**5. Conclusions**

In this paper, an improved inverse-time over-current protection method based on the compound fault acceleration factor and BAS optimization algorithm is proposed. The new method notably increases the speed of the over-current protection and improves the coordination between the adjacent relays. The potential influencing factors on ITOCR protection, including the microgrid operation modes, fault position, and fault types, were evaluated. The simulation results show that the improved inverse-time over-current protection method can quickly and coordinately remove faults under different operation modes, different fault locations, and different fault types of the microgrid, which verifies the speed and coordination of the protection method, and is better than the traditional protection methods. Furthermore, as the proposed method does not require extra devices, it is potentially more economic and easier to implement in the field, thus offering a promising solution for effective microgrid protection.

**Author Contributions:** Author Contributions: Conceptualization, L.J. and Z.C.; methodology, L.J. and Z.C.; software, J.S. and Z.C.; validation, L.J., Z.C. and J.S.; formal analysis, Q.H.; investigation, X.C.; resources, Y.F.; data curation, Y.M.; writing—original draft preparation, L.J. and Z.C.; writing—review and editing, L.J., Y.F. and Z.C.; visualization, Z.L.; supervision, L.J. and Z.L.; project administration, Y.F. and Y.M.; funding acquisition, Y.F. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

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