# Research on Ultra-Fast Transient Overvoltage Characteristics of Electric Locomotive
## 4 Analysis and Discussion
### Formation Mechanism of High-Amplitude and High-Steepness Operating Overvoltage
The equivalent variable RC parallel circuit between the pantograph and the catenary is adopted to simulate the high-frequency electromagnetic oscillation at closing, which may induce the overvoltage over \(3U_{m}\). Figure 9(b) is shown as the waveform diagram of a pantograph lifting test. It can be clearly seen that the overvoltage generated at the moment of pantograph lifting is the largest with the amplitude exceeding 10 times the power frequency voltage. This phenomenon can be explained by the equivalent circuit method on the left side of Figure 9(a). Figure 10: Equivalent circuit and actual condition. Formation Mechanism of Ultra-fast Transient Overvoltage Caused by Pantograph Dropping and Main Breaker Opening  
The process of pantograph dropping and main breaker opening involves a contact-separation operation, which can be classified as an opening operation. When the pantograph is not completely separated from the catenary, the distance between them is short, so the electric field strength is large, which can easily lead to gap breakdown. The equivalent circuit of pantograph dropping is illustrated in Figure 11a. Figure 11b is a simplified circuit without considerations of catenary resistance and transformer inductance. It is assumed that the amplitude of the catenary voltage is \(U_{m}\). In the equivalent circuit shown in Figure 11, the A side represents the catenary and the B side represents the pantograph. The catenary is connected to the 27.5 kV traction power supply system, and the power supply potential is set as:  
\[e(t)=U_{m}\cos\omega t \tag{7}\]  
Then the current is:  
\[i(t)=\frac{U_{m}}{X_{c}-X_{L}}\cos(\omega t+90^{0}) \tag{8}\]  
In the formula, \(X_{c}\) and \(X_{L}\) are \(1/2\pi C_{0}\) and \(2\pi\)f\(L_{0}\) respectively. For the no-load line, the current through the breaker is the capacitive current of the circuit, so the current is ahead of the voltage. Ignoring the influence of line capacitance effect, the line voltage is equal to the power supply voltage before the switch 'S' is off. The first arc-extinguishing process  
Before pantograph dropping, the capacitor voltage is approximated to the power supply voltage due to \(wL_{0}<<1/(wC_{0})\), and the current is ahead of the voltage by \(90^{\circ}\). Supposing the power supply voltage \(u(t)=U_{m}\)cos\(wt\), the power supply current \(i(t)=-U_{m}wC_{0}\)sin\(wt\). In Figure 11b, point A represents the catenary, while point B represents the pantograph. If the pantograph drops at \(t_{1}\), the voltage of point B is kept at \(+U_{m}\) due to the capacitive elements in the circuit. The voltage at point A is consistent with the power supply voltage, which changes according to the cosine law. The recovery voltage \(u_{AB}\) between the contacts of the breaker is [18]:  
\[u_{AB}=e(t)-(-U_{m})=U_{m}(1+\cos\omega t) \tag{9}\]  
When \(t=t_{1}\), \(u_{AB}=0\), then the recovery voltage \(u_{AB}\) becomes higher and higher. After \(t_{1}\), if the deionization effect between the main breaker contact is strong, the contact between the insulating strength recovery exceeds the recovery voltage rise speed, the arc will be extinguished, and the circuit will be truly disconnected [19]. At this time, no matter the pantograph or the catenary side, there will be no overvoltage. On the contrary, arc reignition may occur between pantograph and catenary. The first arc-reignition process  
Considering the most serious case, it is assumed that the arc is reignited when the recovery voltage \(u_{AB}\) reaches the maximum, at time \(t_{2}\) in Figure 12a. Then \(e(t)=U_{m}\), \(u_{AB}=2U_{m}\). At the moment of arc reignition, the catenary voltage Um is suddenly added to  
Figure 11: Pantograph dropping equivalent circuit. **(a)** Equivalent circuit. **(b)** Simplified circuit. the oscillation loop composed of the line inductance \(L_{0}\) and the capacitance \(C_{0}\) with the initial value of \(-U_{m}\), as shown in Figure 11b.