## 4 Simulation Results
### Siting and Timing of Eighth PSs  
Figure 22 shows the optimal siting and timing considering eighth new PSs. This number coincides with the expected number of PSs to be installed by Unareti in the coming five years. As in the previous case, the first PS is settled in Rozzano municipality, in the exact prior position. Even the second and the third PSs are in the same position as when considering just three PSs, which indicates those spots of primary importance for DN development. Two of the remaining new PSs are located in the city center, i.e., numbers 5 and 6, while the last three are more in the neighborhood.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**PSs in** & **X** & **Y** & **Best Average** & **Best Average Weighted** & **Best Average Weighted** \\
**Construction Order** & **Coordinate** & **Coordinate** & **Distance [km]** & **Distance [km]** & **Distance Variation [km]** \\ \hline \hline  & AS-IS & & 1.82 & 1.48 & \\ \hline
1 & 1,513,006 & 5,026,223 & & & 1.54 \\ \hline
2 & 1,513,960 & 5,039,246 & 2.11 & 1.35 & 1.44 \\ \hline
3 & 1,512,544 & 5,033,505 & & & 1.35 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Timing, siting of the new three PSs, and best average weighted distance values.  
Figure 21: Best fitness through iterations and the global best fitness: three additional PSs.  
The PSs service areas are highlighted in Figure 23. The increased number of new PS allowed reducing the PS service areas dimension, giving undoubted advantages in reducing the distance between squares and the related PSs. Again, the cells' colors show that the algorithm does not fail to find a feasible solution, which guarantees a power demand of the PSs lower than 75% of the transformers' nominal power. Nevertheless, several PSs have a loading greater than 50%, even with reduced values lower than the three new PSs.  
Regarding fitness, the average distance between the squares and the related PSs is 1.70 km, while the average weighted distance is 1.08 km. Since the algorithm locates the new PSs closer to the power demand, concerning the seven PSs owned by a competitor DSO, a significant reduction of 27% of the weighted distance can be obtained. Moreover, a slight reduction in the average distance is also recorded, from the current one, i.e., 1.82 km, to 1.70. As already mentioned, the average distance is not the fitness function of the proposed methodology, so its reduction is just a consequence of the average weighted distance optimization.  
Table 5 shows the main outputs of the methodology and reports the siting, timing of the new PSs, the best average distance, and the best average weighted distance compared to the current condition. The last column details the fitness variation while installing, one at the time, the eight new PSs.  
Figure 23: PSs service areas considering eight incremental PS. The colors report the power demand from the PS transformers’ nominal power.  
Figure 22: Output of the simulation results considering eight new PSs. Pink points are the new PSs, while gray are the existing ones.  
Figure 24 reports the best fitness through the 150 iterations and the global best fitness regarding the optimization process. Similarly to the previous case, comparing the two trends, it can be noticed that the starting solution expresses the global best fitness for the first four iterations when the global best fitness first drops. It is also worth noting that the final fitness value is found after 100 iterations instead of 85.  
Finally, the position of the new PS is compared with the areas already investigated by Unareti for the location of the PSs included in the developing plan and the existing MV substations. The new PS called \"3\" is not far away from the MV substation \"SV\", while the new PS called \"6\" is not far away from the MV substation \"CR\". Thus the methodology proposes to revamp them to take advantage of using the existing space.