A method and device for calculating the adjustment distance of induced earth electric field based on finite element method

Abstract

The present application relates to the technical field of induced geoelectric fields during magnetic storms, and in particular to a method and device for calculating the adjustment distance of induced geoelectric fields based on the finite element method. Among them, a method for calculating the adjustment distance of induced geoelectric fields based on the finite element method includes determining a three-dimensional earth conductivity model of the induced geoelectric field, determining a two-dimensional plane earth conductivity model based on the three-dimensional earth conductivity model; determining the distribution of the induced geoelectric field at different frequencies based on the two-dimensional plane earth conductivity model according to the finite element method; and determining the adjustment distance of the induced geoelectric field at different periods according to the distribution of the induced geoelectric field at different frequencies. The present application using the above scheme is not affected by the frequency range, and can be used to calculate the adjustment distance within the entire geomagnetic disturbance cycle, effectively improving the calculation efficiency, and laying the foundation for accurately assessing the geoelectric field and power grid risks of coastal effects during magnetic storms.

Description

Technical Field

[0001] The present application relates to the technical field of magnetic storm induced geoelectric field, and in particular to a method and device for calculating the adjustment distance of the induced geoelectric field based on the finite element method. Background Art

[0002] When a magnetic storm occurs, the violent disturbance of the geomagnetic field generates an induced geoelectric field, which induces a current with a frequency of 0.0001-0.01Hz in the grounded conductor loop, which is called geomagnetic induced current (GIC). GIC flows into the transformer, causing the core half-wave saturation, causing the transformer to experience temperature rise, vibration, and increased noise; the secondary hazards such as harmonics and reactive power fluctuations generated affect the safe operation of the entire power grid and even cause large-scale power outages. In high-latitude areas such as North America, there have been many incidents of magnetic storms invading the power grid, causing tripping and other accidents. In recent years, with the continuous expansion of the scale of the power grid, there have been many incidents of GIC endangering the power grid in low- and medium-latitude areas such as South Africa, Brazil, Australia, and Japan. my country's long-distance and large-capacity transmission lines are gradually increasing, and GIC interference incidents have also occurred in many places such as Jiangsu and Guangdong. For example: When the magnetic storm occurred on November 9, 2004, the maximum GIC recorded at the neutral point of a transformer at the Ling'ao Nuclear Power Station reached 75.5A, and its amplitude even exceeded that of high-latitude areas. Preliminary analysis shows that the cause of the large GIC at the Ling'ao Nuclear Power Plant is related to factors such as the line direction, length, and corner effect of the power grid in which it is located, and is also related to the coastal effect caused by the lateral mutation of the earth's electrical conductivity in coastal areas.

[0003] The disturbed geomagnetic field during a magnetic storm induces geoelectric currents in the ocean and the continent. Charges accumulate at the sea-land interface to ensure the continuity of the current. Since the conductivity of seawater is much greater than that of the adjacent land, the induced currents in the two media are quite different, resulting in a significant increase in the geoelectric field component perpendicular to the coast on the land side. The impact range is approximately between tens to hundreds of kilometers, which increases the GIC in the coastal power grid and may cause the power grid near the coast to suffer a greater risk of GIC. Taking the Guangdong Provincial Power Grid, which is located in the coastal area with a 500kV voltage level as the main grid, as an example, due to the large difference in the conductivity of seawater and land, the geoelectric field will be affected by the coastal effect when a magnetic storm occurs. Obviously, when assessing the risk of magnetic storm disasters in power grids, only considering the change of earth conductivity with depth and ignoring the lateral difference will lead to errors in geoelectric field calculation and distortion of risk assessment, which cannot meet engineering needs. Therefore, considering the influence of complex geoelectric structure on geoelectric field distribution is of great significance for accurately calculating grid GIC and then assessing grid risk. Among them, "adjustment distance" is an important parameter to measure the influence of geoelectric structure on geoelectric field distribution. Summary of the invention

[0004] The present application aims to solve one of the technical problems in the related art at least to some extent.

[0005] To this end, the first purpose of the present application is to propose a method for calculating the induced geoelectric field adjustment distance based on the finite element method to solve the technical problem that the results obtained by the existing method for calculating the adjustment distance are inaccurate.

