Effects of Mooring Line with Different Materials on the Dynamic Response of Offshore Floating Wind Turbine

Abstract

The influence of mooring systems with lines of different material on the dynamic response of a floating wind turbine is studied using a 5 MW OC4-DeepCwind semi-submersible wind turbine as a representative prototype in this study. Two types of mooring systems were designed using the MoorDyn module in OpenFAST software (v3.1.0): one uses chains, and the other uses a hybrid mooring line composed of chains and high-strength polyethylene (HMPE) ropes. A wind turbine with two types of mooring systems was simulated using the OpenFAST software. The results show that the floating wind turbine moored with the hybrid lines exhibited a larger heave and pitch motion than that moored using chains alone. At the same time, the surge displacement was smaller than that of the wind turbine using chains alone. In terms of mooring line tension, the mean and amplitude values of the hybrid mooring system at the location examined were smaller than those of the chain mooring system. Thus, using HMPE ropes in the mooring system can significantly reduce line loads. In addition, the HMPE ropes used in the floating wind turbine mooring system did not affect the power generation of the wind turbine. This study provides promising support data and observations for applying high-strength polyethylene (HMPE) ropes in mooring systems for floating wind turbines.

1. Introduction

As a clean energy source, wind power has become a focal point in energy development worldwide and is also a crucial driver for achieving carbon neutrality goals. Currently, wind energy utilization worldwide is gradually shifting from onshore to offshore. As a necessary technological solution for deep-sea wind energy development, floating wind turbines have become a popular research topic in offshore wind energy utilization. The mooring system is critical in ensuring the safe operation of floating wind turbines in harsh environments [1]. The failure of mooring systems can result in substantial losses [2]. Moreover, reducing the cost of wind power and making floating wind turbine systems more economically viable has garnered significant attention from researchers. Therefore, research on the mooring systems of offshore floating wind turbines is necessary to guarantee the safe and economic operation of these wind turbines.

In the following, we review some of the recent literature on the design technology issues related to the mooring systems of floating wind turbines. Cermelli et al. [3] developed numerical models and conducted scaled-model tests for the mooring system of the WindFloat platform. Brommundt et al. [4] studied the optimal mooring line length, angle, and horizontal distance between anchors and anchor points at different water depths (75 m and 330 m) for semi-submersible wind turbines. Jeon et al. [5] investigated the impact of mooring parameters on the dynamic response of floating wind turbines at a water depth of 200 m, referencing spar-type turbines. Yuan et al. [6] researched a hybrid mooring system equipped with buoys and heavy weights, and their experimental results indicated that a hybrid mooring system can decrease the response of platform motion and line tension for deep-water semi-submersible platforms. Benassai et al. [7] compared the effects of catenary and taut mooring systems on the motion response of floating wind turbines under 50 m and 200 m water-depth conditions. Liu et al. [8] reviewed the developments in semi-submersible floating foundations supporting wind turbines and summarized research methods and challenges for semi-submersible wind turbines. Campanile et al. [9] performed motion simulation analyses at water depths ranging from 50 m to 350 m for the Tri-floater platform with an NREL (National Renewable Energy Laboratory) 5 MW wind turbine and explored permissible offsets and installation costs during the installation process. Xu et al. [10] investigated mooring system designs at three different water depths (50 m, 100 m, and 200 m), concluding that nonlinear line tension becomes more pronounced with decreasing water depth. Ma et al. [11] conducted time-domain coupled simulations on the NREL 5 MW OC4-DeepCwind semi-submersible wind turbine and studied the dynamic response of the mooring system under extreme blasts of wind. Li et al. [12] studied the dynamic response of OC3-Hywind spar-type floating wind turbines after a single anchor chain failure in a sea state and found that wind turbines with an anchor chain failure increase the risk of collision with neighboring wind turbines. Bae et al. [13] analyzed the dynamic response of OC4-DeepCwind semi-submersible floating wind turbines after a single anchor chain failure, and the study showed that anchor chain failure causes a long-distance drifting motion of the platform and has an effect on the anchor chain tension. Pham et al. [14] proposed a practical modeling procedure for conducting numerical mooring analyses for a floating wind turbine considering the dynamic axial stiffness of nylon lines. Xu et al. [15] studied seven mooring concepts for a 5 MW semi-submersible floating wind turbine to identify structurally reliable and economically attractive mooring solutions. Xiang et al. [16] tested the dynamic response of a spar-type floating wind turbine foundation with a taut mooring system using a finite element method (FEM)-based tensile mooring line model. Zhang and Liu [17] proposed a universal framework for complex structural configurations and applied it to shared mooring for wind farms using OpenFAST (v3.1.0) and AQWA codes (v5.5). Sørum et al. [18] described procedures for adapting laboratory test stiffness results to the Syrope model and a bi-linear model and investigated the consequence of using the models for load calculations of polyester mooring lines. Hall et al. [19] proposed that the performance requirements of the real-time hybrid test system are suitable for scale-model floating wind turbine tests and solved the scale incompatibility problem. Chevillotte et al. [20] presented the fatigue data of nylon ropes and provided essential information for designing moorings for floating wind turbines. Xue and Sandy [21] investigated the dynamic responses of the spar platform with mooring lines under various wave loads in tank tests. These test data can be helpful in validating numerical software for the research of mooring line motions.

