Method and System for Obtaining Parameters of High-Current Vacuum Arc under Low-Frequency Current Conditions

Abstract

The present invention discloses a method and a system for obtaining large-current vacuum arc parameters under low-frequency current conditions, belonging to the technical field of vacuum switch process simulation. A three-dimensional model is established for the vacuum interrupter, and the magnetohydrodynamics theory is used to simulate the vacuum arc plasma, thereby establishing a three-dimensional magnetohydrodynamic model of the vacuum arc plasma. During the process of solving the large-current vacuum arc parameters in the model, since the ion parameters, electromagnetic field parameters, and electron parameters are interdependent, based on the degree of dependence between the parameters, the ion parameters and electromagnetic field parameters are calculated first, and then the electron parameters are calculated, which greatly improves the convergence of the calculation. At the same time, the present invention introduces electric potential and vector magnetic potential to solve the electromagnetic field parameters, reduces differential operations, lowers the calculation complexity, and has a relatively high calculation efficiency.

Description

Technical Field

[0001] The present invention belongs to the technical field of vacuum switch process simulation, and more specifically, relates to a method and system for obtaining large current vacuum arc parameters under low frequency current conditions. Background Art

[0002] The performance of a switch depends to a large extent on its insulating medium. Vacuum switches use vacuum as the insulating medium, which has advantages such as a fast dielectric recovery speed, a large current-carrying capacity, high voltage resistance, and environmental friendliness. In the field of power systems, replacing SF6 switchgear with environmentally friendly switches is an important research direction. Many domestic and foreign units have developed medium and high voltage vacuum circuit breakers and put them into operation on the grid. At the same time, taking advantage of the large current-carrying capacity and fast dielectric recovery speed of the vacuum gap, vacuum trigger switches also undertake the task of high-power fast closing in the field of pulsed power technology.

[0003] Taking a common vacuum interrupter as an example, during the process of interrupting current, a huge electric field is formed in the vacuum gap inside the vacuum interrupter. Due to the fine peaks on the surface of the electrode contacts, the current will contract to several contact points of the just-separated contacts, and the temperature at these points will rise rapidly and cause metal evaporation. As the electrode contacts separate, more intense field emission and gap breakdown phenomena will occur to form a vacuum arc. When the arc current is too large, serious metal material evaporation and deposition will occur on the electrode surface, which will in turn lead to a decrease in the insulation performance of the vacuum switch. Therefore, the vacuum arc characteristics are the key factors affecting the performance of the vacuum switch. Since the inside of the vacuum switch is in a fully enclosed state, how to obtain the large current vacuum arc parameters in the vacuum interrupter to study the performance of the vacuum switch has become a technical problem to be solved urgently.

[0004] Currently, some researchers have established a relatively complete magnetohydrodynamic model of vacuum arc under low frequency current conditions. Among them, the fluid equations consider the mass conservation, momentum conservation, energy conservation of ions and the energy conservation of electrons, and the electromagnetic field is solved through the generalized Ohm's law and Maxwell's equations. The final form of the vacuum arc is determined self-consistently by the fluid equations and the electromagnetic field equations. However, in the above scheme, the magnetohydrodynamic model of the vacuum arc plasma needs to implicitly solve a complex magnetic transport equation, and the model involves multi-physical field coupling calculations such as the flow field - temperature field - electromagnetic field. The relationships between variables are complex, the coupling degree is high, and a large number of differential operations are involved. The nonlinear degree of the control equations is high. Even using mature finite element analysis software, it is difficult to obtain a convergent solution of the parameters of the large current vacuum arc under steady state conditions. Summary of the Invention

[0005] In view of the above defects or improvement requirements of the prior art, the present invention provides a method and system for obtaining large-current vacuum arc parameters under low-frequency current conditions, so as to solve the technical problem in the prior art that it is difficult to obtain the large-current vacuum arc parameters during the breaking process of a vacuum interrupter under low-frequency current conditions due to the complex relationship between variables, high coupling degree, and high non-linearity of the control equations.

[0006] To achieve the above object, in a first aspect, the present invention provides a method for obtaining large-current vacuum arc parameters under low-frequency current conditions, including the following steps:

[0007] S1. Perform three-dimensional mesh division on the arcing region of the vacuum interrupter to establish a three-dimensional magnetohydrodynamic model of the vacuum arc plasma; wherein, the three-dimensional magnetohydrodynamic model includes the fluid equation and electromagnetic equation of the vacuum arc plasma; the fluid equation includes the ion mass equation, ion momentum equation, ion energy equation, and electron energy equation; the electromagnetic equation includes the electric potential equation and vector magnetic potential equation;

[0008] S2. Initialize the large-current vacuum arc parameters in the three-dimensional magnetohydrodynamic model; wherein, the large-current vacuum arc parameters include: ion number density, ion temperature, ion velocity, electron number density, electron temperature, electron velocity, and the vector magnetic potential and electric potential of the arcing region;

[0009] S3. Calculate the current value of the electric field strength based on the current value of the electric potential; calculate the current value of the magnetic field strength based on the current value of the vector magnetic potential; calculate the current value of the current density based on the current values of the electric field strength, magnetic field strength, and electron velocity; calculate the current value of the ion viscosity coefficient based on the current value of the ion temperature; calculate the current value of the ion heat transfer coefficient based on the current values of the ion temperature, electron temperature, and electron number density; substitute the current values of the ion number density, ion temperature, ion velocity, current density, magnetic field strength, ion viscosity coefficient, and ion heat transfer coefficient into the ion mass equation, ion momentum equation, and ion energy equation for simultaneous solution to update the ion number density, ion temperature, and ion velocity;

