A method for calculating three-dimensional HVDC grounding current using a multi-resolution model

Abstract

This invention discloses a multi-resolution three-dimensional model calculation method for HVDC grounding current, comprising the following steps: 1) establishing a geological model of the radiation current field region of the HVDC grounding electrode, and meshing the geological model to obtain a geological mesh model; 2) setting potential sampling points at the center of each mesh in the geological mesh model; 3) constructing a multi-resolution three-dimensional resistance network; 4) establishing the node admittance matrix of the three-dimensional resistance network; 5) establishing the system equations, and solving the system equations using the stable double conjugate gradient method with over-relaxation preprocessing to obtain the surface potential distribution information. This method can be widely applied to the measurement work of the electrode sites in the early stages of HVDC transmission planning, and has good practical value and application prospects for quickly and accurately simulating and calculating the surface potential distribution and selecting HVDC grounding electrode sites that meet safety regulations.

Description

Technical Field

[0001] This invention relates to the fields of electrical engineering power systems and electromagnetic calculations, specifically a method for calculating multi-resolution HVDC grounding current three-dimensional model. Background Technology

[0002] High-voltage direct current (HVDC) transmission technology is suitable for long-distance, high-capacity power transmission projects. Due to the special architecture and operation mode of HVDC transmission lines, thousands of amperes of DC current are injected into the ground under unipolar operation, generating ground current resistance (GRC) and electric current surge protection (ESP). Untreated industrial stray currents flowing into the AC power grid can cause DC bias in transformers. Therefore, accurate calculation of the neutral point current in substations is crucial for the safe operation of the power grid.

[0003] Currently, the field-circuit coupling method is widely used for calculating ESP and DC bias current, and can be divided into direct coupling and indirect coupling methods. The direct coupling method uses partial differential equations to solve for the potential distribution caused by surface power sources, and then substitutes the potential difference into the power grid model to calculate the neutral point current. However, it neglects the current shunting effect of overhead lines, leading to inaccurate calculation results. The indirect coupling method treats the ground as an equivalent resistance and calculates GRC and ESP by establishing a circuit model combining the ground and the power grid. However, complex underground electrical structures are difficult to simulate, and the calculation process is very cumbersome. Based on resistivity characteristics, a more practical 3D resistivity network (RN) was directly established, which can simulate complex underground electrical structures. Although this method is accurate, the authors used a structured hexahedral mesh when calculating the underground electric field, which drastically increased the computational load.

[0004] Unstructured hexahedral meshes, used in finite volume methods and finite element methods, have received considerable attention over the past decade. However, unstructured meshes also present several challenges: relatively difficult mesh setup, potential matrix ill-conditioning due to poor aspect ratios, and the need for extensive post-processing. Some researchers have proposed an optimization scheme for FEM, using a basically structured hexahedral finite element mesh but employing non-conforming elements for local refinement. This approach allows for variable resolution within a basically structured mesh while maintaining a consistent aspect ratio. Multi-resolution (MR) meshes have been widely applied in many fields; however, research on calculating the HVDC grounding electrode current field using the 3DRN method with MR meshes is limited. Summary of the Invention

[0005] The purpose of this invention is to provide a method for calculating a three-dimensional model of HVDC grounding current with multi-resolution resolution, comprising the following steps:

[0006] 1) Establish a geological model of the radiation current field region of the grounding electrode of high voltage direct current transmission, and use a multi-resolution method to mesh the geological model to obtain a geological mesh model;

[0007] 2) Set the potential sampling points at the center of each grid in the geological body grid model;

[0008] 3) Calculate the axial resistance within a single grid and linearly combine the axial resistances of adjacent grids to construct a three-dimensional resistance network based on multi-resolution.

[0009] 4) Establish the nodal admittance matrix of the three-dimensional resistive network;

[0010] 5) Based on the nodal admittance matrix and current source of the three-dimensional resistive network, the system equation is established, and the stable double conjugate gradient method with over-relaxation preprocessing is used to solve the system equation to obtain the surface potential distribution information.

[0011] Furthermore, the geological body mesh model includes several coarse meshes; the coarse meshes include several fine meshes.

