**4. Discussion**

### *4.1. Positive E*ff*ects of the Double-Break Vacuum Circuit Breaker*

A vacuum interrupter in the double-break tests (*Test* 3) may have di fferent prestrike characteristics in terms of prestrike gaps and scatters in prestrike gaps compared with that in the single-break tests (*Test* 1 and *Test* 2) due to the voltage-sharing-e ffect, the asynchronous property of the mechanical actuators, and the inhomogeneity of the inherent prestrike characteristics of VIs in a double-break VCB.

From Table 3, it can be noted that the scatters in the prestrike gaps of VI\_A (resp., VI\_B) in the double-break tests, i.e., in *Test* 3 are smaller than that of VI\_A (VI\_B) in the single-break tests, i.e., in *Test* 1 (with respect to *Test* 2). Vacuum interrupters with less scatters in the prestrike gaps would be of grea<sup>t</sup> importance in order to improve the accuracy of the phase-controlled making technique. Therefore, with the same VIs, a double-break VCB would be better suitable for the phase-controlled switching.

The double-break VCB takes full advantage of the good dielectric insulation ability of the vacuum gap. A double-break VCB which has two gaps in series can withstand higher voltage compared to the single-break VCB in the same total break length [27]. The relationship between breakdown voltage and electrodes gap of the single-break VCB has two di fferent expressions. When the electrode gap is less than 5 mm, the breakdown voltage and electrodes gap length is a linear equation, as shown in:

$$
\mathcal{U}\_t = k \cdot d \tag{5}
$$

When the electrode gap is greater than 5 mm, Breakdown voltage and electrodes gap length is a non-linear equation when the electrodes' distance is greater than 5 mm, as shown in:

$$
\mathcal{U}\_t = k \cdot d^m \tag{6}
$$

The value of *m* is between 0.4 to 0.7, *d* stands for the electrodes' gap length, *k* is a constant number.

The relationship between breakdown voltage and electrodes' gap length of the double-break VCB is shown in (7). It is based on the assumption that the voltage distribution value of two interrupters is equal.

$$dL\_t = 2k \cdot d^m \tag{7}$$

However, in the double-break VCB which does not have a grading capacitor in parallel with each VI, the shared voltages of each VI are not equal because of the stray capacitance. It is impossible to realize double withstand voltage as (7) shows [28]. In order to investigate the influence of the voltage-sharing e ffect in double-break VCBs on the prestrike characteristics, the relative variations in the prestrike gaps of each vacuum interrupter under di fferent applied voltage levels are calculated by:

$$\delta(d) = \frac{d^{(DB)} - d^{(SB)}}{d^{(SB)}} \times 100\% \tag{8}$$

where *d*(*DB*) is the prestrike gap of vacuum interrupter VI\_A (resp., VI\_B) obtained from the double-break test, i.e., *Test* 3 and *d*(*SB*) is the prestrike gap from the single-break test, i.e., *Test* 1 (resp., *Test* 2).

Table 4 shows the values of relative variations δ in *d*10, *d*50 and *d*90. The vacuum gaps in VI\_A and VI\_B in the double-break test can be considered as two capacitors in series [29] and each gap shared part of the total applied voltage *U*s. Therefore, the voltage applied to each gap was smaller than *U*s, leading to a smaller prestrike gap. The smaller the prestrike gap was, the shorter the prestrike arcing time was. For a given applied voltage, a double-break VCB has a better performance than a single-break one in terms of reducing the prestrike gaps in the vacuum interrupter, which is termed as the positive e ffects of double-break VCBs.


**Table 4.** Relative variations in the 10%, 50% and 90% prestrike gaps.

### *4.2. Negative E*ff*ects of the Double-Break Vacuum Circuit Breaker*

Due to the voltage-sharing e ffect, the actual voltage applied to each vacuum interrupter VI\_A or VI\_B in the double-break tests was smaller than that in the single-break tests. In order to investigate the prestrike characteristics of vacuum interrupters in double-break tests by comparison with that in single-break tests under the same applied voltage, the influence of the voltage-sharing e ffect has to be eliminated.

