Transient Arcing Characteristics of the Pantograph–Catenary System in Electrical Sectioning Overlaps

Abstract

Transient arcing often occurs as an electric locomotive traverses an electrical sectioning overlap (ESO), deteriorating current collection stability and reducing the durability of the pantograph–catenary (PC) system. In this study, the formation mechanism and electrical evolution characteristics of transient arcing in the ESO region are investigated through theoretical analysis and numerical simulations. First, based on the dynamic motion of the locomotive passing through the ESO, the transient arcing mechanism of the ESO is clarified, and the plasma characteristics of the arc are described. Then, the electromagnetic, airflow, and thermal field interactions within the PC contact gap during arc ignition are analyzed. A Multiphysics coupled PC arc model is developed, incorporating aerodynamic, electromagnetic, and heat transfer effects. Subsequently, finite element meshing and boundary conditions are applied to simulate the transient evolution of the ESO arc. Finally, the transient arcing characteristics of the ESO are analyzed. The results indicate that the current density is highly concentrated at the initial arcing stage and gradually forms an axially symmetric conductive channel (approximately 10⁷ A/m²), which shifts upward as the contact gap increases. Moreover, due to the geometric discontinuity of the ESO, a strong localized electric field develops near the wire edge, leading to arc root migration and reignition.

1. Introduction

The electrical sectioning overlaps (ESO) is a critical structure connecting adjacent power supply segments. With the ongoing development of high-speed railways and increasing train velocities, the current collection stability and electrical safety of locomotives have become increasingly prominent [1]. When the pantograph exits the ESO region, transient arcing is prone to occur between the pantograph slide and the contact wire due to contact wire mechanical vibrations and electrical switching [2]. This phenomenon is accompanied by strongly coupled electromagnetic, thermal, and fluidic effects. It not only induces current collection fluctuations in locomotives but also accelerates the ablation and degradation of pantograph slide and contact wire materials. These effects pose a serious threat to the operational stability and service life of the pantograph–catenary (PC) system. Therefore, investigating the transient arcing characteristics of the ESO is of significant importance.

In recent years, both domestic and international researchers have systematically investigated the arcing characteristics of locomotives passing through articulated split-zone insulators. Their studies have focused on offline arc modeling, key factors affecting PC transient arcing, and arc detection. In terms of offline arc modeling, the Habeadack black-box model serves as the core theoretical framework for characterizing the time-varying voltage–current behavior of arcs [3]. This model neglects microscopic mechanisms such as particle collision ionization and radiative energy dissipation, instead simplifying the complex arc process into a single time-varying resistive element via a macroscopic equivalence strategy [4,5]. By constructing input–output relationships from external electrical characteristic curves, it significantly improves computational efficiency [6]. Furthermore, to comprehensively describe the arc from ignition to extinction, researchers have proposed Multiphysics coupled arc models based on magnetohydrodynamics theory [7,8]. These models reveal the transition of arc morphology from columnar to branched forms and capture the spatiotemporal distribution of temperature and flow fields [9]. However, none of these models account for the dynamic variation of the contact pair gap as locomotives exit the electrical section, limiting their applicability to ESO arcing phenomena.

Regarding the key factors influencing PC transient arcing, existing studies indicate that the locomotive operating state, catenary structural parameters, and environmental conditions jointly govern the arcing characteristics [10,11,12,13,14,15]. Using the entropy-weight method, researchers quantified the influence of train speed, electrical section voltage difference, and current collection magnitude on arc duration [2]. Further studies show that the locomotive speed when passing through the anchored-joint ESO directly affects arc duration. At low speeds, energy accumulates, leading to higher arc temperatures and enhanced ablation, whereas high speeds promote aerodynamic cooling and rapid arc extinction [16]. Additionally, environmental humidity and air pressure modulate the conductivity of arc plasma, thereby altering energy dissipation rates [17,18]. High-altitude, low-pressure conditions significantly prolong arc duration [19]. Nevertheless, the spatiotemporal evolution of temperature fields, current density, and potential distribution in transient arcing under different operating conditions remains to be fully elucidated.

