## 6 Conclusions and Future Work  
The optimal reactive power compensation problem via D-STATCOM location and sizing was studied in this research through the application of master-slave optimization methodology that solves its exact MINLP formulation. In the master stage, the GNDO approach was implemented using a discrete codification that decided the nodes where the D-STATCOMs were to be located in conjunction with their optimal sizes. In the slave stage, a power flow method (the successive approximations approach) was used to define the expected energy loss costs for a daily operation horizon. An improvement stage was implemented in the exact MINLP model that involved fixing the location of the D-STATCOMs provided by the master-slave optimizer in order to obtain an NLP model that could vary the reactive power injection on an hourly basis in order to obtain additional profits for the distribution company. The numerical simulations run in the IEEE 33-bus system with radial and meshed configurations while including residential, industrial, and commercial users demonstrated that:  
1. In the radial configuration scenario, the proposed GNDO approach reached a lower minimum objective function value than the SSA approach. In addition, the improvement stage allowed for an additional reduction of USD 1665.25 regarding the fixed injection case, which confirms that the variable reactive power scenario via the daily control of the D-STATCOMs allows the distribution company to obtain additional profits in the total annual expected operating costs of the network. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Case** & **Min. (USD/year)** & **Max. (USD/year)** & **Mean (USD/year)** & **Std. Dev. (USD/year)** & **Time (s)** \\ \hline Radial & 108,215.94 & 116,992.53 & 109,373.20 & 2053.04 & 42.70 \\ \hline Meshed & 77,834.42 & 80,231.64 & 78,256.17 & 597.01 & 42.94 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Statistical analysis for the radial and meshed configurations of the IEEE 33-bus grid. * In the meshed configuration, the proposed GNDO approach found the same nodal location for the D-STATCOMs as the SSA methodology. However, the sizing was better, which allowed for a better final objective function value. In the variable reactive power scenario, an additional profit of USD 186.39 with respect to the fixed injection scenario was also reached, thus confirming that controlling the reactive power injection as a function of the system's requirements is the better option to operate D-STATCOMs based on utilities. * The expected annual operative gains for the meshed topology are considerably lower than those of the radial grid, i.e., USD 9080.32 for the meshed case vs. USD 22,397.96 for the radial case. This is an expected result since in meshed configurations the energy losses are lower when compared to radial configurations, which is attributed to better flow distribution and voltage profiles. * Regarding the processing times, the proposed GNDO approach found the solution for the MINLP model in less than one minute for both topologies, which confirms the effectiveness and robustness of the master-slave optimization methodology to deal with complex electrical engineering problems involving solution spaces with infinite dimensions and complex nonlinear, non-convex constraints. In future work, the following studies can be conducted: (i) combining the D-STATCOMs with renewable generators in radial and meshed distribution grids by defining their sizes and locations in order to reduce the grid investments and the operating and maintaining costs; and (ii) a comparative study between different reactive power compensators such as D-STATCOMs, Thyristor-controlled series compensators (TCSCs), and Static VAR Compensators (SVCs), as well as their impact on the expected annual grid operating costs. Conceptualization, methodology, software, and writing (review and editing): L.P.G.-P. and O.D.M. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable.