm{N}}\left|u_{\mathrm{N}}\right|$$

(11)

$$F_{\mathrm{DT}i}=\frac{1}{2}\rho C_{\mathrm{DT}}(\pi D)u_{\mathrm{T}}\left|u_{\mathrm{T}}\right|$$

(12)

$$F_{\mathrm{A}i}=\rho C_{\mathrm{M}}V(-a_i)$$

(13)

where $a_i$ is the acceleration of node $i$; $M_i$ is the mass of node $i$; $W_i$ is the gravity of node $i$; $F_{Ti-1}$ and $F_{Ti}$ are, respectively, the tension generated by two elements connected by node $i$; and $F_{Ai}$, $F_{Di}$, and $F_{\mathrm{DT}i}$ are, respectively, the fluid inertia force, normal resistance, and tangential force of node $i$.

2.5. Process of Analysis

For the motion analysis of floating offshore wind turbines, the hydrodynamic model of structure is established in ANSYS-AQWA (ANSYS, 2022 R2), as indicated by the orange part in Figure 1.

The VolturnUS-S semisubmersible platform is used in the calculation, excluding the upper wind turbine structures and mooring cables. Basic parameters, based on the platform’s physical characteristics, are provided, and different incident wave periods are set for the analysis. After solving, an ASCII-formatted hydrodynamic database is generated. The database includes the hydrostatic stiffness matrix, additional mass matrix, radiation damping matrix, and wave excitation force of the structure at the different incident frequencies. These matrices can be programmatically converted into WAMIT format. Subsequently, the hydrodynamic coefficients are transferred to the next stage.

It is worth mentioning that the viscosity of the fluid plays an important role on the calculation [30]. Therefore, the viscous effects of the fluid are taken into account, and details about the viscous damping matrix can be found in another paper [31].

Subsequently, aerodynamic loads, hydrodynamic loads, structural flexibility, and the servo control system are all taken into account in OpenFAST(v3.4.1), as shown in Figure 1. This is another important part during the motion analysis process. OpenFAST is a typical aero-hydro-servo-elastic coupling framework and uses Kane’s method to solve the equations [32]. It takes into account the impact of the control system, and the solution results are more realistic [33]. Additionally, the finite element method (FEM) is utilized to account for the elasticity of the structure. The FWOT is calculated as a coupled system and the structural motion responses can be obtained.

3. Model Data

3.1. Description of the Floating Offshore Wind Turbine

The International Energy Agency (IEA) defines the 15 MW RWT with the aim of assisting researchers in exploring new technologies or design methodologies. This horizontal axis turbine, featuring three blades, is mounted on the VolturnUS-S semisubmersible platform. And the VolturnUS-S semisubmersible platform was designed by the University of Maine (UMaine).

Table 1. Parameters of the IEA 15 MW Reference Wind Turbine.

Parameter	Unit	Value
Number of blades	[pcs]	3
Rotor diameter	[m]	242
Cut-in wind speed	[m/s]	3.0
Rated wind speed	[m/s]	10.6
Power rating	[MW]	15
Hub height	[m]	150
Cut-out wind speed	[m/s]	25.0
Maximum rotor speed	[rpm]	7.6

presents the key parameters of the IEA 15 MW Reference Wind Turbine.

As depicted in Figure 2a, the platform comprises four columns and the heave plate is designed at the bottom to improve the performance in the heave direction. The plat-form is designed with center symmetry, and the wind turbine is arranged on the central column. The dimensions of the hull are given in the technical report [34] and the platform properties are shown in

Table 2. Parameters of the Maine VolturnUS-S semisubmersible platform.

Parameter	Unit	Value
Overall platform mass	[t]	17,854
Displaced water volume	[m3]	20,206
Draft (with mooring system)	[m]	20
Center of mass below SWL	[m]	14.94
Center of buoyancy below SWL	[m]	13.63
Platform roll inertia about center of mass	[kg m2]	1.251 × 1010
Platform pitch inertia about center of mass	[kg m2]	1.251 × 1010
Platform yaw inertia about center of mass	[kg m2]	2.367 × 1010

.