[0012] Furthermore, the grid data storage format in the geological body grid model is as follows:

[0013]

[0014]

[0015] In the formula, CL(i) is the coarseness level of the fine mesh, CL(i+1) is the coarseness level of the coarse mesh, and s(:,:,i) is the mesh data storage format of the i-th layer.

[0016] Furthermore, the three-dimensional resistive network is shown below:

[0017]

[0018] In the formula, S i+1,j,k S represents the area of ​​the fine grid. i,j,k h represents the area of ​​the coarse grid. c h is the length of the coarse grid edge. f R is the length of the fine mesh edge. 粗 R 细 ρ represents the central resistance of the coarse grid and the central resistance of the fine grid in the geological body mesh model, respectively; i,j,k ρ i+1,j,k These represent the resistivity of the coarse grid and the resistivity of the fine grid in the geological body grid model, respectively.

[0019] Furthermore, the system equations are as follows:

[0020]

[0021] In the formula, A is the nodal admittance matrix of the three-dimensional resistive network; The potential to be solved is denoted as ; S is a known power source term.

[0022] Furthermore, the steps for solving the system equations using the stable double conjugate gradient method after over-relaxation preprocessing to obtain the surface potential distribution information include:

[0023] 1) Given the system matrix A, vector b, initial approximate solution x0 of the system equations, and maximum allowable error ε max Maximum number of iterations j max Random numbers Calculate the initial residual value r0 = b - Ax0, set the parameter p0 = r0, and let the iteration number j = 0; where vector b represents the high voltage direct current transmission current;

[0024] 2) Calculation parameters r j Let p be the residual of the j-th iteration; parameter p j p j =r j +β j-1 (p j-1 -ω j-1 Ap j-1 );ω j-1 β j-1 For the (j-1)th iteration;

[0025] 3) Calculate parameter s j =r j -α j Ap j ;

[0026] 4) Calculate parameter ω j =(As j ,s j ) / (As j As j );

[0027] 5) Calculate the initial approximate solution x of the system equations in the (j+1)th iteration. j+1 =x j +α j p j +ω j s j ;

[0028] 6) Calculate the residual r of the (j+1)th iteration. j+1 =s j -ω j As j ;

[0029] 7) Determine the residual r j+1 ≤ε max or j > j maxIf the condition is met, output the initial approximate solution of the system equations; otherwise, let j = j + 1 and proceed to step 8).

[0030] 8) Calculate parameter p j+1 =r j+1 +β j (p j -ω j Ap j ), and return to step 2); where, the parameter

[0031] It is worth noting that this invention specifically relates to the calculation of ground return current (GRC), surface potential (ESP), and transformer neutral point current caused during high-voltage direct current (HVDC) transmission. First, a field-circuit coupling method based on 3D resistive networks is proposed to accurately calculate ESP. Then, a multi-resolution resistive network forward modeling algorithm is proposed to improve computational efficiency. Finally, a method superior in accuracy to the traditional structured grid (SG) method is proposed. The effectiveness of the proposed algorithm is verified through forward modeling of hierarchical models and 3D non-uniform models, as well as response error analysis. Experiments show that, compared with the results of traditional resistive networks, the multi-resolution method improves computational efficiency without affecting the solution accuracy.

[0032] The technical advantages of this invention are undeniable. Compared with existing surface potential simulation techniques, this method improves computational efficiency over large areas by modeling geological bodies and considering a three-dimensional model with arbitrary resistivity distributions, making it closer to reality and resulting in a more reasonable solution process. It solves the problem of low efficiency or even inability to solve the system matrix when the number of grid cells is sufficiently large, and the computational model is essentially consistent with reality, ensuring the accuracy of the calculation results.

[0033] The method of this invention can be widely used in the measurement of pole sites in the early stage of DC transmission planning. It has good practical value and application prospects for quickly and accurately simulating and calculating the surface potential distribution and selecting DC grounding pole sites that meet safety regulations. Attached Figure Description

[0034] Figure 1 This is a flowchart of the method of the present invention;

[0035] Figure 2 This is a schematic diagram of a multi-resolution grid structure;

[0036] Figure 3 A schematic diagram of the axial resistance of a structured grid;

[0037] Figure 4 A schematic diagram of the axial resistance of a multi-resolution grid;

[0038] Figure 5Pseudocode diagram of the BiCGSTAB method;

[0039] Figure 6 This is a schematic diagram of the main cross-section of the three-dimensional layered model;

[0040] Figure 7 This paper compares the forward modeling results of the RN method based on MR meshes with three equivalent resistances (CS, FS, and GF), the RN method based on SG, and the forward modeling results of FEM.

