## 6 Conclusions and Future Research  
An exact MINLP formulation was proposed to solve the problem of determining the maximum loadability in medium-voltage networks by considering the optimal placement and sizing of dispersed generators. The solution of the MINLP model was reached using the BONMIN solver in the GAMS environment. A small 7-bus system was used as a numerical example to illustrate the usage of GAMS from a tutorial perspective. The value of the \(\lambda\)-coefficient provided by GAMS in both the test feeders was verified through evaluations implemented in MATLAB using the successive approximation power flow and also in DigSILENT software using the Newton-Raphson power flow method. Numerical results demonstrated that the \(\lambda\)-coefficient can be improved between 20.96% and 37.43% for the IEEE 33-bus system when one to three dispersed generators are installed and between 18.41% and 41.98% for the IEEE 69-bus system in identical simulation conditions.  
The numerical results indicated that, in both the test feeders, the regions where the dispersed generators corresponded to the nodes were associated with the worst voltage profiles, i.e., node 18 for the IEEE 33-bus system and node 65 for the IEEE 69-bus system. In addition, the number of dispersed generators available for installation in conjunction with the values of the \(\beta\)-coefficient directly influence the total improvement of the loadability coefficient; for two or three dispersed sources, the differences in the indicator were lower than 2%, implying that the limitation imposed by the \(\beta\)-coefficient produces a saturation effect in the \(\lambda\)-coefficient.  
Future studies can consider the following research directions: (i) the reformulation of the exact MINLP model through a mixed-integer conic model to ensure the determination of the global optimum owing to the convexity properties assignable to the conic solution spaces; (ii) the formulation of an optimization model with reactive power compensators (STATCOMs or capacitor banks) to enhance the voltage stability margin in medium-voltage distribution networks; and (iii) economical aspects regarding batteries and renewable generation can be included in the proposed model for stability studies in distribution networks.  
Conceptualization, methodology, software, and writing--review and editing, B.E.A.-A., L.C.G.-B., O.D.M. and F.D.M. All authors have read and agreed to the published version of the manuscript.  
This work was supported in part by the Centro de Investigacion y Desarrollo Cientifico de la Universidad Distrital Francisco Jose de Caldas under grant 2-7-625-20 associated with the project \"Modelo de optimizacion para la gestion colectiva de la demanda en redes electricas de distribucion contemplando alta penetracion de energias renovables y vehiculos electricos\".  
Not applicable.  
This work has been derived from the undergraduate project \"Determinacion del margen de estabilidad de voltaje en sistemas de distribucion empleando optimizacion matematica\" presented by the students [PERSON] and [PERSON] to the Electrical Engineering Program of the Engineering Faculty at Universidad Distrital Francisco Jose de Caldas as a partial requirement for the degree of Bachelor in Electrical Engineering.  
The authors declare no conflict of interest.