Method and device for calculating series vacuum gap breakdown development process

Abstract

The invention relates to a calculation method and device for a series vacuum gap breakdown development process. The method comprises the following steps: constructing a series vacuum gap equivalent circuit model according to a plurality of vacuum gap equivalent vacuum gap parallel circuits; based on the series vacuum gap equivalent circuit model, determining a diversion coefficient of the vacuum gap according to plasma parameters of the cathode plasma and an electric field calculation model of the vacuum gap; based on the series vacuum gap equivalent circuit model, determining vacuum gap equivalent resistance according to the plasma expansion radius of the cathode plasma and the diversion coefficient of the vacuum gap; based on the series vacuum gap equivalent circuit model, determining vacuum gap breakdown voltage according to the vacuum gap breakdown data; and calculating the vacuum gap breakdown development process of the series vacuum gap according to the vacuum gap equivalent resistance and the vacuum gap breakdown voltage. By adopting the method, the application risk of the series vacuum gap in high voltage can be reduced.

Description

Technical Field

[0001] The present application relates to the field of electric power safety technology, and in particular to a method and device for calculating a series vacuum gap breakdown development process. Background Art

[0002] With the development of high voltage technology, vacuum gaps are often used to withstand high voltages. However, their withstand voltage performance shows a significant saturation effect as the gap spacing increases. Therefore, multiple short vacuum gaps are often connected in series in engineering to withstand ultra-high / ultra-high voltages. They are widely used in various fields, such as multi-break vacuum circuit breakers in the field of electrical engineering, compact linear accelerators in the field of high-energy physics, etc.

[0003] The breakdown of the vacuum gap is a key issue that limits the operating performance of the above-mentioned equipment. However, current research on vacuum breakdown is mostly limited to the breakdown of a single vacuum gap. There has been no targeted research on series vacuum breakdown, and it is impossible to describe the breakdown mechanism of series vacuum gaps and the key means to evaluate their insulation performance, resulting in risks in the application of series vacuum gaps at high voltages. Summary of the invention

[0004] Based on this, it is necessary to provide a calculation method, device, computer equipment, computer-readable storage medium and computer program product for the breakdown development process of a series vacuum gap, which can reduce the application risk of the series vacuum gap at high voltage, in order to address the above technical problems.

[0005] In a first aspect, the present application provides a method for calculating the breakdown development process of a series vacuum gap. The method comprises:

[0006] According to the vacuum gap parallel circuit equivalent to several vacuum gaps, a series vacuum gap equivalent circuit model is constructed;

[0007] Based on the series vacuum gap equivalent circuit model, according to the plasma parameters of the cathode plasma and the electric field calculation model of the vacuum gap, determining the conductivity of the vacuum gap;

[0008] Based on the series vacuum gap equivalent circuit model, determining the vacuum gap equivalent resistance according to the plasma expansion radius of the cathode plasma and the conductivity of the vacuum gap;

[0009] Based on the series vacuum gap equivalent circuit model and vacuum gap breakdown data, a vacuum gap breakdown voltage;

[0010] The vacuum gap breakdown development process of the series vacuum gaps is calculated according to the vacuum gap equivalent resistance and the vacuum gap breakdown voltage; the vacuum gap breakdown development process is used to describe the relationship between the breakdown conditions of each vacuum gap in the series vacuum gaps and time, so as to achieve safe application of the series vacuum gaps.

[0011] In a second aspect, the present application also provides a device for calculating the breakdown development process of a series vacuum gap. The device comprises:

[0012] A circuit model building module, used to build a series vacuum gap equivalent circuit model based on a plurality of vacuum gap equivalent vacuum gap parallel circuits;

[0013] A conductivity determination module, for determining the conductivity of the vacuum gap based on the series vacuum gap equivalent circuit model, according to the plasma parameters of the cathode plasma and the electric field calculation model of the vacuum gap;

[0014] An equivalent resistance obtaining module is used to determine the vacuum gap equivalent resistance based on the series vacuum gap equivalent circuit model, according to the plasma expansion radius of the cathode plasma and the conductivity coefficient of the vacuum gap;

[0015] A breakdown voltage obtaining module is used to obtain a vacuum gap breakdown voltage based on the series vacuum gap equivalent circuit model and vacuum gap breakdown data;

[0016] The breakdown process description module is used to calculate the vacuum gap breakdown development process of the series vacuum gap according to the vacuum gap equivalent resistance and the vacuum gap breakdown voltage; the vacuum gap breakdown development process is used to describe the relationship between the breakdown condition of each vacuum gap in the series vacuum gap and time, so as to realize the safe application of the series vacuum gap.

[0017] In a third aspect, the present application further provides a computer device. The computer device includes a memory and a processor, the memory stores a computer program, and the processor implements the following steps when executing the computer program:

[0018] According to the vacuum gap parallel circuit equivalent to several vacuum gaps, a series vacuum gap equivalent circuit model is constructed;

[0019] Based on the series vacuum gap equivalent circuit model, according to the plasma parameters of the cathode plasma and the electric field calculation model of the vacuum gap, determining the conductivity of the vacuum gap;

[0020] Based on the series vacuum gap equivalent circuit model, determining the vacuum gap equivalent resistance according to the plasma expansion radius of the cathode plasma and the conductivity of the vacuum gap;

[0021] Based on the series vacuum gap equivalent circuit model and vacuum gap breakdown data, a vacuum gap breakdown voltage;

[0022] The vacuum gap breakdown development process of the series vacuum gaps is calculated according to the vacuum gap equivalent resistance and the vacuum gap breakdown voltage; the vacuum gap breakdown development process is used to describe the relationship between the breakdown conditions of each vacuum gap in the series vacuum gaps and time, so as to achieve safe application of the series vacuum gaps.

[0023] In a fourth aspect, the present application further provides a computer-readable storage medium. The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the following steps are implemented:

[0024] According to the vacuum gap parallel circuit equivalent to several vacuum gaps, a series vacuum gap equivalent circuit model is constructed;

[0025] Based on the series vacuum gap equivalent circuit model, according to the plasma parameters of the cathode plasma and the electric field calculation model of the vacuum gap, determining the conductivity of the vacuum gap;

[0026] Based on the series vacuum gap equivalent circuit model, determining the vacuum gap equivalent resistance according to the plasma expansion radius of the cathode plasma and the conductivity of the vacuum gap;

[0027] Based on the series vacuum gap equivalent circuit model and vacuum gap breakdown data, a vacuum gap breakdown voltage;

[0028] The vacuum gap breakdown development process of the series vacuum gaps is calculated according to the vacuum gap equivalent resistance and the vacuum gap breakdown voltage; the vacuum gap breakdown development process is used to describe the relationship between the breakdown conditions of each vacuum gap in the series vacuum gaps and time, so as to achieve safe application of the series vacuum gaps.

[0029] In a fifth aspect, the present application further provides a computer program product. The computer program product includes a computer program, and when the computer program is executed by a processor, the following steps are implemented:

[0030] According to the vacuum gap parallel circuit equivalent to several vacuum gaps, a series vacuum gap equivalent circuit model is constructed;

[0031] Based on the series vacuum gap equivalent circuit model, according to the plasma parameters of the cathode plasma and the electric field calculation model of the vacuum gap, determining the conductivity of the vacuum gap;

[0032] Based on the series vacuum gap equivalent circuit model, determining the vacuum gap equivalent resistance according to the plasma expansion radius of the cathode plasma and the conductivity of the vacuum gap;

[0033] Based on the series vacuum gap equivalent circuit model and vacuum gap breakdown data, a vacuum gap breakdown voltage;

[0034] The vacuum gap breakdown development process of the series vacuum gaps is calculated according to the vacuum gap equivalent resistance and the vacuum gap breakdown voltage; the vacuum gap breakdown development process is used to describe the relationship between the breakdown conditions of each vacuum gap in the series vacuum gaps and time, so as to achieve safe application of the series vacuum gaps.

[0035] The above-mentioned calculation method, device, computer equipment, storage medium and computer program product for the breakdown development process of a series vacuum gap construct a series vacuum gap equivalent circuit model based on a vacuum gap parallel circuit equivalent to several vacuum gaps; based on the series vacuum gap equivalent circuit model, the conductivity of the vacuum gap is determined according to the plasma parameters of the cathode plasma and the electric field calculation model of the vacuum gap; based on the series vacuum gap equivalent circuit model, the vacuum gap equivalent resistance is determined according to the plasma expansion radius of the cathode plasma and the conductivity of the vacuum gap; based on the series vacuum gap equivalent circuit model, the vacuum gap breakdown voltage is determined according to the vacuum gap breakdown data; based on the vacuum gap equivalent circuit model, the vacuum gap breakdown development process of the series vacuum gap is calculated according to the vacuum gap equivalent resistance and the vacuum gap breakdown voltage; the vacuum gap breakdown development process is used to describe the relationship between the breakdown of each vacuum gap in the series vacuum gap and time, so as to achieve the safe application of the series vacuum gap.

