Effect of Aged Nonlinear Resistive Field Grading Material on Electric Field Distribution of DC Cone Spacer

<jats:p>Nonlinear resistive field grading materials are widely used in the electrical and electronic applications, and are usually researched based on the initial nonlinear conductivity characteristics of synthetic materials. However, the long-term stability of these materials are rarely reported. In this paper, the effects of thermal ageing on nonlinear resistive field grading material and the electric field distribution of DC cone spacers are studied. The 30 wt.% SiC/epoxy micro-composites are prepared and are thermally aged at 180 °C for 1080 h. The infrared spectroscopy, dielectric properties, breakdown strength and nonlinear conductivity are measured, respectively. In addition, a simulation model for a cone spacer is built, and the electric field and power dissipation density are calculated. With the increasing thermal ageing time, the relative permittivity and loss tangent increase, and the breakdown strength decreases. Besides, the nonlinear coefficient of nonlinear conductivity almost increases, and the switching electric field of nonlinear conductivity decreases. Simulation results show that the aged micro-composites can homogenize the electric field in the cone spacer, but the thermal ageing causes the increase in power dissipation density and threatens the safe operation of the cone spacer.</jats:p>

section_content: Spacers are widely used in HVDC gas-insulated substations (GIS) [1], and its operating stability is threatened by the surface-charge accumulation [2]. The charge accumulated on the cone spacer can distort the electric field along the spacer's surface and cause the decrease in flashover voltage [3]. 

Nonlinear resistive field grading material (NRFGM) is able to homogenize the electric field and suppress the charge accumulation in the bulk or on the surface due to its nonlinear conductivity [4], so it provides an effective way to solve the spacer's surface charge accumulation. The NRFGM is usually composed of polymer matrix, (e. g., epoxy resin and silicon rubber) and semi-conducting filler (e. g., silicon carbide (SiC) and zinc oxide (ZnO)) with an appropriate filler loading [5] [6] [7], and it is widely used in cable accessory [8] and motor end [9], etc. The nonlinear coefficient and switching electric field are two key parameters of this kind of material, which are affected by many factors, such as filler type, filler particle size and filler loading. For example, when the filler loading is the same, the nonlinear coefficient of the SiC-based NRFGM is much smaller than that of ZnO-based NRFGM [10]. The nonlinear conductivity of SiC/epoxy micro-composites increases with the SiC particle size [11]. For example, Tian et al. reported that the greater filler size increases the nonlinear coefficient of NRFGM [12]. Yang et al. found that a smaller filler size can increase the switching electric field of NRFGM [13]. Moreover, it is only when the filler loading is sufficiently high that the SiC-or ZnO-based NRFGMs show distinct nonlinear conductivity. For instance, Du et al. showed that the DC conductivity of SiC-based NRFGM behaves in a field-dependent manner only when the filler loading exceeds 30 wt. % [14]. Yang et al. found that the ZnO-based NRFGM shows nonlinear conductivity characteristics only when the filler loading is more than 33 vol% [15]. 

However, almost all of the studies focus on the initial nonlinear conductivity characteristics after the preparation of NRFGM, and there are few reports on the long-term stability of NRFGM, which affects the insulation reliability and operating safety of electrical equipment. In this paper, we aim to study the effects of thermal ageing on NRFGM and the electric field distribution of cone spacer. The 30 wt. % SiC/epoxy micro-composites are prepared and are thermally aged at 180 • C for 1080 h. The infrared spectroscopy, dielectric properties, breakdown strength and nonlinear conductivity of aged SiC/epoxy microcomposites are studied. In addition, a two-dimension axisymmetric simulation model for a cone spacer is built. The electric field distribution and power dissipation density of the cone spacer are discussed based on the aged SiC/epoxy micro-composites and pure epoxy, respectively.
section_name: Introduction

section_name: Experimental Materials and Methods

section_content: A bisphenol-A epoxy resin (E51) was used to prepare an epoxy matrix with the methyl tetrahydrophthalic anhydride (MTHPA) as curing agent and the tris (dimethylaminomethyl) phenol (DMP-30) as accelerator. The ratio of epoxy resin to curing agent and accelerator was 100:80:1. Commercial SiC powder was used as filler with an average diameter of 23 µm. The filler loading was 30 wt. %. In addition, nano silica (SiO 2 ) was used to prevent the sediment of SiC filler. The weight ratio of epoxy resin to nano SiO 2 was 100:4. The SiC/epoxy micro-composite was prepared as follows. Firstly, the micro-SiC was mechanically mixed with nano-SiO 2, and then was electrically stirred with epoxy matrix at 60 • C for 20 min. After degassing, the mixture of composites was poured into the mold. It was cured at 80 • C for 4 h and was post-cured at 120 • C for 8 h. Finally, the sample with a thickness of 0. 4 mm was obtained.
section_name: Material Preparation

