Polishing basin type insulator surface repairing method based on uniform charge treatment

Abstract

The invention discloses a method for repairing the surface of a polished basin-type insulator based on uniform charge treatment, which comprises the following steps of: setting a stepped repairing material by adopting a method based on uniform charge treatment, repairing the polished insulator through a polished insulator surface repairing device, and keeping the hardness of the surface of the insulator; the method comprises the following steps: determining the shape of an insulator as a sample reference by adopting a three-dimensional scanner before polishing the insulator, polishing the insulator, applying a working voltage to a central conductor of the insulator, calculating a difference value of electric displacements of inner and outer normal lines of a recess after polishing the surface of the insulator, and further solving a surface charge quantity value Q2 of the insulator; the number of repaired step layers of the polishing area can be adjusted along with the process, a sprayed material is a mixture of epoxy resin, aluminum oxide and a curing agent, the dielectric constant of the mixture is 3-10, after preliminary repair, the difference value of measured and calculated surface charge quantity values of the insulator is compared, if the error of the two values is smaller than 10%, repair is finished, and if not, repair is finished. The method can be widely applied to the field of insulating device polishing surface repairing.

Description

Technical Field

[0001] The invention relates to a surface repair method for a polished basin-type insulator based on uniform charge processing, belonging to the technical field of polished surface repair of insulating devices. Background Art

[0002] Basin insulators are key components of gas-insulated transmission pipelines and fully enclosed gas-insulated switchgear in power systems. They face more severe operating conditions and frequently experience accidents such as surface discharge or breakdown and disintegration. During the casting process of basin insulators, surface protrusions of different sizes and directions may appear on the surface of the insulator due to factors such as mold parting lines, mold wear, or embedded impurities, requiring the surface of the insulator to be polished. However, according to statistical data, surface discharge accidents often occur near the polishing area during operation. Therefore, it is particularly important to find a method to reduce the accumulation of charge on the surface of the insulator after polishing to avoid discharge accidents.

[0003] Under the action of high voltage electric field, the accumulation of surface charge on insulator mainly comes from insulator body conduction, insulator surface conduction and gas side space charge accumulation. The accumulation of these charges is related to the conductivity, surface conductivity and gas conductivity of the insulator. In highly electronegative gases, such as SF6, most of the free electrons are attached to gas molecules to form negative ions. The movement and diffusion of these charged particles in the electric field determine the dynamic changes of surface charge.

[0004] The dielectric surface permittivity is an important factor affecting the electric field distribution and charge accumulation. A dielectric with a higher dielectric constant can store charge more efficiently, thus affecting the charge accumulation and distribution. Therefore, by changing the dielectric surface permittivity, the charge accumulation on the insulator surface can be adjusted, thereby affecting its electrical performance.

[0005] At present, the commonly used methods to reduce the accumulation of charge on the surface of insulators are mainly the following: 1. Surface treatment technology: Changing the roughness of the insulator surface by sandblasting and other methods can change the distribution of surface charge. However, when using atomic force microscopy for microscopic inspection, it can be observed that the aluminum oxide protrusions with higher hardness due to sandblasting affect the local electric field on the insulator surface, and ultimately the polished area gathers charges with opposite polarity to the non-polished area, increasing the local potential difference and increasing the risk of partial discharge. Even if epoxy resin is used to repair the insulator surface, it is easy to produce secondary scratches considering that the hardness of epoxy resin is not high, and it cannot play a good role in repair.

[0006] 2. Change the insulator structure: The improved insulator structure can reduce the accumulation of charge on the insulator surface, but it is ineffective for insulators that have been put into operation.

[0007] 3. Regular cleaning and maintenance: Regular cleaning of the insulator surface can remove accumulated dirt and charge and maintain its good insulation performance. However, since the insulators in GIL and GIS are in closed spaces, it is not convenient to perform regular cleaning for a short period of time.

[0008] Therefore, there is currently no more effective solution to suppress the local uneven accumulation of charge on polished insulators.

[0009] In AC power systems, the performance of insulators is crucial to the stability and safety of the system. By uniformly charging the polished insulators, the local potential difference on the surface of the insulators can be further reduced, and the hardness of the surface of the polished insulators can be maintained, thereby avoiding local discharge, improving the performance of the insulators, and ensuring the reliable operation of the power system. Summary of the invention

[0010] The present invention overcomes the shortcomings of the prior art and provides a surface repair method for a polished basin-type insulator based on uniform charge treatment. A step-by-step repair material is set based on the uniform charge treatment method, and the polished insulator is repaired by a polished insulator surface repair device, while the hardness of the insulator surface is maintained.

[0011] In order to solve the above technical problems, the technical solution adopted by the present invention is: a surface repair method of a polished pot-type insulator based on uniform charge treatment, which is implemented according to the following steps: The first step is to use a 3D scanner to determine the micron-level precision morphology of the insulator as a sample reference before polishing the insulator, where the accuracy of the 3D scanner is: 20μm ~ 100μm; The second step is to polish the raised parts or impurities of the insulator, and form a 0-2 mm depression in the polished area by comparing the morphology detected by the 3D scanner; In the third step, the insulator morphology is determined again using a 3D scanner and compared with the sample to determine the depth h of the polishing depression; The fourth step is to apply a working voltage to the central conductor of the insulator, and after power is cut off, use an insulator surface charge measuring device to determine the insulator surface charge distribution shape M1 and the insulator surface charge value Q1; The fifth step is to calculate the difference in normal electric displacement inside and outside the concave surface after polishing of the insulator based on the adsorption and accumulation effect of space charge after dielectric polarization under AC state, and then obtain the surface charge value Q2 of the insulator; Step 6: Determine the number of repair steps and the dielectric constant of the corresponding spray material according to the surface charge value Q2 of the insulator; the number of repair steps in the polished area can be adjusted according to the process. During the repair, it is necessary to first spray a mixture of epoxy resin and aluminum oxide with a high proportion of aluminum oxide of not less than 80%, and the thickness of multiple sprays is the same or different. In the final sprayed epoxy resin and aluminum oxide mixture layer, the aluminum oxide ratio is the original aluminum oxide ratio K in the repaired insulator; the sprayed material is a mixture of epoxy resin, aluminum oxide and curing agent, and the dielectric constant of the mixture is between 3 and 10; In the seventh step, the working voltage is applied to the central conductor of the insulator again. After power is cut off, the insulator surface charge measurement device is used to determine the insulator surface charge distribution shape M3 and the insulator surface charge value Q3. Then, according to the new insulator surface charge distribution shape M3, the fifth step is repeated to calculate Q'2 under the new distribution shape, and Q'2 and Q3 are compared. If the error between Q'2 and Q3 is less than 10%, the repair is completed. Otherwise, the second to seventh steps are repeated.

[0012] Furthermore, in the fifth step, Q1 and Q2 are compared. If the value errors of Q1 and Q2 are both less than 10%, the number of step layers to be repaired and the dielectric constant of the corresponding injection material are determined; if the error is greater than 10%, the scanning angle of the 3D scanner needs to be readjusted and the second to fifth steps are repeated.

[0013] Furthermore, in the sixth step, the sprayed repair layer is multi-layer, wherein the proportion of aluminum oxide is K to 80%, and the sprayed repair material is not higher than the original insulator surface height.

[0014] Furthermore, in the fourth and seventh steps, the insulator surface charge measuring device uses an electrostatic potentiometer or a nanocoulomb meter. During measurement, a stepper motor or a lead screw device is used to control the probe of the above instrument to move on the insulator surface, and the insulator surface charge distribution morphology M1, M3 and the insulator surface charge values ​​Q1, Q3 are obtained directly or indirectly.