[0036] By constructing a series vacuum gap equivalent circuit model of multiple vacuum gaps in series, the series effect of multiple vacuum gaps under the action of the electric field is carefully considered. The physical parameters of the cathode plasma and its expansion radius are combined with the electric field calculation model to accurately determine the conductivity of the vacuum gap, and then the equivalent resistance and breakdown voltage of the vacuum gap are derived. This method not only has high accuracy in predicting the breakdown voltage and resistance of a single vacuum gap, but also can dynamically capture and simulate the breakdown development process of the entire series vacuum gap system in a complex electric field environment, especially the current distribution, breakdown delay time and mutual influence between different vacuum gaps, to achieve early prediction of the breakdown process and scientific evaluation of the safety margin, effectively reduce the application risk of series vacuum gaps in high voltage, greatly improve the reliability and long-term stable operation capability of high-voltage equipment in harsh environments, ensure safe application under high-stress working conditions, thereby extending the service life of the equipment and reducing maintenance costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 An application environment diagram of a method for calculating a series vacuum gap breakdown development process in one embodiment;

[0038] Figure 2A schematic flow chart of a method for calculating a series vacuum gap breakdown development process in one embodiment;

[0039] Figure 3 A schematic flow chart of a first method for determining a conductivity coefficient in an embodiment;

[0040] Figure 4 A schematic diagram of a flow chart of a method for calculating a gap breakdown current in one embodiment;

[0041] Figure 5 is a schematic flow chart of a second method for determining a conductivity coefficient in an embodiment;

[0042] Figure 6 It is a schematic flow chart of a third method for determining a conductivity coefficient in one embodiment;

[0043] Figure 7 A schematic flow chart of a first method for obtaining a vacuum gap equivalent resistance in one embodiment;

[0044] Figure 8 A schematic diagram of a flow chart of a method for constructing a series vacuum gap equivalent circuit model in one embodiment;

[0045] Fig. 9 is a flow chart of a second method for calculating the equivalent resistance of a vacuum gap in one embodiment;

[0046] Fig.10 A block diagram of a device for calculating a series vacuum gap breakdown development process in one embodiment;

[0047] Fig.11 FIG. 4 is a diagram showing the internal structure of a computer device in one embodiment. DETAILED DESCRIPTION

[0048] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0049] The calculation method of the series vacuum gap breakdown development process provided in the embodiment of the present application can be applied to Figure 1In the application environment shown. Among them, the terminal 102 communicates with the server 104 through the network. The data storage system can store the data that the server 104 needs to process. The data storage system can be integrated on the server 104, or it can be placed on the cloud or other network servers. The server 104 obtains the circuit parameters for constructing the series vacuum gap equivalent circuit model from the terminal 102, and the server 104 constructs the series vacuum gap equivalent circuit model according to the vacuum gap parallel circuit equivalent to several vacuum gaps; based on the series vacuum gap equivalent circuit model, the conductivity of the vacuum gap is determined according to the plasma parameters of the cathode plasma and the electric field calculation model of the vacuum gap; based on the series vacuum gap equivalent circuit model, the vacuum gap equivalent resistance is determined according to the plasma expansion radius of the cathode plasma and the conductivity of the vacuum gap; based on the series vacuum gap equivalent circuit model, the vacuum gap breakdown voltage is determined according to the vacuum gap breakdown data; according to the vacuum gap equivalent resistance and the vacuum gap breakdown voltage, the vacuum gap breakdown development process of the series vacuum gap is calculated; the vacuum gap breakdown development process is used to describe the relationship between the breakdown of each vacuum gap in the series vacuum gap and time, so as to realize the safe application of the series vacuum gap. The terminal 102 may be, but is not limited to, various personal computers, laptop computers, smart phones, tablet computers, and IoT devices. The server 104 may be implemented as an independent server or a server cluster consisting of multiple servers.

[0050] In one embodiment, Figure 2 As shown in the figure, a calculation method for the development process of series vacuum gap breakdown is provided. Figure 1 The server in the example is used to illustrate the following steps:

[0051] Step 202, constructing a series vacuum gap equivalent circuit model based on a plurality of vacuum gap equivalent parallel vacuum gap circuits.

[0052] The vacuum gap refers to the actual physical space distance between two electrodes in an electrical system. In this space, breakdown may occur under the action of the electric field, causing current to discharge through the space gap. The characteristics of the vacuum gap (such as spacing, shape, material, electric field strength, etc.) directly affect its breakdown behavior and electrical characteristics.

[0053] The vacuum gap parallel circuit may be a circuit in which the vacuum gap is equivalent to a plurality of circuit elements, and the plurality of equivalent circuit elements are connected in parallel.

[0054] Among them, the series vacuum gap equivalent circuit model can be constructed by combining multiple vacuum gap circuits in series to form an equivalent overall circuit model. In this model, the electrical characteristics of each vacuum gap (such as equivalent resistance and breakdown voltage) can be predicted and analyzed through this model. This model can simulate the series effect of multiple vacuum gaps under the action of electric field, and help study and predict the breakdown development process of each vacuum gap.

[0055] Among them, the power circuit equivalent circuit model can be an equivalent circuit model used to simulate the behavior of the actual power circuit in the electrical system. It replaces the complex actual circuit with equivalent circuit elements (such as resistors, inductors, capacitors, etc.) to simplify analysis and calculation. This model can help study the electrical characteristics of the power circuit under various working conditions, such as voltage, current and power distribution, and facilitate the evaluation of the stability and efficiency of the power circuit.

[0056] Among them, the equivalent circuit model of the measurement and control device can be used to represent the equivalent circuit model of the behavior of the measurement and control equipment in the electrical system. By equating the electrical characteristics of the measurement and control device to a combination of resistors, capacitors or inductors, it is easier to analyze its role and response in a complex system. This model can simplify the analysis and evaluate the performance of the equipment under different electrical conditions when designing and optimizing the measurement and control equipment.

[0057] Among them, the stray parameter equivalent circuit model can be an equivalent circuit model used to describe the non-ideal effects introduced by non-ideal components and circuit layout in the electrical system, such as parasitic capacitance, parasitic inductance or resistance. Although these stray parameters are not deliberately added in the design, they will have an important impact on the performance in high-frequency or high-voltage electrical systems. Through the equivalent circuit model, these stray parameters can be effectively analyzed and compensated to improve the performance and stability of the system.

[0058] The vacuum gap equivalent resistance may be the resistance obtained by converting the vacuum gap into a vacuum gap parallel circuit.

[0059] The vacuum gap breakdown voltage may be a voltage value capable of breaking through the vacuum gap.

[0060] Specifically, in order to accurately simulate the electrical characteristics of multiple vacuum gaps in series under an electric field, the series vacuum gap equivalent circuit model should include an equivalent capacitance model of the vacuum gap, an equivalent variable resistance model, and other auxiliary device models (if any). Therefore, each independent vacuum gap is equivalent to a parallel combination of a vacuum gap equivalent capacitance to be determined and a vacuum gap equivalent resistance to be determined, that is, a vacuum gap parallel circuit; the series connection of multiple vacuum gaps is equivalent to the series connection of multiple vacuum gap parallel circuit combinations. Among them, the parameters of the vacuum gap equivalent capacitance to be determined can be experimentally determined, or determined by finite element method or surface charge method simulation calculation, and the parameters of auxiliary devices, such as voltage-equalizing capacitors, current-limiting resistors, etc., should be experimentally determined.

[0061] In addition to the series vacuum gap equivalent circuit model, it is also necessary to construct the power supply loop equivalent circuit model, the measurement and control device equivalent circuit model, and the equivalent circuit model of the stray parameters.

[0062] The equivalent circuit model of the power supply circuit should include all the main component models of the power supply circuit; in particular, the controlled power supply should also include the corresponding control module and control algorithm to achieve an accurate characterization of the power supply behavior characteristics under the condition of breakdown development. The parameters of the main component models should be determined by actual experiments.

[0063] For the equivalent circuit model of the measurement and control device, since the equivalent capacitance of the vacuum gap is only in the pF order, the parameters of common measurement and control devices are much larger than this order, so it is necessary to establish the equivalent circuit model of the measurement and control device. The relevant parameters in the measurement and control device model should be experimentally determined if conditions permit; if they cannot be experimentally determined, they should be provided by the measurement and control device supplier or determined through simulation calculation.

[0064] For the equivalent circuit model of stray parameters, since the equivalent capacitance of the vacuum gap itself is small and the equivalent frequency of vacuum breakdown is high, the equivalent capacitance and inductance parameters will have a great influence on the breakdown development process. The components included in the stray parameter model should be determined according to the actual arrangement and wiring method of the series vacuum gap, which should at least include: (1) the mutual capacitance between the electrodes of the series vacuum gap; (2) the capacitance of each electrode to the ground; (3) the equivalent inductance of the connecting line between the power supply and the series vacuum gap; (4) the equivalent resistance and inductance of the grounding part.

[0065] Step 204 , based on the series vacuum gap equivalent circuit model, according to the plasma parameters of the cathode plasma and the electric field calculation model of the vacuum gap, the conductivity of the vacuum gap is determined.

[0066] Among them, plasma parameters can be physical quantities that describe the state and characteristics of plasma, usually including electron density, electron temperature, ion density, ion temperature, plasma radius, etc. These parameters determine the behavior of plasma in the electric field, such as conductivity, expansion speed and its interaction with the surrounding medium. In electrical systems, plasma parameters are key inputs in calculating the electric field distribution and breakdown process, affecting the generation, expansion and final breakdown behavior of plasma.

[0067] Among them, the electric field calculation model can be used to simulate the distribution of electric fields in different physical environments, taking into account factors such as electrode structure, spatial geometry, and material properties. By solving Maxwell's equations, the model can accurately predict the electric field strength and direction under different voltages and charge distributions. In vacuum gap research, the electric field calculation model is the basis for predicting charge flow, breakdown paths, and conductive channel formation, helping researchers analyze the impact of breakdown voltage and electric field distribution on system performance.

[0068] Specifically, based on the series vacuum gap equivalent circuit model as a constraint condition, the physical properties of the cathode plasma that can directly affect the distribution of the electric field in the vacuum gap, such as plasma density, electron temperature, expansion radius, and time characteristics of plasma generation, are analyzed in detail to determine how the charge moves between the electrodes. Combined with the electric field calculation model of the vacuum gap, the path of the current through the space gap is calculated by simulating the change of the electric field intensity at different positions. Since the determination of the conductivity is a multi-dimensional process, it not only depends on the geometry of the space gap, but also involves the formation and expansion of the plasma before breakdown and its influence on the local electric field. Therefore, numerical simulation methods are usually used to accurately model the interaction between the plasma and the electric field to obtain the conductivity.

[0069] Step 206 , based on the series vacuum gap equivalent circuit model, according to the plasma expansion radius of the cathode plasma and the conductivity coefficient of the vacuum gap, determine the vacuum gap equivalent resistance.

[0070] The plasma expansion radius refers to the maximum distance that the cathode plasma expands from the electrode surface to the surrounding space under the action of the electric field. It reflects the range of plasma diffusion in the electric field and is a key factor in the interaction between the plasma and the electric field in the vacuum gap. The size of the expansion radius depends on the electric field strength, plasma parameters and dielectric properties, and directly affects the formation of the conductivity channel and the conductive properties in the space gap.

[0071] Specifically, based on the previously constructed series vacuum gap equivalent circuit model as a constraint condition, combined with the expansion of cathode plasma, the expansion radius and distribution characteristics of plasma in the vacuum gap are calculated, especially the influence of the expansion radius on the electric field distribution in the space gap. During the plasma expansion process, the formation of the conductivity channel directly affects the flow path and intensity of the current, which determines the conductivity characteristics of the vacuum gap. Combined with the conductivity coefficient, the flow of current in the vacuum gap is further quantified. The conductivity coefficient not only reflects the flow ability of the current in the electric field, but also combines the geometry of the space gap and the change of the electric field intensity. Considering the dynamic behavior of cathode plasma under different voltage conditions and its influence on the conductive path, the calculation process needs to integrate many factors, such as the geometry of the space gap, electrode materials, electric field intensity, the formation and distribution of the conductivity path, the evolution of plasma, etc., and finally calculate the vacuum gap equivalent resistance of the series vacuum gap equivalent circuit model through numerical simulation or accurate analytical solution.

[0072] Step 208 : determining the vacuum gap breakdown voltage based on the series vacuum gap equivalent circuit model and the vacuum gap breakdown data.

[0073] Specifically, the breakdown voltage values ​​in experimental or historical data are used in combination with the physical parameters of the vacuum gap (such as spacing, shape, material properties, etc.) to compare the actual breakdown voltage with the calculation results of the model. Then, by adjusting the key parameters in the model (such as electric field strength, electrode spacing, etc.) to make it consistent with the actual breakdown data, the calculation accuracy of the breakdown voltage is further optimized. This process needs to comprehensively consider factors such as the local electric field enhancement effect of the space gap, the formation of plasma and its influence on the electric field, to ensure that the calculation results can accurately reflect the actual breakdown behavior of the vacuum gap, and finally obtain the vacuum gap breakdown voltage of each vacuum gap.

[0074] In practical applications, the breakdown voltage can be calculated mainly through three methods: experiment, simulation calculation and approximate estimation by formula.

[0075] If the experimental method is adopted, the vacuum gap should be subjected to no less than 100 breakdown tests, with the breakdown voltage as the horizontal axis and the probability of breakdown below this voltage as the proportion of the total number of breakdowns as the vertical axis, and the three-parameter Weibull cumulative probability formula is used for fitting. Based on the fitting results, the breakdown voltage when the breakdown probability is 50% is obtained, and this voltage is considered to be the breakdown voltage of the vacuum gap.

[0076] If the simulation calculation method is used, the calculation is mainly performed through the electrostatic field of the vacuum gap; the calculated excitation voltage is gradually increased from the first to the highest, until the field strength value on the electrode surface exceeds the breakdown field strength of the material, and the corresponding voltage is considered to be the breakdown voltage of the vacuum gap.

[0077] If approximate estimation is performed through formulas, it is necessary to make estimates based on actual working conditions and commonly used formulas in the industry.

[0078] Step 210 , calculating the vacuum gap breakdown development process of the series vacuum gap according to the vacuum gap equivalent resistance and the vacuum gap breakdown voltage.

[0079] The vacuum gap breakdown development process may be data describing the relationship between the breakdown conditions of each vacuum gap in the series vacuum gap and time, so as to achieve safe application of the series vacuum gap.

[0080] Specifically, after determining the vacuum gap equivalent resistance and vacuum gap breakdown voltage, the voltage distribution and current flow of each vacuum gap at different time points are calculated through the time stepping algorithm. The simulation of the vacuum gap breakdown development process is not only a description of the change in electric field strength, but also involves charge accumulation, the formation of discharge paths, and the mutual influence between space gaps. In the simulation of the entire vacuum gap breakdown development process, it is necessary to pay close attention to the dynamic changes of the local electric field in the vacuum gap and the gradual expansion of the breakdown path. Through the precise simulation of this process, the role of each vacuum gap in the entire system can be fully analyzed, the breakdown moment and the occurrence time of electrical faults can be predicted, and the vacuum gap breakdown development process of the simulated series vacuum gap can be obtained.

[0081] In practical applications, at each time step, the voltage of each vacuum gap is calculated. If the gap voltage is greater than the gap breakdown voltage, the gap is considered to have broken down; otherwise, the gap is considered not to have broken down. If all gaps have broken down, or the calculation time has reached the set maximum calculation time, the calculation ends.

[0082] In the above-mentioned calculation method for the breakdown development process of a series vacuum gap, an equivalent circuit model of a series vacuum gap is constructed by a vacuum gap parallel circuit equivalent to several vacuum gaps; based on the equivalent circuit model of the series vacuum gap, the conductivity of the vacuum gap is determined according to the plasma parameters of the cathode plasma and the electric field calculation model of the vacuum gap; based on the equivalent circuit model of the series vacuum gap, the equivalent resistance of the vacuum gap is determined according to the plasma expansion radius of the cathode plasma and the conductivity of the vacuum gap; based on the equivalent circuit model of the series vacuum gap, the vacuum gap breakdown voltage is determined according to the vacuum gap breakdown data; based on the vacuum gap equivalent resistance and the vacuum gap breakdown voltage, the vacuum gap breakdown development process of the series vacuum gap is calculated; the vacuum gap breakdown development process is used to describe the relationship between the breakdown of each vacuum gap in the series vacuum gap and time, so as to realize the safe application of the series vacuum gap.

[0083] By constructing a series vacuum gap equivalent circuit model of multiple vacuum gaps in series, the series effect of multiple vacuum gaps under the action of the electric field is carefully considered. The physical parameters of the cathode plasma and its expansion radius are combined with the electric field calculation model to accurately determine the conductivity of the vacuum gap, and then the equivalent resistance and breakdown voltage of the vacuum gap are derived. This method not only has high accuracy in predicting the breakdown voltage and resistance of a single vacuum gap, but also can dynamically capture and simulate the breakdown development process of the entire series vacuum gap system in a complex electric field environment, especially the current distribution, breakdown delay time and mutual influence between different vacuum gaps, to achieve early prediction of the breakdown process and scientific evaluation of the safety margin, effectively reduce the application risk of series vacuum gaps in high voltage, greatly improve the reliability and long-term stable operation capability of high-voltage equipment in harsh environments, ensure safe application under high-stress working conditions, thereby extending the service life of the equipment and reducing maintenance costs.

[0084] In one embodiment, Figure 3 As shown, based on the series vacuum gap equivalent circuit model, according to the plasma parameters of the cathode plasma and the electric field calculation model of the vacuum gap, the conductivity of the vacuum gap is determined, including:

[0085] Step 302 , based on the series vacuum gap equivalent circuit model, the radius of the cathode plasma is applied to the electric field calculation model to obtain the spatial potential distribution of the vacuum gap.

[0086] Among them, spatial potential distribution can refer to the potential value at each spatial point in the description of the electric field. It describes the electrostatic energy distribution of the electric field in space, which is usually determined by the charge distribution and boundary conditions. By solving the basic equations of the electrostatic field, such as Poisson's equation or Laplace's equation, the potential distribution in the entire space can be obtained.

[0087] Specifically, in the state of vacuum gap breakdown, based on the series vacuum gap equivalent circuit model as a constraint condition, the electric field calculation model of the vacuum gap under the initial condition (no cathode plasma) is established. The model should include the cathode region, the anode region and the vacuum region; the cathode potential is set to 0 as the reference potential; the anode potential is an arbitrary given value US; the boundary condition is the Neumann boundary condition. The electric field distribution of the vacuum gap under the initial condition can be calculated, and the calculation equation is:

[0088]

[0089] Where: ——The electric potential distribution at a point in space.

[0090] A cathode plasma is added to the model. Its shape is spherical, with the center of the sphere located at the maximum electric field on the cathode surface, and the overlap between the sphere and the cathode is removed; the potential of the cathode plasma is the same as that of the cathode. The ratio of the radius of the hemisphere to the vacuum gap spacing is defined as r. Initially set r = 0.1. Considering the vacuum gap of the cathode plasma, the spatial electric field distribution of the vacuum gap is calculated, and the calculation equation is:

[0091]

[0092] Where: ——potential distribution at a certain point in space; ρ——space charge density; ε——dielectric constant.

