## 4 Results and Discussions
### The Results Obtained by the Two Algorithms in Case 3  
In this subsection, the implementation of placing WTs in the considered RDPG remains the same as in Case 2. However, the range of power factors for WTs is primarily extended. Notably, the range of power factors varies between 0.95 lag and 0.95 lead. As a result, the scale of the considered problem has also vastly increased. The execution of this case is aimed at the following purposes: (1) continuously test the actual performance of the two applied methods while dealing with the larger scale of the considered problem; (2) and improve the practicality of the research while applying the full range of power factors for operating wind turbines, as implemented in practice. Figure 10 describes the results obtained by the OOA and WOA after 50 trial runs in Case 3. Throughout 50 trial runs, WOA is the only method reaching optimal values multiple times, while OOA cannot provide the same capabilities. However, the fluctuation of the power loss value achieved by the WOA is larger than that of the OOA, in this case. This phenomenon results from the increase in search space, as mentioned earlier. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Method** & **WT1** & **WT2** \\
**Location—P (kW)—Q (kvar)** & **Location—P (kW)—Q (kvar)** \\ \hline OOA & 60; 1236.0772; 765.0668 & 32; 1085.5547; 672.2055 \\ WOA & 32; 1085.727; 672.8732 & 60; 1200.4984; 744.0021 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The optimal location, active and reactive power, determined by the two algorithms in Case 2. Figure 9: The voltage profile obtained by the two algorithms in Case 2. The best convergence curves achieved by the OOA and WOA are illustrated in Figure 11. The observation from the figure points out that the WOA only utilized over 30 iterations to reach the best power loss value, while the OOA could not even reach the best run at the last iteration. Clearly, the WOA still offers a surprising performance in Case 3 regardless of the substantial extension in the search space of the considered problem. Similar to the first two cases, the detailed comparison between the OOA and WOA in Case 3 is clearly displayed in Figure 12. It is very easy to see that the WOA results in better power loss values than the OOA in terms of LST. Loss and Aver. Loss. In particular, the WOA reached 0.097 kW for LST. Loss and 16.994 kW for Aver. Loss, while the similar values obtained by the OOA are 1.665 kW and 23.354 kW by converting to percentage, the WOA is better than OOA 94.2% at LST. Loss and 27.23% at Aver. Loss. However, the evaluation of Max. Loss and STD have indicated the opposite. For instance, the Max. Loss and STD achieved by the OOA are 35.670 kW and 9.02, while those of the WOA are 47.785 kW for Max. Loss and up to 12.236 for STD. By using percentages, the OOA is better than WOA 33.97% for Max. Loss and 35.68% at STD, in this case. The voltage magnitude at all buses of the considered RDPG resulting from OOA and WOA in Case 3 is displayed in Figure 13. Firstly, the voltage magnitude at all buses in RDPG are substantially improved in the first two cases in the previous section compared to the base case where WTs are not connected. Secondly, the voltage magnitude at buses achieved by the WOA is vividly enhanced compared to the OOA, especially from bus 24 to the end. Figure 11: The best convergence curves obtained by the two algorithms in Case 3. Figure 10: The results obtained by the two algorithms after 50 trial runs in Case 3. The optimal location, active, and reactive power supplied by WTs results from the two applied methods are given in Table 3. In the table, the negative value of reactive power means that WTs consume reactive power from the grid to reach the main objective function's best value power loss values. The observation in Table 3 indicates that the optimal locations for placing WTs in this case are completely different from each other. For instance, the optimal locations found by WOA are at bus 13 and 60, respectively, while those of OOA are 50 and 59, respectively.