[0015] Furthermore, the calculation process of Q2 in the fifth step is as follows: In an electric field environment, the movement of carriers on the gas side depends on the Coulomb force on the particles, while the diffusion of carriers is determined by the uniformity of their concentration. The dynamic changes in the concentration of positive and negative carriers can be expressed by the generation, recombination, and migration of positive and negative ions, as shown in formulas (1) to (2): (1) (2) In the formula, ∂ n IP / ∂t is the ion pair generation rate; D+ , D − are the diffusion coefficients of positive and negative ions, respectively; k r is the positive and negative ion recombination coefficient; n + , n − are the concentrations of positive and negative ions, respectively; b + , b − are the migration rates of positive and negative ions, respectively; E is the electric field strength; According to Einstein's equation, we can get D + / − = b + / − kT / e ,in e is the electron charge, k is the Boltzmann constant, T is the ambient temperature; Since most of the free electrons in highly electronegative gases attach to gas molecules to form negative ions, ignoring the effect of temperature on gas pressure and field emission of electrodes, it can be assumed that the carriers in the gas are only positive and negative ions, and the recombination coefficient of positive and negative ions is k r According to Langevin's principle, we can get: (3) In the formula ： ε is the dielectric constant of the insulating gas; Based on the accumulation process of the charge on the insulator surface, the current density on the insulator side and the gas side at the gas-solid interface can be used as an important boundary condition at the interface between the insulator and the gas, as shown below: (4) (5) In the formula, J I , J G Current density on the insulator side and insulating gas side respectively; γ 2 is the solid side body conductivity; E n2 , En1 are the normal components of the field strength on the insulator side and the insulating gas side at the gas-solid interface, respectively; The charge accumulation at the gas-solid interface surface is as follows: (6) (7) In the formula, σ s is the surface charge density; n is the surface normal vector of the medium; D 1. D 2 is the electric displacement vector on the solid and gas sides; The charge that causes the change in electric potential and electric field distribution can be obtained by Poisson's equation, as shown in formulas (8) and (9): (8) (9) In the formula, ρ is the charge density of freely moving ions and electrons; By inputting formulas (1) to (9) as constraints and control equations into the electric field analysis software, the normal component of the electric displacement on the interface between the gas side and the substrate side of the insulator surface can be calculated, and the difference in the normal component of the electric displacement, i.e., the surface charge density σ s , as shown in formula (7); Then the surface charge density σ s Substituting into formula (10), we can obtain the surface charge value Q2 of the insulator: (10) In the formula, S is the probe tip area of ​​an electrostatic potentiometer or nanocoulomb meter that can test the surface charge of an insulator.

[0016] Compared with the prior art, the present invention has the following beneficial effects: in order to solve the problem of uneven charge accumulation on the surface of a pot-type insulator after polishing, thereby generating local high potential difference and high distortion electric field causing local discharge, the present invention adopts a method based on uniform charge treatment to set a stepped repair material, develops a polished insulator surface repair device to repair the polished insulator, and maintains the hardness of the insulator surface. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] The present invention will be further described below in conjunction with the accompanying drawings.

[0018] Figure 1 It is a schematic diagram of the local electric field distortion of the polishing depression of the insulator in the present invention.

[0019] Figure 2 It is a schematic diagram of the principle of the present invention.

[0020] Figure 3 It is a schematic diagram of the change of vertical electrical displacement of the polished surface after repair according to the present invention. DETAILED DESCRIPTION

[0021] The present invention will be further described below in conjunction with specific embodiments.

[0022] like Figure 1 to Figure 3 As shown, the surface repair method of polished pot-type insulator based on uniform charge treatment of the present invention is implemented according to the following steps: The first step is to use a 3D scanner to determine the micron-level precision morphology of the insulator as a sample reference before polishing the insulator, where the accuracy of the 3D scanner is: 20μm ~ 100μm; The second step is to polish the raised parts or impurities of the insulator, and form a 0-2 mm depression in the polished area by comparing the morphology detected by the 3D scanner; In the third step, the insulator morphology is determined again using a 3D scanner and compared with the sample to determine the depth h of the polishing depression; The fourth step is to apply a working voltage to the central conductor of the insulator, and after power is cut off, use an insulator surface charge measuring device to determine the insulator surface charge distribution shape M1 and the insulator surface charge value Q1; The fifth step is to calculate the difference in normal electric displacement inside and outside the concave surface after polishing of the insulator based on the adsorption and accumulation effect of space charge after dielectric polarization under AC state, and then obtain the surface charge value Q2 of the insulator; Step 6: Determine the number of repair steps and the dielectric constant of the corresponding spray material according to the surface charge value Q2 of the insulator; the number of repair steps in the polished area can be adjusted according to the process. During the repair, it is necessary to first spray a mixture of epoxy resin and aluminum oxide with a high proportion of aluminum oxide of not less than 80%, and the thickness of multiple sprays is the same or different. In the final sprayed epoxy resin and aluminum oxide mixture layer, the aluminum oxide ratio is the original aluminum oxide ratio K in the repaired insulator; the sprayed material is a mixture of epoxy resin, aluminum oxide and curing agent, and the dielectric constant of the mixture is between 3 and 10; In the seventh step, the working voltage is applied to the central conductor of the insulator again. After power is cut off, the insulator surface charge measurement device is used to determine the insulator surface charge distribution shape M3 and the insulator surface charge value Q3. Then, according to the new insulator surface charge distribution shape M3, the fifth step is repeated to calculate Q'2 under the new distribution shape, and Q'2 and Q3 are compared. If the error between Q'2 and Q3 is less than 10%, the repair is completed. Otherwise, the second to seventh steps are repeated.

