**4. Experimental Results**

### *4.1. Influence of Stray Inductance of the SS*

Under the condition that *Ra* is 5 m Ω, and *Ise* is approximately 0.5, 1, and 1.5 kA, respectively, we obtained the waveforms of vacuum arc commutation with di fferent stray inductances. When the *Ise* is approximately 1 kA, the waveforms when the added stray inductance *La* is 0 and 2 μH are shown in Figure 10a,b, respectively. As shown in Figure 10, when the added stray inductance *La* increases from 0 to 2 μH, *Tc* increases from 66 to 346 μs, and *Uarc-avg* increases from 11.7 to 15.8 V. Both *Tc* and *Uarc-avg* increase with the increase of *La*.

 **Figure 10.** Waveforms of vacuum arc commutation when the added stray inductance *La* is (**a**) 0 and (**b**) 2 μH.

When the added stray inductance *La* ranges from 0 to 4 μH, the relationship curve between *Tc* and *Uarc-avg* and *La* is shown in Figure 11. As shown in Figure 11, the relationship between *Tc* and *La* is approximately linear, which conforms to the law shown in Formula (9), and *Uarc-avg* also increases with the increase of *La*, but the magnitude of the increase becomes smaller and smaller.

**Figure 11.** Curve of *Tc* and *Uarc-avg* with different stray inductances.

### *4.2. Influence of the Final Commutation Current*

Under the condition that *Ra* is 2 <sup>m</sup>Ω, and *La* is 0 μH, we obtained the waveforms of vacuum arc commutation with different commutation currents *Ice*. The waveforms when the commutation current *Ice* is 0.28 and 2.68 kA are shown in Figure 12a,b, respectively. As shown in Figure 12, when the commutation current *Ice* increases from 0.28 to 2.68 kA, *Tc* increases from 13 to 195 μs, *Uarc-avg* increases from 9.2 to 12.9 V, *Use* increases from 2.7 to 11.8 V, and *Isi* increases from 0.02 to 0.48 kA. All of *Tc*, *Uarc-avg*, *Use*, and *Isi* increase with the increase of *Ice*.

**Figure 12.** Waveforms of vacuum arc commutation when the final commutation current *Ice* is (**a**) 0.28 and (**b**) 2.68 kA.

As shown in Figure 12, it is easy to know that changing *Ice* is achieved by changing *Ise*. When the *Ise* ranges from 3.0 to 3.16 kA, the relationship curve between *Uarc-avg*, *Use*, *Ice*, *Isi*, and *Ise* is shown in Figure 13a. As shown in Figure 13a, all of *Uarc-avg*, *Use*, *Ice*, and *Isi* increase with the increase of *Ise*, and according to Figure 5 and Formula (7), as shown in Formula (13), the linear expressions between *Use* and *Ise* and *Usi* and *Isi* can be obtained, respectively, and then we can ge<sup>t</sup> the calculation formula of *k* about *Uarc-avg*, *Use* and *Usi*:

$$\begin{cases} \mathcal{U}\_{\rm s\varepsilon} = \mathcal{U}\_{\rm s0} + \mathcal{R}\_{\rm s} I\_{\rm s\varepsilon} = 2.0 + 3I\_{\rm s\varepsilon} \\ \mathcal{U}\_{\rm si} = \mathcal{U}\_{\rm s0} + \mathcal{R}\_{\rm s} I\_{\rm si} = 2.0 + 3I\_{\rm si} \\ k = \frac{\mathcal{U}\_{\rm l\varepsilon\rm w\rm c\varepsilon} - \mathcal{U}\_{\rm si}}{\mathcal{R}\_{\rm l\varepsilon} I\_{\rm cr}} = \frac{\mathcal{U}\_{\rm l\varepsilon\rm w\rm c\varepsilon} - \mathcal{U}\_{\rm si}}{\mathcal{U}\_{\rm s\varepsilon} - \mathcal{U}\_{\rm si}} \end{cases} \tag{13}$$

**Figure 13.** (**a**) The relationship curve between *Uarc-avg*, *Use*, *Ice*, *Isi*, and *Ise*; (**b**) Curve of *Tc* and *k* with different final commutation currents; (**c**) The relationship curve between *Tc* and *k* in (**b**).