In addition, to develop effective design tools for floating wind turbines, lots of scholars have developed codes or have performed experimental tests. Coulling et al. [22] presented the validation of a model FAST with 1/50th-scale model test data and indicated that FAST captures many of the pertinent physics in the floating wind turbine problem. Azcona et al. [23] developed a simulation code based on a lumped-mass formulation and validated the code by comparing it with tension and motion experimental data. Hall and Goupee [24] developed a lumped-mass mooring line model (MoorDyn code) that is coupled with the FAST code and verified MoorDyn with 1:50-scale floating wind turbine test data. Hall [25] extended MoorDyn to support additional mooring system functions and load situations, such as synthetic cable materials, ballast/buoyancy along the cable, or interconnections between platforms. The updated version of MoorDyn will help address these emerging needs. West et al. [26] modified MoorDyn to allow the addition of nonlinear elastic mooring materials in OpenFAST and compared the numerical results with the 1:52 scale test data of an FOWT to validate the updated MoorDyn.

Although numerous scholars have conducted extensive research on the mooring systems of offshore floating wind turbines, there needs to be more research on the effects of different line materials on the dnamic response of semi-submersible wind turbines using OpenFAST. This need for research may be due to the limited application of fiber ropes in floating wind turbine mooring systems. In 2020, Lankhorst’s Gama98^® HMPE mooring rope was used in the mooring system of the WindFloat Atlantic system and received certification from the American Bureau of Shipping (ABS) [27,28]. While there have been engineering applications of HMPE ropes in floating wind turbines, research on numerical analyses of HMPE ropes as mooring lines for floating wind turbines is relatively scarce. This study focuses on semi-submersible wind turbines and utilizes the MoorDyn open-source code within OpenFAST to design two mooring systems: one using mooring chains and another using a hybrid line consisting of chains and HMPE ropes. This research aims to understand the impact of different line materials on the motion response of semi-submersible wind turbines, with the goal of more effectively employing HMPE rope in the mooring systems of floating wind turbines. The current research, based on OpenFAST, that incorporates the material properties of fiber ropes contributes to the rational design of mooring systems for offshore floating wind turbines.

2. The Theories of Wind Load, Platform Response, and Mooring Line Tension

2.1. Blade Element Momentum Theory

The wind turbine blade is divided into many small segments along its span, called blade elements. The Blade Element Momentum Theory [29] calculates the forces and moments on each blade element along the span to obtain the aerodynamic theory of the forces and moments acting on the wind turbine. The forces and moments acting on each blade element are

$$dT=0.5\rho v^{2}Bc\left(C_{L}cos\phi +C_{D}sin\phi \right)dr$$

(1)

$$dM=0.5\rho v^{2}Bc\left(C_{L}cos\phi +C_{D}sin\phi \right)rdr$$

(2)

where $\rho$ represents air density (kg/m³); $v$ stands for the relative wind speed at the blade element (m/s); $B$ is the number of blades of the wind turbine; $c$ is the chord length of the blade element (m); $C_L$ denotes the lift coefficient; $C_D$ represents the drag coefficient; $\phi$ is the angle of attack of the airflow; $r$ is the radial distance from the blade element to the hub center; and $dr$ is the spanwise length of each blade element (m). These equations are a fundamental part of the Blade Element Momentum Theory, which is used to analyze and predict the performance of wind turbines by considering the interactions between the blade elements and the incoming airflow. It helps in understanding how forces and moments vary along the length of the wind turbine blade and how these factors contribute to the overall performance of the turbine. The current version of OpenFAST uses a one-way coupling method, and the forces and moments distributed along the WTB are not dependent on the type/material of the mooring system.