[0006] The second objective of the present application is to provide a device for calculating the distance of induced earth electric field adjustment based on the finite element method.

[0007] To achieve the above-mentioned purpose, a method for calculating an induced geoelectric field adjustment distance based on a finite element method is proposed in a first aspect of the present application, comprising:

[0008] Determine a three-dimensional earth conductivity model of the induced geoelectric field, and determine a two-dimensional plane earth conductivity model based on the three-dimensional earth conductivity model;

[0009] Based on the two-dimensional plane earth conductivity model, the distribution of the induced geoelectric field at different frequencies is determined according to the finite element method;

[0010] The induced earth electric field adjustment distances at different periods are determined according to the distribution of the induced earth electric field at different frequencies.

[0011] Optionally, in one embodiment of the present application, the three-dimensional earth conductivity model for determining the induced geoelectric field includes:

[0012] The conductivity interface, land area and coastal area in the three-dimensional earth conductivity model are determined; the size of the area on both sides of the conductivity interface is not less than twice the skin depth.

[0013] Based on the three-dimensional earth conductivity model, the three-dimensional field equations with vector magnetic potential and scalar potential as unknown functions are determined according to Maxwell's equations.

[0014] Optionally, in one embodiment of the present application, determining a two-dimensional plane earth conductivity model according to the three-dimensional earth conductivity model includes:

[0015] All field quantities in the three-dimensional earth conductivity model are kept unchanged in the y-axis direction, and the current source is driven parallel to the x-axis, so as to determine the two-dimensional plane earth conductivity model and the two-dimensional field equation.

[0016] Optionally, in one embodiment of the present application, determining the distribution of the induced geoelectric field at different frequencies based on the two-dimensional plane earth conductivity model according to the finite element method includes:

[0017] Determining the control equation of the two-dimensional plane earth conductivity model according to the two-dimensional field equation;

[0018] The boundary conditions of the control equation are determined, and based on the control equation and the boundary conditions, the distribution of the induced geoelectric field at different frequencies is determined according to the finite element method.

[0019] Optionally, in one embodiment of the present application, the control equation of the two-dimensional plane earth conductivity model includes at least one of the following: a control equation of a coastal area, a control equation of a passive area, and a control equation of a land area.

[0020] Optionally, in one embodiment of the present application, the boundary condition includes at least one of the following: an upper boundary condition, a lower boundary condition, a left and right boundary condition, and a conductivity interface condition.

[0021] Optionally, in one embodiment of the present application, determining the distribution of the induced geoelectric field at different frequencies based on the two-dimensional plane earth conductivity model according to the finite element method includes:

[0022] Meshing the two-dimensional plane earth conductivity model to obtain a meshed two-dimensional plane earth conductivity model;

[0023] The grid node spacing in the two-dimensional plane earth conductivity model after the grid division is no greater than one-quarter of the skin depth, and the size of the grid node spacing is determined according to the size of the field gradient;

[0024] Based on the two-dimensional plane earth conductivity model after meshing, the distribution of the induced geoelectric field at different frequencies is determined according to the Galerkin finite element method.

[0025] Optionally, in an embodiment of the present application, determining the distribution of the induced electric field at different frequencies according to the Galerkin finite element method includes:

[0026] Determine a solution region, discretize the solution region into a plurality of triangular units, determine the vector magnetic potential of each triangular unit, and thereby determine the distribution of the induced geoelectric field in the solution region;

[0027] The vector magnetic potential of the triangular unit is determined according to the following formula:

[0028]

[0029]

[0030] Where e is any triangular unit, is the vector magnetic potential of the triangle unit e, n e is the number of nodes in the triangular element e, N i is the shape function, is the vector magnetic potential of node i in triangular element e, Δe is the area of ​​the triangular unit e, a i ,b i ,c i is the coordinate function of node i.

[0031] Optionally, in an embodiment of the present application, determining the induced earth electric field adjustment distances at different periods according to the distribution of the induced earth electric field at different frequencies includes:

[0032] The induced earth electric field adjustment distance under different periods is determined according to the following formula:

[0033]

[0034] Among them, E0 is the base value of the geoelectric field, E max is the maximum distorted electric field value, e is a constant, x is the horizontal distance from the conductivity interface, and the x that satisfies the equation is the adjustment distance of the induced earth electric field.

