## 3 Problem Definition
### Definition of Study Cases  
The comparison of the dynamic responses obtained from the two models considered in this study was conducted for three sets of load cases: (1) parked conditions to obtain the fundamental frequency of the systems, (2) load cases considering just the wind load, and (3) load cases that combine both the wind and wave loads. All OpenFAST simulations were performed over a duration of 400 s with a time step of 0.001 s. For each simulated case, except in the case used to compute the fundamental frequency, the initial 100 s of simulation time were disregarded to ensure that the results were representative of the steady state.  
Fundamental frequencies are first analyzed to ensure that the structural models are comparable. The influence of SSI effects in both models is studied by obtaining the fundamental frequencies under fixed-base and flexible-base assumptions. In the time-domain multi-physics simulation of the system with OpenFAST, simulations are conducted around the static equilibrium of the system, considering only gravitational acceleration. In the simplified model, as mentioned before, the fundamental frequencies are obtained by solving the eigenvalue problem.  
The second set of load cases focuses on the influence of aeroelastic effects on the response of each model. For this purpose, wind-only load cases are defined using three different types of turbulence: the Normal Turbulence Model (NTM), Extreme Turbulence Model (ETM), and Extreme Operating Gust (EOG). Each type of turbulence is described in IEC 61400-1:2020 [2]. Load scenarios are defined for mean wind speeds ranging from 5 to 25 m/s in increments of 5 m/s, resulting in fifteen scenarios for wind-only loads. The turbulent winds are characterized by the IEC Kaimal wind spectrum and a wind power law exponent. Table 5 summarizes the wind-only scenarios. The EOG turbulence in OpenFAST is simulated using the IEC [2] methodology, which defines this turbulence as a combination of NTM turbulence and a disconnection of the wind turbine from the power grid.  
Finally, from the numerous design load combinations defined by the applicable standards and recommendations, four of the five most representative or unfavorable combinations, as described in [6], are considered. These combinations are referred to as environmental load scenarios. The first scenario, E-1, describes the normal operating conditions of the wind turbine, with wind at nominal speed and 1-year extreme wave conditions.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Return Period** & **Sea State** & **Wave Height (m)** & **Peak Spectral Period (s)** \\ \hline \multirow{2}{*}{1 year} & ESS, 1-year & 9.686 & 16.654 \\  & EWH, 1-year & 18.204 & 15.121 \\ \hline \multirow{2}{*}{50 years} & ESS, 50-years & 11.307 & 18.505 \\  & EWH, 50-years & 21.092 & 16.276 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Wave data under extreme conditions.  
Scenario E-2 addresses an extreme wave scenario with a 50-year return period and wind at nominal speed and extreme turbulence. Scenario E-3 focuses on extreme wind loads, with extreme operational turbulence for a 50-year return period and extreme waves with a 1-year return period. Scenario E-4 considers the cut-out wind speed and extreme operational turbulence with extreme wave conditions, both for a 50-year return period. In all these considered scenarios, the wind and wave loads are assumed to be aligned. A summary of the environmental load scenarios is presented in Table 6.