[0093] Step 304, calculating the spatial electric field distribution of the vacuum gap according to the spatial potential distribution.

[0094] The spatial electric field distribution can refer to the strength and direction of the electric field at each point in space. It is determined by the source of the electric field (such as charge or voltage difference) and the spatial geometry, and reflects the effect of the electric field at different locations. The electric field is the result of the potential gradient, that is, it is calculated by differentiating the spatial potential distribution.

[0095] Specifically, after obtaining the spatial potential distribution, the electric field strength and direction at each position in the vacuum gap can be obtained by performing gradient calculations on the spatial potential distribution. This process requires special attention to the local electric field enhancement phenomenon in the cathode plasma expansion region. Near the plasma boundary, the electric field strength usually increases significantly, and the non-uniformity of the electric field is also manifested through the potential distribution. Because the distribution of the electric field directly determines the formation path and development direction of the breakdown current, with the help of numerical simulation tools, the spatial electric field distribution can be more accurately depicted, especially the electric field behavior in complex electrode structures and asymmetric spatial gaps. Based on the spatial potential distribution, the spatial electric field distribution is calculated, and the calculation equation is:

[0096]

[0097] Where: E is the electric field strength at a point in space.

[0098] Step 306: Calculate the gap breakdown current according to the spatial potential distribution and the spatial electric field distribution.

[0099] Among them, the gap breakdown current can refer to the current generated after the dielectric or space gap breaks down and forms a conductive path when the electric field strength reaches a certain critical value. This current is determined by the electric field strength at the time of breakdown, the electron emission density and the formation of the conductive channel. During the breakdown process, the electric field drives the charge through the gap, causing the current to suddenly increase, thereby generating the gap breakdown current.

[0100] Specifically, after obtaining the spatial electric field distribution, based on the acceleration of the electric field on the charge and the formation process of the conductive channel, according to the electric field strength and its distribution in space, the motion trajectory of the free charge (mainly ions and electrons) under the action of the electric field is calculated, especially the charge accumulation and release in the cathode plasma expansion zone. At the moment of breakdown, the charge forms a conductive path under the action of the electric field and begins to flow through the vacuum gap, which can generate a gap breakdown current. The size of the gap breakdown current is directly related to the electric field distribution, charge density and the formation of the conductive channel. The calculation process needs to comprehensively consider the influence of the electric field on the plasma, the conductivity of the medium in the space gap and the time change of the electric field. Through the dynamic simulation of the breakdown process, the gap breakdown current at the time of breakdown and the change law of the gap breakdown current over time can be accurately calculated.

[0101] Step 308: determining the conductivity of the vacuum gap according to the gap breakdown current and the radius of the cathode plasma.

[0102] Specifically, after calculating the gap breakdown current, if the currently calculated gap breakdown current does not converge, the electron emission density generated by the calculated gap breakdown current is used to calculate the spatial potential distribution again and further calculate the gap breakdown current until the calculated gap breakdown current converges, and the obtained gap breakdown current is then combined with the expansion radius of the cathode plasma to calculate the conductivity.

[0103] In this embodiment, by constructing a series vacuum gap equivalent circuit model and applying the radius of the cathode plasma to the electric field calculation, the spatial potential distribution and electric field distribution of the vacuum gap are accurately determined. This method can better capture the local enhancement effect of the electric field in the vacuum gap, and accurately calculate the gap breakdown current by combining the changes in the spatial potential and the electric field. Finally, by analyzing the relationship between the breakdown current and the plasma expansion radius, the conductivity of the vacuum gap is determined. This series of steps enables a more comprehensive characterization of the breakdown behavior of the vacuum gap under different electric field conditions, improves the safety and reliability of the system under high voltage conditions, and provides a strong basis for the prediction of the breakdown current and the design of electrical equipment.

[0104] In one embodiment, Figure 4 As shown, according to the spatial potential distribution and the spatial electric field distribution, the gap breakdown current is calculated, including:

[0105] Step 402: Calculate the initial electron emission density of the vacuum gap according to the spatial potential distribution and the spatial electric field distribution.

[0106] Among them, the initial electron emission density can refer to the number of electrons released per unit area under the initial electric field on the cathode surface. It is related to the electric field strength and plasma characteristics near the cathode, and reflects the ability of electrons to be emitted from the cathode into the vacuum gap at the initial stage of breakdown. The initial electron emission density is an important parameter for calculating the gap breakdown current, which directly affects the start-up stage of the breakdown process.

[0107] Specifically, the initial electrons are released at a certain distance outside the cathode plasma surface, which is less than 0.01r. Under the effect of the spatial point distribution and the spatial electric field distribution on the charged particles, the initial velocity of the electrons is:

[0108]

[0109] Where: v0——initial velocity of electron; ——the potential at the location where the electron is released; ——The normal vector pointing to the outside of the emitting surface.

[0110] The potential boundary condition at the emitting surface is:

[0111]

[0112] Where: d buf ——The distance between the electron emission position and the surface of the cathode gas group.

[0113] On the electron emission surface, the initial electron emission density is:

[0114]

[0115] Where: J0——initial electron emission density.

[0116] Step 404 , performing surface integration on the initial electron emission density of the cathode plasma to obtain the initial gap breakdown current.

[0117] Among them, the initial gap breakdown current can be the initial current passing through the empty gap when the vacuum gap begins to undergo electrical breakdown. It is obtained by performing surface integration of the initial electron emission density and represents the current magnitude when the breakdown process starts. This current magnitude reflects the current conduction capability under the action of the electric field at the initial stage of breakdown and is a key indicator for breakdown analysis.

[0118] Specifically, the initial electron emission density is integrated over the entire surface of the cathode plasma to obtain the initial gap breakdown current I0.

[0119] Under the action of the electric field force, the electrons move from the initial position to the anode, and the motion equation is:

[0120]

[0121] Where: m e ——Electron mass; q e ——Electron charge; ——Electron speed.

[0122] At each time step, the emitted electrons are calculated according to Move, and at the same time emit a new batch of electrons at the emission surface, the number of electrons is determined by the current density and the time step. Advance the time step until all the first batch of emitted electrons have reached the anode.

[0123] Step 406 , when it is detected that all the electrons of the cathode plasma have reached the anode from the cathode, an updated spatial charge distribution is obtained.

[0124] Among them, updating the spatial charge distribution can refer to the redistribution of charge in the vacuum gap after the electrons move from the cathode to the anode. Due to the movement of electrons and the passage of current, the charge density in the space will change, which in turn affects the distribution of the entire electric field and potential. The update of this distribution helps to reflect the dynamics of charge changes during the breakdown process and ensure the accuracy of subsequent calculations.

[0125] Specifically, when it is detected that all the electrons of the cathode plasma have reached the anode from the cathode, the spatial potential distribution is recalculated based on the above-mentioned calculation equation for point distribution for the vacuum gap of the cathode plasma to obtain an updated spatial charge distribution.

[0126] Step 408, calculating the updated spatial potential distribution and the updated spatial electric field distribution of the vacuum gap according to the updated spatial charge distribution.

[0127] The updated spatial electric field distribution can be the electric field distribution recalculated based on the updated spatial charge distribution. With the movement of electrons and the re-accumulation of charges, the electric field strength and direction will also change. The updated electric field distribution reflects the change of the electric field in the vacuum gap with time and space. This plays an important role in regulating the subsequent electron emission and current conduction.

[0128] Specifically, similar to the implementation process of step 302, after adding cathode plasma to the model, its shape is spherical, the center of the sphere is located at the maximum electric field on the cathode surface, and the part overlapping the sphere and the cathode is removed; the potential of the cathode plasma is the same as that of the cathode. The ratio of the radius of the hemisphere to the vacuum gap spacing is defined as r. According to the updated spatial charge distribution, the updated spatial potential distribution of the vacuum gap is calculated for the vacuum gap considering the cathode plasma, and the calculation equation is:

[0129]

[0130] Where: ——potential distribution at a certain point in space; ρ——space charge density; ε——dielectric constant.

[0131] According to the updated space potential distribution, the updated space electric field distribution is calculated, and the calculation equation is:

[0132]

[0133] Where: E is the electric field strength at a point in space.

[0134] Step 410, calculating the updated electron emission density of the vacuum gap according to the updated spatial potential distribution and the updated spatial electric field distribution.

[0135] The updated electron emission density can be the number of electrons emitted per unit area recalculated based on the updated spatial electric field distribution. As the spatial electric field changes, the electron emission capacity of the cathode surface will also be dynamically adjusted. The updated electron emission density can better reflect the emission behavior under the current electric field conditions and provide basic data for calculating the subsequent breakdown current.

[0136] Specifically, similar to the implementation process of step 402, electrons are released at a certain distance outside the cathode plasma surface, and the distance is less than 0.01r. Under the effect of updating the spatial point distribution and updating the spatial electric field distribution on the charged particles, the initial velocity of the electrons is:

[0137]

[0138] Where: v0——initial velocity of electron; ——the potential at the location where the electron is released; ——The normal vector pointing to the outside of the emitting surface.

[0139] The potential boundary condition at the emitting surface is:

[0140]

[0141] Where: d buf ——The distance between the electron emission position and the surface of the cathode gas group.

[0142] On the electron emission surface, update the electron emission density to:

[0143]

[0144] Where: J1 – Updated electron emission density.

[0145] Step 412, performing surface integration on the updated electron emission density of the cathode plasma to obtain the gap breakdown current.

[0146] Specifically, similar to the implementation process of step 404, the updated electron emission density is integrated over the surface of the entire cathode plasma to obtain the gap breakdown current I1.

[0147] Under the action of the electric field force, the electrons move from the initial position to the anode, and the motion equation is:

[0148]

[0149] Where: m e ——Electron mass; q e ——Electron charge; ——Electron speed.

[0150] At each time step, the emitted electrons are calculated according to Move, and at the same time emit a new batch of electrons at the emission surface, the number of electrons is determined by the current density and the time step. Advance the time step until all the first batch of emitted electrons have reached the anode.

[0151] In this embodiment, the initial electron emission density is calculated by the spatial potential and electric field distribution, and the initial gap breakdown current is obtained by surface integration; after the electrons reach the anode, the spatial charge distribution is updated, the new potential and electric field distribution are calculated, the electron emission density is calculated again and the updated breakdown current is obtained. Through repeated iterations, this method can capture the charge accumulation and electric field evolution in the vacuum gap in real time, thereby effectively improving the accuracy and controllability of the breakdown process. It helps to more accurately predict and regulate the breakdown behavior of electrical equipment, significantly improve the stability and safety of the system under high voltage, and provide a reliable basis for equipment design and protection.

[0152] In one embodiment, Figure 5 As shown, the conductivity of the vacuum gap is determined according to the gap breakdown current and the radius of the cathode plasma, including:

[0153] Step 502, calculating the current offset between the initial gap breakdown current and the gap breakdown current.

[0154] Among them, the current offset can be the difference between the initial gap breakdown current and the gap breakdown current, which is usually used to determine whether the calculation has converged. If the current offset is large, it means that there is a large difference between the currently calculated breakdown current and the expected value, and the electron emission density or electric field distribution needs to be further adjusted; if the current offset tends to zero, it indicates that the calculation has converged and the current value has reached a stable state, reflecting the dynamic stability of the breakdown process.

[0155] Specifically, the gap breakdown current is subtracted from the initial gap breakdown current, and the obtained difference is divided by the gap breakdown current. The final calculation result is the current offset.

[0156] Step 504 : When the current offset is not converged, the electron trajectory of the vacuum gap is calculated according to the updated electron emission density.

[0157] Among them, the electron trajectory can refer to the movement path of the electron from the cathode to the anode under the action of the electric field. It describes the specific movement process of the electron in the vacuum gap, which is affected by the electric field strength, charge distribution and external voltage. By calculating the electron trajectory, we can understand how the electron is affected by the electric field force and finally reaches the anode.

[0158] Specifically, when the current offset is not converged, (I1-I1) / I1≥0.1, it is considered that the currently calculated current offset is not converged, and the electron trajectory of the vacuum gap is calculated again based on the updated electron emission density.

[0159] Step 506: recalculate the distribution of electrons in space according to the electron trajectory to obtain an iterative spatial potential distribution.

[0160] The iterative spatial potential distribution can be the potential distribution in the vacuum gap obtained through multiple iterative calculations. With each update of the charge distribution and electron trajectory, the potential distribution will also change accordingly. Each iterative calculation will update the potential distribution according to the new electron emission density and electric field distribution until the system reaches a convergence state.

[0161] Specifically, the spatial charge distribution is calculated again according to the updated electron trajectory of the vacuum gap, and then the iterative spatial potential distribution of the vacuum gap is calculated again according to the updated spatial charge distribution.

[0162] Step 508, taking the iterative spatial potential distribution as the spatial potential distribution, and returning to execute the step of calculating the spatial electric field distribution of the vacuum gap according to the spatial potential distribution, until the current offset is converged.

[0163] Specifically, let the iterative spatial potential distribution be the spatial potential distribution, and return to execute the steps of "calculating the spatial electric field distribution of the vacuum gap according to the spatial potential distribution; calculating the gap breakdown current according to the spatial potential distribution and the spatial electric field distribution; calculating the current offset between the initial gap breakdown current and the gap breakdown current" until the current offset converges, that is, after the iteration to the nth time, it can satisfy: (I n -I n-1 ) / I n-1 ≤0.1.

[0164] Step 510, determining the conductivity coefficient according to the current offset and the anode voltage of the cathode plasma.

[0165] Specifically, the gap breakdown current I nis the current when the radius of the cathode plasma is r. Combined with the anode voltage of the cathode plasma, the conductivity coefficient P at this time can be calculated. By integrating the conductivity coefficients at different times, the final conductivity coefficient can be obtained.

[0166] In this embodiment, the initial gap breakdown current and the current offset in subsequent iterations are used to determine whether the calculation has converged; if it has not converged, the electron emission density continues to be adjusted, and the electron trajectory and spatial potential distribution are recalculated. As the iterations progress, the system gradually approaches a convergence state, and can more accurately capture the dynamic process of electron movement, electric field changes, and charge distribution. Through this iterative update, the conductivity of the vacuum gap can be accurately determined, the system's prediction accuracy for the breakdown current can be improved, and the reliability and safety of the equipment under high voltage conditions can be ensured. This method provides strong support for modeling breakdown behavior in complex electric field environments, helps optimize the design, and reduces the risk of system failure.

[0167] In one embodiment, Figure 6 As shown, the conductivity coefficient is determined according to the current offset and the anode voltage of the cathode plasma, including:

[0168] Step 602, calculating the current conductivity according to the current offset and the anode voltage of the cathode plasma.

[0169] The current conductivity coefficient refers to the ability of the current to pass through the vacuum gap in the current calculation or iteration step. It represents the relationship between the electric field strength and the current and is a dynamically changing coefficient that adjusts with changes in the electric field conditions, electron emission density, and cathode plasma expansion.

[0170] Specifically, since the anode potential is set to an arbitrary given value U in establishing the electric field calculation model S , further calculate the anode potential to the power of two thirds as the denominator for calculating the current conductivity; then calculate the gap breakdown current I n The current when the radius of the cathode plasma is r is divided by the second third power of the anode potential to obtain the current conductivity, which is expressed by the formula:

[0171]

[0172] Step 604: When the radius of the cathode plasma is less than the radius threshold, the radius of the cathode plasma is added to the convergence judgment value of the current offset to obtain an updated radius of the cathode plasma.

[0173] The convergence judgment value may be a threshold used to judge whether the current calculation is close to a stable state. It is usually based on the current offset. If the current difference between two iterations is less than the judgment value, it is considered that the calculation has converged and the system has reached a stable breakdown state.

[0174] The updating radius may refer to readjusting the expansion radius of the cathode plasma according to the convergence of the current offset during the iteration process. After each calculation, if the current offset does not reach the convergence condition, the expansion of the plasma is simulated by adjusting the radius of the plasma. The updating radius is used to further calculate the spatial potential distribution and the electric field distribution, so that the calculation results gradually approach the target radius, thereby optimizing the calculation of the conductivity coefficient.

[0175] Specifically, if the radius of the cathode plasma is less than the radius threshold, that is, the radius of the cathode plasma is less than 1, the radius of the cathode plasma originally obtained is added to the convergence judgment value of the current offset originally obtained, that is, r=r+0.1, as the updated radius of the new cathode plasma.

[0176] Step 606, using the updated radius as the radius, returning to the series vacuum gap equivalent circuit model, applying the radius of the cathode plasma to the electric field calculation model, and obtaining the spatial potential distribution of the vacuum gap, until the radius of the cathode plasma is greater than the radius threshold, thereby obtaining the target radius of the cathode plasma.

[0177] The target radius may refer to the final stable radius to which the cathode plasma expands after multiple iterations and adjustments. When the radius of the cathode plasma reaches a certain threshold and the current offset reaches the convergence condition, the system reaches a stable state, and the target radius is the final cathode plasma expansion size. The target radius is an important parameter for the conductivity coefficient fitting calculation to ensure the stability of current conduction and the accuracy of the system.

[0178] Specifically, let the updated radius be the radius of the cathode plasma, then return to execute the step of "based on the series vacuum gap equivalent circuit model, apply the radius of the cathode plasma to the electric field calculation model to obtain the spatial potential distribution of the vacuum gap", recalculate the radius of the cathode plasma, calculate the radius of the cathode plasma through multiple iterations until the radius of the cathode plasma is greater than the radius threshold, and take the radius of the cathode plasma calculated for the last time as the target radius.

[0179] Step 608, fitting the current offset and the target radius to obtain the conductivity coefficient.

[0180] Specifically, for a set of target radius r and gap breakdown current I obtained by the above calculations, nThe final conductivity coefficient is obtained by fitting the current when the radius of the cathode plasma is r divided by the second power of the anode potential P(r). The fitting formula used is:

[0181] P = ae br +ce dr -(a+c)

[0182] In the formula: a, b, c, d are the parameters to be fitted.

[0183] In this embodiment, when the cathode plasma radius does not reach the threshold, the plasma radius is updated according to the convergence value of the current offset, thereby recalculating the spatial potential distribution and continuously iterating. This process gradually increases the radius of the plasma and eventually reaches a stable target radius. Then, by fitting the relationship between the current offset and the target radius, an accurate conductivity coefficient is obtained. This method effectively improves the simulation accuracy of the electric field and current conduction in the vacuum gap, ensures the accuracy of the conductivity coefficient, and thus improves the reliability of the system in a high-voltage environment and the controllability of the breakdown process, which helps to optimize the design and operation efficiency of electrical equipment.