[0035] In summary, the method proposed in the embodiment of the first aspect of the present application determines a three-dimensional earth conductivity model of the induced geoelectric field, and determines a two-dimensional plane earth conductivity model according to the three-dimensional earth conductivity model; based on the two-dimensional plane earth conductivity model, the distribution of the induced geoelectric field at different frequencies is determined according to the finite element method; and the induced geoelectric field adjustment distance at different periods is determined according to the distribution of the induced geoelectric field at different frequencies. The present application is not affected by the frequency range and can be used to calculate the adjustment distance within the entire geomagnetic disturbance cycle, effectively improving the calculation efficiency and laying the foundation for accurately assessing the geoelectric field and power grid risks of the coastal effect during magnetic storms.

[0036] To achieve the above-mentioned purpose, a device for calculating an induced earth electric field adjustment distance based on a finite element method is proposed in a second aspect of the present application, comprising:

[0037] A model determination module, used to determine a three-dimensional earth conductivity model of the induced geoelectric field, and determine a two-dimensional plane earth conductivity model according to the three-dimensional earth conductivity model;

[0038] An electric field distribution determination module, used to determine the distribution of the induced geoelectric field at different frequencies according to the finite element method based on the two-dimensional plane earth conductivity model;

[0039] The adjustment distance determination module is used to determine the induced earth electric field adjustment distance under different periods according to the distribution of the induced earth electric field under the different frequencies.

[0040] In summary, the device proposed in the second aspect of the present application embodiment determines the three-dimensional earth conductivity model of the induced geoelectric field through the model determination module, and determines the two-dimensional plane earth conductivity model according to the three-dimensional earth conductivity model; the electric field distribution determination module determines the distribution of the induced geoelectric field at different frequencies according to the finite element method based on the two-dimensional plane earth conductivity model; the adjustment distance determination module determines the induced geoelectric field adjustment distance at different periods according to the distribution of the induced geoelectric field at different frequencies. The present application is not affected by the frequency range and can be used to calculate the adjustment distance within the entire geomagnetic disturbance cycle, effectively improving the calculation efficiency and laying the foundation for accurately evaluating the geoelectric field and power grid risks of the coastal effect during magnetic storms.

[0041] Additional aspects and advantages of the present application will be given in part in the description below, and in part will become apparent from the description below, or will be learned through the practice of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] The above and / or additional aspects and advantages of the present application will become apparent and easily understood from the following description of the embodiments in conjunction with the accompanying drawings, in which:

[0043] Figure 1 A flow chart of a method for calculating an induced geoelectric field adjustment distance based on a finite element method provided in an embodiment of the present application;

[0044] Figure 2 The geomagnetic disturbance period in the land area provided in the embodiment of the present application is 10 -1 -10 6 Schematic diagram of the results of adjusting the distance within s.

[0045] Figure 3 The geomagnetic disturbance period in the coastal area provided in the embodiment of the present application is 10 -1 -10 6 Schematic diagram of the results of adjusting the distance within s.

[0046] Figure 4 A schematic diagram of the structure of a device for calculating distance adjusted by induction geoelectric field based on finite element method provided in an embodiment of the present application. DETAILED DESCRIPTION

[0047] Embodiments of the present application are described in detail below, and examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements with the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present application, and cannot be construed as limiting the present application. On the contrary, the embodiments of the present application include all changes, modifications and equivalents that fall within the spirit and connotation of the appended claims.

[0048] The “adjustment distance” represents the distance at which the distortion field attenuates near the interface in the earth’s electrical structure. Based on the thin sheet model, Ranganayaki and Madden (RM) first proposed to determine the adjustment distance according to the following formula:

[0049]

[0050] Among them, r is the adjustment distance, τ is the conductivity of the surface layer, and λ is the resistance of the crust.

[0051] Assuming that each layer of medium is isotropically uniform, the surface conductivity τ and the crustal resistance λ are represented by the product of the conductivity and thickness of the corresponding layer and the product of the resistivity and thickness, respectively. Both high-conductivity and high-resistance media will increase the adjustment distance, and the adjustment distance is independent of the frequency of the electromagnetic field.

