Integrated Design and Experimental–Numerical Validation of a 22 MW TLP FOWT

Abstract

Tension leg platform (TLP) floating offshore wind turbines (FOWTs) show strong potential for future commercial deployment for the advantages in global performance, cost efficiency, and economic spatial utilization. However, as system sizes expand and multi-source vibrations become more prominent, the integrated design and dynamic responses of the FOWT system grow increasingly complex. This research presents the design of a TLP foundation for a 22 MW FOWT and examines its dynamic response under extreme sea states via a combined numerical and experimental approach. An integrated numerical model of the TLP FOWT is established and subsequently calibrated using data obtained from a 1:64 scale physical model test in a wind-wave flume. By using the calibrated model, the reliability of the TLP FOWT was further validated through an extended Ultimate Limit State (ULS) analysis under a 50-year return period metocean data in the East China Sea. Numerical study demonstrates that the extreme motion responses under 50-year return period data comply with safe operational limits, and the safety factors meet standard specifications. Therefore, this study provides a systematic design scheme along with valuable model test data. These contributions serve as a critical reference for the design and research of future large-megawatt TLP FOWTs.

1. Introduction

China faces a substantial electricity demand while concurrently accelerating its transition towards green and low-carbon energy sources. Owing to its prominent advantages, including vast resource potential, high-quality wind resources, and less environmental impact, deep-sea wind energy has emerged as a strategic priority in renewable energy development, demonstrating a clear trend towards deployment in deeper waters, utilization of larger-capacity turbines, and pursuit of higher overall efficiency. The research and deployment of ultra-large-capacity wind turbines, such as the 22-MW, have become a highly anticipated focus within the field of marine renewable energy. However, the growth of capacity has also brought unprecedented challenges. The substantial wind loads, wave loads, and inertial forces generated by ultra-large-capacity FOWTs impose far more stringent demands on the structural performance of floating platforms compared to conventional units.

In recent years, various innovative FOWT designs have been proposed, including semi-submersibles, tension leg platforms, and spar buoys [1]. Compared with truss and semi-submersible FOWT, TLP FOWT has advantages in motion dynamics and lightweight hull structure. TLP FOWT also has a smaller occupied area, which is conducive to its promotion in large-scale commercial applications [2]. Due to these obvious advantages, TLP FOWT has attracted widespread attention, and a series of related experimental studies and numerical simulations have been carried out. In 2004, Withee et al. [3] first designed a 15 MW TLP FOWT suitable for a water depth of 200 m. Through the established design model, key structural dimensions were optimized. Afterwards, Waymen et al. [4] proposed the 5 MW-MIT/NREL TLP concept, which has good stability and supports installation via wet tow. Chandrasekaran et al. [5,6] investigated triangular TLP configurations, analyzing their motion responses in a random wave environment and exploring the effect of wave incidence angles on the motion characteristics of both triangular and quadrilateral TLPs. Lin et al. [7] developed a modular simulation methodology to evaluate the dynamic characteristics of the MIT/NREL TLP. Vardaroglu et al. [8] developed a numerical model of the TLP FOWT and studied its dynamic response, finding that first-order wave force loads may dominate and trigger resonance in the platform’s pitching motion. Chunlei He et al. [9] conducted coupled dynamic analysis on a 15 MW Seastar-type TLP FOWT using the self-developed MeCAP program, calculating the mooring fatigue induced by second-order sum-frequency wave forces and comparing the fatigue effects of first-order and difference-frequency wave forces.

However, despite the increasing number and complexity of numerical models for TLP FOWTs, experimental validation remains a critical step in ensuring model accuracy and reliability. Song et al. [10] took the National Renewable Energy Laboratory (NREL) 5 MW offshore wind turbine as the prototype, designed a modified TLP with additional mooring lines, and verified through 1:200 scale model tests that it has superior stability, smaller wave loads under both regular and extreme wave conditions, and is suitable for deep water. Ricardo et al. [11] adopted the 5 MW reference turbine provided by the NREL, fabricated a 1:40 scale model, and conducted multi-condition tests in two water tanks. The test results were compared with the numerical simulation results. The research findings indicate that the parameters under operational conditions meet the specified limits, which verifies the rationality of the design. Zhao et al. [12,13] studied the dynamic response of a 5-MW WindStar multi-column TLP system under various marine environmental conditions. They found that second-order difference-frequency wave loads were a significant factor governing the motion response of the WindStar TLP system. Oguz et al. [14] coupled the TLP with the NREL 5 MW wind turbine, conducted a 1:36.67 scale model test, and carried out a numerical simulation by FAST. The research results show that this type of tension leg platform structure has significant advantages in terms of motion characteristics. Kim et al. [15] conducted a numerical study using the scaled DTU 10 MW TLP FOWT and compared the numerical results with the experimental data. The comparison between the HAWC2/FAST models and the experimental results shows that both numerical models can well reproduce the dynamic response. Decai Qu et al. [16] established a fully coupled numerical model of a 15 MW TLP FOWT, which was verified by scaled model tests. They compared four inclined tension tendon arrangement schemes and explored the influence of the tension tendon inclination angle on platform motion, mooring tension, structural response, and power generation performance.

The modeling and simulation of extreme environmental conditions are central to ensuring the safety and reliability of the system during the design and verification stages. Siddiqui et al. [17] conducted a reliability analysis of the mooring system of TLPs under extreme sea conditions. By adopting the First-Order Reliability Method (FORM) and the Monte Carlo simulation technique, they explored the influence of various random variables on the overall failure probability. Hsu, W. et al. [18] focused on the prediction of extreme tension in mooring lines of FOWTs under 100-year return period storms. This study verified the effectiveness of numerical tools and provided important references for the safety design and determination of safety factors of FOWT mooring systems. Liu et al. [19] aimed at the 15 MW semi-submersible FOWT, established a numerical model with SIMA, and studied its dynamic performance under extreme conditions. Ha, Yoon Jin et al. [20] took the 15-MW TLP-FOWT as the research object, investigated the nonlinear phenomena under extreme waves, and provided references for TLP design and similar studies.

