Simulation method and device for development process of streamer in gaseous medium, electronic equipment and storage medium

Abstract

The application provides a simulation method and device for streamer development in a gas medium, electronic equipment and a storage medium, and belongs to the technical field of high-voltage streamer generation and simulation, comprising the following steps: calculating electron mobility according to a gas component; calculating an electric field distribution; solving an average electron velocity according to the electric field distribution and the electron mobility; generating a random number by using an elastic collision probability distribution as an electron velocity of a profiled grid; updating an electron position by using a micro electron migration equation to obtain an electron density, and solving a macro ion drift equation to obtain updated positive ion density and negative ion density; calculating collision reactions between different particles by using an improved random dynamics analysis method to obtain the electron density, the positive ion density and the negative ion density which are updated again; iteratively calculating until a set simulation time is reached, and outputting a result. The application can simulate the randomness of a discharge process and the time step is not limited by a CFL condition, and the calculation efficiency is higher.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of high-voltage streamer generation and simulation, and particularly relates to a simulation method and device for streamer development process in a gas medium, an electronic device and a storage medium. BACKGROUND

[0002] Streamer discharge is an important form of gas discharge process, commonly found in gas gap under high voltage, and is a key stage of breakdown process. The lightning phenomenon commonly seen in nature is caused by streamer discharge in air triggered by high electric field generated by accumulated charges in thundercloud. Similarly, streamer discharge in gas is also easily caused by power equipment running under high voltage, such as corona discharge of power transmission line, surface flashover of power transmission line insulator and other phenomena, and understanding the mechanism of streamer discharge is crucial to improving the insulation performance of power equipment.

[0003] Numerical simulation is an effective method for studying the development process and discharge mechanism of streamer, and common streamer simulation models include fluid model, particle model and fluid-particle hybrid model. The fluid model is the most commonly used method for streamer simulation, which regards plasma as a continuous medium and describes the discharge process by solving the macroscopic transport equation of charged particles, but the fluid model has the following problems: the microscopic collision process between particles is ignored, and the random characteristics of streamer discharge cannot be simulated; the time step of the fluid model needs to meet the Courant-Friedrichs-Lewy (CFL) condition, and the electron velocity is extremely high in the strong electric field area, resulting in extremely short simulation step and reducing the calculation efficiency of the fluid model. SUMMARY

[0004] In view of the above problems, the present application provides a simulation method and device for streamer development process in a gas medium, an electronic device and a storage medium, which can simulate the randomness of the discharge process and the time step is not limited by the CFL condition, and has higher calculation efficiency.

[0005] The simulation method for streamer development process in a gas medium provided by the present application comprises:

[0006] defining a gas component, and calculating the electron mobility required for simulation according to the gas component;

[0007] calculating the electric field distribution in the simulation region, and solving the average electron velocity of all sub-divided grids according to the electric field distribution and the electron mobility;

[0008] generating random numbers by using elastic collision probability distribution based on the average electron velocity, and taking the obtained random numbers as the electron velocity of the sub-divided grids;

[0009] According to the electron velocity, the electron position is updated by using a micro-electron migration equation, to obtain an updated electron quantity, the electron density is obtained based on the electron quantity, and a macro-ion drift equation is solved to obtain updated positive ion density and negative ion density;

[0010] The reaction rate required for the calculation simulation is calculated, according to the reaction rate, the collision reaction between different particles is calculated by using the improved stochastic dynamics analysis method, to obtain the quantity of the updated electron, positive ion and negative ion, so as to obtain the updated electron density, positive ion density and negative ion density;

[0011] The electric field distribution, the electron density, the positive ion density and the negative ion density in the simulation region are iteratively calculated until a set simulation time is reached, and the electric field distribution, the electron density, the positive ion density and the negative ion density results are outputted to analyze the streamer development process.

[0012] As a further improvement of the application, the electric field distribution is calculated by the following formula:

[0013]

[0014] In the formula, is the electric field intensity vector of the first +1 simulation step, Δ t is the time step of the streamer simulation, is the space charge density of the first simulation step, e is the dielectric constant of the gas, is the elementary charge amount, is the charge number of the first particle, is the mobility of the first particle in the first simulation step, is the density of the first i particle in the first simulation step, is the divergence operator.

[0015] As a further improvement of the application, according to the calculated electric field distribution and electron mobility, the average electron velocity of all the divided grids is solved by the following formula:

[0016]

[0017] In the formula, is the average electron velocity, E is the electric field intensity amplitude; p ( E ) is the electron mobility, which is a function of the electric field intensity amplitude.

[0018] As a further improvement of the present invention, the step of generating random numbers based on the average electron velocity using the elastic collision probability distribution, and using the resulting random numbers as the electron velocities of the mesh, includes generating random numbers that conform to a gamma distribution. Then, a random number conforming to the elastic collision probability distribution is calculated using the following formula:

[0019]

[0020] In the formula, For electron velocity, β For coefficients;

[0021] The elastic probability distribution of electron velocity is as follows:

[0022]

[0023]

[0024] In the formula, Let be the probability density function of electron velocity. Let Γ be the electron velocity and Γ be the Gamma function. This represents the average electron velocity.

[0025] As a further improvement of the present invention, the gamma distribution is Gamma(0.75,1).

