### Literature Review  
Different methods and proposals for integrating D-STATCOMs into AC distribution networks have been presented in the literature. In 2012, the authors of [16] presented a combination of a genetic algorithm and particle swarm optimization to minimize power losses in the network and improve voltage regulation and stability within the framework of system operation and security restrictions in radial distribution systems. In the same year, the authors of [17] proposed a mathematical model represented by an MINLP algorithm, which was implemented in test systems of 33 and 69 nodes. After comparing the results with those of different methods described in the scientific literature, their approach showed superior efficiency and accuracy in terms of power loss reductions. The authors of [18] worked on an optimization algorithm for ant colonies, which integrates a fuzzy technique with several objectives. This article proposed the implementation of PV sources and D-STATCOMs in the IEEE 33-node system, in which these devices are reconfigured and assigned to meet the objectives of improving voltage profiles and minimizing grid losses. In the same year, the authors of [19] proposed the reduction of power losses in radial networks using a heuristic method based on power loss and voltage metrics for the optimal placement and sizing of D-STATCOMs in radial networks. Nevertheless, the authors only considered the most demanding conditions for the 33-node system when performing the computational validations. In [12], the authors presented a combination between a second-order cone-based mathematical programming method and a genetic algorithm for sizing and locating D-STATCOMs in distribution networks. They made use of commercial, industrial, and residential demand curves in the IEEE 33 and 69 test systems, demonstrating the efficiency of the proposed methodology in comparison with the solution of the model in the GAMS software. The authors of [20] aimed to determine the optimal sizing and positioning of D-STATCOMs in distribution networks through an optimization method based on a multi-objective particle swarm algorithm. The study aimed to stabilize the voltage index and load factor, as well as to minimize the active losses in the distribution network. It should be noted that the method considered the possibility of adapting the network for different demand conditions, and the algorithm only works under load conditions. Therefore, when working with the maximum load, the D-STATCOMs can be oversized. Finally, the authors of [21] modified the sine-cosine algorithm to minimize power losses and improve voltage profiles. In 2021, the authors of [10] addressed the D-STATCOMs integration problem by applying a discrete-continuous version of the [PERSON] and Beasley genetic algorithm. This work aimed at minimizing the total annual operating costs associated with the power losses and installation costs of D-STATCOMs. Numerical results in the 33-node test system with both radial and meshed topologies demonstrated the efficiency and robustness of the proposed methodology when compared to other methods reported in the literature. In the same year, reductions in investment and operating costs were achieved via the discrete-continuous vortex search algorithm [22], genetic algorithms, conic programming [23], and the solution of the exact MINLP model in GAMS software [24]. In 2022, the authors [25], by means of second-order conic mixed-integer programming, sought to minimize energy losses and reduce investment and operating costs. A summary of the implemented algorithms, methodologies, and objective functions, along with their year of publication, can be found in Table 1.  
Note that the objective functions of most methodologies in Table 1 were to minimize power losses and reduce investment costs.