Calculation method and application of discharge voltage of environment-friendly insulating gas in slightly non-uniform electric field

Abstract

In order to solve the problems of many experiment limitations and high time cost and economic cost in the prior art, in order to reduce the experiment amount, the invention provides an environment-friendly insulating gas discharge voltage calculation method and device under a slightly non-uniform electric field, and the method comprises the steps: obtaining the effective ionization coefficients of different types of gases; when the effective ionization coefficient is 0, critical breakdown field strength of various gases under different air pressures is determined; on the basis of axis electric field distribution of a ball-plate electrode gap, calculating critical electron collapse lengths of various gases under different voltages according to a gas discharge theory; determining a critical charge accumulation coefficient based on the effective ionization coefficient, the experimental data and the critical electron collapse length, and obtaining a gas discharge voltage calculation value according to a slightly non-uniform electric field gas discharge calculation model based on the critical charge accumulation coefficient; gas discharge voltage experiment values obtained by different gas impact discharge experiments are compared with a gas discharge voltage calculation value for verification, and a slightly non-uniform electric field discharge calculation model is verified.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of high-voltage discharge, in particular to a calculation method and application of discharge voltage of environment-friendly insulation gas under slightly non-uniform electric field. BACKGROUND

[0002] In electrical equipment, gas insulation materials such as air, nitrogen, SF6 and the like are relatively common, and among them, SF6 is widely used in electrical equipment due to its excellent insulation and arc extinguishing performance. However, due to the fact that the SF6 greenhouse effect potential value is about 23900 times that of CO2, and the atmospheric lifetime is about 3200 years, SF6 has been listed as one of the greenhouse gases to be limited in use in the Kyoto Protocol as early as 1997. For example, the SF6 usage of Sutong 1000kV GIL project is 19 tons / km, and the cumulative amount is 665 tons. If only the greenhouse effect caused by the natural leakage rate of the gas is considered, there will be 16000 tons of CO2 emitted into the atmosphere every year, which has a huge impact. In order to reduce the amount of SF6, it is urgent to find environment-friendly insulation gas with required physical and chemical properties. In recent years, C4F7N / CO2 gas has become a popular alternative to SF6, with good physical and chemical properties and high insulation strength. Existing research shows that the greenhouse effect potential value of C4F7N / CO2 is less than 2100 (not more than 9% of SF6), and the ozone depletion potential value is zero. At present, the cost of synthesis and purification of the new environment-friendly insulation gas is still high.

[0003] The acquisition of gas discharge voltage usually requires a large number of high-voltage experiments, and different engineering application scenarios make the electrode parameters and gas parameters different, resulting in a huge amount of experiments, time-consuming and laborious. High-voltage gas discharge experiments not only have high requirements for high-voltage, extra-high voltage power supply and various equipment (high equipment cost), but also have high cost of synthesis and purification of environment-friendly insulation gas, large gas consumption and huge cost. The experiment cannot exhaust the environment of slightly non-uniform electric field under different sizes, and the sizes of the experimental electrodes used by different research teams are different, which makes it difficult to compare and has other problems. Therefore, there is an urgent need for a relatively universal calculation model to reduce the amount of experiments, improve the efficiency of engineering design and save cost.

[0004] At present, the existing technology uses numerical calculation of the electrostatic field to calculate the impulse discharge voltage of dry air and nitrogen, but this method cannot calculate the changes caused by the change of voltage polarity, different gas pressure and electrode parameter changes. Another study calculates the CF3I / N2 mixed gas and SF6 reduced field strength based on the binomial approximation solution of the Boltzmann equation, which is only limited to uniform electric field and does not involve specific engineering application environment. Another research team calculates the streamer discharge voltage of CF3I / N2 mixed gas under the ball-plate electrode by using the streamer criterion, and calculates the breakdown voltage of air under the ball-plate electrode by using the SVM method and the streamer criterion, but the above methods are limited to specific electric field environment, specific gas, gas pressure and other conditions, and do not consider the influence of multiple factors, and the calculation efficiency is also low. SUMMARY

[0005] In view of the above problems, the present application provides a method for calculating the discharge voltage of environmentally friendly insulating gas under a slightly non-uniform electric field, and establishes a calculation model for the impulse discharge voltage of environmentally friendly insulating gas, which is used for fast and accurate calculation of gas impulse discharge, so as to overcome the above problems or at least partially solve the above problems.

