## 4 Simulation Results and Discussion
### Implementation of JS-MFO for Solving OPF Problems
It is observed from the results that JS-MFO provides simultaneous reductions in quadratic total fuel cost and total voltage deviation of 10.90% and 91.48%, respectively, with reference to the base case, while the other existing techniques, JS, and MFO show less important results. By examining the convergence curves of the JS and JS-MFO algorithms given by Figure 7, it can be seen that the JS-MFO algorithm gives the best final global optimal solution compared to the JS and MFO algorithms. Case 8: Minimization of Quadratic Total Fuel Cost Along With Vulnerability Stability Enhancement  
The present case study examines the minimization of the total fuel cost along with the enhancement of voltage stability by optimizing the objective function mentioned in (22). The optimal settings obtained for the control and state variables after the JS, MFO, and JS-MFO algorithm running processes are illustrated in Table 5 for case 8. The optimal solution presented by JS-MFO gives the best simultaneous reductions in total fuel cost and voltage stability index than that of JS and MFO. By referring to the base case, JS-MFO presents, simultaneously, a percent cost saving of 11.37% and an improvement of the stability margin of 34.08%. A comparison in Table 11 with other meta-heuristics-based optimization techniques such as ESCA [36], PSO-SSA [37], AMTPG-JAYA [42], MVO [43], and ECHT-DE [44] shows that the proposed JS-MFO presents the best global solution among others. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Technique** & **Total Fuel Cost FC (USD/h)** & **Total Voltage Deviation FVD (p.u)** \\ \hline JS-MFO & 803.5549 & 0.0993 \\ JS & 803.5727 & 0.1480 \\ MFO & 803.93 & 0.1136 \\ AGTLBO [14] & 803.738 & 0.0947 \\ DA-PSO [23] & 803.66 & 0.1163 \\ HFA-JAYA [27] & 803.7036 & 0.0948 \\ ESCA [36] & 804.9968 & 0.09163 \\ PSO-SSA [37] & 803.989 & 0.0940 \\ MVO [43] & 803.908 & 0.1056 \\ ECHT-DE [44] & 803.719 & 0.0945 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Comparisons of the results obtained for case 7 of the IEEE 30-bus system. Figure 7: Convergence curves of JS, MFO, and JS-MFO algorithms for case 7. B. Mauritanian electric power system RIM 27-bus:  
B.1. Simulation of various cases for RIM 27-bus  
The RIM 27-bus power grid is controlled by the SOMELEC society, involving three voltage levels: 225 kV, 90 kV, and 33 kV. This system model consists of six generation buses: 1 (slack bus), 8, 10, 23, 24, and 25, feeding a total load of (1.786 + j0.736) p.u. at a base power of 100 MVA, and three shunt compensators at buses 12, 14, and 16. Two solar power plants are installed on buses 8 and 23 with active power capacities of 50 MW and 15 MW, respectively, and a wind power plant on bus 10 with a capacity of 30 MW, as shown in Figure 8. Also, the RIM 27-bus system has 21 load buses and 36 branches. The voltage magnitude of the generation buses is controlled between 0.92 p.u. and 1.08 p.u. The number of control variables for this system is 15. In the base case, the RIM 27-bus system presents the following data: F\({}_{\text{Plosses}}\) = 6.6015 MW, F\({}_{\text{VD}}\) = 1.6358 p.u., and L\({}_{\text{max}}\) = 0. 522. Case 4: Minimization of Total Active Losses for RIM 27-bus system:  
In this case study, the aim is to minimize the transmission active losses of the RIM 27-bus system, adopting (15) as the objective function, and the simulation results are tabulated in \begin{table}
\begin{tabular}{c c c} \hline \hline
**Technique** & **Total Fuel Cost FC (USD/h)** & **Voltage Stability Index F\({}_{\text{Lmax}}\)** \\ \hline JS-MFO & 799.3187 & 0.1141 \\ JS & 801.1621 & 0.1171 \\ MFO & 800.963 & 0.1182 \\ ESCA [36] & 800.410 & 0.1224 \\ PSO-SSA [38] & 830.352 & 0.1250 \\ AMTPG-JAYA [42] & 840.901 & 0.1240 \\ MVO [43] & 802.466 & 0.1146 \\ ECHT-DE [44] & 800.420 & 0.1374 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Comparison of the results obtained for case 8 of the IEEE 30-bus system. Figure 8: Single-line diagram of the Mauritanian electric power system 27 bus.