[0010] S4. Update the electron number density based on the current value of the ion number density; update the electron velocity based on the current values of the ion velocity and current density;

[0011] S5. Substitute the current values of the electron number density, electron temperature, electron velocity, magnetic field strength, and current density into the electric potential equation and vector magnetic potential equation for simultaneous solution to obtain the current values of the electric potential and vector magnetic potential of the arcing region;

[0012] S6. Repeat steps S3 - S5 for iteration until the residual value of the large-current vacuum arc parameters in two adjacent iterations is less than the first preset threshold;

[0013] S7. Calculate the current value of the electron heat transfer coefficient based on the current values of the electron number density and the electron temperature; substitute the current values of the electron number density, the electron velocity, the ion temperature, the current density, and the electron heat transfer coefficient into the electron energy equation for solution to update the electron temperature;

[0014] S8. Repeat steps S3 - S7 for iteration until the residual value of the high - current vacuum arc parameters in two adjacent iterations is less than the second preset threshold, and the high - current vacuum arc parameters at this time are the required parameter values.

[0015] Further preferably, transform the above - mentioned electron energy equation into the form of a fluid convection - diffusion equation, specifically:

[0016]

[0017] where, T e is the electron temperature; k is the Boltzmann constant; n e is the electron number density; U e is the electron velocity vector; e is the elementary charge; J is the current density vector; λ e is the electron heat transfer coefficient; J x 、J y 、J z respectively represent the components of the current density in the x, y, and z directions; σ is the plasma conductivity; m e is the mass of a single electron; m i is the mass of a single ion; v ei is the ion - electron collision frequency; T i is the ion temperature.

[0018] Further preferably, the boundary conditions of the above - mentioned electron energy equation include: electron cathode boundary condition, electron anode boundary condition, and electron edge boundary condition;

[0019] The electron cathode boundary condition is: T e_in = T e0 ;

[0020] The electron anode boundary condition is:

[0021] The electron edge boundary condition is:

[0022] where, T e_in and T e0 are the inlet electron temperature and the initial electron temperature respectively; λ e is the electron heat transfer coefficient; T e is the electron temperature; n e is the electron number density; Uez is the z - component of the electron velocity; k is the Boltzmann constant; T e is the electron temperature; n is the normal direction of the boundary where the vacuum arc is located.

[0023] Further preferably, the above - mentioned electric potential equation is:

[0024]

[0025] The above - mentioned vector magnetic potential equation is:

[0026]

[0027]

[0028]

[0029] where, is the electric potential; U e is the electron velocity vector; B is the magnetic field strength; n e is the electron number density; e is the elementary charge; P e is the electron pressure; T e is the electron temperature; A x 、A y 、A z respectively represent the components of the vector magnetic potential in the x, y, and z directions; μ0 is the vacuum permeability; J x 、J y 、J z respectively represent the components of the current density in the x, y, and z directions.

[0030] Further preferably, the boundary conditions of the electric potential equation include: the electric potential cathode boundary condition, the electric potential anode boundary condition, and the electric potential edge boundary condition;

[0031] The electric potential cathode boundary condition is:

[0032] The electric potential anode boundary condition is:

[0033] The electric potential edge boundary condition is:

[0034] where, is the electric potential; c is a preset constant; n is the normal direction of the boundary where the vacuum arc is located.

[0035] Further preferably, the boundary conditions of the vector magnetic potential equation include: the vector magnetic potential cathode boundary condition, the vector magnetic potential anode boundary condition, and the vector magnetic potential edge boundary condition;

[0036] The vector magnetic potential cathode boundary condition is: A x= 0; A y = 0;

[0037] The boundary condition of the vector magnetic potential at the anode is:

[0038] The boundary condition of the vector magnetic potential at the edge is:

[0039] Where, A x , A y , A z respectively represent the components of the vector magnetic potential in the x, y, and z directions; n is the normal direction of the boundary where the vacuum arc is located; μ0 is the vacuum permeability; J z respectively represent the components of the current density in the z direction; r represents the distance from the calculation point to the electrode axis.

[0040] Further preferably, the above ion mass equation is:

[0041]

[0042] The above ion momentum equation is:

[0043]

[0044]

[0045]

[0046] The above ion energy equation is:

[0047]

[0048] Where, m i is the mass of a single ion; n i is the ion number density; U ix , U iy , U iz respectively represent the components of the ion velocity in the x, y, and z directions; P i is the ion pressure; τ xx , τ yy , τ zz represent the normal stress caused by ion viscosity; τ xy , τ xz , τ yx , τ yz , τ zx , τ zy represent the shear stress caused by ion viscosity; F x , F y , F z respectively represent the components of the body force acting on the ions in the x, y, and z directions; Ui is the expression form of the ion velocity vector; k is the Boltzmann constant; T i is the ion temperature; λ i is the ion heat transfer coefficient; Q i is the internal heat source of the ions.

[0049] In a second aspect, the present invention provides a system for obtaining parameters of a high-current vacuum arc under low-frequency current conditions, including: a memory and a processor, where the memory stores a computer program, and when the processor executes the computer program, it executes the method for obtaining parameters of a high-current vacuum arc under low-frequency current conditions provided in the first aspect of the present invention.

[0050] In a third aspect, the present invention further provides a computer-readable storage medium, where the computer-readable storage medium includes a stored computer program, and when the computer program is run by a processor, it controls the device where the storage medium is located to execute the method for obtaining parameters of a high-current vacuum arc under low-frequency current conditions provided in the first aspect of the present invention.

