## 6 Conclusions and Recommendations  
In this paper we solved the problem of optimal siting and sizing of D-STATCOMs in electrical distribution grids with radial structure considering residential, industrial, and commercial loads, by proposing a new hybrid optimization approach based on the combination of the classical CBGA and the SOCP reformulations of the optimal power flow problem. The former addressed the discrete part of the optimization problem, i.e., the location of the D-STATCOMs, while the latter solved the the optimal sizing problem of the D-STATCOMs via conic optimization. Numerical results demonstrated that with a population size of 20 in the CBGA, the optimal solution was obtained; this solution allowed for reducing the annual operational costs to about 16.20% by inverting about 12, 300 dollars per year of operation.  
The use of D-STATCOMs instead of fixed-step capacitor banks for reactive power compensation in distribution grids demonstrated that the variable reactive power injection as function of the grid demand behaviors allows additional monetary gains per year of operation to be reached, which in the case of the IEEE-bus test feeder was about US$/year 2759.24.  
Numerical comparisons with the MINLP solvers BONMIN and COUENNE (available in the GAMS optimization package) confirmed that these get stuck in local optimal solutions when compared with the results reached by the proposed genetic-convex approach. This situation occurred in the GAMS solvers due to the non-convexity of the solution space, which makes it difficult to explore and exploit the solution space with exact optimization techniques.  
In future, researchers can work on the following aspects: (i) to extend the application of the D-STATCOMs in optimization problems associated with greenhouse gas emission  
Figure 6: Dynamic reactive power behavior during a typical operation day for the D-STATCOMs in electric distribution networks in the IEEE 33-bus test feeder.  
minimization, and (ii) reformulation of the objective functions associated with the costs of the D-STATCOMs, such as a convex quadratic function, which will ensure the finding of the global optimal solution via branch-and-bound and interior point methods to solve the MISOCP equivalent formulation.  
Conceptualization: O.D.M. and W.G.-G.; methodology: O.D.M. and W.G.-G.; investigation: O.D.M. and W.G.-G.; writing, review, and editing: O.D.M., W.G.-G., H.R.C., L.A.-B., and C.O.-H. All authors have read and agreed to the published version of the manuscript.  
This work was partially supported in part by the Laboratorio de Simulacion Hardware-in-the-loop para Sistemas Ciberfisicos under Grant TEC2016-80242-P (AEI/FEDER), and in part by the Spanish Ministry of Economy and Competitiveness under Grant DPI2016-75294-C2-2-R.  
Not applicable.  
No new data were created or analyzed in this study. Data sharing is not applicable to this article.  
The first author was supported by the Centro de Investigacion y Desarrollo Cientifico de la Universidad Distriatal Francisco Jose de Caldas, under grant 1643-12-2020 associated with the project \"Desarrollo de una metodologia de optimizacion para la gestion optima de recursos energeticos distribuidos en redes de distribucion de energia electrica\" and in part by the Direccion de Investigaciones de la Universidad Tecnologica de Bolivar, under grant PS2020002 associated with the project \"Ubicacion optima de balencos de capacitores de paso fijo en redes electricas de distribucion para reducucion de costos y perdidas de energia: Aplicacion de metodos exactos y metaheuristicos.\"  
The authors declare no conflict of interest.