### 1. Introduction

### 2. Dynamics of 15-MW FOWT with Green Hydrogen

*M*,

*M*(∞),

_{a}*C*, and

*K*denote the mass matrix of the floating body, added mass matrix at infinite frequency, additional damping matrix considering viscous effects, and the restoring coefficient matrix based on the wetted surface of the floating body, respectively. The additional damping matrix can be defined in the form of a quadratic damping force proportional to the square of the floating body’s velocity.

*F*

_{w}_{1},

*F*

_{w}_{2},

*F*,

_{C}*F*, and

_{M}*F*denote the matrices for the wave-frequency wave force, second-order wave force, radiated damping force matrix owing to the floating body’s radiation force, mooring force matrix from the coupling effect due to the mooring lines and risers, and the load matrix owing to the tower’s elasticity, respectively.

_{Tower}*ξ*,

*ξ̇*, and

*ξ̈*denote the displacement, velocity, and acceleration matrices of the floating body’s motion, respectively, with the motion of the floating body having six degrees of freedom, comprising three translational motions (surge, sway, and heave) and three rotational motions (roll, pitch, and yaw). The wave-frequency wave force, second-order wave force, and radiated damping force can be expressed as Eqs. (2), (3), and (4), respectively: where

*w*and

_{j}*A*represent the wave frequency and incident wave amplitude at the

_{j}*j*-th frequency component, respectively, and

*N*denotes the number of frequency components of the incident wave. In this study, irregular wave conditions were described based on 300 incident wave frequency components.

_{w}*L*(

*w*) and

*D*(

*ω*

_{1},

*ω*

_{2}) represent the linear transfer function of the wave-frequency wave load and the quadratic transfer function of the low-frequency wave load, respectively. In this study, the Newman approximation was applied to represent the low-frequency wave load.

*R*(

*t*) denotes the impulse response function of the radiation force, which is defined through the Fourier cosine transform of the radiation damping coefficient. The wave-frequency and second-order wave loads and radiation damping coefficient were obtained by solving diffraction and radiation problems.

*ρ*,

*D*,

*l*, and

*Δ*denote the fluid density, object diameter, element length, and element mass, respectively.

*C*,

_{M}*C*, and

_{a}*C*represent the matrices representing the inertia coefficient, added mass coefficient, and drag coefficient, respectively, and

_{D}*v*,

*a*, and

_{f}*a*are the relative velocity between fluid and elements, fluid acceleration, and element acceleration, respectively. By applying these two environmental loads to a lumped-mass model shown in Fig. 1, the behavior and loads of the mooring lines, risers, tower, and turbine blades can be calculated.

_{r}### 3. Numerical Analysis Model

### 3.1 15-MW FOWT Platform

### 3.2 Green Hydrogen Riser

*l*) and the horizontal distance at both ends of the riser were set to 2.8 times and 2 times the water depth (

_{total}*h*), respectively. The length ratio between the upper bare section and the buoyancy module section was set to 0.25 of the total riser arc length. In this study, the total arc length of the riser and the connection locations at both ends were fixed, and optimization was performed on the position and length of the buoyancy module. Detailed riser specifications are provided in Table 3, and the lazy wave riser is shown in Fig. 4. The red part in Fig. 4 indicates the buoyancy module. The representative element length of the mooring line and the riser was set to 10 m, with the element length gradually shortened near each boundary condition to minimize numerical errors.

### 3.3 Environmental Conditions

**(**7

**)**), as follows: where

*V*and

_{c,surf}*V*

_{w}_{,1}

_{H}_{,10}

*denote the current speed at the sea surface and the hourly average wind speed at 10 m above the water surface, respectively. For the extreme load conditions, the wave, current, and wind conditions with a 50-year recurrence period were referenced from Lee et al. (2023), and both the operating and extreme load conditions are summarized in Table 4. In these conditions, the wind, waves, and currents all act in the same direction. Typically, the wind speed criterion used in the design of floating structures refers to the speed at a height of 10 m above sea level, so the extreme wind profile was used to calculate the wind speed at the hub of the floating wind turbine as in Eq.*

_{m}**(**8

**)**(DNV GL, 2021c; IEC TS 61400-3-2:2019, 2019). where

*V*denotes the wind speed at a specific location (

_{w}*z*),

*V*

_{w}_{,}

*denotes the wind speed at the hub location, and*

_{hub}*z*denotes the height of the hub above the water surface. The

_{hub}*α*values 0.14 and 0.11 were used for the operating and extreme conditions, respectively (DNV GL, 2021b; European Commission, 2015).

### 4. Numerical Analysis Results

### 4.1 Validation Test

**(**1

**)**) can be used to describe the global motion of the floating platform. In this study, the total analysis time was 3 hours. The time series data of the platform’s global motion were transformed into a response spectrum using Fourier transformation, and then the incident wave spectrum (Fig. 5(a)) was applied for backward estimation of the motion RAOs (Fig. 5(b)). The time step in numerical analysis was set to 0.025 s. The estimated results generally matched those of Allen et al. (2020).

*g*(= 3.924 m/s²). In this analysis, under operating conditions (DLC 1.1), a maximum nacelle acceleration of 1.5 m/s² was observed, meeting the design requirements. For extreme conditions (DLC 6.1), a maximum of approximately 7 m/s² was evident. Furthermore, in the nacelle acceleration’s Power Spectral Density (PSD) shown in Fig. 8(b), low-frequency components below 0.3 rad/s appear under DLC 6.1 conditions, whereas components around 1.5 rad/s and below 0.3 rad/s were evident under DLC 1.1. The mooring line tensions (Fig. 9) are shown separately for mooring lines 1, 2, and 3, considering the platform’s x-axis symmetry. As shown in Fig. 7(a), the average position of the floating platform moved further in the positive direction of the x-axis under DLC 6.1 than under DLC 1.1. Consequently, mooring line 1 experienced a smaller static tension, while mooring lines 2 and 3 had greater static tension. Additionally, due to the relatively large motion responses of the floating platform under DLC 6.1 conditions, significant dynamic tensions also occurred. However, the maximum tension was approximately 4,500 kN, which is much smaller than the maximum allowable load of the mooring line (13,928 kN). The maximum allowable load is calculated based on a maximum allowable load of 22,286 kN considering a safety factor of 1.6 applied, based on the American Petroleum Institute standards (API, 2008). The PSD of the mooring line tension under extreme loading conditions reveals the behavior characteristics of the mooring line, with relatively large tensions evident at the natural frequencies of the surge, heave, and pitch motions. Importantly, the impact of the surge motion mode, characterized by low-frequency movement, was most significant on the mooring line tension. Table 5 indicates the natural frequencies of the mooring lines, showing that their impact was relatively minor.