Electric Field and Charge Characteristics at the Gas–Solid Interface of a Scaled HVDC Wall Bushing Model

Abstract

Ultra-high-voltage direct current (UHVDC) wall bushings are critical components in DC transmission systems, ensuring insulation integrity and operational reliability. In recent years, surface discharge incidents induced by charge accumulation at the gas–solid interface have become increasingly prominent. A comprehensive understanding of the electric field distribution and charge accumulation behavior of wall bushings under UHVDC is therefore essential for improving their safety and stability. In this work, an electrostatic field model of a ±800 kV UHVDC wall bushing core was developed using COMSOL Multiphysics 6.3. Based on this, a geometrically scaled model of the bushing core was further established to investigate charge distribution characteristics along the gas–solid interface under varying voltage amplitudes, application durations, and practical operating conditions. The results reveal that the maximum surface charge density occurs near the geometric corner of the core, with charge accumulation increasing as the applied voltage amplitude rises. Over time, the accumulation exhibits a saturation trend, approaching a steady state after approximately 480 min. Moreover, under actual operating conditions, the charge accumulation at the gas–solid interface increases by approximately 40%. These findings provide valuable insights for the design optimization of UHVDC wall bushings, thereby contributing to improved insulation performance and enhanced long-term operational reliability of DC transmission systems.

1. Introduction

Ultra-high-voltage direct current (UHVDC) transmission technology is a key approach for achieving large-capacity and long-distance power delivery [1]. As critical insulating components in converter stations, UHVDC wall bushings play an essential role in maintaining system stability and long-term operational reliability [2,3,4,5]. Unlike conventional AC systems, the electric field distribution in wall bushings under DC voltage is primarily governed by the conductivity of the insulating materials [6,7]. The field strength gradually transitions from an initial capacitive distribution to a steady-state resistive distribution [8,9,10]. During this process, charges accumulate at the interface between the bushing core and the surrounding insulating gas, resulting in electric field distortion, partial discharge, and even surface flashover [11,12,13]. Since 2019, three surface discharge incidents involving 400 kV DC bushings have been reported at the Xindong and Chusui DC stations, causing DC lockout and posing serious risks to system safety and stability. At the Yunnan Puer Converter Station, a 400 kV DC wall bushing experienced severe erosion of the outdoor current-carrying strip contacts due to abnormal thermal stress during operation [14], further threatening equipment integrity and overall system reliability [15].

Extensive research has investigated charge accumulation at the gas–solid interface. As early as 1983, Nakanishi [16] employed the dust figure and electrostatic probe methods to examine charge accumulation on solid dielectric surfaces between parallel-plate electrodes under DC voltage. The study concluded that surface charge formation was primarily caused by surface conduction arising from the nonuniform surface conductivity of the insulator. Zhang [17] conducted numerical simulations of charge accumulation on the inner surface of basin-type insulators, demonstrating that variations in charge location and polarity significantly altered the electric field distribution and reduced insulation performance. Li and Peng [18] developed a model describing the transient evolution of bulk and interfacial charge densities in gas–solid insulation systems under DC electric fields. They further proposed a weakly ionized gas conductivity model based on natural ionization, ion drift, and diffusion, which provided a theoretical foundation for subsequent simulations of charge behavior at gas–solid interfaces. Shi [19] independently developed a surface potential measurement system to characterize the potential distribution of a scaled bushing core and simulated the transient evolution of the electric field under DC excitation. The results showed that the surface potential exhibited a nonlinear dependence on the applied voltage and a distinct polarity effect. Chen [20,21] established an electro-thermal coupling model of ±200 kV epoxy-impregnated paper valve-side bushings, identifying the volume conductivity of the core material as the key parameter. The study revealed that reducing core conductivity suppresses positive surface charge accumulation and decreases the tangential electric field on the core surface, but prolongs the transition from capacitive to resistive behavior. Collectively, these studies have deepened the understanding of charge accumulation in insulators and valve-side bushings. However, for wall bushings under HVDC conditions, theoretical frameworks and experimental approaches remain limited [22,23,24], making the investigation of charge accumulation at the gas–solid interface an urgent research priority.

