**5. Conclusions**

In this research work, the APS passed the miscoordination problem between primary and backup DOCRs, as well as miscoordination between DOCRs and distance relays. The results demonstrated that APS has the potential to coordinate protection relays with appropriate settings to face the problem of DGs in the distribution network. Without miscoordination between protection relays, the power system can investigate the advantages of both distance relays and DOCRs. In addition to the role of the modified optimization algorithm, which improved the optimal values and reduced operation relay's time, all operation times of both primary DOCRs and distance second zone's time were set below the maximum operation time. The modified algorithm has better convergence characteristics and achieves better optimal values with fewer iterations.

**Author Contributions:** Conceptualization, S.K. and A.K.; Data curation, S.K. and A.K.; formal analysis, S.K., A.K., M.T.-V., F.A.B. and M.I.M.; funding acquisition, F.A.B. and M.I.M.; investigation, M.A., S.K., A.K. and M.T.-V.; methodology, M.A., S.K. and A.K.; project administration, S.K., M.T.- V., F.A.B. and M.I.M.; resources, S.K. and M.T.-V.; software, S.K.; supervision, S.K., A.K., M.T.- V., F.A.B. and M.I.M.; validation, M.A., S.K. and A.K.; visualization, M.T.-V., F.A.B. and M.I.M.; writing—original draft, M.A. and A.K.; writing—review & editing, S.K. and M.T.-V. All authors have read and agreed to the published version of the manuscript.

**Funding:** The authors thank the support of the National Research and Development Agency of Chile (ANID), ANID/Fondap/15110019.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.