In terms of PC arc detection, current research primarily focuses on identifying the multidimensional physical characteristics of arcs and developing high-precision intelligent detection techniques [20,21,22,23]. Common approaches include arc-light detection using ultraviolet phototubes, high-speed imaging with synchronized arc image–parameter acquisition, and transient temperature measurement of arcs via infrared thermography [24,25]. For intelligent recognition, the integration of traditional signal processing methods, such as wavelet transforms, with machine learning and deep learning has become a major focus [26,27]. Hybrid models combining improved Inception networks with Light GBM achieve recognition accuracies up to 96.3%, while multi-source fusion systems based on convolutional neural networks (CNNs) maintain misclassification rates below 3%. The adoption of edge computing further reduces real-time processing latency. Nevertheless, weak signal extraction under strong electromagnetic interference remains challenging, and the mechanisms by which extreme environmental conditions affect system stability require systematic investigation.

In summary, existing studies have primarily focused on arc behavior under stable contact or general offline conditions. Research on the formation mechanisms, spatial distribution, and energy transfer characteristics of arcs within the ESO region remains limited. In particular, the complex dynamic separation of the PC contact pair as locomotives exit the ESO has not been systematically investigated. Such dynamic variations exacerbate electric field distortions and promote arc reignition, which cannot be accurately captured by conventional steady-state arc models. In this work, we systematically investigate the transient arcing characteristics of the PC system in the ESO region. The main innovations and contributions are as follows:

(1)

A Multiphysics coupled arc model based on magnetohydrodynamics theory is developed, incorporating aerodynamic, electromagnetic, and thermal conduction effects to accurately describe transient arcing in the anchored-joint ESO.

(2)

By analyzing the power supply circuit of the anchored-joint ESO, the transient arcing mechanism is elucidated. Furthermore, the evolution of arc current density and potential distribution is revealed, providing theoretical guidance for the optimization of electrical section structures and the safe operation of high-speed railway power systems.

2. Transient Arcing Model of ESO

The anchored-joint electrical section is a critical structure in high-speed railway catenary systems. This section analyzes the mechanisms underlying transient arcing in the ESO, revealing the Multiphysics coupling between the PC contact pair during arc formation. Based on this analysis, a Multiphysics coupled PC arc model is established, enabling numerical simulation of the arc evolution process within the electrical section.

2.1. Transient Arcing Mechanism in ESO

In actual railway operations, anchored-joint electrical sections are commonly used to separate station catenaries from line catenaries, enabling independent maintenance or fault isolation. A schematic of the power supply is shown in Figure 1. The traction substation feeds the up and down catenaries through two separate feeders. Although electrically isolated, both sides are supplied by the same substation. The electrical section also divides a single feeding arm into two power supply zones, referred to here as Power Supply Zone 1 and Power Supply Zone 2.

When the train travels in the direction shown in Figure 1, the pantograph first collects power from Contact Wire 1 (W₁) in Power Supply Zone 1. As the train enters the electrical section under load, a line voltage drop occurs in Power Supply Zone 1 due to the traction current. This generates a voltage difference ΔU across the gap between the pantograph slide and Contact Wire 2 (W₂). Assuming a source voltage U, Power Supply Zone 1 has a unit impedance Z₁ and length L₁, while Power Supply Zone 2 has a unit impedance Z₂ and length L₂. Given a train impedance Z₃ and train current I₁, the voltage difference ΔU across the gap can be calculated (1).

$$\Delta U=U-I_1(Z_3+Z_1{L}_1)$$

(1)

When the train leaves the electrical section, the pantograph collects power from W₂ in Power Supply Zone 2. W₁ becomes inactive, and its potential remains equal to the source voltage. At this stage, a voltage difference ΔU appears across the gap between the pantograph slide and W₁. Assuming a train current of I₂, the gap voltage ΔU can be expressed by (2).