[0026] As a further improvement of the present invention, the microscopic electron migration equation is as follows:

[0027]

[0028] In the formula, For the first +1 simulation step size of electronic coordinate vector, For the first An electronic coordinate vector with a simulation step size. For the first +1 simulation step size of electric field intensity vector, For the first +1 simulation step size of electric field intensity amplitude, For simulating step size, The electron velocity of the mesh;

[0029] The macroscopic ion drift equation is:

[0030]

[0031] In the formula, For the first k +1 simulation step size of ion density, For the first k Ion density at a simulated step size For the first k One ion source term with a simulation step size, For the first k +1 simulation step size of electric field intensity vector, p i The mobility of ions, For simulating step size, It is the divergence operator.

[0032] As a further improvement of the present invention, the calculation of collision responses between different particles using an improved stochastic dynamics analysis method includes:

[0033] Set the simulation time for dynamic analysis t r At time 0;

[0034] Time step for computational kinetic analysis ;

[0035] Time step based on dynamic analysis Generate binomial distributions that conform to the binomial distribution (Binomial( , random numbers ,in For the first The number of particles, Indicates the first The probability of a collision reaction occurring;

[0036] Based on random numbers Calculate the time step after one dynamic analysis. The vector formed by the number of all particles after ;

[0037] Simulation time for dynamic analysis t r Updated to t r = t r + ;

[0038] Simulation time for comparative dynamic analysis t r With the streamer simulation step size Δ t If the simulation time for dynamic analysis t r Smaller than the streamer simulation step size Δ t Repeat the simulation time for dynamic analysis. t rThe preceding step is performed at a time point other than 0; if the simulation time of the kinetic analysis t r is not less than the streamer simulation step length Δ t The iteration process is terminated, and the vector of all particle quantities finally obtained X ( t r is taken as the quantities of the updated electrons, positive ions and negative ions.

[0039] The simulation device for streamer development in a gas medium provided by the application comprises a gas component definition module, an iterative solution module and a result output module.

[0040] The gas component definition module is configured to define the gas components.

[0041] The iterative solution module is configured to iteratively calculate the electric field distribution, electron density, positive ion density and negative ion density in the simulation region according to the gas components until a set simulation time is reached.

[0042] The result output module is configured to output the electric field distribution, electron density, positive ion density and negative ion density in the simulation region after the simulation time is reached, so as to analyze the streamer development process.

[0043] The iterative solution module comprises a first calculation unit, a second calculation unit, a third calculation unit, a fourth calculation unit and a fifth calculation unit.

[0044] The first calculation unit is configured to calculate the electron mobility required for simulation according to the gas components.

[0045] The second calculation unit is configured to calculate the electric field distribution in the simulation region, and solve the average electron velocity of all the split grids according to the calculated electric field distribution and electron mobility.

[0046] The third calculation unit is configured to generate random numbers by using the elastic collision probability distribution based on the average electron velocity, and take the obtained random numbers as the electron velocities of the split grids.

[0047] The fourth calculation unit is configured to update the electron positions by using the micro-electron migration equation according to the electron velocities, obtain the updated electron quantity, obtain the electron density based on the electron quantity, and solve the macro-ion drift equation to obtain the updated positive ion density and negative ion density.

[0048] The fifth calculation unit is configured to calculate a reaction rate required for simulation, and calculate collision reactions between different particles by using an improved stochastic dynamics analysis method according to the reaction rate, so as to obtain updated numbers of electrons, positive ions and negative ions, and to obtain the updated electron density, the updated positive ion density and the updated negative ion density.

[0049] The electronic device provided by the application comprises a memory, a processor and a computer program stored in the memory, and the processor executes the computer program to realize the steps of the simulation method of the streamer development process in the gas medium.

[0050] The storage medium provided by the application stores a computer program, and the computer program is executed by a processor to realize the steps of the simulation method of the streamer development process in the gas medium.

[0051] The application provides a simulation method, device, electronic equipment and storage medium for a streamer development process in a gas medium, which randomly generates electron velocities of all divided grids by using elastic collision probability distribution, fully considers randomness of electron motion processes, and is more in line with the randomness of actual discharge. BRIEF DESCRIPTION OF DRAWINGS

[0052] Figure 1 Fig. 1 is a flowchart of the simulation method of the streamer development process in the gas medium according to an embodiment of the application.

[0053] Figure 2 Fig. 2 is a simulation geometric model diagram of example 1 in the simulation method of the streamer development process in the gas medium according to an embodiment of the application.

[0054] Figure 3 Fig. 3 is an electron density evolution diagram simulated by the simulation method of the streamer development process in the gas medium according to an embodiment of the application.

[0055] Figure 4 Fig. 4 is an electron density evolution diagram simulated by a fluid model.

[0056] Figure 5 Fig. 5 is an electron density evolution diagram simulated by the simulation method of the streamer development process in the gas medium according to an embodiment of the application.

[0057] Figure 6 Fig. 6 is an electron density evolution diagram simulated by a fluid model.

[0058] Figure 7is a structural schematic diagram of a simulation device for streamer development process in a gas medium according to an embodiment of the present application.

[0059] The reference signs are explained as follows: 1, gas component definition module; 2, iterative solution module; 21, first calculation unit; 22, second calculation unit; 23, third calculation unit; 24, fourth calculation unit; 25, fifth calculation unit; 3, result output module. DETAILED DESCRIPTION

[0060] The specific embodiments are described below with reference to the accompanying drawings and detailed description. Figures 1-7 The invention is described in detail so that those skilled in the art can more fully understand the purpose, features and effects of the invention.

