Method and apparatus for calculating development of a series vacuum gap breakdown

Abstract

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

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of power safety, in particular to a calculation method and device for breakdown development process of series vacuum gaps. BACKGROUND

[0002] With the development of high voltage technology, vacuum gaps are often used to withstand high voltage, but their withstand voltage performance shows a significant saturation effect with the increase of gap spacing. Therefore, multiple vacuum short gaps are often connected in series in engineering to withstand ultra / extra-high voltage, and 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 vacuum gaps is a key problem that limits the operating performance of the above-mentioned devices, but the current research on vacuum breakdown is mostly limited to the breakdown of a single vacuum gap, and there is no targeted research on series vacuum breakdown, which cannot describe the breakdown mechanism of series vacuum gaps and evaluate the key means of their insulation performance, resulting in risks in the application of series vacuum gaps at high voltage. SUMMARY

[0004] Therefore, it is necessary to provide a calculation method and device for breakdown development process of series vacuum gaps, computer equipment, computer readable storage medium and computer program product, which can reduce the application risk of series vacuum gaps at high voltage.

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

[0006] constructing a series vacuum gap equivalent circuit model according to a parallel circuit of several vacuum gaps;

[0007] determining a flow conductance coefficient of the vacuum gap based on the series vacuum gap equivalent circuit model, the plasma parameter of the cathode plasma and the electric field calculation model of the vacuum gap;

[0008] determining a vacuum gap equivalent resistance based on the flow conductance coefficient of the vacuum gap and the plasma expansion radius of the cathode plasma based on the series vacuum gap equivalent circuit model;

[0009] determining a vacuum gap breakdown voltage based on the vacuum gap breakdown data based on the series vacuum gap equivalent circuit model;

[0010] calculating a vacuum gap breakdown development process of 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 gaps and time, so as to realize the safe application of the series vacuum gaps.

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

[0012] a circuit model construction module, configured to construct a series vacuum gap equivalent circuit model according to a parallel circuit of a plurality of vacuum gaps;

[0013] a conductance coefficient determination module, configured to determine a conductance coefficient of the vacuum gap based on the series vacuum gap equivalent circuit model, according to plasma parameters of a cathode plasma and an electric field calculation model of the vacuum gap;

[0014] an equivalent resistance obtaining module, configured to determine a vacuum gap equivalent resistance based on the series vacuum gap equivalent circuit model, according to a plasma expansion radius of the cathode plasma and the conductance coefficient of the vacuum gap;

[0015] a breakdown voltage obtaining module, configured to obtain a breakdown voltage of the vacuum gap based on the series vacuum gap equivalent circuit model and breakdown data of the vacuum gap;

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

[0017] In a third aspect, the application further provides a computer device. The computer device comprises a memory and a processor, the memory storing a computer program, and the processor realizing the following steps when executing the computer program:

[0018] constructing a series vacuum gap equivalent circuit model according to a parallel circuit of a plurality of vacuum gaps;

[0019] determining a conductance coefficient of the vacuum gap based on the series vacuum gap equivalent circuit model, according to plasma parameters of a cathode plasma and an electric field calculation model of the vacuum gap;

[0020] determining a vacuum gap equivalent resistance based on the series vacuum gap equivalent circuit model, according to a plasma expansion radius of the cathode plasma and the conductance coefficient of the vacuum gap;

[0021] obtaining a breakdown voltage of the vacuum gap based on the series vacuum gap equivalent circuit model and breakdown data of the vacuum gap;

[0022] According to the equivalent resistance of the series of the plurality of the real space gaps and the breakdown voltage of the series of the plurality of the real space gaps, a breakdown development process of the series of the plurality of the real space gaps is calculated, the breakdown development process being used to describe a breakdown condition of each of the plurality of the real space gaps in the series of the plurality of the real space gaps and time, so as to realize safe application of the series of the plurality of the real space gaps.

[0023] In a fourth aspect, the present application further provides a computer readable storage medium. The computer readable storage medium has a computer program stored thereon, and the computer program, when executed by a processor, implements the following steps:

[0024] According to the equivalent resistance of the series of the plurality of the real space gaps and the breakdown voltage of the series of the plurality of the real space gaps, a breakdown development process of the series of the plurality of the real space gaps is calculated, the breakdown development process being used to describe a breakdown condition of each of the plurality of the real space gaps in the series of the plurality of the real space gaps and time, so as to realize safe application of the series of the plurality of the real space gaps.

[0025] Based on the equivalent circuit model of the series of the plurality of the real space gaps, a flow conductance coefficient of the real space gap is determined according to plasma parameters of the cathode plasma and an electric field calculation model of the real space gap.

[0026] Based on the equivalent circuit model of the series of the plurality of the real space gaps, a flow conductance coefficient of the real space gap is determined according to plasma parameters of the cathode plasma and an electric field calculation model of the real space gap.

[0027] Based on the equivalent circuit model of the series of the plurality of the real space gaps, a flow conductance coefficient of the real space gap is determined according to plasma parameters of the cathode plasma and an electric field calculation model of the real space gap.

[0028] According to the equivalent resistance of the series of the plurality of the real space gaps and the breakdown voltage of the series of the plurality of the real space gaps, a breakdown development process of the series of the plurality of the real space gaps is calculated, the breakdown development process being used to describe a breakdown condition of each of the plurality of the real space gaps in the series of the plurality of the real space gaps and time, so as to realize safe application of the series of the plurality of the real space gaps.

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

[0030] According to the equivalent resistance of the series of the plurality of the real space gaps and the breakdown voltage of the series of the plurality of the real space gaps, a breakdown development process of the series of the plurality of the real space gaps is calculated, the breakdown development process being used to describe a breakdown condition of each of the plurality of the real space gaps in the series of the plurality of the real space gaps and time, so as to realize safe application of the series of the plurality of the real space gaps.

[0031] Based on the equivalent circuit model of the series of the plurality of the real space gaps, a flow conductance coefficient of the real space gap is determined according to plasma parameters of the cathode plasma and an electric field calculation model of the real space gap.

[0032] Based on the equivalent circuit model of the series of the plurality of the real space gaps, a flow conductance coefficient of the real space gap is determined according to plasma parameters of the cathode plasma and an electric field calculation model of the real space gap.

[0033] determine, based on the series gap equivalent circuit model, a gap breakdown voltage according to gap breakdown data;

[0034] calculate, according to the gap equivalent resistance and the gap breakdown voltage, a gap breakdown development process of the series gap, the gap breakdown development process being used to describe a relationship between a breakdown condition of each gap in the series gap and time, so as to realize safe application of the series gap.

[0035] The above-mentioned calculation method, device, computer equipment, storage medium and computer program product of the series gap breakdown development process, by constructing a series gap equivalent circuit model according to a plurality of gap equivalent parallel circuits, determining a flow conductance coefficient of the gap based on the series gap equivalent circuit model and a plasma parameter of cathode plasma and an electric field calculation model of the gap, determining a gap equivalent resistance of the gap based on the series gap equivalent circuit model and a plasma expansion radius of the cathode plasma and the flow conductance coefficient of the gap, determining a gap breakdown voltage of the gap based on the series gap equivalent circuit model and gap breakdown data, and calculating a gap breakdown development process of the series gap according to the gap equivalent resistance and the gap breakdown voltage, the gap breakdown development process being used to describe a relationship between a breakdown condition of each gap in the series gap and time, so as to realize safe application of the series gap.

[0036] By constructing a series gap equivalent circuit model of a plurality of series gaps, the series effect of the plurality of gaps under the action of an electric field is considered in detail, the flow conductance coefficient of the gap is accurately determined by using the physical parameters of cathode plasma and its expansion radius and combining the electric field calculation model, and then the equivalent resistance and the breakdown voltage of the gap are derived. This method not only has high precision in predicting the breakdown voltage and resistance of a single gap, but also can dynamically capture and simulate the breakdown development process of the entire series gap system in a complex electric field environment, especially the current distribution between different gaps, the breakdown delay time and their mutual influence relationship, realize the early prediction of the breakdown process and the scientific evaluation of the safety margin, effectively reduce the application risk of the series gap in high voltage, greatly improve the reliability and long-time stable operation ability of high-voltage equipment in harsh environments, ensure safe application under high-stress working conditions, thereby prolong the service life of the equipment and reduce the maintenance cost. BRIEF DESCRIPTION OF DRAWINGS

[0037] Figure 1 is an application environment diagram of the calculation method of the series gap breakdown development process in one embodiment;

[0038] Figure 2A flow chart of a calculation method of a series gap breakdown development process in an embodiment;

[0039] Figure 3 A flow chart of a first flow coefficient determination method in an embodiment;

[0040] Figure 4 A flow chart of a gap breakdown current calculation method in an embodiment;

[0041] Figure 5 A flow chart of a second flow coefficient determination method in an embodiment;

[0042] Figure 6 A flow chart of a third flow coefficient determination method in an embodiment;

[0043] Figure 7 A flow chart of a first gap equivalent resistance calculation method in an embodiment;

[0044] Figure 8 A flow chart of a series gap equivalent circuit model construction method in an embodiment;

[0045] Figure 9 A flow chart of a second gap equivalent resistance calculation method in an embodiment;

[0046] Figure 10 A structure block diagram of a series gap breakdown development process calculation device in an embodiment;

[0047] Figure 11 An internal structure diagram of a computer device in an embodiment. DETAILED DESCRIPTION

[0048] In order to make the purpose, technical scheme and advantages of the present application clearer, the present application will be further described in detail below with reference to the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and not used to limit the present application.

[0049] The calculation method of a series gap breakdown development process provided by the embodiments of the present application can be applied to, for example, Figure 1The application environment shown. Among them, the terminal 102 communicates with the server 104 through the network. The data storage system can store the data required by the server 104 to process. The data storage system can be integrated on the server 104, or placed on the cloud or other network servers. The server 104 obtains the circuit parameters for constructing the series gap equivalent circuit model from the terminal 102, and the server 104 constructs the series gap equivalent circuit model according to a plurality of series gap equivalent parallel circuits; based on the series gap equivalent circuit model, the current guide coefficient of the series gap is determined according to the plasma parameters of the cathode plasma and the electric field calculation model of the series gap; based on the series gap equivalent circuit model, the series gap equivalent resistance is determined according to the plasma expansion radius of the cathode plasma and the current guide coefficient of the series gap; based on the series gap equivalent circuit model, the series gap breakdown voltage is determined according to the series gap breakdown data; according to the series gap equivalent resistance and the series gap breakdown voltage, the series gap breakdown development process is calculated; the series gap breakdown development process is used to describe the relationship between the breakdown of each series gap in the series gap and time, so as to realize the safe application of the series gap. Among them, the terminal 102 can be, but not limited to, various personal computers, notebook computers, smart phones, tablet computers and Internet of Things devices. The server 104 can be realized by an independent server or a server cluster composed of multiple servers.

[0050] In one embodiment, as shown in Figure 2 , a series gap breakdown development process calculation method is provided, which is applied to the server in Figure 1 for example, including the following steps:

[0051] Step 202, according to a plurality of series gap equivalent parallel circuits, a series gap equivalent circuit model is constructed.

[0052] Among them, the series gap can refer to the actual physical distance between two electrodes in an electrical system. In this space, breakdown phenomenon may occur under the action of electric field, resulting in discharge through the gap. The characteristics of the series gap (such as distance, shape, material, electric field intensity, etc.) directly affect its breakdown behavior and electrical characteristics.

[0053] Among them, the series gap parallel circuit can be equivalent to a plurality of circuit elements, and the plurality of equivalent circuit elements are connected in parallel.

[0054] In this model, the electrical characteristics of each space gap, such as equivalent resistance and breakdown voltage, can be predicted and analyzed through the model. This model can simulate the series effect of multiple real space gaps under the action of electric field, helping to study and predict the breakdown development process of each real space gap.

[0055] In this model, the power loop equivalent circuit model can be an equivalent circuit model used to simulate the behavior of the actual power loop in the electrical system. It replaces complex actual circuits with equivalent circuit elements such as resistors, inductors, capacitors, etc., simplifying analysis and calculation. This model can help study the electrical characteristics of the power loop under various working conditions, such as voltage, current and power distribution, to evaluate the stability and efficiency of the power loop.

[0056] In this model, the measurement and control device equivalent circuit model can be used to represent the behavior of measurement and control devices in the electrical system. By equivalent to the electrical characteristics of the measurement and control device as a combination of resistance, capacitance or inductance elements, it can be easier to analyze its role and response in complex systems. This model can simplify analysis and evaluate the performance of the device under different electrical conditions when designing and optimizing the measurement and control device.

[0057] In this model, the stray parameter equivalent circuit model can be an equivalent circuit model used to describe the non-ideal effects introduced by non-ideal elements and circuit layout in the electrical system, such as parasitic capacitance, parasitic inductance or resistance, etc. 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] In this model, the real space gap equivalent resistance can be the resistance after the real space gap is equivalent to a parallel circuit of real space gaps.

[0059] In this model, the real space gap breakdown voltage can be the voltage value that can break down the real space gap.

[0060] Specifically, in order to accurately simulate the electrical characteristics of multiple series-connected vacuum gaps under the electric field, the series-connected vacuum gap equivalent circuit model should include the equivalent capacitance model of the vacuum gap, the equivalent variable resistance model, and the model of other auxiliary devices (if any). Therefore, for each independent vacuum gap, it is equivalent to a parallel combination of a to-be-determined vacuum gap equivalent capacitance and a to-be-determined vacuum gap equivalent resistance, 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 circuits. Among them, the parameters of the to-be-determined vacuum gap equivalent capacitance of the vacuum gap can be determined by experiment or simulated and calculated by the finite element method or the surface charge method, and the parameters of the auxiliary devices such as the voltage-sharing capacitor and the current-limiting resistor should be determined by experiment.

[0061] In addition to the series-connected vacuum gap equivalent circuit model, the power supply loop equivalent circuit model, the measurement and control device equivalent circuit model, and the equivalent circuit model of stray parameters also need to be constructed.

[0062] For the power supply loop equivalent circuit model, all main component models of the power supply loop should be included; in particular, for the controlled power supply, the corresponding control module and control algorithm should also be included to accurately depict the behavior characteristics of the power supply under the development of breakdown, and the parameters of each main component model should be determined by actual experiment.

