Electrical Characteristics of the Pantograph-Catenary Arc in Urban Rail Transit Under Different Air Pressure Conditions

Abstract

Nowadays, urban rail transit is expanding towards high-elevation zones, and the effect of the low air pressure environment on the pantograph-catenary system is becoming increasingly prominent. As a key indicator for evaluating the electrical contact performance of a pantograph-catenary system, research on the electrical characteristics of the pantograph-catenary arc is of great significance. For this reason, this paper established a plasma mathematical model applicable to the arc of the urban rail transit bow network based on the theory of magnetohydrodynamics. The mathematical model of the pantograph-catenary arc was used to set the relevant initial conditions. Based on COMSOL Multiphysics finite element simulation software, this study developed a multi-physics simulation model of the pantograph-catenary arc and systematically analysed its voltage characteristics and current density distribution under varying air pressure conditions. The results showed that as the air pressure decreases, the potential at the axial points declines, the pressure drop across the arc poles becomes more pronounced, and the current density decreases accordingly. This study provides theoretical and technical support for optimizing the design of and promoting the sustainable development of urban rail transit pantograph-catenary systems in high-altitude areas.

1. Introduction

With the rapid growth of the economy and accelerated urban development, the urban population has surged, and the demand for transportation has been increasing day by day. Given these considerations, urban rail transit has gradually emerged as the preferred choice for many cities owing to its advantages including dedicated lines, high operational speed, extensive station coverage, and proven safety and reliability. As the number of cities constructing urban rail transit continues to increase, the environmental influencing factors faced by engineering construction are becoming increasingly complex. Among them, the increase in the altitude of the construction area is an important challenge. Currently, the urban railway system with the highest altitude that has been built in China is the Kunming Metro. Its lines are mainly distributed in the plateau area with an altitude of 1800 to 2000 m, and the highest point reaches 2100 m [1].

As the altitude increases, the atmospheric pressure gradually decreases. For urban rail transit operating in high-altitude and low-air-pressure environments, the frequency of pantograph-catenary arcs will be higher [2], and the arc erosion will be more severe [3]. Moreover, the high-altitude environment will significantly change the key characteristic parameters of the pantograph-catenary arc, including electrical conductivity, power characteristics, etc., and these parameters are essentially different from those in plain areas [4]. This series of changes poses new challenges to safe and reliable rail transit operation.

At present, research on pantograph-catenary arcs by domestic and foreign scholars mainly focuses on the analysis of the arc development mechanism and electrical characteristics in a conventional environment. The research on pantograph-catenary arcs under the influence of air pressure is concentrated on two aspects: the arc motion characteristics and the discharge characteristics [5]. Weifeng Han et al. developed a static arc mathematical model and conducted FLUENT-based simulations to analyse thermal distributions across the pantograph-catenary system, including both contact components and the arc plasma [6]. Zefeng Yang et al. investigated the combined effects of crosswind and electrical current on arc dynamics, demonstrating that crosswind conditions lead to arc elongation, while the current magnitude primarily determines the arc’s peak temperature [7]. Min Xu et al. independently designed and built an experimental platform for pantograph-catenary offline arcs. The platform was developed to study voltage, resistance, and power variations during both steady-state and dynamic offline conditions, as well as to analyse the arc’s volt-ampere characteristics [8]. However, the problems of frequent arc occurrences and significant changes in the electrical characteristics of the arc caused by special climates such as high altitude and low air pressure, as well as their influencing mechanisms, have not been studied yet. The main research focuses on the flashover characteristics of insulators and the plasma flow behaviour and development laws of pantograph-catenary arcs. Xingliang Jiang et al. investigated the DC flashover characteristics of iced insulator strings under low pressure conditions [9]. Yue Xu et al. investigated the dynamic development characteristics of pantograph-catenary arcs under low-pressure conditions, elucidating their three-stage development mechanism [10]. Yuhan Zhou et al. revealed the special motion law of a pantograph-catenary arc in a high altitude and low air pressure environment through simulations [11]. Through multi-physics simulations, Tunan Wang et al. analysed both the temperature rise mechanism at the pantograph-catenary contact surface under low-pressure conditions and the effects of varying pressure levels and gas flow rates on the surrounding flow field distribution [12]. Therefore, it is of great significance to study the electrical characteristics of pantograph-catenary arcs in different altitude environments, which has important reference value and guiding significance for the subsequent construction of urban rail transit at different altitudes, especially in high-altitude areas.