[0051] Generally speaking, through the above technical solutions conceived by the present invention, the following beneficial effects can be achieved:

[0052] 1. The present invention provides a method for obtaining parameters of a high-current vacuum arc under low-frequency current conditions. A three-dimensional model is established for the vacuum interrupter, and the magnetohydrodynamic theory is used to simulate the vacuum arc plasma, establishing a three-dimensional magnetohydrodynamic model of the vacuum arc plasma; in the process of solving the high-current vacuum arc parameters in the model, since the ion parameters, electromagnetic field parameters, and electron parameters are interdependent, and the change degree of the electron parameters is relatively small compared with other parameters, the present invention first calculates the ion parameters and electromagnetic field parameters, and then calculates the electron parameters, greatly improving the convergence of the calculation; at the same time, the present invention introduces the electric potential equation and the vector magnetic potential equation to solve the electromagnetic field parameters, reducing the differential operation and lowering the calculation complexity, with a relatively high calculation efficiency.

[0053] 2. The method for obtaining parameters of a high-current vacuum arc under low-frequency current conditions provided by the present invention comprehensively considers the variation laws of each physical field and the dependence relationship between variables, ensures that each parameter starts to be calculated under reasonable initial conditions, and finally realizes the coupled solution of all physical fields, and can effectively obtain the characteristics of each physical parameter of the vacuum arc under low-frequency current conditions, which is of great significance for revealing the mechanism of the vacuum switch breaking process and optimizing the design of the vacuum switch. Description of the Drawings

[0054] Figure 1 is the flowchart of the method for obtaining parameters of a high-current vacuum arc under low-frequency current conditions provided in Embodiment 1 of the present invention;

[0055] Figure 2 Schematic diagram of a three-dimensional simulation model of the vacuum arc arcing region in the vacuum interrupter provided in Embodiment 1 of the present invention;

[0056] Figure 3 Relationship diagram between various physical fields provided in Embodiment 1 of the present invention. Specific embodiments

[0057] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0058] Embodiment 1

[0059] A method for obtaining large-current vacuum arc parameters under low-frequency current conditions is used to solve the large-current vacuum arc parameters generated during the switching process of a vacuum interrupter under low-frequency current conditions. Since the average relaxation time of the vacuum arc plasma driven by low-frequency current (including direct current and power frequency current) is much smaller than the time for the plasma to pass through the electrode gap, the vacuum arc plasma has enough time to return to its equilibrium state under low-frequency current conditions. Therefore, a steady-state mathematical model can be used to model the vacuum arc plasma parameters. Based on this, the method for obtaining large-current vacuum arc parameters under low-frequency current conditions provided by the present invention, as Figure 1 shown, specifically includes the following steps:

[0060] S1. Perform three-dimensional grid meshing based on the arcing region of the vacuum interrupter to establish a three-dimensional magnetohydrodynamic model of the vacuum arc plasma; wherein, the three-dimensional magnetohydrodynamic model includes the fluid equation and electromagnetic equation of the vacuum arc plasma; the fluid equation includes the ion mass equation, ion momentum equation, ion energy equation, and electron energy equation; the electromagnetic equation includes the electric potential equation and vector magnetic potential equation;

[0061] Specifically, in this embodiment, three-dimensional grid meshing is performed on the vacuum arc arcing region according to the structural parameters of the vacuum interrupter, and a three-dimensional simulation model is established in the Cartesian coordinate system, and then a three-dimensional magnetohydrodynamic model of the vacuum arc plasma is established. During the process of establishing the three-dimensional simulation model, considering the computational complexity, the electrode contact structure can be simplified, and the grooves on the electrode surface in the vacuum interrupter can be ignored; specifically, as Figure 2The figure shows a schematic diagram of a three-dimensional simulation model of the vacuum arc burning region in a vacuum interrupter. Among them, 1 is the anode boundary of the vacuum arc burning region, 2 is the edge boundary of the vacuum arc burning region, 3 is the cathode boundary of the vacuum arc burning region, and 4 is the arc burning region. An xyz coordinate system is established with the center of the cathode boundary of the vacuum arc burning region as the origin. The plane where the cathode boundary of the vacuum arc burning region is located is on the xoy plane, the plane where the anode boundary is located is parallel to the plane where the cathode boundary is located, and its center point is on the positive direction of the z-axis. Further, the parameters of a typical three-dimensional simulation model of the vacuum arc burning region are shown in Table 1;

[0062] Table 1

[0063] Electrode material Electrode diameter Electrode spacing Copper 50 mm 10 mm

[0064] It should be noted that since the mass of a single electron is about 9.11×10 -31 kg, which can be ignored compared with the mass of a single copper ion (1.06×10 -25 kg), the three-dimensional magnetohydrodynamic model of the vacuum arc plasma only includes the ion mass equation, the ion momentum equation, the ion energy equation, and the electron energy equation.