section_content: The thermal ageing of SiC/epoxy micro-composites was carried out at 180 • C for 0, 72, 168, 360, 720 and 1080 h, respectively. In each ageing cycle, a set number of ageing samples were taken out to investigate the effects of thermal ageing time on the composites.
section_name: Thermal Ageing Experiment

section_content: The reflectance spectra of aged samples was scanned by the FTIR-6100 Instrument with a resolution of 2 cm -1. The scanning range of wavenumber was from 400 to 4000 cm -1.
section_name: Fourier Transform Infrared Spectroscopy (FTIR) Measurement

section_content: Novocontrol Concept 80 was used to measure the relative permittivity and loss tangent of aged micro-composites under 0. 1 and 50 Hz, respectively. The diameter of the measurement electrode was 25 mm. The applied AC voltage amplitude was 1 V. The test temperature was 25 ± 1 • C. One of the three measurements for each sample is presented.
section_name: Relative Permittivity and Loss Tangent Measurement

section_content: A DC breakdown test device with a maximum output of 60 kV was used to measure the DC breakdown strength of aged samples at 25 ± 1 • C. The sample was placed between two ball electrodes of 25 mm in diameter. In order to prevent surface flashover, the whole electrode system was immersed in silicon oil [16]. During the measurement, the voltage was applied to the sample at an increasing rate of 1 kV/mm until the breakdown occurs. The measurement was performed ten times for each aged composite.
section_name: Breakdown Strength Measurement

section_content: The relationship between current density and applied electric field of aged microcomposites was measured by a three-electrode test system [5] with a high voltage DC power supply (Hb-z203-2ac model) and a pico-ammeter (EST122 model) at 25 ± 1 • C. The measurement electrode was 25 mm in diameter. The current flowing through the sample was close to steady state and was recorded when the DC voltage was applied to the sample for 20 min. Considering the geometry of the sample, the current density and DC conductivity were then obtained. Three measurements were performed for each sample, and one of the measurement results for each sample was used.
section_name: DC Conductivity Measurement

section_name: Experimental Results

section_content: Due to the opacity of the SiC/epoxy micro-composites, the reflective FTIR spectra of aged SiC/epoxy micro-composites is measured, as shown in Figure 1a. It can be seen that, with the increasing ageing time, the carbonyl group (C=O) increases. In addition, a large amount of methylene radical (-CH 2 •) and carboxylic acid (-COOH) occurs in the composites as a result of thermal ageing. 

Energies 2022, 15, x FOR PEER REVIEW 3 of 11
section_name: FTIR Spectroscopy

section_content: The relationship between current density and applied electric field of aged microcomposites was measured by a three-electrode test system [5] with a high voltage DC power supply (Hb-z203-2ac model) and a pico-ammeter (EST122 model) at 25 ± 1 °C. The measurement electrode was 25 mm in diameter. The current flowing through the sample was close to steady state and was recorded when the DC voltage was applied to the sample for 20 min. Considering the geometry of the sample, the current density and DC conductivity were then obtained. Three measurements were performed for each sample, and one of the measurement results for each sample was used.
section_name: DC Conductivity Measurement

section_content: Due to the opacity of the SiC/epoxy micro-composites, the reflective FTIR spectra of aged SiC/epoxy micro-composites is measured, as shown in Figure 1a. It can be seen that, with the increasing ageing time, the carbonyl group (C=O) increases. In addition, a large amount of methylene radical (-CH2•) and carboxylic acid (-COOH) occurs in the composites as a result of thermal ageing. The epoxy matrix includes lots of functional groups, such as hydroxyl group (-OH) and C=O, as shown in Figure 1b. When the SiC/epoxy micro-composites are subject to a high temperature in air, the -OH in the epoxy chain is oxidized by the oxygen in air and the weak bonding of the epoxy macromolecular chains is broken, forming many small molecules and free radicals. It is also accompanied with an increase in C=O and the appearance of -CH2• as well as -COOH.
section_name: FTIR Spectroscopy

section_content: Figure 2 shows the relative permittivity and loss tangent (tanδ) of aged SiC/epoxy micro-composites under 0. 1 and 50 Hz, respectively. It can be seen that the relative permittivity of aged micro-composites increases with the ageing time whether under 0. 1 Hz or 50 Hz, whereas the loss tangent of aged micro-composites also increases when the ageing time increases from 0 to 1080 h. 