[0006] In a first aspect, the embodiments of the present application provide a method for calculating the discharge voltage of environmentally friendly insulating gas under a slightly non-uniform electric field, which comprises: obtaining the effective ionization coefficient of different types of gas; when the effective ionization coefficient is 0, determining the critical breakdown field strength of each type of gas under different gas pressures; based on the axis electric field distribution curve of the ball-plate electrode gap and the critical breakdown field strength, calculating the critical electron avalanche length of each type of gas under different voltages; based on the effective ionization coefficient, the discharge voltage experimental value and the critical electron avalanche length, determining the critical charge accumulation coefficient, and based on the critical charge accumulation coefficient, obtaining the gas discharge voltage calculation value according to the slightly non-uniform electric field gas discharge calculation model; by comparing and verifying the gas discharge voltage experimental value obtained by different gas impulse discharge experiments with the gas discharge voltage calculation value, the slightly non-uniform electric field discharge calculation model is verified.

[0007] Optionally, the critical electron avalanche length of each type of gas under different voltages is calculated based on the axis electric field distribution of the ball-plate electrode gap according to the gas discharge theory, which comprises: obtaining the curvature radius r of the ball electrode and the electrode spacing d between the ball-plate electrode in the slightly non-uniform electric field environment, calculating the axis electric field distribution of the ball-plate electrode gap based on the mirror method, and comparing and verifying by the finite element method; based on the critical breakdown field strength and the axis electric field distribution, the critical electron avalanche length of each type of gas under different voltages V is determined.

[0008] Optionally, the formula for calculating the critical electron avalanche length is: ; Among them, E cr Let q1 be the critical breakdown field strength, r be the radius of curvature of the spherical electrode, q1 be the charge value at any point on the electric field along the electrode axis, and b be a constant.

[0009] Optionally, the step of determining the critical charge accumulation coefficient based on the effective ionization coefficient, experimental discharge voltage, and critical electron avalanche length, and obtaining the calculated gas discharge voltage based on the critical charge accumulation coefficient and a slightly non-uniform electric field gas discharge calculation model, includes: Based on the judgment conditions for the initiation of the stream in the gas discharge theory, as well as the effective ionization coefficient and the critical electron avalanche length, the critical ionization accumulation coefficient corresponding to the critical electron avalanche length is determined. Substitute the critical charge accumulation coefficient into the slightly non-uniform electric field discharge calculation model to calculate the gas discharge voltage.

[0010] Optionally, determining the critical ionization accumulation coefficient corresponding to the critical electron avalanche length based on the judgment conditions for stream initiation in gas discharge theory, as well as the effective ionization coefficient and the critical electron avalanche length, includes: The critical electron avalanche length was determined based on the effective ionization coefficient, the gas pressure, and the temperature collected during the experiment. Determine the critical ionization accumulation coefficient based on the critical electron avalanche length: ; Where A1 is the linear fitting parameter, B1 is the intercept of the linear fitting parameter, P is the air pressure, T is the temperature, and E is the reduced electric field. X is the effective ionization coefficient. cr The critical electron avalanche length.

[0011] Alternatively, the calculation model for a slightly non-uniform electric field discharge is as follows: ; Among them, M cr K is the critical ionization accumulation coefficient. B q1 is the Boltzmann constant, k is the nth charge, r is the position coordinate information of the particle, and X is the distance between any point on the electric field of the electrode axis and the spherical electrode.