[0065] S2. Initialize the parameters of the high-current vacuum arc in the three-dimensional magnetohydrodynamic model; among them, the high-current vacuum arc parameters include: ion number density, ion temperature, ion velocity, electron number density, electron temperature, electron velocity, and the vector magnetic potential and electric potential of the arc burning region;

[0066] Specifically, setting the initial values of the high-current vacuum arc parameters helps the simulation model approach the convergence solution faster. Specifically, it can be set according to the measured values of the vacuum arc, and the parameters lacking experimental data support can be set according to simulation experience; specifically, some initial values of the parameters of a typical 10kA vacuum arc corresponding to Table 1 are shown in Table 2;

[0067] Table 2

[0068] Ion velocity Electron velocity Ion temperature Electron temperature 1000 m / s 10000 m / s 10 eV 2 eV

[0069] S3. Calculate the current value of the electric field strength based on the current value of the electric potential; calculate the current value of the magnetic field strength based on the current value of the vector magnetic potential; calculate the current value of the current density based on the current values of the electric field strength, magnetic field strength, and electron velocity; calculate the current value of the ion viscosity coefficient based on the current value of the ion temperature; calculate the current value of the ion heat transfer coefficient based on the current values of the ion temperature, electron temperature, and electron number density; substitute the current values of the ion number density, ion temperature, ion velocity, current density, magnetic field strength, ion viscosity coefficient, and ion heat transfer coefficient into the ion mass equation, ion momentum equation, and ion energy equation for simultaneous solution to update the ion number density, ion temperature, and ion velocity;

[0070] Specifically, based on the electric potential distribution, the electric field strength distribution is obtained as follows: In the formula: E x 、E y 、E z respectively represent the components of the electric field strength in the x, y, and z directions, with the unit of V / m; is the electric potential, with the unit of V;

[0071] Based on the vector magnetic potential distribution, the magnetic field strength distribution is obtained as follows: In the formula: B x 、B y 、B z respectively represent the components of the magnetic field strength in the x, y, and z directions, with the unit of T; A x 、A y 、A z respectively represent the components of the vector magnetic potential in the x, y, and z directions, with the unit of T / m;

[0072] Based on variables such as the electric field strength, magnetic field strength, and electron velocity, the current density is calculated according to the generalized Ohm's law of plasma as:

[0073]

[0074]

[0075]

[0076] Among them, J x 、J y 、J z respectively represent the components of the current density in the x, y, and z directions of the Cartesian coordinate system, with the unit of A / m 2 ; σ is the plasma conductivity, and the specific expression is with the unit of S / m; U ex 、U ey 、Uez They are the three components of the electron velocity in the x, y, and z directions, with the unit of m / s; e is the elementary charge, and its value is 1.6×10 -19 C; n e represents the electron number density, with the unit of number / m 3 ; P e is the electron pressure, with the unit of Pa; k is the Boltzmann constant, and its value is 1.38×10 -23 J / K; T e represents the electron temperature, with the unit of K;

[0077] The ion viscosity coefficient is calculated based on the ion temperature:

[0078]

[0079] where μ i is the ion viscosity coefficient, with the unit of kg / (m s); ε0 is the vacuum permittivity, and its value is 8.85×10 - 12 F / m; z i is the average ion charge number, with a value of 1.8; lnΛ is the Coulomb logarithm, with a value of 15.93; m i is the mass of a single ion, with the unit of kg; T i represents the ion temperature, with the unit of K;

[0080] In the process of calculating the current value of the ion heat transfer coefficient, the current value of the ion-electron collision frequency can be first calculated based on the current value of the electron temperature, and then the current value of the ion heat transfer coefficient can be calculated based on the current values of the ion temperature, electron temperature, electron number density, and ion-electron collision frequency. Specifically, the ion heat transfer coefficient is calculated based on the ion temperature, electron temperature, and electron number density:

[0081]

[0082] where λ i represents the ion heat transfer coefficient, with the unit of W / (m K); m e is the mass of a single electron, with the unit of kg; v ei is the ion-electron collision frequency, and the calculation formula is:

[0083]

[0084] In the formula: v ei is the ion-electron collision frequency.

[0085] The above ion mass equation is:

[0086]

[0087] The above ion momentum equation is as follows:

[0088]

[0089]

[0090]

[0091] The above ion energy equation is as follows:

[0092]

[0093] Among them, m i is the ion number density, with the unit of kg; n i is the ion number density; U i is the expression form of the ion velocity vector; k is the Boltzmann constant, with a value of 1.38×10 -23 J / K; T i is the ion temperature; U ix 、U iy 、U iz respectively represent the components of the ion velocity in the x, y, and z directions; P i is the ion pressure; τ xx 、τ yy 、τ zz represent the normal stress caused by ion viscosity; τ xy 、τ xz 、τ yx 、τ yz 、τ zx 、τ zy represent the shear stress caused by ion viscosity; F x 、F y 、F z respectively represent the components of the volume force acting on the ions in the x, y, and z directions, with the unit of N / m 3 ; λ i is the ion heat transfer coefficient; Q i is the internal heat source of the ion energy equation, with the unit of W / m 3 .

[0094] Among them, the expressions of the normal stress and shear stress are as follows:

[0095]

[0096]

[0097]

[0098]

[0099]

[0100]

[0101] The body force acting on the ions is the electromagnetic force, and its expression is:

[0102] F x = J y B z - J z B y ;

[0103] F y = J z B x - J x B z ;

[0104] F z = J x B y - J y B x ;

[0105] The expression of the internal heat source of the ion energy equation is:

[0106]

[0107] Specifically, multi-physics simulation software such as ANSYS and Comsol can be used to numerically solve the ion mass equation, ion momentum equation, and ion energy equation to update the ion number density, ion temperature, and ion velocity;

[0108] Solving the ion mass equation, ion momentum equation, and ion energy equation requires ion cathode boundary conditions, ion anode boundary conditions, and ion edge boundary conditions;

[0109] Ion cathode boundary conditions:

[0110] The cathode is the inlet of the plasma, and the inlet parameters include the inlet ion temperature, inlet ion velocity, and inlet electron velocity; the above inlet parameter values all adopt their corresponding initial values, that is, satisfying:

