## 5 Simulation Results and Discussion
### Case 4: Minimization of Total Generation Cost with Valve Point Effect  
In this case, total generation cost with valve point effect of thermal generators is considered as the objection function for optimization. Cost coefficients and all other parameters for wind and SPV sources remain the same as in Case 2. The obtained results from PSO, GWO, HPSO-GWO and SHADE-SF are summarized in Table 6 for comparison with the results obtained by BMO and GOA [46]. Comparing the results of Table 6 with Table 5, it is clear that penetration from thermal generators decreases as we add up valve point effects in the cost function. The convergence curve of four selected algorithms is shown in Figure 19. The voltage deviation VD, power losses, emissions and total generation costs are also provided in the table, and the best value obtained is highlighted in bold. The minimum generation cost obtained by HPSO-GWO is 780.587 $/h, and the worst result obtained by GOA is 785.711 $/h. The difference between total generation cost obtained by HPSO-GWO and GOA is 5.124 $/h, which become a significant amount of (5.124 \(\times\) 24 \(\times\) 365) 44,886.24 $/Y. The minimum power losses and emissions are achieved by PSO, while a minimum voltage deviation is achieved by SHADE-SF. Generator bus voltages, real powers and reactive powers for all algorithms are combined in Figures 20-22, respectively. All of the values obtained by these algorithms are within the defined limits, as shown clearly. The load bus voltages obtained by all algorithms are combined in Figure 23. The five run results of each algorithm are combined in Figure 24, and the minimum value achieved by each algorithm in the respective run of each simulation is indicated by bold. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & **Parameters** & \begin{tabular}{c} **Min.** \\ **Value** \\ \end{tabular} & \begin{tabular}{c} **Max.** \\ **Value** \\ \end{tabular} & **PSO** & **GWO** & **HPSO-GWO** & **SHADE-SF** & **BMO [46]** & **GOA [46]** \\ \hline \begin{tabular}{c} Swing \\ generator \\ \end{tabular} & \(\text{P}_{\text{TG1}(\text{MW})}\) & 50 & 140 & 134.908 & 135.123 & 135.053 & 134.908 & 134.908 & 134.909 \\ \begin{tabular}{c} \(\text{P}_{\text{TG2}(\text{MW})}\) \\ \end{tabular} & 20 & 80 & 29.057 & 27.090 & 27.630 & 27.966 & 26.602 & 28.066 \\ \begin{tabular}{c} \(\text{P}_{\text{W75}(\text{MW})}\) \\ \end{tabular} & 0 & 75 & 43.875 & 42.769 & 43.290 & 43.406 & 43.817 & 42.766 \\ \begin{tabular}{c} \(\text{P}_{\text{TG8}(\text{MW})}\) \\ \end{tabular} & 10 & 35 & 10.000 & 10.000 & 10.000 & 10.000 & 10.000 & 12.241 \\ \begin{tabular}{c} \(\text{P}_{\text{W711}(\text{MW})}\) \\ \end{tabular} & 0 & 60 & 37.192 & 36.822 & 37.224 & 36.727 & 36.047 & 36.468 \\ \begin{tabular}{c} \(\text{Control}\) \\ variables \\ \end{tabular} & \(\text{V}_{\text{1}(\text{p.u.})}\) & 0 & 50 & 33.850 & 37.301 & 35.845 & 36.179 & 37.812 & 35.505 \\ \begin{tabular}{c} \(\text{V}_{\text{1}(\text{p.u.})}\) \\ \end{tabular} & 0.95 & 1.10 & 1.100 & 1.100 & 1.099 & 1.0704 & 1.081 & 1.024 \\ \begin{tabular}{c} \(\text{V}_{\text{2}(\text{p.u.})}\) \\ \end{tabular} & 0.95 & 1.10 & 1.089 & 1.089 & 1.088 & 1.0565 & 0.950 & 1.097 \\ \begin{tabular}{c} \(\text{V}_{\text{5}(\text{p.u.})}\) \\ \end{tabular} & 0.95 & 1.10 & 1.070 & 1.071 & 1.072 & 1.0348 & 1.045 & 1.002 \\ \begin{tabular}{c} \(\text{V}_{\text{8}(\text{p.u.})}\) \\ \end{tabular} & 0.95 & 1.10 & 1.086 & 1.082 & 1.099 & 1.0945 & 1.049 & 1.075 \\ \
\begin{tabular}{c} \(\text{V}_{\text{11}(\text{p.u.})}\) \\ \end{tabular} & 0.95 & 1.10 & 1.100 & 1.097 & 1.099 & 1.0996 & 1.100 & 1.061 \\
\begin{tabular}{c} \(\text{V}_{\text{13}(\text{p.u.})}\) \\ \end{tabular} & 0.95 & 1.10 & 1.091 & 1.099 & 1.095 & 1.0531 & 1.068 & 1.064 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Simulation results for Case 4. Figure 18: Cost comparison of 5 runs (Case 3). Figure 19: OPF convergence curves comparison (Case 4).