3.2. Description of Mooring System

The arrangement of the mooring system is shown in Figure 2b. The mooring system, designed for a water depth of 200 m, consists of three catenary chain mooring lines, with a horizontal angle of 120° between two chains. The diameter of each mooring line is 185 mm, with a length of 837.6 m, and the fairlead is designed at a depth of 14 m below the SWL. Unfortunately, the chain is designed for strength based on the displacement boundaries (with a peak surge-sway offset of under 25 m), and fatigue strength was not studied. The properties of the mooring system are summarized in

Table 3. Parameters of the mooring system.

Parameter	Unit	Value
Effective diameter of the chain	[mm]	185
Unstretched mooring line length	[m]	837.6
Fairlead depth below SWL	[m]	14
Anchor depth below SWL	[m]	13.63
Extensional stiffness EA	[N]	3.27 × 109

.

4. Loads and Model Verification

4.1. Load Case

The wind and wave loads are designed based on the joint probability function, and current load is not considered in the analysis.

Table 4. Design Load Case matrix for the IEC 15 MW wind turbine.

DLC	Name	Turbulence Mode	Wind (m/s)	Wave Condition		Controller
				Hs (m)	Tp (s)
1	Operational 1	NTM	10.00	1.54	7.65	AC
2	Ultimate 1	NTM	10.00	8.10	12.80	AC
3	Extreme	EWM 50 year	42.50	10.70	14.20	Parked

presents the selection of representative Design Load Cases (DLCs). The two-parameter JONSWAP spectrum is utilized to describe the waves [35], incorporating significant wave height (H_s) and wave spectrum peak period (T_p), with wind speed values in Table 4 representing the mean speed at hub height. Turbulent wind conditions are assumed in all scenarios, with the wind spectrum model defined as the IEC Kaimal spectral model. The Normal Turbulence Model (NTM) is adopted in DLC 1-2, while the Extreme Wind Speed Model (EWM), occurring once in 50 years, is utilized in DLC 3. The wind class is set as Class A, and turbulent intensity factors and other parameters can be found in IEC 61400-3 [36]. And the time history curve of wind speed and wave height are shown in Figure 3. In Figure 3, the relationships between time and wave height, as well as time and wind speed, are intuitively illustrated. The wave conditions in DLC 2 and 3 are significantly more severe compared to in DLC 1. Additionally, the wind speed under extreme conditions is approximately four times higher than that under the other conditions.

DLC 1 is the rated working condition, with a 10 m/s wind speed and a 1.54 m wave height. It is used as a reference for comparison. For the DLC 2, the wind speed and wave height (H_s) increases a lot, and it is used to simulate Ultimate conditions. The DLC 3 corresponds to the once-in-50-year wave conditions. Under this extreme condition, the wind turbine is parked and the blades are feathered, while in other cases, wind turbine operation is actively controlled (AC).

4.2. Free Decay Test

By applying initial boundary conditions in each direction of the structure, the natural frequency of the rigid-body modes of the system can be obtained [37]. The vibration frequency of the structure obtained through free decay testing is independent of the initial conditions. It is solely determined by the inherent characteristics of the system. The natural frequency of surge and sway is the same, and roll and pitch are also the same. Therefore, only the calculation results in the surge, heave, roll, and yaw directions are listed, as shown in Figure 4 and

Table 5. Rigid-body natural frequencies.

Natural Frequency [Hz]	Surge	Sway	Heave	Roll	Pitch	Yaw
Present	0.008	0.008	0.050	0.035	0.035	0.012
Reference [34]	0.007	0.007	0.049	0.036	0.036	0.011

.

In Figure 4a, the time history curve of free decay shows a period of around 130 s in the surge direction, and its natural frequency is shown to be 0.008 Hz in the frequency domain in Figure 4e. In general, the free heave motion of the structure can also be used as part of the model’s validation [38]. And the period of the heave motion is approximately 20 s, corresponding to a natural frequency of 0.05 Hz in the heave direction, as shown in Figure 4b,f. Similarly, in Figure 4c,g, the period is around 30 s, and the natural frequency is 0.035 Hz in the pitch direction. In Figure 4d,h, the period is around 80 s, and the natural frequency is 0.012 Hz in the yaw direction. Comparison with the results from the reference [34] reveal a close consistency. The errors are all not greater than 0.001 Hz, which means the results are in good agreement with the reference data. Therefore, the constructed model is validated.