[0111] T i_in = T i0 ;

[0112] U i_in = U i0 ;

[0113] U e_in = U e0 ;

[0114] In the formula, T i_in and T i0are the inlet ion temperature and the initial ion temperature, with the unit of K; U i_in and U i0 are the inlet ion velocity and the initial ion velocity, with the unit of m / s; U e_in and U e0 are the inlet electron velocity and the initial electron velocity, with the unit of m / s;

[0115] Assume that the current at the cathode inlet is evenly distributed on the electrode surface and the charged particles enter the arc combustion area vertically. Then, the inlet current density has only an axial component, and its magnitude is determined according to the actual simulated current magnitude and the electrode size conditions:

[0116]

[0117] In the formula, J in represents the inlet current density, with the unit of A / m 2 ; I is the magnitude of the vacuum arc current, with the unit of A; S is the cathode surface area, with the unit of m 2 ;

[0118] Since the inlet ion velocity is much smaller than the electron velocity, it can be assumed that the inlet current density is all formed by electron motion. Therefore, the inlet electron number density can be obtained from the inlet current density:

[0119]

[0120] In the formula: n e_in is the inlet electron number density, with the unit of number / m 3 ;

[0121] Based on the plasma neutrality assumption, the initial ion number density can be obtained:

[0122]

[0123] In the formula: n i_in is the inlet ion number density, with the unit of number / m 3 ;

[0124] Based on the ideal gas properties, the inlet pressure of the ion flow can be obtained:

[0125] P i_in = n i_in kT i_in ;

[0126] In the formula: P i_in is the ion inlet pressure, with the unit of Pa;

[0127] To determine the stagnation pressure and stagnation temperature at the inlet, conditions such as the Mach number and the adiabatic coefficient need to be obtained; among them, the determination methods of the sound speed and the Mach number are:

[0128]

[0129]

[0130] Where: c is the sonic velocity at the inlet, with the unit of m / s, and M is the fluid Mach number at the inlet;

[0131] The determination methods of the stagnation pressure and stagnation temperature are respectively:

[0132]

[0133]

[0134] Where: P is is the ion stagnation pressure, with the unit of Pa; T is is the ion stagnation temperature, with the unit of K; M is the Mach number; γ is the adiabatic coefficient, taking 5 / 3;

[0135] Ion anode boundary condition:

[0136] At the outlet, the critical pressure corresponding to the local sonic velocity of the fluid is taken as the outlet pressure;

[0137]

[0138] Where: P out is the outlet pressure, with the unit of Pa;

[0139] Ion edge boundary condition:

[0140] There is no inflow and outflow of ions at the edge boundary. The normal velocity of ions at the edge boundary is zero, and the edge boundary makes the vacuum arc plasma system adiabatic to the outside.

[0141] S4. According to the plasma quasi-neutral property, update the electron number density based on the current value of the ion number density; update the electron velocity based on the current values of the ion velocity and current density;

[0142] Specifically, according to the plasma quasi-neutral property, the ion number density and the electron number density satisfy the following relationship:

[0143]

[0144] The difference between the electron velocity and the ion velocity forms a macroscopic current. Therefore, the ion velocity, electron velocity, and current density have the following relationship:

[0145]

[0146]

[0147]

[0148] S5. Substitute the current values of electron number density, electron temperature, electron velocity, magnetic field strength, and current density into the electric potential equation and the vector magnetic potential equation for simultaneous solution to obtain the current values of the vector magnetic potential and electric potential in the arcing region;

[0149] Specifically, both the electric potential equation and the vector magnetic potential equation satisfy the solution conditions of Poisson's equation; according to the current continuity law, the plasma generalized Ohm's law can be rewritten to obtain the electric potential equation; specifically, the electric potential equation is:

[0150]

[0151] The vector magnetic potential equation is:

[0152]

[0153]

[0154]

[0155] where U e is the vector expression form of electron velocity; B is the vector expression form of magnetic field strength; similarly, E is the vector expression form of electric field strength; μ0 is the vacuum permeability, with a value of 4π×10 -7 H / m.

[0156] Correspondingly, the boundary conditions of the electric potential equation include: electric potential cathode boundary condition, electric potential anode boundary condition, and electric potential edge boundary condition;

[0157] The electric potential cathode boundary condition is:

[0158] The electric potential anode boundary condition is:

[0159] The electric potential edge boundary condition is:

[0160] where c is a preset constant, which is taken as -1 V / kA according to the simulated current conditions in this embodiment; n is the normal direction of the boundary where the vacuum arc is located.

[0161] Furthermore, the boundary conditions of the vector magnetic potential equation include: vector magnetic potential cathode boundary condition, vector magnetic potential anode boundary condition, and vector magnetic potential edge boundary condition;

[0162] The vector magnetic potential cathode boundary condition is: A x = 0; A y = 0;

[0163] The vector magnetic potential anode boundary condition is:

[0164] The edge boundary condition of the vector magnetic potential is as follows:

[0165] Among them, r represents the distance from the calculation point to the axis of the electrode.