[0061] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. When the terms of the invention are defined contrary to the meanings commonly understood by those skilled in the art, the definitions described in the invention shall prevail.

[0062] The invention provides a simulation method, device, electronic equipment and storage medium for streamer development process in a gas medium, considering the microscopic motion process of charged particles and the collision between particles, to solve the technical problem that the fluid model cannot simulate the randomness of the discharge process and the time step is limited by the CFL condition.

[0063] Embodiment one

[0064] As a specific embodiment of the invention, the embodiment provides a simulation method for streamer development process in a gas medium, referring to Figure 1 , the specific steps are as follows:

[0065] S100, defining the gas component, and calculating the electron mobility required for simulation according to the gas component;

[0066] S200, calculating the electric field distribution in the simulation area, and solving the average electron velocity of all dissection grids according to the electric field distribution and the electron mobility;

[0067] S300, generating random numbers using elastic collision probability distribution based on the average electron velocity, and taking the obtained random numbers as the electron velocity of the dissection grid;

[0068] S400, updating the electron position using the microscopic electron migration equation according to the electron velocity, obtaining the updated electron number, obtaining the electron density based on the electron number, and solving the macroscopic ion drift equation to obtain the updated positive ion density and negative ion density;

[0069] S500, calculate the reaction rate required for simulation, according to the reaction rate, calculate the collision reaction between different particles by using the improved stochastic dynamics analysis method, obtain the updated number of electrons, positive ions and negative ions, and obtain the updated electron density, positive ion density and negative ion density;

[0070] S600, iteratively calculate the electric field distribution, the electron density, the positive ion density and the negative ion density in the simulation region until a set simulation time is reached, output the electric field distribution, the electron density, the positive ion density and the negative ion density results, and analyze the streamer development process.

[0071] In this embodiment, the iterative solution of the electric field distribution, the electron density, the positive ion density and the negative ion density in the simulation region is performed by S200-S500 until a set simulation time is reached, and the evolution results of the electric field distribution and the particle density can be obtained, and the streamer development process can be analyzed.

[0072] The simulation method of the streamer development process in the gas medium of this embodiment randomly generates the electron velocity of all the divided grids by using the elastic collision probability distribution, fully considers the randomness of the electron motion process, and is more in line with the characteristics of the actual discharge having randomness; the micro-electron migration equation is used to describe the electron motion process, and the problem of low computational efficiency caused by the fact that the simulation time step needs to meet the CFL condition and the simulation step is extremely short is solved.

[0073] In addition, the improved stochastic dynamics analysis method is used to batch process the collision reactions between different particles, the problem of extremely large calculation amount caused by the fact that the traditional particle model processes the motion and collision reactions of charged particles one by one is solved, and the improved stochastic dynamics analysis method considers the randomness of the collision reactions and is in line with the characteristics of the actual discharge having randomness.

[0074] The development process of the streamer to be simulated in this embodiment can be described as follows: under the action of an external electric field, electrons and ions are accelerated by the electric field force and collide with neutral gas molecules in the process of movement, causing the macroscopic migration of the electrons and ions along the electric field direction. However, due to the fact that the mass of the ions is much greater than that of the electrons, the ion mobility is relatively low, and the ion mobility has a relatively small impact on the development process of the streamer. When the speed of the electrons is high enough, the electrons collide with the neutral gas molecules to cause collision ionization, generating new electrons and positive ions, so that the number of the electrons and the positive ions is doubled. This process is also referred to as an electron collision ionization reaction. In the development process of the streamer, electron attachment, electron and positive ion recombination, and positive ion and negative ion recombination also occur, which affect the densities of the electrons, the positive ions, and the negative ions. As can be seen, in the development process of the streamer, there are three important processes, i.e., electron movement, ion movement, and collision reaction, and these processes need to be considered in the simulation of the streamer. Therefore, in the simulation of this embodiment, the core particles are the electrons, the positive ions, and the negative ions, and the simulation calculation is mainly performed on the electrons, the positive ions, and the negative ions.

[0075] The discharge of the gas includes the processes of electron / ion movement and collision reaction. In this embodiment, S400 and S500 simulate the two processes respectively. S400 embodies the process of electron / ion movement. The change of the position of the electrons causes the change of the number of the electrons at different positions. S500 embodies the collision reaction. The electron collision ionization reaction causes the increase of the number of the electrons, so that the number of the electrons changes again due to the collision. Similarly, the number of the ions also changes in the processes of movement and collision.

[0076] Optionally, when the simulation region is meshed, a vertical cross meshing method, a triangular meshing method, or an adaptive density meshing method can be used. Optionally, for the vertical cross meshing method, the meshed grid of the two-dimensional simulation region is a square, and the meshed grid of the three-dimensional simulation region is a cube. The simulation method of the development process of the streamer in the gas medium of this embodiment is used to calculate the meshed grid.

[0077] Specifically, in S100, according to the types of the insulating gases mainly used by the actual power equipment, the types of the gases corresponding to the streamer simulation include air, carbon dioxide CO2, and environmentally friendly insulating gases. The environmentally friendly insulating gases can be perfluoroisobutyl cyanide C4F7N, perfluoroketone C5F 10 O. Taking air as an example, it can be considered in the streamer simulation that the air is composed of 80% of nitrogen N2 and 20% of oxygen O2.

[0078] Further, on the basis of the known gas collision cross-section data, the electron mobility is obtained by solving the Boltzmann equation according to the defined gas composition. Taking air as an example, the BOLSIG+ software can be used to calculate the electron mobility by using the Phelps collision cross-section data set.

