## 4 Simulation Results
### IMGO for PV Source Penetration and Shunt Capacitors in Distribution Systems
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Algorithms** & **MGO** & \multicolumn{3}{c}{**Proposed IMGO**} & \multicolumn{2}{c}{**DE**} \\ \hline  & **Bus** & **Bus** & **Installation** & **Sizing** & **Bus** & **Installation** & **Sizing** \\ \hline  & 12 & 765 kW & 7 & 681 kW & 11 & 197 kW \\ \cline{2-6}  & 17 & 562 kW & 14 & 482 kW & 14 & 622 kW \\ \cline{2-6} PV units & 26 & 676 kW & 22 & 644 kW & 23 & 991 kW \\ \cline{2-6}  & 28 & 329 kW & 26 & 650 kW & 25 & 860 kW \\ \cline{2-6}  & 31 & 417 kW & 29 & 736 kW & 31 & 418 kW \\ \hline  & 4 & 973 kVAr & 5 & 2109 kVAr & 5 & 3093 kVAr \\ \cline{2-6}  & 7 & 1404 kVAr & 11 & 944 kVAr & 24 & 1096 kVAr \\ \cline{2-6} Shunt capacitors & 9 & 2107 kVAr & 13 & 475 kVAr & 28 & 857 kVAr \\ \cline{2-6}  & 26 & 579 kVAr & 25 & 1202 kVAr & \\ \cline{2-6}  & 29 & 247 kVAr & 33 & 260 kVAr & \\ \hline Energy losses/day & \multirow{2}{*}{10,582.90161} & \multirow{2}{*}{10,495.75376} & \multirow{2}{*}{10,780.53569} \\ (kWday) & & & & & \\ \cline{2-6}  & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 14: PV system and capacitor allocations based on MGO, IMGO, and DE. Using the standard MGO, optimal PV placements are identified at buses 12, 17, 26, 28, and 31, with capacities of 765 kW, 562 kW, 676 kW, 329 kW, and 417 kW, respectively. For capacitors, the MGO algorithm selects buses 4, 7, 9, 26, and 29, assigning capacities of 973 kVar, 1404 kVar, 2107 kVar, 579 kVar, and 247 kVar, respectively. Conversely, the proposed IMGO algorithm selects buses 7, 14, 22, 26, and 29 for PV installation with capacities of 681 kW, 482 kW, 644 kW, 650 kW, and 736 kW. For capacitors, it identifies \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Algorithms** & **PSO** & \multicolumn{2}{c}{**GA**} & \multicolumn{2}{c}{**MVO**} \\ \hline  & **Bus** & **Sizing** & **Bus** & **Sizing** & **Bus** & **Bus** \\ \hline  & 5 & 526 kW & 11 & 40 kW & 11 & 529 kW \\ \cline{2-6}  & 9 & 831 kW & 25 & 52 kW & 15 & 943 kW \\ \cline{2-6} PV units & 10 & 861 kW & 31 & 43 kW & 20 & 679 kW \\ \cline{2-6}  & 13 & 392 kW & 32 & 10 kW & 22 & 88 kW \\ \cline{2-6}  & 14 & 516 kW & 37 & 76 kW & 26 & 946 kW \\ \hline  & 4 & 2386 kVar & 4 & 2543 kVar & 5 & 2063 kVar \\ \cline{2-6}  & 7 & 1153 kVar & 5 & 436 kVar & 9 & 2053 kVar \\ \cline{2-6} Shunt capacitors & 15 & 984 kVar & 16 & 758 kVAr & 36 & 83 kVAr \\ \cline{2-6}  & 24 & 1218 kVar & 26 & 1153 kVAr & & \\ \cline{2-6}  & 36 & 140 kVAr & 31 & 1569 kVAr & & \\ \hline Energy losses/day (kWday) & 10,782.79855 & & 21,757.4/7852 & & 10,521.98241 \\ \hline  & & & & & \\ \end{tabular}
\end{table} 
Table 15: PV system and capacitor allocations based on PSO, GA, and MVO. Figure 15: Best convergence curves of MGO, IMGO, DE, PSO, GA, and MVO for energy loss minimization. buses 5, 11, 13, 25, and 33, with sizes of 2109 kVAr, 944 kVAr, 475 kVAr, 1202 kVAr, and 260 kVAr, respectively. These results indicate that the IMGO algorithm achieves daily energy losses equivalent to 10,495.75 kWday, which is a reduction in energy loss compared to the 10,582.90 kWday achieved by the standard MGO, yielding energy savings of over 87 kW per day. Also, the proposed IMGO outperforms DE, PSO, GA, and MVO, which achieve daily energy losses of 10,780.56, 10,782.79, 21,757.48, and 10,521.98 kWday. Figure 16 displays the heatmap of the obtained cost using MGO and IMGO for the 20 separate runs. As shown, IMGO consistently achieves lower energy losses compared to MGO across all runs. In contrast, the MGO results show significant variation, with costs fluctuating much more widely. This suggests that IMGO provides more stable and reliable solutions for this optimization problem. We aimed to assess the four key performance metrics, the best, mean, worst, and standard deviation (STD), of the energy losses observed. The proposed IMGO algorithm outperforms MGO across all metrics, achieving a lower best value (10,495.75 kW/day compared to 10,582.90 kW/day), mean (10,656.25 kW/day vs. 10,878.77 kW/day), and worst-case loss (11,068.10 kW/day vs. 11,735.97 kW/day).