###### Abstract  
This study addresses the problem of the maximization of the voltage stability index (\(\lambda\)-coefficient) in medium-voltage distribution networks considering the optimal placement and sizing of dispersed generators. The problem is formulated through a mixed-integer nonlinear programming model (MINLP), which is solved using General Algebraic Modeling System (GAMS) software. A numerical example with a 7-bus radial distribution network is employed to introduce the usage of GAMS software to solve the proposed MINLP model. A new validation methodology to verify the numerical results provided for the \(\lambda\)-coefficient is proposed by using recursive power flow evaluations in MATLAB and DigSILENT software. The recursive evaluations allow the determination of the \(\lambda\)-coefficient through the implementation of the successive approximation power flow method and the Newton-Raphson approach, respectively. It is effected by fixing the sizes and locations of the dispersed sources using the optimal solution obtained with GAMS software. Numerical simulations in the IEEE 33- and 69-bus systems with different generation penetration levels and the possibility of installing one to three dispersed generators demonstrate that the GAMS and the recursive approaches determine the same loadability index. Moreover, the numerical results indicate that, depending on the number of dispersed generators allocated, it is possible to improve the \(\lambda\)-coefficient between 20.96% and 37.43% for the IEEE 33-bus system, and between 18.41% and 41.98% for the IEEE 69-bus system. voltage stability analysis; mathematical optimization; recursive solution methodologies; dispersed generation +
Footnote †: journal: Applied Mechanics and Physics Letters  
[PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], Optimal Integration of Dispersed Generation in Medium-Voltage Distribution Networks for Voltage Stability Enhancement  
22 January 20  
-banks [7; 8], optimal location of distribution static compensators [9; 10], optimal integration of battery energy storage systems [11; 12], and grid reconfiguration [13; 14], among other strategies. The distinctive characteristic of these approaches is the usage of advanced optimization techniques to improve the grid performance, most of which are from the family of metaheuristic optimization techniques because of their ease of implementation with a master-slave structure using simple power flow formulations [15]. Reducing total grid power losses is, thus, an important and current research aspect in optimization studies for electrical distribution grids [16]. Correspondingly, the voltage stability performance of the network is an additional aspect that has attracted considerable attention owing to its implications in the quality and operation reliability indexes [17]. The voltage stability performance measures the ability of the distribution grid to support load increments without causing a blackout [18; 19]. Several studies have addressed the improvement of grid stability using a simplified line-to-load indicator, primarily using dispersed generators [20]. However, the central drawback of these approaches is that the adopted stability index does not measure the global state of the distribution grid and its ability to support simultaneous load increments [21]. In the specialized literature, the voltage stability issues in distribution grids are usually addressed using numerical indexes that concern the voltage profile and the total power consumption. [PERSON] and [PERSON], in Reference [22], analyzed the voltage stability problem in AC distribution networks considering the large-scale integration of photovoltaic generation. The authors developed a stability index that depends on the line data, active and reactive power demands, and the voltage values, which are obtained using a classical load flow method.