## 6 Results and Discussion
### Case Three  
In this case, there are 21 turbines in the Valfair site in Manjil. The objective function is 2.2251 per year per megawatt. Because of a larger number of turbines compared to the previous cases, there are two turbines with a 60 m height, four with a 50 m height, and the rest have a height of 40 m. The total generated power is 7.75 megawatts. Figures 11 and 12 illustrate the placement and height of turbines in Case 3. In this case, Table 8 provides the coordination of turbines in Case 3. Here, according to [PERSON] et al. [76], as the layout of the turbines is not optimized, wind speed becomes reduced by 0.5 m/s due to the wake effect while the average speed is 14.5 m/s. In this case, the power generation is 6.77 megawatts and the objective function is 2.54 per year per megawatt. This means that optimization gives rise to a 10.75% increase in power generation and a 9.42% reduction in cost per unit of power. To compare power production at different speeds, the following diagram (Figure 13) is derived. Figure 12: Height of turbines in Case 3. Figure 13: Total power for different wind speeds. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & & & & & & \\ \hline
**Number of Turbine** & **X(m)** & **Y (m)** & **Z (m)** & **Number of Turbines** & **X (m)** & **Y  
Moreover, the amount of energy unit cost is in correlation with wind speed. For the wind speed of 1 m/s, the unit cost of power becomes 320 per MW, which is quite high. As the wind speed increases to 10 m/s, the cost reduces drastically to 8.62 per MW, and as wind speed gains its rated value, which is 15 m/s, the unit cost reaches a minimum of 2.22 per MW (Figure 14). This implies that receiving high wind speeds are crucial for the wind farm to operate cost-effectively. The 2-D Layout  
In this section, the hub heights are considered constant and layout optimization for 21 turbines according to what was described in the previous section will be performed (Figure 15). By comparing this layout with the previous one, it is obvious that there are \(800\times 2000\) m\({}^{2}\) of free space in 3-D optimization. The coordinates of the 2-D layout are given in Table 9.  
By investigating and comparing the three scenarios, the following results achieved. The Mossetti's cost function is completely dependent on the number of turbines. It can be stated that by increasing the number of turbines the value of this function also increases, while the relationship between them is characteristically nonlinear. Furthermore, as the number of turbines grow, the function rises at a lower rate (Figure 16). In comparison, the amount of linear growth between the increase in the number of turbines is determined. By increasing the number of turbines from 10 to 15, the wind turbine numbers are multiplied by 1.5, but the cost is multiplied by 1.335, which is less than a linear growth. Another discussion is about the objective function considered for this study. A general survey of the three scenarios is evaluated (Figure 17). Figure 14: The unit cost of power with different wind speeds. Figure 15: Layout of the 2-D case. It is observed that the main objective function in this study decreases with the number of turbines. The reason is that the objective function is defined as the cost per power. Figure 16: Cost of the wind farm in all cases. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{5}{c}{**Turbine Coordinates in the 2-D Case**} \\ \hline
**Number of Turbine** & **X (m)** & **Y (m)** & **Number of Turbine** & **X (m)** & **Y (m)** \\ \hline
1 & 1850 & 400 & 12 & 1750 & 1700 \\ \hline
2 & 1600 & 100 & 13 & 1350 & 750 \\ \hline
3 & 600 & 800 & 14 & 100 & 600 \\ \hline
4 & 300 & 850 & 15 & 1350 & 250 \\ \hline
5 & 750 & 950 & 16 & 350 & 1400 \\ \hline
6 & 1400 & 1850 & 17 & 450 & 400 \\ \hline
7 & 850 & 1500 & 18 & 0 & 1150 \\ \hline
8 & 900 & 200 & 19 & 1350 & 1200 \\ \hline
9 & 1000 & 950 & 20 & 600 & 400 \\ \hline
10 & 1150 & 700 & 21 & 1550 & 800 \\ \hline
11 & 2000 & 700 & & & \\ \hline \hline \end{tabular}
\end{table}