[0012] Secondly, embodiments of this application provide a device for calculating the impulse discharge voltage of environmentally friendly insulating gas under a slightly non-uniform electric field environment, the device comprising: The acquisition module is used to obtain the effective ionization coefficients of different types of gases; The critical breakdown field strength determination module is used to determine the critical breakdown field strength of various gases under different pressures when the effective ionization coefficient is 0. The critical electron avalanche length determination module is used to calculate the critical electron avalanche length of various gases at different voltages based on the axial electric field distribution of the ball-plate electrode gap and the gas discharge theory. The calculation module is used to determine the critical charge accumulation coefficient based on the effective ionization coefficient, experimental data, and critical electron avalanche length, and to obtain the calculated value of the gas discharge voltage based on the critical charge accumulation coefficient and the gas discharge calculation model of a slightly non-uniform electric field. The verification module is used to verify the gas discharge voltage calculation model by comparing the experimental values ​​of gas discharge voltage obtained from different gas impact discharge experiments with the calculated values ​​of gas discharge voltage.

[0013] Thirdly, embodiments of this application provide an electronic device, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the above-described method for calculating the discharge voltage of environmentally friendly insulating gas under a slightly non-uniform electric field.

[0014] Thirdly, embodiments of this application provide a readable storage medium storing a program or instructions, which, when executed by a processor, implements the above-described method for calculating the discharge voltage of environmentally friendly insulating gas under a slightly non-uniform electric field.

[0015] The specific beneficial effects are as follows: This invention derives formulas for calculating the critical charge accumulation coefficient of different gases by using the effective ionization coefficients and critical electron avalanche lengths of different gases. By substituting the critical charge accumulation coefficient into a slightly non-uniform electric field discharge calculation model, this model can calculate the impulse discharge voltage under different conditions. The results were compared with experimental data from high-voltage discharge under the same conditions, showing minimal error and verifying the effectiveness of the proposed slightly non-uniform electric field discharge calculation model. This overcomes the limitation of existing calculation models that can only calculate the gas impulse discharge voltage under specific gases and electric field parameters. By using the calculated gas discharge voltage as a design benchmark, and adjusting parameters such as gap distance, electrode shape, gas medium, and pressure, the actual insulation capacity of the equipment can exceed the potential overvoltage threat while leaving sufficient safety margin, ultimately achieving a safe, reliable, and economical insulation design. The electric field non-uniformity and gas pressure parameters of this invention can be matched to actual engineering equipment, greatly improving insulation design efficiency and saving costs. It can be applied to the design, manufacturing, operation, and maintenance of almost all gas-insulated high-voltage equipment, transmission lines, and substations. Attached Figure Description

[0016] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the description of the embodiments of this application will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 This is a flowchart of the environmentally friendly insulating gas discharge voltage calculation method proposed in this invention.

[0018] Figure 2 The results of the reduced ionization and adsorption coefficients of SF6 for Bolsig+ were calculated.

[0019] Figure 3 This is a schematic diagram of the mirror image method for ball-plate electrodes.

[0020] Figure 4 The simulation results show the electric field distribution in the ball-plate electrode gap.

[0021] Figure 5 This is a comparison of the electric field distribution calculation results between the method of images and finite element simulation. Figure 5 In the middle: (a) is a spacing of 2.5 mm; (b) is a spacing of 5.0 mm; (c) is a spacing of 7.5 mm.

[0022] Figure 6 The results show a comparison between the calculated and experimental values ​​of the SF6 gas discharge voltage.

[0023] Figure 7 The results show the comparison between calculated and experimental values ​​of 9%C4F7N / 91%CO2 mixed gas under different parameter conditions; where (a) is at a spacing of 2.5 mm and (b) is at a spacing of 5 mm. Detailed Implementation

[0024] Exemplary embodiments of this application will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of this application are shown in the drawings, it should be understood that this application may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of this application and to fully convey the scope of this application to those skilled in the art.

