## 5 Computational Implementation
### Optimization Results  
To validate the efficiency of the proposed CBGA-SOCP approach to site and size D-STATCOMs in distribution networks for annual operative cost minimization, we used 100 iterations and population sizes between 20 and 100 in steps of 20, to observe the convergence rate of our proposal as well as the required processing times. Table 4 presents the objective function values reached by each of the proposed master-slave CBGA-SOCP strategies regarding the total annual operating costs and the average processing times after 100 consecutive evaluations. The results in Table 4 present following observations:  
* The best objective function value is reached with population sizes of 20 and 40, with an average processing time of about 3.1144 h; here, nodes 14, 30, and 32 are selected, with nominal rates of 0.2896 MVAr, 0.5593 MVAr, and 0.1177 MVAr, respectively, producing a total annual operating cost of US$/year 109455.96. This solution allows annual cost reductions of 16.20%.
* The worst solution reached by using the hybrid CBGA-SOCP approach corresponding to the nodes 12, 14, and 30, with D-STATCOM capacities of 0.1920 MVAr, 0.1488 MVAr, and 0.6556 MVAr, respectively, generating a final objective function value of US$/year 109498.91; however, the difference with respect to the best objective function is only 42.94 dollars per year of operation. * All the solutions in Table 4 identify nodes 14 and 30 in the final solution, and their differences are associated with the third node, with the particularity that all the D-STATCOMs are located in the commercial and industrial areas, as can be seen in Figure 3.
* Regarding processing times in Table 4, it can be observed that the required processing times increase as a function of population size in the initial population, since to start searching the solution space, the CBGA requires the evaluation of the initial population, which consumes additional processing time. Figure 5 presents the desegregated costs of the solutions reached by using the proposed hybrid CBGA-SOCP approach as a function of the population size. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**No. of Iterations** & **Location and Size Node (MVAr)** & **\(\mathbf{A}_{\text{cost}}\) (US$/year)** & **Proc. Times (h)** \\ \hline Benchmark case & — & 130,613.90 & — \\
20 & \{14(0.2896), 30(0.5593), 32(0.1177)\} & 109,455.96 & 3.0697 \\
40 & \{14(0.2896), 30(0.5593), 32(0.1177)\} & 109,455.96 & 3.1592 \\
60 & \{12(0.1920), 14(0.1488), 30(0.6556)\} & 109,498.91 & 3.3368 \\
80 & \{14(0.2896), 30(0.5489), 31(0.1281)\} & 109,472.55 & 3.4647 \\
100 & \{11(0.1982), 14(0.1539), 30(0.6509)\} & 109,496.84 & 3.6171 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance of the CBGA-SOCP approach with different population sizes. Figure 5: Discriminated costs considering different population sizes for the CBGA. The results in Figure 5 show that in general, the annual investment cost in D-STATCOMs is about US$/year 12300 for the best optimal solutions, which implies that with this inversion, the total reduction in cost of energy losses is about 33,450 dollars per year of operation. This justifies the investments in dynamic reactive power compensators, since the net profit in the best solution is about US$/year 21,150. Table 5 presents the solutions reached by using the proposed CBGA-SOCP when 20 individuals are considered in the population. From this table, it is possible to note that (i) 95% of the solutions include node 30, confirming that this is the most sensitive node in terms of minimizing energy cost reduction, considering daily load profiles; (ii) the difference between the optimal solution (i.e., solution No. 1) and the last solution (i.e., solution No.