## 4 Results and Discussion
### 12-Bus Test System  
The 12-bus radial distribution system is simple and used in order to validate the proposed method. Moreover, most of the algorithm steps for the proposed method are discussed. In order to ensure about the performance and accuracy of the proposed method, the evaluated results are validated by  
Figure 8: Single line diagram of IEEE 33 bus distribution test system. Figure 7: Single line diagram of IEEE 12-bus distribution test system. Figure 9: Single line diagram of IEEE 69 bus distribution test system. comparison with the exact solutions obtained by exhaustive optimal power flow (OPF) algorithm which required excessive calculations efforts. The critical bus, when a single DG is added at a generic bus, is determined by referring to the flowchart of Figure 3. Figure 10 represents the sign of the difference in impedances. The critical bus is the last tested bus which has negative sign in the difference of the resistances. As an example, if the DG is interconnected at bus 8, the critical bus will be bus # 4. And if the DG is interconnected at bus 10, the critical bus will be bus # 7. The proposed method was implemented and compared with the actual values, which are obtained by exhaustive OPF solution, as shown in Figure 11. It is clear that the proposed method performance succeed to give results very close to the actual values. Table 3 represents a comparison between the proposed method and the actual values obtained by exhaustive OPF. The results for the proposed method show that the minimum power losses is 3.1587 kW when the penetration level of the DG is 52.97% with power factor equal to 0.73, also, it was noticed that the optimal location of the DG is at bus 9. While, the actual results showed that the minimum power losses is 3.1561 kW when the penetration level of the DG is 53% with power factor equal to 0.74, also, it was noticed that the optimal location of the DG is at bus 9 which is the same location of the proposed method. Figure 10: The sign of the difference between the impedances of the two paths of the current for each bus when the DG installing at each bus. In order to deal with the case of multiple DGs interconnection. The previous part has been repeated for more than one DG and as an example two DGs are considered. Figure 12 represents a 3D plot of the total power losses with respect to the location of the two DGs added to the system; the diagonal of the x-y plane (locations of the first and second DGs) represents the case of two interconnected DGs on the same bus and simply it can be considered as the case of interconnected single DG. However, it is noticed that for all bus numbers, the single DG added to the system results in higher power losses than the case of two DGs added to the system. Moreover, it is noticed that the optimal location of the first DG in order to reduce the power losses as much as possible is at bus 7, and the location of the second DG is at bus 10. Table 4 presents a comparison between the values of proposed method and the actual ones for the case of 2 DGs interconnection. It is clear from the results that the processed method has an excellent accuracy and the values are very close to the exact ones. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & **DG** & **DG** & **Penetration** & **PF\({}_{\text{DG}}\)** & **Power** & \multirow{2}{*}{**PLS (\%)**} \\  & **Number** & **Location** & **Level (\%)** & **(Lagging)** & **Losses (kW)** & \\ \hline Proposed & DG near & 7 & 41.1558 & 0.7173 & 0.85087 & 95.89 \\ method & DG far & 10 & 30.7418 & 0.7470 & & \\ \hline Actual & DG near & 7 & 41.1665 & 0.7173 & 0.85085 & 95.89 \\  & DG far & 10 & 30.7525 & 0.7469 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison between two methods for adding two DGs using 12-bus test system. Figure 11: Power losses when the DG is connected to each bus with the optimal parameters.