## 4 Results and Discussions
### The Results Obtained by the Two Algorithms in Case 1  
Figure 2 shows the results obtained by OOA and WOA after 50 trial runs. In the figure, OOA shows a high fluctuation among the trial runs, with few optimal runs. On the contrary, WOA offers a lower fluctuation with more optimal values among 50 trial runs. In Figure 2, the results obtained by WOA and OOA after 50 trial runs have been shown. The higher fluctuations between trial runs mean that OOA is less stable than WOA while dealing with the considered problem. The presence of the fluctuations given by the COA and WOA is necessary for judging the stability of these methods. Stability is one of the most crucial factors to acknowledge a powerful meta-heuristic algorithm, besides its capability of determining the best optimal solution to the particular optimization problem. Figure 3 describes the best convergence curves of the OOA and WOA among 50 trial runs. In the figure, WOA is better than OOA by reaching the optimal power loss value after about 20 iterations, while OOA cannot offer the same capability even after the last iteration is reached. Figure 1: The single-line illustration of the IEEE 85-node RDPG. Figure 4 offers more details about the real performance of the two algorithms in terms of different criteria, including the lowest power loss value (LST. Loss), the average power loss value (AVER. Loss), the highest power loss value (HST. Loss) and the standard deviation (STD). For the first criterion, WOA reaches a 155.5636 kW LST. Loss value, while that of OOA is 155.5637 kW. The difference between the WOA and OOA on this criterion is not much. However, while considering the last three criteria, the effectiveness and superiority of the WOA over the OOA started to become clear. Specifically, the WOA not only reaches better values of Aver. Loss and HST. Loss, but also proves itself to be the stable search method with a much better value of STD. For instance, the particular values of these criteria resulting from WOA are 115.6932 kW, 116.5983 kW, and 0.2205, while those of OOA are 117.1884 kW, 122.5941 kW, and 1.7227. By converting to percentage, the superiority of WOA over OOA on the last three criteria is 1.28%, 5.12%, and 87.20%. The voltage profile of the systems with and without the presence of WTs is shown in Figure 5. Clearly, the voltage values at all nodes are substantially improved compared to the original configuration, where WTs were not placed. Additionally, the superiority of the WOA over the OOA in voltage improvement is minor. The WOA can reach better voltage for nodes 9-15, 44-56, 78, and 80-85. Nevertheless, the OOA can reach better voltage for nodes 57-77 and 79. The two algorithms have approximately the same voltage at other remaining nodes, such as nodes 16-43. The improvement in voltage profile achieved after placing WTs to the grid by applying COA and WOA is described in Figure 5, and their capacity is reported in Table 1. The WOA placed a WT with a high power of 1592 kW at node 9. Meanwhile, nodes that received electricity from node 9 are 10-15, 78, 80-85. So, WOA reached better voltage for these nodes. The OOA placed one WT with a high power  
Figure 3: The best convergence curves, drawn by the two algorithms in Case 1. Figure 2: The results obtained by the two algorithms after 50 trial runs in Case 1.  
of 1077 kW at node 59. Nodes that can receive electricity from node 59 are 57, 58, 60-77, and 79. So, OOA reached better voltage than WOA for these nodes. About the second WT, the OOA placed a WT at Node 32 with 928 kW, and the WOA placed a WT at Node 33 with 670 kW. The loads at nodes 34-36 and 40-54 can receive the power from nodes 32 and 33. So, WOA can reach a better voltage for these nodes. Lastly, the optimal locations and power outputs of the two WTs in the grid found by the OOA and WOA are displayed in Table 1. It is easy to recognize that the total power outputs of WTs found by the OOA are smaller than those of the WOA. The difference in the LST.