The relative permittivity is closely related to the polymer matrix, filler and the interface between polymer matrix and fillers. When the SiC/epoxy micro-composites undergo thermal ageing, the epoxy matrix is much easier to be thermally decomposed than the SiC filler, and a large number of small molecules and free radicals are formed. These increase The epoxy matrix includes lots of functional groups, such as hydroxyl group (-OH) and C=O, as shown in Figure 1b. When the SiC/epoxy micro-composites are subject to a high temperature in air, the -OH in the epoxy chain is oxidized by the oxygen in air and the weak bonding of the epoxy macromolecular chains is broken, forming many small molecules and free radicals. It is also accompanied with an increase in C=O and the appearance of -CH 2 • as well as -COOH.
section_name: Dielectric Properties

section_content: Figure 2 shows the relative permittivity and loss tangent (tanδ) of aged SiC/epoxy micro-composites under 0. 1 and 50 Hz, respectively. It can be seen that the relative permittivity of aged micro-composites increases with the ageing time whether under 0. 1 Hz or 50 Hz, whereas the loss tangent of aged micro-composites also increases when the ageing time increases from 0 to 1080 h. 

The relative permittivity is closely related to the polymer matrix, filler and the interface between polymer matrix and fillers. When the SiC/epoxy micro-composites undergo thermal ageing, the epoxy matrix is much easier to be thermally decomposed than the SiC filler, and a large number of small molecules and free radicals are formed. These increase the number of dipoles and are more liable to orient along with the applied electric field than epoxy macromolecular chains. Besides, when the epoxy chain between the epoxy matrix and filler is thermally broken, the dielectric parameters between the epoxy matrix and filler are changed, which means that it is possible to enhance the interface polarization. The increasing orientable dipoles and enhancing interface polarization significantly contribute to the polarization of micro-composite, leading to a much larger relative permittivity of aged micro-composites than unaged ones (i. e., 0 h-aged one). With the increasing ageing time, the degradation of SiC/epoxy micro-composites becomes more serious, many more small molecules and free radicals are formed, and the dipole polarization is further enhanced, resulting in the increase in relative permittivity. 

Energies 2022, 15, x FOR PEER REVIEW 4 of 11 the number of dipoles and are more liable to orient along with the applied electric field than epoxy macromolecular chains. Besides, when the epoxy chain between the epoxy matrix and filler is thermally broken, the dielectric parameters between the epoxy matrix and filler are changed, which means that it is possible to enhance the interface polarization. The increasing orientable dipoles and enhancing interface polarization significantly contribute to the polarization of micro-composite, leading to a much larger relative permittivity of aged micro-composites than unaged ones (i. e., 0 h-aged one). With the increasing ageing time, the degradation of SiC/epoxy micro-composites becomes more serious, many more small molecules and free radicals are formed, and the dipole polarization is further enhanced, resulting in the increase in relative permittivity. In addition, as is known, the dipole or interface polarization belongs to relaxation polarization and is accompanied by relaxation polarization loss. Usually, the increase in relaxation polarization causes the increase in loss tangent. Thus, when the ageing time increases, the loss tangent also increases with the enhancement of relaxation polarization as result of the thermal decomposition of epoxy macromolecular in micro-composites.
section_name: Dielectric Properties

section_content: The breakdown strength of aged SiC/epoxy micro-composites is shown in Figure 3, and the average breakdown strength almost decreases with the ageing time. This is because, when under a high temperature, the epoxy macromolecular is randomly broken into small molecules and free radicals, and the free radicals are highly reactive. In addition, the high thermal temperature causes the thermal expansion and softening of microcomposites, increasing the defects such as impurities and air gaps in the micro-composite. So, the thermal ageing brings about the decrease in the breakdown strength. In addition, as is known, the dipole or interface polarization belongs to relaxation polarization and is accompanied by relaxation polarization loss. Usually, the increase in relaxation polarization causes the increase in loss tangent. Thus, when the ageing time increases, the loss tangent also increases with the enhancement of relaxation polarization as result of the thermal decomposition of epoxy macromolecular in micro-composites.
section_name: DC Breakdown Strength