2.2. Cummin’s Theory

The equations of motion for a wind turbine floating platform, using Cummin’s equation [24,30], are as follows:

$$\left[{\mathit{M}}_{\mathit{p}}+\mathit{A}\right]\ddot{\mathit{x}}\left(\mathit{t}\right)+\mathit{C}\dot{\mathit{x}}\left(\mathit{t}\right)+{\mathit{K}}_{\mathit{t}}\mathit{x}\left(\mathit{t}\right)=\mathit{F}\left(\mathit{t}\right)$$

(3)

$$\mathit{F}\left(\mathit{t}\right)={\mathit{f}}_{\mathit{w}}^1+{\mathit{f}}_{\mathit{w}}^2+{\mathit{f}}_{\mathit{w}\mathit{i}\mathit{n}\mathit{d}}$$

(4)

where ${\mathit{M}}_{\mathit{p}}$ represents the mass matrix of the platform (the unit is kg); $\mathit{A}$ is the added mass matrix of the floating platform (unit in kg); $\mathit{x}\left(\mathit{t}\right)$ corresponds to the displacement of the respective degree of freedom (m); and $\mathit{t}$ represents the time for time-domain simulation (s). $\mathit{C}$ is the damping matrix that includes radiation damping (kg/s); ${\mathit{K}}_{\mathit{t}}$ is the total stiffness matrix that includes mooring stiffness (kg/${\mathrm{s}}^2$); $\mathit{F}\left(\mathit{t}\right)$ represents the external loads (Newton, N); ${\mathit{f}}_{\mathit{w}}^1$ is the first-order wave loads (Newton); ${\mathit{f}}_{\mathit{w}}^2$ is the second-order wave loads (N); and ${\mathit{f}}_{\mathit{w}\mathit{i}\mathit{n}\mathit{d}}$ is the wind loads (N). These equations are used to model and analyze the motion of a wind turbine floating platform, taking into account various forces and environmental conditions that affect the motion of the platform in time-domain simulations.

2.3. Mooring Line Theory

The calculation of mooring line loads is based on the lumped-mass method. The mooring line model is discretized into mass nodes and elements. The mass of the mooring element is concentrated at the corresponding node.

The mooring line is broken up into N evenly sized line segments, and the length element is ${\mathit{l}}_{\mathit{e}}$. The indexing starts at the anchor, with the anchor node given a value of 0 and the line segment between nodes $\mathit{i}$ and $\left(\mathit{i}+1\right)$ given an index of $\mathit{i}+\left(\frac{1}{2}\right)$, as shown in Figure 1. Taking one of the mooring elements in the mooring line of Figure 1, using the force analysis method, the equation for calculating the forces on the element node $\mathit{i}$ is established [24,30]:

$$\left({\mathit{m}}_{\mathit{i}}+{\mathit{A}}_{\mathit{i}}\right)\ddot{{\mathit{R}}_{\mathit{i}} }={\mathit{T}}_{\mathit{i}+\left(\frac{1}{2}\right)}-{\mathit{T}}_{\mathit{i}-\left(\frac{1}{2}\right)}+{\mathit{C}}_{\mathit{i}+\left(\frac{1}{2}\right)}-{\mathit{C}}_{\mathit{i}-\left(\frac{1}{2}\right)}+{\mathit{W}}_{\mathit{i}}+{\mathit{B}}_{\mathit{i}}+{\mathit{D}}_{\mathit{p}\mathit{i}}+{\mathit{D}}_{\mathit{q}\mathit{i}}$$

(5)

$${\mathit{W}}_{\mathit{i}+\left(\frac{1}{2}\right)}=\frac{1}{4}\pi {\mathit{d}}^2{\mathit{l}}_{\mathit{e}}\left({\rho }_{\mathit{w}}-{\rho }_{\mathit{m}}\right)\mathit{g}$$

(6)

where $m_i$ and ${\mathit{A}}_{\mathit{i}}$ represent the diagonal of the mass matrix and the added mass matrix, respectively; ${\mathit{R}}_{\mathit{i}}$ denotes the location position of each node point $\mathit{i}$ on the mooring line; ${\mathit{T}}_{i+\left(\frac{1}{2}\right)}$ is the axial tension in the line segment $\mathit{i}+\left(\frac{1}{2}\right)$, the direction of which is defined as pointing from node $\mathit{i}$ to node $\mathit{i}+1$; and ${\mathit{C}}_{i+\left(\frac{1}{2}\right)}$ is the internal damping forces in the line segment $\mathit{i}+\left(\frac{1}{2}\right)$, which is related to the strain rate of the segments.${\mathit{W}}_{\mathit{i}}$ is the net buoyancy (weight) at node $\mathit{i}$, which relates to the net buoyancy of segments ${\mathit{W}}_{i+\left(\frac{1}{2}\right)}$ and ${\mathit{W}}_{i-\left(\frac{1}{2}\right)}$, (with unit in Newton); $\mathit{d}$ is the volume equivalent diameter of the mooring lines; ${\rho }_{\mathit{w}}$ is the density of sea water; ${\rho }_{\mathit{m}}$ is the density of the line material; ${\mathit{B}}_{\mathit{i}}$ is the contact force of node $\mathit{i}$ when the node contacts the seabed; and ${\mathit{D}}_{\mathit{p}\mathit{i}}$ and ${\mathit{D}}_{\mathit{q}\mathit{i}}$ are the transverse and tangential drag force applied to node$\mathit{i}$, respectively. These terms are used in the force analysis equation for a mooring element and are essential for understanding the forces and stresses acting on the element. This equation is crucial for evaluating the behavior and performance of mooring systems used in maritime and offshore applications.

