###### Abstract
The authors of [23] proposed an improved version of the particle swarm optimizer to locate and size STATCOMs in power systems with photovoltaic sources to minimize the costs of the energy losses and the voltage profile improvement. Numerical results demonstrate the effectiveness of the proposed approach in comparison with the bee colony optimization and the lightening search algorithm, respectively. The following are some additional approaches for locating and sizing STATCOMs in power and distribution networks: the tabu search algorithm [24], bat optimization algorithm [25], discrete-continuous vortex search algorithm [16], genetic algorithms [26; 27], and firefly optimization algorithm [28]. To deal with the problem of power losses minimization in power systems, we propose a mixed-integer nonlinear programming model (MINLP) for optimally locating and sizing STATCOMs in power systems considering different load scenarios (commercial, residential, and industrial) [11]. The aim of the proposed (MINLP) model is to reduce the annual operative cost of the power system. This objective function is composed by the costs of the energy losses during the planning horizon and the installation costs of the STATCOMs. The general algebraic modeling system (GAMS) software with the BONMIN large-scale optimization solver is used to solve the MINLP model; this software was selected as a optimization tool due to the excellent reports presented in the literature for similar MINLP models [29; 30]. The main contributions of our approach are summarized below:  
* To formulate the problem of the optimal siting and sizing of STATCOMs in power systems as a multi-objective optimization problem, where the objective functions in conflict are the cost of annual energy losses and the investments in STATCOM devices. * The solution of the single-objective model and the multi-objective model using the GAMS software and BONMIN, where it was observed that the minimum solution in the Pareto front regarding the total annual operative costs of the network after the installation of the STATCOMs differs by only 0.02% with respect to the single-objective model. * The application of the solution methodology to radial and meshed power systems in high- and medium-voltage levels combined with residential, industrial, and commercial load curves to characterize the behavior of the constant power consumption. It is important to highlight that the proposed optimization methodology with the GAMS optimization package and the BONMIN solver has not been previously reported in specialized literature on radial and meshed power systems with multiple generators considering different load curves; this scenario of optimization was identified as an opportunity of research that this work endeavors to fill. In the recent literature, two works on the optimal installation of STATCOMs in distribution systems have been presented. An algorithm-denominated discrete-continuous vortex search algorithm was proposed by [PERSON] et al. [16] to locate and size STATCOMs in distribution grids with fast convergence and solution repeatability; however, this approach is only applicable to distribution grids with radial or meshed configuration that have only one slack source without voltage controlled nodes, which makes it impossible to extend it to high-voltage power systems with multiple generators. The authors of [11] presented a hybrid optimization approach based on the classical [PERSON] and Beasley genetic algorithm and the conic reformulation of the optimal power flow equations; however, the conic reformulation is only applicable to pure radial distribution grids with only one slack source, which makes this approach non-applicable to power systems in high-voltage levels.