It can be seen from

Table 1. Comparison table of different FOWTs.

Platform Type	Water Depth	Global Performance	Technical Maturity
Barge	Shallow to medium water depth	Poor	Floatgen 2 MW demonstrated
Spar	Deep water preferred	Good	Hywind 6 MW × 5 demonstrated
Semi	Medium to deep water	Fair	Array demonstration (WindFloat Atlantic 3 × 8.4 MW)
TLP	Wide water depth range with advantages in deep water	Excellent	Array demonstration (French PGL project 3 × 8.4 MW)

that the TLP FOWT is superior in various aspects. Therefore, the TLP is finally selected as the floating foundation for the 22 MW wind turbine. Meanwhile, it can be found from the existing research results in

Table 2. Comparative summary of studies on TLP FOWTs.

Capacity	Water Depth	Research Method
5 MW [21]	60 m	Coupled analysis based on WAMIT (2019), ANSYS/AQWA (2017), and FAST
5 MW [22]	100 m	1:50 scale model tests combined with time-domain numerical simulations
10 MW [23]	60 m	Fully coupled numerical simulations in OpenFAST
15 MW [24]	137 m	Conceptual design and extreme response analysis for the typhoon-prone environment
16 MW [25]	136 m	Fully coupled numerical simulations calibrated against experimental results

that the current capacity range of TLP-FOWT is mainly concentrated between 5 MW and 15 MW, and the applicable water depth is mostly between 50 and 200 m. Research on TLPs with ultra-large-capacity wind turbines above 15 MW, particularly the 22-MW, remains largely unexplored.

For ultra-large capacity wind turbines above 15 MW, especially the 22 MW level, the rotor size, hub height, thrust and overturning moment increase significantly, resulting in stronger coupling between the low-frequency platform motion, wave excitation and structural modes. The loads exhibit more obvious scale-up and nonlinear characteristics. Aiming at this problem, this study will design and develop a TLP foundation for the IEA 22-MW wind turbine, with verification through numerical simulations and scaled model experiments.

The structure of the remaining parts of this article is as follows: Section 2 briefly introduces the basic theory of TLP FOWT dynamics. Section 3 selects the best platform among multiple design platforms by considering economy and safety. Section 4 verifies the reliability of the numerical model through model experiments and evaluates the platform’s stability by simulating extreme experiment conditions. Finally, conclusions are presented in Section 5.

2. Methodology and Modeling

This study developed a numerical model for a 22 MW TLP FOWT, and the motion response of the FOWT under extreme conditions was investigated. The methodology section elaborates on the definition of the coordinate system, the establishment of the motion equations, the Blade Element Momentum Theory, the site conditions, and the design criteria.

2.1. The Coordinate System and Dynamic Equation of Motion

The three-dimensional potential flow theory neglects fluid viscosity, which can significantly improve the calculation efficiency and is applicable to the hydrodynamic analysis of fixed/floating structures. To analyze the motion of the FOWT, a global coordinate system OXYZ and a body-fixed coordinate system o-xyz are defined (Figure 1). The global coordinate system is fixed, with its XOY plane coinciding with the sea surface and the OZ axis pointing vertically upward. The origin O of the body-fixed coordinate system coincides with the center of gravity of the platform and moves with the platform.

The 6-DOF nonlinear motion governing equations of a moored floating structure is

$$[M+M_a]\ddot{x}(t)+Kx(t)=F_W^1(t)+F_W^2(t)+F_n(t,\dot{x})+F_C(t,\dot{x})+F_m(t)$$

(1)

where $M$ is the mass matrix, $M_a$ is the additional mass matrix; $x(t)$ is the displacement vector; $F_W^1(t)$ is the first-order wave force, $F_W^2(t)$ is a second-order wave force; $F_n(t,\dot{x})$ is the potential damping force; $F_C(t,\dot{x})$ is the viscous damping force; $F_m(t)$ is the mooring force.

2.2. Blade Element Momentum Theory

For solving the key aerodynamic performances such as aerodynamic load, power, and thrust on rotating blades, the present model is characterized as an aerodynamic modeling framework based on BEM with dynamic inflow, potential-flow tower interference, and tower aerodynamic loading. Neither dynamic stall nor a free-wake vortex method was considered. Blade Element Momentum Theory consists of two components: the blade element theory and the momentum theory.

(1)

Blade Element Theory

As shown in Figure 2, by decomposing the lift and drag of the blade element along the rotational plane and the normal direction of the rotational plane, two component forces $F_{\mathrm{X}}$ and $F_{\mathrm{Y}}$ can be obtained.

According to the derivation from blade element theory, the thrust force and torque acting on the rotor at radius r of the wind turbine can be expressed as follows:

$$\mathrm{d}T=N\mathrm{d}{F}_{\mathrm{X}}={\displaystyle \frac{1}{2}}\rho W^{2}Nc{C}_N\mathrm{d}r$$

(2)

$$\mathrm{d}M=Nr\mathrm{d}{F}_{\mathrm{Y}}={\displaystyle \frac{1}{2}}\rho W^{2}Nrc{C}_T\mathrm{d}r$$

(3)

where $C_N$ is the normal coefficient; $C_T$ is the tangential coefficient; $N$ denotes the number of blades of the rotor; $W$ is the airflow velocity over the blade element; $c$ is the chord length of the blade element; and $\mathrm{d}r$ is the differential length of the blade element segment.

(2)

Momentum Theory

The simplified wind rotor rotation model is shown in Figure 3.