section_content: The breakdown strength of aged SiC/epoxy micro-composites is shown in Figure 3, and the average breakdown strength almost decreases with the ageing time. This is because, when under a high temperature, the epoxy macromolecular is randomly broken into small molecules and free radicals, and the free radicals are highly reactive. In addition, the high thermal temperature causes the thermal expansion and softening of micro-composites, increasing the defects such as impurities and air gaps in the micro-composite. So, the thermal ageing brings about the decrease in the breakdown strength.
section_name: DC Breakdown Strength

section_content: Figure 4 shows the relationship between current density and applied electric field of aged SiC/epoxy micro-composites. For unaged SiC/epoxy micro-composites, the current density almost increases linearly with the applied electric field, whereas when the applied electric field is larger than a certain value (i. e., switching electric field), the current density increases significantly with the applied electric field. In other words, the unaged SiC/epoxy micro-composite shows a distinct nonlinear conductivity characteristic and is a kind of NRFGM. Similarly, the aged SiC/epoxy micro-composites also show nonlinear conductivity characteristics. For this reason, the nonlinear coefficient and switching electric field of aged SiC/epoxy micro-composites is calculated according to Equation (1), as shown in Table 1 :

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where J is the current density; E is the applied electric field; E c is the switching electric field and is defined as the electric field to change the slope of current density against applied electric field in log-log coordinate; J c is the switching current density; and α is the nonlinear coefficient.
section_name: Nonlinear Conductivity

section_content: Figure 4 shows the relationship between current density and applied electric field of aged SiC/epoxy micro-composites. For unaged SiC/epoxy micro-composites, the current density almost increases linearly with the applied electric field, whereas when the applied electric field is larger than a certain value (i. e., switching electric field), the current density increases significantly with the applied electric field. In other words, the unaged SiC/epoxy micro-composite shows a distinct nonlinear conductivity characteristic and is a kind of NRFGM. Similarly, the aged SiC/epoxy micro-composites also show nonlinear conductivity characteristics. For this reason, the nonlinear coefficient and switching electric field of aged SiC/epoxy micro-composites is calculated according to Equation (1), as shown in Table 1 :

where J is the current density; E is the applied electric field; Ec is the switching electric field and is defined as the electric field to change the slope of current density against applied electric field in log-log coordinate; Jc is the switching current density; and α is the nonlinear coefficient.
section_name: Nonlinear Conductivity

section_content: Figure 4 shows the relationship between current density and applied electric field of aged SiC/epoxy micro-composites. For unaged SiC/epoxy micro-composites, the current density almost increases linearly with the applied electric field, whereas when the applied electric field is larger than a certain value (i. e., switching electric field), the current density increases significantly with the applied electric field. In other words, the unaged SiC/epoxy micro-composite shows a distinct nonlinear conductivity characteristic and is a kind of NRFGM. Similarly, the aged SiC/epoxy micro-composites also show nonlinear conductivity characteristics. For this reason, the nonlinear coefficient and switching electric field of aged SiC/epoxy micro-composites is calculated according to Equation (1), as shown in Table 1 :

where J is the current density; E is the applied electric field; Ec is the switching electric field and is defined as the electric field to change the slope of current density against applied electric field in log-log coordinate; Jc is the switching current density; and α is the nonlinear coefficient. It can be learnt that, apart from the 72 h-aged one, the nonlinear coefficient of aged SiC/epoxy micro-composites almost increase with the ageing time. It can also be seen from Figure 4 that, when the applied electric field is the same (e. g., 6 kV/mm), the current density of 72 h-aged micro-composite is slightly smaller than that of unaged one. However, when the ageing time is greater than 72 h, the current density of aged micro-composites is gradually greater than that of the unaged one. Moreover, it can be found from Table 1 that the switching electric field decreases with the increase in ageing time. This is similar to the relationship between breakdown strength and ageing time as shown in Figure 3. 

