## 4 Results and Discussion
### Case 4: Minimization of Fuel Cost, Power Losses, and 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) & 74 & 37.679 & 52.834 & 40.925 & 49.328 & 61.185 \\ P\({}_{\text{G5}}\) (MW) & 43 & 27.4 & 31.536 & 34.88 & 23.033 & 25.226 \\ P\({}_{\text{G8}}\) (MW) & 27.98 & 27.57 & 25.644 & 29.799 & 12.381 & 25.964 \\ P\({}_{\text{G11}}\) (MW) & 20.46 & 16.724 & 23.034 & 19.042 & 27.337 & 17.551 \\ P\({}_{\text{G13}}\) (MW) & 22.17 & 36.527 & 24.915 & 33.37 & 31.2 & 29.078 \\ V\({}_{\text{G1}}\) (p.u.) & 1.0165 & 1.0568 & 1.0586 & 1.0425 & 1.0399 & 1.0254 \\ V\({}_{\text{G2}}\) (p.u.) & 1.0076 & 1.0361 & 1.0348 & 1.0235 & 1.0286 & 1.0116 \\ V\({}_{\text{G5}}\) (p.u.) & 1.0044 & 1.0007 & 0.9678 & 0.9978 & 1.0229 & 1.0229 \\ V\({}_{\text{G8}}\) (p.u.) & 0.998 & 1.0041 & 1.0071 & 1.0205 & 1.0074 & 0.9996 \\ V\({}_{\text{G11}}\) (p.u.) & 1.06 & 1.0858 & 1.0896 & 1.0505 & 1.0512 & 1.058 \\ V\({}_{\text{G13}}\) (p.u.) & 1.0625 & 1.0431 & 1.0375 & 1.014 & 1.0202 & 1.0205 \\ T\({}_{\text{11}}\) (p.u.) & 0.9904 & 0.9408 & 1.0332 & 0.9831 & 0.9333 & 0.9728 \\ T\({}_{\text{12}}\) (p.u.) & 0.9657 & 1.0889 & 0.9662 & 0.9714 & 1.0403 & 0.9575 \\ T\({}_{\text{15}}\) (p.u.) & 1.032 & 1.0504 & 0.9456 & 0.9606 & 0.9977 & 0.9811 \\ T\({}_{\text{36}}\) (p.u.) & 0.952 & 0.9525 & 0.932 & 0.9939 & 0.9345 & 0.9795 \\ Q\({}_{\text{G10}}\) (MVAR) & 3.78 & 3.1662 & 0.0399 & 2.1737 & 2.9341 & 1.4981 \\ Q\({}_{\text{G12}}\) (MVAR) & 4.89 & 1.3741 & 3.112 & 0.6344 & 2.9367 & 3.3776 \\ Q\({}_{\text{C15}}\) (MVAR) & 0.45 & 4.0924 & 4.095 & 0.8095 & 3.8171 & 1.5789 \\ Q\({}_{\text{C17}}\) (MVAR) & 2.92 & 3.4921 & 2.8313 & 1.5141 & 1.3053 & 3.6618 \\ Q\({}_{\text{C20}}\) (MVAR) & 4.41 & 3.3257 & 3.4526 & 3.1292 & 3.7579 & 2.1352 \\ Q\({}_{\text{C21}}\) (MVAR) & 1.82 & 2.1631 & 2.4151 & 2.6551 & 0.9492 & 1.9634 \\ Q\({}_{\text{C23}}\) (MVAR) & 1.64 & 0.2003 & 0.749 & 2.9791 & 0.0918 & 2.5902 \\ Q\({}_{\text{C24}}\) (MVAR) & 0.68 & 0.4166 & 3.8998 & 3.097 & 3.0236 & 2.8996 \\ Q\({}_{\text{C29}}\) (MVAR) & 3.87 & 3.3593 & 4.5961 & 1.0288 & 0.0338 & 3.7976 \\ Cost (USD/h) & 873.1963 & 829.1404 & 827.2878 & 838.8745 & 824.1647 & 825.7937 \\ \(P_{\text{loss}}\) (MW) & 5.55 & 7.22 & 7.059 & 6.38 & 8.13 & 7.65 \\ V.D. (p.u) & 0.1899 & 0.2478 & 0.4756 & 0.2681 & 0.2004 & 0.1851 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Case 4 results. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Function** & **PSO** & **MVO** & **GOA** & **HHO** & **HO** & **ESDO** \\ \hline
**V.D. (p.u)** & 0.1834 & 0.2139 & 0.3048 & 0.2146 & 0.2127 & **0.1466** & **0.1831** \\ \hline Cost (USD/h) & 831.6215 & 885.9045 & 850.2231 & 834.5388 & 837.6748 & 816.9713 & 816.5565 \\ \hline \(P_{\text{loss}}\) (MW) & 6.97 & 5.718 & 8.192 & 7.487 & 6.470 & 9.550 & 9.459 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: V.D. comparison. to some value above 1020. ESDO starts near 1080 with a gradual and steady decrease that resulted in the lowest objective function value of about 1010, which shows the best overall performance on the minimization of the objective function. Table 11 provides a multi-objective comparison of various optimization algorithms based on cost in (USD/h), power loss in MW, and voltage drop in V.D. (p.u.). ESDO Beta Dog yields the lowest cost at USD 819.8483/h with a low voltage drop of 0.2041 p.u., while the power loss is a bit high at 8.01 MW. ESDO Alpha Dog has the best cost efficiency (USD 825.7937/h) among all, along with the lowest voltage drop (0.1851 p.u. ), even though the power loss is at a medium-high 7.65 MW. HO has the best power loss of 6.38 MW with a reasonable voltage drop of 0.2004 p.u., but at a higher cost of USD 824.1647/h compared to both variants of ESDO. The results for PSO show that it has a moderate power loss of 5.55 MW and a moderate cost of USD 873.1963/h, while it presents a good performance in a voltage drop of 0.1899 p.u. The worst voltage drop is represented by GOA, with values of 0.4756 p.u.