[0063] For the measurement and control device equivalent circuit model, since the equivalent capacitance of the vacuum gap is only in the order of pF, the parameters of the commonly used measurement and control devices are much larger than this order of magnitude, so it is necessary to establish the equivalent circuit model of the measurement and control device. The related parameters in the measurement and control device model should be experimentally determined under the condition of allowing; those that cannot be experimentally determined should be provided by the supplier of the measurement and control device or determined by 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 development process of breakdown. The devices included in the stray parameter model should be determined according to the actual arrangement and wiring method of the series-connected vacuum gap, and at least include: (1) mutual capacitance between electrodes of the series-connected vacuum gap; (2) capacitance of each electrode to ground; (3) equivalent inductance of the connection line between the power supply and the series-connected vacuum gap; (4) equivalent resistance and inductance of the grounding part.

[0065] Step 204, based on the series-connected vacuum gap equivalent circuit model, the plasma parameters of the cathode plasma and the electric field calculation model of the vacuum gap are used to determine the current conduction coefficient of the vacuum gap.

[0066] wherein the plasma parameters can be physical quantities describing the state and characteristics of the plasma, typically including electron density, electron temperature, ion density, ion temperature, plasma radius, etc. These parameters determine the behavior of the 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 the plasma.

[0067] wherein the electric field calculation model can be a model used to simulate the distribution of the electric field in different physical environments, taking into account factors such as electrode structure, spatial geometry, material properties, etc. This model can accurately predict the electric field strength and direction under different voltage and charge distributions by solving Maxwell's equations. In the study of real space gaps, the electric field calculation model is the basis for predicting charge flow, breakdown path, and the formation of conduction channels, helping researchers analyze the impact of breakdown voltage and electric field distribution on system performance.

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

[0069] Step 206, based on the series real space gap equivalent circuit model, according to the plasma expansion radius of the cathode plasma and the conduction coefficient of the real space gap, the equivalent resistance of the real space gap is determined.

[0070] wherein the plasma expansion radius can refer 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 plasma and the electric field in the real space gap. The size of the expansion radius depends on the electric field strength, plasma parameters, and medium characteristics, and directly affects the formation of the conduction channel and the conduction characteristics in the space gap.

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

[0072] Step 208, based on the series of vacuum gap equivalent circuit model, the vacuum gap breakdown voltage is determined according to the vacuum gap breakdown data.

[0073] Specifically, the breakdown voltage value in the experiment or historical data is used, combined with the physical parameters of the vacuum gap (such as spacing, shape, material characteristics, etc.), and the actual breakdown voltage is compared with the calculation results of the model. Then, by adjusting the key parameters (such as electric field intensity, electrode spacing, etc.) in the model to match the actual breakdown data, the calculation accuracy of the breakdown voltage is further optimized. This process needs to consider factors such as the local electric field enhancement effect of the vacuum gap, the formation of the plasma and its influence on the electric field, etc., 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 formula approximation.

[0075] If the experimental method is used, the vacuum gap should be tested for breakdown not less than 100 times, taking the breakdown voltage as the abscissa and the proportion of the breakdown probability below the voltage as the ordinate, and applying the three-parameter Weibull cumulative probability formula for fitting. According to the fitting results, the breakdown voltage when the breakdown probability is 50% is obtained, which is considered as the breakdown voltage of the vacuum gap.

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

[0077] If the approximate estimate is made by formula, it needs to be estimated according to the actual working condition and the commonly used formula in the industry.

[0078] In step 210, the breakdown development process of the series gap is calculated according to the equivalent resistance of the series gap and the breakdown voltage of the series gap.

[0079] The breakdown development process of the series gap can be data describing the relationship between the breakdown of each series gap and time in the series gap to realize the safe application of the series gap.

[0080] Specifically, after the equivalent resistance of the series gap and the breakdown voltage of the series gap are determined, the voltage distribution and current flow of each series gap at different time points are calculated by a time stepping algorithm. The breakdown development process simulation of the series gap not only describes the change of the electric field strength, but also involves the accumulation of electric charge, the formation of the discharge path and the mutual influence between the series gaps. In the simulation of the entire breakdown development process of the series gap, the dynamic change of the local electric field in the series gap and the gradual expansion of the breakdown path need to be closely observed. Through the accurate simulation of this process, the role of each series gap in the entire system can be comprehensively analyzed, the breakdown time and the occurrence time of the electrical fault can be predicted, and the breakdown development process of the simulated series gap is obtained.

[0081] In actual application, at each time step, the voltage of each series gap is calculated. If the gap voltage is greater than the breakdown voltage of the gap, it is determined that the gap breaks down. Otherwise, it is considered that the gap does not break down. If all the gaps break down or the calculation time reaches the set maximum calculation time, the calculation is ended.

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

[0083] By constructing a series of vacuum gaps in series of series vacuum gap equivalent circuit model, the series effect of multiple vacuum gaps under the action of electric field is considered in detail, the flow coefficient of the vacuum gap is accurately determined by using the physical parameters of the cathode plasma and its expansion radius, combined with the electric field calculation model, and then the equivalent resistance and breakdown voltage of the vacuum gap are derived. This method not only has high precision 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 between different vacuum gaps, the breakdown delay time and their mutual influence relationship, realize the early prediction of the breakdown process and the scientific evaluation of the safety margin, effectively reduce the application risk of series vacuum gaps in high voltage, greatly improve the reliability and long-time stable operation ability of high-voltage equipment in harsh environment, ensure the safe application under high stress working conditions, thereby prolong the service life of the equipment and reduce the maintenance cost.

[0084] In one embodiment, as shown in Figure 3 Based on the series vacuum gap equivalent circuit model, the flow coefficient 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, 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] Wherein, the spatial potential distribution can refer to the potential value of 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 electrostatic field such as Poisson equation or Laplace equation, the potential distribution in the whole 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 (without cathode plasma) is established, which 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 any given value US; the boundary condition is 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] In the formula: The potential distribution of a point in space.

[0090] In the model, the cathode plasma is added, which is in the shape of a sphere with its center at the position of the maximum surface electric field of the cathode, and the part of the sphere overlapping 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 distance between the space and the gap is defined as r. The initial setting is r = 0.1. For the space gap considering the cathode plasma, the spatial electric field distribution of the space gap is calculated, and the calculation equation is:

[0091]

[0092] In the formula: The potential distribution of a point in space; p is the space charge density; and ε is the dielectric constant.

[0093] In step 304, the spatial electric field distribution of the space gap is calculated according to the spatial potential distribution.

[0094] The spatial electric field distribution can refer to the intensity 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 positions. The electric field is the result of the potential gradient, which is calculated by differentiating the spatial potential distribution.

[0095] Specifically, after obtaining the spatial potential distribution, the electric field intensity and direction at each position in the space gap can be obtained by gradient operation on the spatial potential distribution. This process needs to pay special attention to the local electric field enhancement phenomenon in the extended area of the cathode plasma. Near the boundary of the plasma, the electric field intensity usually increases significantly, and the non-uniformity of the electric field is also exhibited 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 space gaps. According to the spatial potential distribution, the spatial electric field distribution is calculated, and the calculation equation is:

[0096]

[0097] In the formula: E is the electric field intensity at a point in space.

[0098] In step 306, the gap breakdown current is calculated according to the spatial potential distribution and the spatial electric field distribution.

[0099] The gap breakdown current can refer to the current generated after the dielectric or space gap is broken down to form a conductive path when the electric field intensity reaches a certain critical value. The current is determined by the electric field intensity at the time of breakdown, the electron emission density, and the formation of the electrically conductive channel. During the breakdown process, the electric field drives the charges through the gap, resulting in a sudden increase in current, thereby generating the gap breakdown current.

