## 5 Conclusions  
The complexity of today's distribution networks and the increasing presence of renewable DG require smarter and more adaptive protection schemes. In a context where distribution networks are expected to operate under different scenarios, traditional approaches for OCR coordination may not be reliable for certain distribution network conditions. In this paper, a novel application of HS and HS-SA is proposed regarding the optimal coordination of OCRs in distribution networks with DG. Several tests were performed on a test distribution network, which featured different types of DG units and several operational modes. A comparison of GA, PSO, HS, PSO-HS and HS-SA techniques was carried out. The implemented algorithms proved to be effective for solving the optimal coordination problem, presenting low operating times and quickly reaching convergence; however, HS-SA was the metaheuristic with the best performance in terms of quality of the objective function. The results evidenced the applicability and effectiveness of HS-SA to  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Fault** & \multicolumn{3}{c}{**Operating Times of OCRs (s)**} \\ \hline  & **Main** & & **Backup** \\ \hline Fault 1 & R1 & R13 & \\  & 0.44 & 0.74 & \\  & R2 & R4 & \\  & 0.12 & 0.42 & \\ Fault 2 & R3 & R1 & \\  & 0.17 & 0.47 & \\  & R4 & R6 & R15 \\  & 0.42 & 0.72 & 0.72 \\ Fault 3 & R5 & R15 & \\  & 0.41 & 0.78 & \\  & R6 & R7 & R8 \\  & 0.69 & & 1.00 \\ Fault 4 & R8 & R11 & \\  & 0.95 & 1.28 & \\  & R12 & R5 & R7 \\  & 0.13 & 0.43 & \\ Fault 5 & R9 & R14 & \\  & 0.21 & 0.51 & \\  & R10 & R6 & R15 \\  & 0.12 & 0.88 & 0.9 \\ \hline \hline \end{tabular}
\end{table}
Table 10: Operating times for Scenario 4.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Relay** & \(TMS_{i}\) & \(PSM_{imax}\) \\ \hline R1 & 0.1511 & 76.23 \\ R2 & 0.05 & 49.59 \\ R3 & 0.05 & 47.71 \\ R4 & 0.1552 & 56 \\ R5 & 0.1571 & 90.12 \\ R6 & 0.1477 & 42.65 \\ R7 & & \\ R8 & 0.2176 & 40.8 \\ R9 & 0.05 & 32.32 \\ R10 & 0.05 & 53.89 \\ R11 & 0.2396 & 58.28 \\ R12 & 0.05 & 57.41 \\ R13 & 0.1669 & 95.87 \\ R14 & 0.0998 & 83.93 \\ R15 & 0.1371 & 61.34 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Coordination parameters for Scenario 4.  
tackle the optimal coordination problem in modern DNs, achieving high-quality solutions. Other alternatives might be explored regarding HS approaches, such as online applications in real DNs which might require parallelization techniques to reduce computation time, clustering of operational scenarios and exploring other hybrid versions of HS. This opens a new field of applications for the HS technique regarding the safe operation of modern DNs and microgrids.  
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, [PERSON]-L. and [PERSON]-G.; investigation, S.D.S.-Z., [PERSON] and [PERSON]-L.; methodology, S.D.S.-Z.; project administration, S.D.S.-Z., [PERSON]-G. and [PERSON]-L.; resources, S.D.S.-Z., [PERSON]-G. and [PERSON]-L.; software, S.D.S.-Z.; supervision, [PERSON]-G. and [PERSON]-L.; validation, S.D.S.-Z., [PERSON]-G. and [PERSON]-L.; visualization, S.D.S.-Z., [PERSON]-G. and [PERSON]-L.; writing--original draft, S.D.S.-Z.; writing--review and editing, [PERSON], [PERSON] and [PERSON]. 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.  
Data availability statement: Data is available in the cited references and via authors on request.  
The authors gratefully acknowledge the support from the Colombia Scientific Program within the framework of the so-called 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 no conflict of interest.