[0166] It should be noted that the present invention introduces the electric potential equation and the vector magnetic potential equation to calculate the electric field and magnetic field in the arcing region, reduces the differential operation, lowers the calculation complexity, and has a relatively high calculation efficiency. The specific description is as follows:

[0167] In the traditional method, under the condition of low-frequency current, the magnetohydrodynamic model of vacuum arc uses the magnetic transport equation to solve the electromagnetic field:

[0168]

[0169] In the above formula, the magnetic field intensity is calculated through the electron velocity, electron temperature, and electron number density. Then, according to Maxwell's equations, the current density and electric potential are solved through the magnetic field intensity. Finally, the electric field intensity is calculated through the electric potential:

[0170]

[0171]

[0172]

[0173] The calculation order of the electromagnetic field-related parameters in the above calculation scheme is: magnetic field intensity - current density - electric field intensity. It is necessary to calculate the magnetic transport equation, which contains a large number of curl operations and gradient operations. In the calculation process of the three-dimensional model, the magnetic transport equation needs to be expanded along the x, y, and z directions of the Cartesian coordinate system, involving a large number of differential operations, and the calculation complexity is relatively high.

[0174] In the present invention, under the condition of low-frequency current, the magnetohydrodynamic model of vacuum arc introduces the vector magnetic potential and electric potential to assist in calculating the electromagnetic field; the electric potential equation and the vector magnetic potential equation are calculated through the electron number density, electron temperature, electron velocity, magnetic field intensity, and current density:

[0175]

[0176]

[0177] Then, the electric field intensity and magnetic field intensity are solved according to the electric potential and vector magnetic potential. Finally, the current density is calculated through the generalized Ohm's law:

[0178]

[0179]

[0180]

[0181] It can be seen from this that the calculation order of the electromagnetic field related parameters in the present invention is: electric field strength - magnetic field strength - current density; obviously, the present invention avoids solving the magnetic transmission equation by calculating the vector magnetic potential equation, and the former reduces the differential operation in numerical calculation, reduces the calculation complexity, and has a higher calculation efficiency.

[0182] S6. Repeat steps S3 - S5 for iteration until the residual value of the high - current vacuum arc parameters under two adjacent iterations is less than the first preset threshold;

[0183] It should be noted that when the residual value of the parameters under two adjacent iterations of each parameter value of the high - current vacuum arc parameters is less than the first preset threshold, the iteration stops. In actual calculation, due to the correlation between parameters, as long as the ion temperature, electron temperature, ion velocity, ion number density, vector magnetic potential and electric potential in the arc - burning region meet the above - mentioned iteration stop conditions. In this embodiment, the first preset threshold is taken as 1×10 -3 .

[0184] S7. Calculate the current value of the electron heat transfer coefficient based on the current values of the electron number density and electron temperature; substitute the current values of the electron number density, electron velocity, ion temperature, current density and electron heat transfer coefficient into the electron energy equation for numerical solution to update the electron temperature;

[0185] Among them, the electron heat transfer coefficient is:

[0186]

[0187] In the formula: λ e represents the electron heat transfer coefficient, and the unit is W / (m K).

[0188] Specifically, when the flow field and electromagnetic field calculations are stable, specify the boundary conditions to calculate the electron energy equation; the electron energy equation is essentially the same as the ion energy equation, but in multi - physical - field coupling calculations, the electron energy equation often needs to be rewritten in the form of a convection - diffusion equation to facilitate custom calculations, including a diffusion term, a convection term, and a source term, which are respectively:

[0189] Diffusion term:

[0190] Convection term:

[0191] Source term:

[0192] In the formula: J is the current density vector;

[0193] To improve the calculation efficiency and ensure the calculation stability, in an alternative embodiment, the solution of the electron energy equation can utilize a commercial software based on the finite volume method (such as ANSYS Fluent), adopt the first-order upwind scheme or the second-order upwind scheme, and be based on coupled implicit solution; after combining the terms of the above electron energy equation, expand it in the Cartesian coordinate system, specifically as follows:

[0194]

[0195] Furthermore, the boundary conditions of the above electron energy equation include: the electron cathode boundary condition, the electron anode boundary condition, and the electron edge boundary condition;

[0196] The electron cathode boundary condition is: T e_in = T e0 ;

[0197] The electron anode boundary condition is:

[0198] The electron edge boundary condition is:

[0199] Wherein, T e_in and T e0 are the inlet electron temperature and the initial electron temperature respectively, with the unit of K; λ e is the electron heat transfer coefficient; T e is the electron temperature; n e is the electron number density; U ez is the component of the electron velocity in the z direction; k is the Boltzmann constant; T e is the electron temperature; n is the normal direction of the boundary where the vacuum arc is located.

[0200] Specifically, in the solution process, the current value of the conductivity can be calculated first based on the current values of the electron number density and the ion-electron collision frequency; then the current values of the electron number density, electron velocity, ion temperature, current density, conductivity, and electron heat transfer coefficient are substituted into the electron energy equation for numerical solution to update the electron temperature.

[0201] S8. Repeat steps S3 - S7 for iteration until the residual value of the high-current vacuum arc parameters in two adjacent iterations is less than the second preset threshold, and the high-current vacuum arc parameters at this time are the required parameter values.

[0202] It should be noted that when the parameter values of the high-current vacuum arc parameters all satisfy that the residual value of the parameters under two adjacent iterations is less than the second preset threshold, the iteration stops. In actual calculation, due to the correlation between parameters, as long as the ion temperature, electron temperature, ion velocity, ion number density, vector magnetic potential and electric potential in the arcing region satisfy the above iteration stop condition. In this embodiment, the second preset threshold is taken as 1×10 -3 .

[0203] As Figure 3 shown is the relationship diagram between each physical field. The present invention comprehensively considers the variation laws of each physical field and the dependence relationship between variables to realize the start calculation of each parameter under its reasonable initial conditions, and finally realizes the coupled solution of multiple physical fields step by step. In this process, since the ion parameters, electromagnetic field parameters and electron parameters in the high-current vacuum arc parameters are interdependent, and the change degree of the electron parameters is relatively small compared with other parameters, therefore, in the calculation process, it can be tentatively considered that the electron parameters are constant values. First, calculate the ion parameters and electromagnetic field parameters, and then calculate the electron parameters, which is easier to converge.

