# Optimal Control Strategy for Floating Offshore Wind Turbines Based on Grey Wolf Optimizer
## 4 Results and Discussion
### OGSPI vs. Classical GSPI  
Figure 7 displays the acquired pitch angle in proportion to the wave elevation for both the OGSPI and the GSPI techniques. The graph clearly shows the significant difference in pitch corrections made using the OGSPI and GSPI techniques. This comparison demonstrates optimization's significant effect on pitch angle accuracy.  
Figure 8 depicts the power curves in relation to their influence on produced power. In terms of electricity generation, these numbers support the distinction between the OGSPI and the GSPI. The OGSPI improved power generation by providing 63.9496 kWh of energy throughout the simulation duration, whereas the GSPI generated 63.1237 kWh under the same conditions.  
Regarding the platform motions, Figure 9 in the right displays the inclinations of the platform using the GSPI controller for each axis: yaw, pitch, and roll. On the other hand, Figure 9 in the left portrays the platform inclinations using the proposed OGSPI. From these figures, it can be seen that the proposed OGSPI successfully decreased the floating platform's pitch angle. In addition, the roll has also been reduced. This confirms its ability to handle the platform inclinations better.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & \
\begin{tabular}{c} **Complexity for a** \\ **Single Iteration** \\ \end{tabular} &
\begin{tabular}{c} **Complexity for All** \\ **Iterations** \\ \end{tabular} & **Elapsed Time (s)** \\ \hline AVOA & \(O(Npop\),\(D)\) & \(O(Npop\),\(D\),\(T_{max})\) & 298.44 \\ COOT & \(O(Npop\),\(D)\) & \(O(Npop\),\(D\),\(T_{max})\) & 777.52 \\ HHO & \(O(Npop\),\(D)\) & \(O(Npop\),\(D\),\(T_{max})\) & 2947.40 \\ SCA & \(O(Npop\),\(D)\) & \(O(Npop\),\(D\),\(T_{max})\) & 1594.34 \\ WOA & \(O(Npop\),\(D)\) & \(O(Npop\),\(D\),\(T_{max})\) & 1544.83 \\ GWO & \(O(Npop\),\(D)\) & \(O(Npop\),\(D\),\(T_{max})\) & 1192.00 \\ \hline \hline \end{tabular}
\end{table}
Table 3: The time complexity of each algorithm.  
Figure 6: Average fitness evolution.  
Figure 8: The generated power using the OGSPI and the GSPI.  
Figure 7: The resulting pitch angle of the OGSPI and the GSPI as a function of the wave elevation.  
Acting on the platform inclinations will lead to reducing the platform motions. The motions of the platform center of gravity (surge (x), sway (y), and heave (z)) are illustrated in Figure 8. Of these motions, sway stands out as particularly significant, as it reflects the changes in the platform's pitch. Based on these figures, the OGSPI method demonstrated a notably improved reduction in platform motions compared to the GSPI approach. This is apparent from the more confined range of variations in sway motions depicted in Figure 8. Furthermore, a discernible reduction in the platform's pitch angle can be observed in Figure 10 providing clear evidence of GSPI's superior capability in mitigating motions compared to the conventional GSPI method.  
Figure 10: The platform motions using: blue—GSPI; red—OGSPI.  
Figure 9: The platform inclinations using: (**right**)—GSPI; (**left**)—OGSPI.  
The above results prove the OOSPI-based RTH's capability to increase power generation while decreasing platform movements. Reducing the platform motion will reduce the applied loads on the WT body, reduce structure fatigue, increase the lifespan of the whole structure, and reduce maintenance costs [31]. For this reason, it is necessary to reduce these motions. In addition, these motions can lead to fluctuation in the output power, consequently affecting the electrical efficiency of the WT. This can be mitigated when these motions are attenuated.