2.4. Wind Turbine Power Output Theory

The wind turbine power output can be calculated using the following formula:

$$P=\frac{1}{2}{\mathit{C}}_{\mathit{p}}\rho A{V}^3$$

(7)

where $P$ is the power output in watts (W) or kilowatts (kW); $\rho$ is the air density in kilograms per cubic meter (kg/m³); $A$ is the swept area of the wind turbine rotor in square meters (m²), which is a function of the radius of the rotor (the center point of the rotor to the tip of a blade); $V$ is the wind speed in meters per second (m/s); and $C_p$ is the power coefficient, which represents the efficiency of the wind turbine in converting the kinetic energy of the wind into electrical power. The power coefficient varies with the design and efficiency of the wind turbine and typically ranges from 0 to 0.59 for high-efficiency turbines (in this study, the value of $C_p$ = 0.30 is assumed).

3. Numerical Model of Mooring Systems for Offshore Floating Wind Turbines

3.1. Numerical Model of the Floating Wind Turbine

The present study uses a 5 MW wind turbine model from the U.S. National Renewable Energy Laboratory’s (NREL) OC4 (Offshore Code Comparison Collaborative Continuation) project. This wind turbine is a conventional three-blade upwind-type turbine installed on a semi-submersible floating platform. The floating platform consists of three offset columns, one main column supporting the turbine, and numerous cross members and cross-braces. The connection between the base column and the upper column prevents the excessive swaying motion of the platform. The main column of the floating platform has a diameter of 6.5 m and a length of 30 m, while the upper column has a diameter of 12 m and a length of 26 m. The base column has a diameter of 24 m and a length of 6 m. The connections between the three offset columns are completed using 1.6 m diameter cross members, as shown in Figure 2a [31].

3.2. Validation of Numerical Simulation Technology Using Literature Data

To validate the numerical simulation technology, the results of mooring systems of the same floating wind turbine from the literature (Coulling et al., 2013) [22] were compared with numerical simulation results obtained using OpenFAST. The same mooring system design as the mooring design presented in Coulling et al. [22] was adopted. The mooring line fairlead and the float were the same as in the reference [22]. The fairlead positions of the mooring lines were set according to Coulling et al. [22]. The fairlead positions for lines 1 to 3 were (20.434, 35.393, −14.0), (−40.868, 0, −14.0), and (20.434, −35.393, −14.0), respectively. This shows that the angle between adjacent lines was 120°, and the depth to the fairleads below the still-water line (SWL) was 14 m. The mooring line parameters are listed in

Table 1. Parameters of chains (Coulling et al., 2013) [22].

Mooring Assembly	Parameter	Value
Chain lines	Diameter/mm	76.6
	$\mathrm{Weight} \mathrm{in} \mathrm{air}/(\mathrm{kg}·{\mathrm{m}}^{-1}$)	113.35
	Material damping ratio	−1.0
	EA/kN	$7.536\times {10}^6$
	Lateral additional-mass coefficient	0.8
	Tangential additional-mass coefficient	0.25
	Lateral drag coefficient	2.0
	Tangential drag coefficient	0.4

.

The same environmental loads as those in Coulling et al. [22] were used. The wave and wind were aligned and directed along the positive surge direction, as shown in Figure 2b. The dynamic wind and wave spectrum parameters were the same as those described in

Table 2. Parameters of wind and wave spectra (data from Coulling et al., 2013) [22].

National Petroleum Directorate (NPD) Wind Spectrum		JONSWAP Wave Spectrum
$\mathbf{Mean} \mathbf{Wind} \mathbf{Speed}$ $\mathbf{at} \mathbf{Hub} \mathbf{Height}$ ${\mathbf{U}}_{\mathbf{HubHt}}/\mathbf{m}·{\mathbf{s}}^{-1}$	HubHt/m	${\mathbf{H}}_{\mathbf{s}}/\mathbf{m}$	${\mathbf{T}}_{\mathbf{P}}/\mathbf{s}$	$\mathbf{\gamma }$
20.6	90	10.5	14.3	3.0

.

