## 5 Simulation Results and Discussion
### Case 3: Minimization of Total Generation Cost without Valve Point Effect  
In this case, total generation costs without considering valve point effects of thermal generators is optimized. Cost coefficients and all other parameters for wind and SPV sources remain the same, as in Case 2. The optimized values obtained for all thermal generators, RES and other computed parameters are given in Table 5. The obtained results from PSO, GWO, HPSO-GWO and SHADE-SF are summarized in Table 5 for comparison. The convergence curve of four selected algorithms is shown in Figure 13. 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 772.736 $/h, and the worst result obtained by SHADE-SF is 773.979 $/h. The difference between the total generation cost obtained by HPSO-GWO and SHADE-SF is 1.243 $/h, which becomes a significant amount of (1.243 \(\times\) 24 \(\times\) 365) 10,889 $/Y. The minimum power losses and emissions are achieved by HPSO-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 14-16, respectively. All of the values obtained by these algorithms are within specified limits, as shown clearly. The load bus voltages profile obtained through all algorithms is combined in Figure 17. The five run results of each algorithm are combined in Figure 18, and the minimum value achieved by each algorithm in the respective run of the simulation is indicated by bold.  
Figure 14: Generator bus voltages comparison (Case 3).  
Figure 13: OPF convergence curves comparison (Case 3).  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **Parameters** & **Min. Value** & **Max. Value** & **PSO** & **GWO** & **HPSO-GWO** & **SHADE-SF** \\ \hline \multirow{4}{*}{Generator reactive power} & \(Q_{\text{TG1(MVAr)}}\) & \(-20\) & \(150\) & \(-11.682\) & \(-18.768\) & \(-6.721\) & \(-2.494\) \\  & \(Q_{\text{TG2(MVAr)}}\) & \(-20\) & \(60\) & \(18.863\) & \(27.808\) & \(4.773\) & \(12.444\) \\  & \(Q_{\text{WT5(MVAr)}}\) & \(-30\) & \(35\) & \(25.510\) & \(23.526\) & \(35.000\) & \(22.954\) \\  & \(Q_{\text{TGS(MVAr)}}\) & \(-15\) & \(40\) & \(40.000\) & \(40.000\) & \(40.000\) & \(40.000\) \\  & \(Q_{\text{WT11(MVAr)}}\) & \(-25\) & \(30\) & \(19.147\) & \(19.221\) & \(17.862\) & \(30.000\) \\  & \(Q_{\text{SPV13(MVAr)}}\) & \(-20\) & \(25\) & \(21.706\) & \(21.759\) & \(22.235\) & \(14.879\) \\ \hline \multirow{4}{*}{Objective functions} & Gen. cost (5/h) & - & - & \(773.213\) & \(773.566\) & \(772.736\) & \(773.979\) \\  & \(P_{\text{loss (MW)}}\) & - & - & \(5.841\) & \(5.821\) & \(5.763\) & \(6.107\) \\ \cline{1-1}  & Emission (t/h) & - & - & \(1.890\) & \(1.712\) & \(1.570\) & \(1.798\) \\ \cline{1-1}  & V.D (p.u.) & - & - & \(1.033\) & \(0.999\) & \(1.047\) & \(0.452\) \\ \hline \hline \end{tabular}
\end{table}
Table 5: _Cont._Figure 16: Generators reactive powers comparison (Case 3).  
Figure 17: Load buses voltage profile comparison (Case 3).  
Figure 15: Generators real power comparison (Case 3).