Differential Investigation of the Internal Electric Field Distribution in Gas-Insulated Switchgear Based on Different Nanomaterials (https://doi.org/10.63386/620101)

Yueyao Wu¹*

¹                   China Three Gorges University, No. 8 University Road, Xiling District, Yichang City 443002, Hubei province, China; 202210120704@ctgu.edu.cn

*                  Correspondence: 202210120704@ctgu.edu.cn; Tel: +86 15907930136

Abstract: Gas Insulated Switchgear (GIS) is a core component of the power grid. Internal metal particles can cause electric field distortion and partial discharge, severely affecting operational reliability. Mixing nanoparticles with SF₆ gas can effectively enhance insulation. This study investigates the influence of nanoparticles of different materials on the distorted electric fields induced by metal particles with different geometric shapes and spatial positions inside GIS. A three-dimensional finite element model was developed in COMSOL Multiphysics, incorporating key GIS components such as basin-type insulators, central conductor rods, and enclosures.Set the dimensions of each component and environmental parameters such as SF₆ gas and nanoparticle concentration. Using the professional simulation tool COMSOL, the electric field distribution was solved by setting the voltage of the central conductor rod and defining the boundary conditions of the bushing and insulator. This study systematically evaluates how nanoparticle materials regulate the electric field distortion induced by different scenarios within the GIS cavity. Quantitative analysis shows that the composition of nanoparticles has a relatively small difference in the degree of influence on the distorted electric field under the same conditions. Compared with the distorted electric field caused by spherical metal particles, nanoparticles exhibit better insulation performance for the distorted electric field induced by conica metal particles, with a potential drop of approximately 45% at the distorted position. As the distance between the metal particles and the conductor rod decreases, the electric field homogenization and insulation enhancement effects of the nanoparticles gradually increase.

Keywords: Gas-Insulated Switchgear; Electric field distribution; Nanoparticles; Material Differences; Influence of Geometric Shapes; Influence of Spatial Positions

1. Introduction

Gas-insulated switchgear (GIS), a critical component in power grids, is prone to electric field distortion and partial discharge due to metallic particle contamination, which compromises operational reliability[1-2]. However, in the past decade, GIS has frequently experienced abnormal surface discharge faults of insulators during operation[3]. The surface discharge of GIS can be induced by various defects[4]. Insulation surface defects are common factors, as they can change the electric field distribution and trigger partial discharges[5]. The discharge of micro metal particles on the insulator surface is also generally regarded as one of the triggers for GIS surface discharge 6]. Therefore, a large number of studies have been carried out on the partial discharge characteristics of micro metal particles on the GIS insulator surface in the past [7-9].However, the main research directions in the past decade have included not only traditional metallic particle defects but also a new direction of nano-dielectric material modulation [10-11].

Recent studies have shown that nanoparticles such as SiO₂ and Al₂O₃ can homogenize the electric field and suppress the development of discharge through the interfacial polarization effect and charge trapping mechanism [12]. Li Jian et al. conducted a detailed study on the influence of nano-Al₂O₃ particles on the power frequency breakdown voltage of SF₆, and found that there exists an optimum filling ratio. The study focused on analyzing the impact of the “interface region” formed at the nano-particle-gas interface on charge trapping and electric field distortion, and explored that the interface effect is the key mechanism for performance enhancement [13]. Liao Ruijin et al. systematically summarized the research progress on interface effects in nano-dielectrics. They elaborated in detail on the physical and chemical properties of the interface region, the formation and role of interface traps (charge trapping, conductance suppression), the interface polarization mechanism, and the influence of these effects on the electrical properties of materials, providing a comprehensive theoretical framework for understanding the core mechanism of nano-modified SF₆ [14]. Chen Wei et al. directly studied the enhancement effect of nano-SiO₂ on the power frequency and lightning impulse breakdown voltage of SF₆ under extremely non-uniform electric fields such as needle-plate electrodes. They analyzed how nanoparticles inhibit the initial discharge in high-field regions and hinder the continuous development of discharge channels by adsorbing free electrons and forming space charge barriers, thereby improving the uniformity of the electric field distribution in the entire gap and significantly enhancing the insulation strength [15].