According to the above information, a combined dynamic wind-and-wave case of 100,800 s in length was found. These results are compared with the numerical mooring simulation results found using OpenFAST in the present study. A comparison of the results can be found in

Table 3. Comparison of OpenFAST prediction value and test data statistics (data from Coulling et al., 2013) [22].

Comparison Item	Source	Mean Values	St. Dev. Values	Max Values	Min Values	Errors of Mean Values
Surge	Lab data	3.78	2.99	18.01	−4.41	0
	FAST (Coulling et al., 2013)	−0.14	2.01	8.09	−6.79	147%
	OpenFAST	5.48	2.10	23.54	−3.86	44.97%
Heave/m	Lab data	−0.07	1.73	5.87	−6.50	0
	FAST (Coulling et al., 2013)	0.00	1.42	4.27	−4.17	100%
	OpenFAST	−0.06	1.12	4.37	−3.81	14.29%
Pitch/°	Lab data	−0.02	1.55	6.94	−6.09	0
	FAST (Coulling et al., 2013)	−0.01	1.20	4.83	−3.75	50%
	OpenFAST	−0.015	1.14	6.97	−5.11	25%
Fairlead 1 tension/kN	Lab data	990.60	91.91	1403.00	431.80	0
	FAST (Coulling et al., 2013)	1111.00	60.05	1338.00	918.60	12.15%
	OpenFAST	1013.23	58.59	1332.64	588.01	2.28%
Fairlead 2 tension/kN	Lab data	1344.00	468.00	5774.00	95.25	0
	FAST (Coulling et al., 2013)	1105.00	82.68	1541.00	879.50	17.78%
	OpenFAST	1389.16	398.60	5880.67	89.80	3.36%

and Figure 3. We observe that the simulated values from OpenFAST agree well with the experimental data. This shows that numerical simulation technology based on OpenFAST can be used to design new mooring systems and that the simulated results are accurate and reliable.

3.3. Mooring Systems of Floating Wind Turbines at 200 Water Depth

Because of the complex nonlinear behavior of fiber ropes, including creep performance, fatigue performance, load history effects, dynamic stiffness effects, and material damping, it is important to select rope parameters such as rope density, axial stiffness, drag coefficient, and additional-mass coefficient [32]. In this study, the floating wind turbine used a catenary mooring system, and the three lines were evenly distributed around the turbine. Two types of mooring systems were set to investigate the impact of line materials on the dynamic response of the floating wind turbine. One mooring system adopted a chain mooring configuration. In contrast, the other mooring system used a hybrid line configuration consisting of chains and HMPE ropes. The difference between the two mooring configurations lies in the material of the suspension segment of the mooring lines. The suspension segment was made of chains for the first mooring configuration, while for the second mooring configuration, it was made of chains and HMPE ropes. The arrangement of the mooring system is shown in Figure 2b [33,34].

This study used the fairlead positions of the mooring lines set in the experiments of Robertson et al. [31] and Coulling et al. [22]. The fairlead positions for lines 1 to 3 were (20.434, 35.393, −14.0), (−40.868, 0, −14.0), and (20.434, −35.393, −14.0), respectively. The anchor points for each line were located at (418.8, 725.383, −200.00), (−837.6, 0, −200.00), and (418.8, −725.383, −200.00), respectively. In addition, the positions where the HMPE ropes were connected to the lower chains were (138.486, 239.865, −110.0), (−276.972, 0, −110.0), and (138.486, −239.865, −110.0), respectively. In the hybrid mooring configuration, HMPE ropes were used, which reduce the overall weight of the mooring lines and increase the flexibility (elongation) of the lines, making them easier to install and transport, thus reducing transportation and installation costs. The present study provides specific information about the total length of the ropes, the length of the touchdown segment, the suspension segment, and the length of the HMPE ropes, as listed in

Table 4. Main parameters of mooring lines.

Parameters	Chain Mooring System	Hybrid Line Mooring System
Length/m	835.5	835.5
Length of touchdown segment/m	243.7	243.7
Clump weight	-	3
HMPE line length/m	-	306.8
Suspension length/m	591.8	591.8

and

Table 5. Parameters of components of mooring lines.