[0041] Figure 8 The relative errors of MR-RN, SG-RN and FEM using CS, FS, and GP are compared.

[0042] Figure 9 (a)-(e) Comparison of the relative error (%) of ESP for MR grids and SG boundary strategies with different scaling factors (log10 transformation). Detailed Implementation

[0043] The present invention will be further described below with reference to embodiments, but it should not be construed that the scope of the present invention is limited to the following embodiments. Various substitutions and modifications made based on ordinary technical knowledge and common practices in the art without departing from the above-described technical concept of the present invention should be included within the scope of protection of the present invention.

[0044] Example 1:

[0045] See Figures 1 to 9 A method for calculating a three-dimensional model of HVDC grounding current with multi-resolution resolution includes the following steps:

[0046] 1) Establish a geological model of the radiation current field region of the grounding electrode of high voltage direct current transmission, and use a multi-resolution method to mesh the geological model to obtain a geological mesh model;

[0047] The geological body grid model includes several coarse grids; the coarse grids include several fine grids.

[0048] The data storage method for MR meshes differs from that of SG meshes, referencing the data storage method of octree meshes. A coarse mesh consists of eight identical fine meshes. The array space occupied by the coarse mesh should be the same as that occupied by the fine meshes. The thickness is placed in the top left corner of the array, and missing positions are filled with 0s. This allows for quick identification of adjacent meshes, represented as:

[0049]

[0050]

[0051] Where CL(i) is the coarseness level of the fine mesh, CL(i+1) is the coarseness level of the coarse mesh, and s(:,:,i) is the data storage format of the mesh at layer i. Because there are columns with all values ​​of 0 in the rows and arrays, the loaded system matrix is ​​unordered and cannot be solved. The conjugate Hermite matrix can be obtained by deleting all rows and columns with 0 values ​​from the array. This solves the data storage problem of the MR mesh, and the positions of each component are easy to sort and locate.

[0052] 2) Set the potential sampling points at the center of each grid in the geological body grid model;

[0053] 3) Calculate the axial resistance within a single grid and linearly combine the axial resistances of adjacent grids to construct a three-dimensional resistance network based on multi-resolution.

[0054] The three-dimensional resistor network is shown below:

[0055]

[0056] In the formula, S i+1,j,k S represents the area of ​​the fine grid. i,j,k h represents the area of ​​the coarse grid. c h is the length of the coarse grid edge. f R is the length of the fine mesh edge. 粗 R 细 ρ represents the central resistance of the coarse grid and the central resistance of the fine grid in the geological body mesh model, respectively. i,j,k ρ i+1,j,k These represent the resistivity of the coarse grid and the resistivity of the fine grid in the geological body grid model, respectively.

[0057] 4) Establish the nodal admittance matrix of the three-dimensional resistive network;

[0058] 5) Based on the nodal admittance matrix and current source of the three-dimensional resistive network, the system equation is established, and the stable double conjugate gradient method with over-relaxation preprocessing is used to solve the system equation to obtain the surface potential distribution information.

[0059] The system equations are as follows:

[0060]

[0061] In the formula, A is the nodal admittance matrix of a three-dimensional resistive network with conductivity as a parameter; The potential to be solved is denoted as ; S is a known power source term.

[0062] The steps for solving the system equations using the stable biconjugate gradient method with over-relaxation preprocessing to obtain the surface potential distribution information include:

[0063] 5.1) Given the system matrix A, vector b, initial approximate solution x0 of the system equations, and maximum allowable error ε max Maximum number of iterations j max Random numbers Calculate the initial residual value r0 = b - Ax0, set the parameter p0 = r0, and let the iteration number j = 0; where b is the ground current of the grounding electrode, which is the high voltage DC transmission current of 6250A.

