## 4 Results and Discussion  
### Comparison of Computational Results  
Figure 4 shows the comparative results of cost of energy using the 20 \(\times\) 30 grid method, 40 \(\times\) 60 grid method, and coordinate method for the wind farm layout optimization. Various numbers of wind turbines from 40 to 46 are studied in this paper. As can be seen, there is a large improvement \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Design Methods** & **Grid Method (20 \(\times\) 30 grid)** & **Grid Method (40 \(\times\) 60 grid)** & **Coordinate Method** \\ \hline Population type & Binary & Binary & Real \\ Number of variables & 600 & 2400 & 2 N \\ Population size & 600 & 600 & 600 \\ Generations & 1 million & 0.5 million & 0.5 million \\ \hline \hline \end{tabular} N is number of wind turbines.  
\end{table} 
Table 3: Setting of genetic algorithm (GA) parameters of the wind farm layout optimization using different design methods. in the cost of energy for the 40 \(\times\) 60 grid method and coordinate method when compared with the 20 \(\times\) 30 grid method. The discrepancy between the 20 \(\times\) 30 grid method and coordinate method can be up to 0.19 million dollars per megawatt when there are 46 wind turbines, while the 40 \(\times\) 60 grid method yields a slightly larger cost of energy than the coordinate method. As the number of wind turbines increases, at a certain number of wind turbines there may be some fluctuations of the cost of energy (especially for the two grid methods), which is possibly because the sub-optimal results are obtained. In general, the cost of energy increases for all of the wind farm design methods as the number of wind turbines increases. According to the cost of energy results, it is concluded that the coarse 20 \(\times\) 30 grid method is not sufficient for wind farm layout optimization, as it yields significantly inferior results when compared to other methods. In comparison, the results of the refined 40 \(\times\) 60 grid method and coordinate method are much closer. In addition, the performance of the coordinate method is particularly stable, showing steadily increasing cost of energy with more turbines installed. The comparative results of wind farm efficiency are presented in Figure 5 using different design methods for the number of wind turbines between 40 and 46. The wind farm efficiency is defined as the real wind farm power output when considering the wake losses divided by the theoretical wind farm power output neglecting the wake losses:  
\[\text{Wind~{}fan~{}efficiency}=\frac{P_{tot}(\text{wake losses})}{P_{tot}( \text{wake losses neglected})} \tag{21}\]  
as can be seen from Figure 5, the trend of variation of wind farm efficiency is opposite to the cost of energy. When the number of wind turbines increases, the wind farm efficiency decreases. The decrease of wind farm efficiency for the 20 \(\times\) 30 grid is the most prominent as compared to the other two methods. The maximum discrepancy of wind farm efficiency between the 20 \(\times\) 30 grid method and coordinate method is 2% with 46 wind turbines. When applying the coordinate method, the wind farm efficiency is able to maintain above 99% for all different numbers of wind turbines, while the wind farm efficiency for the 40 \(\times\) 60 grid is slightly smaller and fluctuating from approximately 99.1% to 98.8% as the number of wind turbines increases. The total wind farm power outputs that were obtained by different wind farm design methods are presented in Figure 6 for different wind turbine numbers. Evidently, 20 \(\times\) 30 grid method yields the lowest power output, which is approximately 200 kW less than the other two methods. The difference between the produced power predicted by the 40 \(\times\) 60 grid method and the coordinate method are small. In general, the total power output linearly increases with the wind turbine number.