Mooring Assembly	Parameter	Value
Chain	Diameter/mm	124
	$\mathrm{Weight} \mathrm{in} \mathrm{air}/(\mathrm{kg}·{\mathrm{m}}^{-1}$)	308
	Material damping ratio	1.0
	EA/kN	$1.31\times {10}^6$
	Lateral additional-mass coefficient	3.1
	Tangential additional-mass coefficient	1.7
	Lateral drag coefficient	2.6
	Tangential drag coefficient	1.4
	Minimum breaking strength/kN	14,358
HMPE	Diameter/mm	147

. The chain parameters for the mooring system were primarily based on information from Xu et al. [33]. The selection of the HMPE rope parameters was made by referencing mainly Lankhorst’s rope parameters and DNVGL standards [35,36]. Furthermore, it is essential to clarify that the primary difference between the two mooring configurations is the use of HMPE ropes in the hybrid line configuration, and the HMPE ropes have different self-weight, material damping ratios, and stiffness compared to chains.

3.4. Environmental Load Cases

To study the dynamic response of the floating wind turbine, the environmental loads were set as listed in

Table 6. Parameters of the wind spectrum.

Sea State	Wind Spectrum	${\mathbf{U}}_{\mathrm{HubHt}}/\mathbf{m}·{\mathbf{s}}^{-1}$	HubHt/m	ShearExp
Operational sea state	API	11	90	0.2
Extreme sea state	API	35	90	0.2

and

Table 7. Parameters of the wave spectrum.

Sea State	Wave Spectrum	${\mathbf{H}}_{\mathbf{s}}/\mathbf{m}$	${\mathbf{T}}_{\mathbf{P}}/\mathbf{s}$	$\mathbf{\gamma }$
Operational sea state	JONSWAP	5	10	3.3
Extreme sea state	JONSWAP	8	12	3.3

, and the water depth was set at 200 m [37].

The wind speed is determined using the wind spectrum, as shown in Equation (8),

$$\mathrm{U}\left(\mathrm{Z}\right)={\mathrm{U}}_{\mathrm{HubHt}}\times (\frac{\mathrm{Z}}{\mathrm{HubHt}}{)}^{\mathrm{ShearExp}}$$

(8)

where ${\mathrm{U}}_{\mathrm{HubHt}}$ is the steady wind speed located at elevation HubHt; 𝑍 is the instantaneous elevation of the blade or tower node above the ground; and ShearExp is the power-law shear exponent. The parameters of the wind spectrum are listed in Table 6. The JONSWAP wave spectrum was used, and the parameters are listed in Table 7. The current velocity can be considered a steady flow field where the velocity vector (magnitude and direction) is a function of depth. Here, we assumed that the current velocity is 0.25 m/s for the operational sea state and 0.5 m/s for the extreme sea state.

For semi-submersibles with spread moorings, the collinear condition is usually the most critical combination of environment directionality, which governs the mooring system design. Here, the wind, wave, and current directions were set in the same direction, and environmental loads were applied along the positive x-axis direction, as shown in Figure 2b. The simulation duration was set to 10,800 s, according to Liu et al. [38]. Note that to clearly show the results of the comparison of the two mooring systems, only the stationary results between 2000 s and 8000 s are plotted in Figure 4. The comparison was made under the same environmental loads to evaluate the impact of the two mooring systems on the motion response and line tension of the floating wind turbine. The wind speed and wave load sequences for the two sea conditions are shown in Figure 4. The current speed was constant (current speed curve is not provided).

4. Results and Discussion

4.1. Blade Forces

A floating wind turbine is a complex system composed of a turbine, a floating platform, and a mooring system. Because of the coupling between the turbine and the floating platform, the aerodynamic loads on the turbine affect the hydrodynamic response of the floating platform and the tension response of mooring lines [30]. Therefore, the aerodynamic loads on the turbine are one of the key external loads on the wind turbine platform. Hence, it is essential to calculate the blade forces of wind turbines with mooring systems. During simulations, the turbine blades generate disturbances when starting up, which disappear when the blades reach the rated rotational speed [39]. Following this principle, only stable data within the interval 2000 s–8000 s were selected for analysis in this study. Figure 5 shows the blade forces on the floating wind turbine using different mooring systems under various environmental loads.

Table 8. Statistical data of the load on wind turbine.

Sea State	Mooring Arrangement	Average Value/kN	Standard Deviation/kN	Maximum Value/kN	Minimum Value/kN
Operational sea state	Chain	202.97	0.52	204.37	200.46
	Hybrid line	202.92	0.54	204.31	201.32
Extreme sea state	Chain	661.49	1.13	664.51	650.39
	Hybrid line	661.45	1.12	664.45	649.93

presents the statistical values of the blade forces. According to the results shown in Figure 5 and Table 8, in the operational sea state, the mean blade force for the floating wind turbine with chain mooring was 202.97 kN, while that for the one with hybrid mooring lines was 202.92 kN. The mean blade force of the wind turbine was slightly lower when using hybrid mooring lines compared to chains, but the difference is practically negligible. In the extreme sea state, the blade forces of the wind turbine exhibited a similar pattern for the wind turbine across both mooring systems. Note that OpenFAST is a one-way coupling method. Mooring line responses are affected by the thrust load and turbine passing frequency. Hence, the blade forces should be accurately determined.

