## 5 Numerical Results, Analysis, and Discussions
### Meshed Configuration  
As in the previous case, for this configuration, the proposed methodology was executed one time for 100 iterations, and the results obtained are shown in Table 7. In this case, the number of solutions was higher than those found in Section 5.1. These results are presented together with the sizes and locations of the D-STATCOMs nodes. Based on the information in Table 7, it can be concluded that:  
* The results confirmed that, for this scenario, node 30, being in all the solutions obtained by the proposed methodology, is the most sensitive to the minimization of operating costs. Additionally, the two other nodes found in most of the reported solutions are node 33, with a percentage of 57.14%, and node 14, with 28.57%, which are related to the total responses. This occurs when considering discriminated sectors and hourly load profiles. As for nodes 30 and 33, they are nodes located in the commercial zone, and node 14 belongs to the industrial zone (Figure 3). * The difference between solution 7 (the best) and solution 1 (the worst) is 236.78 USD, which corresponds to a 0.3039% improvement between the first and the optimal solutions obtained. As a result, as the number of iterations increases, the solutions in Table 7 improve in quality. This result confirms the accuracy of the DSCA-BONMIN method when it comes to minimizing operating costs in this distribution network. * In the solutions, with regard to the total costs, the costs associated with energy losses represent 87.82% (solution 1), 87.55% (solution 2), 87.68% (solution 3), 87.14% (solution 4), 86.98% (solution 5), 87.21% (solution 6), and 87.08% (solution 7); and the investment costs represent 12.17% (solution 1), 12.44% (solution 2), 12.31% (solution 3), 12.85% (solution 4), 13.01% (solution 5), 12.78% (solution 6), and 12.91% (solution 7). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Solution No.**} & \multirow{2}{*}{**Node Location**} & \multirow{2}{*}{**Sizes (Mvar)**} & **Energy Loss Costs** & **Investment Costs** & **Annual Cost** \\  & & & **(USD/Year)** & **(USD/Year)** & **(USD/Year)** \\ \hline
1 & [30; 19; 32] & [0.5107, 0.2348] & 68,433.39 & 9488.47 & 77,921.86 \\
2 & [30; 33; 27] & [0.5238, 0.2113, 0.0266] & 68,201.11 & 9694.85 & 77,895.96 \\
3 & [30; 18; 22] & [0.5644, 0.1890, 0] & 68,299.6 & 9588.11 & 77,887.74 \\
4 & [4; 14; 30] & [0, 0.1510, 0.6358] & 67,860.69 & 10,011.27 & 77,871.96 \\
5 & [9; 30; 33] & [0.0846, 0.5163, 0.1941] & 67,656.69 & 10,120.19 & 77,776.88 \\
6 & [15; 30; 33] & [0.1049, 0.5279, 0.1480] & 67,776.07 & 9,938.80 & 77,714.87 \\
7 & [14; 33; 30] & [0.1104, 0.1524, 0.5256] & 67,649.24 & 10,035.84 & 77,685.08 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Results obtained by the metaheuristic optimizers and the proposed methodology for the meshed configuration. Figure 5: Convergence curve of the IEEE 33-node system with a radial configuration. This means that the costs of energy losses represent a higher percentage of the total cost than the investment costs. Table 8 shows the results for the location, size, and annual costs of the D-STATCOMs, as obtained by the comparison methodologies and the one proposed in this research. Based on the information in Table 8, the following was concluded:  
* In comparison with the developed DSCA-BONMIN methodology, the local optima used by the GAMS solvers stagnate. The SBB, DISCOPT, and LINDO solvers reduced the annual network operating costs by 8.67%, while XPRESS only reduced them by 8.46%. The solvers define the exact same nodes for reactive compensation. The dimensions of the D-STATCOM range from 0.104 Mvar at node 13, 0.0078 Mvar at node 16, and 0.0557 Mvar at node 32. The most noticeable size variation takes place at node 13, suggesting that this compensator overcomes the higher capital costs that are not included in the energy loss cost.