# Optimal Siting and Sizing of FACTS in Distribution Networks Using the Black Widow Algorithm
## 5 Numerical Results
### Location and Sizing of FACTS in the IEEE 33- and 69-Bus Grids  
This section presents the general objective function behavior and the nodes and sizes of the different FACTS analyzed when implementing the BWO approach. Table 6 presents the best numerical solutions with the proposed BWO approach in both test feeders. The numerical results in Table 6 show the following:  
1. In the IEEE 33-bus grid, the selected nodes for installing FACTS are 14, 30, and 32, with node 30 being the most sensitive regarding reactive power injection, given that this node was assigned the largest FACTS size. In addition, the most efficient FACTS element regarding the final objective function value corresponds to SVCs, with a reduction of about 12.63% in the expected annual operating costs, followed by TCSCs with a reduction of about 11.22% concerning the benchmark case. ii. In the IEEE 69-bus grid, the BWO approach identifies nodes 21, 61, and 64 as the most effective for optimal reactive power compensation, where node 61 is the most sensitive to locate and size compensation devices, with values larger than 400 kvar for \begin{table}
\begin{tabular}{l c c c c c} \hline \hline \multicolumn{6}{c}{**IEEE 33-Bus Grid**} \\ \hline \hline
**FACTS Devices** & **Location** & **Size** (Mvar) & \(\mathbf{z_{cost}}\) **(USD/Year)** & **Reduction (\%)** & **Time (s)** \\ \hline Benchmark case & — & — & 112,740.90 & — & — \\ UPFC & [14; 30; 32] & [0.1340, 0.2980, 0.1074] & 102,043.23 & 9.49 & 43.94 \\ TCSC & [14; 30; 32] & [0.1486, 0.3337, 0.1064] & 100,093.29 & 11.22 & 43.97 \\ SVC & [14; 30; 32] & [0.1599, 0.3591, 0.1072] & 98,497.90 & 12.63 & 44.08 \\ \hline \hline \multicolumn{6}{c}{**IEEE 69-Bus Grid**} \\ \hline \hline
**FACTS Device** & **Location** & **Size (Mvar)** & \(\mathbf{z_{cost}}\) **(USD/Year)** & **Reduction (\%)** & **Time (s)** \\ \hline Benchmark case & — & — & 119,715.63 & — & — \\ UPFC & [21; 61; 64] & [0.0397, 0.4008, 0.1142] & 106,679.88 & 10.89 & 177.72 \\ TCSC & [21; 61; 64] & [0.0647, 0.4363, 0.1125] & 104,658.03 & 12.58 & 173.12 \\ SVC & [21; 61; 64] & [0.0839, 0.4601, 0.1139] & 102,990.79 & 13.97 & 176.74 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results in the IEEE 33- and 69-bus grids regarding the integration of FACTS with the proposed BWO approach. all the FACTS analyzed. As with the IEEE 33-bus grid, the most effective device for the reduction in the objective function value corresponds to SVCs, which allow reaching a reduction of about 13.97%, followed by the TCSCs with a reduction of about 12.58%. It is worth mentioning that the main result in Table 6 is that, regardless of the FACTS analyzed, the BWO approach identifies the same set of nodes for the IEEE 33- and 69-bus grids. This can be attributed to the fact that (2) is a cubic function with the same numerical structure as that seen in Table 4, i.e., the same signs for the \(\omega\) coefficients. In addition, the variations in the final objective functions, as expected, are associated with the \(\omega\) coefficients in this objective function; the FACTS device with the most expensive linear costs (i.e., the value of \(\omega_{3}\)) reaches the lowest reduction in the annual grid operating costs. In this sense, the expected reductions regarding the general objective function are highly dependent on the linear coefficient. In this regard, note that, in Table 6, these reductions are ordered increasingly by the integration of the UPFC, the TCSC, and the SVC. Finally, with respect to the processing times spent in locating the FACTS in the IEEE 33- and 69-bus grids, Table 6 shows that less than 45 s and 177 s are required to deal with the efficient integration of reactive power compensators in both test feeders, respectively.