Based on this, this paper built upon MHD principles, combining Maxwell equations with fluid equations to establish a mathematical model of the plasma suitable for the pantograph-catenary arc in urban rail transit. By using the four major modules of current, magnetic field, heat transfer, and laminar flow in the finite element software COMSOL Multiphysics 6.2, a pantograph-catenary arc model was established. This framework enables systematic analysis of pressure-dependent electrical characteristics in pantograph-catenary arcing.

2. Pantograph-Catenary Arc Model

2.1. Establishment of the Mathematical Model

The pantograph-catenary arc model integrates fundamental principles from both fluid dynamics and electromagnetic field theory [13]. The equations of fluid dynamics are the basic equation sets for describing the motion of fluids, mainly including the fluid mass conservation equation, the momentum conservation equation, and the energy conservation equation. The formulations of the electromagnetic field are described by Maxwell equations [14].

1.

Hydrodynamic Equations

The specific equations used when establishing the model are as follows:

• Mass Conservation Equation

$${\displaystyle \frac{\partial \mathrm{\rho }}{\partial \mathrm{t}}}+\nabla \cdot (\mathrm{\rho } \mathrm{v})=0,$$

(1)

where $\mathrm{\rho }$ is the arc density, t is the time, and v is the flow field velocity of the arc plasma.

• Momentum Equation

$${\displaystyle \frac{\partial (\mathrm{\rho } {\mathrm{v}}_{\mathrm{i}})}{\partial \mathrm{t}}}+\nabla \cdot (\mathrm{\rho } \mathrm{v} {\mathrm{v}}_{\mathrm{i}})=\nabla \cdot (\mathrm{\eta } \mathrm{g} \mathrm{r} \mathrm{a} \mathrm{d} {\mathrm{v}}_{\mathrm{i}})-{\displaystyle \frac{\partial \mathrm{p}}{\partial {\mathrm{x}}_{\mathrm{i}}}}+{(\mathrm{J}\times \mathrm{B})}_{\mathrm{i}},$$

(2)

where ${\mathrm{v}}_{\mathrm{i}}$ is the velocity component, $\mathrm{\eta }$ is the kinetic viscosity, p is the pressure, J is the current density, and B is the magnetic induction intensity.

• Energy Conservation Equation

$${\displaystyle \frac{\partial (\mathrm{\rho } \mathrm{h})}{\partial \mathrm{t}}}+\nabla \cdot (\mathrm{\rho } \mathrm{h} \mathrm{v})=\nabla \cdot ({\displaystyle \frac{\mathrm{\lambda }}{{\mathrm{c}}_{\mathrm{p}}}}\mathrm{g}\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{h})+{\mathrm{S}}_{\mathrm{h}},$$

(3)

where h is the enthalpy, $\mathrm{\lambda }$ is the thermal conductivity, ${\mathrm{c}}_{\mathrm{p}}$ is the heat capacity, and ${\mathrm{S}}_{\mathrm{h}}$ is the source term of the energy control equation, which is composed of the Joule heat source term, the radiative source term, and the viscous dissipation term, and it is calculated as follows:

$${\mathrm{S}}_{\mathrm{h}}={\displaystyle \frac{\partial \mathrm{p}}{\partial \mathrm{t}}}+\mathrm{V}+{\displaystyle \frac{{\mathrm{J}}^2}{\mathrm{\sigma }}}-{\mathrm{Q}}_{\mathrm{R}},$$

(4)

where $\mathrm{\sigma }$ is the electrical conductivity of the arc plasma, V is the fluid viscous dissipation term, ${\displaystyle \frac{{\mathrm{J}}^2}{\mathrm{\sigma }}}$ is the Joule heat generated when the current passes through the arc plasma, and ${\mathrm{Q}}_{\mathrm{R}}$ is the energy radiated outward by the arc plasma through radiation. Owing to the high temperatures involved, thermal radiation plays a significant role. In this paper, the volume net radiation coefficient method is calculated as follows [15]:

$${\mathrm{Q}}_{\mathrm{r}\mathrm{a}\mathrm{d}}=4\mathrm{\pi }{\mathrm{\epsilon }}_{\mathrm{n}},$$

(5)

where ${\mathrm{\epsilon }}_{\mathrm{n}}$ is the temperature-dependent volume net radiation coefficient.