5. Results and Discussion

In this section, the motion characteristics, nacelle acceleration responses, and mooring forces of the IEA 15 MW Reference Wind Turbine are studied under different wind and wave combination conditions.

5.1. Motion Responses

The motion responses under different conditions are calculated and the simulation time is set to 3500 s. Then, the influence of different conditions on the motion response is obtained. Figure 5 shows the time history curve of the pitch, heave, and surge motions of the floating platform under different conditions. It can be seen from Figure 5 that the surge and sway motion are the main motion forms.

Transient effects can be observed in approximately the first 200 s and are not significant in the heave direction. The motion in all three directions starts from an initial position of 0 m. The most substantial change was observed in the surge direction, where the motion increased from 0 m to approximately 25 m under Ultimate 1 and Extreme conditions, and from 0 m to 15 m under the Operational 1 condition, before beginning to fluctuate. Similarly, in the pitch direction, the motion increased from 0 m to approximately 6 m under the Ultimate 1 and Extreme conditions, and from 0 m to 2 m under the Operational 1 condition, before beginning to fluctuate.

Table 6. Statistics of the platform motions for different load cases.

DOF	Name	Max	Min	Mean	STD	Range
Surge (m)	Operational 1	24.680	11.190	18.243	2.945	13.490
	Ultimate 1	24.610	12.470	19.509	2.209	12.140
	Extreme	19.910	5.394	12.231	2.404	14.516
Heave (m)	Operational 1	−0.244	−0.741	−0.477	0.079	0.498
	Ultimate 1	3.129	−3.404	−0.432	0.962	6.533
	Extreme	4.548	−4.191	−0.188	1.340	8.739
Pitch (°)	Operational 1	5.756	1.416	3.789	0.814	4.340
	Ultimate 1	6.110	0.945	3.648	0.904	5.165
	Extreme	2.509	−2.777	−0.224	0.907	5.286

describes the statistical parameters of motion response in each degree of freedom direction under different conditions. Here, ‘Max’, ‘Min’, and ‘Mean’ denote the maximum, minimum, and average values of motion response, respectively. ‘STD’ represents the standard deviation, and ‘Range’ indicates the difference between the maximum and minimum values (maximum–minimum). The values presented here are derived from data between 500 s and 3500 s, with transient results excluded from the statistical analysis.

Based on the calculation results, it is evident that when only the wave height and wave period are increased, the wind turbine can still operate normally, without a corresponding increase in wind speed (referred to as ‘Ultimate 1’). Furthermore, the responses in the surge and pitch directions exhibit minimal variation compared to the rated working condition (Operational 1). Specifically, the average motion response amplitude increased by 7% in the surge direction and decreases by 4% in the pitch direction.

Under the extreme environmental condition, occurring once in 50 years (referred to as ‘Extreme’), the average motion response amplitude is reduced by 33% in the surge direction, and is reduced by 106% in the pitch direction, compared to the rated working condition. This reduction is likely due to the pitched blades and braked generator.

However, the influence of waves on wind turbine response is most notable in the heave direction, where the ‘Range’ increased by a factor of 12 in ‘Ultimate 1’ and by a factor of 16 in ‘Extreme’ scenarios.

5.2. Nacelle Acceleration Responses

The acceleration of the nacelle has an important influence on the force exerted on the structure, and the nacelle acceleration responses serve as a reference for studying the tower responses. Therefore, the nacelle acceleration responses are obtained. Figure 6 presents the acceleration responses in the x and y directions, while Figure 7 displays the maximum (Max) values and standard deviation (STD) values of the response. The effects of transient phenomena are hardly noticeable in the acceleration response.