[0100] Specifically, after obtaining the spatial electric field distribution, based on the acceleration effect of electric field on charges and the formation process of conductive channel, according to the electric field intensity and its distribution in space, the trajectory of free charges (mainly ions and electrons) under the action of electric field is calculated, especially the accumulation and release of charges in the cathode plasma expansion region. At the breakdown moment, the charges form a conductive path under the action of electric field and start to flow through the vacuum gap, that is, the gap breakdown current is generated. The size of the gap breakdown current is directly related to the electric field distribution, charge density and the formation of the conductive channel, and the influence of the electric field on the plasma, the conductivity of the medium in the gap and the time variation of the electric field need to be considered comprehensively in the calculation process. Through dynamic simulation of the breakdown process, the gap breakdown current at the breakdown moment and the variation law of the gap breakdown current with time can be accurately calculated.

[0101] Step 308, according to the gap breakdown current and the radius of the cathode plasma, the conductive coefficient of the vacuum gap is determined.

[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 calculation of the 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 gap breakdown current is obtained. Then combined with the expansion radius of the cathode plasma, the conductive coefficient is calculated.

[0103] In this embodiment, by constructing a series of vacuum gap equivalent circuit model and applying the radius of the cathode plasma to the electric field calculation, the spatial potential distribution and the 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 of the spatial potential and the electric field. Finally, by analyzing the relationship between the breakdown current and the plasma expansion radius, the conductive coefficient of the vacuum gap is determined. This series of steps makes it possible to more comprehensively characterize 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, as shown in Figure 4 According to the spatial potential distribution and the spatial electric field distribution, the gap breakdown current is calculated, including:

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

[0106] Wherein, the initial electron emission density can refer to the number of electrons released per unit area under the action of the initial electric field on the cathode surface. It is related to the electric field intensity near the cathode and the plasma characteristics, and reflects the ability of electrons to be emitted from the cathode to the vacuum gap in the initial stage of breakdown. The initial electron emission density is an important parameter for calculating the gap breakdown current, and directly affects the opening stage of the breakdown process.

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

[0108]

[0109] In the formula: v0——initial velocity of the electron; ——potential of the electron release position; ——normal vector pointing to the outside of the emission surface.

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

[0111]

[0112] In the formula: d buf ——distance of the electron emission position from the surface of the cathode gas group.

[0113] The initial electron emission density on the electron emission surface is:

[0114]

[0115] In the formula: J0——initial electron emission density.

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

[0117] Wherein, the initial gap breakdown current can be the initial current through the space gap when the electric breakdown of the space gap starts. It is obtained by surface integrating the initial electron emission density, and represents the current size at the start of the breakdown process. The current size reflects the current conduction ability under the action of the electric field in the initial stage of breakdown, and is a key indicator for breakdown analysis.

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

[0119] The electron moves from the initial position to the anode under the action of the electric field force, and the motion equation is:

[0120]

[0121] m e - electron mass; q e - electron charge; - electron velocity.

[0122] At each time step, the emitted electrons move according to the movement, while a new batch of electrons is emitted at the emission surface, the number of electrons being determined by the current density and the time step. The time step is advanced until all the first batch of emitted electrons reaches the anode.

[0123] At step 406, upon detecting that the electrons of the cathode plasma have all reached the anode from the cathode, an updated space charge distribution is obtained.

[0124] The updated space charge distribution can refer to the redistribution of charges in the real space gap after the movement of the electrons from the cathode to the anode. Due to the movement of the electrons and the passage of the current, the charge density in the space changes, which in turn affects the distribution of the entire electric field and potential. The update of this distribution helps to reflect the dynamic changes of the charges in the breakdown process, ensuring the accuracy of subsequent calculations.

[0125] Specifically, upon detecting that the electrons of the cathode plasma have all reached the anode from the cathode, the space potential distribution is recalculated for the real space gap considering the cathode plasma according to the above calculation equation for the point potential distribution, obtaining the updated space charge distribution.

[0126] At step 408, the updated space potential distribution and the updated space electric field distribution of the real space gap are calculated based on the updated space charge distribution.

[0127] The updated space electric field distribution can be the electric field distribution recalculated based on the updated space charge distribution. With the movement of the electrons and the accumulation of the charges, the electric field strength and direction also change, and the updated electric field distribution reflects the changes of the electric field in the real space gap over 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 the cathode plasma in the model, its shape is spherical, the spherical center is located at the maximum of the cathode surface electric field, 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 distance of the real space gap is defined as r. According to the updated space charge distribution, the updated space potential distribution of the real space gap considering the cathode plasma is calculated, and the calculation equation is:

[0129]

[0130] In the formula: Potential distribution of a point in space; p - 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] In the formula: E - Electric field intensity of a point in space.

[0134] Step 410, according to the updated space potential distribution and the updated space electric field distribution, the updated electron emission density of the real space gap is calculated.

[0135] Wherein, the updated electron emission density can be the number of electron emission per unit area calculated based on the updated space electric field distribution. With the change of space electric field, the electron emission capacity of cathode surface will also be dynamically adjusted, and the updated electron emission density can better reflect the emission behavior under the current electric field condition, providing basic data for calculating subsequent breakdown current.

[0136] Specifically, similar to the implementation process of step 402, the electron is released at a distance outside the cathode plasma surface, which is less than 0.01r, and under the action of the updated space point potential distribution and the updated space electric field distribution, the initial velocity of the electron is:

[0137]

[0138] In the formula: v0 - Initial velocity of electron; - Potential of electron release position; - Normal vector pointing to the outside of the emission surface.

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

[0140]

[0141] In the formula: d buf - Distance from the electron emission position to the surface of the cathode gas group.

[0142] At the electron emission surface, the updated electron emission density is:

[0143]

[0144] In the formula: J1 - Updated electron emission density.

[0145] Step 412, surface integration is performed 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 gap breakdown current I1 can be obtained by integrating the updated electron emission density over the surface of the entire cathode plasma.

[0147] The motion equation of the electron moving from the initial position to the anode under the action of the electric field force is:

[0148]

[0149] In the formula, m e - electron mass; q e - electron charge quantity; - electron velocity.

[0150] At each time step, the emitted electrons move according to the movement of the emitted electrons, and a new batch of electrons is emitted at the emission surface, the number of electrons being determined by the current density and the time step. The time step is advanced until all the first batch of emitted electrons reach 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 iteration, this method can capture the charge accumulation and electric field evolution in the real space gap in real time, thereby effectively improving the accuracy and controllability of the breakdown process. It helps to more accurately predict and control the breakdown behavior of electrical equipment, significantly improves the stability and safety of the system under high voltage, and provides a reliable basis for equipment design and protection.

[0152] In one embodiment, as Figure 5 shown, the conductance coefficient of the real space gap is determined according to the gap breakdown current and the radius of the cathode plasma, including:

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

[0154] The current offset can be the difference between the initial gap breakdown current and the gap breakdown current, which is usually used to judge whether the calculation converges. If the current offset is large, it indicates that there is a large difference between the calculated breakdown current and the expected value, and the electron emission density or the electric field distribution needs to be further adjusted; if the current offset tends to zero, it indicates that the calculation converges, and the current value reaches 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 difference is divided by the gap breakdown current. The final calculation result is the current offset.

[0156] Step 504, in the case of non-convergence of the current offset, the electron trajectory of the real space gap is calculated according to the updated electron emission density.