• Gaseous State Equation

Prior to establishing the mathematical model for the urban rail pantograph-catenary arc, the arc plasma flow characteristics are modelled as laminar gas flow. To ensure the solvability of the governing equations, the state equation of gas must be added.

$$\mathrm{p}=\mathrm{p}\left(\mathrm{\rho },\mathrm{T}\right),$$

(6)

2.

Maxwell’s Electromagnetic Equation

Arc plasma behaviour emerges from interactions with both externally imposed and current-derived magnetic fields, and a complex electromagnetic process occurs during its development. The joule heating contribution to the energy balance and the influence of the Lorentz force on the momentum equation that the arc plasma is subjected to can be obtained by computing the electromagnetic field distribution in the solution domain [16], and the specific calculation equations are as follows:

$$\mathrm{J}=\mathrm{\sigma }\mathrm{E},$$

(7)

$$\mathrm{E}=-\nabla \mathrm{\phi },$$

(8)

$$\nabla \cdot (\mathrm{\sigma }\nabla \mathrm{\phi })=0.$$

(9)

Therefore, the arc magnetic field can be calculated according to the following formulae:

$$\mathrm{B}=\nabla \times \mathrm{A},$$

(10)

$${\nabla }^2\mathrm{A}=-{\mathrm{\mu }}_{\mathrm{v}}\mathrm{\sigma }\mathrm{E},$$

(11)

where E is the electric field strength, $\mathrm{\phi }$ is the electric potential, A is the electric field strength, and ${\mathrm{\mu }}_{\mathrm{v}}$ is the magnetic permeability of a vacuum.

2.2. Geometric Modelling and Physical Parameters

Prior to conducting simulation analysis on the pantograph-catenary arc, it is essential to first establish the geometric model of the system under study. Considering the symmetrical characteristics of the pantograph-catenary system in three-dimensional space, this study employed a two-dimensional modelling approach to establish a simplified arc model as shown in Figure 1 for enhanced the computational efficiency while maintaining simulation accuracy. Unlike most existing studies that omit the contact line groove structure from their models, the present work retains this feature, along with other essential components including the contact line and collector bow skateboard. The diameter of the contact line is 13 mm, the thickness of the collector bow skateboard is 14 mm, and the groove angle of the contact wire is 90° [17].

In this paper, when performing the simulation, the electric field, magnetic field, etc. need to be calculated in the areas of the contact line and the electric shock bow skateboard, and physical parameters such as the density and thermal conductivity of the materials used need to be considered. The material of the contact line in this paper is a copper–tin alloy contact line, and the electric shock bow skateboard’s construction employs pure carbon fibre material. The specific parameters are shown in

Table 1. Physical Property Parameters of the Contact Line and the Electric Shock Bow Skateboard.

Parameter	Copper–Tin Alloy Contact Line	Pure Carbon Strip
Density/(kg/m3)	9020	8100
Specific Heat Capacity/(J/(kg·K))	384	376
Thermal Conductivity/(W/(m·K))	398	80
Electrical Conductivity/(S/m)	4.17 × 107	2.86 × 106

[18].

When simulating arcs, the air parameters cannot be treated as constants. These parameters vary with both temperature and pressure. To improve the simulation accuracy, our model incorporates temperature and pressure dependent data for air density, specific heat capacity, electrical conductivity, and thermal conductivity at four pressure levels of 1.0, 0.9, 0.8 and 0.7 atm. These material properties were obtained from the plasma physical parameters database published by Professor Rong Mingzhe of Xi’an Jiaotong University [19].

2.3. Boundary Condition Configuration and Mesh Division

To solve the pantograph-catenary arc model for urban rail systems, given its strong multi-physics coupling involving aerodynamics, electromagnetics, and thermal dynamics, in order to ensure the convergence of the numerical solution and the physical accuracy of the results, it is necessary to impose boundary condition constraints that conform to the dynamic characteristics of the pantograph-catenary arc on each physical field [20,21].