Based on the momentum theory, we can obtain the following:

$${\displaystyle \frac{\alpha }{1-\alpha }}={\displaystyle \frac{Nc{C}_N}{8\pi r {\sin }^2 \varphi }} , {\displaystyle \frac{{\alpha }^{\prime }}{1-{\alpha }^{\prime }}}={\displaystyle \frac{Nc{C}_T}{4\pi r \sin 2\varphi }}$$

(4)

If the airfoil drag in the equation is neglected, the following can be obtained:

$$\tan \varphi ={\displaystyle \frac{1-\alpha }{\lambda \left(1+{\alpha }^{\prime }\right)}}$$

(5)

where $\lambda =\Omega r/V_1$ is the tip speed ratio at the radius.

(3)

Blade Element Momentum Theory

Blade Element Momentum Theory (BEM) combines the blade element theory and the momentum theory, and solves for the normal and tangential induction factors through an iterative method. It defines the solidity $\sigma (r)$ as the ratio of the total blade area to the area of the entire wind rotor disk:

$$\sigma (r)={\displaystyle \frac{c(r)B}{2\pi r}}$$

(6)

where $c(r)$ is the local chord length of the blade; $B$ is the number of blades; $r$ is the blade radius. By solving the coupled equations, the expressions for the axial induction factor $a$ and the tangential induction factor $a^{\prime }$ can be obtained as follows:

$$a={\displaystyle \frac{1}{\frac{4 {\mathit{sin}}^2 \varphi }{\sigma C_N}+1}}\hspace{1em},\hspace{1em}{a}^{\prime }={\displaystyle \frac{1}{\frac{4\mathit{sin}\varphi \mathit{cos}\varphi }{\sigma C_T}-1}}$$

(7)

2.3. Site Conditions, Turbine Standards and Design Criteria

2.3.1. Site Conditions

In this study, Wenzhou, Zhejiang (East China Sea), and Rongcheng, Shandong (Yellow Sea) are selected as the typical sea areas for research. These two regions represent the two major typical environmental types (north and south) in China’s offshore wind energy-rich areas. The research will focus on studying the dynamic response under two extreme environments to better verify the safety and reliability of the design scheme. The operating water depth in both sea areas is calculated as 100 m, and the 50-year return period wind, wave, and current environmental conditions are presented in

Table 3. Environmental parameters.

Parameter	Wenzhou, Zhejiang	Rongcheng, Shandong
Water Depth (m)	100	100
Wind Speed (m/s)	55	40.59
Significant Wave Height (m)	15.10	11
Wave Periods (s)	21.71	15.50
Surface Current Velocity (m/s)	2.17	1.8

.

2.3.2. Design Criteria

According to API RP 2SK standard [26], the equivalent safety factors for different loadcases and analysis methods are summarized in

Table 4. Safety factors under different loadcases and analysis methods.

Loadcase	Analysis Method	Equivalent Factor of Safety
Intact	Quasi-static	2.0
Intact	Dynamic	1.67
Damaged	Quasi-static	1.43
Damaged	Dynamic	1.25

. Which are applicable to mooring systems that are used in FOWT. Since a dynamic analysis method was employed in this study, a safety factor of 1.67 was adopted as the design criterion.

According to BV NI638 [27], the statistical value of long-term response extreme values under time-domain coupled calculations is given by the following equation:

$$X_d=X_M+\mathrm{a}{X}_S$$

(8)

where $X_k$ is the extreme value of the k-th calculation; $X_M$ is the average value of the maximum values $X_k$ from k calculations; $X_S$ is the standard deviation of $X_k$; $n$ is the number of time-domain simulations under the sea condition; and the value of $\mathrm{a}$ is determined in accordance with

Table 5. Relationship between factor a and number of simulated sea conditions.

$\mathit{n}$ = 5	$\mathit{n}$ = 6	$\mathit{n}$ = 10	$\mathit{n}$ = 12	$\mathit{n}$ = 20	$\mathit{n}$ = 30
0.6	0.54	0.3	0.26	0.1	0

:

3. Numerical Studies

This section introduces the design of the TLP FOWT and the mechanical properties of tendons. Subsequently, hydrodynamic coefficients are obtained via HydroDyn, and a numerical model is established via the latest version of OpenFAST with all its sub-modules to analyze its hydrodynamic performances as well as the dynamic responses under various sea conditions, including wind, wave–current coupling, and wind–wave–current coupling, to evaluate the motion performance of different schemes and conduct model selection. Among them, MoorDyn is adopted for mooring modeling, ServoDyn is used for servo control, and AeroDyn is employed as the aerodynamic module.

3.1. Conceptual Design and Screening of Schemes A, B and C

The present platform design follows our previously developed 15 MW TLP FOWT [6], which demonstrated good global performance and stability. On this basis, a global sizing of the TLP hull is designed for supporting the IEA-22 MW wind turbine. The mooring system of the TLP FOWT consists of three groups of tendons with identical material properties. A comprehensive evaluation is conducted on the operational performance of the system matching the 22 MW wind turbine under extreme sea conditions. In the preliminary design, each group comprises 4 tendons, totaling 12 in all. The fairleads are positioned at the outermost part of the bottom of the three pontoons. The mooring layout of the platform is illustrated in Figure 4, and the general design drawing of the floating platform is shown in Figure 5

Considering that the TLP FOWT operates at a water depth of 100 m, Xtreme steel wire is used for the tendons, and the mooring constraints are articulated at both upper and lower nodes. Meanwhile, the drag coefficient Cd is 1.6, and detailed information on the wire is presented in

Table 6. Detailed information on the wire.

Parameters	Value
Length/m	78
Diameter/m	0.153
Axial stiffness EA/N	$2.146\times {10}^9$
Minimum breaking load (MBL)/t	2579
Wet weight/(kg/m)	99.1
Dry weight/(kg/m)	123

.

This study comprehensively considers design factors such as the mechanical properties of mooring lines, the weight of the platform and displacement, and proposes three schemes (A, B, and C) for the mooring system. The specific design parameters are presented in

Table 7. Differences in parameters of different schemes.