In an ideal case, if both interrupters VI\_A and VI\_B share the same percentile of the total applied voltage *U*s, i.e., both share 50% out of *U*s, then the sharing voltage of VI\_A (resp., VI\_B) in *Test* 3 would be 10 kV or 20 kV, i.e., the same voltage applied to VI\_A (resp., VI\_B) in *Test* 1 (resp., *Test* 2), when the applied voltage to the double-break *U*s in *Test* 3 is 20 kV or 40 kV. Figure 10 shows the 50% prestrike gap *d*50 of VI\_A and VI\_B in the single-break tests compared with that in the double-break tests where the value of applied voltage *U*s in *Test* 3 is twice as large as that in single-break tests (*Test* 1 and *Test* 2).

(**a**) **Figure 10.** *Cont.*

**Figure 10.** The negative effects of double-break vacuum circuit breakers (VCBs) on the prestrike gaps of vacuum interrupters. (**a**) The single-break VCB under 10 kV compared with the double-break under 20kV. (**b**) The single-break VCB under 20 kV compared with the double-break under 40kV.

However, the voltage-sharing ratio of VI\_A and VI\_B in double-break VCBs was not the same due to the stray capacitance to ground. In fact, from the previous studies the voltage-sharing ratio of the vacuum interrupter installed on the high voltage side (i.e., VI\_A in our case) is larger than that on the low voltage side (VI\_B) [30]. Note that a larger applied voltage leads to a higher prestrike gap. Therefore, the prestrike gaps of VI\_A in *Test* 3 should be larger than that in *Test* 1, while the prestrike gaps of VI\_B in *Test* 3 should be smaller than that in *Test* 2 when *U*s in *Test* 3 is twice as large as that in *Test* 1 and *Test* 2. This can be verified for the vacuum interrupter VI\_A from Figure 10, but not for VI\_B. As can be observed from Figure 10, the prestrike gap of VI\_B in *Test* 3 is larger. To be precise, the voltage applied to VI\_B in *Test* 3 with *U*s = 20 kV (resp., 40 kV) is lower than 10 kV (resp., 20 kV) due to the voltage-sharing effect while the 50% prestrike gaps *d*50 is larger than that in *Test* 2 with an applied voltage of 10 kV (with respect to 20 kV) instead. That is to say, the double-break VCB does not make fully advantage of the dielectric strength of the vacuum gap on the low voltage side, which is termed as the negative effects of double-break VCBs.

The negative effects of double-break VCBs may be caused by the asynchronous property of the mechanical actuators, the inhomogeneity of the inherent prestrike characteristics and the unequal voltage-sharing ratio of VIs in a double-break VCB.

The double-break VCB is closed or interrupted by the mechanical actuators. In the ideal case, the two VIs of the double-break VCB moves at the same velocity and the operating characteristics are same too. Due to the inevitable performance differences between the mechanism's actuators of the double-break VCB, and their tolerance to various environmental changes not being the same, the effect caused by the asynchronous property of the mechanical actuators on the double-break VCB must not be underestimated. In the breaking process, when the operating time interval of two breaks is 2 ms, the distance difference between two vacuum gaps is significant. The arcing time of the two VIs is different, which makes the sharing voltage of each VI is unequal in the breaking process. In the most serious situation, reignition will occur [31]. On the other hand, in the current-making process, considering a double-break VCB with two vacuum interrupters VI\_A and VI\_B in series, we denote by *<sup>d</sup>*<sup>∗</sup>50(VI\_A) and *<sup>d</sup>*<sup>∗</sup>50(VI\_B) the inherent 50% prestrike gaps of VI\_A and VI\_B, which is the 50% prestrike gap when tested separately in the single-break tests. Due to the asynchronous property of the mechanical actuators in the double-break VCB, one of the moving contacts, for example the moving contact in VI\_A, moves faster than the other, as shown in Figure 11a. Let both VI\_A and VI\_B share half of the applied voltage (*Us*/2) and have a same inherent 50% prestrike gap, i.e., *<sup>d</sup>*<sup>∗</sup>50(VI\_A) = *<sup>d</sup>*<sup>∗</sup>50(VI\_B). During the closing operation, the vacuum gap length between the contacts in VI\_A is smaller than that in VI\_B (*lA* < *lB*). Therefore, it is very possible for VI\_A to breakdown earlier than VI\_B. As soon as the prestrike occurs in VI\_A, the total voltage *U*s would be applied to the vacuum gap in VI\_B. Then the prestrike occurs in VI\_B. In this case, the measured prestrike gap of VI\_B is the same as *l*A, which is larger than *<sup>d</sup>*<sup>∗</sup>50(VI\_B) the inherent 50% prestrike gap of VI\_B.