The top of the electric shock bow skateboard is set as a grounded cathode with an electric potential of 0 V; the contact line underside serves as the anode; and the pantograph–catenary gap is set to 4 mm. The initial temperatures of AB, BC, and DA are set to 300 K, and the interface of the electric shock bow skateboard is set as natural heat convection. The air domain is fixed at 4 mm, with a primary temperature of 300 K, under a standard atmospheric pressure (101,325 Pa). The fluid domain is initialized with zero electric field intensity; the magnetic field strength of the fluid is set to 0 A/m; and other boundaries are not involved in the flow field calculation. The arcing time of the pantograph-catenary arc in urban rail transit is set to 50 ms, so the arc current is 50 A.

To ensure the simulation model is well-posed, both solution accuracy and computational efficiency must be considered. For this purpose, we adopted an optimized mesh strategy for the pantograph-catenary arc geometry. As shown in Figure 2, the carefully designed mesh distribution enhances numerical accuracy while maintaining a reasonable computation time.

3. Analysis of the Simulation Results

3.1. Voltage Distribution of the Pantograph-Catenary Arc

With the aim of studying the discharge characteristics of the pantograph-catenary arc in different altitude environments, the voltages of the pantograph-catenary arc in different altitude environments were studied. The altitudes studied were 0 m, 1000 m, 2000 m, and 3000 m; that is, the atmospheric pressures were 101 Kpa, 90 Kpa, 80 Kpa, and 70 Kpa, respectively. The potential distribution diagrams of the pantograph-catenary system under different air pressures were modelled in COMSOL, as shown in Figure 3.

To systematically analyse the effect of air pressure variations on pantograph-catenary arc potential, axial potential data were extracted under four distinct air pressure conditions. The corresponding potential distribution curves were subsequently plotted for comparative analysis, as presented in Figure 4.

From the trends in Figure 4, the axial potential of the pantograph-catenary arc under the four different air pressures studied can be observed to increase steadily and then trend linearly between the axial distances of 0.3 mm and 3.7 mm, and it begins to change abruptly in the two near-electrode regions. The maximum values of the anode region are 37.5 V, 36.2 V, 34.8 V, and 33.6 V, respectively, and the mutation rates are 63.04%, 64.55%, 65.71% and 76.84%, respectively. These results demonstrate that higher pressure leads to more significant arc potential variations. From this, it can be concluded that when the air pressure decreases, the axial voltage of the pantograph-catenary arc gradually decreases.

To explain this finding, consider that when the air pressure decreases, the gas concentration decreases, and the mean free path of charged particles increases. Electrons can accumulate sufficient kinetic energy between collisions to reach the ionization threshold, thereby reducing the electric field strength required for arc maintenance. In addition, the electrical conductivity of the arc depends on the degree of ionization of the plasma. When the air pressure decreases, the energy losses due to heat conduction and convection in the arc plasma diminish, and more energy is used to maintain the high-temperature ionization state and the ionization efficiency is improved, thereby lowering the necessary electric field intensity under identical current conditions.

3.2. Current Density Distribution of the Pantograph-Catenary Arc

In order to study the influence of different altitude environments on the current density of the pantograph-catenary arc, the environmental pressures were regulated at 101 Kpa, 90 Kpa, 80 Kpa, and 70 Kpa, respectively, and the current density distribution of the pantograph-catenary system under the set air pressures was simulated.

To better assess the effect of atmospheric pressure on the current density characteristics of the pantograph-catenary arc, the longitudinal and transverse current density profiles of the pantograph-catenary arc were extracted, and the distributions of current density along both axes were plotted. The axial and radial current densities of the pantograph-catenary arc at varying atmospheric pressures are shown in Figure 5.

It can be seen from Figure 5 that the axial current density of the pantograph-catenary arc under different air pressure levels is relatively high in the two-pole region. The peak region is shown in Figure 6, and it is basically stable in the arc column region.

When the air pressures are 101 kPa, 90 kPa, 80 kPa, and 70 kPa, the highest axial current densities of the pantograph-catenary arc in the cathode region are 9.12 × 10⁷, 8.43 × 10⁷, 7.83 × 10⁷, and 6.89 × 10⁷ A/m², respectively, and the highest axial current densities within the anodic zone exist at 5.28 × 10⁷, 4.66 × 10⁷, 4.32 × 10⁷, and 3.52 × 10⁷ A/m², respectively; the highest radial current densities of the pantograph-catenary arc are 4.36 × 10⁶, 4.03 × 10⁶, 3.69 × 10⁶, and 3.28 × 10⁶ A/m², respectively.