Key Parameters	Scheme A	Scheme B	Scheme C
Column diameter/m	14	13	13
Pontoon width/m	10	10	8.5
Pontoon height/m	8–12	8–10	8–10
Height of center of gravity/m	15.45	23.90	24.46
Total mass/t	9619	7458	7358
Displacement/t	16,819.23	14,558.08	13,308.60
Steel consumption per Megawatt	229	198	181
Number of tendons	12	12	9
Pretension/t	600	600	650
Radius of gyration/m	65.55, 65.55, 25.57	71.46, 71.46, 25.92	71.17, 71.17, 25.55

. The study finds that scheme A adopts a ballast water configuration of nearly 2000 tons. Although it can meet the basic stability requirements, it will directly increase the steel consumption, thereby significantly raising the initial construction cost of the platform, making it difficult to reflect the economic advantages of the TLP foundation in engineering applications. The comparison diagram of the floating foundation steel consumption, total mass, displacement and mooring design of the three schemes (A, B, and C) is illustrated in Figure 6. It can be clearly seen that the comprehensive cost–performance ratio of scheme A can hardly meet the economic indicators required for TLP selection, so this scheme will be excluded from the scope of subsequent analysis. The response analysis in this paper will focus on schemes B and C for calculation, verify the operational performance differences between the two schemes under the same sea conditions by comparing with relevant standards, and finally determine the optimal floating foundation design scheme.

3.2. OpenFAST Modeling, ULS Checks for B and C, and Final Selection of Option B

This section verifies the mechanical properties and motion response of the FOWT under different sea conditions. It verifies the dynamic responses of schemes B and C under wind, wave–current coupling, and wind–wave–current coupling conditions, with the upper wind turbine and tower adopting the IEA 22 MW wind turbine. In line with the standard requirements, 5 random seeds are selected for each design sea area. During the subsequent verification process, the extreme values of platform motion response and mooring tension are further checked to meet the standard.

To verify the sensitivity of numerical results to discretization, a grid independence test is performed in GeniE using characteristic grid sizes of 0.75, 1.00 and 1.25 m, with consistent physical models, boundary conditions and solution control parameters, and the schematic diagram is shown in Figure 7. The response amplitude operator (RAO) is taken as the criterion: the amplitude and curves of RAOs for each degree of freedom under different grids are compared within the same incident wave direction and frequency range. The results show that the RAO curves tend to be stable as the grid is refined from 1.25 m to 1.00 m and further to 0.75 m. The differences in key resonance frequencies and peak responses remain within an acceptable range, indicating that the numerical results are insensitive to grid size. Therefore, a grid size of 1 m is adopted in this paper to ensure the accuracy of the calculation results while taking computational efficiency into account.

Meanwhile, this section conducts hydrodynamic performance analysis of the TLP floating foundation using the HydroD. To obtain the motion characteristics of the platform in still water—including key parameters such as natural frequency and damping coefficient—RAO and free decay numerical analysis is carried out. This calculation not only verifies the accuracy of the numerical simulation model and clarifies the platform’s hydrodynamic characteristics but also provides reliable basic parameter support for subsequent platform motion performance evaluation and operational safety verification.

Figure 8 shows the 6-DOF RAO curves of the platform under wave directions of 0°, 45°, 90°, 135°, and 180°. Only the RAOs of scheme B are presented below. It can be seen that the peak values and trends of the surge and sway RAO curves are similar, reaching peaks at a period of approximately 27.5 s. The heave RAO peaks at around 12 s, and different wave directions have little influence on its amplitude. In addition, the roll and yaw RAO curves are nearly zero at 0° and 180°, while the curves at other angles reach maxima at 7.5 s and 27.5 s, respectively. The pitch curves at 0° and 180° almost coincide, with peaks at approximately 7.5 s and 16 s, and the peak at 16 s is larger than that at 7.5 s.

Figure 9 illustrates the free decay characteristics of schemes B and C in the surge, heave, and pitch degrees of freedom, and the free decay period of schemes B and C in six DOF is presented in

Table 8. Natural periods of B/C scheme.

Natural Periods	Scheme B	Scheme C
Surge period/s	30.3	34.48
Sway period/s	30.3	34.48
Heave period/s	1.56	1.8
Roll period/s	5.18	5.37
Pitch period/s	5.18	5.37
Yaw period/s	15.15	16.95

. It can be seen from the comparison that due to the increase in the number of mooring tendons, the overall natural period of scheme B is shorter than that of scheme C, indicating that scheme C has a more flexible structural dynamic characteristic. Both schemes have relatively long natural periods in the surge and sway directions, while the roll and pitch periods are relatively small, and they are more easily excited by waves. Once excited, the platform will exhibit obvious frequency coupling and resonance amplification trends. Therefore, subsequent focus should be placed on verifying the coupled response characteristics between wave loads and the pitch-roll motion of the platform. Nevertheless, its coupling characteristics may be affected by aerodynamic damping and viscous damping. Thus, to better describe the coupled response characteristics, scaled model tests were carried out in the follow-up study for verification.

The cut-out wind speed of the wind turbine is 25 m/s; when the wind speed exceeds this value, the turbine will automatically switch to shutdown mode and stop energy generation. To evaluate the dynamic response characteristics and structural safety of schemes B and C under such extreme wind conditions, this study selects extreme wind parameters from two typical offshore wind farm sites in China—Wenzhou, Zhejiang, and Rongcheng, Shandong—for numerical calculation. Among them, the extreme verification wind speeds for the two sea areas are set at 40.59 m/s and 55 m/s. Both are significantly higher than the turbine’s cut-out wind speed, which can fully demonstrate the platform’s dynamic response under extreme wind load conditions, and the turbulent wind curve used in the calculation is illustrated in Figure 10. In addition, the JONSWAP spectrum is adopted for waves, and wave spreading is not considered. Meanwhile, the key parameters for the numerical simulation are set as follows: the time step is 0.0125 s, and the total simulation duration is 3600 s to ensure the stability and representativeness of the results. The initial 50 s of the transient period are excluded and not presented; only the steady-state data are retained for subsequent analysis to guarantee the reliability of the results, and the condition parameter settings are detailed in

Table 9. Dynamic response coupling calculation condition.