Therefore, according to Figure 13a and Formula (13), the *k* value corresponding to different *Ice* values can be calculated, and the relationship curve between *k* and *Tc* and *Ice* is shown in Figure 13b. As shown in Figure 13b, *k* decreases with the increase of *Ice*, and the rate of decrease becomes slower and slower; *Tc* increases with the increase of *Ice*, and the rate of increase becomes faster and faster. The relationship curve between *Tc* and *k* was plotted according to Figure 13b, as shown in Figure 13c. It can be seen from Figure 13c that *Tc* decreases with increasing *k*, and the rate of decrease becomes slower and slower; the change law shown in Figure 13c basically coincides with the change law shown in Formula (11) and Figure 6.

### *4.3. Influence of the On-State Resistance of the SS*

Under the condition that *La* is 0 μH, and *Ice* is approximately 1 and 2 kA, respectively, we obtained the waveforms of vacuum arc commutation with different on-state resistances. When the *Ice* is approximately 1 kA, the waveforms when the added on-state resistances *Ra* is 0 and 9 mΩ are shown in Figure 14a,b, respectively. Because when the added on-resistance is different, the value of *Isi* will also be different; so, to eliminate the impact of different *Isi*, as shown in Figure 14, the IGBT module is turned on after the vacuum arc is generated, and in this case, *Isi* = 0 and *Ice* = *Ise*. As shown in Figure 14, when the added on-state resistances *Ra* increases from 0 to 9 <sup>m</sup>Ω, *Tc* increases from 34 to 99 μs, *Uarc-avg* increases from 9.5 to 12.8 V, and *Use* increases from 3 to 12.1 V. All of *Tc*, *Uarc-avg*, and *Use* increase with the increase of *Ra*. Meanwhile, it can be seen in Figure 14 that when the IGBT module is turned on, the vacuum arc voltage drops.

**Figure 14.** Waveforms of vacuum arc commutation when the added on-state resistances *Ra* is (**a**) 0 and (**b**)9mΩ.

When *Ice* is 1 and 2 kA, respectively, the relationship between *Uarc-avg*, *Use*, and *Ra* is shown in Figure 15a. It can be seen from Figure 15a that whether *Ice* is 1 or 2 kA, both *Uarc-avg* and *Use* grow approximately linearly with *Ra*. As it is known from the previous section that *Us*0 = 2.0, and *Isi* = 0, we can easily ge<sup>t</sup> *Usi* = *Us*0 + *IsiRs* = 2.0. Therefore, according to Figure 15a and Formula (13), the *k* value corresponding to di fferent *Ra* values can be calculated, and the relationship between *k* and *Tc* and *Ra* is shown in Figure 15b. It can be seen from Figure 15b that whether *Ice* is 1 or 2 kA, *k* decreases with the increase of *Ra*, and the rate of decrease becomes slower and slower; *Tc* increases with the increase of *Ra*, and the rate of increase becomes faster and faster; the change law shown in Figure 15b basically coincides with the change law shown in Figure 7. Meanwhile, when *Ra* = 0, the corresponding *k*0 value is 8.2 when the *Ice* is 1 kA, and the corresponding *k*0 value is 4.3 when the *Ice* is 2 kA. The relationship curve between *Tc* and *k* was plotted according to Figure 15b, as shown in Figure 15c. It can be seen from Figure 15c that *Tc* decreases with increasing *k*, and the rate of decrease becomes slower and slower and even tends to be constant; the change law shown in Figure 15c basically coincides with the change law shown in Formula (12) and Figure 8.

**Figure 15.** (**a**) Curve of *Uarc-avg* and *Use* with di fferent on-state resistances; (**b**) Curve of *Tc* and *k* with di fferent on-state resistances; (**c**) The relationship curve between *Tc* and *k* in (**b**).