[0184] In one embodiment, Figure 7 As shown, based on the series vacuum gap equivalent circuit model, according to the plasma expansion radius of the cathode plasma and the conductivity coefficient of the vacuum gap, the vacuum gap equivalent resistance is determined, including:

[0185] Step 702, calculating the plasma expansion radius according to the cathode plasma expansion speed and the relative time of the cathode plasma.

[0186] Specifically, in the actual calculation process, if the vacuum gap is at time t BD If breakdown occurs, then at the later time point t n , calculate the time t n Plasma expansion radius:

[0187] r=v c (t n -t BD )

[0188] Where: v c ——The expansion speed of cathode plasma is related to the electrode material, and the typical value is 2×104m / s.

[0189] Step 704: when the plasma expansion radius is less than 0, outputting error information of the equivalent resistance of the vacuum gap.

[0190] Among them, the equivalent resistance error information can be a warning or error prompt automatically output when the system detects an unreasonable negative value in the expansion radius of the cathode plasma during the calculation process. This usually means that there is an abnormality in the calculation, which may be caused by incorrect input parameters, values exceeding the physically reasonable range, or an inappropriate model.

[0191] Specifically, if the plasma expansion radius is less than 0, that is, in the case of r < 0, the equivalent resistance error information of the vacuum gap is directly output, which means that the equivalent resistance cannot be obtained.

[0192] Step 706, when the plasma expansion radius is greater than 0 and less than 1, determine the equivalent resistance of the vacuum gap according to the conductance coefficient of the vacuum gap.

[0193] Specifically, if the plasma expansion radius is greater than 0 and less than 1, that is, in the case of 0 < r < 1, the specific value of the equivalent resistance of the vacuum gap to be determined is calculated as the equivalent resistance of the vacuum gap according to the conductance coefficient of the vacuum gap. Representing the process with a formula, since where P(r) = ae br + ce dr -(a + c), where a, b, c, d are the fitting parameters obtained previously; the equivalent resistance R of the vacuum gap can be obtained gap = U / I.

[0194] Step 708, when the plasma expansion radius is greater than or equal to 1, determine that the specific value of the equivalent resistance of the vacuum gap to be determined is zero and use it as the equivalent resistance of the vacuum gap.

[0195] Specifically, if the plasma expansion radius is greater than or equal to 1, that is, in the case of r ≥ 1, it is considered that the gap plasma has completed expansion and a vacuum arc connecting the cathode and anode is formed. Considering that the voltage of the vacuum arc is very low and the equivalent resistance can be approximately ignored, it is considered that the equivalent resistance R of the vacuum gap gap = 0.

[0196] In this embodiment, by accurately calculating the expansion speed and moment of the cathode plasma, the expansion radius of the plasma is determined, thereby dynamically adjusting the equivalent resistance of the vacuum gap. During the calculation process, when the plasma expansion radius is less than 0, the system immediately outputs an error message, indicating that the equivalent resistance calculation is abnormal, thereby ensuring the safety of the system under extreme conditions. If the expansion radius is greater than 0 but less than 1, the equivalent resistance of the vacuum gap is accurately calculated according to the conductivity coefficient to ensure the accuracy of the calculation and the stability of the system. When the expansion radius is greater than or equal to 1, the system automatically sets the equivalent resistance of the vacuum gap to zero, reflecting the end of the breakdown process. In this way, the method can effectively prevent calculation errors, dynamically adjust the resistance value, ensure the reliability and accuracy of the system under different expansion conditions, thereby improving the operating stability and breakdown protection effect of electrical equipment.

[0197] In one embodiment, Figure 8 As shown, according to a plurality of vacuum gap equivalent parallel circuits, a series vacuum gap equivalent circuit model is constructed, including:

[0198] Step 802: construct an equivalent capacitance model and an equivalent variable resistance model according to vacuum gap parameters of a plurality of vacuum gaps.

[0199] Among them, vacuum gap parameters can refer to key variables that describe the physical and electrical properties of the vacuum gap. These parameters include the geometric dimensions of the space gap (such as gap distance, area), material properties (such as dielectric constant, conductivity, breakdown voltage), electric field strength, temperature conditions, etc. These parameters jointly determine the behavior of the vacuum gap under different voltage and electric field conditions, affecting the calculation of capacitance and variable resistance and the generation of breakdown current.

[0200] Specifically, according to the geometric parameters, material properties (such as dielectric constant, breakdown strength, etc.) and electric field conditions of each vacuum gap, a geometric structure based on the vacuum gap is constructed, especially the spacing between the electrodes and the dielectric properties of the material, which reflects the ability of the space gap to store electrical energy under an applied electric field, and obtains an equivalent capacitance model. At the same time, the equivalent variable resistance model is defined according to parameters such as electric field strength, breakdown voltage, and conductivity of the material. As the electric field strength changes, the resistance of the vacuum gap is not fixed, but changes dynamically as the breakdown conditions approach. Therefore, the resistance model is a nonlinear, dynamically adjusted model that reflects the gradual reduction of resistance during the breakdown process.

[0201] Step 804: for any vacuum gap, based on an equivalent capacitor model and an equivalent variable resistor model, the vacuum gap is equivalent to a capacitor-resistor parallel circuit.

[0202] Specifically, for any vacuum gap, the vacuum gap is represented by an equivalent capacitor and an equivalent resistor, respectively, by combining the previously constructed equivalent capacitance model and equivalent variable resistor model, and the equivalent capacitance and equivalent resistor are connected in parallel to obtain a capacitor-resistance parallel circuit. This capacitor-resistance parallel circuit can reflect the dynamic behavior of the vacuum gap under different electric field conditions: the capacitance part characterizes the ability of the vacuum gap to store electric field energy, and the resistance part characterizes the conductivity of the vacuum gap before and after breakdown. In particular, when the breakdown begins, the resistance will drop sharply, the current through the resistance channel will increase significantly, and the effect of the capacitor will gradually weaken.

[0203] Step 806, connect the capacitor and resistor parallel circuits in series to obtain a series vacuum gap equivalent circuit model.

[0204] Specifically, considering the different electrical characteristics of each space gap, for example, some space gaps may break down at a lower voltage, while other space gaps may have a higher breakdown voltage. Connecting the capacitor and resistor parallel circuits in series means that when the current passes through each space gap, the electrical characteristics of the overall circuit are a combination of the electrical behaviors of multiple vacuum gaps, and finally the series vacuum gap equivalent circuit model is obtained. This model can not only simulate the independent behavior of each vacuum gap, but also reflect the interaction between multiple space gaps. For example, a space gap that breaks down earlier may change the voltage distribution of other space gaps, thereby affecting their breakdown moment and current conduction capacity.

[0205] In this embodiment, by constructing an equivalent capacitance model and an equivalent variable resistance model, each vacuum gap is converted into an equivalent circuit in which a capacitor and a resistor are connected in parallel, and multiple parallel circuits are connected in series to form an overall series vacuum gap equivalent circuit model. This process can accurately simulate the electrical behavior of the vacuum gap in the electric field, especially the dynamic changes during the breakdown process. The capacitance part reflects the energy storage characteristics of the space gap, while the variable resistance part reflects its conductive characteristics and the resistance change during the breakdown process. By combining these circuits, the system can more accurately describe the breakdown process of multiple vacuum gaps in a complex electric field, improve the prediction ability of the breakdown current, and ensure the stability and safety of the system. This model effectively supports the optimization of electrical equipment design and reduces the risk of breakdown failure.

[0206] In one embodiment, Fig. 9 As shown, the method also includes:

[0207] Step 902: Obtain the relationship between the gap emission current value and the gap applied voltage of the vacuum gap.

[0208] The gap emission current value refers to the current value generated by the electron flow emitted from the cathode in the vacuum gap under a specific electric field. It indicates the intensity of the electron emission behavior caused by the electric field before breakdown, is the initial performance of the conductivity of the space gap under different voltages, and directly affects the size of the breakdown current.

[0209] The gap applied voltage refers to the voltage directly applied to both ends of the vacuum gap, which determines the electric field strength in the space gap. The higher the applied voltage, the stronger the electric field, the greater the probability of electron emission and current conduction in the space gap, which may eventually lead to breakdown.

[0210] Specifically, the gap emission current value of the vacuum gap under different applied voltages is measured through experiments or simulations. During the measurement process, a series of different gap applied voltages need to be applied at both ends of the vacuum gap, and the emission current changes under each voltage need to be recorded, so as to fit the relationship curve between voltage and current, reflecting the emission characteristics of the vacuum gap under different electric field conditions.

[0211] Step 904, obtaining the actual emission current value according to the change relationship and the actual applied voltage.

[0212] The actual applied voltage may refer to the voltage value actually applied to the vacuum gap by the system under actual operating conditions. It may be different from the theoretical or designed voltage, depending on the external power supply, load conditions, and specific operating conditions of the electrical system. The actual applied voltage determines the electric field distribution and current emission in the vacuum gap under the current conditions.

[0213] The actual emission current value may refer to the current value generated by the electron flow emitted from the cathode under the current actual applied voltage condition. It represents the influence of the electric field on the electron emission under the actual working condition, and can reflect the actual conductive state in the space gap through measurement or calculation.

[0214] Specifically, the current value is determined by searching or interpolating according to the variation relationship in combination with the current actual applied voltage, ensuring that a true current response can be obtained under actual voltage conditions, and the actual emission current value under this voltage is derived.

[0215] Step 906, constructing a resistance function relationship according to the actual applied voltage and the actual emission current value.