Although previous studies have clarified the key aspects of the modulating effect of nanoparticles on the partial discharge characteristics of tiny metal particles on the surface of GIS insulators, there are still some deficiencies in the existing research, especially the lack of research on the degree of influence of nanoparticles on the electric field when there are irregular metal particle geometric shapes and non-uniform particle distribution.

(1) Considering the actual manufacturing conditions, the nanomaterial used is typically not of a single type, so it is necessary to explore the effects of nanoparticles of different materials on the distorted electric field in GIS.

(2) The particles causing discharge in GIS are not necessarily regular, and the size of metal particles is usually submillimeter-scale and millimeter-scale. It is necessary to investigate the influence of nanoparticles on the distorted electric field caused by particles of different shapes.

(3) Metal particles at different spatial positions in GIS have different distortion effects on the electric field, so it is essential to explore the effects of nanoparticles on the distorted electric field caused by particles at different spatial positions.

Based on the above studies, this paper establishes a three-dimensional model of 110 kV voltage class GIS, and uses COMSOL simulation software to explore the influence laws of three different materials of nanoparticles on the distorted electric fields induced by metal particle models with three different shapes and spatial positions in GIS. The influence laws of nanoparticles on the partial discharge characteristics caused by the geometric shapes and spatial positions of tiny metal particles on the surface of GIS insulators are revealed, and feasible methods for suppressing GIS partial discharge faults caused by metal particles are proposed. This provides reasonable guidance for solving GIS discharge faults in the future.

2. Materials and Methods

2.1. Computational model

In this paper, a GIS simulation model was established by using three-dimensional drawing software. See Figure 1. In Figure 1, the GIS is composed of basin-type insulators, central conducting rods, outer shells, etc. The space between the outer shell and the central conductor is filled with SF6 gas. The radius of the basin-type insulator is 185 mm, the radius of the central conducting rod is 50 mm, the thickness is 5 mm, and the radius of the outer shell is 215 mm.

Figure 1. GIS Geometric Model.

2.2. Particle model

Metal particles in GIS are usually generated due to the friction of metal components. Under the action of electric field force, these particles will cause electric field distortion and partial discharge in GIS, thus affecting the normal operation of GIS. In this paper, materials such as copper is used to create three types of metal particles as shown in the figure.1.

Figure 2. Metal Particle Modeling: (a) Spherical; (b) Cylindrical; (c) Conical.

Meanwhile, in this paper, 5% of 50 nm-sized Al₂O₃ (εᵣ=9.0), TiO₂ (εᵣ=10), and SiO₂ (εᵣ=3.9) nanoparticles will be filled in the distorted electric field induced by copper particles.

2.3. Computational method

The electrostatic field distribution was numerically solved using the Laplace equation under Dirichlet boundary conditions in the space within the GIS cavity. During the operation process, the load applied to the central conducting rod is the power frequency voltage, the casing serves as the solution boundary, and the internal space within the insulator is taken as the solution region.

The solution to electrostatic field problems is the process of solving Poisson’s equation or Laplace’s equation under given conditions. In this paper, the electric potential  in the electrostatic field to be solved satisfies Laplace’s equation:

In the equation,  is the Laplace operator， is the vacuum permittivity， is the relative permittivity.

According to the uniqueness theorem of electrostatic fields, the interface between nanoparticles and SF₆ gas must satisfy the polarization charge condition:

(2)

whereis the polarization charge density at the interface,  and  are the relative permittivities of nanoparticles and SF₆, respectively. Given, the equation simplifies:

(3)

This reveals that the polarization charge density is proportional to the permittivity difference between nanoparticles and SF₆, governing the electric field homogenization mechanism.

According to the uniqueness theorem of electrostatic fields, on the premise that the electric potential  satisfies Laplace’s equation, on the interface between different media, it is required to satisfy the interface connection condition formula (4), and on the boundary of the solution domain, it is required to satisfy the given boundary condition formula (5):

In the equation,  and  are the electric potentials on both sides of the interface, n represents the normal direction,  and  are the dielectric constants of the dielectrics on both sides.

