## 4 Method Application and Resulting Discussion
### Method Application in Three Cases
The results show that the wind farm has a minimum COE of 0.089 $/kwh at a rated speed of 10 m/s and a rotor radius of 60 m. The power of the turbine was about 2.9 MW and the hub height was 109.5 m. The actual wind turbines installed in the XIPP offshore wind farm included the GW 109/2500 (Goldwind, Beijing, China) and the W2000/93 (Sewind, Shanghai, China). The main parameters of these wind turbines are detailed in Table 4. Compared with the optimal turbine, the actual wind turbines had slightly higher speeds and lower rotor radii. When comparing the two actual turbines, the GW 109/2500 was the optimal turbine due to its lower COE. Figure 4: The relationship between the speed, rotor radius and COE: (**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 SWT-3.6-120 (Siemens) & 3–5 & 25 & 12–13 & 3.6 & 90 & 60 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Main parameters of the wind turbine installed in NNW, USA. The analytical comparison of the minimum COE of the optimal turbine, GW 109/2500 and W2000/93 was adopted in terms of the optimal wind turbine layout obtained by the IPSO algorithm. As the planned-installed capacity of offshore wind farms was 60 MW, 24 GW 109/2500 wind turbines were expected to be installed, \(N\) = 24. The number of W2000/93 wind turbine was 30. These optimization results and the optimal layouts of the two wind turbines obtained by the IPSO algorithm are shown in Figure 7. It can be seen from Figure 7a that the GW 109/2500 had a smaller COE than the W2000/93. The former had the same result as that of the developed optimization method. In Figure 7b,c, the layouts of the wind turbines are arranged into three rows: Two rows are located in the outermost zone of the grid and one row is located in the medial grid. In this way, the spacing between the two wind turbines is biggest in the wind direction. Consequently, the influence of the wake-effect on the energy production was reduced and, again, the effectiveness of the layout optimization was confirmed. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Types**} & **Cut-in** & **Cut-off** & **Speed** & **Power** & **Hub Height** & **Rotor** \\  & **Speed (m/s)** & **Speed (m/s)** & **(m/s)** & **(MW)** & **(m)** & **Radius (m)** \\ \hline GW 109/2500 & 3 & 25 & 10.1 & 2.5 & 80 & 54.5 \\ (Goldwind) & 3 & 25 & 10.8 & 2.0 & 80–90 & 46.5 \\ \hline W2000/93 & 3 & 25 & 10.8 & 2.0 & 80–90 & 46.5 \\ (Sewind) & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Main parameters of the wind turbine installed in XIPP, China. Figure 5: The results of the objective function (COE) and optimal layout: (**a**) result of objective function and (**b**) optimal layout. Figure 6: The relationship between the speed, rotor radius and COE at XIPP, China: (**a**) 3D graphic and (**b**) contour map. Case 3: The \(R\phi nland\) offshore wind farm, Denmark, is located at latitude \(56.662^{\circ}\) and longitude \(8.221^{\circ}\). At this wind farm, the mean wind speed was about 10.20 m/s and the shape factor \(k_{0}\) of the Weibull distribution function was equal to 2.0. The optimization results are shown in Figure 8a,b. The results showed that the wind farm had a minimum COE of 0.0695 $/kwh at a speed of 12 m/s and a rotor radius of 40 m. The power of the turbine was about 2.23 MW and the hub height was 80.26 m. The two actual wind turbines installed at the \(R\phi nland\) wind farm included the SWT-2.3-93 (Sewind) and the Vestas v80-2000.