## 5 Operating Overvoltage Variation Law of Dropping Pantograph under Different Conditions  
### Influence of Pantograph Dropping Speed on Dropping Pantograph Operating Overvoltage  
Due to the elongation of the arc column in the process of pantograph dropping, the power injected into the arc and the arc voltage will increase [20]. With the gradual elongation of the pantograph arc, the arc column expands and the contact area between the arc and the air increases, which contributes to the dissipation of energy [21]. Especially when the pantograph and the catenary are separated at a fast speed, the expansion effect may be aggravated, which helps to accelerate the extinction of the arc. In order to study the influence of dropping speed on overvoltage, different conditions are simulated by changing the dropping speed in the model, and the results are shown in Table 2.  
It can be seen in Table 2 that the arc duration is generally a few microseconds. When the pantograph dropping speed is 0.30 m/s, the amplitude of overvoltage reaches its highest value of 298.20 kV, and the arc duration is the longest. When the pantograph dropping speed is 0.90 m/s, the overvoltage amplitude is the lowest (39.48 kV) and the operating overvoltage is almost unobservable in the system. This is due to the faster pantograph dropping speed compressing the space and time available for arc development, causing the arc energy to dissipate rapidly during the process. When the rate of energy dissipation exceeds the rate of energy accumulation, the temperature of the plasma in the arc decreases as the arc resistance increases. The capacitive discharge process is rapid, which induces a weak transient oscillation, and the overvoltage amplitude is relatively small. The law of the variation in the operating overvoltage of the dropping pantograph as dictated by pantograph dropping speed is shown in Figure 12, and it is evident that the amplitude of the operating overvoltage decreases with the increase in pantograph dropping speed.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Pantograph Dropping Speed (m/s)**} &
\begin{tabular}{c} **Operating Overvoltage of** \\ **Dropping Pantograph (kV)** \\ \end{tabular} & **Arc Duration (\(\upmu\)s)** \\ \hline
0.30 & 298.20 & 2.35 \\
0.40 & 201.39 & 1.96 \\
0.50 & 122.95 & 1.90 \\
0.60 & 94.12 & 2.34 \\
0.70 & 78.24 & 1.96 \\
0.80 & 78.85 & 2.22 \\
0.90 & 39.48 & 2.02 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Operating overvoltage of dropping pantograph at different pantograph dropping speeds.  
Figure 11: Comparison of simulated and test waveforms. (**a**) First time. (**b**) Second time. (**c**) Third time.  
Figure 13 presents the overvoltage waveforms for four different pantograph dropping speeds (0.30 m/s, 0.50 m/s, 0.70 m/s, 0.90 m/s) given by simulations. The overvoltage at the pantograph dropping speed of 0.30 m/s takes a long time to re-attain the stable state, whereas the overvoltage at a high pantograph dropping speed of 0.90 m/s can rapidly re-attain its steady-state value. This is because when the pantograph is dropping at a low speed, the energy stored in the circuit will oscillate for a long time in the RC components, such as the parasitic capacitance of the cable or the magnetizing inrush current of the voltage transformer, resulting in a large amplitude. On the contrary, the oscillation time is short and the amplitude is small when the pantograph is dropping at high speed.