*2.5. Brief Description of F2A*

The baseline version of AQWA was incapable of predicting the aero-servo-elastic of floating offshore wind turbines, but it accepted time domain analysis of external forces implemented by dynamic link library (.dll). In order to enable AQWA to form a fully coupled analysis of floating offshore wind turbines, FAST was integrated in AQWA with some simulation function implemented [36]. Therefore, the coupling framework was "FAST2AQWA", denoted as F2A. The coupling of AQWA and FAST was accomplished by user\_force.dll and source code subroutine of FAST. Related simulation capabilities of FAST were completely implemented in time domain analysis in the DLL that can be called by AQWA during the simulation.

#### **3. Numerical Model of Combined System**

The combined system was composed of a semisubmersible platform and a heavingtype WEC connected by a guide-roller system in the middle and an upper connecting system [50]. The wind turbine model used for this study is the NREL 5-MW baseline wind turbine. The main parameters of the 5-MW wind turbine are shown in Table 1 [2]. An illustration of the combined system is shown in Figure 1, and the main parameters of the combined system are shown in Table 2. In this study, the time-domain hydrodynamic simulation of the combined system was based on AQWA. Hydrodynamic panel models are shown in Figure 2.

**Table 1.** The main parameters of the 5-MW wind turbine.


**Figure 1.** Sketch map of the combined system.


**Table 2.** The main parameters of the combined system.

**Figure 2.** Panel models for the hydrodynamic analysis.

The PTO system (shown in Figure 3), which captures the wave energy through the relative heave motion of the semisubmersible platform and the WEC, was simplified as a linear spring and a linear damper. This model was accomplished by establishing a fender element in ANSYS/AQWA. Based on the discussion of damping coefficient of Fender and stiffness coefficient of linear spring [27–29,33,34,50], it was found that a large value of *Bpto* value may lead to air compressibility that cannot be ignored, while a small *Kpto* coefficient may ignore the influence of stiffness coefficient on the produced power [19]. Therefore, 1.5 × <sup>10</sup><sup>6</sup> Ns2/m was selected for *Bpto* and 1 N/m for *Kpto* in this study. The force of PTO was calculated by the following equation:

$$F\_{pto} = B\_{pto} \cdot (v\_2 - v\_1) + K\_{pto} \cdot (x\_2 - x\_1) \tag{19}$$

where *Bpto* and *Kpto* are the linear damping coefficient and linear spring stiffness coefficient, respectively; *v*<sup>1</sup> and *x*<sup>1</sup> are the velocity and displacement of the semisubmersible platform; and *v*<sup>2</sup> and *x*<sup>2</sup> are the velocity and displacement of the WEC, respectively.

**Figure 3.** Simplified dynamic coupling model between the WEC and braceless.

Knowing the damping force of the PTO system and the relative velocity between the platform and WEC, the produced power of the WEC can be calculated through the following equation:

$$P\_{\rm PTO} = F\_{\rm PTO} \cdot (v\_2 - v\_1) \tag{20}$$

#### **4. Results and Discussion**

The simulations conducted in this study were primarily carried out under typical operational conditions and extreme conditions from a typical site at 61◦21' N latitude and 0◦0' E longitude near the Shetland Islands, northeast of Scotland, UK. The water depth at the site was 200 m [51]. The examined load cases are listed in Table 3. For regular wave case (LC1), the 1800 s–1900 s was used in the comparison to get rid of transient effect. For irregular wave cases (LC2–LC4), the total simulation time is 4600 s, and the first 1000 s has been excluded to avoid the transient effect. It should be noted that the time series results of the motion and force responses between 3500 to 3700 s are displayed to better present the difference between different codes.


**Table 3.** Load cases table.
