## 3 Solution Methodology  
To solve the MINLP model (1)-(7) and define the optimal location and sizing of STATCOMs in power systems, the GAMS software was employed. This is an optimization tool to solve large-scale optimization problems from linear programming to MINLP models, among others. The main advantage of using GAMS to solve optimization problems is the possibility of separating the solution technique from the mathematical modeling, which helps concentrating efforts for proposing a mathematical model that adequately represents the studied problem. Table 1 presents a lists of different optimization problems solved with the GAMS optimization package.  
In Table 1, it is possible to observe that the GAMS optimization package is suitable for solving different optimization problems such as the non-linear programming (NLP), mixed-integer linear programming models (MILP), and MINLP models, respectively.  
The main aspects of the implementation of an optimization model in the GAMS package are listed as follows [42]:  
\begin{tabular}{l l} ✓ & Definition of the sets (nodes and periods of time), tables, parameters, and scalars (i.e., nodal admittance matrix, demands, costs, etc.). \\ ✓ & Definition of the continuous and discrete variables, i.e., nodal voltages and angles, active and reactive powers, among others. \\ ✓ & Selection of the equations' names and writing all these (optimization models (1)-(7)) \\  & using the symbolic structure of the GAMS software [29]. \\ ✓ & Selection of the model type and the direction of optimization, i.e., minimization. \\ ✓ & Solution of the model using an adequate solver for MINLP problems. \\ \end{tabular}  
Note that the main requirement is associated with an implementation in GAMS, that is, the mathematical formulation, as these must be consistent and faithfully represent the studied problem with a feasible solution space.  
To summarize the optimization methodology, in the flow-chart presented in Figure 2, the sequential steps for implementing any optimization model using the GAMS optimization package are provided.  
It is important to mention that the flow diagram presented in Figure 2 is a general procedure for solving different optimization models with the help of the GAMS software, and it only requires basic programming skills using a structured programming language. For more details regarding GAMS implementations, see the works of [PERSON] [29] and [PERSON] [43].  
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Problem** & **Model Type** & **Ref.** & **Year** \\ \hline Optimal design of osmotic power plants & NLP & [30] & 2015 \\ Optimal location and sizing of batteries in power systems & MINLP & [29] & 2017 \\ A mixed-integer linear model for thermal generating units in the & MILP & [32] & 2018 \\ economic dispatch & MILP & [33] & 2018 \\ Integrated transmission and generation expansion planning & MILP & [33] & 2018 \\ considering safety constraints & MILP & [34] & 2018 \\ Design of optimal mixtures from atom groups & MINLP & [35] & 2019 \\ Optimal allocation model of water resources & NLP & [36] & 2019 \\ Optimal power flow studies & NLP & [37] & 2020 \\ Parameter estimation in single-phase transformers & NLP & [38] & 2020 \\ Optimal location and sizing of distributed generators in & MINLP & [39] & 2020 \\ distribution networks & MINLP & [39] & 2020 \\ Multi-objective electric vehicles scheduling & NLP & [39] & 2020 \\ Optimal selection of calibers of conductors in DC radial & MINLP & [40] & 2021 \\ distribution networks & NLP & [41] & 2021 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Different optimization models solved using the GAMS optimization package.