[0064] 5.2) Calculation parameters r j Let be the residual of the j-th iteration;

[0065] 5.3) Calculate parameter s j =r j -α j Ap j ;

[0066] 5.4) Calculate parameter ω j =(As j ,s j ) / (As j As j );

[0067] 5.5) Calculate the initial approximate solution x of the system equation in the (j+1)th iteration. j+1 =x j +α j p j +ω j s j ;

[0068] 5.6) Calculate the residual r of the (j+1)th iteration. j+1 =s j -ω j As j ;

[0069] 5.7) Determine the residual r j+1 ≤ε max or j > j max If the condition is met, output the initial approximate solution of the system equations; otherwise, let j = j + 1 and proceed to step 5.8.

[0070] 5.8) Calculate parameter p j+1 =r j+1 +β j (p j -ω j Ap j ), and return to step 5.2); where, the parameter

[0071] Example 2:

[0072] A forward modeling method for HVDC grounding current based on a multi-resolution three-dimensional model includes the following steps:

[0073] First, the geological body of the HVDC transmission grounding electrode radiation current field region is divided into a hexahedral grid using a multi-resolution method, and potential sampling points are set at the grid center. Axial resistance within a single grid is calculated in the structured grid region. All grid center units are connected along the x, y, and z directions. To address the issue of dangling nodes between grids with different edge lengths, the equivalent resistance between coarse and fine grids is calculated. A three-dimensional resistance network based on multi-resolution is constructed by linearly combining the axial resistance of adjacent units. By finding the coupling coefficients between nodes, the nodal admittance matrix of the three-dimensional resistance network is established, and combined with the current field source to form a system equation. The stable double conjugate gradient (BICDSTAB) method with over-relaxation preprocessing (SOR) is used to solve the system equation to obtain the surface potential distribution information. The specific implementation steps are as follows:

[0074] (1) Discrete subdivision of geological bodies

[0075] The propagation of direct current through the geoelectric structure involves only the resistive effect of the structure on the current. This effect can be achieved by transforming the resistivity structure into a resistive structure, which requires discretization of the geoelectric structure. Multi-resolution methods, unlike structured meshes, possess spatial recursive properties, such as... Figure 2 As shown, the coarse grid consists of multiple sub-grids, and its data storage method differs from that of the structured grid. Figure 2 Taking a medium MR mesh as an example, the coarse mesh consists of 8 identical fine meshes. Based on the fine meshes, the array space occupied by the coarse mesh should be the same as that of the fine meshes. We place the coarse mesh's thickness in the top left corner of the array, and fill missing positions with 0s. This allows us to quickly find neighboring meshes.

[0076]

[0077]

[0078] Where 1 represents the fine mesh coarseness, 2 represents the coarse mesh coarseness, and s(:,:,i) is the data storage format for the i-th layer mesh. Because the array contains rows and columns of all zeros, the loaded system matrix is ​​not full rank and cannot be solved. Removing the rows and columns of all zeros yields the conjugate Hermite matrix. This solves the data storage problem of the MR mesh, and the positions of each component are easy to sort and locate.

[0079] (2) Establishment of multi-resolution three-dimensional resistive network

[0080] When a structured grid exists in a geological body region, connecting all cell centers along the x, y, and z directions and linearly combining the axial resistances of adjacent cells can form an attached grid. Figure 3 The three-dimensional resistor network shown.

[0081]

[0082] In the formula, ρ i Let be the resistivity of the i-th cell, and dx, dy, and dz be the lengths of the cell grid in the three directions, respectively.

[0083] The connection method between coarse mesh elements and their associated fine mesh elements in three-dimensional space is as follows: Figure 4 As shown, two resistors are connected between nodes. These two resistors are the coarse grid suspension resistor and the fine grid suspension resistor, respectively. This method avoids the ambiguity of the definition when they are coplanar and coaxial.

[0084]

[0085] Here S i+1,j,k From the area of ​​the fine grid, S i,j,k h represents the area of ​​the coarse grid. c h is the length of the coarse mesh edge. f This represents the length of the fine grid edge.