Loadcase	155 m Average Wind Speed (m/s)	Significant Wave Height (m)/ Wave Period (s)	Peak Enhancement Factor	Surface Current Velocity (m/s)	Random Seed Number	Incident Direction
LC-BW/CW-WD	55	-	-	-	1	0°/180°
LC-BR/CR-WD	40.59	-	-	-	1	0°/180°
LC-BW/CW-WC	-	15.1/21.7	3.3	2.17	10	0°/180°
LC-BR/CR-WC	-	11/15.5	3.3	1.8	10	0°/180°
LC-BW/CW	55	15.1/21.7	3.3	2.17	10	0°/180°
LC-BR/CR	40.59	11/15.5	3.3	1.8	10	0°/180°

. Herein, BW/CW denotes scheme B and scheme C under the Wenzhou sea state, while BR/CR denotes scheme B and scheme C under the Rongcheng sea state. The abbreviation WD stands for wind conditions, and WC stands for combined wind and current conditions. Cases without additional abbreviations refer to the combined wind–wave–current conditions.

To analyze the influence of second-order waves on the TLP, we first compared the responses of the TLP floating platform under first-order and second-order sum-frequency extreme sea conditions, and presented the frequency-domain diagram and time-domain diagram of Mooring Line 1, as shown in Figure 11. It can be seen from the comparison results that the influence of second-order waves on the long-period wave band above 10 s is not significant under this extreme sea condition. In Figure 8a, the spectral lines of “without adding second-order waves” and “with adding second-order waves” basically overlap in the low-frequency region, and the energy distribution is almost consistent with the spectral peak position, indicating that the second-order sum-frequency does not significantly increase the amplitude of the long-period response. Figure 8b also shows that the two working conditions are highly consistent. It can be clearly seen that the response of the structure to long-period waves is mainly controlled by the first-order component under this working condition, and the second-order sum-frequency response is relatively weak. Therefore, we will just analyze the response of the TLP under first-order waves in the following sections.

The statistical values of the TLP FOWT motion and tension response under wind load conditions are illustrated in Figure 12. The dynamic response characteristics were analyzed, and the results show: the maximum mooring tension of scheme B is 7969 kN, and the maximum pitch angle of the platform is 0.09237°; the maximum mooring tension of scheme C reaches 9060 kN, while the maximum pitch angle of the platform is 0.0892°. It can be seen from the comparison that scheme B is superior to scheme C in both controlling the extreme mooring tension and the platform pitch, and it also has better fluctuation stability in overall dynamic response. Further statistics show that the fluctuation amplitude of the mooring tension of both schemes does not exceed 50 tons, and the fluctuation amplitudes of the mooring tension on the windward and leeward sides are of the same order of magnitude, showing no significant difference.

The statistical values of the mooring tension of #1, #5 and #9 under the combined wave–current sea conditions in Wenzhou and Rongcheng are presented in

Table 10. Statistical values of tension under wave–current conditions.

Tendon	Wenzhou		Rongcheng
	Mean (kN)	Standard Deviation (kN)	Mean (kN)	Standard Deviation (kN)
LC-B-0-WC-#1	6191	1619	6264	1381
LC-B-0-WC-#5	5990	687	5844	723
LC-B-0-WC-#9	5957	850	5786	885
LC-C-0-WC-#1	6778	1891	6851	1743
LC-C-0-WC-#5	6476	861	6257	970
LC-C-0-WC-#9	6479	774	6275	880
LC-B-180-WC-#1	5903	1355	5664	1351
LC-B-180-WC-#5	6106	983	6089	889
LC-B-180-WC-#9	6139	1196	6148	1088
LC-C-180-WC-#1	6372	1604	6051	1753
LC-C-180-WC-#5	6674	1239	6650	1190
LC-C-180-WC-#9	6671	1126	6632	1081

. It can be clearly observed that schemes B and C exhibit the same trend in influencing mooring tension under wave–current sea conditions. Therefore, to clearly demonstrate the performance gap between schemes B and C under the same sea conditions, the dynamic response of the platform under the sea conditions in Rongcheng is taken as an example for illustration.

As can be seen from Figure 13, the maximum pitch angle of the platform in scheme B is 0.3838°. However, since scheme C has three fewer tension tendons than scheme B, the motion response of scheme C increases significantly, with the maximum pitch angle of its platform reaching 0.5809°, an increase of 51.62%. Furthermore, due to the increase in the extreme value of the motion response of the floating foundation, the extreme mooring tension also rises significantly, increasing from 11,760 kN in scheme B to 16,330 kN in scheme C, a growth of 38.86%. Thus, under the same wave–current coupling conditions, scheme B has a significantly better ability to restrict the motion of the wind turbine platform than scheme C.

The statistical values of the mooring tension of #1, #5 and #9 under the wind–wave–current coupled sea conditions in Wenzhou and Rongcheng are shown in

Table 11. Statistical values of mooring tension under wind–wave–current coupling condition.

Tendon	Wenzhou Site		Rongcheng Site
	Mean (kN)	Standard Deviation (kN)	Mean (kN)	Standard Deviation (kN)
LC-B-0-#1	5401	1580	5827	1434
LC-B-0-#5	6705	762	6211	785
LC-B-0-#9	6376	878	6010	942
LC-C-0-#1	5742	1921	6275	1740
LC-C-0-#5	7559	981	6796	1008
LC-C-0-#9	6816	861	6458	939
LC-B-180-#1	6923	1330	6205	1379
LC-B-180-#5	5617	981	5823	906
LC-B-180-#9	5949	1206	6025	1138
LC-C-180-#1	7752	1642	6769	1711
LC-C-180-#5	5936	1265	6254	1162
LC-C-180-#9	6677	1197	6591	1123

. It can be clearly observed that the variation trend of the dynamic response of the platform in Rongcheng is basically consistent with that in Wenzhou; thus, the dynamic response of the platform under the sea conditions in Rongcheng is taken as an example for demonstration.