In the equation,  represents the electric potential of the field point in the space.  is on the conductor side, with a voltage  applied, and  represents the grounding of the casing boundary.

By solving Equations (1), (4), and (5), the potential distribution function  in the space can be obtained. And the relationship between the electric field intensity E and the potential function  is shown in Equation (4) as follows:

In the equation,  represents the electric field intensity in the space, with the unit of V/m.

The spatial electric field solution can be equivalently formulated as a variational problem to minimize the functiona :

In the equation,  represents the solution domain,  denotes the electric potential of the field point in the space, and  is the boundary on the conductor side.

3. Results

3.1. Electric field distribution in the absence of defects

Figure 3 shows the electric field distribution of GIS when there are no defects under normal conditions. During normal operation, the electric field distribution is circular and uniform, and the electric field lines extend outward in a radial pattern. The electric field intensity near the central conductor can reach up to 1.77×10⁶ V/m. The farther away from the central conductor, the lower the electric field intensity, and the rate of decrease of the electric field intensity slows down. When approaching the outer shell, the electric field begins to increase.

Figure 4 shows the potential distribution at the insulator when there are no defects under normal conditions. The potential is highest at the central part of the insulator, close to 2.2×10⁵ V. From the center outward, it shows a concentric – circular distribution pattern, indicating that the potential decreases gradually along the radial direction on the insulator plane. In the region near the center, the color changes more dramatically, while in the region far away from the center, the color changes are relatively gentle. The potential is lowest in the outermost region.

At the position of the central conductor, due to the high voltage of the conductor, there is a large voltage drop in the surrounding insulating gas, thus showing that the electric field intensity is the largest at the central conductor. Near the outer shell, since the outer shell is grounded and has a potential of 0, a relatively large voltage drop occurs near the outer shell, resulting in an increase in the electric field intensity. In GIS, the center of the insulator is connected to the high – potential conductor, and the high potential is concentrated in the central region. In the region near the center, the potential gradient in this region is large, that is, the potential change rate is high. However, in the region far away from the center, the potential gradient in this region is small, and the potential change rate is low. The GIS outer shell is grounded with a potential of 0, so a negative potential value appears at the edge of the insulator.

Figure 3. Electric field distribution in the defect-free GIS configuration.

Figure 4. Potential Distribution without Defects.

3.2.Effects of Nanoparticles of Different Materials on Electric Field Distortion Induced by Defects

Fig. 5 (a) shows the electric field distribution in the presence of spherical copper particle defects before adding Al₂O₃ nanoparticles. The central part of the insulator still has a relatively high-strength electric field, indicating a large electric field intensity. This is similar to the electric field distribution without defects, suggesting that the high voltage of the central conductor still dominates the electric field distribution. In the figure, there is a distinct dark red area representing the region with higher electric field strength, which corresponds to the position of the copper particles. The presence of copper particles leads to a significant increase in the local electric field strength, forming an electric field distortion region. Electric field lines near the copper particles are obviously bent and concentrated. When approaching the copper particles, the initially uniformly radiating electric field lines converge toward the copper particles, demonstrating the attractive effect of the copper particles on the electric field lines. This is because the copper particles, as conductors, alter the surrounding electric field distribution, causing the electric field lines to concentrate on their surface. The maximum electric field occurs on the particles, with a value of 2.8×10⁷ V/m, and the minimum electric field strength appears in the radial direction far from the center, with a similar order of magnitude. The most likely positions for electrical breakdown are between the particles and the conductor.