[0204] In order to further illustrate the performance of the method for obtaining high-current vacuum arc parameters under low-frequency current conditions provided by the present invention, the calculation results obtained by the method for obtaining high-current vacuum arc parameters provided by the present invention will be compared with existing relevant measurement experiments:

[0205] The maximum value of the electron number density calculated by the present invention is distributed at the cathode center of the arcing region of the vacuum arc, and the minimum value is distributed at the anode edge of the arcing region of the vacuum arc. The variation range of the electron number density is 5.5×10 21 pieces / m 3 —2.1×10 21 pieces / m 3 ; Under the same conditions, the relevant measurement experiment measures that the electron number density in the arcing region is about 4.0×10 21 pieces / m 3 ; It can be seen that the calculation result obtained by the present invention is relatively close to the experimental measurement result, and the accuracy is relatively high.

[0206] The variation range of the ion temperature calculated by the present invention in most calculation regions is 7.1-9.3 eV, and the variation range of the electron temperature calculated by the present invention in most calculation regions is 3-4.5 eV; Under the same conditions, the relevant measurement experiment measures that the ion temperature in the arcing region is about 10 eV, and the electron temperature is about 3.5 eV; It can be seen that the calculation result obtained by the present invention is also relatively close to the experimental measurement result, and the accuracy is relatively high.

[0207] Furthermore, comparing the ion number density calculated by the present invention with the vacuum arc column morphology captured by a high-speed camera in relevant measurement experiments, the two show basically the same distribution trend, mainly manifested as follows: (1) In the relevant experimental photos, the vacuum arc plasma is mainly distributed inside the contracted arc column, and the plasma density outside the arc column is relatively low; the calculation results of the present invention also show the morphology of the contracted arc column; (2) In the relevant experimental photos, the luminescence intensity is the strongest in the cathode center region of the vacuum arc plasma and the lowest in the anode edge region; the calculation results of the present invention show that the maximum value of the ion number density is distributed in the cathode center and the minimum value is distributed in the anode edge; From the above two aspects, it can be shown that the accuracy of the method for obtaining large-current vacuum arc parameters provided by the present invention is relatively high.

[0208] In summary, the present invention models the arcing region of the vacuum interrupter and establishes a three-dimensional magnetohydrodynamic model of the vacuum arc plasma; among them, the fluid equations consider the mass equation, momentum equation, and energy equation of the plasma, and the electromagnetic field is solved through the generalized Ohm's law and Maxwell's equations. The initial values and boundary conditions are set according to experimental results, relevant research reports, and theoretical values. The simulation method of the present invention comprehensively considers the variation laws of each physical field and the dependence relationship between variables, realizes the calculation of each parameter starting from its reasonable initial conditions, and finally realizes the coupled solution of multiple physical fields. The present invention can effectively obtain the characteristics of various physical parameters of the vacuum arc under low-frequency current conditions, which is of great significance for revealing the mechanism of the vacuum switch breaking process and optimizing the design of the vacuum switch.

[0209] Example 2

[0210] A system for obtaining large-current vacuum arc parameters under low-frequency current conditions, comprising: a memory and a processor, the memory stores a computer program, and when the processor executes the computer program, it executes the method for obtaining large-current vacuum arc parameters under low-frequency current conditions provided in Embodiment 1 of the present invention.

[0211] The related technical solutions are the same as those in Embodiment 1 and will not be elaborated here.

[0212] Example 3

[0213] A computer-readable storage medium, the computer-readable storage medium includes a stored computer program, wherein when the computer program is run by a processor, it controls the device where the storage medium is located to execute the method for obtaining large-current vacuum arc parameters under low-frequency current conditions provided in Embodiment 1 of the present invention.

[0214] The related technical solutions are the same as those in Embodiment 1 and will not be elaborated here.

[0215] Those skilled in the art can easily understand that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for obtaining large-current vacuum arc parameters under low-frequency current conditions, characterized in that It includes the following steps: S1. Conduct three-dimensional grid meshing on the arcing region of the vacuum interrupter to establish a three-dimensional magnetohydrodynamic model of the vacuum arc plasma. Among them, the three-dimensional magnetohydrodynamic model includes the fluid equations and electromagnetic equations of the vacuum arc plasma. The fluid equations include the ion mass equation, ion momentum equation, ion energy equation, and electron energy equation. The electromagnetic equations include the electric potential equation and vector magnetic potential equation. S2. Initialize the high-current vacuum arc parameters in the three-dimensional magnetohydrodynamic model. The high-current vacuum arc parameters include: ion number density, ion temperature, ion velocity, electron number density, electron temperature, electron velocity, and the vector magnetic potential and electric potential of the arcing region. S3. Calculate the current value of the electric field strength based on the current value of the electric potential. Calculate the current value of the magnetic field strength based on the current value of the vector magnetic potential. Calculate the current value of the current density based on the current values of the electric field strength, magnetic field strength, and electron velocity. Calculate the current value of the ion viscosity coefficient based on the current value of the ion temperature. Calculate the current value of the ion heat transfer coefficient based on the current values of the ion temperature, electron temperature, and electron number density. Substitute the current values of the ion number density, ion temperature, ion velocity, current density, magnetic field strength, ion viscosity coefficient, and ion heat transfer coefficient into the ion mass equation, ion momentum equation, and ion energy equation for simultaneous solution to update the ion number density, ion temperature, and ion velocity. S4. Update the electron number density based on the current value of the ion number density. Update the electron velocity based on the current values of the ion velocity and current density. S5. Substitute the current values of the electron number density, electron temperature, electron velocity, magnetic field strength, and current density into the electric potential equation and vector magnetic potential equation for simultaneous solution to obtain the current values of the electric potential and vector magnetic potential of the arcing region. S6. Repeat steps S3 - S5 for iteration until the residual value of the high-current vacuum arc parameters in two adjacent iterations is less than the first preset threshold. S7. Calculate the current value of the electron heat transfer coefficient based on the current values of the electron number density and electron temperature. Substitute the current values of the electron number density, electron velocity, ion temperature, current density, and electron heat transfer coefficient into the electron energy equation for solution to update the electron temperature. S8. Repeat steps S3 - S7 for iteration until the residual value of the high-current vacuum arc parameters in two adjacent iterations is less than the second preset threshold. At this time, the high-current vacuum arc parameters are the required parameter values.