[0216] The resistance function relationship can be a mathematical relationship that describes how the equivalent resistance in the space gap changes with applied voltage or emitted current. Since the resistance in the space gap is not a constant value, it is affected by voltage, current and material properties. Therefore, by establishing a resistance function, the change of resistance in the space gap can be dynamically reflected, especially its significant change before and after breakdown.

[0217] Specifically, after the actual applied voltage and the actual emission current value, a resistance function relationship is constructed through Ohm's law (voltage equals current multiplied by resistance), which describes how the equivalent resistance of the vacuum gap changes with the change of voltage and current. Since the resistance is not linearly fixed, but changes dynamically under different conditions of voltage or current, the function needs to take into account nonlinear effects, especially when approaching breakdown, the resistance may drop significantly.

[0218] Step 908: determining the gap field emission current value according to the resistance function relationship and the simulated gap voltage value.

[0219] The simulated gap voltage value may be the voltage value at both ends of the vacuum gap during the numerical simulation or experimental simulation. The voltage is accurately calculated by the simulation model to understand the electrical behavior of the vacuum gap under different electric field conditions, thereby estimating the performance of the system in actual operation.

[0220] Among them, the gap field emission current value can refer to the current value caused by the electric field directly driving electrons to emit from the cathode under the action of a high-intensity electric field. This current is closely related to the electric field strength and is a key phenomenon in the breakdown process. It can reflect the conductivity of the vacuum gap under specific electric field conditions.

[0221] Specifically, the gap field emission current value is further calculated based on the resistance function relationship combined with the simulated gap voltage value. The gap field emission current value refers to the electron flow emitted from the electrode surface when the electric field strength is high enough. The resistance function can be used to determine the current generated in the vacuum gap under simulation conditions (such as a specific voltage).

[0222] Step 910, calculating the vacuum gap equivalent resistance according to the simulated gap voltage value and the gap field emission current value.

[0223] Specifically, the simulated gap voltage value and gap field emission current value obtained by simulation are used in combination with the resistance function relationship to calculate the vacuum gap equivalent resistance, that is, the vacuum gap equivalent resistance value at the current moment is the ratio of the current gap voltage value to the corresponding field emission current value, reflecting the electrical conduction characteristics of the vacuum gap under different electric field conditions. Through accurate resistance calculation, the electrical performance of the vacuum gap can be further analyzed, especially when it is close to breakdown or in actual operation, to ensure the safety and reliability of system design and operation.

[0224] In this embodiment, by obtaining the changing relationship between the emission current and the applied voltage of the vacuum gap, combined with the actual voltage conditions, the emission current is accurately calculated and the resistance function is constructed, and the field emission current is further determined in combination with the simulated voltage value, thereby calculating the equivalent resistance of the vacuum gap. This process can more accurately reflect the conductive characteristics of the vacuum gap under different electric field conditions, especially the dynamic changes of the breakdown behavior under high voltage conditions. Modeling. By establishing a resistance function, the system can adjust the resistance value as the voltage changes, effectively improve the ability to predict the breakdown current, ensure the stability and reliability of electrical equipment under different working conditions, and optimize its design to reduce the risk of breakdown.

[0225] It should be understood that, although the steps in the flowcharts involved in the above embodiments are displayed in sequence according to the indication of the arrows, these steps are not necessarily executed in sequence according to the order indicated by the arrows. Unless there is a clear explanation in this article, the execution of these steps is not strictly limited in order, and these steps can be executed in other orders. Moreover, at least a part of the steps in the flowcharts involved in the above embodiments may include multiple steps or multiple stages, and these steps or stages are not necessarily executed at the same time, but can be executed at different times, and the execution order of these steps or stages is not necessarily carried out in sequence, but can be executed in turn or alternately with other steps or at least a part of the steps or stages in other steps.

[0226] Based on the same inventive concept, the embodiment of the present application also provides a device for calculating the development process of a series vacuum gap breakdown for realizing the method for calculating the development process of a series vacuum gap breakdown involved above. The implementation scheme for solving the problem provided by the device is similar to the implementation scheme recorded in the above method, so the specific limitations in the embodiments of one or more devices for calculating the development process of a series vacuum gap breakdown provided below can refer to the limitations of the method for calculating the development process of a series vacuum gap breakdown above, and will not be repeated here.

[0227] In one embodiment, Fig.10 As shown, a device for calculating the breakdown development process of a series vacuum gap is provided, comprising: a circuit model building module 1002, a conductivity determination module 1004, an equivalent resistance obtaining module 1006, a breakdown voltage obtaining module 1008 and a breakdown process description module 1010, wherein:

[0228] The circuit model building module 1002 is used to build a series vacuum gap equivalent circuit model based on a plurality of vacuum gap equivalent vacuum gap parallel circuits;

[0229] The conductivity determination module 1004 is used to determine the conductivity of the vacuum gap based on the series vacuum gap equivalent circuit model, according to the plasma parameters of the cathode plasma and the electric field calculation model of the vacuum gap;

[0230] An equivalent resistance obtaining module 1006 is used to determine the vacuum gap equivalent resistance based on a series vacuum gap equivalent circuit model, according to the plasma expansion radius of the cathode plasma and the conductivity of the vacuum gap;

[0231] A breakdown voltage obtaining module 1008 is used to determine the vacuum gap breakdown voltage based on the series vacuum gap equivalent circuit model and the vacuum gap breakdown data;

[0232] The breakdown process description module 1010 is used to calculate the vacuum gap breakdown development process of the series vacuum gaps according to the vacuum gap equivalent resistance and the vacuum gap breakdown voltage; the vacuum gap breakdown development process is used to describe the relationship between the breakdown of each vacuum gap in the series vacuum gap and time, so as to realize the safe application of the series vacuum gaps.

[0233] In one embodiment, the conductivity determination module 1004 is also used to apply the radius of the cathode plasma to the electric field calculation model based on the series vacuum gap equivalent circuit model to obtain the spatial potential distribution of the vacuum gap; calculate the spatial electric field distribution of the vacuum gap according to the spatial potential distribution; calculate the gap breakdown current according to the spatial potential distribution and the spatial electric field distribution; determine the conductivity of the vacuum gap according to the gap breakdown current and the radius of the cathode plasma.

[0234] In one embodiment, the conductivity coefficient determination module 1004 is also used to calculate the initial electron emission density of the vacuum gap according to the spatial potential distribution and the spatial electric field distribution; perform surface integration on the initial electron emission density of the cathode plasma to obtain the initial gap breakdown current; obtain the updated spatial charge distribution when it is detected that all the electrons of the cathode plasma reach the anode from the cathode; calculate the updated spatial potential distribution and the updated spatial electric field distribution of the vacuum gap according to the updated spatial charge distribution; calculate the updated electron emission density of the vacuum gap according to the updated spatial potential distribution and the updated spatial electric field distribution; perform surface integration on the updated electron emission density of the cathode plasma to obtain the gap breakdown current.

[0235] In one embodiment, the conductivity determination module 1004 is also used to calculate the current offset between the initial gap breakdown current and the gap breakdown current; when the current offset is not converged, the electron trajectory of the vacuum gap is calculated according to the updated electron emission density; the distribution of electrons in space is recalculated according to the electron trajectory to obtain an iterative spatial potential distribution; the iterative spatial potential distribution is used as the spatial potential distribution, and the step of calculating the spatial electric field distribution of the vacuum gap according to the spatial potential distribution is returned to execute until the current offset is converged; the conductivity is determined according to the current offset and the anode voltage of the cathode plasma.

[0236] In one embodiment, the conductivity determination module 1004 is also used to calculate the current conductivity according to the current offset and the anode voltage of the cathode plasma; when the radius of the cathode plasma is less than the radius threshold, the radius of the cathode plasma is added to the convergence judgment value of the current offset to obtain the updated radius of the cathode plasma; using the updated radius as the radius, returning to the step of applying the radius of the cathode plasma to the electric field calculation model based on the series vacuum gap equivalent circuit model to obtain the spatial potential distribution of the vacuum gap, until the radius of the cathode plasma is greater than the radius threshold, and the target radius of the cathode plasma is obtained; fitting the current offset and the target radius to obtain the conductivity.

[0237] In one embodiment, the equivalent resistance obtaining module 1006 is also used to calculate the plasma expansion radius according to the expansion speed of the cathode plasma and the relative time of the cathode plasma; the relative time is any time other than the breakdown time of the vacuum gap; when the plasma expansion radius is less than 0, the equivalent resistance error information of the vacuum gap is output; when the plasma expansion radius is greater than 0 and less than 1, the vacuum gap equivalent resistance is determined according to the conductivity coefficient of the vacuum gap; when the plasma expansion radius is greater than or equal to 1, the specific value of the vacuum gap equivalent resistance to be determined is determined to be zero, and is used as the vacuum gap equivalent resistance.

[0238] In one embodiment, the circuit model construction module 1002 is also used to construct an equivalent capacitance model and an equivalent variable resistance model according to the vacuum gap parameters of several vacuum gaps; for any vacuum gap, according to the equivalent capacitance model and the equivalent variable resistance model, the vacuum gap is equivalent to a capacitor-resistance parallel circuit; the capacitor-resistance parallel circuit includes a gap equivalent capacitance and a gap equivalent resistance, and the gap equivalent capacitance and the gap equivalent resistance are in a parallel relationship; the capacitor-resistance parallel circuits are connected in series to obtain a series vacuum gap equivalent circuit model.