[0157] Wherein, 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 real space gap, which is affected by the electric field intensity, charge distribution and external voltage. By calculating the electron trajectory, it can be understood how the electron is affected by the electric field force and finally reaches the anode.

[0158] Specifically, in the case of non-convergence of the current offset, (I1-I1) / I1≥0.1, it is considered that the current offset calculated at present is not convergent, and the electron trajectory of the real space gap is calculated again according to the updated electron emission density.

[0159] Step 506, the distribution of the electron in the space is recalculated according to the electron trajectory, and the iterative space potential distribution is obtained.

[0160] Wherein, the iterative space potential distribution can be the potential distribution in the real space gap obtained by multiple iteration calculations. With each update of the charge distribution and the electron trajectory, the potential distribution will also change accordingly. Each iteration calculation will update the potential distribution according to the new electron emission density and electric field distribution until the system reaches a convergent state.

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

[0162] Step 508, the iterative space potential distribution is taken as the space potential distribution, and the step of calculating the space electric field distribution of the real space gap according to the space potential distribution is returned to execute until the current offset is convergent.

[0163] Specifically, the iterative space potential distribution is taken as the space potential distribution, and the step of calculating the space electric field distribution of the real space gap according to the space potential distribution is returned to execute until the current offset is convergent, that is, after iteration to the nth time, it can meet: (I n - n-1 ) / I n-1 ≤0.1.

[0164] Step 510, the current offset and the anode voltage of the cathode plasma are used to determine the current guide coefficient.

[0165] Specifically, the gap breakdown current I nThe current when the radius of the cathode plasma is r, combined with the anode voltage of the cathode plasma, can be used to calculate the current conduction coefficient P at this time. By fusing the current conduction coefficients at different times, the final current conduction coefficient is obtained.

[0166] In this embodiment, whether the calculation converges is determined by the initial gap breakdown current and the current offset in subsequent iterations. In the case of non-convergence, the electron emission density is continuously adjusted, and the electron trajectory and spatial potential distribution are recalculated. As the iteration deepens, the system gradually approaches a convergent state, enabling more accurate capture of the dynamic processes of electron motion, electric field changes, and charge distribution. Through this iterative update, the current conduction coefficient of the real gap can be accurately determined, improving the prediction accuracy of the breakdown current and ensuring the reliability and safety of the equipment under high voltage conditions. This method provides strong support for modeling breakdown behavior in complex electric field environments, helping to optimize design and reduce the risk of system failure.

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

[0168] Step 602, according to the current offset and the anode voltage of the cathode plasma, the current conduction coefficient is calculated.

[0169] The current conduction coefficient can refer to the ability of the current to pass through the real 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 electric field conditions, electron emission density, and cathode plasma expansion.

[0170] Specifically, since the anode potential is set to an arbitrary given value U S in the establishment of the electric field calculation model, the cube of the anode potential is further calculated as the denominator for calculating the current conduction coefficient; then the gap breakdown current I n is divided by the cube of the anode potential to obtain the current conduction coefficient, which is expressed as:

[0171]

[0172] Step 604, in the case where 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.

[0173] The convergence judgment value can be a threshold value for judging whether the current calculation has approached a stable state. Generally, 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 reaches a stable breakdown state.

[0174] The update radius can refer to adjusting 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 meet the convergence condition, the plasma radius is adjusted to simulate its expansion. The update radius is used for further calculation of the spatial potential distribution and the electric field distribution, so that the calculation result gradually approaches the target radius, thereby optimizing the calculation of the flow 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 original obtained radius of the cathode plasma is added to the convergence judgment value of the original obtained current offset, that is, r = r + 0.1, as the new update radius of the cathode plasma.

[0176] Step 606, taking the update 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, obtaining the target radius of the cathode plasma.

[0177] The target radius can 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 meets the convergence condition, the system reaches a stable state, and the target radius is the final expansion size of the cathode plasma. The target radius is an important parameter for fitting and calculating the flow conductivity coefficient, ensuring the stability of current conduction and the accuracy of the system.

[0178] Specifically, taking the update radius as the radius of the cathode plasma, then returning to execute 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, recalculating the radius of the cathode plasma, and through multiple iterations of the radius of the cathode plasma, until the radius of the cathode plasma is greater than the radius threshold, taking the last calculated radius of the cathode plasma as the target radius.

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

[0180] Specifically, a group of target radii r and gap breakdown currents I nThe final conductance coefficient is obtained by fitting P(r) which is the current of the cathode plasma with a radius of r divided by the cube of two-thirds of the anode potential, and the fitting formula applied is:

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

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

[0183] In this embodiment, the plasma radius is updated according to the convergence value of the current offset when the cathode plasma radius does not reach the threshold value, so as to recalculate the spatial potential distribution and continuously iterate. This process gradually increases the radius of the plasma, and finally reaches the stable target radius. Further, by fitting the relationship between the current offset and the target radius, the accurate conductance 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 conductance coefficient, and further improves the reliability of the system in the 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, as shown in Figure 7 , based on the series vacuum gap equivalent circuit model, the equivalent resistance of the vacuum gap is determined according to the plasma expansion radius of the cathode plasma and the conductance coefficient of the vacuum gap, including:

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

[0186] Specifically, in the actual calculation process, if the vacuum gap breaks down at time t BD , then at the time point t n , the plasma expansion radius at time t n is calculated:

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

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

[0189] Step 704, if the plasma expansion radius is less than 0, then output the equivalent resistance error information of the vacuum gap.

[0190] The equivalent resistance error information can be a warning or error prompt automatically output when the system detects that the expansion radius of the cathode plasma has an unreasonable negative value in the calculation process. This usually means that there is an anomaly in the calculation, which can be caused by input parameter errors, numerical values exceeding the physically reasonable range, or an unsuitable model.

[0191] Specifically, if the plasma expansion radius is less than 0, i.e., r < 0, the equivalent resistance error information of the real space gap is directly output, indicating that the equivalent resistance cannot be obtained.

[0192] Step 706, in the case where the plasma expansion radius is greater than 0 and less than 1, the equivalent resistance of the real space gap is determined according to the flow coefficient of the real space gap.

[0193] Specifically, if the plasma expansion radius is greater than 0 and less than 1, i.e., 0 < r < 1, the specific value of the equivalent resistance of the real space gap to be determined is calculated as the equivalent resistance of the real space gap according to the flow coefficient of the real space gap. The formula is as follows: where P(r) = ae br + ce dr -(a+c), where a, b, c, and d are the fitting parameters obtained above; the equivalent resistance R gap of the real space gap can be obtained as U / I.

[0194] Step 708, in the case where the plasma expansion radius is greater than or equal to 1, the specific value of the equivalent resistance of the real space gap to be determined is determined as zero, and is taken as the equivalent resistance of the real space gap.

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

[0196] In this embodiment, the expansion speed and time of the cathode plasma are accurately calculated to determine the expansion radius of the plasma, so as to dynamically adjust the equivalent resistance of the vacuum gap. In the calculation process, when the expansion radius of the plasma is less than 0, the system immediately outputs an error message to prompt 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 flow coefficient, thereby ensuring the accuracy and stability of the system. When the expansion radius is greater than or equal to 1, the equivalent resistance of the vacuum gap is automatically set 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, and thus improve the operation stability and breakdown protection effect of the electrical equipment.

