**5. Conclusions**

In this study, the islanding detection method based on perturbation signal injection and the rate of change of output power in a DC grid-connected photovoltaic system is investigated.

The impact of injected signal cancellation on the islanding detection method in [16] is significant. The islanding detection method in [16] cannot detect the islanding phenomenon but works well without injected signal cancellation (detection time is 56 ms).

The solution of using the new perturbation factors (n = 0.9–1 in normal condition) is proposed. With this solution, the improved islanding detection method can detect the islanding phenomenon after 40 ms (two-PV scenario), 64 ms (three-PV scenario), and 48 ms (four-PV and eight-PV scenarios) when the injected signal cancellation appears.

Through the mathematical explanations and simulation results, the injected signal cancellation is eliminated. Moreover, the improved islanding detection method by applying the proposed solution is correct not only in specified cases but also in the general case.

**Author Contributions:** T.S.T. and D.T.N. extensively reviewed the literature and drafted the manuscript and G.F. provided feedback and critical comments for inclusions and finally helped in revising the manuscript to improve the quality of paper. All authors provided critical feedback and helped shape the research, analysis and manuscript. Besides, all authors discussed the results and contributed to the final manuscript.

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

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