This study investigates ±800 kV ultra-high-voltage direct current (UHVDC) wall bushings. A scaled model of the bushing core was developed and analyzed using electric-field and charge-coupled simulations, focusing on the three primary mechanisms of surface charge accumulation at the gas–solid interface. The study examined the spatial distribution of positive and negative charges at the interface between the insulating core and SF₆ gas, and further characterized the evolution of charge accumulation under varying voltage amplitudes, pressurization times, and realistic operating conditions. The resulting charge distribution patterns and the underlying mechanisms were elucidated, offering theoretical insights to guide insulation optimization and structural design improvements for UHVDC wall bushing cores.

2. Mathematical Model

2.1. Charge Density Distribution Equation

Within the solid domain, the electric field satisfies Gauss’s law, expressed as follows:

$$\nabla ·\left(-\epsilon ·\nabla \phi \right)=\rho$$

(1)

where ε is the relative permittivity of the material, $\rho$ is the free charge density, C/m³; $\phi$ is the electric potential, V.

According to Ohm’s law, the current density in the core is:

$$J=-\gamma ·\nabla \phi$$

(2)

where $\gamma$ is the surface conductivity, and $J$ is the gas-side current density, A/m².

According to the current continuity equation:

$$\nabla ·J+{\displaystyle \frac{\partial \rho }{\partial t}}=0$$

(3)

The relationship between the current and the charge in material can be obtained by combining (1)–(3) and shown as Equation (4):

$${\displaystyle \frac{\partial \rho }{\partial t}}+{\displaystyle \frac{\gamma }{\epsilon }}\rho -{\displaystyle \frac{\gamma }{\epsilon }}J·\nabla {\displaystyle \frac{\epsilon }{\gamma }}=0$$

(4)

2.2. Accumulation Equation of Gas–Solid Interface Charge

Charge accumulation on the insulating core of a wall bushing can be classified into three primary components: (1) accumulation resulting from gas generation, recombination, migration, and diffusion in the SF₆ atmosphere; (2) volumetric accumulation induced by temperature gradients within the solid insulating material; (3) surface accumulation caused by differences in material properties across the interface. The governing equations for these processes are given as follows:

2.2.1. Weak Ionized Gas Conductance Model

Under DC voltage, positive and negative ions migrate and diffuse in SF₆ gas, generating the ion current density as expressed in Equation (5):

$$J=J^{+}-J^{-}=\left({\mu }^{+}{\rho }^{+}+{\mu }^{-}{\rho }^{-}\right)E-\left(D^{+}\nabla {\rho }^{+}-D^{-}\nabla {\rho }^{-}\right)$$

(5)

where ${\mu }^{+}$ and ${\mu }^{-}$ are the positive and negative ion mobility, m²/(V∙s); ${\rho }^{+}$ and ${\rho }^{-}$ are the positive and negative ion charge density, C/m³; $D$ is the diffusion coefficient, m²/s.

By substituting Equation (3) into Equation (5), the constraint equations for positive and negative ions are obtained (6):

$$\left\{\begin{array}{c}{\displaystyle \frac{\partial {\rho }^{+}}{\partial t}}+{\mu }^{+}E·\nabla {\rho }^{+}+{\mu }^{+}{\rho }^{+}\nabla ·E-D{\nabla }^2{\rho }^{+}=e{\displaystyle \frac{dN}{dt}}-{\displaystyle \frac{k{\rho }^{+}{\rho }^{-}}{e}}\\ {\displaystyle \frac{\partial {\rho }^{-}}{\partial t}}+{\mu }^{-}E·\nabla {\rho }^{-}+{\mu }^{-}{\rho }^{-}\nabla ·E-D{\nabla }^2{\rho }^{-}=e{\displaystyle \frac{dN}{dt}}-{\displaystyle \frac{k{\rho }^{+}{\rho }^{-}}{e}}\end{array}\right.$$

(6)

where $dN/dt$ is the ionization rate, (m³·s)⁻¹; $k$ is the recombination coefficient, m³/s; $e$ is the elementary charge, commonly taken as 1.6 × 10⁻¹⁹ C.

The relationship between the composite coefficient and ion mobility is:

$$k={\displaystyle \frac{\left({\mu }^{+}+{\mu }^{-}\right)e}{\epsilon }}$$

(7)

The ion diffusion coefficient is defined by Einstein’s equation as:

$$D={\displaystyle \frac{\mu k_{B}T}{e}}$$

(8)

where $k_B$ is the Boltzmann constant, commonly taken as 1.38 × 10⁻²³ J/K; T is the temperature, K.