[0025] A slightly non-uniform electric field refers to an electric field where the charge on an object and the electric potential in space are slightly non-uniform. It is essentially a variant of the electric field. Because the potential and energy distribution are not uniform in a specific direction, it generates electrodynamic forces, affecting physical phenomena such as the movement of electrons in the medium. For electrical equipment using environmentally friendly insulating gases such as C4F7N / CO2, the internal electric field distribution is designed and manufactured according to a slightly non-uniform electric field. Therefore, obtaining the gas discharge voltage under a slightly non-uniform field has significant application value for the insulation design of electrical equipment.

[0026] This invention proposes a method for calculating the discharge voltage of environmentally friendly insulating gas under a slightly non-uniform electric field, which includes the following steps: Step 1: Obtain the effective ionization coefficients of different types of gases; In the embodiments of this application, the effective ionization coefficient can be calculated using the Boltzmann equation or obtained through SST experiments. The Boltzmann equation describes the evolution of the particle distribution function in the position, velocity, and time dimensions, as shown in equation (1). The particle distribution function in the six-dimensional phase space (r,v) is f(r,v,t), where r is the particle's position coordinates, v is the particle's velocity, and t is time. It is assumed that the particle's velocity v is independent of its position r; the particle's acceleration is a = F / m, which is also independent of its position r. The right side of equation (1) is the collision term parameter, which considers the influence of the collision process on the distribution function.

[0027] (1) in, This represents the local rate of change of the distribution function f with time t; The gradient operator represents the location space. The gradient operator represents the velocity space; F represents the external force, and m represents the particle mass. Indicates a collision term.

[0028] Using the two-term approximation method, f can be simplified to obtain equation (2): (2) in, The simplified distribution function, for The 0th order term, v z The velocity in the Z direction, for The first-order term.

[0029] Download the Phelps collision cross-section database from https: / / nl.lxcat.net / data / download.php to obtain the main collision cross-sections of SF6. Then, use Bolsig+ to simulate and calculate the reduced ionization coefficient and reduced adsorption coefficient of the SF6 edge gas, such as... Figure 2 As shown.

[0030] Based on the reduced ionization coefficient and the reduced adsorption coefficient, the reduced effective ionization coefficient can be obtained according to formula (3). : (3) Where N is the number of molecules per unit volume. is the reduced ionization coefficient of the gas. is the reduced adsorption coefficient.

[0031] In addition, environmentally friendly insulating gases can be verified through the SST (Steady-State Thomson) experiment, which can test the ionization characteristics of gases (such as ionization coefficient and adsorption coefficient) to evaluate their insulation performance. The SST experiment yields environmentally friendly insulating gases, and it can be seen that the effective ionization coefficient of the novel environmentally friendly insulating gas C4F7N / CO2 shows a linear increasing trend, resulting in equation (4): (4) Where A1 is the linear fitting parameter, i.e., the slope, E is the reduced electric field, and Td is the Thomson voltammetry, 1 / Td = 10. -21 V*m 2 B1 is the intercept of the linear fitting parameters; Based on the data fitting from the SST experiment, we can conclude that: (5) Where k is the mixing ratio of the mixed gases, for example, if the mixed gases are 20% C4F7N / 80% CO2, then k = 20; Multiplying both sides of formula (4) by (N / P) yields formula (6): (6) Where P is air pressure; From the ideal gas law, after reduction, the formula for calculating the effective ionization coefficient is: (7) Where, k B K is the Boltzmann constant. B =1.38*10 -23 J / K; T is temperature.

[0032] Step 2: When the effective ionization coefficient is 0, determine the critical breakdown field strength of various gases under different gas pressures; Specifically, let equation (7) be the effective ionization coefficient. When the value equals 0, the critical reduced electric field strength (E / N) of the gas can be calculated. cn That is, the critical breakdown field strength Ecr.