[0197] In one embodiment, as shown in FIG. 1, a series vacuum gap equivalent circuit model is constructed according to a plurality of vacuum gap equivalent vacuum gap parallel circuits, including: Figure 8

[0198] Step 802, according to the vacuum gap parameters of a plurality of vacuum gaps, an equivalent capacitance model and an equivalent variable resistance model are constructed.

[0199] The vacuum gap parameters can be key variables that describe the physical and electrical characteristics of the vacuum gap. These parameters include the geometric dimensions of the gap (such as gap distance, area), material properties (such as dielectric constant, conductivity, breakdown voltage), electric field strength, temperature conditions, etc. These parameters together determine the behavior of the vacuum gap under different voltage and electric field conditions, affect 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, an equivalent capacitance model is constructed based on the geometric structure of the vacuum gap, especially the distance between the electrodes and the dielectric properties of the material, which reflects the ability of the gap to store electrical energy under an applied electric field. At the same time, the equivalent variable resistance model is defined according to parameters such as electric field strength, breakdown voltage, and material conductivity. As the electric field strength changes, the resistance of the vacuum gap is not fixed, but dynamically changes as the breakdown condition approaches. Therefore, this resistance model is a nonlinear and dynamically adjusted model that reflects the gradual reduction of resistance during the breakdown process.

[0201] Step 804, for any vacuum gap, according to the equivalent capacitance model and the equivalent variable resistance model, the vacuum gap is equivalent to a capacitance-resistance parallel circuit.

[0202] ​Specifically, for any real space gap, by combining the previously constructed equivalent capacitance model and equivalent variable resistance model, the real space gap is represented by an equivalent capacitance and an equivalent resistance in parallel, and the equivalent capacitance and the equivalent resistance are connected in parallel to obtain a capacitance-resistance parallel circuit. The capacitance-resistance parallel circuit can reflect the dynamic behavior of the real space gap under different electric field conditions: the capacitance part represents the ability of the real space gap to store electric field energy, and the resistance part represents the conductive ability of the real space gap before and after breakdown. In particular, when breakdown begins, the resistance will decrease sharply, the current passing through the resistance channel will increase greatly, and the role of the capacitance will gradually weaken.

[0203] Step 806, connecting each capacitance-resistance parallel circuit in series to obtain a series real space gap equivalent circuit model.

[0204] Specifically, considering the different electrical characteristics of each space gap, such as some space gaps may break down at lower voltages, while other space gaps may have higher breakdown voltages, connecting each capacitance-resistance parallel circuit in series means that the electrical characteristics of the overall circuit when current passes through each space gap are a combination of the electrical behavior of multiple real space gaps, ultimately obtaining a series real space gap equivalent circuit model. This model not only can simulate the independent behavior of each real space gap, but also can reflect the interaction between multiple space gaps. For example, the space gap that breaks down earlier may change the voltage distribution of other space gaps, thereby affecting their breakdown time and current conduction ability.

[0205] In this embodiment, by constructing an equivalent capacitance model and an equivalent variable resistance model, each real space gap is converted into an equivalent circuit with a capacitance and a resistance in parallel, and multiple parallel circuits are connected in series to form an overall series real space gap equivalent circuit model. This process can accurately simulate the electrical behavior of real space gaps in an 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 conduction characteristics and resistance changes during breakdown. By combining these circuits, the system can more accurately describe the breakdown process of multiple real space gaps in a complex electric field, improving the prediction ability of the breakdown current, while ensuring 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, as shown in Figure 9 the method further comprises:

[0207] Step 902, obtaining the relationship between the gap emission current value and the change of the gap applied voltage of the real space gap.

[0208] The gap emission current value can refer to the current value generated by the electron flow emitted from the cathode in the vacuum gap under the action of a certain electric field. It represents the intensity of electron emission behavior caused by the electric field before breakdown, and is the initial performance of the conduction capability of the gap under different voltages, directly affecting the size of the breakdown current.

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

[0210] Specifically, by experimental or simulation means, the gap emission current value of the vacuum gap under different applied voltages is measured. During the measurement, a series of different gap applied voltages are applied across the vacuum gap, and the emission current change under each voltage is 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, according to the change relationship and the actual applied voltage, the actual emission current value is obtained.

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

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

[0214] Specifically, according to the change relationship combined with the current actual applied voltage, the current value is determined by looking up or interpolation, ensuring that the real current response can be obtained under the actual voltage conditions, and the actual emission current value under this voltage is derived.

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

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

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

[0218] Step 908, according to the resistance function relationship and the simulation gap voltage value, determine the gap field emission current value.

[0219] Wherein, the simulation gap voltage value can be the voltage value between the real space gap in the process of numerical simulation or experimental simulation. The voltage is accurately calculated by the simulation model to understand the electrical behavior of the real space gap under different electric field conditions, so as to estimate the performance of the system in actual operation.

[0220] Wherein, the gap field emission current value can refer to the current value caused by the direct emission of electrons from the cathode driven by the electric field under the action of high intensity electric field. This current is closely related to the electric field strength, and is a key phenomenon in the breakdown process, which can reflect the conduction ability of the real space gap under certain electric field conditions.

[0221] Specifically, according to the resistance function relationship combined with the simulation gap voltage value, the gap field emission current value is further calculated. The gap field emission current value refers to the electron flow emitted from the electrode surface when the electric field strength is high enough, and the resistance function can determine the current value generated in the real space gap under simulation conditions (such as a certain voltage).

[0222] Step 910, according to the simulation gap voltage value and the gap field emission current value, calculate the equivalent resistance of the real space gap.

[0223] Specifically, the simulation gap voltage value and the gap field emission current value obtained by simulation are combined with the resistance function relationship to calculate the equivalent resistance of the real space gap, that is, the current equivalent resistance value of the real space gap is the ratio of the current gap voltage value and the corresponding field emission current value, which reflects the electrical conduction characteristics of the real space gap under different electric field conditions. Through accurate resistance calculation, the electrical performance of the real space gap can be further analyzed, especially the performance under the condition of approaching breakdown or actual operation, to ensure the safety and reliability of system design and operation.

[0224] In this embodiment, by obtaining the change relationship between the emission current of the real space gap and the applied voltage, combining the actual voltage condition, accurately calculating the emission current and constructing the resistance function, further combining the simulation voltage value to determine the field emission current, the equivalent resistance of the real space gap is calculated. This process can more accurately reflect the conduction characteristics of the real space gap under different electric field conditions, especially the dynamic changes of the breakdown behavior under high voltage conditions. By establishing the resistance function, the system can adjust the resistance value with the change of the voltage, effectively improve the prediction ability of the breakdown current, ensure the stability and reliability of the electrical equipment under different working conditions, optimize the design, and reduce the risk of breakdown.

[0225] It should be understood that, although each step in the flowchart involved in the above embodiments is displayed in sequence according to the arrow, these steps are not necessarily executed in the order indicated by the arrow. Unless otherwise specified herein, the execution of these steps is not strictly limited in sequence, and these steps can be executed in other orders. Moreover, at least part of the steps in the flowchart involved in the above embodiments can include multiple steps or stages, which 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 sequential, but can be alternately executed with at least part of other steps or steps or stages in other steps.

