## 4 Results and Discussion
### 33-Bus Test System  
The second test system used in the study is 33-bus test system, this test system is a widely used in the literature. To evaluate and validate the performance of the proposed method, results have been compared with hybrid approach, improved analytical (IA) method, and particle swarm optimization (PSO) technique [36; 37; 38; 39]. Referring to the proposed method and considering the case when a single DG is interconnected at each bus, Figure 14 shows the critical buses. After that, assessing the optimal penetration level of  
Figure 12: Minimum power losses for the combination of two DGs using the proposed approach. Figure 13: Voltage profile of 12-bus distribution test system. the DG at each bus in the network is required; finally, the optimal location that minimizes the power losses in the network is evaluated. The power losses have been calculated when the DG is installed at each bus as presented in Figure 15 which shows that the minimum power losses that can be achieved when a single DG unit is added at each bus. As a result, it is noticed that the minimum power losses is 67.75 kW and occurred when the DG is added to the bus 6 with penetration level of 70.444% and power factor of 0.8255. Tables 5-7 summarize the results of the proposed method for single, two, three DG units interconnection in terms of optimal DG location, DG penetration level, DG power factor, and total power losses. The results of the proposed method have been compared with the hybrid, PSO, and IA methods. The last column in these tables presents the amount of power loss reduction achieved by the above-mentioned methods. The results in Table 5 show that better PLR values are attained with the proposed method in the one DG interconnection scenario. On the other hand, the results of the other three methods are the same in terms of PLR, optimal DG locations, and optimal PF with negligible change in the penetration level. In contrast, for the scenario of 2 DG interconnection, it was noticed  
Figure 14: The critical bus when the DG is tested at each bus. Figure 15: Power losses when the DG is connected to each bus with the optimal parameters. from Table 6 that the IA method provides power losses of 44.39 kW compared to 28.60 kW obtained by the proposed method and other two methods. This is because IA often fails to succeed in determining the optimal locations, especially for multiple DG interconnections. From Table 7, the proposed method and hybrid method achieved a PLR of 94.455%, compared to 94.408% for PSO method which is nearly the same. Again, IA failed to succeed in determining the optimal locations and hence achieves the lowest PLR values. Regarding the voltage profile for 33-bus test system, it is clear from Figure 16 that the presence of DG in the system improves the voltage profile. The case of interconnecting more than one DG provides more voltage improvement. However, the improvement in the voltage profile in the case of two DGs and three DGs are nearly the same. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & **DG** & **DG** & **Penetration** & **PF\({}_{\text{DG}}\)** & **Total Power** & **PlR (\%)** \\  & **Number** & **Location** & **Level (\%)** & **(Lagging)** & **Losses (kW)** & **PlR (\%)** \\ \hline Proposed & DG1 & 13 & 22.403 & 0.90 & 28.60 & 86.445 \\ method & DG2 & 30 & 35.422 & 0.72 & & \\ \hline Hybrid & DG1 & 13 & 31.813 & 0.91 & 28.60 & 86.445 \\  & DG2 & 30 & 34.513 & 0.72 & & \\ \hline PSO & DG1 & 13 & 20.918 & 0.91 & 28.60 & 86.445 \\  & DG2 & 30 & 35.131 & 0.73 & & \\ \hline IA & DG1 & 6 & 50.236 & 0.82 & 44.39 & 78.962 \\  & DG2 & 30 & 25.130 & 0.82 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison between methods for adding two DGs using 33-bus test system.