[0079] Specifically, in S200, the formula for calculating the electric field distribution is as follows:

[0080]

[0081] In the formula, For the first +1 simulation step size of electric field intensity vector, Δ t The time step for the streamer simulation. For the first Space charge density of a simulated step size e The dielectric constant of the gas is The elementary charge, For the first The charge number of a type of particle, For the first The first type of particle The mobility of a simulation step size For the first The first type of particle Density of each simulation step size It is the divergence operator.

[0082] In this embodiment, the formula for calculating the electric field distribution is an iterative form with time step, and is solved using the finite volume method.

[0083] Furthermore, based on the calculated electric field distribution and electron mobility, the average electron velocity of all meshes is calculated using the following formula:

[0084]

[0085] In the formula, The average electron velocity, E The magnitude of the electric field intensity; p ( E ) represents electron mobility, which is a function of the electric field strength amplitude.

[0086] In the prior art, electron velocity is calculated using the following formula:

[0087]

[0088] In the formula, For electronic quality, The electric field intensity vector, The elementary charge, This is the electron velocity vector.

[0089] In this embodiment, the average electron velocity is calculated using the electric field distribution and the electron mobility, which reduces the solution time of the above-mentioned electron velocity equation and can speed up the calculation efficiency of streamer simulation.

[0090] Specifically, in S300, the elastic collision probability distribution of the electron velocity is:

[0091]

[0092]

[0093] wherein, is the probability density function of the electron velocity, is the electron velocity, β is a coefficient, and Γ is the Gamma function, is the average electron velocity.

[0094] In actual scenarios, the electron is affected by multiple factors such as electric field intensity, thermal motion, and collision process, and thus the electron velocity has a certain randomness. In order to consider the randomness of the electron velocity, the embodiment generates a random number as the electron velocity by using the elastic collision probability distribution, which is more in line with the actual motion process of the electron.

[0095] Preferably, a random number conforming to the Gamma distribution is generated , and then a random number conforming to the elastic collision probability distribution is calculated by the following formula:

[0096]

[0097] wherein, is the random number conforming to the elastic collision probability distribution, which is used as the electron velocity of the split grid. The Gamma distribution is Gamma(0.75, 1).

[0098] Since the elastic collision probability distribution of the electron velocity is a non-standard probability distribution function, it is difficult to directly generate a random number conforming thereto. Therefore, in the embodiment, based on the transformation method, a random number conforming to the Gamma distribution Gamma(0.75, 1) is first generated , and then the random number conforming to the elastic collision probability distribution is obtained by using the above formula.

[0099] In the embodiment, in order to simulate the randomness of the streamer discharge process, the elastic collision probability distribution is introduced to randomly generate the electron velocity.

[0100] Specifically, in S400, since the electron mobility is much higher than the ion mobility, the electron collision ionization is the main process of the streamer discharge, and thus the micro-electron migration equation is used to describe the electron motion process, and the macro-ion drift equation is used to describe the ion motion process.

[0101] The electron position is updated by the following micro-electron migration equation:

[0102]

[0103] In the formula, For the first +1 simulation step size of electronic coordinate vector, For the first An electronic coordinate vector with a simulation step size. For the first +1 simulation step size of electric field intensity vector, For the first +1 simulation step size of electric field intensity amplitude, For simulating step size, The random number conforming to the elastic collision probability distribution is the electron velocity of the grid.

[0104] The direction of electron velocity is set to the direction of the electric field at the mesh, thus maintaining consistency with the assumptions of the fluid model.

[0105] After determining the position coordinates of all electrons, the grid containing all electrons can be obtained, leading to the updated electron count for all meshes. Electron density and electron count are correlated; electron density is derived from electron count. Given the electron count within a given mesh, the electron count is divided by the mesh volume Δ. V That is, electron density.

[0106] Furthermore, the macroscopic ion drift equation is as follows:

[0107]

[0108] In the formula, For the first +1 simulation step size of ion density, For the first Ion density at a simulated step size For the first One ion source term with a simulation step size, For the first +1 simulation step size of electric field intensity vector, p i Δ represents the mobility of ions. t For simulating step size, It is the divergence operator.

[0109] Since the mobility of ions is much smaller than that of electrons, in this embodiment, in order to speed up the simulation, a macroscopic ion drift equation is used to describe the motion process of ions, and the ion source term is obtained by calculating the collision reaction between different particles using an improved stochastic dynamics analysis method.

[0110] Optionally, since the ion mobility is much smaller than the electron mobility, the ion mobility has little effect on the development of the flow injection, and can be set as a constant. The ion mobility in air can be set as 2 x 10 -4 m 2 (V·s) -1 .

[0111] Specifically, in S500, reaction rates required for simulation are calculated, and collision reactions between different particles are calculated by using an improved stochastic dynamics analysis method according to the reaction rates, wherein the collision reactions considered include electron collision ionization reactions, electron attachment reactions, electron and positive ion recombination reactions, and positive ion and negative ion recombination reactions.

[0112] In this embodiment, the reaction rates are calculated by using a reaction frequency method. Reaction frequencies of the electron collision ionization reactions, the electron attachment reactions, the electron and positive ion recombination reactions, and the positive ion and negative ion recombination reactions are set, and then the reaction frequencies are converted into the reaction rates.