[0226] Based on the same inventive concept, the embodiments of the present application also provide a series of real space gap breakdown development process calculation device for realizing the above-mentioned series of real space gap breakdown development process calculation method. The implementation scheme for solving the problem provided by the device is similar to the implementation scheme described in the above method, so the specific limitations in one or more series of real space gap breakdown development process calculation device embodiments provided below can refer to the limitations of the series of real space gap breakdown development process calculation method in the above text, which will not be repeated here.

[0227] In one embodiment, as shown in Figure 10 A series of real space gap breakdown development process calculation device is provided, including: a circuit model construction module 1002, a flow coefficient 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 construction module 1002 is configured to construct a series of real space gap equivalent circuit model according to a plurality of real space gaps in parallel.

[0229] The conductance coefficient determination module 1004 is configured to determine the conductance coefficient of the vacuum gap based on the series vacuum gap equivalent circuit model, and according to the plasma parameter of the cathode plasma and the electric field calculation model of the vacuum gap.

[0230] The equivalent resistance obtaining module 1006 is configured to determine the equivalent resistance of the vacuum gap based on the series vacuum gap equivalent circuit model, and according to the plasma expansion radius of the cathode plasma and the conductance coefficient of the vacuum gap.

[0231] The breakdown voltage obtaining module 1008 is configured to determine the breakdown voltage of the vacuum gap based on the series vacuum gap equivalent circuit model, and according to the breakdown data of the vacuum gap.

[0232] The breakdown process description module 1010 is configured to calculate the breakdown development process of the series vacuum gap based on the equivalent resistance of the vacuum gap and the breakdown voltage of the vacuum gap. The 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.

[0233] In an embodiment, the conductance coefficient determination module 1004 is further configured 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 based on the spatial potential distribution; calculate the gap breakdown current based on the spatial potential distribution and the spatial electric field distribution; and determine the conductance coefficient of the vacuum gap based on the gap breakdown current and the radius of the cathode plasma.

[0234] In an embodiment, the conductance coefficient determination module 1004 is further configured to calculate the initial electron emission density of the vacuum gap based on 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 an updated space charge distribution when it is detected that the electrons of the cathode plasma are all transferred from the cathode to the anode; calculate the updated spatial potential distribution and the updated spatial electric field distribution of the vacuum gap based on the updated space charge distribution; calculate the updated electron emission density of the vacuum gap based on the updated spatial potential distribution and the updated spatial electric field distribution; and perform surface integration on the updated electron emission density of the cathode plasma to obtain the gap breakdown current.

[0235] In one embodiment, the flow coefficient determination module 1004 is further configured to calculate a current offset between the initial gap breakdown current and the gap breakdown current; in a case that the current offset is not converged, calculate an electron trajectory of the real space gap according to the updated electron emission density; re-calculate the distribution of the electrons in the space according to the electron trajectory to obtain an iterative space potential distribution; return to execute the step of calculating the space electric field distribution of the real space gap according to the space potential distribution with the iterative space potential distribution as the space potential distribution until the current offset is converged; and determine the flow coefficient according to the current offset and the anode voltage of the cathode plasma.

[0236] In one embodiment, the flow coefficient determination module 1004 is further configured to calculate a current offset between the initial gap breakdown current and the gap breakdown current; in a case that the current offset is not converged, calculate an electron trajectory of the real space gap according to the updated electron emission density; re-calculate the distribution of the electrons in the space according to the electron trajectory to obtain an iterative space potential distribution; return to execute the step of calculating the space electric field distribution of the real space gap according to the space potential distribution with the iterative space potential distribution as the space potential distribution until the current offset is converged; and determine the flow coefficient according to the current offset and the anode voltage of the cathode plasma.

[0237] In one embodiment, the equivalent resistance obtaining module 1006 is further configured to calculate a plasma expansion radius according to the expansion speed of the cathode plasma and a relative time of the cathode plasma; the relative time is any time except the breakdown time of the real space gap; in a case that the plasma expansion radius is less than 0, output an error information of the equivalent resistance of the real space gap; in a case that the plasma expansion radius is greater than 0 and less than 1, determine the equivalent resistance of the real space gap according to the flow coefficient of the real space gap; in a case that the plasma expansion radius is greater than or equal to 1, determine that the specific value of the equivalent resistance of the real space gap to be determined is zero and take the specific value as the equivalent resistance of the real space gap.

[0238] In one embodiment, the circuit model construction module 1002 is further configured to construct an equivalent capacitance model and an equivalent variable resistance model according to the real space gap parameters of the plurality of real space gaps; for any real space gap, equivalently connect the real space gap into a capacitance-resistance parallel circuit according to the equivalent capacitance model and the equivalent variable resistance model; the capacitance-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 parallel connection; and connect the capacitance-resistance parallel circuits in series to obtain the series real space gap equivalent circuit model.

[0239] In one embodiment, the equivalent resistance obtaining module 1006 is also configured to obtain a change relationship between the gap emission current value of the real space gap and the gap applied voltage; obtain an actual emission current value according to the change relationship and the actual applied voltage; construct a resistance function relationship according to the actual applied voltage and the actual emission current value; determine the gap field emission current value according to the resistance function relationship and the simulation gap voltage value; and calculate the equivalent resistance of the real space gap according to the simulation gap voltage value and the gap field emission current value.

[0240] The modules in the above-mentioned device for calculating the development process of the series real space gap breakdown can be implemented by software, hardware, or a combination thereof. The modules can be embedded in or independent of a processor in a computer device in hardware form, or stored in a memory in the computer device in software form, so as to be called and executed by the processor to perform the operations corresponding to the modules.

[0241] In one embodiment, a computer device is provided, which can be a server. An internal structure diagram of the computer device can be as shown in FIG. 8. Figure 11 The computer device includes a processor, a memory, and a network interface connected by a system bus. The processor of the computer device is configured 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 running the operating system and the computer program in the non-volatile storage medium. The database of the computer device is configured to store server data. The network interface of the computer device is configured to communicate with an external terminal through a network connection. The computer program is executed by the processor to implement the method for calculating the development process of the series real space gap breakdown.

[0242] Those skilled in the art can understand that Figure 11 The structure shown in FIG. 8 is only a block diagram of part of the structure related to the scheme of the present application, and does not limit the computer device to which the scheme of the present application is applied. Specifically, the computer device can 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 also provided, which includes a memory and a processor. The memory stores a computer program. The processor executes the computer program to implement the steps in the above-mentioned method embodiments.

[0244] In one embodiment, a computer readable storage medium is provided, which stores a computer program. The computer program is executed by a processor to implement the steps in the above-mentioned method embodiments.

[0245] In an embodiment, a computer program product or computer program is provided, which includes computer instructions 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 to cause the computer device to perform 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 for analysis, stored data, displayed data, etc.) involved in the present application are all information and data authorized by the user or authorized by all parties.

[0247] It can be understood by those skilled in the art that all or part of the processes in the above-mentioned embodiment methods can be completed by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer readable storage medium, and when executed, can include the processes of the above-mentioned embodiments. Any reference to a memory, database or other medium used in the embodiments provided by the present application can include at least one of a non-volatile and volatile memory. The non-volatile memory can include a read-only memory (ROM), a magnetic tape, a floppy disk, a flash memory, an optical memory, a high-density embedded non-volatile memory, a resistive memory (ReRAM), a magnetoresistive random access memory (MRAM), a ferroelectric memory (FRAM), a phase change memory (PCM), a graphene memory, etc. The volatile memory can include a random access memory (RAM) or an external cache memory, etc. As an illustration but not limitation, the RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc. The database involved in the embodiments provided by the present application can include at least one of a relational database and a non-relational database. The non-relational database can include a distributed database based on a block chain, etc., without being limited thereto. The processor involved in the embodiments provided by the present application can be a general-purpose processor, a central processing unit, a graphics processing unit, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, etc., without being limited thereto.

