## 4 Simulation Results
### IMGO for PV Source Penetration and Shunt Capacitors in Distribution Systems
The terms \(Loss_{h}\) and \(Loss\_{h}\) account for the hourly active and reactive power losses within the system, ensuring that all power flows are balanced and that system demands are met across each time period. \[\left(2<PV\_bus_{j}\leq N_{bus}\right)_{j=1:N_{PV}} \tag{23}\]  
\[\left(0<P_{PV,j}\leq P_{PV,limit,j}\right)_{j=1:N_{PV}} \tag{24}\]  
\[\left(2<CP_{k}\leq N_{bus}\right)_{k=1:N_{CP}} \tag{25}\]  
\[\left(0<Q_{CP,k}\leq Q_{CP,limit,k}\right)_{k=1:N_{CP}} \tag{26}\]  
\[\left(V_{Bs,min}<V_{Bs}\leq V_{Bs,max}\right)_{Bs=1:N_{bus}} \tag{27}\]  
\[\left(I_{LD}\leq I_{LD,limit}\right)_{LD=1:N_{LD}} \tag{28}\]Figure 12:0 Figure 12:1  
The proposed IMGO and standard MGO are evaluated on a practical Egyptian distribution network, specifically the Tala distribution feeder in the Minuofia governorate, as detailed in reference [79]. This system includes 37 nodes and 36 lines, as shown in Figure 13, and operates at a rated voltage of 11 kV. Under normal load conditions, the system's total active and reactive power demands reach 4801.9 kW and 2975.9 kVAr, respectively. To ensure reliability, the operating voltage is maintained within a permissible range of 10%. Additionally, variations in the hourly load, expressed as percentages of the nominal load, are considered, as illustrated in Figure 12:2  
Figure 12:3 Hourly loading variations. Figure 12:4 Tala distribution feeder. The maximum allowable size for capacitor installations is limited to 3600 kVAr, with a cap of five units that can be deployed across the system. Similarly, the maximum capacity for each PV system is set at 1000 kW, with a limit of five PV units permitted for installation. Within this setup, both the proposed IMGO and the standard MGO algorithms are tailored to optimize the placement and sizing of the PV units and shunt capacitors to reduce energy losses, taking into account fluctuations in load demand and PV power generation. The IMGO and MGO algorithms are utilized to determine the most efficient locations and capacities for both PV units and capacitors. Also, classical and widely accepted metaheuristic techniques are employed, such as the Genetic algorithm (GA) [80] in its real coded version, DE [81], PSO [82], and Multi-Verse Optimizer (MVO) [83]. Their settings are comprehensively tabulated in Figure 12:5 Each algorithm undergoes 20 separate runs to ensure a comprehensive assessment is carried out and reliable results are obtained [84]. The results of MGO, IMGO, and DE are outlined in Table 14, while the results of PSO, GA, and MVO are outlined in Figure 12:6 This comparison would provide greater reliability in the proposed metaheuristic results. Their convergence behavior for each algorithm is shown in Figure 12:7 \begin{table}
\begin{tabular}{c l} \hline \hline
**Algorithm** & **Parameter Settings** \\ \hline MGO and IMGO & 30 search agents per run and a maximum of 100 iterations \\ \hline GA & BLX-alpha crossover with crossover percentage (pc = 0.6); normally distributed mutation with mutation percentage (pm = 0.4); 30 solutions and a maximum of 100 iterations \\ \hline PSO & Cognitive parameter (c1 = 2.05); Social parameter (c2 = 2.05); 30 solutions and a maximum of 100 iterations \\ \hline MVO & Minimum and maximum of Wormhole Existence Probability (WEP_Max = 1; WEP_Min = 0.2); 30 solutions and a maximum of 100 iterations \\ \hline DE & Differentiation (or mutation) constant (F = 0.5); crossover constant (R = 0.5); 30 solutions and a maximum of 100 iterations \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Parameter settings of MGO, IMGO, GA, PSO, MVO, and DE.