## 4 Electrical Distribution Grid Under Study  
The proposed master-slave optimization methodology for the optimal siting and dimensioning of D-STATCOMs in electric distribution grids was tested in a classical and well-known distribution grid composed of 33 nodes and 32 lines (radial topology), which is denominated in this research as the IEEE-33 bus test feeder. This test feeder was operated at medium-voltage levels with 12.66 kV at the substation node (see Figure 3). The total active and reactive power consumption in the peak load condition are 3715 kW and 2300 kvar, respectively. In addition, this test feeder has 210.9876 kW of power losses in this operative scenario. The information about active and reactive power consumption during the peak load case and the branch parameters for the IEEE-33 bus test feeder are listed in Table 1[26].  
The shaded areas in Figure 3 represent the types of consumer connected to the distribution grid, i.e., industrial, commercial, and residential loads. Each of the per-unit demand curves are depicted in Figure 4.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline
**Node \(i\)** & **Node \(j\)** & \(R_{ij}\) **(\(\Omega\))** & \(X_{ij}\) **(\(\Omega\))** & \(P_{j}\) **(kW)** & \(Q_{j}\) **(kvar)** & **Node \(i\)** & **Node \(j\)** & \(R_{ij}\) **(\(\Omega\))** & \(X_{ij}\) **(\(\Omega\))** & \(P_{j}\) **(kW)** & \(Q_{j}\) **(kvar)** \\ \hline
1 & 2 & 0.0922 & 0.0477 & 100 & 60 & 17 & 18 & 0.7320 & 0.5740 & 90 & 40 \\
2 & 3 & 0.4930 & 0.2511 & 90 & 40 & 2 & 19 & 0.1640 & 0.1565 & 90 & 40 \\
3 & 4 & 0.3660 & 0.1864 & 120 & 80 & 19 & 20 & 1.5042 & 1.3554 & 90 & 40 \\
4 & 5 & 0.3811 & 0.1941 & 60 & 30 & 20 & 21 & 0.4095 & 0.4784 & 90 & 40 \\
5 & 6 & 0.8190 & 0.7070 & 60 & 20 & 21 & 22 & 0.7089 & 0.9373 & 90 & 40 \\
6 & 7 & 0.1872 & 0.6188 & 200 & 100 & 3 & 23 & 0.4512 & 0.3083 & 90 & 50 \\
7 & 8 & 1.7114 & 1.2351 & 200 & 100 & 23 & 24 & 0.8980 & 0.7091 & 420 & 200 \\
8 & 9 & 1.0300 & 0.7400 & 60 & 20 & 24 & 25 & 0.8960 & 0.7011 & 420 & 200 \\
9 & 10 & 1.0400 & 0.7400 & 60 & 20 & 6 & 26 & 0.2030 & 0.1034 & 60 & 25 \\
10 & 11 & 0.1966 & 0.0650 & 45 & 30 & 26 & 27 & 0.2842 & 0.1447 & 60 & 25 \\
11 & 12 & 0.3744 & 0.1238 & 60 & 35 & 27 & 28 & 1.0590 & 0.9337 & 60 & 20 \\
12 & 13 & 1.4680 & 1.1550 & 60 & 35 & 28 & 29 & 0.8042 & 0.7006 & 120 & 70 \\
13 & 14 & 0.5416 & 0.7129 & 120 & 80 & 29 & 30 & 0.5075 & 0.2585 & 200 & 600 \\
14 & 15 & 0.5910 & 0.5260 & 60 & 10 & 30 & 31 & 0.9744 & 0.9630 & 150 & 70 \\
15 & 16 & 0.7463 & 0.5450 & 60 & 20 & 31 & 32 & 0.3105 & 0.3619 & 210 & 100 \\
16 & 17 & 1.2890 & 1.7210 & 60 & 20 & 32 & 33 & 0.3410 & 0.5302 & 60 & 40 \\ \hline \end{tabular}
\end{table}
Table 1: Electrical parameters of the 33-node test feeder.  
Figure 3: Grid configuration for the IEEE 33-bus system, with different shaded areas representing different types of load.  
To compare the results of future works regarding D-STATCOMs in distribution grids with the results of the proposed CBGA-SOCP approach, in Table 2 is presented the information depicted in Figure 4 for all the load types.  
The objective function defined in Equation (1) was evaluated using the parameters presented in Table 3. Note that some of these values have been taken from [27] and [10]. It is also important to highlight that to evaluate the objective function regarding the annual costs of the installation of D-STATCOMs, i.e., \(z_{2}\), the values of the variable \(q_{j}^{\sigma\tau}\) must be defined in MVAr [27].