### 1. Introduction

### 2. Fixed Offshore Wind Turbine

### 2.1 Fixed Substructure

### 2.2 Load Analysis of Wind Turbine

*dL*, N) and drag (

*dD*, N) forces applied to the two-dimensional airfoil of each element to calculate the force and moment applied to the entire wind turbine using the sum of longitudinal forces (Faltinsen, 1993). The force acting on the blade can be obtained using the induced velocity vector

*W*of the cross-section of the blade in the momentum conservation equation based on the momentum and angle, and the torque and power applied to the rotor shaft based on the force acting on the blade (Snel, 2003). The relative velocity

*V*can be separated and expressed as follows. where

_{rel}*x*is the vertical direction with respect to the rotational axis of the rotor and

*z*is the longitudinal direction of the blade.

*ω*represents the angular velocity of the rotor, and the angle of attack (

*α*) and inflow angle (

*ϕ*) on the airfoil plane in Fig. 1 can be expressed as in the following equations using the torsional angle (

*θ*) and pitch angle (

*θ*) (Burton et al., 2001).

_{p}*dT*, N) that is applied to the blade element and obtained by numerical calculation can be expressed as in Eq. (5), and the torque (

*dQ*, N·m) can be expressed as in Eq. (6) based on the horizontal force (

*dH*, N), where

*ρ*is the air density (kg/m

^{3}),

*V*is the wind speed (m/s),

_{rel}*B*is the number of blades,

*r*is the distance (m) from the hub to the blade sector,

*c*is the chord length, and the lift coefficient

*c*and drag coefficient

_{l}*c*are dimensionless coefficients of the airfoil associated with the Reynolds number (Lanzafame and Messina, 2007).

_{d}*C*is the drag coefficient and

_{d}*C*is the inertial coefficient. The load of a fixed structure created by accelerating the fluid particles is expressed as an inertial force as in Eq. (8).

_{m}*η*and water depth

*d*can be obtained using the water particle velocity

*u*as in Eq. (9) below.

### 3. Calculation Results and Analysis

### 3.1 Numerical Analysis

*V*(

*z*) is the wind speed at a spot where the vertical displacement from the mean water level is

*z*.

*V*represents the wind speed at the hub height

_{hub}*z*. The hub height of the NREL 5 MW wind turbine used as a calculation model in this paper is 90 m.

_{hub}*α*represents the wind shear index indicating an abrupt change in the wind speed or direction. The international standard for designing fixed wind turbines recommends that an

*α*value of 0.14 be used (IEC, 2019), but this value is set to 0 in this study to linearly increase the wind speed from the water surface.

*M*and

*K*are global matrices consisting of the element unit mass matrix and stiffness matrix of the substructure, respectively.

*U*represents the displacement and

*F*is the external force (Damiani et al., 2015).

*x*-axis direction displacement,

*x*-

*z-*direction rotational displacement, and

*z*-direction vertical displacement) of the fixed wind turbine was designated as the main motion response for analyzing the calculation results because this motion response is most affected by winds and waves entering in the

*x*-direction. It is also important to examine the rotor rotation speed and thrust determined according to the effect of the wind and the nacelle acceleration directly connected to the actual power generation efficiency of the wind turbine. Another important result to be analyzed in this study is the bending moment of the base connection of the tower created by fore-aft shearing loads, the largest force acting on the turbine. Lastly, the effects of the wind and wave forces were compared by checking the shear force in the

*x*-direction to identify changes in the force applied to the jacket. Specific information on the model used in this study is described through Table 1 and Figs. 3–4.

### 3.2 Design Load Case

*V*) were inputted for steady winds, and the results calculated by turbulent wind simulations with designated speeds (

_{Steady}*V*) were used as input values for the turbulent winds. The wind speeds were set based on the point of the hub height of 90 m. In the windless scenario (DLC 1), the wind turbine was in a parked condition and the analysis was carried out in the state where the rotors were fixed. The fixed wave height and wave period values were inputted for regular incident waves, and the significant wave height

_{Turbulence}*H*and peak period

_{S}*T*were designated by applying the JONSWAP spectrum for irregular incident waves.

_{P}### 3.3 Analysis of Calculation Results

#### 3.3.1 Wave Only Case

*x*-

*z*-direction rotational displacement, and jacket shear force of the structure match the wave frequency of 0.17 Hz, and the thrust, nacelle acceleration, and bending moment have the same frequency response as the wave frequency in the windless state. There is also a response at 0.32 Hz, which represents the natural frequency of the analysis model as reported by Jonkman et al.(2009). Therefore, the tower of the wind turbine has a considerable response in the natural frequency band even in the windless state simply by the effect of the incident wave.

#### 3.3.2 Wind Only Case

#### 3.3.3 Response to Combined Wind and Wave Case

*V*) and turbulent wind speed (

_{Steady}*V*) of 6 m/s were substituted in the regular wave condition (

_{Turbulence}*H*= 2 m,

*T*= 6 s) in Fig. 10 to compare the response changes in the difference between the steady wind and turbulent wind in the regular incident wave condition (DLCs 6 and 7). The turbulent wind spectrum is dominant at a low frequency in comparison to the incident wave frequency, and the frequency change from a Fourier analysis is 0 because a constant-speed wind was inputted for the steady wind.

*V*= 6 m/s) condition. All the responses of the analysis model are affected by the low-frequency turbulent wind speed. The vertical displacement is relatively less affected because the wind turbine is a fixed structure. The shear force of the jacket and vertical displacement have their maximum responses at the incident wave peak frequency (period of 6 s, 0.17 Hz), which means that they are significantly affected by the incident wave. However, the horizontal displacement and

_{Turbulence}*x*-

*z*-direction rotational displacement of the structure have their maximum responses near 0.4 Hz outside the low-frequency region, which indicates that they are predominantly affected at a frequency of 0.39 Hz (rpm = 7.8/60 s × 3 blades) resulting from multiplying the rotor rotation speed frequency by the number of blades at the inputted wind speed (

*V*) of 6 m/s. The shear force also has a large value at the same frequency.

_{Turbulence}*V*) of 6 m/s. The nacelle acceleration has its maximum response at 0.39 Hz resulting from multiplying the rotor rotation speed of 7.8 rpm by the number of the blades. The bending moment of the tower has a large response at the frequency (0.39 Hz) by the rotor rotation and low-frequency region of the turbulent wind spectrum and shows a trend similar to the

_{Turbulence}*x*-

*z*-direction rotational displacement response, which shows a correlation between the bending moment and rotational displacement.

### 4. Conclusions

In the incident wave-only condition, the motion response and load response of the wind turbine structure were dominant at the wave frequency; the rotor thrust, nacelle acceleration, and bending moment of the tower base had high responses in the natural frequency band of the structure.

In the wind-only condition, all the responses except for the vertical displacement of the structure were dominant at the frequency resulting from multiplying the rotor rotation frequency caused by the wind and number of blades.

In a combined external force where the wind and wave are simultaneously applied, the vertical displacement of the structure was mainly affected by the incident wave; the shear force applied to the jacket was affected by both the wind and incident wave; the bending moment in the tower base was predominantly affected by the wind.