In conclusion, as the atmospheric pressure declines, the current density of the pantograph-catenary arc gradually diminishes, and the change is most obvious in the two-pole region of the arc. The reasons for this are as follows: with decreasing ambient pressure, the electron mean free path lengthens, resulting in reduced electron-neutral collision frequency, resulting in a decrease in plasma ion concentration, thereby reducing the current density. In addition, the decrease in air pressure leads to a decrease in gas concentration, and the limitation imposed on the arc plasma is weakened, resulting in the transverse plasma channel enlargement in the pantograph-catenary arc and a decrease in air conductivity, reducing the current density.

4. Model Verification

In Reference [22], an experimental study was conducted on the variation of pantograph-catenary arc distance at the extension limit points under different air pressures. As illustrated in Figure 7, the longitudinal axis represents the distance at the extension limit points. The distance at the extension limit points of the pantograph-catenary arc exhibits an exponential dependence on air pressure. The experimental results show that as the air pressure decreases, the distance at the extension limit points of the pantograph-catenary arc intensifies non-linearly. The lower the air pressure, the longer the distance at the extension limit points of the pantograph-catenary arc.

Consistent with the electric field strength theory of gaseous medium [23], reduced air pressure induces a proportional decrease in the arc column’s electric field strength under the given conditions. That is, when the air pressure decreases, the electric field strength of the arc column decreases in a proportional relationship. Simultaneously, to satisfy the arc extinction criteria under reduced atmospheric pressure, the pantograph-catenary gap must be enlarged to maintain the supply voltage below the arc sustainability threshold, thereby ensuring reliable arc interruption. According to this theoretical analysis, under the condition of decreasing air pressure, the voltage threshold required to maintain an arc discharge decreases accordingly. This means that with the same electrode spacing, the arc voltage changes in a positive correlation with the air pressure.

The common analysis shows that with a gradual decrease in air pressure, the voltage required to maintain the arc decreases. Specifically, at a constant electrode gap distance, the arc voltage demonstrates an inverse dependence on ambient pressure. The conclusion is the same as the simulation results in this paper, so the rationality of the pantograph arc model is verified. These findings show excellent agreement with our simulation results, thereby validating the physical soundness of the proposed pantograph arc model.

5. Conclusions

This study developed a simulation model of the pantograph-catenary arc with the finite element software COMSOL. At the same time, based on this model, a simulation study was carried out regarding the impact of the pantograph-catenary arc voltage and current density under four air pressure intensities (101 kPa, 90 kPa, 80 kPa, and 70 kPa), and the influence of the atmospheric pressure on the electrical phenomenological features of the pantograph-catenary arc were analysed. From the above research contents, the following conclusions were drawn:

1.

When the atmospheric pressure decreases, the voltage of the pantograph-catenary arc decreases. As the atmospheric pressure declines from 101 kPa to 70 kPa, the potential at each point along the axis of the pantograph-catenary arc keeps decreasing, and the voltage decrease at the two poles of the arc is significantly greater than that in the arc column region, namely, the reduction rate at 70 kPa is 13.8% higher than that at 101 kPa. As the air pressure diminishes, the potential in the arc column region is lower, but the change of potential in the near-electrode region is also slower, resulting in a relatively small overall decrease in the arc voltage.

2.

As the air pressure declines, the pantograph-catenary arc’s current density decreases. The radius of the pantograph-catenary arc increases as the air pressure decreases and the distribution range of the current density becomes wider and generally shows a downward trend. This phenomenon is more obvious the closer it is to the axis of the arc. As a whole, the energy distribution of the arc in hypobaric environment is more dispersed, the current density near the axis weakens, and the influence range of the peripheral area expands.

Combined with the influence of the above voltage levels on the electrical properties, in the subsequent configuration of urban rail transit in high-altitude areas, the voltage threshold of the traction power supply system can be adjusted or dynamic compensation devices can be added to avoid problems such as a decrease in energy transmission efficiency or arc stability caused by a voltage drop, maintaining a homogeneous current density profile and offsetting the contact instability problems caused by arc diffusion, which reduces the risk of local overheating. Therefore, urban metro systems can be constructed throughout high altitude areas to support sustainable development.