[0239] In one embodiment, the equivalent resistance obtaining module 1006 is also used to obtain the changing relationship between the gap emission current value and the gap applied voltage of the vacuum gap; obtain the actual emission current value based on the changing relationship and the actual applied voltage; construct a resistance function relationship based on the actual applied voltage and the actual emission current value; determine the gap field emission current value based on the resistance function relationship and the simulated gap voltage value; calculate the vacuum gap equivalent resistance based on the simulated gap voltage value and the gap field emission current value.

[0240] Each module in the above-mentioned computing device for the development process of series vacuum gap breakdown can be implemented in whole or in part by software, hardware and a combination thereof. Each of the above-mentioned modules can be embedded in or independent of a processor in a computer device in the form of hardware, or can be stored in a memory in a computer device in the form of software, so that the processor can call and execute operations corresponding to each of the above modules.

[0241] In one embodiment, a computer device is provided. The computer device may be a server, and its internal structure diagram may be as follows: Fig.11 As shown. The computer device includes a processor, a memory and a network interface connected through a system bus. Among them, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The database of the computer device is used to store server data. The network interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, a method for calculating the development process of a series vacuum gap breakdown is implemented.

[0242] Those skilled in the art will understand that Fig.11 The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than those shown in the figure, or combine certain components, or have a different arrangement of components.

[0243] In one embodiment, a computer device is further provided, including a memory and a processor, wherein a computer program is stored in the memory, and the processor implements the steps in the above method embodiments when executing the computer program.

[0244] In one embodiment, a computer-readable storage medium is provided, storing a computer program, which implements the steps in the above method embodiments when executed by a processor.

[0245] In one embodiment, a computer program product or computer program is provided, the computer program product or computer program includes computer instructions, the computer instructions are stored in a computer-readable storage medium. A processor of a computer device reads the computer instructions from the computer-readable storage medium, and the processor executes the computer instructions, so that the computer device performs the steps in the above-mentioned method embodiments.

[0246] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, stored data, displayed data, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties.

[0247] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to the memory, database or other medium used in the embodiments provided in the present application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetoresistive random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. As an illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM). The database involved in each embodiment provided in this application may include at least one of a relational database and a non-relational database. Non-relational databases may include distributed databases based on blockchains, etc., but are not limited to this. The processor involved in each embodiment provided in this application may be a general-purpose processor, a central processing unit, a graphics processor, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, etc., but are not limited to this.

[0248] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0249] The above-described embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be construed as limiting the scope of the present application. It should be noted that, for a person of ordinary skill in the art, several modifications and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the present application shall be subject to the attached claims.

Claims

1. A method for calculating the breakdown development process of a series vacuum gap, characterized in that: The method comprises: According to the vacuum gap parallel circuit equivalent to several vacuum gaps, a series vacuum gap equivalent circuit model is constructed; Based on the series vacuum gap equivalent circuit model, according to the plasma parameters of the cathode plasma and the electric field calculation model of the vacuum gap, determining the conductivity of the vacuum gap; Based on the series vacuum gap equivalent circuit model, determining the vacuum gap equivalent resistance according to the plasma expansion radius of the cathode plasma and the conductivity of the vacuum gap; Based on the series vacuum gap equivalent circuit model and vacuum gap breakdown data, a vacuum gap breakdown voltage; The vacuum gap breakdown development process of the series vacuum gaps is calculated according to the vacuum gap equivalent resistance and the vacuum gap breakdown voltage; the vacuum gap breakdown development process is used to describe the relationship between the breakdown conditions of each vacuum gap in the series vacuum gaps and time, so as to achieve safe application of the series vacuum gaps.

2. The method according to claim 1, characterized in that The method of determining the conductivity of the vacuum gap based on the series vacuum gap equivalent circuit model according to the plasma parameters of the cathode plasma and the electric field calculation model of the vacuum gap includes: Based on the series vacuum gap equivalent circuit model, applying the radius of the cathode plasma to the electric field calculation model to obtain the spatial potential distribution of the vacuum gap; Calculating the spatial electric field distribution of the vacuum gap according to the spatial potential distribution; Calculating the gap breakdown current according to the spatial potential distribution and the spatial electric field distribution; The conductance of the vacuum gap is determined according to the gap breakdown current and the radius of the cathode plasma.

3. The method according to claim 2, characterized in that The calculating the gap breakdown current according to the spatial potential distribution and the spatial electric field distribution comprises: Calculating the initial electron emission density of the vacuum gap according to the spatial potential distribution and the spatial electric field distribution; Performing surface integration on the initial electron emission density of the cathode plasma to obtain an initial gap breakdown current; When it is detected that all the electrons of the cathode plasma have reached the anode from the cathode, obtaining an updated spatial charge distribution; Calculating the updated spatial potential distribution and the updated spatial electric field distribution of the vacuum gap according to the updated spatial charge distribution; Calculating the updated electron emission density of the vacuum gap according to the updated space potential distribution and the updated space electric field distribution; The updated electron emission density of the cathode plasma is surface integrated to obtain the gap breakdown current.

4. The method according to claim 3, characterized in that: The step of determining the conductivity of the vacuum gap according to the gap breakdown current and the radius of the cathode plasma comprises: calculating a current offset between the initial gap breakdown current and the gap breakdown current; When the current offset is not converged, calculating the electron trajectory of the vacuum gap according to the updated electron emission density; Recalculating the distribution of electrons in space according to the electron trajectory to obtain an iterative spatial potential distribution; Taking the iterative spatial potential distribution as the spatial potential distribution, returning to the step of calculating the spatial electric field distribution of the vacuum gap according to the spatial potential distribution until the current offset is converged; The conductivity is determined according to the current offset and the anode voltage of the cathode plasma.

5. The method according to claim 4, characterized in that The determining the conductivity coefficient according to the current offset and the anode voltage of the cathode plasma includes: Calculating a current conductivity according to the current offset and the anode voltage of the cathode plasma; When the radius of the cathode plasma is less than a radius threshold, adding the radius of the cathode plasma to the convergence judgment value of the current offset to obtain an updated radius of the cathode plasma; The step of taking the updated radius as the radius, returning to the equivalent circuit model based on the series vacuum gap, applying the radius of the cathode plasma to the electric field calculation model, and obtaining the spatial potential distribution of the vacuum gap, until the radius of the cathode plasma is greater than a radius threshold, thereby obtaining a target radius of the cathode plasma; The current offset and the target radius are fitted to obtain the conductivity coefficient.

6. The method according to claim 1, characterized in that The method of determining the vacuum gap equivalent resistance based on the series vacuum gap equivalent circuit model according to the plasma expansion radius of the cathode plasma and the conductivity of the vacuum gap includes: Calculating the plasma expansion radius according to the expansion speed of the cathode plasma and the relative time of the cathode plasma; the relative time is any time other than the breakdown time of the vacuum gap; When the plasma expansion radius is less than 0, the equivalent resistance error information of the vacuum gap is output; When the plasma expansion radius is greater than 0 and less than 1, determining a specific value of the vacuum gap equivalent resistance to be determined according to the conductivity of the vacuum gap, and obtaining the vacuum gap equivalent resistance; When the plasma expansion radius is greater than or equal to 1, the specific value of the vacuum gap equivalent resistance is determined to be zero.

7. The method according to claim 1, characterized in that The method of constructing a series vacuum gap equivalent circuit model based on a plurality of vacuum gap equivalent vacuum gap parallel circuits includes: According to the vacuum gap parameters of the plurality of vacuum gaps, an equivalent capacitance model and an equivalent variable resistance model are constructed; For any of the vacuum gaps, according to the equivalent capacitance model and the equivalent variable resistance model, the vacuum gap is equivalent to a capacitor-resistance parallel circuit; the capacitor-resistance parallel circuit includes a gap equivalent capacitance and a gap equivalent resistance, and the gap equivalent capacitance and the gap equivalent resistance are in a parallel relationship; The capacitor-resistor parallel circuits are connected in series to obtain the series vacuum gap equivalent circuit model.

8. The method according to claim 1, characterized in that The method further comprises: Obtaining a change relationship between a gap emission current value and a gap applied voltage of the vacuum gap; According to the variation relationship and the actual applied voltage, an actual emission current value is obtained; Constructing a resistance function relationship according to the actual applied voltage and the actual emission current value; Determining a gap field emission current value according to the resistance function relationship and the simulated gap voltage value; The vacuum gap equivalent resistance is calculated according to the simulated gap voltage value and the gap field emission current value.

9. A device for calculating the breakdown development process of a series vacuum gap, characterized in that: The device comprises: A circuit model building module, used to build a series vacuum gap equivalent circuit model based on a plurality of vacuum gap equivalent vacuum gap parallel circuits; A conductivity determination module, for determining the conductivity of the vacuum gap based on the series vacuum gap equivalent circuit model, according to the plasma parameters of the cathode plasma and the electric field calculation model of the vacuum gap; An equivalent resistance obtaining module is used to determine the vacuum gap equivalent resistance based on the series vacuum gap equivalent circuit model, according to the plasma expansion radius of the cathode plasma and the conductivity coefficient of the vacuum gap; A breakdown voltage obtaining module is used to obtain a vacuum gap breakdown voltage based on the series vacuum gap equivalent circuit model and vacuum gap breakdown data; The breakdown process description module is used to calculate the vacuum gap breakdown development process of the series vacuum gap according to the vacuum gap equivalent resistance and the vacuum gap breakdown voltage; the vacuum gap breakdown development process is used to describe the relationship between the breakdown condition of each vacuum gap in the series vacuum gap and time, so as to realize the safe application of the series vacuum gap.

10. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 8 are implemented.

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