[0113] Preferably, the reaction rate of the collision ionization reaction is calculated by the following formula: p 1

[0114]

[0115] In the formula, f is the reaction frequency of the collision ionization reaction, the unit is 1 / s, and n is the number of electrons in each grid.

[0116] The reaction rate of the electron attachment reaction is calculated by the following formula: p 2

[0117]

[0118] In the formula, f is the reaction frequency of the electron attachment reaction, the unit is 1 / s, and n is the number of electrons in each grid.

[0119] The reaction rate of the electron and positive ion recombination reaction is calculated by the following formula: p 3

[0120]

[0121] In the formula, f is the reaction frequency of the electron and positive ion recombination reaction, the unit is m / s, Δ is the volume of the divided grid, n is the number of electrons in each grid, and m is the number of positive ions in each grid. 3 V ​​​​​​​​​

[0122] Reaction rate of positive ion and negative ion recombination reaction p 4 is calculated by the following formula:

[0123]

[0124] In the formula, is the reaction frequency of positive ion and negative ion recombination reaction, unit is m 3 / s; Δ V is the volume of the split grid, is the number of positive ions in each grid, is the number of negative ions in each grid.

[0125] In the prior art, the fluid model usually uses the reaction frequency to describe the reaction intensity between particles, and the reaction rate can be converted by the reaction frequency. The increase of particles can be calculated by using the reaction rate.

[0126] In another possible embodiment, the calculation of the reaction rate of the electron impact ionization reaction and the electron attachment reaction uses the collision cross section method, and the reaction rate of the electron impact ionization reaction is calculated by the following formula:

[0127]

[0128] In the formula, is the density of background gas molecules, unit is 1 / m 3 ; s i is the collision cross section of the electron impact ionization reaction, unit is m 2 ; is the electron velocity, unit is m / s.

[0129] The reaction rate of the electron attachment reaction is calculated by the following formula:

[0130]

[0131] In the formula, is the density of background gas molecules, unit is 1 / m 3 ; s a is the collision cross section of the electron attachment reaction, unit is m 2 , is the electron velocity, unit is m / s.

[0132] If the cross section data of the gas electron impact ionization and electron attachment are known, the reaction rate of the gas electron impact ionization reaction and the electron attachment reaction can be directly calculated by using the collision cross section method.

[0133] Further, in S500, the collision reactions between different particles are calculated by using the improved stochastic dynamics analysis method, to obtain the re-updated electron, positive ion and negative ion quantities, including:

[0134] Setting the simulation time of the dynamics analysis t r to be 0;

[0135] Calculating the time step of the dynamics analysis ;

[0136] Based on the time step of the dynamics analysis , a random number conforming to the binomial distribution Binomial( , ) is generated , where is the quantity of the i-th particle, and represents the probability of occurrence of the i-th collision reaction; Based on the random number

[0137] , the vector of all particle quantities after a time step of the dynamics analysis is calculated ;

[0138] The simulation time of the dynamics analysis t r is updated to t r = t r + ;

[0139] The simulation time of the dynamics analysis t r is compared with the stream simulation step Δ t . If the simulation time of the dynamics analysis t r is less than the stream simulation step Δ t , the above steps except the first step are repeated. If the simulation time of the dynamics analysis t r is not less than the stream simulation step Δ t , the iteration process is terminated, and the finally obtained vector of all particle quantities X ( t r ) is taken as the re-updated electron, positive ion and negative ion quantities.

[0140] Preferably, the time step of the dynamics analysis is calculated by the following formula: ​

[0141]

[0142]

[0143]

[0144] wherein, is the time step of the kinetic analysis, e is the error tolerance, is the number of the i-th particle, is the vector of the number of all particles, X is the change of the number of the i-th particle caused by the j-th collision reaction, is the reaction rate of the i-th collision reaction. The stochastic kinetic analysis method needs to satisfy the condition that the number of particles is approximately constant within the time step , so the time step needs to be small enough, which can be selected by the above method. The error tolerance affects the size of the time step, the larger the error tolerance, the larger the time step obtained.

[0145] Preferably, the probability of the i-th collision reaction is calculated by the following formula:

[0146] In this embodiment, the randomness of the change of the number of particles in the collision reaction process is simulated by generating random numbers, and the binomial distribution can avoid the number of particles becoming negative in the kinetic analysis.

[0147]

[0148] The particle density and the number of particles are corresponding, the particle density is obtained by converting the number of particles, given the number of particles in a certain partition grid, the number of particles divided by the grid volume Δ is the particle density.

[0149]

[0150]

[0151] The particle density and the number of particles are corresponding, the particle density is obtained by converting the number of particles, given the number of particles in a certain partition grid, the number of particles divided by the grid volume Δ V is the particle density.

[0152] ​​​​​​The particle model in the streamer simulation model tracks the movement process of a single charged particle, and uses a Monte Carlo collision (MCC) method to simulate the collision effect between particles, but the particle model has a huge amount of calculation and a high complexity in processing the collision process, which seriously limits the development and application of the particle model. The improved random dynamics analysis method can batch process the collision reaction between different particles, solving the technical problem of huge calculation amount caused by processing the movement and collision reaction of charged particles one by one.

[0153] Finally, through iterative solving of the electric field distribution, the electron and ion movement equation and the particle collision reaction, the evolution results of the electric field distribution and the particle density with time can be obtained, and then the streamer development process is analyzed.

