## 6 Conclusions  
Modern distribution networks include MGs that exhibit several operative scenarios based on topology changes, making their protection coordination a difficult task. This paper presented a novel approach for optimal coordination of directional OCRs in MGs that integrate DG and feature several operative modes. The coordination is carried out by performing a clustering of the operational modes by means of K-means and PCA techniques and then solving the coordination constraints through a GA. Several tests were carried out with an IEC benchmark microgrid. Initially, both K-means and PCA methodologies were tested separately, but coordination was not satisfactorily achieved; nonetheless, the  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{5}{c}{**K-Means as in [20,23]**} & \multicolumn{5}{c}{**Proposed (K-Means via PCA)**} \\ \hline
**Cluster** & **OS** & **OT** & **Viol** & **OS** & **OT** & **Viol** \\ \hline \multirow{2}{*}{1} & OS4 OS8 & \multirow{2}{*}{109.15} & \multirow{2}{*}{0} & OS4 OS8 & \multirow{2}{*}{109.15} & \multirow{2}{*}{0} \\  & OS12 OS16 & & & OS12 OS16 & & \\ \hline \multirow{2}{*}{2} & OS1 OS55 OS9 & \multirow{2}{*}{113.73} & \multirow{2}{*}{2} & OS1 OS2 OS3 & \multirow{2}{*}{82.32} & \multirow{2}{*}{0} \\  & OS13 OS15 & & & OS13 OS15 & & \\ \hline \multirow{2}{*}{3} & OS6 OS7 OS10 & \multirow{2}{*}{214.31} & \multirow{2}{*}{0} & OS5 OS6 & \multirow{2}{*}{290.37} & \multirow{2}{*}{0} \\  & OS11 OS14 & & & OS7 OS10 & & \\ \hline
4 & OS2 OS3 & 34.28 & 0 & OS9 OS11 & 37.10 & 0 \\ \hline Total & & 471.49 & 2 & & 518.94 & 0 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Comparison of results using K-means and PCA technique.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Relay** & **ipickup** & **TMS C1** & **TMS C2** & **TMS C3** & **TMS C4** \\ \hline R1 & 200 & 0.3042 & 0.1871 & 0.4115 & 0.4963 \\ R2 & 200 & 0.1000 & 0.1762 & 0.4124 & 0.1000 \\ R3 & 200 & 0.2171 & 0.1000 & 0.3073 & 0.4535 \\ R4 & 200 & 0.2071 & 0.3085 & 0.  
combination of both clustering techniques resulted in a successful coordination for all clusters of operative scenarios. These results evidenced the effectiveness and applicability of hybridizing the proposed techniques and open the possibility of exploring new approaches to solve the optimal protection coordination in modern MGs.  
Conceptualization, S.D.S.-Z. and J.M.L.-L.; Data curation, S.D.S.-Z.; Formal analysis, S.D.S.-Z., N.M.-G. and J.M.L.-L.; Funding acquisition, J.M.L.-L. and N.M.-G.; Investigation, S.D.S.-Z., N.M.-G. and J.M.L.-L.; Methodology, S.D.S.-Z.; Project administration, S.D.S.-Z., N.M.-G. and J.M.L.-L.; Resources, S.D.S.-Z., N.M.-G. and J.M.L.-L.; Software, S.D.S.-Z.; Supervision, N.M.-G. and J.M.L.-L.; Validation, S.D.S.-Z., N.M.-G. and J.M.L.-L.; Visualization, S.D.S.-Z., N.M.-G. and J.M.L.-L.; Writing--original draft, S.D.S.-Z.; Writing--review and editing, S.D.S.-Z., N.M.-G. and J.M.L.-L. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Colombia Scientific Program within the framework of the so-called Ecosistema Cientifico (Contract No. FP44842- 218-2018).  
Not applicable.  
The authors gratefully acknowledge the support from the Colombia Scientific Program within the framework of the call Ecosistema Cientifico (Contract No. FP44842- 218-2018). The authors also want to acknowledge Universidad de Antioquia for its support through the project \"estrategia de sostenibilidad\".  
The authors declare that they have no conflict of interest.