As can be seen from Figure 14, the maximum pitch angle of the platform of scheme B is 0.5983°. However, since the mooring restoring force provided by scheme C is significantly smaller than that of scheme B under the same displacement, the extreme value of the platform motion response increases remarkably, with the maximum pitch angle of the wind turbine platform reaching 0.9387°, an increase of 56.89%. Moreover, due to the increase in the extreme value of the motion response of the floating foundation, the extreme mooring tension also increases significantly, rising from 12,070 kN in scheme B to 17,680 kN in scheme C, an increase of 46.48%. Under the combined wind–wave–current sea conditions, scheme B still outperforms scheme C in terms of displacement restriction effect on the wind turbine platform, and also has a significant improvement in the ability to control the extreme tension of the mooring system.

3.3. Comparison of Key Responses and Selection of Option B

As can be seen from the analysis of the dynamic response of the FOWT under different combined sea conditions in the previous section, the number of tension tendons in scheme B is larger than that in scheme C. The extreme values of the main DOF motion response and mooring tension of the floating foundation of scheme B are significantly lower than those of scheme C under the same sea conditions, and the effect becomes more pronounced as the components of the combined sea conditions increase. During the operational period, TLP FOWT are subject to the impacts of extreme sea conditions; therefore, the extreme values of the dynamic response of the TLP FOWT under the wind–wave–current combined sea conditions are selected for standard verification. In accordance with the requirements of core standards,

Table 12. Extreme value parameter statistics table.

Loadcase	Extreme Tension (kN)	Safety Factor (Breaking Tension/Extreme Tension)	Maximum Pitch Angle (°)
LC-BW-0	11,528	2.19	0.547
LC-BR-0	11,432	2.21	0.443
LC-BW-180	11,473	2.20	0.274
LC-BR-180	11,427	2.22	0.252
LC-CW-0	15,149	1.670	0.830
LC-CR-0	15,076	1.677	0.679
LC-CW-180	13,375	1.890	0.324
LC-CR-180	13,451	1.879	0.318

verifies the operational performance of the schemes B and C proposed in this paper.

As can be seen from Figure 15a, the vertical tension mooring layout selected in this paper exerts good constraints on the extreme pitch motion value of the TLP FOWT, resulting in a maximum pitch angle significantly lower than the 5°/10° requirement specified in the standards. Meanwhile, the increase in the number of tendons enables scheme B to have better constraint capacity than scheme C.

Figure 15b shows the comparison between the maximum tension values of scheme B and C and the standard verification values under wind–wave–current combined sea conditions. According to the API RP 2SK [26], the safety factor of 1.67 is used for the mooring system. It is evident that the safety factors of the mooring tension for scheme B are all greater than 1.67. For scheme C, however, due to the smaller number of mooring tendons, its constraint on the motion response of main DOF, such as pitch, is relatively poorer than that of scheme B. This leads to a significant increase in the maximum mooring tension of scheme C, making its safety factor approach 1.67. Meanwhile, it can be seen from the standard verification value curve of scheme C that the TLP FOWT of scheme C is more sensitive to the incident direction of sea conditions.

Under sea conditions with the same parameters but different incident directions, there are significant differences in the standard verification values of the mooring tension for scheme C. Under 180° incidence, the verification values of scheme C are 1.89 and 1.88; when the incident direction of sea conditions changes to 0°, the verification values reach 1.67 and 1.68, which are very close to the standard requirements. Since TLP FOWT are exposed to complex and variable sea conditions, scheme C poses certain risks when facing complex sea conditions. Therefore, this paper selects the floating foundation and mooring system design of scheme B as the final design scheme.

4. Model Tests and Numerical Model Calibration

In this section, physical model tests under Rongcheng sea conditions are adopted to verify the reliability of numerical analysis results. Furthermore, for the validated numerical model, multiple sets of extended extreme conditions are set to analyze the FOWT’s dynamic responses, comprehensively evaluating the hydrodynamic performance of the FOWT.

4.1. Model Tests Setup

For simulating viscous damping on TLP’s hull, model tests are conducted to calibrate the numerical model, and both the linear and quadratic damping terms were calibrated to characterize the viscous damping and nonlinear effects on the TLP’s hull in extreme sea conditions. The tests were carried out at the State Key Laboratory of Coastal and Offshore Engineering at Ocean University of China. The dimensions of the wave–current flume are 60 m × 3 m × 1.5 m, and the schematic diagram of the flume is shown in Figure 16a. The model tests follow the Froude Criteria, neglecting the Reynold Criteria, and the scale ratio is 1:64, determined by the sizes of the flume. The detailed dimensions of the prototype and the physical model are listed in

Table 13. Dimensions of the prototype and the physical model.

Parameter	Prototype	Model
Column diameter/m	13	0.203
Pontoon width/m	10	0.156
Pontoon length/m	8–10	0.125–0.156
Height of center of gravity/m	23.9	0.373
Total mass/t	7458	0.0278
Displacement/t	14,558.08	0.0542
Estimated steel consumption/t	4367	0.01625
Pretension/t	600	0.0022
Radius of gyration/m	71.46, 71.46, 25.92	1.12, 1.12, 0.41

.

A water depth of 1.7 m in the model corresponds to a water depth of 108.8 m in the prototype, which can simulate the 100 m water depth. The maximum simulated wave height of the wave maker is 0.3 m, which corresponds to a prototype wave height of 19.2 m, which can meet the wave-making requirements of most sea conditions. The maximum flow rate of the flume is 2 m³/s, and when the cross-sectional area is 3.6 m², the average flow velocity can reach 0.56 m/s, which corresponds to a prototype flow velocity of 4.44 m/s, which is significantly higher than the required value. A wind load simulation device with a maximum output thrust of 5 kg was selected, which can meet the requirements of the environmental setting.