Fig. 5 (b) shows the electric field distribution after adding Al₂O₃ nanoparticles to the distorted electric field with spherical copper particle defects. After addition, it can be observed that the overall field strength decreases, the variation of field strength becomes more uniform, the field strength in the electric field distortion region is significantly reduced, changing from dark red to red and orange, and the distortion region shrinks. This is because when the copper particles cause electric field distortion, polarization charges with opposite polarity to the charges of the copper particles are induced on the surface of the nanoparticles (for example, if the copper is positively charged, the surface of the nanoparticles is negatively charged). These polarization charges form a reverse electric field, directly counteracting the charge aggregation effect on the surface of the copper particles, thereby reducing the local field strength. Meanwhile, the high dielectric constant of the nanoparticles makes the internal electric field strength much lower than that of the SF₆ gas, so the nanoparticles form a low-field-strength buffer layer around the copper particles, hindering the further concentration of electric field lines and changing the field strength gradient from “abrupt drop” to “gentle transition”. It can also be seen from the potential distributions in Figs. 6 (a) and (b) that due to the presence of copper particles and the bending of electric field lines, at the same radius, the potential at the particle position is lower, and the electric field strength between the particles and the conductor increases, making electrical breakdown more likely to occur. When nanoparticles are added, the potential distribution shows gentle variation in concentric circles, and the potential at the particle position is improved, decreasing to 1.9×10⁷ V/m, a decrease of about 33%. This means that adding a certain concentration of nanoparticles to the insulating gas will increase the power frequency breakdown voltage and improve the insulation performance of the gas.

Figure 5. Electric field distortion caused by copper particles before and after adding Al₂O₃ nanoparticles

Figure 6. The potential distortion caused by copper particles before and after adding Al₂O₃ nanoparticles

Figs. 7(a) and 7(b) show the electric field and potential distributions after adding TiO₂ nanoparticles to the distorted electric field induced by copper particles. After adding TiO₂ nanoparticles, the electric potential decreases to 1.97×10⁷ V/m, a decrease of about 30%. Figs. 7(c) and 7(d) show the electric field and potential distributions after adding SiO₂ nanoparticles to the distorted electric field induced by copper ions. After adding SiO₂ nanoparticles, the electric potential decreases to 2.1×10⁷ V/m, a decrease of about 26%. In terms of the distribution of electric potential and field, the electric field homogenization effect is similar to that when Al₂O₃ nanoparticles are added, mainly because:

(1) Although the εᵣ of TiO₂ (εᵣ=10), Al₂O₃ (εᵣ=9.0), and SiO₂ (εᵣ=3.9) are different, the εᵣ of SF₆ is ≈1, and the formula is simplified to be proportional to (). However, the high specific surface area effect of nanoparticles makes the interface area dominate the polarization contribution, offsetting the difference in εᵣ.

(2) The surfaces of Al₂O₃, TiO₂, and SiO₂ all contain hydroxyl (-OH) groups, forming deep trap energy levels that capture free electrons to suppress discharge.

(3) In the simulation, the concentration, particle size, and dispersibility of the three types of nanoparticles are the same, excluding the interference of non-material factors. When the concentration and size are the same, the influence of the dielectric constant on the electric field strength accounts for <15%, and the interfacial effect accounts for >85%.

Because the effects of the three particles on homogenizing the distorted electric field are similar, Al₂O₃ nanoparticles are selected for subsequent research below.

Figure 7. The electric field and potential distortion caused by copper particles after adding TiO₂/SiO₂ nanoparticles.

3.3. Effects of Nanoparticles on Distorted Electric Fields Induced by Metal Particles with Different Shapes

Fig. 8 (a) shows the distortion effect of cylindrical copper metal particles on the spatial electric field. Similar to spherical particles, the electric field lines bend at the particle position, forming an elliptical-like high electric field region. The value can reach up to 1.02×10⁸ V/m, which is higher than the electric field strength formed by spherical particles. The potential distribution is shown in Fig. 9 (a). The form of electric field distortion is similar to that of spherical particles, but the amplitude of potential distortion is smaller than that of spherical particles. This is because the cylindrical particles are placed radially, and the bending degree of electric field lines is smaller than that of spherical particles. However, due to the higher order of magnitude of the electric field strength, cylindrical particles are more likely to experience electrical breakdown.

Fig. 8 (b) shows the electric field distribution after adding Al₂O₃ nanoparticles to the distorted electric field with spherical-cylindrical copper particle defects. It can be seen that the overall spatial electric field strength decreases, and the distribution becomes more uniform. The field strength in the electric field distortion region changes from dark red to red and orange, and the distortion region is significantly reduced. Fig. 9 (b) shows that the concentric circles of the potential distribution change more gently, and the potential at the particle position is improved more significantly, decreasing to 0.65×10⁸ V/m, a decrease of about 36%. The results show that nanoparticles can effectively reduce the electric field strength gradient in the distorted electric field caused by cylindrical particles, and the influence effect is stronger than that in the distorted electric field caused by spherical particles.