For the 72 h-aged micro-composite, it is in the early stages of thermal ageing, so the macromolecular decomposition and re-cross-linking reaction of the epoxy matrix may occur at the same time. The re-cross-linking reaction suppresses the mobility of free carriers and results in the reduction of current density or nonlinear coefficient. However, the macromolecular decomposition generates free radicals, which increase the carrier density. With the ageing time, a large number of free radicals are formed in the aged micro-composites and cause the huge increase in free-carrier density, leading to the larger current density or nonlinear coefficient. Due to the presence of a large number of carriers, a partial quantity or the total of carriers are able to take part in the DC conduction under a smaller applied electric field compared with the few carriers in unaged micro-composites, which indicates that the increasing ageing time brings about the reduction in the switching electric field.
section_name: Nonlinear Conductivity

section_name: Simulation and Discussion

section_content: A two-dimension axisymmetric simulation model for a cone spacer of GIS [17] is built as shown in Figure 5, in order to study the effect of aged SiC/epoxy micro-composites on its electric field distribution. The model is solved by the finite element method (FEM). The cone spacer is located between a high voltage (HV) electrode and a grounded (GND) electrode in a coaxial arrangement. A voltage of 220 kV is applied to the HV electrode. The diameter of HV electrode is 80 mm, whereas the inner diameter of GND electrode is 340 mm. The thickness of spacer is 30 mm. The insulating material for the spacer is the aged SiC/epoxy micro-composite. The pure epoxy with a conductivity of 3 × 10 -14 S/m and relative permittivity of 4. 6 is also used for spacer as a contrast. In addition, the conductivity and relative permittivity of gas in the model are 10 -20 S/m and 1, respectively. The electric field profiles along the upper and lower surfaces (i. e., Paths #1 and #2 in Figure 5 ) of spacer are analyzed.
section_name: Cone Spacer Model

section_content: Electric field distributions around the cone spacer with pure epoxy and 1080 SiC/epoxy micro-composite are shown in Figure 6. Compared with the pure epoxy as shown in Figure 6a, the electric field distribution around the HV electrode sur well as in and around spacer is greatly improved as shown in Figure 6b even by plication of the 1080 h-aged SiC/epoxy micro-composite spacer. 

Figure 7a shows the electric field profiles along the upper surface of pure epo aged SiC/epoxy micro-composite spacers. It can be seen that the maximum electr strength along the upper surface of pure epoxy spacer occurs near the HV electro
section_name: Electric Field Distribution

section_content: Electric field distributions around the cone spacer with pure epoxy and 1080 h-aged SiC/epoxy micro-composite are shown in Figure 6. Compared with the pure epoxy spacer as shown in Figure 6a, the electric field distribution around the HV electrode surface as well as in and around spacer is greatly improved as shown in Figure 6b even by the application of the 1080 h-aged SiC/epoxy micro-composite spacer. 

composite than the unaged one, as shown in Figure 4 and Table 1. By contrast, when the ageing time is longer than 72 h, the conductivity and nonlinear coefficient of aged microcomposites are higher than that of the unaged one and increase with the increase in ageing time, which seems to be helpful in homogenizing the electric field distribution around the spacer. Figure 7a also shows that the electric field near the HV electrode almost decreases with the increase in ageing time (>72 h), and the whole electric field profile along the aged micro-composite spacer is much more uniform compared with the pure epoxy spacer. Figure 7a shows the electric field profiles along the upper surface of pure epoxy and aged SiC/epoxy micro-composite spacers. It can be seen that the maximum electric field strength along the upper surface of pure epoxy spacer occurs near the HV electrode and is about 3. 52 kV/mm, whereas it reduces to 1. 9 kV/mm by the unaged SiC/epoxy microcomposite spacer. For the 72 h-aged micro-composite spacer, the electric field strength near the HV electrode increases slightly and is about 2. 1 kV/mm compared with the unaged micro-composite spacer; however, it is still lower than that of pure epoxy spacer. This is caused by the lower conductivity and nonlinear coefficient of the 72 h-aged microcomposite than the unaged one, as shown in Figure 4 and Table 1. By contrast, when the ageing time is longer than 72 h, the conductivity and nonlinear coefficient of aged micro-composites are higher than that of the unaged one and increase with the increase in ageing time, which seems to be helpful in homogenizing the electric field distribution around the spacer. Figure 7a also shows that the electric field near the HV electrode almost decreases with the increase in ageing time (>72 h), and the whole electric field profile along the aged micro-composite spacer is much more uniform compared with the pure epoxy spacer. Figure 7b shows the electric field profiles along the lower surface of pure epoxy and aged SiC/epoxy micro-composite spacers. They are similar to the electric field profiles along the upper surface of spacers. Due to their nonlinear conductivity, the unaged and aged SiC/epoxy micro-composites are able to reduce the high electric field strength on the spacer's lower surface near the HV electrode in contrast with pure epoxy. These results imply that the thermal ageing has little or no effect on homogenizing the electric field distribution around spacer. Figure 7b shows the electric field profiles along the lower surface of pure epoxy and aged SiC/epoxy micro-composite spacers. They are similar to the electric field profiles along the upper surface of spacers. Due to their nonlinear conductivity, the unaged and Energies 2022, 15, 8361 8 of 10 aged SiC/epoxy micro-composites are able to reduce the high electric field strength on the spacer's lower surface near the HV electrode in contrast with pure epoxy. These results imply that the thermal ageing has little or no effect on homogenizing the electric field distribution around spacer.
section_name: Electric Field Distribution

