## 1 Introduction  
When the locomotive pantograph is dropping, the interruption of the pantograph-catenary contact causes a sudden change in circuit, triggering electromagnetic oscillation. During this process, an ultra-fast transient overvoltage with an amplitude and steepness far higher than normal levels (AC 27.5 kV 50 Hz) is generated, which can be detected on the high-voltage equipment on the roof of the electric locomotive. This type of overvoltage is similar to the VFTO, which shows high amplitude and high steepness. This extreme electromagnetic phenomenon poses a threat to the electrical system of electric locomotives, resulting in frequent overvoltage shocks, insulation breakdown in high-voltage equipment, and train outages [1]. Accurately simulating ultra-fast transient operating overvoltage is crucial for revealing its generation mechanisms and evolution law. In order to replicate the overvoltage wave by simulation, domestic and foreign scholars have proposed a variety of overvoltage simulation methods based on the arc model. [PERSON] utilized a [PERSON] arc model combined with the Cassie and Mayr model to study the pantograph dropping of a CR400 BF high-speed train under different operating speeds,revealing the arc voltage peak was up to 30.00 kV at a speed of 350 km/h [2]. [PERSON] improved the dissipative power expression of the [PERSON] arc model and integrated the optimized model with a traction substation-catenary-train model to simulate the dropping pantograph overvoltage of the CR400 BF train. The results show the amplitude of overvoltage around 70.00 kV [3]. [PERSON] combined the [PERSON] arc model with an equivalent circuit model of the CRH2 train and a simulated operating overvoltage amplitude ranging from 60.00 to 75.00 kV, where the oscillation frequency of the voltage was around 60 kHz [4]. [PERSON] proposed a pantograph arc modeling method by combining the [PERSON] and Cassie arc models, which achieved state switching through boundary length determination. In this method, the transient processes of arc extinction and reignition were considered, and it was observed that the voltage peak was 72.00 kV on the catenary at the moment of arc extinction during pantograph dropping [5]. [PERSON] et al. studied the influence of electromagnetic voltage transformer iron core resonance on the dropping of operating overvoltage in the locomotive equivalent circuit, using the Mayr arc model. The results indicate that the overvoltage amplitude ranged from 39.00 to 77.00 kV [6]. [PERSON] et al. simulated arc reignition by analyzing the multiple transient processes of the circuit. The results show that when the phase angle of the catenary voltage was 90\({}^{\circ}\), the maximum catenary overvoltage was 66.45 kV [7]. [PERSON] et al. studied the characteristics and generation mechanism of very fast transient overvoltage caused by disconnector operation. The simulation results show that the maximum amplitude of VFTO at the circuit breaker reached 1.45 p.u. [8]. [PERSON] et al. established a monitoring system: by paralleling a voltage transformer next to the arrester and transmitting the low-voltage side signal to the data acquisition card through a coaxial cable, the roof overvoltage waveform data during train operation were collected. The maximum overvoltage amplitude of a CRH2A train during pantograph dropping was 67.10 kV; the maximum peak value of harmonic overvoltage on the CR400 BF train was 52.80 kV [9]. At present, the arc model considering a locomotive equivalent circuit is primarily adopted in simulations performed to research operational overvoltage, and the simulation results are generally in the range of 50.00-77.00 kV. GB/T 11032 standard [10] stipulates that the power-frequency flashover voltage of the arrester is generally 2.5 to 4.0 times the rated voltage (100 kV). The IEC60850 standard [11] points out that when the overvoltage exceeds three times the rated voltage (>75.00 kV), the risk of high-voltage equipment (especially high-voltage circuit breakers) massively increases.