4.2. Motion Response of the Floating Wind Turbine

The motion response of the floating wind turbine for the two mooring systems under environmental loads is shown in Figure 6, and the corresponding statistics are listed in

Table 9. Statistical data of the motion response of FOWT under different sea states.

Sea State	Motion Response	Mooring Line Types	Average Value/kN	Standard Deviation/kN	Maximum Value/kN	Minimum Value/kN
Operational sea state	Sway/m	Chain	−0.11	0.00	−0.10	−0.12
		Hybrid line	−0.10	0.05	0.06	−0.26
	Surge/m	Chain	2.69	0.37	3.87	1.63
		Hybrid line	2.87	0.40	4.16	1.71
	Heave/m	Chain	−0.82	0.01	−0.73	−0.84
		Hybrid line	0.03	0.01	0.13	0.01
	Roll/°	Chain	0.09	0.00	0.10	0.08
		Hybrid line	0.10	0.01	0.14	0.05
	Pitch/°	Chain	1.59	0.04	1.71	1.48
		Hybrid line	1.71	0.05	1.87	1.56
	Yaw/°	Chain	−0.03	0.00	−0.02	−0.04
		Hybrid line	−0.06	0.01	−0.02	−0.09
Extreme sea state	Sway/m	Chain	−0.11	0.00	0.01	−0.12
		Hybrid line	0.01	0.07	0.22	−0.23
	Surge/m	Chain	3.98	0.48	5.33	2.77
		Hybrid line	4.22	0.48	5.53	3.01
	Heave/m	Chain	−0.81	0.02	−0.55	−0.85
		Hybrid line	0.04	0.02	0.30	0.00
	Roll/°	Chain	0.30	0.00	0.31	0.27
		Hybrid line	0.34	0.01	0.36	0.31
	Pitch/°	Chain	2.21	0.06	2.47	2.05
		Hybrid line	2.36	0.07	2.61	2.16
	Yaw/°	Chain	0.10	0.01	0.13	0.07
		Hybrid line	0.19	0.02	0.25	0.13

.

The results of Figure 6 and Table 9 show that under environmental loads (operational or extreme sea state), both mooring systems have a relatively minor impact on the sway, roll, and yaw motions of the floating wind turbine. However, the two mooring systems have a more substantial effect on the surge, heave, and pitch motions of the floating wind turbine. Note that there is a slight increase in the heave motion of the mooring system with hybrid lines compared to the chain mooring system. This phenomenon is due to the difference in the materials used in the suspension segment. While both mooring systems used the same length of ground chains (528.76 m for each line), the hybrid mooring system employed HMPE rope for the 306.59 m suspension segment, which has a lower weight than chains. Therefore, for the hybrid mooring system, one sinker was deployed for each hybrid line with HMPE ropes to limit the heave displacement of the floating wind turbine. Also, the average roll motion for the floating wind turbine using the hybrid mooring system was 0.15° greater than that using the chain mooring system, with a standard deviation of 0.07°, which is higher than the chain mooring system’s 0.06°. The increased value in terms of the roll motion for the hybrid line mooring system is due to the lighter self-weight of the hybrid lines and their lower torsional stiffness compared to all chains in the suspension system. Hence, this phenomenon should be taken into account when designing a HMPE hybrid mooring system for wind turbines.

The floating wind turbine with the hybrid mooring system experienced a 0.77 m reduction in surge displacement compared to the one with the chain mooring system. The impact on the surge motion of the chain mooring system is attributed to the larger self-weight of the chains, resulting in a greater draft for the floating platform.

In this study, the floating wind turbine using the hybrid mooring lines achieved a maximum horizontal displacement of 4.22 m (2% of water depth), which is below the maximum allowable horizontal displacement of 30 m to 50 m (15% to 25% of water depth) as required by API RP 2FP1 [40]. The maximum rotation angle was 2.36°, which is below the maximum allowable rotation angle of 10° required by API RP 2FP1 [40]. Therefore, the motion response of the floating wind turbine using the HMPE hybrid mooring system satisfies safety requirements.

4.3. Analysis of Line Tension Values of the Floating Wind Turbine

Two different environmental-load scenarios are considered in this study to compare and analyze the line tension at the fairlead point of the floating wind turbine for the two mooring systems. The tension variations for line 1 and line 2 in both mooring systems are presented in Figure 7, and the corresponding statistics are summarized in

Table 10. Statistical data on line tension in two mooring systems under different sea states.