[0052] Since the electromagnetic induction of the earth is frequency-dependent, Weaver and Dawson (WD) gave an analytical algorithm for the frequency-dependent adjustment distance based on the generalized thin sheet model. However, since the calculation of the adjustment distance is based on the thin sheet model, the analytical calculation using the thin sheet model is subject to constraints. The thin sheet model needs to ensure that the first layer is thin enough so that the electromagnetic field remains approximately unchanged in the depth direction. The attenuation rate of the geoelectric field in the surface layer decreases with the increase of the period. For a thin sheet model with given parameters, there should be a minimum period, and all calculations should be performed within a valid range greater than the minimum period. This results in the calculation result of the adjustment distance may be incorrect under high-frequency conditions. Therefore, it is of great significance to explore the calculation method of the adjustment distance within the entire geomagnetic disturbance period range.

[0053] Example 1

[0054] Figure 1 A flow chart of a method for calculating an induced geoelectric field adjustment distance based on a finite element method provided in an embodiment of the present application.

[0055] like Figure 1 As shown, an embodiment of the present application provides a method for calculating an induced geoelectric field adjustment distance based on a finite element method, comprising the following steps:

[0056] Step 110, determining a three-dimensional earth conductivity model of the induced geoelectric field, and determining a two-dimensional plane earth conductivity model according to the three-dimensional earth conductivity model;

[0057] Step 120, based on the two-dimensional plane earth conductivity model, determine the distribution of the induced geoelectric field at different frequencies according to the finite element method;

[0058] Step 130: determining the induced earth electric field adjustment distances at different periods according to the distribution of the induced earth electric field at different frequencies.

[0059] It should be noted that the frequency of changes in the geoelectric field induced by magnetic storms is low, which meets the quasi-steady condition. For a quasi-steady electromagnetic field, the conduction current density is much greater than the displacement current density; therefore, when performing electromagnetic calculations, the displacement current density is ignored, and only the electric field generated by the change in the magnetic field is considered, while the magnetic field generated by the change in the electric field is ignored.

[0060] In an embodiment of the present application, determining a three-dimensional earth conductivity model for an induced geoelectric field includes:

[0061] The conductivity interface, land area and coastal area in the three-dimensional earth conductivity model are determined; the size of the area on both sides of the conductivity interface is not less than twice the skin depth.

[0062] Based on the three-dimensional earth conductivity model, the three-dimensional field equations with vector magnetic potential and scalar potential as unknown functions are determined according to Maxwell's equations.

[0063] Specifically, the following is a three-dimensional field equation with vector magnetic potential and scalar electric potential as unknown functions:

[0064]

[0065] in, is the driving current source, μ is the magnetic permeability, is the vector magnetic potential, σ is the conductivity, is a scalar potential.

[0066] Furthermore, the driving current source is a surface current at a certain height in the air.

[0067] Specifically, the induced electric field is only generated by the changing magnetic field, ignoring the electric field generated by stationary charges in the earth, and assuming that the earth's electrical conductivity is isotropic and does not change with time.

[0068] In an embodiment of the present application, determining a two-dimensional plane earth conductivity model according to a three-dimensional earth conductivity model includes:

[0069] All field quantities in the three-dimensional earth conductivity model are kept constant in the y-axis direction, and the current source is driven parallel to the x-axis, thereby determining the two-dimensional plane earth conductivity model and the two-dimensional field equation.

[0070] Specifically, in the two-dimensional plane earth conductivity model, the magnetic field has y and z direction components, the vector magnetic potential has only x component, and the electric field intensity and induced current have only x and z components. Therefore, the unknown function vector magnetic potential in the three-dimensional field equation becomes

[0071] In the embodiment of the present application, based on a two-dimensional planar earth conductivity model, the distribution of the induced earth electric field at different frequencies is determined according to the finite element method, including:

[0072] Determine the governing equations of the two-dimensional plane earth conductivity model based on the two-dimensional field equations;

[0073] The boundary conditions of the control equations are determined, and based on the control equations and the boundary conditions, the distribution of the induced geoelectric field at different frequencies is determined using the finite element method.