[0086] (3) Establishment and post-processing of system matrix equations

[0087] The numerical discretization method will ultimately assemble into a system equation:

[0088]

[0089] Where A is the system matrix with conductivity parameters. The potential to be solved is denoted by S, and S is a known power source term. Only the node containing the ground electrode has a value in this column vector; all other nodes are zero. It is worth noting that the nodal admittance matrix A typically has a large dimension, and most of its area is zero. Therefore, to save computational memory and reduce computation time, A needs to be stored as a sparse matrix. To quickly and accurately solve the nodal voltage equations, considering the sparsity, symmetry, and large dimension of the nodal admittance matrix A, the stable biconjugate gradient (BiCGSTAB) method is used to iteratively solve the equations. Then, the surface potential distribution can be obtained by taking the node potential at the ground surface location. The pseudocode for the BiCGSTAB method is attached. Figure 5 As shown.

[0090] Example 3:

[0091] Multi-resolution methods were applied to 3DRN numerical simulation studies. Based on a fine mesh, the empty spaces in the coarse mesh of the system matrix were filled with zeros, solving the matrix storage problem of the MR mesh. The challenge lies in the suspended surfaces and nodes at the interface between the coarse and fine meshes. Differential operators of varying precision were used, and spatial element interpolation was employed to address the current transfer problem at the coarse-fine mesh interface. The effectiveness of the MR-RN method based on second-order precision differential operators was verified by comparing the calculated equivalent resistances of suspended nodes with different precisions. In the layered model, the MR mesh was used to effectively subdivide the outer boundary. The calculation results were compared with those from CDEGS software, demonstrating the accuracy of the proposed boundary strategy. In the heterogeneous geological model, a comparison of the computational accuracy and time with the finite element method showed that the RN method based on the MR mesh can improve computational efficiency. In the field-circuit coupling model, the MR method was used to refine the mesh in the area near the substation, and the model's accuracy was verified by comparing it with the finite element method. To demonstrate the necessity of using the MR method in large-area models, the influence of resistivity changes near the grounding electrode and the large fault zone of the substation on the neutral current was analyzed. The specific implementation steps are as follows:

[0092] (1) Layered model

[0093] To verify the feasibility and accuracy of MR mesh calculation for ESP, this embodiment first considers a simple multi-layer soil model. In this model, the DC currents entering and exiting the soil are set to 6250A and -6250A respectively (ignoring the influence of current shunting from other grounding electrodes), representing the actual injected current values ​​of the HVDC transmission system. This embodiment uses three suspension resistance setting methods: CS, FS, and GF. The calculation results are compared with the forward modeling results of FEM.

[0094] like Figure 7 As shown, the forward modeling results of the MR mesh are highly consistent with those of the SG mesh, with the CS-RN curve (yellow) nearly coinciding with the FS-RN (blue) and SG-RN (red) curves. This indicates that the forward modeling algorithm in this embodiment is accurate and reliable, and the forward modeling time of the MR mesh is reduced by 96% compared to SG.

[0095] Figure 8 An error comparison plot is shown for MR grids using three suspension resistors CS, FS, and GF. (See figure) Figure 8 As shown, the relative error of GF near the source and model center is approximately 1%, while the relative errors of CS and FS near the source and model center are approximately 20%. The difference operators have a significant impact on the computational accuracy across the entire region. The accuracy of GF with second-order equivalent resistance is equivalent to that of SG with a fully fine mesh.

[0096] (2) Boundary Strategy

[0097] To improve calculation accuracy near the underground boundary, a region expansion is performed at the model boundary. When sufficiently far from the electrode center, an appropriate potential value can be zero. When the model is symmetrically set, the origin is located at the center of the surface.

[0098] exist Figure 9 In this embodiment, the ESP results of truncated and extended boundaries are compared with those of various meshing strategies. The boundary ESPs corresponding to the different boundary strategies are completely different. This embodiment uses the calculation results of CDEGS software as the benchmark solution, calculates the relative error (%) distribution of surface potential, and performs a logarithmic transformation.

