## 2 Transient Characteristics of DC Forced Interruption
### Voltage Transient Characteristics in Forced-Commutation Interruption  
The voltages in the current-commutation stage demonstrate two types of waveforms with different frequencies. Only the low-frequency vibrations are determined by inductance \(L_{1}\). There are two high-frequency oscillations. The first high frequency is influenced by the frequency-modulation circuit and the forced-commutation branch. When the parameters in the forced-commutation branch are fixed, \(dv/dt\) is determined by the \(R\) and \(C\) in the frequency-modulation circuit alone, in the current-commutation stage. The voltage of the VI in the current-commutation stage for different frequency-modulation circuit parameters is shown in Figure 3. It is suggested that the decreased value of \(C_{3}\) will lead to a rise in \(dv/dt\) and in the oscillation frequency. The change in \(R_{3}\) does not affect the slope of \(dv/dt\), but it affects the oscillation amplitude. When the circuit is not connected parallel to the frequency-modulation circuit, the transient recovery voltage is mainly influenced by the capacitance \(C\) of the forced-commutation branch and the main circuit current \(i_{0}\)[28]. \[dv/dt=i_{0}/C \tag{8}\] \begin{table}
\begin{tabular}{c c c c c c c} \hline  & **Main Circuit** & **Precharged** & & & & \(di/dt\) **(A/\(\mu\)s)** & \\  & **Current (A)** & **Voltage (V)** & & & **Formulation (7)** & **Simulation** & **Experiments** \\ \hline
1 & 1120 & 100 & 1.40 & 27.72 & 24.92 & 28.5 \\
2 & 1120 & 120 & 1.68 & 33.26 & 31.56 & — \\
3 & 1120 & 140 & 1.96 & 38.80 & 37.98 & — \\
4 & 1740 & 120 & 1.08 & 27.71 & 25.68 & — \\
5 & 1740 & 140 & 1.26 & 38.8 & 33.42 & 37.9 \\
6 & 1740 & 160 & 1.45 & 44.35 & 40.36 & — \\
7 & 1740 & 180 & 1.63 & 49.89 & 47.00 & — \\
8 & 2240 & 180 & 1.26 & 49.89 & 42.84 & 47.6 \\ \hline \end{tabular}
\end{table} 
Table 1: Comparisons of the \(di/dt\) obtained through Equation (7), simulation, and experiments. The frequency of the second high-frequency oscillation is influenced by the frequency-modulation circuit and the inductance \(L_{0}\) in the main circuit. The oscillation amplitude is determined by the breaking current \(I_{0}\), the residual voltage in \(C_{1}\), and the \(L_{1}\). By changing the parameters of the forced-commutation branch, the change in VI voltage can be obtained through simulations, as shown in Figure 4. By comparing the three simulation conditions and results, we can observe that, when the inductance of the commutation inductor is halved and the capacitance of the commutation capacitor is doubled, the commutation frequency remains unchanged, and the peak value of the VI voltage will be lower. With an increase in the commutation capacitance, the commencement of the voltage oscillations is delayed, but the three interruptions shown in Figure 4 end at the same time. This is due to the reduction in the precharged voltage of the commutation capacitor by the smaller inductance under the same \(k\). The increased capacitance leads to a delay in the start of oscillation, but dampens the oscillation amplitude and period. Furthermore, with a smaller commutation inductance, the amplitude and period of the VI voltage can be effectively suppressed in the two oscillation processes. Besides, when \(k\) is set to be larger, the voltage increases with a higher precharged voltage of \(C_{1}\). Figure 4: Voltage transient characteristics of VI for various forced-commutation parameters and \(k\) (\(L\) is the inductance of the commutating inductor \(L_{1}\), \(C\) is the capacitance of the commutating capacitor \(C_{1}\), and \(U\) is the precharged voltage of the commutating capacitor). Figure 3: Voltage of VI in the circuit-commutation stage under different frequency-modulation circuit parameters. From the above analysis, it can be inferred that the selection of the reverse peak-current coefficient \(k\) affects not only the \(di/dt\) in the current-commutation process, but also the VI voltage transient characteristics in interruption.