[0074] In an embodiment of the present application, the control equation of the two-dimensional plane earth conductivity model includes at least one of the following: a control equation of the coastal area, a control equation of the passive area, and a control equation of the land area.

[0075] Specifically, the following is the governing equation for the coastal area:

[0076]

[0077]

[0078] Where μ0 is the magnetic permeability, is the vector magnetic potential, σ is the conductivity, is the driving current source.

[0079] Specifically, the following is the governing equation for the passive region:

[0080]

[0081]

[0082]

[0083] Where σ is the conductivity, is the magnetic field intensity, μ is the magnetic permeability, is the scalar of magnetic field intensity in the y direction, is the electric field strength, e x , e y , e z is a unit vector.

[0084] Specifically, the following is the governing equation for the land area:

[0085]

[0086]

[0087]

[0088] in, is the vector magnetic potential, μ is the magnetic permeability, is the scalar of the vector magnetic potential in the y direction, σ is the conductivity, is the magnetic field strength, e x , e y , e z is a unit vector.

[0089] It should be noted that in typical finite element simulation software, since the eddy current field is parallel to the y-axis, the directly obtained vector magnetic potential has only the y component, the magnetic field intensity has only the x and z components, and the electric field intensity and induced current have only the y-direction component. Therefore, parameter conversion is required when calculating the distribution of the induced geoelectric field using the typical finite element simulation software 2D-FEM.

[0090] Specifically, when using the typical finite element simulation software 2D-FEM to calculate the distribution of the induced geoelectric field, the actual magnetic permeability value is assigned to the electrical conductivity, and the actual electrical conductivity value is assigned to the magnetic permeability. The vector magnetic potential in the simulation result represents the actual magnetic field intensity, the magnetic field intensity corresponds to the actual electric field intensity, and the magnetic induction intensity corresponds to the actual geocurrent density.

[0091] In the embodiment of the present application, the boundary condition includes at least one of the following: an upper boundary condition, a lower boundary condition, a left and right boundary condition, and a conductivity interface condition.

[0092] Specifically, when the distribution of the induced electric field is calculated using the typical finite element simulation software 2D-FEM,

[0093] In the upper boundary condition, the ground serves as the upper boundary of the two-dimensional planar earth conductivity model, the magnetic field is parallel to the conductivity interface, and the magnetic field intensity is assigned to the vector magnetic potential according to parameter conversion.

[0094] In the lower boundary condition, the vector magnetic potential decays to 0 when it is far enough away from the driving current source, that is,

[0095] In the left and right boundary conditions, the ground current and magnetic field are perpendicular to the boundary respectively, and the scalar potentials of the left and right boundaries are equal to ensure the continuity of the current, that is,

[0096] In the conductivity interface condition, the normal component of the current density and the tangential component of the magnetic field intensity are both continuous.

[0097] In the embodiment of the present application, based on a two-dimensional planar earth conductivity model, the distribution of the induced earth electric field at different frequencies is determined according to the finite element method, including:

[0098] Meshing the two-dimensional plane earth conductivity model to obtain a two-dimensional plane earth conductivity model after meshing;

[0099] The grid node spacing in the two-dimensional plane earth conductivity model after grid division is no more than one quarter of the skin depth, and the size of the grid node spacing is determined according to the size of the field gradient;

[0100] Based on the two-dimensional plane earth conductivity model after meshing, the distribution of the induced geoelectric field at different frequencies is determined according to the Galerkin finite element method.

[0101] Specifically, the mesh node spacing close to the boundary is less than one-quarter of the skin depth.

[0102] Specifically, when the field gradient is less than a set threshold, a sparse grid is used; otherwise, a dense grid is used.

[0103] In the embodiment of the present application, the distribution of the induced geoelectric field at different frequencies is determined according to the Galerkin finite element method, including:

[0104] Determine the solution area, discretize the solution area into a plurality of triangular units, determine the vector magnetic potential of each triangular unit, and thus determine the distribution of the induced geoelectric field in the solution area;

[0105] The vector magnetic potential of the triangular unit is determined according to the following formula:

[0106]

[0107]

[0108] Where e is any triangular unit, is the vector magnetic potential of the triangle unit e, n e is the number of nodes in the triangular element e, N i is the shape function, is the vector magnetic potential of node i in triangular element e, Δ e is the area of ​​the triangular unit e, a i ,b i ,c i is the coordinate function of node i.

[0109] Specifically, according to the Galerkin weighted residual method, the weight function Q is i is the shape function N i , we get the following formula:

[0110]

[0111] Where e is any triangular unit, ΔΩ is the subdomain corresponding to the triangular unit, μ0 is the magnetic permeability, and n e is the number of nodes in the triangular element e, is the vector magnetic potential of node i in triangular unit e, σ is the conductivity, is the driving current source, and Ω is the solution region. In the formula, the weighted integral of the residual of each triangular element is calculated, and the cumulative sum is zero.

[0112] In the embodiment of the present application, determining the adjustment distance of the induced geoelectric field in different periods according to the distribution of the induced geoelectric field at different frequencies includes:

[0113] Determine the adjustment distance of the induced geoelectric field in different periods according to the following formula:

[0114]

[0115] where E0 is the base value of the geoelectric field, E max is the maximum distorted electric field value, e is a constant, x is the horizontal distance from the conductivity interface, and the x that satisfies the equation is the adjustment distance of the induced geoelectric field.

[0116] Taking a scenario as an example, based on a three-dimensional earth conductivity model with the conductivity interface at x = 0, the land area at x < 0 and x > 0 and z < -0.2 km, and the seawater area at x > 0 and -0.2 km < z < 0, calculate the adjustment distance of the induced geoelectric field. The specific steps are as follows:

[0117] Step 210, simplify the three-dimensional earth conductivity model into a two-dimensional earth conductivity model;

[0118] Step 220, determine the control equation and boundary conditions in the two-dimensional earth conductivity model; among them, in the upper boundary condition

[0119] Step 230, perform mesh division on the two-dimensional planar earth conductivity model. Based on the two-dimensional planar earth conductivity model after mesh division, set the frequency range, and determine the distribution of the induced geoelectric field at different frequencies according to the Galerkin finite element method.

[0120] Step 240, calculate the adjustment distance of the induced geoelectric field in different periods according to the horizontal distance from the conductivity interface corresponding to the distance where the electric field base value near the conductivity interface increases by 1 / e of the electric field distortion value.

[0121] Specifically, Figure 2 is the result of the adjustment distance in the land area when the geomagnetic disturbance period is within 10 -1 -10 6 s, Figure 3 is the adjustment distance in the coastal area when the geomagnetic disturbance period is within 10 -1 -10 6The result of the adjustment distance within s, wherein the solid line is the adjustment distance calculated by the method proposed in the embodiment of the present application; the dashed line is the frequency-dependent adjustment distance proposed by WD; the dotted line is the frequency-independent adjustment distance defined by RM; the dotted line is the adjustment distance obtained by the analytical solution of dErceville and G.Kunetz;

[0122] Furthermore, for long periods, the electric field attenuates only a small amount when passing through the surface layer, meeting the thin sheet standard. At this time, the calculation results of WD, RM and the method proposed in the embodiment of the present application are all valid; for the intermediate frequency range, only the method proposed in the embodiment of the present application can be used to calculate the adjustment distance; for short periods, since the skin depth is easily less than the surface thickness at high frequencies, the areas on both sides of the coastline are regarded as uniform quarter spaces. In summary, the calculation results further verify that the method proposed in the embodiment of the present application is applicable to the calculation of the adjustment distance within the entire period range.

[0123] In summary, the method proposed in the embodiment of the first aspect of the present application determines the three-dimensional earth conductivity model of the induced geoelectric field, and determines the two-dimensional plane earth conductivity model according to the three-dimensional earth conductivity model; based on the two-dimensional plane earth conductivity model, the distribution of the induced geoelectric field at different frequencies is determined according to the finite element method; according to the distribution of the induced geoelectric field at different frequencies, the induced geoelectric field adjustment distance at different periods is determined. The present application is not affected by the frequency range and can be used to calculate the adjustment distance within the entire geomagnetic disturbance cycle, effectively improving the calculation efficiency and laying the foundation for accurately assessing the geoelectric field and power grid risks of the coastal effect during magnetic storms.

[0124] In order to implement the above embodiment, the present application also proposes a device for calculating the distance of adjusting the induction electric field based on the finite element method.