[0154] In addition, in the fluid model, the particles are regarded as a continuous medium, and the particle velocity and density present average characteristics in a certain area, and a large error is easily generated when the small size structure is averaged, so the fluid model is not suitable for simulation of small size structure. The movement and reaction process of the electron is processed by the particle movement method, the movement process of all the electrons is calculated one by one by using the microscopic electron migration equation, and the randomness of the electron velocity is considered by using the elastic collision probability distribution, which is suitable for streamer simulation of small size structure, solving the problem that the fluid model based on the continuous medium assumption is not suitable for simulation of small size structure. The electron is regarded as an independent individual in the embodiment, which overcomes the problem of analyzing the movement process of all the electrons one by one and overcomes the problem caused by the average characteristics of the continuous medium.

[0155] In order to more clearly embody the effect of the simulation method of the streamer development process in the gas medium of the embodiment, examples one and two are used for detailed description.

[0156] Example one

[0157] The streamer simulation is carried out by using the needle-plate electrode, as shown in Figure 2 , the size of the simulation area is 80mmx80mm, the distance between the needle electrode and the plate electrode is 40mm, and the needle electrode applies a positive polarity voltage of 100kV. The gas component is air, that is, 80% of N2 and 20% of O2, the electron mobility and reaction frequency and other parameters are calculated by using the Phelps collision cross section data set by using the BOLSIG+ software, and the reaction rate is calculated by using the reaction frequency method. The electron density distribution at different simulation times is shown in Figure 3 , and the electron density distribution obtained by using the fluid model simulation is shown in Figure 4 . It can be seen that the electric field strength near the needle electrode is the highest, the streamer starts from the needle electrode, and gradually develops to the lower part. By comparing the results of the embodiment and the fluid model, it can be seen that the streamer development lengths of the two models at different times are very close, verifying the accuracy of the streamer simulation method of the embodiment.

[0158] Example Two

[0159] The simulation of streamer development in a solid dielectric with a porous structure is carried out. The size of the simulation region is 1mmx0.5mm, the length and width of the porous solid dielectric are 1mm and 0.25mm respectively, the upper half of the model is air, and the medium in the air gap inside the porous solid dielectric is also air. The parameters such as electron mobility and reaction frequency are calculated by using the Phelps collision cross-section data set by the BOLSIG+ software, and the reaction rate is calculated by the reaction frequency method. The rod electrode has a length of 0.05mm and a diameter of 0.01mm. The boundary conditions of the rod electrode and the left boundary are set to 15kV potential, the right boundary condition is set to ground, and the upper and lower boundary conditions are set to Neumann boundary conditions. The electron density distribution at different simulation times obtained by simulation is shown in Figure 5 , and the electron density distribution obtained by fluid model simulation is shown in Figure 6 . It can be seen that the streamer development processes obtained by the two simulation models are basically consistent, that is, the streamers are all initiated from the inside of the pores and gradually merge with the external streamers to cause breakdown. The simulation of this embodiment takes about 35 minutes, and the simulation of the fluid model takes about 1 hour and 45 minutes, so the streamer simulation method of this embodiment has higher calculation efficiency. Because the size of the pore structure is small and the size of the split grid is small, the simulation time step used by the fluid model needs to satisfy the CFL condition, so the simulation time step is very small, which significantly increases the simulation time; while the simulation of this embodiment is not limited by the CFL condition, the simulation time step is still large, and the simulation efficiency is high.

[0160] Example Two

[0161] As another specific embodiment of the present application, this embodiment provides a simulation device for the development process of a streamer in a gas medium, which refers to Figure 7 , comprising a gas component definition module 1, an iterative solution module 2, and a result output module 3.

[0162] The gas component definition module 1 is used to define the gas components.

[0163] The iterative solution module 2 is used to iteratively calculate the electric field distribution, electron density, positive ion density and negative ion density in the simulation region according to the gas components until a set simulation time is reached.

[0164] The result output module 3 is used to output the electric field distribution, electron density, positive ion density and negative ion density in the simulation region after the simulation time is reached, so as to analyze the development process of the streamer.

[0165] The iteration solving module 2 comprises a first calculation unit 21, a second calculation unit 22, a third calculation unit 23, a fourth calculation unit 24 and a fifth calculation unit 25.

[0166] The first calculation unit 21 is configured to calculate the electron mobility required for simulation according to the gas component.

[0167] The second calculation unit 22 is configured to calculate the electric field distribution in the simulation region, and solve the average electron velocity of all the divided grids according to the calculated electric field distribution and the electron mobility.

[0168] The third calculation unit 23 is configured to generate random numbers based on the average electron velocity and the elastic collision probability distribution, and take the random numbers as the electron velocity of the divided grids.

[0169] The fourth calculation unit 24 is configured to update the electron position according to the electron velocity and the microscopic electron migration equation, obtain the updated electron quantity, obtain the electron density based on the electron quantity, and solve the macroscopic ion drift equation to obtain the updated positive ion density and negative ion density.

[0170] The fifth calculation unit 25 is configured to calculate the reaction rate required for simulation, calculate the collision reaction between different particles according to the reaction rate and the improved stochastic kinetic analysis method, obtain the updated electron quantity, positive ion quantity and negative ion quantity, and obtain the updated electron density, positive ion density and negative ion density.

[0171] Embodiment Three

[0172] As another specific embodiment of the present application, the embodiment provides an electronic device comprising a memory, a processor and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the simulation method for the streamer development process in a gas medium according to Embodiment One.

[0173] S100, defining the gas component, and calculating the electron mobility required for simulation according to the gas component;

[0174] S200, calculating the electric field distribution in the simulation region, and solving the average electron velocity of all the divided grids according to the electric field distribution and the electron mobility.

