# Optimal Siting and Sizing of FACTS in Distribution Networks Using the Black Widow Algorithm
## 1 Introduction
### Literature Review  
With the advancements made in power electronics, different devices have been created to maximize the use of existing transmission and distribution networks, as is the case of FACTS devices. These not only allow increasing the changeability of the circuits but also reducing losses, regulating voltage values, and improving the power quality and stability of the system [18]. Several authors have focused on establishing different models that enhance the performance of distribution networks via shunt reactive power compensators. The authors of [19] proposed a particle swarm optimization model to determine the optimal location of various types of controlled FACTS devices and thus increase the power transmission capacity of the lines. The study included selecting the optimal device among three options (UPFC, TCSC, and SVC), as well as their location and selection of parameters. The article aimed to maximize the cost-benefit, increase grid loadability, and reduce power losses. The IEEE 30-bus grid was used to evaluate the effectiveness of this optimization approach. The location and configuration of FACTS devices by means of the cross-entropy method were presented in [20]. The main idea of integrating FACTS into power systems is to reduce congestion and line losses by minimizing the number of devices used. A simulation of a 30-node IEEE test system was performed through the implementation of an optimal power solution that considered an economic objective function. In [21], the moth flame optimization algorithm was implemented to solve the optimal power flow in power grids by including FACTS in the existing infrastructure. The objective of this solution is achieving the reduction in the grid power losses and keeping the voltage levels stable. Variable control was carried out by controlling the reactive power of the generator, configuring the TAPs in the transformers, and setting the parameters of the FACTS. Numerical validations were carried out in the IEEE 57-node test system using SVCs, TCSCs, and thyristor-controlled phase angle regulators. In [22], the maximization of the power system's loadability was sought through the optimal location of FACTS devices. For this case, TCSC and UPFC devices were used. The improved moth flame optimization method was implemented to obtain the maximum objective function values, and numerical simulations were implemented in the IEEE 30-bus system. It is worth noting that this study aimed to maximize the loadability of the power system, reduce power losses, and minimize voltage variations. A new multi-objective optimization algorithm was proposed in [13], known as a _multi-objective multiverse optimizer_, which is employed to determine the location of FACTS in the power system. Thus, it is possible to establish the optimal configurations of the FACTS in order to improve the voltage profiles and reduce power losses. Numerical validations were performed in the IEEE 57-node test system. In the case of medium-voltage distribution networks, some of the applications regarding FACTS are associated with the optimal integration of distribution static compensations (D-STATCOMs), which essentially correspond to the use of SVC technology with regard to voltage distribution levels [23]. The authors of [24] proposed the optimal integration of D-STATCOMs in radial distribution networks to minimize the expected annual costs of energy losses while considering the investments associated with reactive power compensators. The IEEE 33- and IEEE 69-bus grids were employed as test systems. The resulting mixed-integer nonlinear programming (MINLP) model was solved by implementing the discrete-continuous version of the vortex search algorithm. Numerical results improved the values reached with some exact MINLP solvers available in the General Algebraic Modeling System (GAMS) software. In [25], the discrete-continuous version of the vortex search algorithm was implemented to define the optimal location and sizing of D-STATCOMs in radial distribution networks.