[0099] like Figure 9 As shown in Figure a, compared to the benchmark solution, SG0 with truncated boundaries deviates by 100% at the ESP boundary. The mesh aspect ratio of SG5 in the extended edge region is significantly different from that of the regular hexahedron. Figure 9 b shows that the potential at the boundary of the computational region has a large relative error compared with the reference solution, approximately 10%. Figure 9 c and 9e show the computational accuracy of SG1.75 and SG1.05. In the extended region, the mesh aspect ratio of SG1.2005 is close to that of a regular hexahedron, and the relative error of the potential at the boundary of the computational region is less than 1% compared with the benchmark solution. Therefore, as the edge expansion coefficient decreases, the accuracy of the forward simulation results at the computational boundary is improved, but at the same time, the number of mesh elements increases, which directly leads to an increase in the degrees of freedom of the system matrix and the computation time of SG1.05.

[0100] When this embodiment uses MR mesh to extend the boundary, such as Figure 9 As shown in d, the relative error of the boundary potential is less than 1%, and the number of mesh elements is only half that of SG1.05. Compared with SG1.2005, the MR mesh saves 99%.

[0101] Example 3:

[0102] A method for calculating a three-dimensional model of HVDC grounding current with multi-resolution includes the following steps:

[0103] 1) Establish a geological model of the radiation current field region of the grounding electrode of high voltage direct current transmission, and use a multi-resolution method to mesh the geological model to obtain a geological mesh model;

[0104] 2) Set the potential sampling points at the center of each grid in the geological body grid model;

[0105] 3) Calculate the axial resistance within a single grid and linearly combine the axial resistances of adjacent grids to construct a three-dimensional resistance network based on multi-resolution.

[0106] 4) Establish the nodal admittance matrix of the three-dimensional resistive network;

[0107] 5) Based on the nodal admittance matrix and current source of the three-dimensional resistive network, the system equation is established, and the stable double conjugate gradient method with over-relaxation preprocessing is used to solve the system equation to obtain the surface potential distribution information.

[0108] Example 4:

[0109] A method for calculating HVDC grounding current using a three-dimensional model with multi-resolution resolution is described in Example 3. The geological grid model includes several coarse grids, and the coarse grids include several fine grids.

[0110] Example 5:

[0111] A method for calculating HVDC grounding current using a three-dimensional model with multi-resolution resolution is described in Example 3. The grid data storage format in the geological body grid model is as follows:

[0112]

[0113]

[0114] In the formula, CL(i) is the coarseness level of the fine mesh, CL(i+1) is the coarseness level of the coarse mesh, and s(:,:,i) is the mesh data storage format of the i-th layer.

[0115] Example 6:

[0116] A method for calculating a three-dimensional model of HVDC grounding current with multi-resolution is described in Example 3, wherein the three-dimensional resistance network is as follows:

[0117]

[0118] In the formula, S i+1,j,k S represents the area of ​​the fine grid. i,j,k h represents the area of ​​the coarse grid. c h is the length of the coarse grid edge. f R is the length of the fine mesh edge. 粗 R 细 ρ represents the central resistance of the coarse grid and the central resistance of the fine grid in the geological body mesh model, respectively; i,j,k ρ i+1,j,k These represent the resistivity of the coarse grid and the resistivity of the fine grid in the geological body grid model, respectively.

[0119] Example 7:

[0120] A method for calculating HVDC grounding current using a three-dimensional model with multi-resolution resolution is described in Example 3, where the system equations are as follows:

[0121]

[0122] In the formula, A is the nodal admittance matrix of the three-dimensional resistive network; The potential to be solved is denoted as ; S is a known power source term.

[0123] Example 8:

[0124] A method for calculating a three-dimensional model of HVDC grounding current with multi-resolution is described in Example 3. The steps for solving the system equations using the stable double conjugate gradient method with over-relaxation preprocessing to obtain the ground surface potential distribution information include:

[0125] 1) Given the system matrix A, vector b, initial approximate solution x0 of the system equations, and maximum allowable error ε max Maximum number of iterations j max Random numbers Calculate the initial residual value r0 = b - Ax0, set the parameter p0 = r0, and let the iteration number j = 0; where vector b represents the high voltage direct current transmission current;

[0126] 2) Calculation parameters r j Let p be the residual of the j-th iteration; parameter p j p j =r j +β j-1 (p j-1 -ω j-1 Ap j-1 );ω j-1 β j-1 For the (j-1)th iteration;

[0127] 3) Calculate parameter s j =r j -α j Ap j ;

[0128] 4) Calculate parameter ω j =(As j ,s j ) / (As j As j );

[0129] 5) Calculate the initial approximate solution x of the system equations in the (j+1)th iteration. j+1 =x j +α j p j +ω j s j ;

[0130] 6) Calculate the residual r of the (j+1)th iteration. j+1 =s j -ω j As j ;

[0131] 7) Determine the residual r j+1 ≤ε max or j > j max If the condition is met, output the initial approximate solution of the system equations; otherwise, let j = j + 1 and proceed to step 8).