$$\Delta U=U-I_2(Z_3+Z_2{L}_2)$$

(2)

Once the voltage difference at the electrical section exceeds the minimum breakdown voltage of the gap, the air is ionized, and an arc is initiated. The relationship between the breakdown voltage difference and the gap distance can be described by an empirical formula derived from electrical breakdown experiments, as given in (3).

$$\Delta U=25.4d+6.64\sqrt{d}$$

(3)

Previous studies have shown that, compared with the entering process, arcing during train departure from the electrical section involves higher input energy. The arcing is also more intense, posing greater threats to the PC system [28]. Therefore, this paper focuses on the arcing characteristics during the train’s departure from the electrical section.

2.2. ESO Arc Plasma Characteristics

The arc plasma belongs to the category of low-temperature thermal plasma, with heavy-particle temperatures typically ranging from 3 × 10³ K to 3 × 10⁴ K. Under such conditions, the plasma is approximately in local thermodynamic equilibrium (LTE). Neutral particles, ions, and electrons can therefore be assumed to share a common characteristic temperature, allowing their state to be described by a unified thermodynamic temperature. The properties of arc plasma can thus be characterized using the Saha equation, the Boltzmann energy-level distribution, and the Maxwell velocity-distribution function. This provides the theoretical foundation for establishing the magnetohydrodynamic model of the arc.

After ignition, the arc can be divided into three typical regions: the cathode region, the arc column, and the anode region (as shown in Figure 2). In the arc column, the electric field strength can be approximately regarded as constant, whereas it increases significantly near the electrodes. The near-cathode region is rich in positive ions and exhibits a steep potential gradient. The voltage drop across this region, denoted U_c, is approximately on the order of the electron mean free path (<10⁻⁴ cm). This region plays a dominant role in electron field emission, surface bombardment, and secondary electron emission from the cathode. Correspondingly, the near-anode region receives a large flux of electrons from the arc column, forming a negative space-charge layer. Its length is several times that of the near-cathode region, and its voltage drop is denoted as U_a. Under steady arcing conditions, the voltage drops across both electrode regions vary slightly and can be considered approximately constant.

The arc column lies between the near-cathode and near-anode regions and exhibits an elliptical cylindrical shape under free-burning conditions. Its voltage drop is denoted as U_z. Since no significant space charge exists in this region, the axial electric field remains nearly constant. Consequently, the voltage distribution approximately follows Ohm’s law, showing resistive characteristics similar to those of a metallic conductor. As the main channel for charged-particle transport, the arc column hosts continuous recombination of electrons and positive ions, releasing energy in the form of radiation. This process enhances particle thermal motion, leading to a temperature rise and promoting thermal ionization. As a result, the electrical conductivity gradually increases while the voltage drop decreases. When the rates of ionization and recombination reach a dynamic equilibrium, the arc column attains a stable burning state.

The PC electrical section arc is essentially an ionized gas, exhibiting not only significant electrical conductivity but also interactions with magnetic fields during particle motion. Internally, it displays transport properties of mass, momentum, and energy, and can thus be regarded as a typical magnetofluid. To accurately describe the arc’s evolution and energy transfer under Multiphysics coupling, this study is conducted based on magnetohydrodynamics theory. By combining the Navier–Stokes equations with Maxwell’s equations, a mathematical model of the PC electrical section arc is established, revealing the fundamental dynamics of its Multiphysics coupling.

