Regulation of the pantograph-catenary arc by an alternating transverse magnetic field

1.   Introduction

The sliding electrical contact of the pantograph-catenary system has been recognized as the most reliable method of energy transfer due to its exceptional electrical conductivity, high transmission power and superior transmission quality [1–4]. However, with the rapid advancement of high-speed trains, the operating speeds are increasing [5], and the operational environment is becoming more complex. This results in frequent separation between the pantograph and the contact line, generating severe drifting of the arc. This not only causes extensive ablation damage to the pantograph carbon slide, but also damages the insulation system of the train, seriously impacting train safety [6, 7]. Previous research has focused on the effects of various environmental factors on the pantograph-catenary arc. For instance, during high-speed operation, the arc root exhibits three motion modes: single arc root, alternating single and double arc roots, and multiple arc roots, leading to complex and disturbed arc motion [1]. Furthermore, the arc burning time is extended under low-air-pressure environment, which causes the arc to exhibit an increased tendency to drift [8–10]. Therefore, to maintain arc stability in complex environments and alleviate overvoltage damage to the train caused by arc a regulation method is required to decrease arc drifting.

Plasma regulation involves magnetic fields [11–13], airflow [14, 15] and ultrasound [16, 17]. Among these, magnetic field regulation is technically mature and adaptable, making it particularly suitable for ensuring arc stability. It is widely employed in vacuum interrupters [18, 19] and arc welding [20–22]. The arc of a vacuum interrupter is usually extinguished or completely rotated by a magnetic field in a vacuum environment, to minimize damage to equipment. Dullni et al [23] and Liu et al [24] used radial magnetic field (RMF) and transverse magnetic field (TMF) to drive the arc onto the contact to extinguish the arc. Liao et al investigated the regulation mechanism of bias magnetic field (BMF) on motion characteristics of vacuum arc [25]. Subsequently, the welding arc regulates the size, profile and intensity of the cross-section of the arc root mainly by magnetic field. For instance, Wang et al explored the mechanism of motion behavior of a welding arc under a rotating magnetic field [26]. Luo et al [27], Wu et al [28] and Wang et al [29] used high-frequency longitudinal magnetic field (LMF) to regulate the arc and found that it becomes more concentrated and generates a greater amount of heat. Nomura et al found that regulating arc with a cusp-type magnetic field results in an elliptical distribution of arc cross-section [30]. Yue et al found that the use of TMF in laser-MIG hybrid welding can increase arc stability and compress the weld area by up to 50% [31]. Wang et al [32] and Chen et al [33] found that arc temperature was more evenly distributed using a composite magnetic field. However, in the pantograph-catenary system, the problem of arc column drift poses a potential threat to the train. Moreover, high-speed airflow increases the likelihood of pantograph-catenary arc drift during train operation. Therefore, to suppress the drift of the pantograph-catenary arc, investigating the mechanism of magnetic field regulation of the pantograph-catenary arc is essential.

In this study, an experimental platform for pantograph-catenary arc with an externally applied AC transverse magnetic field (ATMF) was constructed, and characterization of the arc under ATMF and regulation of magnetic field for pantograph-catenary arc with airflow environment were investigated, when changes in morphological characteristics of arc and voltage waveforms were recorded.

2.   Experimental platform and test method

To investigate the regulation of pantograph-catenary arc under ATMF, an experimental platform capable of precisely manipulating the applied ATMF has been constructed in this study. The electrical schematic diagram and partial physical diagrams of the equipment are shown in figures 1(a) and (b), respectively. The experimental platform consists of an arcing device, an ATMF generator, an airflow generator device and a series of measurement devices. The arcing device is supplied by a DC constant current power source with output range of 0–1500 V and 0–150 A. The electrodes are constructed of copper and copper-impregnated carbon slide, and the latter depends on a precision elevator to control offline speed as well as distance. The signal generator produces a signal, which is amplified by a power amplifier and then used to drive the Helmholtz coil to create a stable ATMF. The airflow loading device employs a stepless speed regulation blower to generate airflow ranging from 0 to 20 m/s. The measurement equipment consists of an oscilloscope (Tektronix MDO3024), a high-speed camera (FASTCAM Nova S6) and a spectrometer (ANDOR Mechelle 5000).

Figure  1.  Experimental platform of arcing. (a) Electrical schematic diagram and (b) pictures of partial experimental equipment.

