## 5 Numerical Results, Analysis, and Discussions
### Radial Configuration  
To validate the effectiveness of the proposed solution methodology and visualize the best results for this configuration, the proposed methodology was executed one time for 100 iterations, whose different solutions could be observed, as shown in Table 5. Here, the evaluated fitness function (operation costs), node locations, and sizes of the D-STATCOM are shown. The following remarks can be made from Table 5:  
* The solution with the best annual operating costs is number 3, with 106,528.98 USD per year. For this solution, the selected nodes are 14, 8, and 30, which connect D-STATCOMs of 0.1992, 0.1174, and 0.6721 Mvar. This scenario reduces the annual operating costs by 18.42% when compared to the base case. * The worst cost function achieved by the DSCA-BONMIN corresponds to solution 1. In this scenario, nodes 13, 30, and 24 connect D-STATCOMs of 0.2503, 0.6923, and 0.0668 Mvar. The difference between the best and worst fitness functions is 182.69 USD per year of operation. * Node 30 appears for all solutions to the problem. Node 13 appears in solutions 1 and 2. The former is located in the commercial zone, and the latter is in the industrial zone. Finally, nodes 8 and 14, which are within the optimal solution, are also located in the industrial zone, which means that the most suitable locations for a D-STATCOM are in the industrial and commercial zones (Figure 2). * The difference between solution 3 (the best) and solution 1 (the worst) is approximately 183 USD per year of operation, which corresponds to 0.1712%. Therefore, when it comes to minimizing operating costs in this distribution network with a higher number of nodes at a higher number of iterations, the annual cost solutions can be considered efficient, which indicates the accuracy of the implemented algorithm. * In the solutions, the costs associated with energy losses are 87.96% (solution 1), 88.77% (solution 2), and 88.19% (solution 3). In turn, the investment costs are 12.03% (solution 1), 11.34% (solution 2), and 11.80% (solution 3), which corresponds to the fact that the costs associated with energy losses represent a higher percentage of the total cost than those related to investment. Table 6 presents the results regarding the location, size, and annual operating costs of the D-STATCOMs, as obtained with the proposed methodology and the methods used for comparison. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Solution No.** & **Node Location** & **Sizes (Mvar)** & \begin{tabular}{c} **Energy Loss Costs** \\ **(USD/Year)** \\ \end{tabular} & \
\begin{tabular}{c} **Investment Costs** \\ **(USD/Year)** \\ \end{tabular} &
\begin{tabular}{c} **Annual Cost** \\ **(USD/Year)** \\ \end{tabular} \\ \hline
1 & [13; 30; 24] & [0.2503, 0.6923, 0.0668] & 93,867.77 & 12,843.90 & 106,711.67 \\
2 & [13; 15; 30] & [0.1476, 0.1054, 0.6983] & 94,574.27 & 12,103.25 & 106,677.52 \\
3 & [14; 8; 30] & [0.1992, 0.1174, 0.6721] & 93,949.70 & 12,579.28 & 106,528.98 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: List of best results obtained for a radial configuration with the proposed methodology. Based on the information in Table 6, the following can be concluded:  
* The GAMS solvers used to solve the MINLP model are stuck when in local optima compared to the developed DSCA-BONMIN methodology. The SBB, DISCOPT, and LINDO solvers reduce the annual operating costs of the distribution network by 15.94%, while the XPRESS solver only reduces it by 12.94%. In addition, the solvers identify similar locations and sizes for the D-STATCOMs. * The DCCBGA methodology reduces the annual operating costs of this radial distribution network by 17.14%, which is an improvement compared to the GAMS solvers and the genetic-convex methodology. However, the DSCA-BONMIN proposed in this article reduces annual costs by 1,667.48 USD compared to the DCCBGA. This result represents a reduction of 18.42% in the objective function value with respect to the base case, which represents savings of 24,051.84 USD for the network operator.