Mooring Number	Sea State	Mooring Line Types	Average Value/kN	Standard Deviation/kN	Maximum Value/kN	Minimum Value/kN
1	Operational sea state	Chain	2696.75	19.39	2746.78	2599.75
		Hybrid line	1034.40	17.11	1082.17	959.66
	Extreme sea state	Chain	2752.66	14.33	2789.64	2677.44
		Hybrid line	1087.59	12.85	1124.45	1032.30
2	Operational sea state	Chain	3239.90	33.30	3404.43	3162.43
		Hybrid line	1575.67	31.21	1742.04	1507.99
	Extreme sea state	Chain	3421.43	53.32	3779.37	3315.09
		Hybrid line	1758.97	50.55	2172.45	1640.58

. The minimum breaking strength of the chains used in the mooring system and the HMPE ropes is 14,358 kN and 14,595 kN, respectively, within two percent of each other.

Upon examination of Figure 7 and Table 10, we found that the hybrid mooring system exhibited smaller variations in line tension with notably lower line tension at the same fairlead positions compared to the chain mooring system. The difference is due to the significant self-weight of the chain mooring system, while the hybrid mooring system incorporated 306.59 m of HMPE ropes, reducing the overall weight of the lines and increasing their flexibility (stretch ability). For both mooring systems of the wind turbine, mooring line 2 experienced much higher tension than line 1, as the environmental loads were applied in the direction of line 2, which corresponds to the surge direction. Note that the safety factors of the mooring lines, which are determined as the ratio of break strength to the maximum tension value, were higher than 1.67, complying with the requirements of API RP 2SM [41]. However, the safety factor of the HMPE mooring lines is higher than the one for the chain system.

4.4. Analysis of the Power Generation of the Floating Wind Turbine

As much as the safety of the mooring system of the floating wind turbine is a concern, the power generation capacity of the floating wind turbine is also a critical consideration. Thus, it is essential to evaluate the impact of the two mooring systems on the power generation of the floating wind turbine under load conditions. Power generation is influenced by the six degrees of freedom of the floating wind turbine due to the combined excitation from wind, waves, and currents.

This excitation leads to the tilting of the platform and tower structure, causing significant changes in the spatial operating posture of the floating wind turbine. This, in turn, affects the inflow wind speed at various radial positions of the blades, ultimately impacting the power generation of the floating wind turbine. The wind turbine power generation, as calculated using Equation (7), is presented in Figure 8, and the corresponding statistics are summarized in

Table 11. Statistical data of power generation under two mooring systems.

Mooring Line Types	Average Value/kN	Standard Deviation/kN	Maximum Value/kN	Minimum Value/kN
Chain	1650.50	7.44	1670.93	1625.99
Hybrid line	1651.68	7.19	1672.11	1632.25

.

According to the one-way coupling from OpenFAST, the results from Figure 8 and Table 11 show that under the operational sea state, both mooring systems had a minimal impact on the power generation of the floating wind turbine. As indicated by Equation (7), the main factor influencing wind turbine power generation is the wind speed. According to the analysis of the blade forces in Section 4.2, it is evident that the wind loads acting on the turbine were nearly identical. Therefore, the power generation using either of the two mooring systems was also virtually the same. This suggests that the choice of mooring system should prioritize safety and stability, while its impact on power generation should be evaluated. In this case, both mooring systems demonstrate the ability to maintain a similar power generation capacity. However, the fairlead tension with the hybrid mooring lines was lower than that with the all-chain system.

5. Conclusions

In the present study, two mooring systems were designed to investigate the impact of different line materials on the dynamic response of a floating wind turbine. One system used all chains, while the other utilized a combination of chains and HMPE ropes. Using OpenFAST for the dynamic response analysis of floating wind turbines, we draw the following key conclusions. One is that the blade forces and the turbine power generation capacity are almost the same under the intact condition of the mooring systems. The other is that the mooring system with the hybrid lines exhibited greater surge and pitch motions compared to that with the chains. However, it had lower heave displacements compared to the mooring system with all chains. The mooring line tension at the same fairlead positions in the mooring system with hybrid lines was lower than that in the mooring system with all chains.

This research provides valuable insights into the effects of mooring lines with different materials on the dynamic response of offshore floating wind turbines. It emphasizes that the selection of HMPE ropes for the floating wind turbine does not affect the power generation of the wind turbine. However, HMPE rope can significantly reduce mooring line loads. However, using HMPE fiber ropes in the moorings of floating wind farms will make them cheaper to install and maintain. This study provides a reference for the assessment of HMPE ropes for the mooring of floating wind turbines.