[0033] Step 3: Based on the axial electric field distribution curve and critical breakdown field strength of the ball-plate electrode gap, calculate the critical electron avalanche length of various gases under different voltages; Optionally, step 3 may include the following sub-steps: Step 3.1: Obtain the radius of curvature r of the spherical electrode and the electrode spacing d between the spherical and plate electrodes in a slightly non-uniform electric field environment. Calculate the axial electric field distribution of the spherical-plate electrode gap based on the image method and verify it by comparison using the finite element method. In this embodiment, the axial electric field distribution of the ball-plate electrode gap can be determined by comparing and calculating using the method of images and the finite element method. Specifically: (1) Mirror method A sphere-plate electrode refers to a capacitor structure composed of a sphere and a plate, where the sphere acts as electrode A and the plate as electrode B. In the method of images, an identical sphere electrode 2, symmetrical to sphere electrode 1, is imaginarily placed on the other side of the plate. The charge originally distributed on the plate is equivalently distributed on sphere electrode 2, making the original electric field between the sphere and plate equal to the electric field vector between the two spheres. For example... Figure 3 As shown in the figure, point C is any point on the electric field of the electrode axis, at a distance X from spherical electrode 1, with a radius of curvature r, and the electrode spacing d between spherical electrode 1 and the plate electrode. The following equation can be obtained: (8) (9) Where D1 is the distance of the first charge q1 from the plate electrode, D n-1 q is the distance between the (n-1)th charge and the plate electrode. n For the nth charge, q n-1 This is the (n-1)th charge.

[0034] The electric field intensity at point C can be equivalent to the superposition of the electric fields of countless charges at point C. According to equations (8)-(9), we can obtain: (10) Where k represents the electrostatic constant, k = 9.0 × 10⁻⁶ 9 N·m 2 / C 2 ; Since the charge gradually decreases as n increases, the influence of the later terms becomes smaller and smaller, and the above can be simplified to equation (11): (11) Where C represents a relatively small constant value that can be ignored within the actual engineering calculation error range.

[0035] Combining the last two parameters in parentheses of equation (11) into parameter b, we can obtain the expression for the sphere-plate electric field as shown in equation (12): (12) Where b is a constant, and the calculated value of b based on experiments is approximately 0.05. q 1 represents the first charge.

[0036] (2) Finite element method Finite element simulation of the electric field was performed, and the simulation results are as follows: Figure 4 As shown in the figure, the maximum electric field intensity is near the surface of the spherical electrode, and the electric field intensity decreases with distance from the spherical electrode. Let the distance from any point on the axis between the spherical electrode and the plate electrode be denoted as . X ,like Figure 5 As shown, the analytical formula derived by the mirror method has a calculation result that is basically consistent with the finite element simulation result, with a maximum relative error of about 4.7%.

[0037] Step 3.2: Based on the axial electric field distribution and critical breakdown field strength, determine the appropriate voltage to apply. V Critical electron avalanche lengths for various gases; Specifically, firstly, based on the axial electric field distribution of the ball-plate electrode gap (Equation 12), the critical breakdown field strength is determined. E cr Substituting into equation (12) and transforming it, we can obtain the formula for calculating the critical electron avalanche length: (13) in, X cr The critical electron avalanche length.

[0038] Secondly, the formula for calculating the charge distribution of a charged spherical conductor under different voltages is as follows: (14) Where ε represents the dielectric constant, ε = ε r ε0, the relative permittivity of the gas is approximately 1, ε0 = 8.85 × 10⁻¹² F / m; R is the radius of the spherical electrode.

[0039] In this embodiment, the critical breakdown field strength of gaseous SF6 is known. E cr (SF6) = 8.8 kV / (mm*bar), then when P =0.1MPa Ecr (SF6) = 8.8 kV / mm. ① Using a graphical method, the distance between any point on the electrode axis and the ball electrode when different voltages are applied can be plotted. X With electric field strength E The curve. Based on this curve, when the electric field strength reaches the critical breakdown field strength... E cr hour, X The value is the corresponding critical electron avalanche length. X cr When plotting, input voltage values ​​are used, for example, when the input voltage is 15kV and 16kV, the charge q1 value under different voltages is obtained based on equation (14), and multiple electric field distribution curves are obtained based on equation (12). Finally, the critical breakdown field strength is used as the basis for the calculation. E cr Determine the critical electron avalanche length X cr .