[0248] Any technical features in the above embodiments can be combined, and for the sake of brevity, not all possible combinations are described above, however, as long as the combinations of technical features do not have contradictions, they shall be considered within the scope of the present disclosure.

[0249] The above embodiments only express several implementation manners of the present application, and the description is relatively specific and detailed, but it shall not be understood as a limitation on the patent scope of the present application. It shall be pointed out that, for ordinary skilled persons in the art, several modifications and improvements can be made without departing from the concept of the present application, and these shall be within the protection scope of the present application. Therefore, the protection scope of the present application shall be subject to the appended claims.

Claims

1. A method of calculating the development of a series vacuum gap breakdown, characterized in that The method comprises: constructing a series gap equivalent circuit model according to a plurality of parallel gap circuits equivalent to a real gap; determining a current conduction coefficient of the real gap based on the series gap equivalent circuit model, plasma parameters of a cathode plasma, and an electric field calculation model of the real gap, including: applying a radius of the cathode plasma to the electric field calculation model based on the series gap equivalent circuit model to obtain a spatial potential distribution of the real gap; calculating a spatial electric field distribution of the real gap according to the spatial potential distribution; calculating a gap breakdown current according to the spatial potential distribution and the spatial electric field distribution; and determining the current conduction coefficient of the real gap according to the gap breakdown current and the radius of the cathode plasma; determining a real gap equivalent resistance based on the series gap equivalent circuit model, a plasma expansion radius of the cathode plasma, and the current conduction coefficient of the real gap; determining a real gap breakdown voltage of the series gap based on the series gap equivalent circuit model and real gap breakdown data; calculating a real gap breakdown development process of the series gap based on the real gap equivalent resistance and the real gap breakdown voltage, wherein the real gap breakdown development process is used to describe a relationship between a breakdown condition of each real gap in the series gap and time, so as to realize safe application of the series gap.

2. The method of claim 1, wherein, The calculation of the gap breakdown current according to the spatial potential distribution and the spatial electric field distribution comprises: calculating an initial electron emission density of the real 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; obtaining an updated space charge distribution when it is detected that electrons of the cathode plasma have all arrived at the anode from the cathode; calculating an updated spatial potential distribution and an updated spatial electric field distribution of the real gap according to the updated space charge distribution; calculating an updated electron emission density of the real gap according to the updated spatial potential distribution and the updated spatial electric field distribution; performing surface integration on the updated electron emission density of the cathode plasma to obtain the gap breakdown current.

3. The method of claim 2, wherein, The determination of the current conduction coefficient of the real 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; calculating an electron trajectory of the real gap according to the updated electron emission density when the current offset is not convergent; recomputing a distribution of electrons in space according to the electron trajectory to obtain an iterative spatial potential distribution; returning to execute the step of calculating the spatial electric field distribution of the real gap according to the spatial potential distribution until the current offset is convergent, with the iterative spatial potential distribution as the spatial potential distribution; determining the current conduction coefficient according to the current offset and an anode voltage of the cathode plasma.

4. The method of claim 3, wherein, The determining the flow conductance coefficient according to the current offset and the anode voltage of the cathode plasma comprises: calculating a current flow conductance coefficient according to the current offset and the anode voltage of the cathode plasma; in the case that the radius of the cathode plasma is less than a radius threshold, adding the radius of the cathode plasma to a convergence judgment value of the current offset to obtain an updated radius of the cathode plasma; returning to the step of applying the radius of the cathode plasma to the electric field calculation model based on the series gap equivalent circuit model until the radius of the cathode plasma is greater than the radius threshold to obtain a target radius of the cathode plasma; fitting the current offset and the target radius to obtain the flow conductance coefficient.

5. The method of claim 1, wherein, The determining the gap equivalent resistance according to the plasma expansion radius of the cathode plasma and the flow conductance coefficient of the gap based on the series gap equivalent circuit model comprises: calculating the plasma expansion radius according to the expansion speed of the cathode plasma and a relative time of the cathode plasma; the relative time is any time except the breakdown time of the gap; in the case that the plasma expansion radius is less than 0, outputting an error information of the gap equivalent resistance; in the case that the plasma expansion radius is greater than 0 and less than 1, determining a specific value of the gap equivalent resistance to be determined according to the flow conductance coefficient of the gap to obtain the gap equivalent resistance; in the case that the plasma expansion radius is greater than or equal to 1, determining the specific value of the gap equivalent resistance to be determined as zero.

6. The method of claim 1, wherein, The constructing the series gap equivalent circuit model according to a plurality of gap equivalent gaps in parallel comprises: constructing an equivalent capacitance model and an equivalent variable resistance model according to a plurality of gap parameters of the gaps; for any gap, equivalent the gap to a capacitance-resistance parallel circuit according to the equivalent capacitance model and the equivalent variable resistance model; the capacitance-resistance parallel circuit comprises a gap equivalent capacitance and a gap equivalent resistance, and the gap equivalent capacitance and the gap equivalent resistance are in parallel; connecting the capacitance-resistance parallel circuits in series to obtain the series gap equivalent circuit model.

7. The method of claim 1, wherein, The method further comprises: obtaining a change relationship between a gap emission current value and a gap applied voltage of the gap; obtaining an actual emission current value according to the change relationship and an actual applied voltage; 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 a simulation gap voltage value; calculating the gap equivalent resistance according to the simulation gap voltage value and the gap field emission current value.

8. A device for calculating the development of a series vacuum gap breakdown, characterized by The device comprises: The circuit model construction module is configured to construct a series gap equivalent circuit model according to a plurality of parallel gaps equivalent to a real gap. The flow conductance coefficient determination module is configured to determine a flow conductance coefficient of the real gap based on the series gap equivalent circuit model, plasma parameters of the cathode plasma, and an electric field calculation model of the real gap. The flow conductance coefficient determination module is specifically configured to apply a radius of the cathode plasma to the electric field calculation model to obtain a spatial potential distribution of the real gap based on the series gap equivalent circuit model; calculate a spatial electric field distribution of the real gap according to the spatial potential distribution; calculate a gap breakdown current according to the spatial potential distribution and the spatial electric field distribution; and determine the flow conductance coefficient of the real gap according to the gap breakdown current and the radius of the cathode plasma. The equivalent resistance obtaining module is configured to determine a real gap equivalent resistance based on the series gap equivalent circuit model, a plasma expansion radius of the cathode plasma, and the flow conductance coefficient of the real gap. The breakdown voltage obtaining module is configured to determine a real gap breakdown voltage based on the series gap equivalent circuit model and real gap breakdown data. The breakdown process description module is configured to calculate a real gap breakdown development process of the series real gaps based on the real gap equivalent resistance and the real gap breakdown voltage. The real gap breakdown development process is used to describe a relationship between a breakdown condition of each real gap in the series real gaps and time, so as to realize safe application of the series real gaps. 9.A computer device, comprising a memory and a processor, wherein the memory stores a computer program, and the computer device is configured to perform the method according to any one of claims 1-8 when the computer program is executed by the processor. The processor implements the steps of the method in any one of claims 1 to 7 when executing the computer program.

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