## 4 Simulation Results
### Siting and Timing of Eleven PSs  
The last case presented considers the installation of eleven new PSs. Figure 25 shows the optimal siting and timing of the PSs. It is worth noticing that the additional PSs are all located closer to the city center, where the load density is high. It has to be considered that siting a PS in the center is not always easy or possible. Therefore, it is reasonable to think that the number of new PSs that could realistically be settled cannot be much more than eleven.  
Figure 24: Best fitness through iterations and the global best fitness: eight additional PSs.  
\begin{table}
\begin{tabular}{c c c c c c} \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 \multicolumn{5}{c}{AS-IS} & \multicolumn{2}{c}{1.82} & \multicolumn{2}{c}{1.48} \\ \hline
1 & 1,513,007 & 5,026,217 & & & 1.54 \\ \hline
2 & 1,513,754 & 5,039,166 & & & 1.44 \\ \hline
3 & 1,512,619 & 5,033,319 & & & 1.35 \\ \hline
4 & 1,509,507 & 5,032,761 & & & 1.28 \\ \hline
5 & 1,515,013 & 5,034,529 & 1.70 & 1.08 & 1.22 \\ \hline
6 & 1,512,011 & 5,037,233 & & & 1.17 \\ \hline
7 & 1,516,543 & 5,040,503 & & & 1.12 \\ \hline
8 & 1,507,716 & 5,035,412 & & & 1.08 \\ \hline \end{tabular}
\end{table}
Table 5: Timing, siting of the new eight PSs, and best average weighted distance values.  
The PSs service areas are highlighted in Figure 26. The increased number of new PSs allowed reducing the PS service areas dimension again, giving undoubted advantages in reducing the distance between squares and the related PSs. Even in this case, 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, one PS has a loading greater than 50%, but just a little to have enough capacity to face additional future load increases.  
Regarding fitness, the average distance between the squares and the related PSs is 1.73 km, slightly higher than the case of eight PSs, while the average weighted distance is 0.98 km. Regarding the current situation, the reduction of the weighted distance resulted in about 35%.  
As usual, Table 6 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 eleven new PSs.  
Figure 26: PSs service areas considering eleven incremental PS. The colors report the power demand outside the PS transformers’ nominal power.  
Figure 25: Output of the simulation results considering eleven new PSs. Yellow points are the new PSs, while gray is the existing ones.  
Figure 27 reports the best fitness through the 150 iterations and the global best fitness regarding the optimization process. Different from the previous cases, comparing the two trends, it can be noticed that the starting solution expresses the global best fitness for the first 50 iterations. This is because the algorithm needs more iterations when the number of PSs increases. It is worth noting that the final fitness value is found after 120 iterations.  
Finally, the position of the new PSs 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\"; the new PS called \"6\" from the MV substation \"CR\"; the new PS called \"9\" from the MV substation \"PO\"; the new PS called \"10\" from the MV substation \"MU\". Thus, the methodology proposes to revamp them to take advantage of using the existing space.