## 6 Conclusions and Future Works  
The problem of the optimal siting and sizing of D-STATCOMs in electric distribution networks to minimize the annual operational costs of the grid caused by the energy losses during a typical day of operation was formulated as an MINLP model in research. The model proposed in this study incorporates of the a new version of the VSA that uses a discrete-continuous codification (DCVSA) and the SAPF method. The DCVSA is used for determining the optimal locations for and sizes of the D-STATCOMs and the SAPF method entrusted determines the voltage variables to calculate the annual energy losses of the grid and their cost. Numerical results in the IEEE 33- and IEEE 69-bus test feeders demonstrated that the proposed hybrid optimization approach showed a better numerical performance than the MINLP solvers BONMIN and COUENNE in the GAMS package. With the IEEE 33-bus test feeder, the DCVSA caused an annual reduction about 12.63%, while the BONMIN and the COUENNE solvers could bring about reductions of about 9.13% and 4.57%, respectively. With the IEEE 69-node test feeder, the reduction with DCVSA was about 13.97% and that with the GAMS solvers was variable.  
The evaluation of the dynamic reactive power compensation using the D-STATCOMs sized and located by the proposed DCVSA approach showed that depending on the amount of active and reactive power demands throughout the day, the reactive power injection must be varied to achieve even greater improvement in the annual performance of the grid. Numerical results showed that for the IEEE 33-bus and IEEE 69-bus test feeders, additional  
Figure 4: Dynamic reactive power behavior in a typical operation day for the D-STATCOMs in electric distribution networks: (a) IEEE 33-bus, and (b) IEEE 69-bus.  
annual reductions of about US $1231.41 and US $1590.87 were achieved as compared to fixed reactive power injections.  
As future works, the following research topics may explore: (i) the reformulation of the MINLP model into a mixed-integer convex model to find the global optimum with the application of the Branch and Bound and the interior point methods; and (ii) the simultaneous location and sizing of the renewable energy resources and D-STATCOMs to improve the grid performance during the planning horizon, considering annual load increments.  
Conceptualization, O.D.M. and W.G.-G.; Methodology, O.D.M. and W.G.-G.; Investigation, O.D.M., W.G.-G., and J.C.H.; Writing--review and editing, O.D.M., W.G.-G., and J.C.H. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Centro de Investigacion y Desarrollo Cientifico de la Universidad Distrital 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.\"  
This work was supported in part by the Direccion de Investigaciones de la Universidad Tecnologica de Boliv under grant PS2020002 associated with the project: \"Ubicacion optima de bancos de capacitores de paso fijo en redes electricas de distribucion para reduccion de costos y perdidas de energia: Aplicacion de metodos exactos y metaheuristics.\"  
The authors declare no conflict of interest.