[0175] S300, generating random numbers based on the average electron velocity and the elastic collision probability distribution, and taking the random numbers as the electron velocity of the divided grids.

[0176] S400, updating the electron position according to the electron velocity by using a micro electron migration equation to obtain an updated electron number, obtaining the electron density based on the electron number, and solving a macro ion drift equation to obtain updated positive ion density and negative ion density;

[0177] S500, calculating a reaction rate required for simulation, calculating collision reactions between different particles according to the reaction rate by using an improved stochastic kinetics analysis method to obtain again updated electron number, positive ion number and negative ion number, so as to obtain again updated electron density, positive ion density and negative ion density;

[0178] S600, iteratively calculating the electric field distribution, the electron density, the positive ion density and the negative ion density in the simulation region until a set simulation time is reached, and outputting the electric field distribution, the electron density, the positive ion density and the negative ion density results to analyze the streamer development process.

[0179] Embodiment four

[0180] As another specific embodiment of the present application, the embodiment provides a storage medium having a computer program stored thereon, the computer program being executed by a processor to implement the steps of the simulation method of the streamer development process in a gas medium according to the embodiment one:

[0181] S100, defining a gas component, and calculating an electron mobility required for simulation according to the gas component;

[0182] S200, calculating an electric field distribution in a simulation region, and solving an average electron velocity of all dissection grids according to the electric field distribution and the electron mobility;

[0183] S300, generating a random number by using an elastic collision probability distribution based on the average electron velocity, and taking the obtained random number as an electron velocity of a dissection grid;

[0184] S400, updating the electron position according to the electron velocity by using a micro electron migration equation to obtain an updated electron number, obtaining the electron density based on the electron number, and solving a macro ion drift equation to obtain updated positive ion density and negative ion density;

[0185] S500, calculating a reaction rate required for simulation, calculating collision reactions between different particles according to the reaction rate by using an improved stochastic kinetics analysis method to obtain again updated electron number, positive ion number and negative ion number, so as to obtain again updated electron density, positive ion density and negative ion density;

[0186] S600, iteratively calculating the electric field distribution, the electron density, the positive ion density and the negative ion density in the simulation region until a set simulation time is reached, outputting the electric field distribution, electron density, positive ion density and negative ion density results to analyze the streamer development process.

[0187] The above description is only the preferred embodiment of the present application, not any other form of the application is limited, and any modification or equivalent change according to the technical essence of the present application still belongs to the scope of the present application.

Claims

1. A method of simulating the development of streamers in a gas medium, characterized by, The method comprises: defining a gas component, and calculating an electron mobility required for simulation according to the gas component; calculating an electric field distribution in a simulation region, solving an average electron velocity of all dissection grids according to the electric field distribution and the electron mobility; generating random numbers by using an elastic collision probability distribution based on the average electron velocity, and taking the obtained random numbers as electron velocities of the dissection grids; updating electron positions by using a micro electron migration equation according to the electron velocities, obtaining updated electron quantities, obtaining electron densities based on the electron quantities, and solving a macro ion drift equation to obtain updated positive ion densities and negative ion densities; calculating reaction rates required for simulation, calculating collision reactions between different particles by using an improved stochastic kinetic analysis method according to the reaction rates, obtaining again updated electron quantities, positive ion quantities and negative ion quantities, so as to obtain again updated electron densities, positive ion densities and negative ion densities; iteratively calculating the electric field distribution, the electron densities, the positive ion densities and the negative ion densities in the simulation region until a set simulation time is reached, and outputting electric field distribution, electron density, positive ion density and negative ion density results to analyze a streamer development process; wherein, the micro electron migration equation is: wherein is the electron coordinate vector at the +1 simulation step, is the electron coordinate vector at the +1 simulation step, is the electron coordinate vector at the +1 simulation step, is the electric field intensity vector at the +1 simulation step, is the electric field intensity amplitude at the +1 simulation step, is the electron velocity of the discretized grid; the macro ion drift equation is: wherein is the ion density at the +1 simulation step, is the ion density at the simulation step, is the ion source term at the simulation step, is the electric field strength vector at the +1 simulation step, μ i is the mobility of the ions, Δ t is the simulation step, is the divergence operator; the collision reactions between different particles are calculated by using the improved stochastic kinetic analysis method, which comprises: Setting the simulation time for the kinetic analysis t r is the time instant 0. Time step for computational dynamics analysis ; Time step based on dynamic analysis Generate binomial distributions that conform to the binomial distribution (Binomial( , random numbers ,in For the first The number of particles, Indicates the first The probability of a collision reaction occurring; Based on random numbers , calculate the number of all particles after a time step of a kinetic analysis constituted by a vector ; Simulated time for the kinetic analysis t r Updated to t r = t r + ; simulation time of the kinetic analysis t r and the streamer simulation step size Δ t , if the simulation time of the kinetic analysis t r is smaller than the streamer simulation step size Δ t , the simulation time of the kinetic analysis t r is repeated for the aforementioned step for a time other than 0; if the simulation time of the kinetic analysis t r is not smaller than the streamer simulation step size Δ t , the iteration process is terminated, and the vector X ( t r ) of the final number of all particles is taken as the number of electrons, positive ions, and negative ions after the renewed update.