[0040] ②Based on formula (13) and the critical electron avalanche length calculated by finite element simulation, such as Figure 5 As shown. The results obtained using methods ① and ② X cr The results of the comparison are shown in Table 1.

[0041] When determining the critical electron avalanche length, the critical electron avalanche length under different applied voltages can also be calculated based on equation (14) and the different influencing charge q1 values ​​under different voltages. X cr .

[0042] Table 1 Critical Electron Avalanche Length X cr Calculation results ; Step 4: Based on the gas's effective ionization coefficient, experimental discharge voltage, critical electron avalanche length, and critical charge accumulation coefficient, the calculated discharge voltage of the gas at this time is obtained according to the slightly non-uniform electric field discharge calculation model. Optionally, step 4 may include the following steps: Step 4.1: Based on the judgment conditions for the initiation of the stream in the gas discharge theory, as well as the effective ionization coefficient and the critical electron avalanche length, determine the critical ionization accumulation coefficient corresponding to the critical electron avalanche length; Specifically, the criteria for determining the initiation of a stream in gas discharge theory are as follows: (15) in, N crThis is the critical electron avalanche charge quantity. When the charge quantity at the electron avalanche head exceeds this value, the electric field becomes distorted and photoionization is enhanced, transforming into streamer discharge.

[0043] After transforming equation (15), the calculation model for gas impact voltage discharge voltage can be obtained: (16) Next, in equation (16) Defined as the ionization accumulation coefficient M Combining this with the expression for the effective ionization coefficient (Equation 7), the final ionization accumulation coefficient can be obtained as follows: (17) Since high-voltage discharge has already occurred, the discharge voltage obtained from high-voltage gas discharge experiments with different polarities is... V (i.e., the experimental voltage value), calculate X The length obtained when it is the critical electron avalanche length M The value represents the critical charge accumulation coefficient of the gas under different conditions. Mcr For example, the following three steps are required to calculate the critical charge accumulation coefficient of different gases using SF6 gas breakdown test data (i.e., actual experimental data values ​​of high-voltage discharge) and equation (17).

[0044] S1: High-voltage discharge voltage test data V Substituting the values ​​into the charge distribution calculation formula (Equation 14), we obtain the charge value, and then the electrode parameters are... r and d Substitute the electric field distribution analytical expression (Equation 12) to determine the parameter b; S2: The gas-reduced effective ionization coefficient was obtained through SST experiments and Bolsig+ simulations. Thus, parameters A1 and B1 are obtained; S3: Substituting the gas pressure and temperature collected during the experiment into equation (13), the critical electron avalanche length can be obtained. X cr ; S4: Substituting A1, B1, air pressure, and temperature into equation (17), the critical charge accumulation coefficient can be obtained. Mcr .

[0045] Based on the above steps, the effects of different types of gases under power frequency voltage and impulse voltages of different polarities can be obtained. Mcr The results are shown in Table 2.

[0046] Table 2 Critical Charge Accumulation Coefficient of Gas Mcr ; As mentioned above, the calculation model for gas impulse voltage discharge is derived from the classical gas streamer discharge theory, as shown in equation (16). Furthermore, by combining equations (7), (12), (14), and (17) above, the calculation model for slightly non-uniform electric field discharge can be obtained as follows: (18) Finally, based on the voltage polarity parameter, electric field distribution, electrode parameters, experimental voltage value of high-voltage discharge, gas pressure, effective ionization coefficient of gas, critical electron avalanche length of gas, and critical charge accumulation coefficient, the calculated value of gas discharge voltage can be calculated according to the slightly non-uniform electric field discharge calculation model (Equation 18).

[0047] Step 5: By comparing and verifying the experimental values ​​of gas discharge voltage obtained from different gas impact discharge experiments with the calculated values ​​of gas discharge voltage, the calculation model for slightly non-uniform electric field discharge is verified.

