## 5 Numerical Results, Analysis, and Discussions
### Meshed Configuration
* The SSA methodology reduces the annual operating costs by 10.37%, and the DC-CBGA methodology shows a 10.44% reduction in the operating costs of this meshed distribution network, where the locations of the nodes are the same, unlike the sizes, which vary by 0.0328 Mvar at node 14, 0.052 Mvar at node 32, and 0.0761 Mvar at node 30. Of all, the most notable size difference is at node 30, suggesting that this compensator offsets the higher capital cost, which is not included in the reduction of the energy losses cost. * The DSCA-BONMIN methodology reduces the annual operating costs by 1667.48 USD compared to DCCBGA. This result represents a reduction of 10.59% in the objective function evaluated for the base case, as well as savings of 9197.73 USD for the network operator. * A notable aspect of the DSCA-BONMIN methodology is the existence of D-STATCOMs in the commercial and industrial zones (Figure 3), similar to the SSA and DCCBGA. In addition, the sizes of the D-STATCOMs located by the DCCBGA and DSCA-BONMIN are similar. The only representative differences with respect to the methodology to be compared are the change from node 32 to node 33 and reductions of 2.65% for node 14 and 11.711% for node 30 with respect to the size of each of the locations mentioned. Therefore, these differences represent an improvement in annual operating costs. Finally, Figure 6 shows the convergence graph of the implemented methodology for the 33-node IEEE test system in its meshed version, from which the following can be concluded. In its first iteration, the DSCA-BONMIN finds a value of 77,921.86 USD/year. In the third iteration, it reduces the value of the objective function to 77,895.96 USD/year, thus showing the efficiency of the proposed methodology. In the fourth iteration, it shows a reduction to 77,871.9 USD/year. As of iteration 7, there is an annual cost of 77,871.96 USD/year. In iteration 28, there is a cost of 77,871.96 USD/year. In iteration 42, there is a reduction to 77,714.87 USD/year. Around iteration 93, the DSCA-BONMIN finds the lowest objective function value for the system, which is 77,685.08 USD/year. This indicates that the \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Methodology** & **Node Location** & **Sizes (Mvar)** & **Annual Cost (USD/Year)** & **Reduction (\%)** \\ \hline Benchmark case & - & - & 86,882.81 & - \\ \hline XPRESS & [13; 16; 32] & [0.2000, 0.0453, 0.3923] & 79,535.02 & 8.46 \\ SBB, DICOPT, and LINDO & [13; 16; 32] & [0.0960, 0.0531, 0.4480] & 79,350.36 & 8.67 \\ SSA [47] & [32; 30; 14] & [0.2023, 0.3944, 0.1462] & 77,870.17 & 10.37 \\ DCCBGA [48] & [14; 30; 32] & [0.1134, 0.4705, 0.1503] & 77,809.98 & 10.44 \\ \hline DSCA-BONMIN & [14; 33; 30] & [0.1104, 0.1524, 0.5256] & 77,685.08 & 10.59 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Results obtained by the metaheuristic optimizers and the proposed methodology for the meshed configuration. proposed methodology, by increasing the number of iterations, quickly converges to the global optimum. This confirms that the DSCA-BONMIN is an effective and robust tool to solve the problem regarding the location and sizing of D-STATCOMs in power distribution systems in order to reduce annual operating costs. Thus, the proposed methodology is the best option to solve the studied problem in 33-node IEEE test systems with a meshed topology, as it achieves the best solution from an economic point of view while respecting all of the system operator's constraints.