section_content: The power dissipation density distributions of pure epoxy and 1080 h-aged SiC/epoxy micro-composite spacer are shown in Figure 8. For the pure epoxy spacer, the power dissipation is mainly located in the spacer near the HV electrode. By comparison, for the 1080 h-aged SiC/epoxy micro-composite spacer, the power dissipation density is much larger and the power dissipation region is enlarged to the whole spacer. Figure 7b shows the electric field profiles along the lower surface of pure epoxy and aged SiC/epoxy micro-composite spacers. They are similar to the electric field profiles along the upper surface of spacers. Due to their nonlinear conductivity, the unaged and aged SiC/epoxy micro-composites are able to reduce the high electric field strength on the spacer's lower surface near the HV electrode in contrast with pure epoxy. These results imply that the thermal ageing has little or no effect on homogenizing the electric field distribution around spacer.
section_name: Power Dissipation Density Distribution

section_content: The power dissipation density distributions of pure epoxy and 1080 h-aged SiC/epoxy micro-composite spacer are shown in Figure 8. For the pure epoxy spacer, the power dissipation is mainly located in the spacer near the HV electrode. By comparison, for the 1080 h-aged SiC/epoxy micro-composite spacer, the power dissipation density is much larger and the power dissipation region is enlarged to the whole spacer. Figure 9 illustrates the power dissipation density profiles along the upper and lower surfaces of spacer with pure epoxy and aged SiC/epoxy micro-composite, respectively. It can be observed that the relationship between the power dissipation density and ageing time of the spacer's upper surface is similar to that of spacer's lower surface. Moreover, Figure 9 illustrates the power dissipation density profiles along the upper and lower surfaces of spacer with pure epoxy and aged SiC/epoxy micro-composite, respectively. It can be observed that the relationship between the power dissipation density and ageing time of the spacer's upper surface is similar to that of spacer's lower surface. Moreover, the 72 h-aged SiC/epoxy micro-composite spacer shows much higher power dissipation density than unaged one, but exhibits much lower power dissipation density than pure epoxy spacer. This is attributed to the lower conductivity of 72 h-aged SiC/epoxy microcomposite compared with unaged one as shown in Figure 4. When the ageing time increases from 72 to 720 h, the power dissipation density of the aged SiC/epoxy micro-composite spacers are still lower than that of the pure epoxy spacer. This suggests that a short-term thermal ageing of the SiC/epoxy micro-composite has little effect on the power dissipation density. Combined with the electric field distribution of aged SiC/epoxy micro-composite spacer as shown in Figure 7, it can be concluded that the short-term aged SiC/epoxy micro-composites are capable of homogenizing the electric field distribution around the GIS spacer with less power-dissipation density. 

However, when the ageing time is 1080 h, the power dissipation density of the aged SiC/epoxy micro-composite spacer is much higher than that of the pure epoxy spacer. The long-term ageing makes the SiC/epoxy micro-composite have very much higher conductivity and a much stronger nonlinear conductivity characteristic than short-term ageing, as shown in Figure 4 and Table 1. So, the power dissipation density of 1080 haged SiC/epoxy micro-composite spacer increases greatly according to the product of conductivity and the square of applied electric field. This leads to generate excessive heat in the spacer and to further accelerate the ageing degree of the SiC/epoxy micro-composite. 