The total wind load on the TLP wind turbine is composed of the rotor load and the tower load. At low wind speeds, the total wind load comes almost entirely from the rotor thrust. At high wind speeds, however, the blade feathering leads to a significant increase in the proportion of the wind load acting on the tower. Therefore, the magnitude and action point of the wind load vary with different wind speeds. The thrust output by the wind load simulation device is variable, yet the device itself cannot move actively. Therefore, to achieve accurate simulation of aerodynamic loads, a special device was customized in this test to carry the wind load simulation device and sensors, enabling the wind load simulation device to move up and down along the tower, as shown in Figure 16b. In addition, tension sensors and six DOF displacement sensors were employed in the tests. The maximum error rate of the tension sensor is 0.5% FSO (Full Scale Output), while the maximum error of the 6 DOF displacement sensors is 0.5 mm. The schematic diagram of the experimental setup is shown in Figure 17.

Prior to the formal experiments, wind speed calibration and wave calibration were first carried out, as shown in Figure 18a. It can be seen that the calibrated wind speed agrees well with the target wind speed, indicating a high accuracy of the simulated wind field. Meanwhile, Figure 18b shows that the peak locations of the spectral curves are in close agreement, and the overall spectral distributions remain highly consistent, indicating that the simulated waves can accurately reproduce the characteristics of the target spectrum.

4.2. Experimental Validation

The free decay tests were conducted to characterize the natural periods of the TLP FOWT. Each group of tests was repeated multiple times to reduce errors caused by experimental deviations. The tests were carried out by displacing the model in the corresponding direction and releasing it carefully, while the numerical tests were completed by setting the wind direction and waves to zero and introducing a small initial offset in the FAST file, and a numerical–experimental comparison diagram was plotted in Figure 19. It can be observed that there exists a good consistency in the free decay curves in surge, heave, and pitch. Although there are minor deviations in the response amplitude, the attenuation trends and vibration frequencies of the two remain consistent. The statistics of the natural periods are summarized in

Table 14. TLP FOWT natural period comparison.

Natural Period	Numerical Value	Experimental Value
Surge(s)	28.57	27.86
Sway(s)	28.57	27.95
Heave(s)	1.56	1.58
Roll(s)	3.00	3.04
Pitch(s)	3.06	3.01
Yaw(s)	14.25	14.17

. Calculations show that the maximum difference in natural periods does not exceed 2.5%, demonstrating that the numerical and experimental results match well.

To ensure the accuracy of the mooring horizontal stiffness at the Froude model scale, calibration tests were conducted on the model system: during the model test, the traction effect of the weights will cause the offset of the FOWT model system, and the horizontal stiffness curve is obtained by measuring the force–displacement relationship with force sensors.

The comparison results between the experiment and numerical simulation are shown in Figure 20. It is worth noting that the horizontal stiffness curve obtained from the test shows a good coincidence with the numerical results. The slope deviation between the two is always maintained within an extremely small range, and with the increase in displacement, the deviation between the simulated values and the experimental values does not show an obvious divergent trend, and the error rates are all controlled within 5%. Meanwhile, the force–displacement relationship exhibits significant linear characteristics, which indicates that the pretension of the tendons is uniformly distributed and the floating foundation has good geometric symmetry, thus verifying the rationality of the design scheme.

To verify the reliability of the numerical simulation for the dynamic response of the TLP FOWT under extreme sea conditions, model test verification was carried out under extreme conditions in this section. It can be seen from the frequency domain comparison diagram and the dynamic response extreme value comparison curve under extreme sea conditions shown in Figure 21: the energy of the surge motion of the TLP FOWT is mainly concentrated in the low-frequency range of 0–0.2 Hz, and the amplitude approaches zero after 0.2 Hz. This indicates that the surge response of the platform is dominated by low-frequency environmental excitation, with no obvious high-frequency resonance characteristics observed.

Meanwhile, thetension time history curve shows that the mooring tension exhibits significant random fluctuation characteristics within 3600 s. The tension values are generally distributed in the range of 4 × 10⁶–1 × 10⁷ N, and the fluctuation trends and amplitude variations in the two curves from the experiment and simulation show a good consistency, with the deviation within an acceptable range.

Based on the data from the free decay tests, horizontal stiffness tests, and coupled wind–wave–current tests under extreme sea conditions, the deviation between the experimental and numerical results is less than 5%. The good agreement between the two results fully verifies the safety and reliability of the numerical model.

4.3. Extended Ultimate Limit State Analysis with the Calibrated Model

Although the aforementioned model tests have preliminarily verified the reliability and safety of the numerical simulation model for the mooring system of the TLP FOWT. But to further examine the applicability and robustness of the model under extreme sea conditions, this section selects typical sea condition parameters based on marine environment statistical analysis data, and constructs a dynamic response analysis, providing more comprehensive theoretical support for the model. To verify the safety of the numerical model of scheme B under different return periods, three groups of extreme working conditions are set according to the environmental contour, and the working condition settings are shown in

Table 15. Extreme condition settings.

Return Period (RP)	Significant Wave Height (m)	Wave Period (s)	Wind Speed (m/s)	Current Speed (m/s)
1	8	12	24.8543	1.6
10	11	14	28.9	2
50	13	16	31.2124	2.6

. Regarding the acting direction of environmental loads, the wind, wave and current are set to be in the same direction; for the 180° environmental load acting angle, the coordinate system established for the model test is consistent with that used in the numerical calculation, and the results are shown in

Table 16. Extreme value statistics.

Loadcase	Maximum Tension/kN	Maximum Pitch Angle/°	Maximum Surge/m	Maximum Tension Position
RP-1	11,690	0.1861	10.11	4#
	10,520	0.2018	9.314	9#
	11,020	0.1904	8.747	4#
	10,810	0.2047	9.372	8#
	11,400	0.2021	9.667	4#
RP-10	12,730	0.2955	15.03	4#
	11,760	0.2613	16.7	4#
	11,560	0.2167	15.2	4#
	10,900	0.2083	14.74	4#
	12,230	0.3211	14.95	1#
RP-50	11,820	0.2719	15.42	4#
	12,910	0.5057	16.01	1#
	12,890	0.4252	16.47	4#
	12,140	0.3086	18.21	4#
	12,910	0.3358	19.32	4#

.

