## 5 Simulation Results and Discussion
### Case 5: Minimization of Total Generation Cost with Valve Point Effect and Carbon Tax  
In this case, total generation cost with valve point effects and carbon tax imposed on emission of thermal generators is considered as the main objective function for optimization. The rate of carbon tax is kept the same, as in [8] and [46], that is 205/ton. Cost coefficients and all other parameters for wind and SPV sources remained the same, as in Case 2. The obtained results from PSO, GWO, HPSO-GWO and SHADE-SF are summarized in Table 7 for a comparison with the results achieved by BMO and GOA [46]. Due to carbon tax imposed on emissions of thermal generators, their penetration decreases whereas RES penetration increases in the system; this can be noticed by comparing the results of Tables 5-7. The convergence curve of four selected algorithms is shown in Figure 25. 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 809.277 $/h, and the worst result obtained by GOA is 822.307 $/h. The difference between total generation cost obtained by HPSO-GWO and GOA is 13.03 $/h, which become a significant amount of (13.03 \(\times\) 24 \(\times\) 365) 114,142.8 $/Y. The minimum power losses and emissions are achieved by GWO 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 26-28, respectively. All of the values obtained by these algorithms are within specified limits, as shown clearly. The load bus voltages obtained by all algorithms are illustrated in Figure 29. The five run results of each algorithm are combined in Figure 30, 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} & \(\mathrm{P_{TGI(MW)}}\) & 50 & 140 & 123.663 & 122.783 & 123.956 & 123.123 & 123.127 & 134.908 \\ \(\mathrm{P_{TG2(MW)}}\) & 20 & 80 & 33.350 & 33.424 & 33.605 & 31.994 & 31.947 & 25.215 \\ \(\mathrm{P_{PVTS(MW)}}\) & 0 & 75 & 46.061 & 45.098 & 46.226 & 45.470 & 45.403 & 41.755 \\ \(\mathrm{P_{TG3(MW)}}\) & 10 & 35 & 10.000 & 10.010 & 10.000 & 10.000 & 10.000 & 14.648 \\ \(\mathrm{P_{WT1(MW)}}\) & 0 & 60 & 38.838 & 37.739 & 39.033 & 38.310 & 38.270 & 34.946 \\ \(\mathrm{P_{SPV13(MW)}}\) & 0 & 50 & 36.616 & 39.372 & 35.785 & 39.783 & 39.865 & 38.053 \\ \(\mathrm{V_{1(p.u.)}}\) & 0.95 & 1.10 & 1.100 & 1.100 & 1.100 & 1.070 & 1.078 & 1.092 \\ \(\mathrm{V_{2(p.u.)}}\) & 0.95 & 1.10 & 0.950 & 1.089 & 1.090 & 1.056 & 1.064 & 0.958 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Simulation results for Case 5. Figure 24: Cost comparison of 5 runs (Case 4). Figure 26: Generator bus voltages comparison (Case 5).