Energies 2022, 15, 8361 9 of 10 creases from 72 to 720 h, the power dissipation density of the aged SiC/epoxy micro-composite spacers are still lower than that of the pure epoxy spacer. This suggests that a shortterm thermal ageing of the SiC/epoxy micro-composite has little effect on the power dissipation density. Combined with the electric field distribution of aged SiC/epoxy microcomposite spacer as shown in Figure 7, it can be concluded that the short-term aged SiC/epoxy micro-composites are capable of homogenizing the electric field distribution around the GIS spacer with less power-dissipation density. However, when the ageing time is 1080 h, the power dissipation density of the aged SiC/epoxy micro-composite spacer is much higher than that of the pure epoxy spacer. The long-term ageing makes the SiC/epoxy micro-composite have very much higher conductivity and a much stronger nonlinear conductivity characteristic than short-term ageing, as shown in Figure 4 and Table 1. So, the power dissipation density of 1080 h-aged SiC/epoxy micro-composite spacer increases greatly according to the product of conductivity and the square of applied electric field. This leads to generate excessive heat in the spacer and to further accelerate the ageing degree of the SiC/epoxy micro-composite. 

Note that the above calculated electric field distribution and power dissipation density was carried out under DC steady state, only the DC conductivity of insulating material determines the electric field distribution and power dissipation density. In fact, the DC cone spacer may suffer from the overvoltage (i. e., lightning and switching overvoltage) and polarity reversal voltage, which are transient; the polarization of the insulating material determines the electric field distribution and power dissipation density at this time. As the aged SiC/epoxy micro-composite has a much greater relative permittivity and loss tangent than the unaged one, the power dissipation density of the cone spacer under transient state is about to become aggravated compared with the DC steady state. Thus, the thermal ageing effect and improvement in NRFGM should be paid attention to, in order to enhance the reliability of electrical applications with NRFGM.
section_name: Power Dissipation Density Distribution

section_content: A kind of nonlinear resistive field-grading material is prepared by the introduction of micro-SiC filler into epoxy matrix with 30 wt. %. The thermal ageing characteristics of SiC/epoxy micro-composites are studied experimentally, and the effects of aged micro- Note that the above calculated electric field distribution and power dissipation density was carried out under DC steady state, only the DC conductivity of insulating material determines the electric field distribution and power dissipation density. In fact, the DC cone spacer may suffer from the overvoltage (i. e., lightning and switching overvoltage) and polarity reversal voltage, which are transient; the polarization of the insulating material determines the electric field distribution and power dissipation density at this time. As the aged SiC/epoxy micro-composite has a much greater relative permittivity and loss tangent than the unaged one, the power dissipation density of the cone spacer under transient state is about to become aggravated compared with the DC steady state. Thus, the thermal ageing effect and improvement in NRFGM should be paid attention to, in order to enhance the reliability of electrical applications with NRFGM.
section_name: Conclusions

section_content: A kind of nonlinear resistive field-grading material is prepared by the introduction of micro-SiC filler into epoxy matrix with 30 wt. %. The thermal ageing characteristics of SiC/epoxy micro-composites are studied experimentally, and the effects of aged microcomposites on the electric field distribution of cone spacer are discussed. Several significant conclusions are obtained as below:

1. 

The high temperature ageing causes the breaks in the epoxy macromolecular chain and the formation of a number of small molecules and free radicals; 2. 

With the increase in ageing time, the relative permittivity and loss tangent increases, whereas the breakdown strength decreases; 3. 

The aged SiC/epoxy micro-composites shows distinct nonlinear conductivity. The nonlinear coefficient nearly increases from 3. 7 to 6. 56, and the switching electric field decreases from 5. 4 to 1. 03 kV/mm when the ageing time ranges from 0 to 1080 h; 4. 

The short-term (≤720 h) aged SiC/epoxy micro-composite not only homogenizes the electric field in the cone spacer, but also generates less power dissipation density compared with pure epoxy. By contrast, the long-term (1080 h) aged SiC/epoxy micro-composite is also able to homogenize the electric field in the cone spacer, but it causes a much higher power dissipation density. We should pay attention to the long-term stability of nonlinear resistive field grading material, and its improvement method will be carried out in future.
section_name: Conclusions

section_content: Funding: This research was funded by the Natural Science Foundation of China, grant number 51837003, 52007043 and Natural Science Foundation of Heilongjiang Province, grant number LH2021E085.

section_name: Conflicts of Interest:

section_content: Data Availability Statement: Not applicable.

section_content: The authors declare no conflict of interest.
section_name: Conflicts of Interest: