Grounding grid induced apparent magnetic impedance forward method and device based on finite difference method

Abstract

The application discloses a grounding net induced apparent magnetic impedance forward method and device based on a finite difference method, and the method realizes three-dimensional forward simulation of induced apparent magnetic impedance based on the finite difference method, starts from a differential equation satisfied by a scalar potential, deduces a partial differential equation of the scalar potential, then solves the partial differential equation by using a solving method of the finite difference method, and sequentially solves differential equations of current density and induced apparent magnetic impedance according to a Maxwell equation set, so that three-dimensional forward simulation of the induced apparent magnetic impedance is realized, researchers can more conveniently, intuitively and quickly understand the spatial distribution and change rule of the induced apparent magnetic impedance, and the method has great significance for detecting and identifying corrosion and breakpoints of the grounding net.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of grounding grid detection, and in particular to a grounding grid induced apparent magnetic impedance forward method and device based on finite difference method. BACKGROUND

[0002] There are many factors causing the failure of a substation, most of which are due to the poor corrosion resistance of the steel material of the grounding grid, resulting in corrosion of the grounding grid and ultimately causing accidents in the substation. Therefore, it is of great significance to carry out detection and identification of the corrosion and breakpoint of the grounding grid.

[0003] The buried grounding conductor is very concealed, although the performance of the grounding grid can be indirectly checked and judged by measuring the grounding resistance and combining local excavation, but this method is difficult to accurately check the corrosion condition of the entire grounding grid. For a long time, there has been no breakthrough in the method of solving the corrosion and breakpoint of the grounding grid, and establishing an electromagnetic characteristic model of the grounding grid is beneficial to the research of the internal performance of the grounding grid and has important significance for the research of the corrosion detection of the grounding grid.

[0004] Although there are currently a small number of methods for detecting the grounding grid by establishing an electromagnetic characteristic model of the grounding grid, but all of them are based on the model established by the electric network method, the transient electromagnetic method or the electromagnetic induction method, and the universality is not enough, so there is an urgent need for a modeling method with high universality for detecting the underground condition of the grounding grid. SUMMARY

[0005] In order to solve the defects of the prior art, the present application provides a grounding grid induced apparent magnetic impedance forward method based on finite difference method. The method realizes three-dimensional forward simulation of induced apparent magnetic impedance based on finite difference method, derives the partial differential equation of scalar potential from the differential equation satisfied by scalar potential, then solves the partial differential equation by using the solving method of finite difference method, and then sequentially solves the differential equations of current density and induced apparent magnetic impedance according to Maxwell's equations, to realize three-dimensional numerical simulation of induced apparent magnetic impedance, helping researchers to more conveniently, intuitively and quickly understand the spatial distribution and variation law of induced apparent magnetic impedance.

[0006] In order to achieve the above purpose, the present application provides a grounding grid induced apparent magnetic impedance forward method based on finite difference method, which specifically comprises the following steps:

[0007] S1: setting the grid division mode and solving method of finite difference method;

[0008] S2: setting the excitation mode of the grounding grid, constructing the partial differential equation of scalar potential based on Maxwell's equations and the characteristics of scalar potential itself, solving the partial differential equation of scalar potential by using the set solving method, and obtaining the value of scalar potential;

[0009] S3: Obtain the relationship between scalar potential and current density based on Maxwell's equations, construct the partial differential equation of current density, and solve the partial differential equation of current density using a set of solving methods according to the value of the scalar potential to obtain the value of the current density;

[0010] S4: Based on Maxwell's equations and the characteristics of induced apparent magnetic impedance, construct the partial differential equation of induced apparent magnetic impedance, and solve the partial differential equation of induced apparent magnetic impedance using a set of solving methods according to the value of the current density to obtain the three-dimensional forward modeling result of induced apparent magnetic impedance.

[0011] Further, in S1, the grid division method of the finite difference method is set, including:

[0012] The scalar potential is divided into grids by adopting the cuboid division method in the finite difference method, a plurality of cuboids are formed into grids, and the nodes of the grids are used to replace the values of the equations at each node; the entire calculation space is discretized in a range large enough for the grounding grid model, and each small cuboid unit is divided by continuously dividing the space with three planes parallel to the three coordinate axes; the vertices of these cuboids are called nodes;

[0013] The conductivity σ of each node is defined (o,p,q) The conductivity of the cuboid to the right of the node is defined, and a small enough cuboid around the node is used to replace the node, and ΔV (o,p,q) is used to replace the volume of the node (o, p, q).

[0014] Further, S2 specifically includes:

[0015] S21: Set the applied excitation as a sinusoidal alternating current Ie -jωt The Maxwell equations of the sinusoidal time-varying electromagnetic field are as follows

[0016]

[0017] Where E is the electric field intensity, the unit is V / m, H is the magnetic field intensity, the unit is A / m, D is the electric displacement, the unit is C / m 2 , B is the magnetic induction intensity, the unit is T, J is the conduction current density, the unit is A / m 2 , q is the charge density, the unit is C / m 2 , is the Hamiltonian operator, and the "×" represents the curl, and the "·" represents the divergence;

[0018] A sinusoidal alternating current Ie -jωt is injected into a homogeneous medium with conductivity σ at a point (x0, y0, z0), and for the current density, there is:

[0019]

[0020] In the formula, V is the volume of the calculation area, I0 is the peak value of the excitation current, △V represents the change in volume, and ds represents the integral;

[0021] According to the properties of the Dirichlet function, we have:

[0022]

[0023] In the formula, δ is the impulse function, r is the distance between the calculation point and the injection point, and r0 is the distance coordinate of the injection point;

[0024] Suppose that the anisotropy of the medium is uniform, and a sinusoidal alternating current Ie is injected at a point -jωt The formula of the scalar potential u of the electromagnetic field generated is

[0025]

[0026] In the formula, j is the complex unit, ω is the frequency of the excitation current, represents the partial derivative, and x, y, and z represent the three coordinate axes, respectively;

[0027] S22: According to the grid division result, the formula of the scalar potential u is rewritten at the node (o, p, q) using the finite difference method

[0028]

[0029] S o,p,q is the total area of each face of the cuboid at the node (o, p, q), n is the normal direction of the face, V o,p,q is the volume of the cuboid, so the right side of the above formula can be integrated for the six faces, respectively, and then the results of the six faces are added up;

[0030] S23: Each divided node is processed according to the formula (5), and the matrix equation of the scalar potential can be obtained. The value of the scalar potential can be obtained by using the set solving method to calculate the equation.

[0031] Further, S3 specifically includes:

[0032] S31: According to the Maxwell equation set, the relationship between the current density J and the scalar potential u is:

[0033]

[0034]

[0035] In the formula, u x , u y , and u z are the scalar potentials in the x, y, and z directions, respectively;

[0036] S32: The relationship between the current density J and the scalar potential u is replaced by the partial differential with the difference quotient by using the finite difference method:

[0037]

[0038] In the formula, J o,p,q is the current density of the node (o, p, q), σ o,p,q is the conductivity of the node (o, p, q), u o+1,p,q is the value of the scalar potential of the next node in the positive direction of the x-axis of the node (o, p, q), u o-1,p,q is the value of the scalar potential of the next node in the negative direction of the x-axis of the node (o, p, q), u o,p+1,q is the value of the scalar potential of the next node in the positive direction of the y-axis of the node (o, p, q), u o,p-1,q is the value of the scalar potential of the next node in the negative direction of the y-axis of the node (o, p, q), u o,p,q+1 is the value of the scalar potential of the next node in the positive direction of the z-axis of the node (o, p, q), u o,p,q-1 is the value of the scalar potential of the next node in the negative direction of the z-axis of the node (o, p, q), Δx o is the distance between the node (o, p, q) and the next node in the positive direction of the x-axis, Δx o-1 is the distance between the node (o, p, q) and the next node in the negative direction of the x-axis, Δy p is the distance between the node (o, p, q) and the next node in the positive direction of the y-axis, Δy p-1 is the distance between the node (o, p, q) and the next node in the negative direction of the y-axis, Δz q is the distance between the node (o, p, q) and the next node in the positive direction of the z-axis, Δz q-1 is the distance between the node (o, p, q) and the next node in the negative direction of the z-axis.

[0039] The current density J is expanded in three directions of the rectangular coordinate system

[0040]

[0041] In the formula, Jx o,p,q , Jy o,p,q and Jz o,p,q are the components of the current density J at the node (o, p, q) in the x, y and z axes, respectively.

[0042] S33: Each node is processed according to formula (8), and the matrix equation of the relationship between the current density and the scalar potential can be obtained. The value of the current density can be obtained by using the set solving method to calculate the matrix equation.

[0043] Furthermore, S4 specifically includes:

[0044] S41: According to Maxwell's equations, the relationship between magnetic field intensity H and current density J is:

[0045]

[0046] Expand the left side of formula (9)

[0047]

[0048] Expand equation (10) in three directions according to the rectangular coordinate system

[0049]

[0050]

[0051]

[0052] Where H x 、H y and H z are the components of the magnetic field intensity H in the x, y, and z directions, J x 、J y and J z are the components of the current density J in the x, y, and z directions respectively;

[0053] S42: Construct the wave equation of magnetic induction intensity from Maxwell's equations:

[0054]

[0055] Where k is the complex wave number, B is the magnetic induction intensity, μ is the magnetic permeability, ε is the dielectric constant, is the phase coefficient, δ is the attenuation coefficient;

[0056] The frequency ω of the grounding grid excitation current, the conductivity σ of the soil, and the dielectric constant ε of the soil satisfy the following conditions:

[0057]

[0058] Then the attenuation coefficient in the wave equation is approximately:

[0059]

[0060] S43: Based on S41 and S42, the calculation formula for magnetic induction intensity B is derived:

[0061]

[0062] Let the number of turns of the sensor be N, and the area of the hollow in the middle of the coil be S, then the magnetic flux passing through the coil is:

[0063]

[0064] The induced electromotive force υ output by the coil is:

[0065]

[0066] Let the total resistance in the signal conditioning circuit be R 电路 , the total inductance be L 电感 , the output capacitance be C 输出 , and the other total capacitance be C 电路 , then the voltage output by the conditioning circuit is:

[0067]

[0068] The calculation formula of the induced apparent magnetic impedance Z is derived as:

[0069]

[0070] S44: Use finite difference method to replace partial derivatives with difference quotient for formula (11) to formula (13):

[0071]

[0072]

[0073]

[0074] Bring the value of the magnetic field strength into formula (21) to calculate the induced apparent magnetic impedance of each node, and list the matrix equation of the induced potential magnetic impedance:

[0075]

[0076] In the formula, A is the coefficient matrix, N is the order of the matrix, Z x , Z y and Z z are the components of the induced apparent magnetic impedance Z in the x, y, and z directions respectively;

[0077] Use the set solving method to solve the matrix equation (25) to obtain the induced apparent magnetic impedance of any point in space.

[0078] Preferably, the set solving method is the Seidel iteration method.

[0079] Alternatively, the set solving method is the bisection method.

[0080] Alternatively, the set solving method is the Newton iteration method.

[0081] In addition, in order to achieve the above object, the application further provides a ground net induced apparent magnetic impedance forward device based on finite difference method, comprising the following modules:

[0082] The finite difference setting module is used for setting a mesh division mode and a solving method of the finite difference method;

[0083] The scalar potential solving module is used for setting a mode of ground net excitation, constructing a partial differential equation of the scalar potential based on a Maxwell equation set and characteristics of the scalar potential itself, solving the partial differential equation of the scalar potential by using the set solving method, and obtaining a value of the scalar potential;

[0084] The current density solving module is used for obtaining a relationship between the scalar potential and the current density based on the Maxwell equation set, constructing a partial differential equation of the current density, solving the partial differential equation of the current density by using the set solving method according to the value of the scalar potential, and obtaining a value of the current density;

[0085] The induced apparent magnetic impedance simulation module is used for constructing a partial differential equation of the induced apparent magnetic impedance based on the Maxwell equation set and characteristics of the induced apparent magnetic impedance, solving the partial differential equation of the induced apparent magnetic impedance by using the set solving method according to the value of the current density, and obtaining a three-dimensional simulation result of the induced apparent magnetic impedance.

[0086] Finally, in order to achieve the above object, the application further provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and capable of running on the processor, wherein the processor implements the steps of the ground net induced apparent magnetic impedance forward method when executing the program.

[0087] The technical scheme provided by the application has the following beneficial effects:

[0088] The application realizes three-dimensional forward simulation of the induced apparent magnetic impedance based on the finite difference method, derives a partial differential equation of the scalar potential from a differential equation satisfied by the scalar potential, then solves the partial differential equation by using a solving method of the finite difference method, and then sequentially solves differential equations of the current density and the induced apparent magnetic impedance based on the Maxwell equation set, so as to realize three-dimensional numerical simulation of the induced apparent magnetic impedance, and help researchers to more conveniently, intuitively and quickly understand spatial distribution and variation rules of the induced apparent magnetic impedance. BRIEF DESCRIPTION OF DRAWINGS

[0089] The application will be further described below in combination with the drawings and embodiments, wherein:

[0090] Figure 1 is a flow chart of the ground net induced apparent magnetic impedance forward method based on the finite difference method in the embodiments of the application;

[0091] Figure 2 is a 3*3 grounding grid induced apparent magnetic impedance amplitude distribution diagram calculated by the grounding grid induced apparent magnetic impedance forward method based on the finite difference method in the embodiment of the present application;

[0092] Figure 3 is an irregular grounding grid induced apparent magnetic impedance amplitude distribution diagram calculated by the grounding grid induced apparent magnetic impedance forward method based on the finite difference method in the embodiment of the present application;

[0093] Figure 4 is a structural diagram of the grounding grid induced apparent magnetic impedance forward device based on the finite difference method in the embodiment of the present application;

[0094] Figure 5 is a schematic diagram of an electronic device in the embodiment of the present application. DETAILED DESCRIPTION

[0095] In order to have a clearer understanding of the technical features, objectives and effects of the present application, the specific embodiments of the present application will be described in detail with reference to the drawings.

[0096] Reference Figure 1 The embodiment of the present application provides a grounding grid induced apparent magnetic impedance forward method based on the finite difference method, and specifically includes the following steps:

[0097] S1: according to the characteristics of induced apparent magnetic impedance calculation, determine the section method and solving method of the finite difference method;

[0098] S1 specifically includes:

[0099] S11: adopt the cuboid section method in the finite difference method to perform grid section on the scalar potential, form a grid with multiple cuboids, and replace the value of the equation at each node with the node of the grid; discretize the entire calculation space in a large enough range of the grounding grid model, divide the space into each small cuboid unit by continuously sectioning three planes parallel to the three coordinate axes, and refer to the vertices of these cuboids as nodes;

[0100] It should be noted that large enough means that the size of the grounding grid model should be larger than the size of the sectioned grid, which can be determined according to the specific model.

[0101] S12: define the conductivity of each node (o,p,q) the conductivity of the cuboid above the right of the node, and the conductivity of the cuboid composed of the eight nodes is replaced with a small enough cuboid around the node, and ΔV (o,p,q) replaces the volume of the node (o, p, q);

[0102] It should be noted that small enough means that the size of the cuboid should be smaller than the size of the grounding grid model.

[0103] S13: solving linear equations by using the Seidel iteration method, setting matrix

[0104] A=(a i,j ) n×n (1)

[0105] wherein n represents the dimension of the matrix, a i,j is the value of the matrix in the i-th row and the j-th column; for a general n-order linear equation group, the matrix A has:

[0106] Ax=b (2)

[0107] wherein x is the solution of the matrix A, and b is the coefficient matrix; which is equivalent to the following transformation:

[0108]

[0109] wherein g is the coefficient of each x, x=(x1,x2,…,x n ) T , g=(g1,g2,…,g n ) T , B=(b ij ) n×n , and the matrix form of the above equation group is:

[0110] x=Bx+g (4)

[0111] For the linear equation group with a strictly diagonally dominant coefficient matrix, the Seidel iteration format is as follows:

[0112] x (k+1) =B1x (k+1) +B2x (k) +g (5)

[0113] wherein the matrix

[0114]

[0115] The Seidel iteration format converges to the solution vector of the equation group for any initial vector x (0) and g.

[0116] It should be noted that the Seidel iteration method is used to solve the partial differential equation in steps S2-S4 in this embodiment, but the Seidel iteration method is only a preferred solving method, and other finite difference methods, such as the bisection method and the Newton iteration method, can also be used.

[0117] S2: setting the mode of grounding grid excitation, constructing the partial differential equation of scalar potential based on Maxwell equations and the characteristics of scalar potential itself, solving the partial differential equation of scalar potential by using the set solving method, and obtaining the value of scalar potential;

[0118] S2 specifically comprises:

[0119] S21: setting the applied excitation as a sinusoidal alternating current Ie -jωt The Maxwell equations of the sinusoidal time-varying electromagnetic field are as follows

[0120]

[0121] wherein E is the electric field intensity, the unit is V / m, H is the magnetic field intensity, the unit is A / m, D is the electric displacement, the unit is C / m 2 B is the magnetic induction intensity, the unit is T, J is the conduction current density, the unit is A / m 2 q is the charge density, the unit is C / m 2 , is the Hamiltonian operator, the operator "x" represents the curl, and "·" represents the divergence;

[0122] In a homogeneous medium with conductivity σ, a sinusoidal alternating current Ie -jωt is injected at a point (x0, y0, z0), and for the current density

[0123]

[0124] In the formula, V is the volume of the calculation region, I0 is the peak value of the excitation current, △V represents the change amount of the volume, and ds represents the integral;

[0125] According to the properties of the Dirichlet function, we have:

[0126]

[0127] In the formula, δ is the impulse function, r is the distance between the calculation point and the injection point, and r0 is the distance coordinate of the injection point;

[0128] If the anisotropy of the medium is uniform, a sinusoidal alternating current Ie -jωt is injected at a point, and the formula of the scalar potential u of the generated electromagnetic field is

[0129]

[0130] In the formula, j is a complex unit, ω is the frequency of the excitation current, represents the partial derivative, and x, y and z respectively represent the three coordinate axes;

[0131] S22: According to the grid division result, using finite difference method, formula (10) is written as

[0132]

[0133] S o,p,q is the total area of each face of the cuboid at the node (o, p, q), n is the normal direction of the face, V o,p,q is the volume of the cuboid, so the right side of the above formula can be integrated for the six faces respectively, and then the results of the six faces are added up;

[0134] S23: Each divided node is processed according to formula (11), and the matrix equation of the scalar potential can be obtained, and the value of the scalar potential can be obtained by using the set solving method to calculate the equation.

[0135] S3: The relationship between the scalar potential and the current density is obtained based on the Maxwell equation set, the partial differential equation of the current density is constructed, the value of the current density is obtained by using the set solving method to solve the partial differential equation of the current density according to the value of the scalar potential;

[0136] S3 specifically includes:

[0137] S31: According to the Maxwell equation set, the relationship between the current density J and the scalar potential u is:

[0138]

[0139]

[0140] S32: The finite difference method is used to replace the partial derivative of formula (13) with the difference quotient:

[0141]

[0142] In the formula, J o,p,q is the current density of the node (o, p, q), σ o,p,q is the conductivity of the node (o, p, q), u o+1,p,q is the value of the scalar potential of the next node in the positive direction of the x-axis of the node (o, p, q), u o-1,p,q is the value of the scalar potential of the next node in the negative direction of the x-axis of the node (o, p, q), u o,p+1,q is the value of the scalar potential of the next node in the positive direction of the y-axis of the node (o, p, q), u o,p-1,q is the value of the scalar potential of the next node in the negative direction of the y-axis of the node (o, p, q), u o,p,q+1 is the value of the scalar potential of the next node in the positive direction of the z-axis of the node (o, p, q), u o,p,q-1 is the value of the scalar potential of the next node in the negative direction of the z-axis of the node (o, p, q), Δxo is the distance of the node (o, p, q) to the next node along the positive direction of the x-axis, Δx o-1 is the distance of the node (o, p, q) to the next node along the negative direction of the x-axis, Δy p is the distance of the node (o, p, q) to the next node along the positive direction of the y-axis, Δy p-1 is the distance of the node (o, p, q) to the next node along the negative direction of the y-axis, Δz q is the distance of the node (o, p, q) to the next node along the positive direction of the z-axis, Δz q-1 is the distance of the node (o, p, q) to the next node along the negative direction of the z-axis;

[0143] The current density J is expanded in three directions of the rectangular coordinate system

[0144]

[0145] In the formula, Jx o,p,q , Jy o,p,q and Jz o,p,q are respectively the components of the current density at the node (o, p, q) along the x, y and z axes;

[0146] S33: For each dissected node, the matrix equation set of the relationship between the current density and the scalar potential is obtained by processing according to formula (15), and the value of the current density can be obtained by using the set solving method to calculate the matrix equation set.

[0147] S4: Based on the Maxwell equation set and the characteristics of the induced apparent magnetic impedance, the partial differential equation of the induced apparent magnetic impedance is constructed, the partial differential equation of the induced apparent magnetic impedance is solved according to the value of the current density, and the three-dimensional forward modeling result of the induced apparent magnetic impedance is obtained by using the set solving method.

[0148] S4 specifically includes:

[0149] S41: According to the Maxwell equation set, the relationship between the magnetic field intensity H and the current density J is:

[0150]

[0151] The left side of formula (16) is expanded

[0152]

[0153] Formula (17) is expanded in three directions of the rectangular coordinate system

[0154]

[0155]

[0156]

[0157] H x , H y and H z are the components of the magnetic field strength in the x, y, z directions respectively, J x , J y and J z are the components of the current density J in the x, y, z directions respectively;

[0158] S42: Construct the wave equation of magnetic induction intensity from the Maxwell equations:

[0159]

[0160] where k is the complex wave number, B is the magnetic induction intensity, μ is the magnetic permeability, ε is the dielectric constant, is the phase coefficient, and δ is the attenuation coefficient;

[0161] The frequency ω of the grounding grid excitation current is generally 100-1000 Hz, and the conductivity σ of the soil is generally 1-1000 Ω·m, so the maximum value of the ratio of the displacement current to the conduction current is 5×10 -5 , that is:

[0162]

[0163] Then the attenuation coefficient in the wave equation is approximately:

[0164]

[0165] S43: Derive the calculation formula of the magnetic induction intensity B according to S41 and S42:

[0166]

[0167] Let the number of turns of the sensor be N, and the area of the hollow in the middle of the coil be S, so the magnetic flux passing through the coil is:

[0168]

[0169] The induced electromotive force υ output by the coil is:

[0170]

[0171] Let the total resistance in the signal conditioning circuit be R 电路 , the total inductance be L 电感 , the output capacitance be C 输出 , and the other total capacitance be C 电路 , then the voltage output by the conditioning circuit is:

[0172]

[0173] The calculation formula of the induced apparent magnetic impedance Z is derived as follows:

[0174]

[0175] S44: the partial derivatives of formula (18) to formula (20) are replaced by difference quotients by using the finite difference method:

[0176]

[0177]

[0178]

[0179] The value of the magnetic field strength is brought into formula (28) to calculate the induced apparent magnetic impedance of each node, and the matrix equation of the induced apparent magnetic impedance is listed:

[0180]

[0181] In the formula, A is the coefficient matrix, N is the order of the matrix, Z x , Z y and Z z are the components of the induced apparent magnetic impedance in the x, y and z directions respectively;

[0182] The matrix equation is solved by using the finite difference solving method in S13, and the induced apparent magnetic impedance of any point in space is obtained.

[0183] The key point of the embodiment of the application is:

[0184] In order to quickly obtain the spatial distribution and variation law of the induced apparent magnetic impedance of the grounding grid under different three-dimensional model parameters, the differential equation of the induced apparent magnetic impedance is derived from the scalar potential and the boundary value problem is studied, and based on the MATLAB platform, according to the proposed mathematical model of the induced apparent magnetic impedance, the calculation process is currently written as code to realize the forward method of the induced apparent magnetic impedance of the grounding grid based on the three-dimensional finite difference method, and the correctness of the algorithm is verified by testing and verifying different shapes of the grounding grid model, as shown in Figure 2 , 3 , wherein Figure 2 shows the induced apparent magnetic impedance amplitude distribution diagram of a 3*3 grounding grid, Figure 3 shows the induced apparent magnetic impedance amplitude distribution diagram of an irregular grid grounding grid, which proves that the method can realize the calculation of the induced apparent magnetic impedance of the grounding grid of any shape, and the obtained induced apparent magnetic impedance distribution diagram can well reflect the distribution law of the induced apparent magnetic impedance of the grounding grid.

[0185] In addition, refer to Figure 4The embodiment of the present application also provides a ground net induced apparent magnetic impedance forward device based on the finite difference method, comprising the following modules.

[0186] The finite difference setting module 001 is used for setting a mesh division mode and a solving method of the finite difference method.

[0187] The scalar potential solving module 002 is used for setting a mode of ground net excitation, constructing a partial differential equation of the scalar potential based on a Maxwell equation set and characteristics of the scalar potential itself, solving the partial differential equation of the scalar potential by using the set solving method, and obtaining a value of the scalar potential.

[0188] The current density solving module 003 is used for obtaining a relationship between the scalar potential and the current density based on the Maxwell equation set, constructing a partial differential equation of the current density, solving the partial differential equation of the current density by using the set solving method according to the value of the scalar potential, and obtaining a value of the current density.

[0189] The induced apparent magnetic impedance simulation module 004 is used for constructing a partial differential equation of the induced apparent magnetic impedance based on the Maxwell equation set and characteristics of the induced apparent magnetic impedance, solving the partial differential equation of the induced apparent magnetic impedance by using the set solving method according to the value of the current density, and obtaining a three-dimensional forward simulation result of the induced apparent magnetic impedance.

[0190] Please refer to Figure 5 , an example of a physical structure diagram of an electronic device is shown, which can include: a processor 610, a communications interface 620, a memory 630 and a communications bus 640, wherein the processor 610, the communications interface 620, the memory 630 complete the communication between each other through the communications bus 640. The processor 610 can call the logic instructions in the memory 630 to execute the steps of the above ground net induced apparent magnetic impedance forward method, specifically including: setting a mesh division mode and a solving method of the finite difference method; setting a mode of ground net excitation, constructing a partial differential equation of the scalar potential based on a Maxwell equation set and characteristics of the scalar potential itself, solving the partial differential equation of the scalar potential by using the set solving method, and obtaining a value of the scalar potential; obtaining a relationship between the scalar potential and the current density based on the Maxwell equation set, constructing a partial differential equation of the current density, solving the partial differential equation of the current density by using the set solving method according to the value of the scalar potential, and obtaining a value of the current density; constructing a partial differential equation of the induced apparent magnetic impedance based on the Maxwell equation set and characteristics of the induced apparent magnetic impedance, solving the partial differential equation of the induced apparent magnetic impedance by using the set solving method according to the value of the current density, and obtaining a three-dimensional forward simulation result of the induced apparent magnetic impedance.

[0191] In addition, the logic instructions in the memory 630 described above can be implemented in the form of a software function unit and sold or used as an independent product, and can be stored in a computer readable storage medium. Based on such understanding, the technical solutions of the present application essentially or the parts that contribute to the prior art or parts of the technical solutions can be embodied in the form of a software product. The computer software product is stored in a storage medium, and includes a plurality of instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the method described in the various embodiments of the present application. The aforementioned storage medium includes: a U disk, a mobile hard disk, a read-only memory (ROM, Read-Only Memory), a random access memory (RAM, Random Access Memory), a magnetic disk or an optical disk, and various media that can store program codes.

[0192] In another aspect, the embodiments of the present application also provide a storage medium having a computer program stored thereon, the computer program being executed by a processor to implement the steps of the grounding grid induced apparent magnetic impedance forward method, and specifically includes: setting a mesh division mode and a solving method of the finite difference method; setting a grounding grid excitation mode, constructing a partial differential equation of a scalar potential based on a Maxwell equation set and characteristics of the scalar potential itself, using the set solving method to solve the partial differential equation of the scalar potential to obtain a value of the scalar potential; obtaining a relationship between the scalar potential and a current density based on the Maxwell equation set, constructing a partial differential equation of the current density, using the set solving method to solve the partial differential equation of the current density according to the value of the scalar potential to obtain a value of the current density; constructing a partial differential equation of the induced apparent magnetic impedance based on the Maxwell equation set and characteristics of the induced apparent magnetic impedance, using the set solving method to solve the partial differential equation of the induced apparent magnetic impedance according to the value of the current density to obtain a three-dimensional forward simulation result of the induced apparent magnetic impedance.

[0193] The technical solutions provided by the present application have the following beneficial effects:

[0194] The induced apparent magnetic impedance forward method and device provided by the present application can realize three-dimensional numerical simulation of the induced apparent magnetic impedance, and programming under MATLAB enables numerical calculation and three-dimensional visualization to be performed simultaneously. This helps researchers to more conveniently, intuitively and quickly understand the spatial distribution and variation law of the induced apparent magnetic impedance.

[0195] It should be noted that, in the present document, the terms "comprising", "comprising" or any other variant thereof are intended to cover non-exclusive inclusions, so that a process, method, article or system that includes a list of elements not only includes those elements, but also includes other elements not explicitly listed, or inherent to such a process, method, article or system. Without more limitations, the element defined by the statement "comprising a" does not exclude the presence of other identical elements in the process, method, article or system that includes the element.

[0196] The above-mentioned embodiment numbers of the present application are only for description, and do not represent the advantages and disadvantages of the embodiments. In the unit claims of several devices, several of these devices can be embodied by the same hardware item. The use of the words first, second, and third does not represent any order, and these words can be interpreted as identification.

[0197] The above is only the preferred embodiment of the present application, and does not limit the patent scope of the present application. Any equivalent structure or equivalent process transformation, or direct or indirect application in other related technical fields, is also included in the patent protection scope of the present application.

Claims

1. A finite-difference method-based ground net induced apparent magnetic impedance forward method, characterized in that, The method comprises the following steps: S1: setting the mesh partitioning mode and solving method of finite difference method; S2: setting the mode of grounding grid excitation, constructing the partial differential equation of scalar potential based on the Maxwell equations and the characteristics of scalar potential itself, solving the partial differential equation of scalar potential using the set solving method to obtain the value of scalar potential; The applied excitation is set to be a sinusoidal alternating current Ie -jωt The Maxwell equations for a sinusoidal time-varying electromagnetic field are given by where E is the electric field intensity in V / m, H is the magnetic field intensity in A / m, D is the electric displacement in C / m 2 , B is the magnetic induction in T, J is the conduction current density in A / m 2 , q is the charge density in C / m 2 , is the Hamiltonian operator, the "x" represents the curl, the "·" represents the divergence, j is the complex unit, and ω is the frequency of the excitation current S3: obtaining the relationship between scalar potential and current density based on the Maxwell equations, constructing the partial differential equation of current density, and solving the partial differential equation of current density using the set solving method according to the value of scalar potential to obtain the value of current density; According to the Maxwell equations, the relationship between current density J and scalar potential u is: wherein u x , u y , and u z are scalar potentials in x, y, and z directions, respectively, denotes partial differentiation, and σ is the electrical conductivity. S4: based on the Maxwell equations and the characteristics of induced apparent magnetic impedance, constructing the partial differential equation of induced apparent magnetic impedance, and solving the partial differential equation of induced apparent magnetic impedance using the set solving method according to the value of current density to obtain the three-dimensional forward modeling result of induced apparent magnetic impedance; According to the Maxwell equations, the relationship between magnetic field intensity H and current density J is:

2. The ground net induced visual magnetic impedance forward method according to claim 1, characterized in that, In S1, the setting of the mesh partitioning mode of finite difference method comprises: The scalar potential is mesh partitioned in the way of cuboid partitioning in the finite difference method, a plurality of cuboids are used to form a mesh, and the nodes of the mesh are used to replace the value of the equation at each node; the entire calculation space is discretized in a range large enough for the grounding grid model, and each small cuboid unit is divided by continuously partitioning the space with three planes parallel to the three coordinate axes; the vertices of these cuboids are called nodes; Define the conductivity σ of each node (o,p,q) For the conductivity of the cuboid to its right and above, take a sufficiently small cuboid around the node to replace the node with ΔV (o,p,q) Replace the volume of the node (o,p,q) with ΔV 3. The ground net induced visual magnetic impedance forward method of claim 1, wherein, S2 specifically comprises: S21: A sinusoidal alternating current Ie is injected in a homogeneous medium of conductivity σ at a point (x0, y0, z0) -jωt For the current density we have: In the formula, V is the volume of the calculation region, I0 is the peak value of the excitation current, ΔV represents the volume change, and ds represents the integral; According to the properties of the Dirichlet function, we have: In the formula, δ is the impulse function, r is the distance between the calculation point and the injection point, and r0 is the distance coordinate of the injection point; Let the medium be isotropic, and inject a sinusoidal AC current Ie at a point -jωt The resulting electromagnetic field has a scalar potential u given by In the formula, x, y, and z represent the three coordinate axes, respectively; S22: according to the mesh partitioning result, the formula of scalar potential u is rewritten as S o,p,q is the total area of each face of the cuboid at the node (o, p, q), n is the normal direction of the face, V o,p,q is the volume of the cuboid, so the right side of the above equation can be integrated for the six faces respectively, and then the results of the six faces are added up; S23: each partitioned node is processed according to formula (7), and the matrix equation of scalar potential can be obtained, and the value of scalar potential can be obtained by using the set solving method to calculate the equation.

4. The ground net induced visual magnetic impedance forward method of claim 3, wherein, S3 specifically comprises: S31: the relationship between current density J and scalar potential u is replaced by difference quotient using finite difference method: Where, J o,p,q is the current density at the node (o, p, q), σ o,p,q is the conductivity of the node (o, p, q), u o+1,p,q is the scalar potential value of the node (o, p, q) along the positive direction of the x-axis, u o-1,p,q is the scalar potential value of the node (o, p, q) along the negative direction of the x-axis, u o,p+1,q is the scalar potential value of the node (o, p, q) along the positive direction of the y-axis, u o,p-1,q is the scalar potential value of the node (o, p, q) along the negative direction of the y-axis, u o,p,q+1 is the scalar potential value of the node (o, p, q) along the positive direction of the z axis, u o,p,q-1 is the scalar potential value of the node (o, p, q) along the negative direction of the z-axis, Δxo is the distance between the node (o, p, q) and the next node along the positive direction of the x-axis, Δxo-1 is the distance between the node (o, p, q) and the next node along the negative direction of the x-axis, Δy p is the distance between the node (o, p, q) and the next node along the positive direction of the y-axis, Δy p-1 is the distance between the node (o, p, q) and the next node along the negative direction of the y-axis, Δzq is the distance between the node (o, p, q) and the next node along the positive direction of the z-axis, and Δzq-1 is the distance between the node (o, p, q) and the next node along the negative direction of the z-axis; The current density J is expanded in three directions of the rectangular coordinate system Where, Jx o,p,q 、Jy o,p,q and Jz o,p,q are the components of the current density J at the node (o, p, q) along the x, y, and z axes respectively; S32: each partitioned node is processed according to formula (9), and the matrix equation of current density and scalar potential can be obtained, and the value of current density can be obtained by using the set solving method to calculate the matrix equation.

5. The ground net induced magneto-impedance forward method of claim 4, wherein, S4 specifically comprises: S41: expand the left side of formula (3) Expand formula (10) in three directions of the rectangular coordinate system where H x , H y , and H z are the components of the magnetic field strength H in the x, y, z directions, respectively, and J x , J y , and J z are the components of the current density J in the x, y, z directions, respectively. S42: construct the wave equation of magnetic induction intensity from the Maxwell equations: where k is the complex wave number, B is the magnetic induction, μ is the magnetic permeability, ε is the dielectric constant, is the phase coefficient and δ is the attenuation coefficient. The frequency ω of the grounding grid excitation current, the conductivity σ of the soil, and the dielectric constant ε of the soil satisfy: Then the attenuation coefficient in the wave equation is approximately: S43: derive the calculation formula of magnetic induction intensity B according to S41 and S42: Let the number of turns of the sensor be N, and the area of the hollow in the middle of the coil be S, then the magnetic flux passing through the coil is: The induced electromotive force υ output by the coil is: Let the total resistance in the signal conditioning circuit be R 电路 , the total inductance be L 电感 , the output capacitance be C 输出 , and the other total capacitance be C 电路 , then the voltage output by the conditioning circuit is: The formula for calculating the induced apparent magnetic impedance Z is derived as: S44: Use finite difference method to replace partial differential of formula (11) to formula (13) with difference quotient: The value of the magnetic field intensity is brought into formula (21) to calculate the induced apparent magnetic impedance of each node, and the matrix equation of the induced potential magnetic impedance is listed: In the formula, A is a coefficient matrix, N is the order of the matrix, Z x , Z y , and Z z are components of the induced magneto-optic impedance Z in the x, y, and z directions, respectively. The matrix equation (25) is solved using the set solving method to obtain the induced apparent magnetic impedance of any point in space.

6. The ground net induced magneto-impedance forward method of claim 1, wherein, In S1, the set solving method is Seidel iteration method.

7. The ground net induced magneto-impedance forward method of claim 1, wherein, In S1, the set solving method is dichotomy.

8. The ground net induced magneto-impedance forward method of claim 1, wherein, In S1, the set solving method is Newton iteration method.

9. A device for the forward calculation of the apparent magnetic impedance of a grounding grid based on the finite difference method, characterized in that, The device applies the method of claim 1, comprising the following modules: A finite difference setting module for setting the mesh partitioning method and solving method of the finite difference method; A scalar potential solving module for setting the excitation mode of the grounding grid, constructing the partial differential equation of the scalar potential based on the Maxwell equation set and the characteristics of the scalar potential itself, using the set solving method to solve the partial differential equation of the scalar potential to obtain the value of the scalar potential; A current density solving module for obtaining the relationship between the scalar potential and the current density based on the Maxwell equation set, constructing the partial differential equation of the current density, and using the set solving method to solve the partial differential equation of the current density according to the value of the scalar potential to obtain the value of the current density; An induced apparent magnetic impedance simulation module for constructing the partial differential equation of the induced apparent magnetic impedance based on the Maxwell equation set and the characteristics of the induced apparent magnetic impedance, using the set solving method to solve the partial differential equation of the induced apparent magnetic impedance according to the value of the current density to obtain the three-dimensional forward simulation result of the induced apparent magnetic impedance.

10. An electronic device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The processor implements the steps of the grounding grid induced apparent magnetic impedance forward method of any one of claims 1-8 when executing the program.

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