**6. Conclusions**

In this paper, the vacuum arc commutation model of NHCB was established by simplifying SS and vacuum arc voltage, and the vacuum arc commutation characteristics of NHCB were studied through theoretical analysis and experiments. The mathematical expression of the relationship between the main parameters of the vacuum arc voltage, on-state resistance, and stray inductance and the duration of vacuum arc commutation was obtained.

The concept of the vacuum arc commutation coe fficient was proposed based on the mathematical expressions and experiments, and it is a key parameter that influences the vacuum arc commutation characteristics. The value of the vacuum arc commutation coe fficient should not be small; when it is small, the duration of vacuum arc commutation will increase significantly. Further, it is not the bigger the better, as when it is bigger, the duration of vacuum arc commutation will decrease slowly. Meanwhile, it must always be ensured that the value of the vacuum arc commutation coe fficient is greater than one, so that the current can be commutated to the SS branch.

In the process of vacuum arc commutation, when the di fficulty of vacuum arc commutation increases, the vacuum arc voltage will also increase, and from the extremely di fficult vacuum arc commutation to the easier vacuum arc commutation, the vacuum arc voltage will also be reduced immediately. This paper can provide the theoretical foundation for the structure and parameter optimization of NHCB and other devices using vacuum arc commutation.

**Author Contributions:** D.W. and M.L. contributed to the research idea. D.W., X.D. and J.Z. designed the experiments. D.W. worked on the theoretical analysis, data analysis and drafted the manuscript. R.W. and T.L. helped to do the experiments. J.Q. and J.L. worked on editing and revising of the manuscript. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded in part by the National Natural Science Foundation of China (No. 51777025) and in part by the Fundamental Research Funds for the Central Universities (No. DUT19ZD219).

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