[0023] Furthermore, in the fifth step, Q1 and Q2 are compared. If the value errors of Q1 and Q2 are both less than 10%, the number of step layers to be repaired and the dielectric constant of the corresponding injection material are determined; if the error is greater than 10%, the scanning angle of the 3D scanner needs to be readjusted and the second to fifth steps are repeated.

[0024] Furthermore, in the sixth step, the sprayed repair layer is multi-layer, wherein the proportion of aluminum oxide is K to 80%, and the sprayed repair material is not higher than the original insulator surface height.

[0025] Furthermore, in the fourth and seventh steps, the insulator surface charge measuring device uses an electrostatic potentiometer or a nanocoulomb meter. During measurement, a stepper motor or a lead screw device is used to control the probe of the above instrument to move on the insulator surface, and the insulator surface charge distribution morphology M1, M3 and the insulator surface charge values ​​Q1, Q3 are obtained directly or indirectly.

[0026] Furthermore, the calculation process of Q2 in the fifth step is as follows: In an electric field environment, the movement of carriers on the gas side depends on the Coulomb force on the particles, while the diffusion of carriers is determined by the uniformity of their concentration. The dynamic changes in the concentration of positive and negative carriers can be expressed by the generation, recombination, and migration of positive and negative ions, as shown in formulas (1) to (2): (1) (2) In the formula, ∂ n IP / ∂t is the ion pair generation rate; D + , D − are the diffusion coefficients of positive and negative ions, respectively; k r is the positive and negative ion recombination coefficient; n + , n − are the concentrations of positive and negative ions, respectively; b + , b − are the migration rates of positive and negative ions, respectively; E is the electric field strength; According to Einstein's equation, we can get D + / − = b + / − kT / e ,in e is the electron charge, k is the Boltzmann constant, T is the ambient temperature; Since most of the free electrons in highly electronegative gases attach to gas molecules to form negative ions, ignoring the effect of temperature on gas pressure and field emission of electrodes, it can be assumed that the carriers in the gas are only positive and negative ions, and the recombination coefficient of positive and negative ions is k r According to Langevin's principle, we can get: (3) In the formula ： ε is the dielectric constant of the insulating gas; Based on the accumulation process of the charge on the insulator surface, the current density on the insulator side and the gas side at the gas-solid interface can be used as an important boundary condition at the interface between the insulator and the gas, as shown below: (4) (5) In the formula, J I , J G Current density on the insulator side and insulating gas side respectively; γ 2 is the solid side body conductivity; E n2 , E n1 are the normal components of the field strength on the insulator side and the insulating gas side at the gas-solid interface, respectively; The charge accumulation at the gas-solid interface surface is as follows: (6) (7) In the formula, σ s is the surface charge density; n is the surface normal vector of the medium; D 1. D 2 is the electric displacement vector on the solid and gas sides; The charge that causes the change in electric potential and electric field distribution can be obtained by Poisson's equation, as shown in formulas (8) and (9): (8) (9) In the formula, ρ is the charge density of freely moving ions and electrons; By inputting formulas (1) to (9) as constraints and control equations into the electric field analysis software, the normal component of the electric displacement on the interface between the gas side and the substrate side of the insulator surface can be calculated, and the difference in the normal component of the electric displacement, i.e., the surface charge density σ s , as shown in formula (7); Then the surface charge density σ s Substituting into formula (10), we can obtain the surface charge value Q2 of the insulator: (10) In the formula, S is the probe tip area of ​​an electrostatic potentiometer or nanocoulomb meter that can test the surface charge of an insulator.

[0027] The present invention combines the process of ejecting materials such as magnetron sputtering and the simplicity of operation. Figure 2 First, a mixture of epoxy resin and alumina with a total height of h / 3 and a proportion of more than 80% of alumina is sprayed in the depression; finally, a mixture of original epoxy resin and alumina with a total height of h / 3 is sprayed (wherein the proportion of alumina is the proportion K of the original alumina in the repaired insulator); the middle can be divided into multiple layers, with a proportion of alumina ranging from K to 80%. The total spraying height is less than or equal to the surface height of the original epoxy resin. On the basis of the epoxy resin and alumina mixture, the spraying material increases the proportion of alumina to control the change of electrical displacement and reduce surface accumulation; the last layer of the surface is kept as the original epoxy resin and alumina mixture, maintaining the surface hardness of the insulator.

