# Research on Ultra-Fast Transient Overvoltage Characteristics of Electric Locomotive
## 4 Analysis and Discussion  
### Formation Mechanism of High-Amplitude and High-Steepness Operating Overvoltage  
Very fast transient overvoltage (VFTO) refers to the transient overvoltage phenomenon with a very short wavefront time (about 3-20 ns) caused by disconnector operation in the power system, whose amplitude can exceed 2.50 p.u. [13]. As shown in Figure 6, the detailed waveform of VFTO is similar to the operation overvoltage in Section 2, both of which are ultra-fast transient overvoltage in the power system. The formation mechanism of VFTO is equipment in GIS (Gas Insulated Switchgear) and works in a slightly inhomogeneous electric field. When the disconnector or main breaker is in operation, the electric field of the air gap changes accordingly. Once the gap breakdown condition is satisfied, equipment will undergo multiple pre-breakdowns and re-breakdowns in SF\({}_{6}\) gas, resulting in very fast transient overvoltage. The overvoltage  
Figure 5: The global graph and fractionated gain figure of the four operating overvoltages. (**a**) Pantograph lifting. (**b**) Main breaker closing. (**c**) Main breaker opening. (**d**) Pantograph dropping. Figure 6: Typical VFTO waveform caused by disconnector closing. transmits along the electric wires on both sides of breaker, thus affecting the internal equipment of GIS. The formation mechanism of operating overvoltage in electric locomotives is similar to VFTO. It is found that the overvoltage waveform is also equipped with the characteristics of high amplitude and high steepness. Because it can be found in the test results that the operating overvoltage has the same high-amplitude and high-steepness characteristics as VFTO, it should be regarded as the ultra-fast transient overvoltage of the high-voltage system of the electric locomotive and the electromagnetic transient process should be fully considered instead of only considering the arc between the pantograph and the catenary. (1) Arc theory  
The locomotive operating overvoltage is often accompanied by the arc phenomenon, and the corresponding formation condition is that the gap electric field is stronger than that of the air breakdown. The formation and development process of the arc is depicted in Figure 7. In the initial stage, the atoms in the gas are ionized by the electric field. As the field strength continues to increase, free electrons accelerate and collide continuously, resulting in more atoms ionizing and forming an electron avalanche. In this process, the energy is gradually accumulated, leading to the partial heating and expansion of the air gap and the formation of a plasma [14]. Finally, the arc is formed when the plasma region penetrates the pantograph-catenary poles. The expression of arc resistance \(R_{arc}\) is:  
\[R_{arc}=R_{0}e^{-1/T}+r \tag{1}\]  
It is illustrated that \(R_{arc}\) varies with time \(T\) (3 ns \(\leq T\leq\) 20 ns), where the arc resistance value is reduced from \(R_{0}\) (a few megaohms) to \(r\) (0.5 \(\Omega\)). The arc will extinguish after the arc current crosses zero, and there is no conductance between the contacts. Therefore, the voltage-recovery process and the dielectric strength-recovery process are individual in the arc gap. If the arc gap voltage recovery speed is larger than the dielectric strength recovery speed, re-breakdown will occur and the arc reignites. Therefore, the AC arc-reignition condition is the voltage-recovery speed and is larger than the dielectric strength-recovery speed after the first arc extinguishing. As shown in Figure 8, \(u_{3}\) represents the arc gap voltage, and the strength of the arc gap changes according to \(u_{2}\). Then, after point A, \(u_{3}>u_{2}\), the gap will be reignited due to the breakdown, and the voltage between the contacts will be converted to the arc voltage \(u_{4}\)[15]. Figure 7: Development process of pantograph–catenary arc. Formation Mechanism of Overvoltage induced by Arc  
Burning, extinguishing, and reignition of the arc changes the circuit structure and circuit parameters.