2.2.2. Solid-Side Charge Accumulation Model

Temperature gradients within solid insulating materials induce a nonlinear distribution of core conductivity, resulting in significant charge accumulation within the core. The charge dynamics in solid dielectrics can be described as follows:

$${\displaystyle \frac{\partial \rho }{\partial t}}+\nabla ·\left(\gamma E\right)=0$$

(9)

2.2.3. Surface Charge Accumulation Model

The process of charge accumulation at the gas–solid interface can be expressed as:

$${\displaystyle \frac{\partial \sigma }{\partial t}}=J_1-J_2-\nabla ·\left({\gamma }_s{E}_{\tau }\right)$$

(10)

$${\gamma }_s=\gamma ·∆L$$

(11)

where $J_1$ and $J_2$ are the normal current densities on the solid side and gas side, respectively, ${\gamma }_s$ is the surface conductivity, and $E_{\tau }$ is the tangential electric field strength.

2.3. Boundary Conditions

Under positive voltage, the current originates from the surface of the high-voltage conductor rod and from specific regions of the insulating surface:

$$U_h=U$$

(12)

$$n^{+}=0$$

(13)

$$\nabla ·n^{-}=0$$

(14)

The points where current enters the grounded shielding side and the insulated surface are as follows:

$$U_g=0$$

(15)

$$n^{-}=0$$

(16)

$$\nabla ·n^{+}=0$$

(17)

2.4. Parameters of the Simulation

The simulation parameters and the corresponding values are shown in

Table 1. Simulation parameters.

Parameters	Value
$k [{\mathrm{c}\mathrm{m}}^3/\mathrm{s}]$	${2.7\times 10}^{-7}$
${\mu }^{+} [{\mathrm{c}\mathrm{m}}^2/(\mathrm{V}·\mathrm{s}\left)\right]$	${7.5\times 10}^{-2}$
${\mu }^{-} [{\mathrm{c}\mathrm{m}}^2/(\mathrm{V}·\mathrm{s}\left)\right]$	${7.5\times 10}^{-2}$
$D^{+} [{\mathrm{c}\mathrm{m}}^2/\mathrm{s}]$	${2.1\times 10}^{-3}$
$D^{-} [{\mathrm{c}\mathrm{m}}^2/\mathrm{s}]$	${2.1\times 10}^{-3}$
${\gamma }_s \left[\mathrm{S}\right]$	${1.0\times 10}^{-17}$
${\gamma }_v [\mathrm{S}/\mathrm{m}]$	${2.3\times 10}^{-16}$

.

3. Simulation Analysis

3.1. Electrostatic Field Simulation of an 800 kV Wall Bushing

This section uses COMSOL Multiphysics to model and simulate an 800 kV DC wall bushing. The 2D plan view of the bushing is shown in Figure 1. The central current-carrying conductor is made of copper and has a total length of 21.25 m. The inner insulation system consists of SF₆ gas and an epoxy-impregnated paper core with a total length of 11.61 m. The core includes multiple layers of aluminum-foil shielding to ensure a uniform electric field distribution within the core. According to IEC 62199-2004 [25], the long-term withstand voltage for ±800 kV DC wall bushings is 880 kV. Therefore, the electromagnetic field module in COMSOL was used to simulate the steady-state operating condition of the DC wall bushing, yielding the potential and electric field distributions under stable operation.

Figure 2 shows the overall potential and electric field strength distributions during the steady-state operation of the wall bushing. In Figure 2a, the equipotential lines within the SF₆ gas are nearly parallel to the bushing’s axial direction. Near the SF₆-sheath interface adjacent to the equalizing ring, the equipotential lines are almost perpendicular to the interface. Figure 2b presents the overall electric field distribution, while Figure 3 and Figure 4 illustrate the electric field at the gas–solid interface and the radial electric field distribution of the core, respectively.

Figure 3 shows the electric field distribution at the interface between SF₆ gas and the insulating core, exhibiting an oscillatory decreasing trend along the indicated direction. The inclination angle of the gas–solid interface is machined according to the configuration of the embedded aluminum foils. The proximity of the foil ends to the gas–solid interface edge results in localized enhancement of the electric field in these regions. This interaction gives rise to periodic fluctuations in the electric field strength along the interface, corresponding to the axial locations of the foil terminations. Figure 4 illustrates the core’s radial electric field distribution, which follows a U-shaped trend, with higher field strength near the zero-layer electrode compared to the grounded electrode.