Figure 8. The electric field distortion caused by cylindrical copper particles before and after adding Al₂O₃ nanoparticles

Figure 9. The potential distortion caused by cylindrical copper particles before and after adding Al₂O₃ nanoparticles

Fig. 10 (a) shows the distortion effect of conical copper metal particles with sharp tips on the electric field. This effect is similar to that of cylindrical particles, forming an elliptical high-field-strength region around the particles, with values even higher than those of cylindrical defects, reaching 3.98×10⁸ V/m. For conical, cylindrical, and spherical particles, the region with the lowest field strength is in the radial direction away from the center, and the value is relatively large. Fig. 11 (a) shows the influence of conical defects on the potential distribution. Its variation trend is the same as the former two, that is, the field strength decreases radially. Based on the above analysis, particles with sharp tips cause the most severe electric field distortion and have the maximum electric field strength, making electrical breakdown more likely to occur. Compared with the baseline electric field strength (1.77×10⁶ V/m), the conical particles induce a 225% amplification at their tips, which is derived from local COMSOL simulations.

Fig. 10 (b) shows the electric field distribution after adding Al₂O₃ nanoparticles to the distorted electric field with conical copper particle defects featuring sharp tips. It can be seen that the overall spatial electric field strength also decreases at this time, with a more uniform distribution. The field strength in the electric field distortion region changes from dark red to orange-red and orange, and the distortion region shrinks the most in proportion. Fig. 11 (b) shows that the concentric circles of the potential distribution change more gently, approaching the normal electric field without defects, and the potential at the particle position decreases to 2.1×10⁸ V/m, a decrease of about 45%. Al₂O₃ nanoparticles form a dielectric shielding layer (thickness ≈200 nm) near the tips, reducing the local field strength through Maxwell-Wagner polarization. The results show that nanoparticles have the best effect of homogenizing the electric field and enhancing insulation in the distorted electric field caused by tip-shaped conical particles, with a stronger influence than that in the distorted electric field caused by cylindrical particles. Therefore, conical copper particles are selected for the study of position changes.

Figure 10. Electric field distortion caused by conical copper particles before and after adding Al₂O₃ nanoparticles

Figure 11. Potential distortion caused by conical copper particles before and after adding Al₂O₃ nanoparticles

3.4. Effects of Nanoparticles on Distorted Electric Fields Induced by Metal Particles at Different Spatial Positions

Figure 12. The electric field distortion before and after adding Al₂O₃ nanoparticles when conical copper particles are far away from the central conductor, located in the middle between the central conductor and the electric field boundary, or close to the central conductor.

By placing conical copper particles at three different positions away from the central conductor rod, three different distorted electric field diagrams can be obtained, as shown in Figs. 12 (a), (c), and (e). Observing Fig. 12 (a), it is found that when the copper particles are far from the central conductor, the electric field distortion region and intensity are the smallest. This is because the electric field strength around the central conductor decreases significantly with the increase of distance. When the copper particles are far from the conductor, the “base electric field” at their position is inherently weak, and even if the copper particles have a tip shape, it is difficult to induce strong electric field distortion in the weak electric field. When observing 12 (e) where the copper particles are close to the central conductor, the electric field distortion region and intensity are the largest. This is because the “base electric field” near the central conductor is extremely strong, and the tips of the copper particles will produce a significant “tip effect” in the strong electric field. The surface of the copper particles will accumulate more charges due to electrostatic induction, and the charge density at the tip is extremely high, further exacerbating the electric field distortion, expanding the distortion region and enhancing the intensity.