It can be seen from Figure 6 that the nacelle acceleration responses are all between −2 m/s and 2 m/s in the x direction, and are between −1 m/s and 1 m/s in the y direction under different conditions. In Figure 7, the maximum nacelle acceleration response is measured at 1.65 m/s². According to relevant regulations, when the nacelle acceleration response exceeds 6 m/s², the risk of structural failure is expected to rise. Therefore, the floating offshore wind turbine structure is within a safe range.

It can also be found that the acceleration response of the structure is notably affected by the wave height and wave period. And the acceleration response of structure in the windward direction (X direction) is significantly greater than that in the lateral direction (Y direction). There is little difference in the acceleration response between the Ultimate 1 and Extreme conditions in the X direction. However, the acceleration response is larger under both the Ultimate 1 and Extreme conditions compared to the rated working condition. Under the Extreme condition, the maximum acceleration response in the Y direction is approximately three times greater than that under rated conditions, with the standard deviation being approximately 3.6 times larger.

5.3. Mooring Force Responses

There is no doubt that the state of the mooring cable is particularly important for the safety of floating wind turbine structures. The force responses of three mooring lines can be calculated under different conditions. Figure 8 shows the time history curve of fairlead tensions, and Figure 9 shows the statistic characteristics of fairlead tensions.

Transient effects, observable within the initial 100 s, exhibit different trends in mooring cables distributed in two directions around the FOWT. Due to the presence of initial tension, the tension in the mooring lines initially changes from 2.5 MN.

The tension of fairlead 1 increased from 2.5 MN to approximately 5 MN under the Ultimate 1 and Extreme conditions, and from 2.5 MN m to 4 MN under the Operational 1 condition, before beginning to fluctuate. Similarly, the tension of fairleads 2 and 3 decreased from 2.5 MN to approximately 1.8 MN under the Ultimate 1 and Extreme conditions, and from 2.5 MN to 2 MN under the Operational 1 condition, before beginning to fluctuate.

From the results, it can be observed that the tension of the mooring cable increases with deteriorating environmental conditions. When the wind turbine is operational, the average tension of the cable on the windward side (fairlead 1) is greater than that on the leeward side. Under DLC3, the average tension of the cable on the windward side decreased, while the tension of the two mooring cables on the leeward side increased. In all conditions, the mooring cable tension is far below its breaking strength (22 MN [34]), indicating a large safety margin.

6. Conclusions

This paper focuses on the IEA 15 MW ultra-large-scale wind turbine structure, to solve hydrodynamic coefficients and to study the platform’s dynamic responses under different environmental conditions. The conclusions can be summarized as follows:

(1)

When facing extreme environmental conditions, accurately determining the timing of generator shutdown is essential. During such conditions, particular emphasis should be placed on monitoring the wind turbine’s motion response in the heave direction.

(2)

Wave conditions significantly influence the acceleration response of the wind turbine. In extreme environmental conditions, the nacelle acceleration response of the wind turbine notably increases even during shutdown. Therefore, careful observation of the tower’s acceleration response is necessary.

(3)

During wind turbine shutdown, the cable tension on the windward side decreases by approximately 20%, while the mooring tension on the leeward side increases by about 8%. In all scenarios, the mooring tension on the windward side is greater and should be prioritized.

In this study, the motion response of the IEA 15 MW floating wind turbine under extreme condition is investigated to gain its motion responses in challenging environmental conditions. This research holds significance as a reference for the safety monitoring of wind turbine structures. However, there is a gap in the research regarding whether wind turbines should be shut down when encountering complex sea conditions. It is necessary to explain the limitations of this study. The research method used in this study is singular. Due to the limitations of experimental equipment, experimental analysis could not be conducted, and there is no publicly available dataset for comparison. The accuracy of the analysis may be validated in future studies. Additionally, due to limitations in funds and personnel, this paper only analyzes a small number of extreme conditions. The accuracy of the analysis and the verification of a wider range of working conditions may be achieved in future research. Increasing the number of design conditions to examine the optimal timing for wind turbine shutdowns can also be beneficial in future studies.