[0028] When the polishing process of the insulator makes the hard particles in the insulator matrix protrude, such as the protrusion of alumina particles in the pot insulator, local electric field distortion will be generated in the middle of the epoxy resin particles and at the junction with the most concave polishing, and the electric field strength value will be significantly enhanced, such as Figure 1 As shown. Since the dielectric constant of the epoxy resin matrix is ​​higher than that of the gas side, the electric displacement in the matrix is ​​generally higher than that on the gas side, and the surface charge density on the gas side is generally negative, that is, negative charges generally accumulate on the surface of the insulator. However, the locally enhanced field strength enhances the electric displacement on the gas side, resulting in the electric displacement on the gas side being higher than that on the matrix side, so positive charges tend to accumulate on the surface of the polished insulator. Charges of opposite polarity cause high potential difference and distorted electric field on the surface of the insulator, increasing the possibility of local discharge on the surface of the insulator and subsequent flashover.

[0029] In order to reduce the electric displacement difference on both sides of the polished insulator surface, the dielectric constant of the alumina particles raised on the polished surface is larger than that of the epoxy resin matrix. Figure 1The polishing area in the process uses a material spraying method such as magnetron sputtering to spray a filler with a dielectric constant between 3 and 10 into the polishing area.

[0030] In summary, in order to solve the problem of uneven charge accumulation on the surface of pot-type insulators after polishing, which leads to local high potential difference and high distortion electric field causing local discharge, a method based on uniform charge treatment is adopted to set the stepped repair material, and a polished insulator surface repair device is developed to repair the polished insulator and maintain the hardness of the insulator surface.

[0031] In the embodiment, a concave portion after polishing of the insulator surface is selected, and based on the fact that the micron-sized particles of aluminum oxide are more prominent than the epoxy resin after polishing, the insulator is step-repaired at the height of the concave portion. Assuming that the dielectric constant of the insulator base is 3, during multi-step repair, dielectrics with dielectric constants of 8, 5, and 3 are sprayed respectively from the concave base surface side by a method of spraying materials such as magnetron sputtering, and the surface height after repair is less than or equal to the original surface height.

[0032] from Figure 3 It can be seen that when step repair is used, the change in electric displacement at the interface between the repair medium and the SF6 medium after under-height repair or equal-height repair is much smaller than that of pure epoxy repair. According to formula (7), the low electric displacement difference reduces the charge accumulated on the insulator surface, making the charge distribution on the insulator surface more uniform and reducing the risk of partial discharge.

[0033] The embodiments of the present invention are described in detail above in conjunction with the accompanying drawings, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge scope of ordinary technicians in this field without departing from the purpose of the present invention.

Claims

1. A surface repair method for a polished pot-type insulator based on uniform charge treatment, characterized in that: Follow these steps to implement: The first step is to use a 3D scanner to determine the micron-level precision morphology of the insulator as a sample reference before polishing the insulator, where the accuracy of the 3D scanner is: 20μm ~ 100μm; The second step is to polish the raised parts or impurities of the insulator, and form a 0-2 mm depression in the polished area by comparing the morphology detected by the 3D scanner; In the third step, the insulator morphology is determined again using a 3D scanner and compared with the sample to determine the depth h of the polishing depression; The fourth step is to apply a working voltage to the central conductor of the insulator, and after power is cut off, use an insulator surface charge measuring device to determine the insulator surface charge distribution shape M1 and the insulator surface charge value Q1; The fifth step is to calculate the difference in normal electric displacement inside and outside the concave surface after polishing of the insulator based on the adsorption and accumulation effect of space charge after dielectric polarization under AC state, and then obtain the surface charge value Q2 of the insulator; Step 6: Determine the number of repair steps and the dielectric constant of the corresponding spray material according to the surface charge value Q2 of the insulator; the number of repair steps in the polished area can be adjusted according to the process. During the repair, it is necessary to first spray a mixture of epoxy resin and aluminum oxide with a high proportion of aluminum oxide of not less than 80%, and the thickness of multiple sprays is the same or different. In the final sprayed epoxy resin and aluminum oxide mixture layer, the aluminum oxide ratio is the original aluminum oxide ratio K in the repaired insulator; the sprayed material is a mixture of epoxy resin, aluminum oxide and curing agent, and the dielectric constant of the mixture is between 3 and 10; In the seventh step, the working voltage is applied to the central conductor of the insulator again. After power is cut off, the insulator surface charge measurement device is used to determine the insulator surface charge distribution shape M3 and the insulator surface charge value Q3. Then, according to the new insulator surface charge distribution shape M3, the fifth step is repeated to calculate Q'2 under the new distribution shape, and Q'2 and Q3 are compared. If the error between Q'2 and Q3 is less than 10%, the repair is completed. Otherwise, the second to seventh steps are repeated.