[0125] Figure 4 A schematic diagram of the structure of a device for calculating distance adjustment by induction geoelectric field based on finite element method provided in an embodiment of the present application.

[0126] like Figure 4 As shown, a device for calculating the distance of adjusting the induction earth electric field based on the finite element method comprises:

[0127] A model determination module 410 is used to determine a three-dimensional earth conductivity model of the induced geoelectric field, and determine a two-dimensional plane earth conductivity model according to the three-dimensional earth conductivity model;

[0128] The electric field distribution determination module 420 is used to determine the distribution of the induced geoelectric field at different frequencies based on the two-dimensional plane earth conductivity model and the finite element method;

[0129] The adjustment distance determination module 430 is used to determine the induced earth electric field adjustment distances at different periods according to the distribution of the induced earth electric field at different frequencies.

[0130] In summary, the device proposed in the second aspect of the embodiment of the present application determines the three-dimensional earth conductivity model of the induced geoelectric field through the model determination module, and determines the two-dimensional plane earth conductivity model according to the three-dimensional earth conductivity model; the electric field distribution determination module determines the distribution of the induced geoelectric field at different frequencies according to the finite element method based on the two-dimensional plane earth conductivity model; the adjustment distance determination module determines the induced geoelectric field adjustment distance at different periods according to the distribution of the induced geoelectric field at different frequencies. The present application is not affected by the frequency range and can be used to calculate the adjustment distance within the entire geomagnetic disturbance cycle, effectively improving the calculation efficiency and laying the foundation for accurately assessing the geoelectric field and power grid risks of the coastal effect during magnetic storms.

[0131] It should be noted that, in the description of this application, the terms "first", "second", etc. are only used for descriptive purposes and cannot be understood as indicating or implying relative importance. In addition, in the description of this application, unless otherwise specified, the meaning of "plurality" is two or more.

[0132] Any process or method description in a flowchart or otherwise described herein may be understood to represent a module, segment or portion of code that includes one or more executable instructions for implementing the steps of a specific logical function or process, and the scope of the preferred embodiments of the present application includes alternative implementations in which functions may not be performed in the order shown or discussed, including performing functions in a substantially simultaneous manner or in the reverse order depending on the functions involved, which should be understood by technicians in the technical field to which the embodiments of the present application belong.

[0133] It should be understood that the various parts of the present application can be implemented by hardware, software, firmware or a combination thereof. In the above-mentioned embodiments, multiple steps or methods can be implemented by software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented by hardware, as in another embodiment, it can be implemented by any one of the following technologies known in the art or their combination: a discrete logic circuit having a logic gate circuit for implementing a logic function for a data signal, a dedicated integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0134] A person skilled in the art may understand that all or part of the steps in the method for implementing the above-mentioned embodiment may be completed by instructing related hardware through a program, and the program may be stored in a computer-readable storage medium, which, when executed, includes one or a combination of the steps of the method embodiment.

[0135] In addition, each functional unit in each embodiment of the present application may be integrated into a processing module, or each unit may exist physically separately, or two or more units may be integrated into one module. The above-mentioned integrated module may be implemented in the form of hardware or in the form of a software functional module. If the integrated module is implemented in the form of a software functional module and sold or used as an independent product, it may also be stored in a computer-readable storage medium.

[0136] The storage medium mentioned above can be a read-only memory, a magnetic disk or an optical disk, etc.

[0137] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner.

[0138] Although the embodiments of the present application have been shown and described above, it can be understood that the above embodiments are exemplary and cannot be understood as limitations on the present application. Ordinary technicians in this field can change, modify, replace and modify the above embodiments within the scope of the present application.

Claims

1. A method for calculating the induced geoelectric field adjustment distance based on the finite element method, characterized in that: The method comprises: Determine a three-dimensional earth conductivity model of the induced geoelectric field, and determine a two-dimensional plane earth conductivity model based on the three-dimensional earth conductivity model, wherein the conductivity interface, land area and coastal area in the three-dimensional earth conductivity model are determined; the size of the area on both sides of the conductivity interface is not less than twice the skin depth, and based on the three-dimensional earth conductivity model, determine a three-dimensional field equation with vector magnetic potential and scalar potential as unknown functions according to Maxwell's equations, keep all field quantities in the three-dimensional earth conductivity model unchanged in the y-axis direction, and drive the current source parallel to the x-axis, so as to determine the two-dimensional plane earth conductivity model and the two-dimensional field equation; Based on the two-dimensional plane earth conductivity model, the distribution of the induced geoelectric field at different frequencies is determined according to the finite element method; The induced earth electric field adjustment distances at different periods are determined according to the distribution of the induced earth electric field at different frequencies.