Moreover, let both VI\_A and VI\_B be synchronized perfectly and share half of the applied voltage (*U*s/2), as shown in Figure 11b. The inherent 50% prestrike gap of VI\_A is larger than that of VI\_B, i.e., *<sup>d</sup>*<sup>∗</sup>50(VI\_A) > *<sup>d</sup>*<sup>∗</sup>50(VI\_B). Then, it is very possible that the prestrike occurs in VI\_A earlier that in VI\_B, leading to a higher prestrike gap of VI\_B (that is *l*B) than *<sup>d</sup>*<sup>∗</sup>50(VI\_B).

Similar effects can also be found in the case when the voltage-sharing ratios of VI\_A and VI\_B are not equal to each other. As shown in Figure 11c, both VI\_A and VI\_B are synchronized perfectly and have the same inherent 50% prestrike gap, since VI\_A on the high voltage side shares voltage higher than *U*s/2. The interrupter VI\_A is highly possible to breakdown when the vacuum gap length is larger than the inherent 50% prestrike gap, i.e., *l*A > *<sup>d</sup>*<sup>∗</sup>50(VI\_A). Noting VI\_A and VI\_B are perfectly synchronized (*l*A = *l*B), the measured 50% prestrike gap of VI\_B would be larger than its inherent one.

The mechanical actuators of the double-break VCB used in this work are not perfectly synchronized, which is practically impossible. The mechanical actuator installed on the low-voltage side moves slower than that on the high voltage side with a time delay of 0.1 ms. Moreover, from Table 3, the inherent 50% prestrike gap of VI\_A is always larger than that of VI\_B under the tested applied voltages. Together with the effect of the unequal voltage-sharing ratio, the negative effects of double-break VCBs are observed as shown in Figure 10.

**Figure 11.** *Cont.*

**Figure 11.** Schematic diagram of the negative effects of the double-break VCBs in terms of the asynchronous property of the mechanical actuators (**a**), the inhomogeneity of the inherent prestrike gaps (**b**), and the unequal voltage-sharing ratio (**c**).

The prestriking phenomena are irrelevant to the initial contact gaps in the double break and the single break in this work. As for the experimental setup, the double-break VCB consisted of two VIs. When carrying out the single-break tests, only one vacuum interrupter (VI\_A or VI\_B) was connected into the experimental circuit while the other one was shorted to ground by the busbar. The initial gaps of both VIs were 10 mm. Therefore, the initial gap of the single-break VCBs was 10 mm, and the initial gap of the double-break VCB was 20 mm (two 10 mm gaps in series). There are mainly two theories about the breakdown in the vacuum. One is that field emission induces breakdown, the other is that particles induce vacuum breakdown [6]. If the vacuum gap is less than 2 mm, the field emission plays the dominant role in the breakdown process [9]. In these tests, all the prestrike gaps were less than 2 mm. The prestrike was field-emission induced. The prestrike arc current during each making operation was only tens to hundreds of amperes, the erosion effect on the contact surfaces can be neglected. During the making process of the VCB, there is a threshold electric field strength that determined whether breakdown occurs or not [32]. When the electric field strength exceeds the threshold electric field strength between the contacts, the prestrike arc occurs and the gap between the contacts at that instant is called prestrike gap, which is independent of the initial gap of the VCB [33]. However, if there is an inrush current in the prestrike process that causes erosion on contacts or the prestrike gaps are larger than 2 mm, the initial gap of the single-break VCB and the double-break VCB must be kept the same in order to compare the characteristics of prestrike gaps.