2.3. Multiphysics Coupling Mechanism of PC Transient Arcing

During the transient arcing process in the anchored-joint electrical section of the PC system, significant Multiphysics coupling occurs among the thermal, electromagnetic, and flow fields. Thermal parameters of the arc, such as temperature, pressure, and electrical conductivity, serve as the key link among the three fields. Joule heating in the electromagnetic field raises the arc temperature. This, in turn, alters the thermal conductivity and specific heat capacity, causing the thermal field to influence the flow field through buoyancy and pressure gradients. Meanwhile, gas motion in the flow field redistributes temperature and charged-particle concentrations, thereby modifying the plasma conductivity and viscosity. The electromagnetic field responds to these changes, adjusting current density and Lorentz forces to realize coupled feedback. This closed-loop interaction among the three fields jointly governs the dynamic evolution, energy dissipation, and stability characteristics of the ESO arc. The Multiphysics coupling mechanism of transient arcing in the anchored-joint electrical section is illustrated in Figure 3.

2.4. Multi-Physics Coupling Model of the ESO Arc

To accurately describe the dynamic characteristics of PC transient arcing when a locomotive passes through the anchored-joint electrical section, a thermal–flow–electromagnetic Multiphysics coupling model was established based on magnetohydrodynamics theory. This model comprehensively accounts for the interactions among aerodynamic forces, electromagnetic forces, and heat conduction, revealing the distributions of arc temperature, current density, and electric potential. In addition, to reduce model complexity and improve numerical stability and convergence efficiency, the following key assumptions are introduced in the development of the multiphysics PC arc model:

(1)

During PC transient arcing, the arc plasma is assumed to remain in a state of local thermodynamic equilibrium (LTE);

(2)

The arc sheath effects and the microscopic interactions between the high-temperature plasma and the contact pair materials are not explicitly considered;

(3)

The arc plasma within the computational domain is treated as an electrically neutral Newtonian fluid, and the influence of electric body forces on the arc is neglected.

These assumptions ensure that the model retains the interpretability of the dominant physical processes while enabling stable and efficient numerical solutions. Additionally, the PC arc is treated as a weakly compressible conducting plasma, whose behavior is governed by the continuity, momentum, and energy equations. The governing equations are expressed in (4).

$$\left\{\begin{array}{l}{\displaystyle \frac{\partial \rho }{\partial t}}+\nabla \cdot (\rho \mathbf{u})=0\hfill \\ \rho {\displaystyle \frac{\partial \mathbf{u}}{\partial t}}+\rho (\mathbf{u}\cdot \nabla )\mathbf{u}=-\nabla p+\nabla \cdot (\mu \nabla \mathbf{u})+\mathbf{J}\times \mathbf{B}\hfill \\ \rho C_p{\displaystyle \frac{\partial T}{\partial t}}+\rho C_p(\mathbf{u}\cdot \nabla T)=\nabla \cdot (k\nabla T)+\mathbf{J}\cdot \mathbf{E}-Q_{\mathrm{rad}}\hfill \end{array}\right.$$

(4)

where ρ is the gas density, and t is the transient arcing time in the PC electrical section. u is the velocity vector, p is the pressure, and μ is the dynamic viscosity. J × B represents the Lorentz force, one of the dominant driving forces for arc plasma motion. T is the temperature, C_p is the specific heat capacity, and k is the thermal conductivity. J·E denotes Joule heating, and Q_rad is the radiative heat power density.

In addition, under quasi-static conditions, the electromagnetic field of the PC arc can be described by the Maxwell equations, as expressed in (5).

$$\left\{\begin{array}{l}\nabla \times B={\mu }_0 \mathbf{J}\hfill \\ \mathbf{J}=\sigma (\mathbf{E}+\mathbf{u}\times \mathbf{B})\hfill \\ \nabla \cdot \mathbf{B}=0\hfill \\ \nabla \times E=-{\displaystyle \frac{\partial B}{\partial t}}\hfill \end{array}\right.$$

(5)

where μ₀ is the vacuum magnetic permeability (4π × 10⁻⁷ H/m), and σ is the electrical conductivity, which varies with temperature as expressed in (6).

$$\sigma (T)={\sigma }_0 \exp (-{\displaystyle \frac{E_a}{k_{B}T}})$$

(6)

where σ₀ is the reference conductivity, E_a is the effective activation energy, and k_B is the Boltzmann constant. In addition, the material parameters used in this study are listed in

Table 1. Physical parameters of the contact pair materials.