2. The method for obtaining the large-current vacuum arc parameters under low-frequency current conditions according to claim 1, wherein Transform the electron energy equation into the form of a fluid convection-diffusion equation, specifically: Among them, T e is the electron temperature; k is the Boltzmann constant; n e is the electron number density; U e is the electron velocity vector; e is the elementary charge; J is the current density vector; λ e is the electron heat transfer coefficient; J x 、J y 、J z respectively represent the components of the current density in the x, y, and z directions; σ is the plasma conductivity; m e is the mass of a single electron; m i is the mass of a single ion; v ei is the ion-electron collision frequency; T i is the ion temperature.

3. The method for obtaining the large current vacuum arc parameters under low frequency current conditions according to claim 2, characterized in that, The boundary conditions of the electron energy equation include: electron cathode boundary condition, electron anode boundary condition, and electron edge boundary condition. The boundary condition of the electronic cathode is: T e_in = T e0 ; The boundary conditions of the electronic anode are as follows: The electronic edge boundary conditions are as follows: where, T e_in and T e0 are the inlet electron temperature and the initial electron temperature respectively; λ e is the electron heat transfer coefficient; T e is the electron temperature; n e is the electron number density; U ez is the component of the electron velocity in the z direction; k is the Boltzmann constant; n is the normal direction of the boundary where the vacuum arc is located.

4. The method for obtaining the large current vacuum arc parameters under low frequency current conditions according to claim 1, characterized in that, The electric potential equation is: The vector magnetic potential equation is: Wherein, is the electric potential; U e is the electron velocity vector; B is the magnetic field strength; n e is the electron number density; e is the elementary charge; P e is the electron pressure; T e is the electron temperature; A x and A y and A z respectively represent the components of the vector magnetic potential in the x, y, and z directions; μ0 is the vacuum permeability; J x and J y and J z respectively represent the components of the current density in the x, y, and z directions.

5. The method for obtaining the large current vacuum arc parameters under low frequency current conditions according to claim 4, characterized in that, The boundary conditions of the electric potential equation include: electric potential cathode boundary condition, electric potential anode boundary condition, and electric potential edge boundary condition. The potential cathode boundary condition is as follows: The potential anode boundary condition is as follows: The potential edge boundary condition is as follows: Wherein, is the electric potential; c is a preset constant; n is the normal direction of the boundary where the vacuum arc is located.

6. The method for obtaining the large current vacuum arc parameters under low frequency current conditions according to claim 4, characterized in that, The boundary conditions of the vector magnetic potential equation include: vector magnetic potential cathode boundary condition, vector magnetic potential anode boundary condition, and vector magnetic potential edge boundary condition. The vector magnetic potential cathode boundary condition is: A x = 0; A y = 0; The vector magnetic potential anode boundary condition is as follows: The edge boundary condition of the vector magnetic potential is as follows: Among them, A x , A y , A z respectively represent the components of the vector magnetic potential in the x, y, and z directions; n is the normal direction of the boundary where the vacuum arc is located; μ0 is the vacuum permeability; J z represents the component of the current density in the z direction; r represents the distance from the calculation point to the axis of the electrode.

7. The method for obtaining the large current vacuum arc parameters under low frequency current conditions according to claim 1, characterized in that, The ion mass equation is as follows: The ion momentum equation is as follows: The ion energy equation is as follows: where m i is the mass of a single ion; n i is the ion number density; U ix , U iy , U iz represent the components of the ion velocity in the x, y, and z directions respectively; P i is the ion pressure; τ xx , τ yy , τ zz represent the normal stresses caused by ion viscosity; τ xy , τ xz , τ yx , τ yz , τ zx , τ zy represent the shear stresses caused by ion viscosity; F x , F y , F z represent the components of the body force acting on the ions in the x, y, and z directions respectively; U i is the vector expression of the ion velocity; k is the Boltzmann constant; T i is the ion temperature; λ i is the ion heat transfer coefficient; Q i is the internal heat source of the ions.

8. A system for obtaining parameters of a high-current vacuum arc under low-frequency current conditions, characterized in that, including: a memory and a processor, where the memory stores a computer program, and when the processor executes the computer program, it executes the method for obtaining large current vacuum arc parameters under low frequency current conditions according to any one of claims 1-7.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium includes a stored computer program, wherein when the computer program is run by a processor, it controls the device where the storage medium is located to execute the method for obtaining large current vacuum arc parameters under low frequency current conditions according to any one of claims 1-7.

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