## 4 Results and Discussion
### Case 2: Minimization of Power Loss  
In Case 2, minimization of power loss was aimed for. This occurs due to the resistance in transmission lines that tends to impede the flow of power from generators into the loads. Power loss minimization directly enhances the efficiency of the system and strengthens the reliability of power delivery. ESDO optimizes reactive power flows, transformer tap settings, and voltage control measures to reduce the active power losses in the network. The transmission losses are significantly reduced by ESDO when comparing methods like MVO and GOA in Case 2. ESDO manages to provide a balance between global exploration and local exploitation, and it could determine the voltage profiles and tap settings which gave the minimum losses when maintaining system stability. This will make ESDO a very important tool in enhancing energy efficiency in power systems since a reduction in power losses implies more sustainable operations and reduced operational costs in the long run. Figure 5: Fuel cost for different algorithms. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Function**} & \multirow{2}{*}{**PSO**} & \multirow{2}{*}{**MVO**} & \multirow{2}{*}{**GOA**} & \multirow{2}{*}{**HHO**} & \multicolumn{2}{c}{**ESDO**} \\ \cline{5-6}  & & & & & & **Alpha Dog** & **Beta Dog** \\ \hline
**Cost (USD/h)** & 812.2991 & 811.2007 & 819.1972 & 810.3851 & 808.1815 & **804.8769** & **805.6415** \\ \hline Ploss (kW) & 9.05 & 8.7858 & 9.0376 & 9.394 & 8.75 & 8.360 & 8.132 \\ \hline V.D. (p.u) & 0.4778 & 0.39458 & 0.43427 & 0.39237 & 0.4276 & 0.42463 & 0.58534 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Fuel cost comparison. In this case, the proposed algorithms aim to reduce the power losses, which means that Equation (22) is selected as the objective function for the OPF algorithm. Table 6 shows the best control parameter values for ESDO and compares them to other techniques. The results presented indicate the suggested techniques perform better in terms of achieving the lowest power loss, showing greater optimization capabilities in this case. Figure 6 shows the convergence curve in Case 2, where ESDO achieves the lowest power loss (-4.5 MW) at the 25 th iteration and continues to improve, indicating a strong capability for optimization. PSO and HO also perform well, soon converging at around 6 MW without additional improvement. MVO quickly converged to about 8 MW, but GOA and HHO showed a modest but steady decline in power loss, with a sharp drop around the 40 th iteration in the case of HHO. In summary, ESDO's superior performance demonstrated its ability to reduce power loss more efficiently than the other algorithms examined in this study. Figure 7 shows that the ESDO variants have very superior performance regarding minimal power loss, with the lowest values at 4.62 MW and 4.67 MW for the ESDO Alpha Dog and ESDO Beta Dog, respectively. This is far better than other tested algorithms. The MVO has the highest power loss of 7.98 MW and thus is the least effective in this context. PSO, HO, HHO, and GOA present moderate performance with a power loss ranging from 5.74 MW to 6.15 MW. It can, therefore, be concluded that ESDO variants are better at optimizing this specific case study. Table 7 compares the power loss for all the algorithms and the corresponding values for cost and voltage drop where ESDO Alpha Dog has the least power loss of 4.617 MW, closely followed by ESDO Beta Dog at 4.673 MW. This demonstrates superior performance in reducing power loss as against other algorithms. While the variants of ESDO--Alpha Dog and Beta Dog--have the best performances in the minimization of power loss, they are rather expensive in terms of their cost and voltage