###### Abstract
However, the main problem of the capacitor banks is that they inject only in fixed steps of reactive power (discrete nature of the capacitive compensation with shunt capacitors), while the daily active and reactive power demands along the electric distribution grids are highly variables and continuous [10]. Recognizing the power saving that can be achieved with reactive power compensation with shunt devices, in recent decades, compensators based on power electronics have gained taken importance in distribution levels due to their versatility and capacity to vary the reactive power injections as a function of the demand behavior. These devices are the distribution static compensators (D-STATCOMs) [11], which have, among others, such advantages as: (i) high reliability, (ii) low operative costs, and (iii) long useful life (typically 5 to 15 years). The literature on this specific topic has reported several approaches regarding the use of D-STATCOMs for dynamic reactive power compensation at medium-voltage levels. Some of these approaches are presented below. The authors of [11] presented the complete of determining the optimal placement and sizing of D-STATCOMs using analytical and heuristic optimization methods. Also, they presented some objective classical functions used for improving the grid performance, such as voltage stability and power loss indices. In [6] the authors proposed a multi-objective particle swarm optimizer to locate and size D-STATCOMs considering the simultaneous reconfiguration of the electrical network. As objective functions are considered the minimizing the active power losses, the voltage stability index and the loadability factor of the distribution lines, the main characteristic of this approach is that the optimization process is made only during the peak load condition, which is not considered a proper scenario due to possible over-sizing of the compensator devices, since the active and reactive power consumptions are variable inputs. The authors in [12] presented a heuristic cost-based approach to evaluate the impact of the optimal placement and sizing of D-STATCOMs in isolated power systems for automatic voltage support. However, the model considers the unique nodal representation of the power system, which oversimplifies the real behavior of the power system. The authors of [7] presented a fuzzy multi-objective approach based on the ant colony optimization algorithm to solve the simultaneous reconfiguration and optimal allocation (sizing and siting) of photo-voltaic sources and D-STATCOMs in the distribution system. The goal of the authors was to minimize the grid losses, improve the voltage profiles and increase in the feeder load balancing. Numerical results were tested in the IEEE 33-bus test feeder. A heuristic method based on voltage and power losses indices was proposed in [13] to locate and size D-STATCOMs in radial electric distribution networks. Numerical validations of this heuristic approach were made in the IEEE 33-bus test feeder. However, the authors consider only the peak load condition in their analysis. In [14] the authors presented the implementation of a genetic algorithm to locate and size D-STATCOMs in distribution systems using the optimal power flow tool available in the DigSILENT software. The main advantage of this approach is that it is tested in a real distribution grid. However, the authors do not present any cost analysis. In [15] the authors analyze the problem of the optimal location of D-STATCOMs considering simultaneous grid reconfiguration to reduce the amount of active power losses. The solution of the problem is derived using the differential evolution algorithm. However, the authors only consider the peak load condition in their analysis.