Parameter	Pantograph Slide	Contact Wire
Conductivity [S/m]	2.857 × 107	4.167 × 107
Specific heat [J/(kg·K)]	376	385
Density [kg/m3]	8100	9020
Thermal conductivity [W/(m·K)]	80	400
Melting point [K]	--	1356
Boiling point [K]	--	2840

.

2.5. Solution of the Transient Arcing Model

The transient solver was adopted for the simulation, with a time step of 0.1 ms and a total simulation duration of 100 ms. A segregated solution strategy was employed, where the linear systems of all physical field variables were solved using the PARDISO solver. This solver provides high computational efficiency, supports out-of-core memory management, and limits the number of iterations per step to 20 to ensure numerical stability and convergence. The overall solution procedure of the model is illustrated in Figure 4.

3. Model Validation

To validate the proposed model, the geometric configuration and physical scenario reported in reference [29] were first reconstructed. The same boundary conditions and simulation settings as those in the reference were strictly adopted to ensure the comparability of the results. On this basis, key simulation outputs, including the temperature field distribution, were extracted and compared with the corresponding results reported in reference [29]. As shown in Figure 5 and Figure 6, a high level of agreement is observed in terms of characteristic spatial patterns, temporal evolution trends, and order of magnitude. These results demonstrate the reliability and applicability of the proposed model.

4. Results and Discussion

Based on the developed multi-field coupled model of the electrical section arc, a systematic numerical simulation was conducted to investigate the electrical characteristics and multi-physics evolution of the ESO arc during its burning process. By analyzing the dynamic responses of arc current density and potential distributions at different arcing durations, the coupled interactions among the electromagnetic, thermal, and fluid fields were elucidated.

4.1. Current Density Distribution of the ESO Arc

The power locomotive is assumed to traverse the anchored-joint electrical section at a speed of 9 km/h, with an AC voltage difference of 500 V at 50 Hz applied across the section terminals. Figure 7 presents the simulated arc current density distribution and its longitudinal profile at t = 45 ms. This instant corresponds to the decay stage of typical transient arcing events and thus characterizes the late-stage evolution of the concentrated arc current density. At this stage, the contact wire functions as the anode, whereas the pantograph slide acts as the cathode.

As shown in Figure 7a, the magnitude of the current density reaches its maximum near both the anode and the cathode, gradually decreasing along the central axis of the arc column. Overall, the distribution exhibits a saddle-like profile. The maximum current density at the anode surface is 1.85 × 10⁸ A/m², while that at the cathode surface is 6 × 10⁷ A/m². Both electrode regions display a pronounced self-constriction behavior. This is primarily caused by the self-induced magnetic field generated by the arc current and the resulting Lorentz force, as illustrated by the vector arrows in Figure 7b. Near the central region of the plasma arc column, the Lorentz force is significantly enhanced and consistently directed toward the column axis. Simultaneously, the arc plasma expands due to heating. Under mechanical and thermal equilibrium, the contraction radius r of the plasma arc column can be obtained, as expressed in (7). Compared with the arc column region, the near-electrode regions exhibit higher temperature and pressure, resulting in smaller contraction radii. Moreover, the arc root in the anode region contracts more significantly than that in the cathode region.

$$r={\left({\displaystyle \frac{I^2{\mu }_0}{16{\pi }^{2}P}}\right)}^{{\displaystyle \frac{1}{4}}}$$

(7)

4.2. Electric Potential Distribution of the ESO Arc

To further investigate the electric potential distribution of the PC arc in the anchored-joint ESO, the arc potential cloud maps at arcing times t = 25 ms and t = 35 ms were extracted, as shown in Figure 8. These two arcing instants correspond, respectively, to the early stage following arc-root formation, during which the current density rapidly establishes, and to the intermediate stage of a typical ESO arcing event, when the arc enters a quasi-stable evolution regime. The former captures the current density characteristics associated with the initial formation of the arc channel, whereas the latter reflects the electric potential distribution after the multiphysics coupling effects have fully developed. Together, these instants represent the key states in the evolution of transient arcing.