3.2. Scaled Model of the Core of a DC Wall Bushing

During prolonged DC operation, the electric field in a DC bushing transitions from a capacitive to a resistive state. This transition involves charge accumulation at the gas–solid interface of the bushing core. Such accumulation modifies the DC electric field distribution in the bushing core under steady-state conditions, resulting in field distortion and potentially compromising the long-term reliability of the bushing. To examine charge distribution at the gas–solid interface of the bushing core under prolonged DC voltage, a scaled model of the ±800 kV wall-penetrating insulation core was developed, as shown in Figure 5, serving as the primary subject of this study. A simulation model describing charge accumulation at the gas–solid interface was established to analyze the charge distribution under DC voltage. This approach simplifies the simulation process, reduced computational complexity, and provides guidance for core design optimization.

Figure 6 and Figure 7 show the electric field distribution at the gas–solid interface and the radial electric field of the core in the scaled model. These distributions are consistent with the trends observed during long-term operation of the 800 kV wall bushing, indicating that the scaled model accurately represents the behavior of the actual bushing.

4. Discussion

To better understand the charge accumulation characteristics under DC stress, the charge density distributions at the gas–solid interface of the bushing core were analyzed. The following figures illustrate how the spatial charge patterns evolve under steady-state conditions.

Figure 8 shows charge accumulation at the gas–solid interface of the scaled model upon reaching saturation. On the core’s inclined surface, positive and negative charges are alternately distributed, following the same pattern as the electric field at the core interface. As the voltage application time increases, the surface charge density on the core rises accordingly. After 480 min of voltage application, the charge accumulation stabilizes. Figure 9 illustrates the influence of the three dominant currents on charge accumulation at the core’s gas–solid interface during long-term operation. Among these, the currents on the solid and gas sides of the interface have a minor effect on charge accumulation, whereas the primary factor influencing charge accumulation is the core’s surface current.

Figure 10 presents the charge distribution on the vertical surface of the core’s gas–solid interface in the scaled model. Similarly, after 480 min of voltage application, charge accumulation stabilizes. At the core’s corner, the accumulated charge reaches a maximum negative charge density of −1.28 × 10⁻⁵ C/m². Just below the corner, the accumulated charge reaches a maximum of 1.5 × 10⁻⁵ C/m², with a corresponding maximum electric field strength of 0.8 kV/mm at this location on the core’s gas–solid interface. This indicates that the vicinity of the core corner represents a weak insulation region, where charge accumulation increases the electric field and induces field distortion, thereby compromising the core’s insulation performance. On the core interface, the accumulated charge at the gas–solid interface gradually decreases from its maximum value toward the flange, with a small amount of negative charge remaining near the flange.

4.1. Different Voltage Levels

Figure 11 shows the stabilized charge accumulation on the central conductor of the scaled model core under applied voltages of 10 kV, 20 kV, 30 kV, and 40 kV. The applied voltages do not alter the charge distribution trend at the interface, but they affect the magnitude of accumulated charge. As the voltage level rises, the accumulated charge increases monotonically. Figure 12 illustrates the relationship between the maximum charge density and the applied voltage.

4.2. Different Voltage Application Times

As shown in Figure 13, the charge accumulation on the gas–solid interface increases with exposure time. However, prolonging the exposure does not change the overall charge distribution on the interface. At 480 min, the charge accumulation at the gas–solid interface reaches saturation. As the voltage application continues, the rate of charge accumulation at the interface gradually slows. However, at 600 min, the maximum charge density decreases slightly by about 2%, from 1.5 × 10⁻⁵ C/m² to 1.47 × 10⁻⁵ C/m², and continues to decrease thereafter. This indicates that as charge accumulation increases at the gas–solid interface, the induced electric field generated by the accumulated charge gradually strengthens and begins to counteract the externally applied DC field. As the induced field continues to intensify, the superposition of the two fields partially cancels the externally applied field, thereby weakening the driving force for further charge migration and deposition. Nevertheless, the inhibitory effect is minor and insufficient to eliminate insulation defects caused by high charge accumulation at this location.