2. The method for simulation of streamer development in a gas medium according to claim 1, characterized in that, the electric field distribution is calculated by: wherein is the electric field intensity vector at the nth simulation step, +1 is the electric field intensity vector at the (n+1)th simulation step, t is the time step of the streamer simulation, is the electric field intensity vector at the nth simulation step, is the space charge density at the nth simulation step, ε is the dielectric constant of the gas, is the elementary charge, is the number of charges of the nth species of particles, is the number of charges of the nth species of particles, is the mobility of the nth species of particles at the nth simulation step, is the density of the nth species of particles at the nth simulation step, is the density of the nth species of particles at the nth simulation step, is the density of the nth species of particles at the nth simulation step, is the density of the nth species of particles at the nth simulation step, is the density of the nth species of particles at the nth simulation step, is the divergence operator.

3. The method of simulating the development of streamers in a gas medium according to claim 2, characterized in that, the average electron velocity of all dissection grids is solved according to the electric field distribution and the electron mobility by: In the formula, The average electron velocity, E The magnitude of the electric field intensity; μ ( E ) represents electron mobility, which is a function of the electric field strength amplitude.

4. The method for simulation of streamer development in a gas medium according to claim 1, characterized in that, The generating, based on the average electron speed, of a random number using an elastic collision probability distribution, and the including of the resulting random number as an electron speed of the dissected grid includes generating a random number that conforms to a gamma distribution and thereafter calculating a random number that conforms to an elastic collision probability distribution by the following equation: wherein is the electron velocity, β is the coefficient; wherein, the elastic probability distribution of the electron velocity is: wherein is the probability density function of the electron velocity, is the electron velocity, and Γ is the Gamma function, is the average electron velocity.

5. The method of simulating the development of a streamer in a gas medium according to claim 4, characterized in that, the gamma distribution is Gamma(0.75, 1).

6. A device for simulating the development of streamers in a gas medium, characterized in that The device comprises a gas component definition module (1), an iterative solving module (2) and a result output module (3); the gas component definition module (1) is used for defining a gas component; the iterative solving module (2) is used for iteratively calculating an electric field distribution, electron densities, positive ion densities and negative ion densities in a simulation region according to the gas component until a set simulation time is reached; the result output module (3) is used for outputting the electric field distribution, the electron densities, the positive ion densities and the negative ion densities in the simulation region after the simulation time is reached to analyze a streamer development process; wherein, the iterative solving module (2) comprises a first calculation unit (21), a second calculation unit (22), a third calculation unit (23), a fourth calculation unit (24) and a fifth calculation unit (25); the first calculation unit (21) is used for calculating an electron mobility required for simulation according to the gas component; the second calculation unit (22) is used for calculating an electric field distribution in a simulation region, and solving an average electron velocity of all dissection grids according to the calculated electric field distribution and the electron mobility; the third calculation unit (23) is used for generating random numbers by using an elastic collision probability distribution based on the average electron velocity, and taking the obtained random numbers as electron velocities of the dissection grids; The fourth calculation unit (24) is configured to update the electron position according to the electronic velocity by using a micro-electron migration equation, to obtain an updated electron number, to obtain an electron density based on the electron number, and to solve a macro-ion drift equation to obtain updated positive ion density and negative ion density; The fifth calculation unit (25) is configured to calculate a reaction rate required for simulation, to calculate collision reactions between different particles by using an improved stochastic kinetics analysis method according to the reaction rate, to obtain again updated electron number, positive ion number and negative ion number, and to obtain again updated electron density, positive ion density and negative ion density; wherein, The micro-electron migration equation is: In the formula, For the first +1 simulation step size of electronic coordinate vector, For the first An electronic coordinate vector with a simulation step size. For the first +1 simulation step size of electric field intensity vector, For the first +1 simulation step size of electric field intensity amplitude, For simulating step size, The electron velocity of the mesh; The macro-ion drift equation is: wherein is the ion density at the +1 simulation step, is the ion density at the simulation step, is the ion source term at the simulation step, is the electric field strength vector at the +1 simulation step, μ i is the mobility of the ions, Δ t is the simulation step, is the divergence operator; The collision reactions between different particles calculated by using the improved stochastic kinetics analysis method include: Setting the simulation time for the kinetic analysis t r is 0 for time 0; Time step for computational dynamics analysis ; Time step based on kinetic analysis , generating random numbers that conform to a binomial distribution Binomial , ) of order n , where is the number of particles of the first type, denotes the probability of occurrence of a collision reaction of the first type; Based on random numbers , calculate the number of all particles after a time step of a kinetic analysis constitute a vector ; Simulate time for dynamics analysis t r Update to t r = t r + ; simulation time of the kinetic analysis t r with the streamer simulation step size Δ t , if the simulation time of the kinetic analysis t r is smaller than the streamer simulation step size Δ t , the simulation time of the kinetic analysis t r is set to zero and the aforementioned steps are repeated for a time of 0; if the simulation time of the kinetic analysis t r is not smaller than the streamer simulation step size Δ t , the iteration process is terminated and the vector of the final number of particles X ( t r ) is taken as the number of electrons, positive ions, negative ions, respectively, after the renewed update.

7. An electronic device comprising a memory, a processor, and a computer program stored on the memory, wherein the computer program comprises instructions that, when executed by the processor, cause the electronic device to perform the method of any one of claims 1-6. The processor executes the computer program to implement the steps of the method in any one of claims 1-5.

8. A storage medium having stored thereon a computer program, characterized in that The computer program is executed by the processor to implement the steps of the method in any one of claims 1-5.

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