## 4 Method Application and Resulting Discussion
### Discussion  
In order to check the advantages of the proposed optimization method, the differences between the optimal COE of the three optimized wind farms and the actual wind turbines were calculated and are shown in Table 6. The results show that these differences are positive and their values are in a range of 0-0.001 \(\$\)/kWh, and the reduced ratio of the COE is in the range 0-1.27%. Thus, it seems that the actual wind turbines may have been optimally designed before being installed in the offshore wind farms [33; 34]. On the other hand, the positive differences mean that it is necessary to simultaneously optimize the wind turbines and their layout to achieve the minimal energy cost of the offshore wind farms. Figure 8: The relationship between the speed, rotor radius and COE at the \(R\phi\)_nland_ offshore wind farm, Denmark: (**a**) 3D graphic and (**b**) contour map. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Types** & \begin{tabular}{c} **Cut-in** \\ **Speed (m/s)** \\ \end{tabular} & \begin{tabular}{c} **Cut-off** \\ **Speed (m/s)** \\ \end{tabular} & \begin{tabular}{c} **Speed** \\ **(m/s)** \\ \end{tabular} & \begin{tabular}{c} **Power** \\ **(mw)** \\ \end{tabular} & \begin{tabular}{c} **Hub Height** \\ **(m)** \\ \end{tabular} & \begin{tabular}{c} **Rotor** \\ **Radius (m)** \\ \end{tabular} \\ \hline \
\begin{tabular}{c} Swt-2.3-93 \\ (Siemens) \\ \end{tabular} & 3 & 25 & 11.0 & 2.3 & 80 & 46.5 \\ \hline
\begin{tabular}{c} Vestas \\ v80-2000 \\ \end{tabular} & 3–5 & 25 & 11.5 & 2.0 & 60–101 & 40 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Main parameters of the wind turbine installed in \(R\phi\)_nland_, Denmark. In order to check the optimization rules of the designed parameters of the wind turbines in the offshore wind farms, considering the optimal value of the COE varying in the range of 0.002 $/kWh, the range of the optimally designed parameters are shown in Table 7. From Table 7, it is clear that when the mean wind speed is increased, the optimally designed rotors slightly decrease their size, while the rate wind speeds are higher. Although it seems contradictory to the current trend of offshore wind turbines towards having long blades, it is acceptable as the optimization results actually confirm the fact that the COE is more sensitive to the variation of the wind speed rather than the rotor radius. Furthermore, the final capacities of the optimally designed wind turbines are calculated by using the \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Wind Farm** & **NNW, USA** & \multicolumn{3}{c}{**XIPP, China**} & \multicolumn{3}{c}{_Rap inland, Denmark_} \\ \hline Annual mean wind speed (m/s) & \multicolumn{3}{c}{8.23} & \multicolumn{3}{c}{6.94} & \multicolumn{3}{c}{10.2} \\ \hline Type & \begin{tabular}{c} The optimal \\ one \\ \end{tabular} & \begin{tabular}{c} SWT-3.6-120 \\ \end{tabular} & \begin{tabular}{c} The optimal \\ one \\ \end{tabular} & \begin{tabular}{c} GW \\ \(109/2500\) \\ \end{tabular} & \begin{tabular}{c} W2000/93 \\ \end{tabular} & \
\begin{tabular}{c} The optimal \\ one \\ \end{tabular} &
\begin{tabular}{c} Swt-2.3 \\ \(\star\)80 \\ \end{tabular} \\ \hline COE\({}_{\text{min}}\) ($/kWh) & 0.0777 & 0.0787 & 0.0892 & 0.0892 & 0.0902 & 0.0695 & 0.0699 & 0.0698 \\ \hline Difference & - & 0.001 & - & 0 & 0.001 & - & 0.0004 & 0.0003 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The results of minimum COE corresponding to the optimal layout. Figure 9: The results of the objective function (COE) and optimal layout: (**a**) results of objective function, (**b**) optimal layout of Swt-2.3-93, and (**c**) optimal layout of Vestas v80-2.0 MW. optimal rotor radius and wind speed, and their results are 2.0-3.9, 2.4-4.5, and 1.7-5.6 MW for the annual mean wind speed with 6.94, 8.23, and 10.2 m/s, respectively. These results reveal that the wind farm with a high mean wind speed can have a wider range of the turbine capacities than one with a low wind speed.