**5. Discussion**

### *5.1. Vacuum Arc Commutation Coe*ffi*cient*

Compared to the theoretical analysis and experiments above, it is easy to find that the experimental results can better match the theoretical Formulas (9)–(12). This shows that Formulas (9)–(12) can better reflect the influence of the main parameters, such as the vacuum arc voltage *Uarc*, final commutation current *Ice*, on-state resistance *Rs*, and stray inductance *Ls*, on the vacuum arc commutation characteristics. Meanwhile, according to Formulas (11) and (12) and Figures 6, 8, 13c and 15c, the ratio *k* of *Uarc-avg*-*Usi* to *RsIce* is a key parameter that a ffects *Tc*; and according to Formula (10), it is necessary to ensure that *k* > 1 so that the current can be commutated to the SS branch. Overall, *k* is a very important parameter during the vacuum arc commutation. Therefore, this paper defines *k* as the vacuum arc commutation coe fficient.

According to Figures 6, 8, 13c and 15c, when *k* is small, *Tc* will increase significantly. Therefore, in order to reduce *Tc*, the value of *Uarc-avg* − *Usi* should be increased or the value of *RsIce* should be decreased. The main method of increasing the value of *Uarc-avg* − *Usi* is to increase the vacuum arc voltage. Applying an external magnetic field and connecting multiple MSs in series are currently common methods of increasing the arc voltage [25,26]. The main method to reduce the value of *RsIce* is to reduce the on-resistance *Rs* and final commutation current *Ice*, but reducing *Ice* will reduce the interrupting ability of NHCB. The method to reduce the on-resistance *Rs* is to select FPEDs with low on-resistance or to increase the number of parallel FPEDs [27,28]. Meanwhile, it can be seen from Formula (9) and Figure 11 that reducing the stray inductance *Ls* in the SS is also an e ffective method to reduce *Tc*.

### *5.2. Influence of the Main Parameters on the Vacuum Arc Voltage*

It can be seen from the experiment that when the parameters *Ls*, *Ice*, and *Rs* increase, not only *Tc* increases but the vacuum arc voltage also increases, which is consistent with the positive feedback characteristics of the vacuum arc voltage. This can explain the sudden drop of the vacuum arc voltage in Figure 14, before the IGBT module is turned on, the vacuum arc commutation is very di fficult, so the vacuum arc voltage at this time is higher. When the IGBT module is turned on, the di fficulty of vacuum arc commutation decreases rapidly, so the vacuum arc voltage also decreases accordingly. Meanwhile, to better describe the influence of parameters *Ls*, *Ice*, and *Rs* on *Tc*, in the future work, the influence of the parameters *Ls*, *Ice*, and *Rs* on the vacuum arc voltage should be considered in Formula (9).

Although this paper focuses on NHCB, it is also applicable to other devices that use vacuum arc commutation, such as fault current limiters [29,30]. In the future work, further research will be conducted on other devices that use vacuum arc commutation.
