###### Abstract
The main contribution of the authors relates to their identification of the possible positive and negative effects associated with the installation of renewable energy resources, which allowed the authors to provide some guidelines regarding the optimal location of these devices in electrical distribution grids. The authors of Reference [21] presented the voltage stability analysis in AC distribution grids using a second-order cone programming model. Numerical simulation shows that the conic formulation allows for the maximum simultaneous increment in all the loads of the network by ensuring the global optimum finding. Numerical results in the IEEE 33- and IEEE 69-node test feeders demonstrated the effectiveness of the conic model when compared with the exact nonlinear model and classical recursive approaches based on power flow solutions. Reference [17] proposed a stability indicator that allowed identifying nodes on the verge of voltage collapse. This indicator is calculated for each node using a modification of the load flow method for voltage stability analysis, which incorporates the load variations and composite load models. Numerical results demonstrated the effectiveness of the proposed index when compared with others in the existing literature. [PERSON] and [PERSON], in Reference [23], proposed an extension of the classical Newton-Raphson power flow method through the continuation approach. Numerical results in the IEEE 33-bus system demonstrate the effectiveness of the proposed method to obtain the voltage collapse point. Their results were corroborated with the PSAT tool for MATLAB software (2021a, Natick, MA, USA). In the case of the optimal placement of dispersed generators for distribution networks, most of the approaches, in their objective formulations, consider the improvement of the voltage stability index of the network [24]. Some of these approaches include population-based incremental learning [25], genetic algorithms [26; 27], particle swarm optimization [28], and heuristic-based methods based on sensitive formulas [29; 30]. In general, these approaches are based on the calculation of a voltage stability index based on the branch-to-load equivalent of each branch of the network. Further, as mentioned previously, these approaches do not consider in their formulations the simultaneous increment of the loads in all the nodes, which is indeed a complication. The present study aims to contribute to the current literature by addressing the aforementioned complication. In this study, we propose a mixed-integer nonlinear programming (MINLP) model for voltage stability improvement in medium-voltage distribution networks that includes the possibility of optimal siting and sizing of dispersed generators considering a global stability index named the \(\lambda\)-coefficient [21]. The solution of this MINLP model was achieved using the General Algebraic Modeling System (GAMS) and the large-scale solver BONMIN [31; 32]. In addition, we propose two recursive validations using the successive approximation power flow method in the MATLAB programming environment [33] and the Newton-Raphson power flow method in DigSILENT software [34], which allow the final value of the \(\lambda-\)coefficient to be verified via an iterative procedure by fixing the sizes and locations of the dispersed generators based on the solution provided by GAMS software. The main contributions of this study include: (i) the validation of the optimal value of the \(\lambda\)-coefficient using two recursive power flow methods programmed in MATLAB and DigSILENT programming environments based on the successive approximation power flow method and the Newton-Raphson approach, respectively; and (ii) the evaluation of multiple simulation scenarios with different numbers of available dispersed generators with limitations of 40% and 60% in the total injection of active power by the distributed sources. These simulation cases demonstrate that the areas with the worse voltage profiles are the best places for locating the dispersed generators.