[0048] In this embodiment, the calculation results are experimentally verified through gas impact discharge experiments with different gas pressures, voltage polarities, and electrode parameters, proving that the error is small and meets engineering requirements. The calculated gas discharge voltage was compared with the experimental value provided by the high-voltage gas discharge control experiment under the same conditions, and the following results were obtained: (1) SF6 gas With a spherical-plate electrode spacing of 5 mm, the radius of curvature of the spherical electrode was calculated at atmospheric pressure (0.1 MPa) and high pressure (0.5 MPa). r =3mm, ball-plate electrode spacing d The lightning impulse 50% breakdown voltage of the SF6 gas gap with a diameter of 5mm was measured and compared with experimental values, such as... Figure 6 As shown in the figure, the maximum relative error for a typical insulating gas SF6 is 5.1%, which meets the engineering requirements.

[0049] (2) 9%C4F7N / 91%CO2 mixed gas The gas was chosen at this mixing ratio because its insulation properties are close to those of SF6, a typical insulating gas. Figure 1 The calculation process yielded the lightning impulse discharge voltage of the C4F7N / CO2 ball-plate electrode under this mixing ratio. The calculation results and the results of the high-voltage gas discharge experiment are as follows: Figure 7 As shown.

[0050] Gas discharge voltage was calculated using methods based on non-uniformity coefficients, corona charge criterion, Raether-Meek criterion, and the method proposed in this invention, respectively. The results are shown in Table 3. Table 3 shows that the method proposed in this application has the lowest calculation error.

[0051] Table 3. Differences between different calculation methods

[0052] Example 2: This application also provides an embodiment of an environmentally friendly insulating gas discharge voltage calculation device under a slightly non-uniform electric field, implemented based on the method in Embodiment 1 above, including: The acquisition module is used to obtain the effective ionization coefficients of different types of gases; The critical breakdown field strength determination module determines the critical breakdown field strength of various gases under different pressures when the effective ionization coefficient is 0. The critical electron avalanche length determination module is used to calculate the critical electron avalanche length of various gases under different voltages based on the axial electric field distribution curve and critical breakdown field strength of the ball-plate electrode gap. The calculation module is used to determine the critical charge accumulation coefficient based on the effective ionization coefficient, experimental discharge voltage, and critical electron avalanche length, and to obtain the calculated gas discharge voltage based on the critical charge accumulation coefficient and the gas discharge calculation model of a slightly non-uniform electric field. The verification module is used to verify the gas discharge voltage calculation model by comparing the experimental values ​​of gas discharge voltage obtained from different gas impact discharge experiments with the calculated values ​​of gas discharge voltage.

[0053] Although preferred embodiments of the present application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the embodiments of the present application.

[0054] The above provides a detailed description of the calculation method and application of the environmentally friendly insulating gas discharge voltage under a slightly non-uniform electric field provided in this application. Specific examples are used in this article to illustrate the principle and implementation of this application. The description of the above embodiments is only for the purpose of helping to understand the method and core idea of ​​this application. At the same time, for those skilled in the art, there will be changes in the specific implementation and application scope based on the idea of ​​this application. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for calculating the discharge voltage of environmentally friendly insulating gas under a slightly non-uniform electric field, characterized in that, The method includes: Obtain the effective ionization coefficients of different types of gases; When the effective ionization coefficient is 0, determine the critical breakdown field strength of various gases under different gas pressures; Based on the axial electric field distribution curve and critical breakdown field strength of the ball-plate electrode gap, the critical electron avalanche length of various gases under different voltages is calculated. Based on the effective ionization coefficient, experimental discharge voltage, and critical electron avalanche length, the critical charge accumulation coefficient is determined, and based on the critical charge accumulation coefficient, the calculated gas discharge voltage is obtained according to the gas discharge calculation model of a slightly non-uniform electric field. By comparing and verifying the experimental values ​​of gas discharge voltage obtained from different gas impact discharge experiments with the calculated values ​​of gas discharge voltage, the calculation model for slightly non-uniform electric field discharge is validated.