It can be seen from the analysis of the tension and safety factor response characteristics of the TLP mooring system for FOWT under sea conditions with different return periods in Figure 22a that the maximum tension of Mooring Line #1 on the wave-facing side under the 1-year, 10-year and 50-year return period sea conditions is 11,690 kN, 12,640 kN and 12,910 kN in sequence. That of Mooring Line #5 is 11,250 kN, 11,000 kN and 11,950 kN, while that of Mooring Line #9 on the wave-back side is 10,950 kN, 10,700 kN and 11,210 kN, showing the distribution characteristic that the tension on the wave-facing side is generally higher than that on the wave-back side. Moreover, Mooring Line #1 is most significantly affected by the increase in the return period of sea conditions, with its tension continuously rising as the return period increases. The tension of Mooring Line #5 shows a slight decline under the 10-year return period sea conditions, then rebounds under the 50-year return period sea conditions. The tension variation range of Mooring Line #9 on the wave-back side is relatively gentle, with only a slight increase observed under extreme sea conditions.

The safety factor of the mooring system shows a continuous downward trend as the return period of sea conditions increases from 1-year to 50-year, which is 2.16, 1.99 and 1.96 in sequence. This reflects that the safety margin of the mooring system gradually decreases under extreme sea conditions, but it is still higher than the minimum safety factor limit of 1.67 for mooring systems specified in standards, indicating that the bearing safety of the mooring system can be guaranteed.

Combined with the law of tension distribution, it can be concluded that Mooring Line #1 on the wave-facing side is the key load-bearing component of the mooring system under extreme sea conditions, and its tension response and safety factor variation directly determine the overall safety performance of the mooring system. In contrast, the tendons on the wave-back side are weakly excited by environmental loads, and the fluctuation ranges of both tension and safety factor remain at a low level.

In addition, the long-term response extreme value statistics of surge and pitch are calculated according to the formula for long-term response extreme value statistics, as shown in Figure 22b. It can be seen that the values show a significant nonlinear growth with the increase in sea condition return period; under the 50-year return period sea conditions, the surge is 17.96 m, and the pitch is 0.5057°. This motion amplitude does not exceed the 5°/10° requirement, and will not cause potential safety hazards such as collisions between wind turbine blades and towers, and excessive slackness of mooring lines. Overall, under the sea conditions ranging from a 1-year to 50-year return period, the mooring system meets the safety requirements in terms of both the bearing capacity of the mooring system and the motion response of the platform.

5. Conclusions

This study aims to propose an economical and reliable TLP foundation for a 22 MW wind turbine in the 100 m water depth of the East China Sea. To this end, three TLP schemes with corresponding mooring systems are initially designed. Subsequently, hydrodynamic analysis and dynamic response assessment are conducted for these schemes under extreme conditions. By comparing their global performance and mooring tensions, the optimal design is identified. A fully coupled integrated numerical model is then established for this optimal design and calibrated against 1:64-scale physical model tests in a flume. Finally, the validated model is employed to simulate multiple sets of extended extreme conditions, analyzing the platform’s dynamic responses to comprehensively evaluate its global performance and structural stability. The main conclusions are as follows.

(1)

Three different schemes of TLP foundation are designed, and a comprehensive evaluation is carried out from both economic and structural safety standpoints. Among them, scheme A is eliminated due to excessive steel consumption and high construction cost; scheme C is also ruled out because global performance, mooring tensions are not sufficient, and the fatigue life is prone to being insufficient. Eventually, scheme B is identified as the optimal design scheme in both economy and structural safety.

(2)

To verify the reliability of numerical analysis, model scale tests with a scale ratio of 1:64 are conducted, including free decay tests, horizontal stiffness tests, and extreme condition response tests. The results show a good consistency between numerical simulations and test data: the maximum difference between the numerical and experimental natural periods is no more than 2.5%, and that of horizontal stiffness is within 5%. Under extreme sea conditions, the frequency spectra of surge motion and mooring tension derived from experimental data are highly consistent with the numerical model established in OpenFAST.

Based on the calibrated numerical model, the global performance of the TLP FOWT under sea conditions with different return periods is carried out. The results show that the maximum mooring tension (12,910 kN), maximum pitch angle (0.5057°), and maximum surge (19.32 m). Moreover, the statistical values of response extremes of 5 simulations are calculated. Under the 50-year RP sea conditions, the maximum surge is 17.96 m and the maximum pitch angle is 0.4204°, which is less than 1°, demonstrating the good performance in pitch and thus is very friendly to the wind turbine. The safety factor of the mooring system remains above 1.96, which satisfied the safety factor of 1.67 specified in API RP 2SK [26]. This verifies the safety the designed TLP foundation under extreme seaenvironments.

By adding an extra mooring line, scheme B significantly optimizes the global force configuration of the TLP, achieving a more efficient load transfer path and more uniform tension distribution under extreme sea conditions, which effectively reduces the extreme loads and improves the fatigue performance. Meanwhile, the additional mooring line adjusts the horizontal and vertical stiffness of the mooring system, thereby avoiding the risk of wave-frequency resonance and suppressing large-amplitude motion responses. Consequently, the mooring positioning ability, mooring safety, and operational stability of the TLP under extreme sea conditions are all improved. However, more mooring lines mean more costs, and the system’s vertical stiffness increases, which alters the natural frequency of the system and possibly introduces the risk of high-frequency vibrations. In future work, the multi-source vibrations of the TLP FOWT and the corresponding mooring fatigue performance will be investigated and evaluated for future deployment in deep-water wind farms.