2. The method according to claim 1, characterized in that The method of determining the distribution of the induced geoelectric field at different frequencies based on the two-dimensional plane earth conductivity model according to the finite element method includes: Determining the control equation of the two-dimensional plane earth conductivity model according to the two-dimensional field equation; The boundary conditions of the control equation are determined, and based on the control equation and the boundary conditions, the distribution of the induced geoelectric field at different frequencies is determined according to the finite element method.

3. The method according to claim 2, characterized in that The control equation of the two-dimensional plane earth conductivity model includes at least one of the following: a control equation for a coastal area, a control equation for a passive area, and a control equation for a land area.

4. The method according to claim 2, characterized in that The boundary conditions include at least one of the following: an upper boundary condition, a lower boundary condition, a left boundary condition, a right boundary condition, and a conductivity interface condition.

5. The method according to claim 1, characterized in that The method of determining the distribution of the induced geoelectric field at different frequencies based on the two-dimensional plane earth conductivity model according to the finite element method includes: Meshing the two-dimensional plane earth conductivity model to obtain a meshed two-dimensional plane earth conductivity model; The grid node spacing in the two-dimensional plane earth conductivity model after the grid division is no greater than one-quarter of the skin depth, and the size of the grid node spacing is determined according to the size of the field gradient; Based on the two-dimensional plane earth conductivity model after meshing, the distribution of the induced geoelectric field at different frequencies is determined according to the Galerkin finite element method.

6. The method according to claim 5, characterized in that Determining the distribution of the induced geoelectric field at different frequencies according to the Galerkin finite element method includes: Determine a solution region, discretize the solution region into a plurality of triangular units, determine the vector magnetic potential of each triangular unit, and thereby determine the distribution of the induced geoelectric field in the solution region; The vector magnetic potential of the triangular unit is determined according to the following formula: Where e is any triangular unit, is the vector magnetic potential of the triangle unit e, n e is the number of nodes in the triangular element e, N i is the shape function, is the vector magnetic potential of node i in triangular element e, Δ e is the area of ​​the triangular unit e, a i ,b i ,c i is the coordinate function of node i.

7. The method according to claim 1, characterized in that The step of determining the induced geoelectric field adjustment distances at different periods according to the distribution of the induced geoelectric field at different frequencies includes: The induced earth electric field adjustment distance under different periods is determined according to the following formula: Among them, E0 is the base value of the geoelectric field, E max is the maximum distorted electric field value, e is a constant, x is the horizontal distance from the conductivity interface, and the x that satisfies the equation is the adjustment distance of the induced earth electric field.

8. A device for calculating the distance of induced earth electric field adjustment based on finite element method, characterized in that: The device comprises: A model determination module is used to determine a three-dimensional earth conductivity model of an induced geoelectric field, and to determine a two-dimensional plane earth conductivity model according to the three-dimensional earth conductivity model, wherein a conductivity interface, a land area, and a coastal area in the three-dimensional earth conductivity model are determined; the size of the area on both sides of the conductivity interface is not less than twice the skin depth, and based on the three-dimensional earth conductivity model, a three-dimensional field equation with vector magnetic potential and scalar potential as unknown functions is determined according to Maxwell's equations, and all field quantities in the three-dimensional earth conductivity model are kept unchanged in the y-axis direction, and a current source is driven parallel to the x-axis, thereby determining a two-dimensional plane earth conductivity model and a two-dimensional field equation; An electric field distribution determination module, used to determine the distribution of the induced geoelectric field at different frequencies according to the finite element method based on the two-dimensional plane earth conductivity model; The adjustment distance determination module is used to determine the induced earth electric field adjustment distance under different periods according to the distribution of the induced earth electric field under the different frequencies.

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