2. The surface repair method of polished pot-type insulator based on uniform charge treatment according to claim 1 is characterized in that: In the fifth step, Q1 and Q2 are compared. If the value errors of Q1 and Q2 are both less than 10%, the number of repaired step layers and the corresponding dielectric constant of the injection material are determined; if the error is greater than 10%, the scanning angle of the 3D scanner needs to be readjusted and the second to fifth steps are repeated.

3. The surface repair method of polished pot-type insulator based on uniform charge treatment according to claim 1 is characterized in that: In the sixth step, the spray repair layer is multi-layer, wherein the proportion of aluminum oxide in the spray repair layer is K to 80%, the proportion of aluminum oxide in the first layer is greater than 80%, and the proportion of aluminum oxide in the last layer is K. The closer to the concave surface after polishing, the higher the proportion of aluminum oxide in the spray repair layer; the sprayed repair material is not higher than the original insulator surface height.

4. The surface repair method of polished pot-type insulator based on uniform charge treatment according to claim 1 is characterized in that: In the fourth and seventh steps, the insulator surface charge measuring device uses an electrostatic potentiometer or a nanocoulomb meter. During measurement, a stepper motor or a lead screw device is used to control the probe of the above instrument to move on the insulator surface, and the insulator surface charge distribution form M1, M3 and the insulator surface charge value Q1, Q3 are directly or indirectly obtained.

5. The surface repair method of polished pot-type insulator based on uniform charge treatment according to claim 1 is characterized in that: The calculation process of Q2 in the fifth step is as follows: In an electric field environment, the movement of carriers on the gas side depends on the Coulomb force on the particles, while the diffusion of carriers is determined by the uniformity of their concentration. The dynamic changes in the concentration of positive and negative carriers can be expressed by the generation, recombination, and migration of positive and negative ions, as shown in formulas (1) to (2): （1） （2） In the formula, ∂ n IP / ∂t is the ion pair generation rate; D + , D − are the diffusion coefficients of positive and negative ions, respectively; k r is the positive and negative ion recombination coefficient; n + , n − are the concentrations of positive and negative ions, respectively; b + , b − are the migration rates of positive and negative ions, respectively; E is the electric field strength; According to Einstein's equation, we can get D + / − = b + / − kT / e ,in e is the electron charge, k is the Boltzmann constant, T is the ambient temperature; Since most of the free electrons in highly electronegative gases attach to gas molecules to form negative ions, ignoring the effect of temperature on gas pressure and field emission of electrodes, it can be assumed that the carriers in the gas are only positive and negative ions, and the recombination coefficient of positive and negative ions is k r According to Langevin's principle, we can get: （3） In the formula ： ε is the dielectric constant of the insulating gas; Based on the accumulation process of the charge on the insulator surface, the current density on the insulator side and the gas side at the gas-solid interface can be used as an important boundary condition at the interface between the insulator and the gas, as shown below: （4） （5） In the formula, J I , J G Current density on the insulator side and insulating gas side respectively; γ 2 is the solid side body conductivity; E n2 , E n1 are the normal components of the field strength on the insulator side and the insulating gas side at the gas-solid interface, respectively; The charge accumulation at the gas-solid interface surface is as follows: （6） （7） In the formula, σ s is the surface charge density; n is the medium surface normal vector; D 1. D 2 is the electric displacement vector on the solid and gas sides; The charge that causes the change in electric potential and electric field distribution can be obtained by Poisson's equation, as shown in formulas (8) and (9): （8） （9） In the formula, ρ is the charge density of freely moving ions and electrons; By inputting formulas (1) to (9) as constraints and control equations into the electric field analysis software, the normal component of the electric displacement on the interface between the gas side and the substrate side of the insulator surface can be calculated, and the difference in the normal component of the electric displacement, i.e., the surface charge density σ s , as shown in formula (7); Then the surface charge density σ s Substituting into formula (10), we can obtain the value of the insulator surface charge Q2: （10） In the formula, S is the probe tip area of ​​an electrostatic potentiometer or nanocoulomb meter that can test the surface charge of an insulator.

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