DownLoad: Full-Size Img PowerPoint

In this experiment, the power source supplied a fixed DC current of 10 A at 200 V. Before starting the experiment, the air density measurement instrument was employed to monitor and ensure the consistency of air density throughout the testing process, with a temperature of 25 °C and a humidity of 35%, and the copper electrode and copper-impregnated carbon slide were in stable contact. The copper-impregnated carbon slide was then separated downwards by a precision elevator to initiate an arc, with the separation speed and distance set at 8 cm/s and 3 cm, respectively. Once the arc stabilized, an ATMF with a magnetic induction strength of 10 Gs was applied to confine the arc. Subsequently, the airflow loading device induced transverse airflow. Voltage and current data were captured using an oscilloscope at a sampling frequency of 10 kHz for 1 s. High-speed photography at 6400 fps was employed to capture arc morphology, while spectral information of the arc was obtained using a spectrometer.

3.   Characterization of arc under ATMF

To investigate the characteristics of pantograph-catenary arc under different frequencies of ATMF, arc discharge experiments were performed across frequencies ranging from 0 to 1000 Hz. Specifically, the four typical frequencies, 0 Hz, 5 Hz, 10 Hz and 50 Hz, are shown in figure 2.

Figure  2.  Motion characteristics of arc under ATMF with different frequencies of (a) 0 Hz, (b) 5 Hz, (c) 10 Hz and (d) 50 Hz.

DownLoad: Full-Size Img PowerPoint

From figure 2(a), it is shown that the arc is in the original position at time t_a1 and the arc voltage is 78.1 V. After applying ATMF with a frequency of 0 Hz and magnetic induction intensity of 10 Gs (i.e. DC magnetic field), the magnetic induction intensity B_ATMF in position x can be given as [34]:

where ${\mu _0}$ represents the vacuum permeability, N₀ is the number of coil turns, I_ATMF is the excitation current and R is the effective radius of the coil.

The magnetic induction intensity B_ATMF is directly proportional to the excitation current I_ATMF. Consequently, the waveform of the excitation current is utilized to map the waveform of the magnetic field. The arc is continuously driven by Lorentz force F_L to the right, as shown in figure 3(a), in which F_L can be expressed as follows:

Figure  3.  Schematic diagram of the arc force.

DownLoad: Full-Size Img PowerPoint

where I_A is the arc current vector and L is the arc length.

At t_a2 = 167.9 ms, the arc extends to form a complete semicircle. This phenomenon occurs because the force F_L acting on the arc is directed to the left, as illustrated in figure 3(b). Arc has an overall tendency to drift upwards at moment t_a3 = 214.9 ms since the arc is continuously influenced by the upward thermal buoyancy force F_T due to its particularly large thermal volume and low density in the air medium [35]. The thermal buoyancy force can be expressed as:

where ${\rho _0}$ is the ambient air density, $\rho$ is the density of the arc, g is the acceleration of gravity and R is the radius of the arc.

Ultimately, at t_a4 = 264.7 ms the arc voltage reaches 349.8 V, and the arc can no longer sustain stable burning under the effects of F_L, leading to its extinguishment. As depicted in figure 2(b), an arc is initially positioned at t_b1 = 0 ms. Upon application of a 5 Hz ATMF, the arc is driven leftwards by the reverse Lorentz force $F'_{\mathrm{L}}$. The arc continuously oscillates to the left, but $F'_{\mathrm{L}}$ gradually decreases as magnetic field excitation current diminishes, eventually reaching zero and reversing to become F_L at t_b2 = 56.4 ms, and the arc voltage increases to 94.9 V. Subsequently, the arc is driven back to its initial position by the force of F_L at t_b3 = 102.4 ms, where the voltage drops to 80.5 V, as F_L reaches its maximum and then begins to decrease. The arc then continuously oscillates towards the right, stopping at t_b4 = 161.7 ms, at which point the voltage is 97.9 V. Following this, F_L reverses, driving the arc back to its initial position. This sequence represents one complete period of ATMF. Arc motion characteristics at an ATMF frequency of 10 Hz are shown in figure 2(c). The motion of the arc is similar to that at 5 Hz. The arc is in the initial position at t_c1 = 0 ms and t_c3 = 48.9 ms, with minimum voltage. Meanwhile, the arc oscillates to the farthest point at t_c2 = 27.5 ms and t_c4 = 73.6 ms, where the voltage is maximum. The ATMF frequency of 50 Hz is shown in figure 2(d). The lowest arc voltage is 72.7 V at t_d1 = 0 ms, which then increases until it reaches 76.8 V at t_d2 = 30.4 ms. Subsequently, at t_d3 = 75.2 ms and t_d4 = 126.7 ms, the arc voltage becomes 71.6 V and 78.8 V, respectively.

It can be seen that at 0 Hz the ATMF as a DC magnetic field exerts a magnetic blowing effect, which extinguishes the arc. In addition, the arc motion characteristics are similar at 5 Hz and 10 Hz. The arc oscillates with the variation of ATMF, causing the arc voltage to fluctuate twice within one ATMF period, due to the arc oscillating towards the left and right sides, after which it reaches its maximum voltage value. Moreover, it can be clearly seen that the fluctuation of arc voltage and width of arc column transverse drift at 10 Hz are less than those at 5 Hz. This indicates that as the frequency increases, the arc voltage and width of the arc column transverse drift decreases. In other words, the arc becomes more stable at higher frequency. However, the arc voltage does not fluctuate with variation of ATMF when the frequency is 50 Hz. This phenomenon can be attributed to the sufficiently high ATMF frequency, which causes the arc to oscillate within a tiny, confined space smaller than the dimension of the arc, thus maintaining stability. The voltage fluctuations occur due to the arc being influenced by its electromagnetic force, analogous to the contraction and expansion of breathing, resulting in the voltage constantly rising and falling.

Figure 4 shows the arc fluctuation magnitude V_F and fluctuation rate δ under ATMF from 0 to 1000 Hz, where δ can be expressed as $\delta = \dfrac{{{V_{\text{F}}}}}{{{V_{\text{I}}}}}$ and V_I is the arc initial voltage. When the ATMF frequency is lower than 4 Hz, the voltage fluctuation is approximately 210 V, the arc length is about 12 cm and the arc column transverse drift width is about 3 cm, as can be seen in figure 5. The details of arc column transverse drift width and arc length under ATMF from 0 to 1000 Hz are shown in figure 5. The reason for this behavior is that at very low frequency, the arc is subjected to the unidirectional Lorentz force similar to a DC magnetic field for an extended period, causing the arc to continuously move towards one side until it can no longer maintain stable combustion, and ultimately the arc extinguishes. At the frequency of 5–10 Hz, the arc can burn stably and be effectively influenced by ATMF, enabling it to oscillate regularly from side to side. Specifically, at a frequency of 5 Hz, the average voltage fluctuation observed is 8.06 V and the arc fluctuation rate δ is only 9.48%. The arc length and arc width are 2.36 cm and 5.84 cm, respectively. This stability is attributed to ATMF reversing before the arc oscillates to the extinguishing threshold, thereby sustaining burning. In addition, the amplitude of oscillations decreases as the frequency increases because the magnetic field direction alternates faster, causing the confinement space to gradually decrease. This ensures that the arc can be effectively influenced to oscillate regularly. When the frequency is greater than 10 Hz, it can be observed that arc voltage fluctuation, arc length and arc column transverse drift width remain essentially unchanged. The voltage fluctuation is maintained at approximately 3 V with 3.5% of δ, which has resulted from the electromagnetic force of the arc itself, and the morphological parameters of the arc are nearly identical to those observed in the absence of a magnetic field. This phenomenon occurs because relatively high-frequency ATMF creates a confined space, forcing the arc to remain within that space.

Figure  4.  Arc voltage fluctuation magnitude V_F and fluctuation rate δ under ATMF with different frequencies.

DownLoad: Full-Size Img PowerPoint

Figure  5.  Arc transverse drift width and arc length under ATMF with different frequencies.

DownLoad: Full-Size Img PowerPoint

To investigate the effect of different ATMF frequencies on the internal temperature of the arc, the emission spectrum of the arc was collected using a spectrometer. Due to the relatively large width of arc column transverse drift at frequencies below 10 Hz, which makes accurate collection difficult, the emission spectrum was collected for frequencies above 10 Hz. The emission spectra for conditions of no magnetic field and ATMF frequencies of 10 Hz and 100 Hz are shown in figure 6(a). The signal-to-noise ratio of the Cu atomic peak spectrum between 500 nm and 600 nm is significant. Therefore, five Cu I atomic peaks were used to calculate the arc temperature using the Boltzmann plot method [36], calculated as:

Figure  6.  Arc spectrum analysis under ATMF of different frequencies. (a) Spectra and (b) temperature.

DownLoad: Full-Size Img PowerPoint

where $I$ is the intensity of the atomic peak spectrum, λ is the wavelength of the atomic spectrum in air, g is the upper-level statistical weight, A is the transition probability, T is the plasma temperature, E_exc is high-energy-state excitation energy, h is the Planck constant 6.63×10⁻³⁴ J·s, c is the light velocity, n is the neutral particle number density of plasma, and Z is the atomic partition function.

Specifically, the calculation involves plotting E_exc on the horizontal axis and $\ln \dfrac{{I\lambda }}{{gA}}$ on the vertical axis. The wavelengths 510.55 nm, 515.32 nm, 521.82 nm, 570.024 nm and 578.21 nm of the Cu I atomic spectra were used. These data points were fitted to a straight line, and the slope of this line was multiplied by −5040 to obtain the arc temperature, as shown in the inset of figure 6(b). From calculations in figure 6(b), the arc temperature is 4625 K in the absence of a magnetic field. When ATMF is applied, the arc temperature increases, reaching 4743 K at 10 Hz and 4976 K at 1000 Hz. It can be observed that the arc temperature rises under the influence of ATMF, and this temperature increase continues with rising frequency, although the temperature gradient decreases gradually. This phenomenon is attributed to the formation of a constrained space by ATMF, which limits the movement of arc plasma. This restriction leads to more frequent plasma collisions within a narrowly confined space, thereby increasing the temperature. As the frequency increases, the constrained space becomes progressively smaller until it reaches a critical value.

Figure 7 shows the characteristics of arc under ATMF with different current excitation waveforms. The data indicate that the arc fluctuates most violently under a rectangular magnetic field, with a voltage fluctuation of 4.07 V and a fluctuation rate of 5.16%. This is followed by the sinusoidal magnetic field. In contrast, the triangular magnetic field exhibits the least fluctuation, with a voltage fluctuation of 3.04 V and a fluctuation rate of only 3.81%. Further temperature measurements reveal that the highest arc temperature under the triangular magnetic field is 4981 K, whereas the lowest arc temperature under a rectangular magnetic field is 4609 K. Thus, it can be concluded that arc temperature is the highest under a triangular magnetic field, resulting in the highest energy density and plasma density. Consequently, the plasma is more centralized, leading to the lowest voltage fluctuation and more stabilized arc.

Figure  7.  Characteristics of arc under ATMF with different current excitation waveforms. (a) Sinusoidal, (b) triangular and (c) rectangular.

DownLoad: Full-Size Img PowerPoint

4.   Motion characteristics of arc under ATMF regulation for airflow environment

The regulation of arc by ATMF under a transverse airflow of 5 m/s is shown in figure 8. Initially, the case without ATMF regulation is depicted in figure 8(a). At t_a1 = 0 ms, the arc is in its initial position and a rightward transverse airflow is applied, causing the arc to drift towards the right. By t_a2 = 72.3 ms, the arc takes on an elliptical shape and is unable to maintain stable burning, eventually extinguishing at t_a4 = 257.1 ms. As can be seen in figure 8(b), when both airflow and 5 Hz ATMF are applied at t_b1 = 0 ms, the arc begins to gradually move to the right, and the voltage starts to increase slowly. By t_b2 = 202.4 ms, the arc adopts a twisted shape, with voltage of 200.1 V. At this point, the upper part of the arc is on the right side while the lower part is on the left. This phenomenon occurs because the arc is simultaneously influenced by the electromagnetic force $F'_{\mathrm{L}}$ to the left and the airflow force F_A to the right. In addition, due to the high number of electrons at the cathode and numerous ions at the anode, electrons experience a stronger electromagnetic force than ions, causing the arc to drift leftwards near the cathode. Consequently, the arc near the cathode drifts to the left, while the rest of the arc drifts to the right by airflow force F_A. As the twisting becomes more pronounced, the arc extinguishes and restrikes at t_b3 = 223.3 ms, but ultimately extinguishes under the combined forces of rightward F_L and F_A. Figure 8(c) shows ATMF that regulated the arc at 10 Hz in a transverse airflow environment. The arc continuously drifts to the right driven by the combined effects of rightward F_L and $F'_{\mathrm{L}}$ from t_c1 to t_c2, causing the arc voltage to reach a maximum value of 95.5 V at t_c2 = 26.5 ms. After t_c2, F_L reverses to $F'_{\mathrm{L}}$, resulting in the arc drifting to the left at t_c2–t_c3. This continues until the magnetic field reverses again, starting the next period, with voltage at t_c3 = 93.3 ms being 76.8 V. Figure 8(d) shows the ATMF at 50 Hz. It can be seen that the arc plasma is confined in a much smaller space compared to at 10 Hz. The voltage reaches a maximum at both t_d2 and t_d4, while the voltages at t_d1 and t_d2 are at a minimum. Therefore, it can be clearly concluded that arc voltage does not fluctuate with a period of ATMF.

Figure  8.  Motion characteristics of arc under different frequencies of ATMF in an airflow environment. (a) Non-magnetic, (b) 5 Hz, (c) 10 Hz and (d) 50 Hz.

DownLoad: Full-Size Img PowerPoint

Based on these observations, it can be concluded that without magnetic field regulation, the arc constantly drifts under the influence of airflow until the energy supply unit is insufficient to sustain the burning of the arc, leading to its extinguishment. At 5 Hz, a relatively low frequency, the shape of the arc is distorted under external forces, making it difficult to maintain stable burning, and ATMF cannot achieve the regulating effect of stabilizing the arc. At 10 Hz, considered a medium frequency, the arc achieves a stable state, oscillating with fluctuations of ATMF. In this case, arc voltage experiences only one rise and fall in one ATMF period, with voltage fluctuation frequency equal to ATMF frequency. This behavior is markedly different from the motion of arc characteristics in an airflow-free environment. As shown in figure 2(c), in the absence of airflow, the arc voltage rises and falls twice in one ATMF cycle, with voltage fluctuations occurring twice as frequently as ATMF frequency. This is due to the arc oscillating towards both left and right sides in the absence of airflow, where arc voltage reaches its maximum value at both extremes. However, in an airflow environment, the arc can only oscillate on the same side, causing the voltage to show a minimum value and a maximum value as it reaches the left and right sides, respectively. At 50 Hz, a relatively high frequency, the arc is essentially without oscillatory action and can be stabilized quite well, with arc voltage fluctuation not changing with ATMF variation.

Figure 9 illustrates the voltage fluctuations V_F and arc fluctuation rate δ within an airflow environment under ATMF regulation. In addition, figure 10 presents the arc length and the arc column transverse drift width. At frequencies ranging from 0 to 5 Hz, the maximum arc voltage fluctuation reaches approximately 200 V, primarily due to arc extinguishment. When ATMF frequency exceeds 10 Hz, the regulation effect becomes significant. Specifically, at 10 Hz, arc voltage fluctuation is 8.73 V with a δ of 10.27%, and arc length and arc column transverse drift width are 7.70 cm and 2.11 cm, respectively. Furthermore, at 30 Hz, arc voltage fluctuation decreases to 5.23 V with a δ of 6.15%, and arc length is 5.67 cm. It is revealed that the stability of arc is improved with increasing frequency. By 50 Hz, arc voltage fluctuation further reduces to 4.65 V with a δ of 5.47%, and arc length and transverse drift width are 4.85 cm and 1.67 cm, respectively. At this frequency, the regulation effect stabilizes and reaches its limit, indicating that further increases in ATMF frequency do not significantly enhance the regulation effect.

Figure  9.  Arc voltage fluctuation magnitude V_F and fluctuation rate δ under ATMF with different frequencies in an airflow environment.

DownLoad: Full-Size Img PowerPoint

Figure  10.  Arc transverse drift width and arc length under ATMF with different frequencies in an airflow environment.

DownLoad: Full-Size Img PowerPoint

5.   Conclusion

In this study, the regulatory effect of AC transverse magnetic field on the pantograph-catenary arc is systematically investigated.

(1) The regulation law of arc by different ATMF frequencies was found. ATMF exerts a significant stabilizing effect on the arc under an airflow environment, and the effect is enhanced with increasing frequency. Among them, the arc voltage fluctuation is 8.73 V with a fluctuation rate of 10.27% at a frequency of 10 Hz, while that at 30 Hz is 5.23 V and 6.15%, respectively. When the frequency increases to 50 Hz, the threshold of stabilization effect is reached, while the voltage fluctuation is 4.65 V and voltage fluctuation rate is 5.47%.

(2) It is found that arc temperature increases with frequency, reaching 4743 K at 10 Hz and 4976 K at 1000 Hz. This increase is attributed to the higher frequency of plasma collisions at elevated frequencies, which intensifies plasma reactions and consequently raises the temperature.

(3) The arc is regulated by three different waveforms of excitation current, revealing that the arc exhibits the greatest stability under a triangular magnetic field, with a voltage fluctuation of 3.04 V. This is followed by a sinusoidal magnetic field with a voltage fluctuation of 3.38 V, and the least stability is observed under a rectangular magnetic field, with a voltage fluctuation of 4.07 V.