2. The method according to claim 1, characterized in that, The basis is the axial electric field distribution of the ball-plate electrode gap. The critical electron avalanche lengths of various gases at different voltages are calculated based on gas discharge theory, including: The radius of curvature r of the spherical electrode and the electrode spacing d between the spherical and plate electrodes are obtained in a slightly non-uniform electric field environment. The axial electric field distribution of the spherical-plate electrode gap is calculated based on the image method and verified by comparison using the finite element method. Based on the critical breakdown field strength and the axial electric field distribution, the critical electron avalanche length of various gases under different applied voltages V is determined.

3. The method according to claim 1, characterized in that, The formula for calculating the critical electron avalanche length is as follows: ； Among them, E cr Let q1 be the critical breakdown field strength, r be the radius of curvature of the spherical electrode, q1 be the charge value at any point on the electric field along the electrode axis, and b be a constant.

4. The method according to claim 3, characterized in that, The critical charge accumulation coefficient is determined based on the effective ionization coefficient, experimental discharge voltage, and critical electron avalanche length. Based on this critical charge accumulation coefficient, the calculated gas discharge voltage is obtained using a slightly non-uniform electric field gas discharge calculation model. This includes: Based on the judgment conditions for the initiation of the stream in the gas discharge theory, as well as the effective ionization coefficient and the critical electron avalanche length, the critical ionization accumulation coefficient corresponding to the critical electron avalanche length is determined. Substitute the critical charge accumulation coefficient into the slightly non-uniform electric field discharge calculation model to calculate the gas discharge voltage.

5. The method according to claim 4, characterized in that, The determination of the critical ionization accumulation coefficient corresponding to the critical electron avalanche length, based on the judgment conditions for stream initiation in gas discharge theory, the effective ionization coefficient, and the critical electron avalanche length, includes: The critical electron avalanche length was determined based on the effective ionization coefficient, the gas pressure, and the temperature collected during the experiment. Determine the critical ionization accumulation coefficient based on the critical electron avalanche length: ； Where A1 is the linear fitting parameter, B1 is the intercept of the linear fitting parameter, P is the air pressure, T is the temperature, and E is the reduced electric field. X is the effective ionization coefficient. cr The critical electron avalanche length.

6. The method according to claim 5, characterized in that, The calculation model for discharge in a slightly non-uniform electric field is as follows: ； Among them, M cr K is the critical ionization accumulation coefficient. B q1 is the Boltzmann constant, k is the nth charge, r is the position coordinate information of the particle, and X is the distance between any point on the electric field of the electrode axis and the spherical electrode.

7. A device for calculating the discharge voltage of environmentally friendly insulating gas under a slightly non-uniform electric field, characterized in that, The method described in any one of claims 1-6 includes: The acquisition module is used to obtain the effective ionization coefficients of different types of gases; The critical breakdown field strength determination module determines the critical breakdown field strength of various gases under different pressures when the effective ionization coefficient is 0. The critical electron avalanche length determination module is used to calculate the critical electron avalanche length of various gases under different voltages based on the axial electric field distribution curve and critical breakdown field strength of the ball-plate electrode gap. The calculation module is used to determine the critical charge accumulation coefficient based on the effective ionization coefficient, experimental discharge voltage, and critical electron avalanche length, and to obtain the calculated gas discharge voltage based on the critical charge accumulation coefficient and the gas discharge calculation model of a slightly non-uniform electric field. The verification module is used to verify the gas discharge voltage calculation model by comparing the experimental values ​​of gas discharge voltage obtained from different gas impact discharge experiments with the calculated values ​​of gas discharge voltage.

8. An electronic device, characterized in that, The device includes a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the method for calculating the discharge voltage of environmentally friendly insulating gas under a slightly non-uniform electric field as described in any one of claims 1-6.

9. A readable storage medium, characterized in that, The readable storage medium stores a program or instructions that, when executed by a processor, implement the method for calculating the discharge voltage of environmentally friendly insulating gas under a slightly non-uniform electric field as described in any one of claims 1-6.

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