[0132] 8) Calculate parameter p j+1 =r j+1 +β j (p j -ω j Ap j ), and return to step 2); where, the parameter

Claims

1. A method for calculating a three-dimensional model of HVDC grounding current with multi-resolution, characterized in that, Includes the following steps: 1) Establish a geological model of the radiation current field region of the grounding electrode of high voltage direct current transmission, and use a multi-resolution method to mesh the geological model to obtain a geological mesh model; 2) Set the potential sampling points at the center of each grid in the geological body grid model; 3) Calculate the axial resistance within a single grid and linearly combine the axial resistances of adjacent grids to construct a three-dimensional resistance network based on multi-resolution. 4) Establish the nodal admittance matrix of the three-dimensional resistive network; 5) Based on the nodal admittance matrix and current source of the three-dimensional resistive network, establish the system equations and solve the system equations using the stable double conjugate gradient method with over-relaxation preprocessing to obtain the surface potential distribution information. The steps for solving the system equations using the stable biconjugate gradient method with over-relaxation preprocessing to obtain the surface potential distribution information include: 5.1) Given the system matrix A, vector b, initial approximate solution x0 of the system equations, and maximum allowable error ε max Maximum number of iterations j max Random numbers Calculate the initial residual value r0 = b - Ax0, set the parameter p0 = r0, and let the iteration number j = 0; where vector b represents the high voltage direct current transmission current; 5.2) Calculation parameters r j The residual of the j-th iteration; parameter p j p j =r j +β j-1 (p j-1 -ω j-1 Ap j-1 );ω j-1 β j-1 For the (j-1)th iteration; 5.3) Calculate parameter s j =r j -α j Ap j ; 5.4) Calculate parameter ω j =(As j ,s j ) / (As j As j ); 5.5) Calculate the initial approximate solution x of the system equation in the (j+1)th iteration. j+1 =x j +α j p j +ω j s j ; 5.6) Calculate the residual r of the (j+1)th iteration. j+1 =s j -ω j As j ; 5.7) Determine the residual r j+1 ≤ε max or j > j max If the condition is met, output the initial approximate solution of the system equations; otherwise, let j = j + 1 and proceed to step 5.

8. 5.8) Calculate parameter p j+1 =r j+1 +β j (p j -ω j Ap j ), and return to step 5.2); where, the parameter 2. The method for calculating a three-dimensional model of multi-resolution HVDC grounding current according to claim 1, characterized in that, The geological body grid model includes several coarse grids; the coarse grids include several fine grids.

3. The method for calculating a three-dimensional model of multi-resolution HVDC grounding current according to claim 1, characterized in that, The grid data storage format in the geological body grid model is as follows: In the formula, CL(i) is the coarseness level of the fine mesh, CL(i+1) is the coarseness level of the coarse mesh, and s(:,:,i) is the mesh data storage format of the i-th layer.

4. The method for calculating a three-dimensional model of multi-resolution HVDC grounding current according to claim 1, characterized in that, The three-dimensional resistor network is shown below: In the formula, S i+1,j,k S represents the area of ​​the fine grid. i,j,k h represents the area of ​​the coarse grid. c h is the length of the coarse grid edge. f R is the length of the fine mesh edge. 粗 R 细 ρ represents the central resistance of the coarse grid and the central resistance of the fine grid in the geological body mesh model, respectively; i,j,k ρ i+1,j,k These represent the resistivity of the coarse grid and the resistivity of the fine grid in the geological body grid model, respectively.

5. The method for calculating a three-dimensional model of multi-resolution HVDC grounding current according to claim 1, characterized in that, The system equations are as follows: In the formula, A is the nodal admittance matrix of the three-dimensional resistive network; The potential to be solved is denoted as ; S is a known power source term.

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