## 4 Results and Discussion
### Case 3: Minimization of Voltage Drops
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Parameter** & **PSO** & **MVO** & **GOA** & **HHO** & **HO** & **ESDO** \\ \hline P\({}_{\text{G2}}\) (MW) & 47.44 & 20.155 & 23.466 & 54.822 & 58.048 & 26.137 \\ P\({}_{\text{G3}}\) (MW) & 38.3 & 45.481 & 45.129 & 38.159 & 30.547 & 21.297 \\ P\({}_{\text{G8}}\) (MW) & 21.48 & 34.892 & 22.86 & 12.108 & 31.922 & 22.968 \\ P\({}_{\text{G11}}\) (MW) & 17.59 & 21.796 & 13.901 & 26.986 & 20.923 & 22.007 \\ P\({}_{\text{G13}}\) (MW) & 24.36 & 36.976 & 12 & 16.792 & 30.202 & 18.583 \\ V\({}_{\text{G1}}\) (p.u.) & 1.0583 & 1.0424 & 1.0684 & 1.0576 & 1.0512 & 1.0335 \\ V\({}_{\text{G2}}\) (p.u.) & 1.0482 & 1.0177 & 1.0376 & 1.0546 & 1.0384 & 1.0169 \\ V\({}_{\text{G5}}\) (p.u.) & 1.0018 & 0.9972 & 0.9941 & 1.0068 & 1.0184 & 1.0043 \\ V\({}_{\text{G8}}\) (p.u.) & 1.0157 & 1.0058 & 1.0175 & 1.0039 & 0.9931 & 0.9941 \\ V\({}_{\text{G11}}\) (p.u.) & 1.0455 & 1.0079 & 1.0411 & 1.0275 & 1.0052 & 1.0166 \\ V\({}_{\text{G13}}\) (p.u.) & 1.0051 & 1.0466 & 1.0641 & 0.9961 & 1.0341 & 1.0185 \\ T\({}_{\text{11}}\) (p.u.) & 0.947 & 0.9758 & 1.025 & 0.9441 & 0.9376 & 0.9886 \\ T\({}_{\text{12}}\) (p.u.) & 0.9752 & 0.9998 & 0.9949 & 0.9436 & 1.0248 & 0.9378 \\ T\({}_{\text{15}}\) (p.u.) & 0.9776 & 0.923 & 1.0639 & 1.0097 & 0.9461 & 0.9685 \\ T\({}_{\text{36}}\) (p.u.) & 0.9971 & 0.9624 & 0.9475 & 0.9489 & 0.9557 & 0.9528 \\ Q\({}_{\text{G10}}\) (MVAR) & 2.43 & 1.7223 & 2.0907 & 3.5273 & 1.4147 & 2.3706 \\ Q\({}_{\text{G12}}\) (MVAR) & 1.07 & 2.9249 & 4.2781 & 2.7519 & 3.5379 & 0.8577 \\ Q\({}_{\text{C15}}\) (MVAR) & 2.77 & 1.2178 & 2.8611 & 4.8386 & 2.1059 & 4.3805 \\ Q\({}_{\text{C17}}\) (MVAR) & 2.44 & 0.536 & 2.6467 & 1.3469 & 4.1553 & 4.0145 \\ Q\({}_{\text{C20}}\) (MVAR) & 1.75 & 2.0567 & 2.9978 & 1.7484 & 1.1842 & 4.9584 \\ Q\({}_{\text{C21}}\) (MVAR) & 1.77 & 4.9961 & 0.9558 & 4.9585 & 3.6636 & 3.9269 \\ Q\({}_{\text{C23}}\) (MVAR) & 5 & 1.5199 & 2.2352 & 2.6712 & 2.0054 & 3.3669 \\ Q\({}_{\text{C24}}\) (MVAR) & 1.35 & 1.5641 & 0.2538 & 2.8402 & 2.3734 & 5.2544 \\ Q\({}_{\text{C29}}\) (MVAR) & 5 & 4.2558 & 4.553 & 0.1266 & 3.7256 & 1.9815 \\
**V.D. (p.u)** & **0.1834** & **0.2139** & **0.3048** & **0.2146** & **0.2127** & **0.1466** \\ Cost (USD/h) & 831.6215 & 885.9045 & 850.2231 & 834.5388 & 837.6748 & 816.9713 \\ \(P_{\text{loss}}\) (MW) & 6.97 & 5.718 & 8.192 & 7.487 & 6.470 & 9.550 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Case 3 results. lowest voltage drop of 0.1466 p.u., while both versions have the cheapest cost, where ESDO Beta Dog results in the cheapest cost of USD 816.5565/h. However, they give very high values of power loss of 9.550 MW and 9.459 MW. In contrast, HO has the lowest power loss of 6.470 MW, though the voltage drop in this case is moderate, and it has a higher cost compared to the ESDO variants. On the other hand, GOA has the worst voltage drop of 0.3048 p.u. and high power loss of 8.192 MW, while MVO is the most expensive regarding cost, at USD 885.9045/h. Overall, the ESDO Alpha Dog and Beta Dog are very good in terms of voltage stability and cost efficiency but at the expense of higher power losses.