## 4 Method Application and Resulting Discussion
### Method Application in Three Cases  
Three real installations were used as case studies: Newport nearshore windpark (NNW) wind site in the USA, Xiangshui intertidal Pilot project (XIPP) offshore wind farm in China, and _Rphland_ offshore wind farm in Denmark. The wind statistical data of the three wind sites is given in References [30; 31; 32], respectively, and the Weibull distribution parameters of wind speed are summarized in Table 2. The wind direction is assumed to be constant. The distribution curves of the wind speed are plotted in Figure 3.  
Case 1: NNW offshore wind farm, USA, is located at latitude 39.201\({}^{\circ}\) and longitude \(-75.241^{\circ}\). At this wind farm, the mean wind speed was 8.23 m/s and the shape factor \(k_{0}\) of the Weibull distribution function was 2.0. Based on the presented cost of energy and the optimization approach, the results about the relationships among the rated speed, rotor radius and COE were obtained and are shown in Figure 4a,b. As seen in Figure 4, the results show that the wind farm has a minimum COE of 0.077 $/kWh for turbines with a rated speed of 11 m/s and a rotor radius of 50 m. By calculation, the rated power of the turbine is about 2.7 MW, and the hub height is 95.23 m. The actual wind turbines installed in NNW wind farm include the SWT-3.6-120 for which the main parameters are given in Table 3. It is shown that the optimization results are close to the values of the actual wind turbine. However, compared to the wind turbine with the minimum COE, the actual wind turbine has a higher speed and rotor radius. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Offshore Wind Farm** & **Mean Wind Speed (m/s)** & **Shape Factor (\(k_{0}\))** & **Scale Factor (\(c_{0}\), m/s)** \\ \hline NNW, USA & 8.23 & 2.0 & 9.29 \\ \hline XIPP, China & 6.84 & 2.0 & 7.83 \\ \hline _Rphland_, Denmark & 10.2 & 2.0 & 11.51 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Wind statistic data of three offshore wind farms. Figure 3: Weibull probability distribution functions of three cases at reference hub height \(H_{0}\). In order to prove the effectiveness of the proposed COE method, an analytical comparison about the minimum COE of an optimal turbine and SWT-3.6-120 was performed. It considered the optimal wind turbine layout obtained by the IPSO algorithm. As the planned-installed capacity of offshore wind farms is 60 MW, 17 wind turbines were expected to be installed, \(N=17\). The optimization results and the optimal layout obtained by the IPSO algorithm are shown in Figure 5a,b, respectively. In Figure 5a, when the value of the minimum COE of the SWT-3.6-120 (\(COE_{min}\) = 0.0787 $/kWh) is higher than the COE value of the optimal wind turbine, of which the value is 0.0774 $/kWh, the minimum COE of the actual wind turbine is very close to the minimum COE value of the optimal wind turbine. In Figure 5b, as expected, the layout of the wind turbines has a tendency to locate the turbines in the outermost zone of the grid and the distance between two wind turbines is higher in the wind direction. As such, the layout of the wind turbines can reduce the influence of the wake-effect and, accordingly, the effectiveness of the layout optimization is confirmed. The IPSO was used to search for the optimal layout of wind turbines and, thus, the convergence of the IPSO could be judged by checking the final layout of the wind turbines. Since the optimized layout in Figure 5b is consistent with the expected results, it can be determined that the IPSO converged after 200 iterations. Case 2: The XIPP offshore wind farm in China is located at latitude \(34.464^{\circ}\) and longitude \(119.871^{\circ}\). At this wind farm, the mean wind speed was 6.94 m/s and the shape factor, \(k_{0}\), of the Weibull distribution function was equal to 2.0. Based on the cost of energy presented and the two optimization methods, the results about the relationships between the speed, rotor radius and COE were obtained, as shown in Figure 6a,b.