4.3. Actual Operating Conditions

Under actual operating conditions, DC wall bushings not only withstand DC voltage but also experience thermal effects from the DC current flowing through the central conductor. The heat primarily consists of two components: Joule heat generated by the central conductor and dielectric loss in the insulating material. However, compared with the Joule heat from the central conductor, the dielectric loss in the insulating material is negligible. Therefore, the heat generated during bushing operation is essentially the Joule heat produced by the current-carrying conductor [26,27,28,29], calculated using Equation (18):

$$P={\displaystyle \frac{I^2\rho l}{\pi \left(r_1^2-r_2^2\right)}}$$

(18)

where $I$ is the current flowing through the central conductor, A; $\rho$ is the resistivity of the current-carrying conductor, Ω/m; l is the length of the current-carrying conductor, m; r₁ and r₂ are the outer and inner diameters of the current-carrying conductor, m.

Therefore, according to Equation (18), the Joule heat generated by the ±800 kV ultra-high-voltage wall bushing under a 5454 A DC current can be calculated. Simulations indicate that the maximum core temperature under normal operating conditions reaches 90.6 °C [2]. To simulate the bushing’s temperature distribution during actual operation in a scaled model, a thermal power of 1 W was applied to the current-carrying conductor. Since both the volume and surface conductivities of the core material depend on temperature, they were fitted using the Ockhlin-Nius equation [19,30]:

$$k_v={\displaystyle \frac{1}{4.74\times {10}^6\exp \left(\frac{5826}{T}\right)}}$$

(19)

$$k_s={\displaystyle \frac{1}{1.38\times {10}^9\exp \left(\frac{4278}{T}\right)}}$$

(20)

Figure 14 shows the charge distribution at the core’s gas–solid interface after charge accumulation stabilizes under actual operating conditions. The temperature gradient causes discontinuities in the core’s bulk conductivity, leading to bulk charge accumulation and increased bulk current density. Consequently, at this temperature, the charge density at the tubular core’s gas–solid interface exceeds the room-temperature peak, while the maximum charge density decreases to 1.39 × 10⁻⁵ C/m². On the core’s inclined surface, the charge distribution still alternates between positive and negative charges at the same frequency as at room temperature, indicating that the overall distribution trend remains largely unchanged. However, the peak values of positive charges increased by approximately 35%, while those of negative charges rose by about 45%, indicating a significant aggravation of interfacial charge accumulation. On the vertical surface, unlike at room temperature, the maximum charge density occurs at the core interface corner, followed by a gradual decrease in positive charge accumulation and a localized accumulation of negative charge near the flange.

5. Conclusions

This paper presents a scaled model of the ±800 kV ultra-high-voltage direct-current wall bushing core, based on its radial electric field and the electric field distribution at the gas–solid interface. An electrothermal coupled mathematical model of the scaled core is constructed to analyze the electric field and charge distribution characteristics at the gas–solid interface under various conditions. The main conclusions are summarized as follows:

• On the inclined surface of the gas–solid interface in the scaled-down core model, accumulated charges alternate between positive and negative. The maximum charge density, 1.5 × 10⁻⁵ C/m², occurs near the core corner, where the electric field strength is also highest. Consequently, the vicinity of the core corner represents a weak insulation region on the gas–solid interface, where insulation failures, including partial discharges caused by electric field distortion, are likely to occur. This region requires enhanced insulation optimization. Near the flange, the interface predominantly accumulates negative charges.
• Charge accumulation increases with rising voltage levels. Under a 20 kV positive voltage, charge accumulation stabilizes after 480 min. However, as the voltage application continues, the overall charge distribution remains unchanged, while the maximum charge density begins to decrease after 480 min. The charge density in this region remains the highest.
• Simulating the scaled model at actual operating conditions, specifically at 90 °C, induces temperature gradients within the core. These gradients create discontinuities in the core’s bulk conductivity, resulting in bulk charge accumulation. Charges on the core’s inclined surface continue to alternate between positive and negative, maintaining a distribution trend consistent with room temperature. However, the peak charge density on the inclined surface increases, whereas the maximum charge density on the vertical surface decreases to 1.39 × 10⁻⁵ C/m², occurring at the core corner. Under actual operating conditions, charge accumulation at the core’s gas–solid interface becomes more pronounced, with the peak charge density increasing by approximately 40% relative to room temperature.