As shown in Figure 8a, at t = 25 ms, the electric potential distribution exhibits significant spatial non-uniformity. At this stage, the contact wire serves as the anode and is maintained at a constant potential of 60.7 V, while the slide functions as the grounded cathode. Near the electrode regions, the equipotential lines are densely packed, indicating a strong electric field. In contrast, the equipotential lines in the arc column region are relatively uniform, corresponding to smaller electric field gradients. The electric field is directed from the contact wire to the slide, with the potential gradually decreasing from the anode to the cathode. At this moment, the electric field is mainly concentrated near the electrodes, reflecting strong energy exchange and current-carrying characteristics at both ends of the arc.

After the polarity reversal, as shown in Figure 8b, the slide becomes the anode and is maintained at 0 V, while the contact wire acts as the cathode, with its potential decreasing to −64.8 V. Compared with the positive polarity state, the potential distribution exhibits an approximately mirror-reversed pattern. The electric field is now directed from the slide to the contact wire. High electric field intensity and densely packed equipotential lines appear again near the electrodes, whereas the arc column region maintains a relatively gentle potential gradient. This field reversal alters the direction of energy and charged particle transport within the arc, reflecting the dynamic reconfiguration of the arc channel during PC electrical section switching.

The longitudinal electric potential distributions of the PC arc at different times were further extracted, as shown in Figure 9. At t = 25 ms, the potential gradient in the arc column region is relatively gentle, while the gradient near the cathode is the steepest. The potential gradient in the anode region lies approximately between one-third and two-thirds of that in the cathode region. This distribution arises from the significant differences in the physical mechanisms at the two electrodes. Electron emission at the cathode primarily relies on the field emission process. This process requires a strong electric field on the order of 10⁹ V/m to overcome the electron tunneling barrier, resulting in a sharp potential gradient. In contrast, the anode mainly serves as the electron collection terminal, where energy dissipation is dominated by Joule heating. This process is less dependent on the electric field, leading to a more gradual potential variation. After polarity reversal at t = 35 ms, the sign and magnitude of the potential change accordingly. However, the characteristic distribution of the potential gradient in both electrode regions remains largely unchanged. This indicates that, regardless of polarity, the local electric field structure of the PC arc is constrained by the electrode material properties and plasma dynamics. It exhibits strong symmetry and stability.

5. Conclusions

This study employs a numerical simulation approach to investigate the current density and electric potential characteristics of PC transient arcing occurring during locomotive passage through the anchored-joint ESO. The spatiotemporal evolution of these characteristics is analyzed under representative operating conditions and predefined modeling assumptions. The main conclusions are summarized as follows:

(1)

By analyzing the power supply network topology during the passage of a power locomotive through an anchored-joint ESO, a method is established to calculate the open-circuit voltage difference between the working and non-working contact wires. This result provides a quantitative theoretical reference for evaluating the triggering conditions and voltage-driven characteristics of PC transient arcing under ESO scenarios.

(2)

By analyzing the multiphysics coupling mechanisms during PC contact pair separation, a coupled multiphysics model for transient arcing in ESO is developed. Under the prescribed boundary conditions, the model can reasonably capture the dominant evolution features of the current density concentration and electric potential, providing a reference for arcing risk assessment in ESO sections.

(3)

The arc plasma is in dynamic equilibrium between thermal expansion and Lorentz force contraction. Under a constant arc current, higher arc temperatures result in smaller plasma contraction radii and higher current densities. The direction of the electric potential gradient changes with polarity. The overall distribution pattern remains largely unchanged, showing rapid potential variation near the electrodes and relatively gentle variation along the arc column.