## 4 Results and Discussion
### Case 1: Minimization of Fuel Cost
\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) & 38.14 & 57.005 & 42.448 & 35.455 & 37.748 & 52.466 \\ P\({}_{\text{G5}}\) (MW) & 26.2 & 25.697 & 35.154 & 25.514 & 24.486 & 21.587 \\ P\({}_{\text{G8}}\) (MW) & 21.56 & 10 & 22.275 & 14.132 & 20.141 & 23.425 \\ P\({}_{\text{G11}}\) (MW) & 20.71 & 14.655 & 12.859 & 13.038 & 19.536 & 16.481 \\ P\({}_{\text{G13}}\) (MW) & 19.17 & 23.882 & 14.988 & 22.873 & 18.647 & 17.671 \\ V\({}_{\text{G1}}\) (p.u.) & 1.0508 & 1.0659 & 1.0306 & 1.0799 & 1.0724 & 1.0662 \\ V\({}_{\text{G2}}\) (p.u.) & 1.0445 & 1.0469 & 1.0125 & 1.0677 & 1.0592 & 1.0553 \\ V\({}_{\text{G5}}\) (p.u.) & 0.9857 & 1.0134 & 1.0238 & 1.0359 & 1.0211 & 1.0328 \\ V\({}_{\text{G8}}\) (p.u.) & 0.9985 & 1.0236 & 1.0068 & 1.0292 & 1.05 & 1.027 \\ V\({}_{\text{G11}}\) (p.u.) & 1.0062 & 1.0886 & 1.0319 & 1.0306 & 1.0587 & 1.0558 \\ V\({}_{\text{G13}}\) (p.u.) & 0.9894 & 1.0223 & 1.0301 & 1.0247 & 1.0478 & 1.0157 \\ T\({}_{\text{11}}\) (p.u.) & 0.9539 & 0.963 & 1.0714 & 0.9614 & 1.0717 & 1.0394 \\ T\({}_{\text{12}}\) (p.u.) & 1.0542 & 0.9984 & 1.0145 & 1.0057 & 1.0637 & 0.9512 \\ T\({}_{\text{15}}\) (p.u.) & 1.0119 & 1.0838 & 1.0184 & 1.0702 & 0.9866 & 0.9574 \\ T\({}_{\text{36}}\) (p.u.) & 0.9229 & 1.0111 & 0.9149 & 0.9542 & 0.9792 & 0.9945 \\ Q\({}_{\text{G10}}\) (MVAR) & 2.49 & 3.0136 & 0.9194 & 1.5328 & 1.6327 & 5.2471 \\ Q\({}_{\text{G12}}\) (MVAR) & 1.95 & 2.5849 & 3.0701 & 2.3717 & 1.5815 & 4.7483 \\ Q\({}_{\text{G15}}\) (MVAR) & 1.44 & 2.9703 & 2.626 & 0.6234 & 0.7791 & 1.54 \\ Q\({}_{\text{G17}}\) (MVAR) & 1.7 & 3.8087 & 2.7184 & 0.7575 & 0.7785 & 4.2336 \\ Q\({}_{\text{G20}}\) (MVAR) & 4.05 & 0.6324 & 2.1094 & 2.3747 & 1.0707 & 5.4377 \\ Q\({}_{\text{G21}}\) (MVAR) & 3.37 & 0.1162 & 1.7526 & 0.2875 & 1.4405 & 2.3971 \\ Q\({}_{\text{G23}}\) (MVAR) & 2.66 & 1.5749 & 4.1688 & 2.5882 & 3.5704 & 6.5002 \\ Q\({}_{\text{Q24}}\) (MVAR) & 0.77 & 2.9851 & 2.1707 & 0.6439 & 1.1696 & 2.6493 \\ Q\({}_{\text{G29}}\) (MVAR) & 2.68 & 3.0164 & 1.1151 & 1.3092 & 2.5822 & 1.3045 \\
**Cost (USD/h)** & **812.2991** & **811.2007** & **819.1972** & **810.3851** & **808.1815** & **804.8769** \\ \(P_{\text{loss}}\) (MW) & 9.05 & 8.7858 & 9.0376 & 9.394 & 8.75 & 8.360 \\ V.D. (p.u) & 0.4778 & 0.39458 & 0.43427 & 0.39237 & 0.4276 & 0.42463 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Case 1 results. Figure 4: Case 1 convergence curve. As previously mentioned in the pseudo-code in Algorithm 1; after completing the iterations, the algorithm returns the best energy, second-best energy found and the corresponding best and second-best positions which are the alpha and beta dogs. Figure 5 represents the values of the fuel cost which are the objective function values for each algorithm and compares it with alpha and beta dog's values obtained by ESDO, which are highlighted in green and yellow, respectively. The curve shows that the ESDO obtained the best values for the given objective function compared to the other algorithms. Table 5 compares fuel cost and their corresponding values for power loss and V.D. for all the techniques including the best and the second-best values for the ESDO. ESDO Alpha Dog is the best algorithm when the cost and power loss are considered, but HHO is the best in voltage deviation. On the other hand, ESDO Beta Dog also gives very good performance considering cost and power loss but has high voltage deviation.