# Optimal Control Strategy for Floating Offshore Wind Turbines Based on Grey Wolf Optimizer
## 4 Results and Discussion
### Simulation Results Comparison  
Table 2 highlights the optimization technique's statistical outputs, including the best, worst, mean, and standard deviation (STD) findings. This table describes the results obtained by each algorithm. The best result is the lower one, which indicates the best performance of the corresponding set of parameters. The worst corresponds to the higher fitness, meaning that the corresponding set of parameters performed worst. The mean value expresses the average performance, and the standard deviation (STD) indicates the algorithm's robustness. All these indicators should be considered to evaluate the performance of each algorithm. From these results, the following observations can be drawn:  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Symbol** & **Value** & **Unit** \\ \hline \multicolumn{4}{c}{Turbine parameters (NREL 5 MW ITI energy barge)} \\ The radius of wind turbine & \(R\) & 63 & m \\ Air density & \(\rho\) & 1.225 & kg/m\({}^{3}\) \\ Optimal tip–speed ratio & \(\lambda_{opt}\) & 9.7 & \\ Wind turbine inertia moment & \(J_{tr}\) & 115,926 & kg.m\({}^{2}\) \\ Maximum power coefficient & \(Cp_{max}\) & 0.465 & \\ Wind cut in speed & \(V_{cut\_in}\) & 3 & m/s \\ Wind rated speed & \(V_{ntled}\) & 11.4 & m/s \\ Wind cut out speed & \(V_{cut\_out}\) & 25 & m/s \\ Generator reference speed & \(\omega_{nref}\) & 1173.7 & rpm \\ MPPT gain & \(k_{mpt}\) & 2.8805 & \\ \multicolumn{4}{c}{Drivetrain parameters (NREL 5 MW ITI energy barge)} \\ Gearbox ratio & \(n\) & 97 & \\ \multicolumn{4}{c}{Drivetrain torsional spring} & \(k_{s}\) & \(8.67637\times 10^{8}\) & Nm/rad \\ \multicolumn{4}{c}{Drivetrain torsional damper} & \(k_{d}\) & \(6.215\times 10^{6}\) & Nm/(rad/s) \\ \multicolumn{4}{c}{Environmental conditions} \\ Significant wave height & \(H_{s}\) & 5 & m \\ Peak frequency of the significant wave height & \(f_{p}\) & 12.4 & Hz \\ Wind speed & \(V_{w}\) & 13 & m/s \\ \hline \hline \end{tabular}
\end{table}
Table 1: Simulation parameters.  
Figure 5: Wave elevations as a function of the time.  
* GWO provided the best result (lower fitness value) of 169.964, outperforming all the other algorithms, including HHO with a result of 169.976 and WOA with a result of 170.341.
* The GWO algorithm showed good robustness, as demonstrated by a standard deviation (STD) of 3.913. This is confirmed by the mean value (170.423) and max value (171.035), which are close to the best result (169.964). The COOT also provided a good STD indicator at 4.726. However, the mean value is relatively significant, meaning the COOT is trapped in a local solution.
* The GWO provided the best motion reduction ratio (16.118), which approves its contribution to finding the best parameters for reducing the platform motions.
* Compared to the best outcomes produced by each algorithm (except for the AVOA), the total of the square platform motions acquired by the traditional GSPI approach is 203.170, which is much higher. These results clearly highlight a significant difference between the classical GSPI method and the OGSPI provided by the metaheuristic optimization algorithms.  
\(\eta\) is the motion reduction ratio that can be calculated as follows:  
\[\eta=(f_{GSPI}-f_{mean})/f_{GSPI} \tag{30}\]  
where \(f_{GSPI}\) is the sum of squared platform motions attained through the classical GSPI controller and \(f_{mean}\) is the mean of squared platform motions achieved by each optimizer to assess its average performance.  
Figure 6 depicts the fitness progression of several algorithms based on their mean fitness values and convergence speed. This graph shows how the algorithms' performance varies through optimization cycles. When compared to the other methods, the GWO algorithm has a quicker convergence curve from the curves. This means that the GWO algorithm can arrive at optimal or near-optimal solutions quickly. The GWO algorithm utilizes a three-point leading technique. These leading points will most likely guide the algorithm's search across the solution space.