# Optimal Siting and Sizing of FACTS in Distribution Networks Using the Black Widow Algorithm
## 6 Conclusions and Future Work  
Via a master-slave methodology, this research analyzed the problem regarding the optimal integration of FACTS in electrical distribution networks in order to minimize the expected annual costs of energy losses, added with the investments in compensation devices. Discrete-continuous codification was employed to represent the set of nodes where the FACTS must be placed and their corresponding size. The exact MINLP model was  
Figure 5: Percent improvement in the objective function with different FACTS. solved using a decoupling methodology, where the BWO approach defines the location and size of the FACTS, and a power flow solution based on the SAPF approach evaluates the multi-period power flow to determine the expected annual costs of the energy losses. A comparative analysis with the BONMINN and COUENNE solvers and the VSA and GA/PSO approaches was carried out in two test feeders, considering the existing literature reports with respect to D-STATCOMs (SVCs in this research), which showed that the BWO approach reaches the exact numerical solution found with the VSA in both test feeders, with the main advantage being that the expected processing times are minimal in comparison with the methods used for comparison. On the other hand, the GAMS solvers, due to the complexity of the exact MINLP formulation, converged to locally optimal solutions in the IEEE 33-bus grid and did not provide any feasible solution for the IEEE 69-bus grid. In addition, the GA/PSO approach, even though it efficiently dealt with the solutions of the exact MINLP model in both test feeders, required very long processing times (more than 6400 s), thus affecting the expected trade-off between the objective function value and the computational resources. The optimal location of the FACTS with the proposed BWO approach, evaluated in the IEEE 33-, 69-, and 85-bus grids, yielded the same set of nodes regardless of the FACTS device analyzed. In the case of the IEEE 33-bus grid, the set of nodes with the best numerical performance included 14, 30, and 32. Node 30 exhibits the most sensitive performance regarding the reactive power required for installation. As for the IEEE 69-bus grid, the set of nodes identified for the optimal location of FACTS included 21, 61, and 64, where node 61 was the most sensitive for installing reactive power compensators. Regarding the IEEE 85-bus grid, the set of nodes identified for the optimal location of FACTS included 12, 34, and 67, where node 34 was the most sensitive. As for the final objective function value, it was observed that the best FACTS corresponded to SVCs. In the IEEE 33-bus grid, the final reduction obtained by SVCs in the objective function was about 12.63%, followed by TCSCs with a value of 11.22%. In the case of the IEEE 69-bus grid, these reductions were about 12.58% and 13.97%. UPFCs ranked last, with reductions of about 9.49% and 10.89% in the IEEE 33- and 69-bus grids, respectively. For the IEEE 85-bus grid, these reductions were 22.87% with UPFCs, 24.91% using TCSCs, and 26.53% with SVCs. The processing times required by the proposed BWO for the optimal location of FACTS in the IEEE 33-, 69-, and 85-bus grids (i.e., about 45 s, 177 s, and 266 s, respectively) confirmed the effectiveness of the master-slave approach proposed in this research, considering the infinite dimensions of the solution space for each possible nodal combination. For future works, the following works can be conducted: (i) the reformulation of the exact MINLP model through a mixed-integer convex formulation to ensure solution uniqueness in each execution, as well as the possibility of finding the best possible solution, i.e., the global optimum, and (ii) the combination of the FACTS analyzed with renewable generation and energy storage systems to reduce the energy purchasing costs in isolated electrical networks fed by diesel sources.