At this time, adding Al₂O₃ nanoparticles to the three distorted electric fields respectively can obtain three different electric field diagrams, as shown in Figs. 12 (b), (d), and (f). By comparing the three electric field diagrams, it can be seen that when nanoparticles are added when the metal particles are at the far end of the conductor rod, the shrinkage ratio of the distortion region is the smallest, and the electric potential at the particle position decreases to 1.87×10⁸ V/m, a decrease of about 40%. When nanoparticles are added when the metal particles are in the middle between the conductor rod and the boundary, the shrinkage ratio of the distortion region is moderate, and the electric potential at the particle position decreases to 2.74×10⁸ V/m, a decrease of about 48%. When nanoparticles are added when the metal particles are at the proximal end of the conductor rod, the shrinkage ratio of the distortion region is the largest, and the electric potential at the particle position decreases to 3.72×10⁸ V/m, a decrease of about 53%.

Therefore, for the distorted electric field generated when metal particles are close to the central conductor rod, nanoparticles exhibit the best homogenization and insulation enhancement effects. This is because the background electric field strength near the central conductor is extremely high. When metal particles are close, their tip effect overlaps with the strong background field, causing the local field strength to be further amplified to 5-10 times that of the background field. This extremely inhomogeneous electric field provides strong driving conditions for nanoparticles to play their role. Under the strong field, high-density reverse polarization charges are induced on the surface of nanoparticles, maximizing the excitation of their interfacial effect. The reverse electric field formed by these charges can directly counteract the charge accumulation at the tips of metal particles, thereby reducing the local field strength. Meanwhile, the surface of nanoparticles has a large number of deep trap energy levels. When the strong field near the conductor triggers an electron avalanche, these deep traps can efficiently capture high-energy electrons, inhibiting the growth of electron concentration and thus weakening the further distortion of the electric field by space charges.

4. 4. Conclusion

This paper simulated different electric fields using three types of nanoparticles with different materials. By modeling the distorted electric fields induced by metal particles with different shapes and spatial positions in GIS, observing the degree of homogenization of the distorted electric fields and the reduction of field strength at the distorted positions after adding nanoparticles, and summarizing and analyzing the insulation enhancement of SF₆ gas mixed with nanoparticles based on the simulation data, the following conclusions are drawn:

(1) This paper selects three nanomaterials, namely Al₂O₃, TiO₂, and SiO₂ for research. For different nanomaterials, their homogenizing effects on the distorted electric field are similar. Their reduction of the distorted field strength at the same position is consistent, both leading to the decrease of the electric field strength induced by metal particles, thereby reducing the probability of electrical breakdown, which is also the main reason why nanoparticles can be used to avoid flashover.

(2) Through the study of nanoparticles made of different nanomaterials, it was found that under the same conditions, the materials showed little difference in their influence on the homogenization of electric field distortion, with potential drops of approximately 33%, 30%, and 26% respectively. Al₂O₃ nanoparticles were selected as a representative material to explore the influence of distorted electric fields induced by metal particles with different geometric shapes. The results show that nanoparticles have the best effect in homogenizing the electric field and enhancing insulation in the distorted electric field caused by tip-shaped conical metal particles, with a potential drop of about 45%. Their influence on the distorted electric field caused by cylindrical metal particles is moderate, with a potential drop of about 36%. However, their influence is the weakest in the distorted electric field caused by spherical metal particles, with a potential drop of about 33%.

(3) Regarding the influence of nanoparticles on the distorted electric fields induced by metal particles at different spatial positions, when the metal particles causing the distorted electric field are close to the central conductor rod, nanoparticles exhibit the best electric field homogenization and insulation enhancement effects, with a potential drop of approximately 53%. When the metal particles are in the middle between the central conductor rod and the boundary, the influence of nanoparticles is secondary, with a potential drop of about 48%. When the metal particles are far away from the central conductor rod, the influence of nanoparticles is the weakest, with a potential drop of about 40%.

Based on the above conclusions, a nanoparticle concentration gradient can be considered at the junction of the GIS conductor and the insulator. The positive correlation between the polarization charge density and the electric field strength under high field strength is utilized to enhance the local field strength suppression effect.

Data Availability Statement: The raw data supporting the conclusions of this article will be made available by the authors on request.

Acknowledgments: I sincerely thank my tutor and classmates for their help in writing this article.

Conflicts of Interest: The authors declare no conflicts of interest.

Abbreviations

The following abbreviations are used in this manuscript:

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