A Mesh-Adaptive Method for Optimizing Electric Field Distribution in High-Voltage Switchgear

Abstract

This invention relates to the field of high-voltage switchgear technology, specifically to a method for optimizing the electric field distribution of high-voltage switchgear based on adaptive mesh partitioning. The method includes: analyzing a three-dimensional geometric model to locate singular junctions, extracting local geometric parameters, and solving for singularity indices, storing them in a singularity index table; performing finite element analysis to obtain basic error indices, determining whether mesh cells are within the singular influence domain based on the singularity index table, and correcting mesh cells within the singular influence domain using the singularity index to obtain a correction error index; selecting a subset of refined cells based on the correction error index and performing adaptive mesh refinement until the maximum correction error index is below a termination threshold, outputting the final converged mesh and convergence profile; extracting numerical solutions of the electric field from the final converged mesh, and performing singular series extrapolation based on the convergence profile to obtain an extrapolated peak field strength estimate, generating an insulation safety margin classification label. This invention improves the reliability of insulation safety margin assessment.

Description

Technical Field

[0001] This invention relates to the field of high-voltage switchgear technology, and more specifically to a method for optimizing the electric field distribution of high-voltage switchgear based on adaptive grid partitioning. Background Technology

[0002] The insulation design quality of high-voltage switchgear such as GIS switchgear, vacuum circuit breakers, and disconnectors directly determines the safety margin of power grid operation. During equipment development and type testing, numerical simulation of the electric field is used to predict the internal field strength distribution, guiding the design choices for grading ring dimensions, insulator profiles, and gas gaps. The finite element method (FEM) is currently the mainstream electric field simulation method in industry. Its core lies in discretizing the three-dimensional geometry of the equipment into a finite number of mesh elements and solving a numerical approximate solution to the Poisson equation on each element. Furthermore, existing technologies also employ methods to homogenize the electric field and alleviate local overvoltages by controlling the spatial distribution of the dielectric constant or conductivity of insulating materials. For example, Chinese patent document CN116936009B discloses a method and system for controlling the electric field distribution of high-voltage insulating dielectric functional graded materials. The specific scheme includes: dividing the high-voltage insulating dielectric functional graded material to be controlled into a mesh to obtain multiple cells; calculating the potential value of the cells based on their current dielectric constant distribution and determining the degree of electric field non-uniformity; and when the degree of electric field non-uniformity exceeds a preset threshold, iteratively optimizing the electric field distribution until a comprehensive evaluation function for the electric field distribution is satisfied. This type of method optimizes the electric field distribution at the material parameter level and is also an important branch of technology in this field.

[0003] To overcome the computational explosion caused by globally uniform meshing, this paper introduces adaptive mesh refinement technology and calculates the error estimate of each element in each iteration. Elements with errors exceeding a threshold are locally refined, thus effectively reducing computational load while maintaining accuracy, allowing computational resources to be concentrated in regions with drastic field strength changes. The commonly used error estimate in industry is the Zienkiewicz-Zhu type posterior estimator, which performs super-convergent gradient recovery on the finite element solution gradient of each element to recover the difference between the gradient and the original element gradient. The norm serves as an error metric for the unit, thereby driving subsequent grid encryption decisions.

[0004] High-voltage switchgear contains three junctions where conductors, solid insulators, and gaseous insulating media converge. At these junctions, the abrupt changes in the dielectric constants of the different media, coupled with the corner effect of wedge geometry, cause the electric field solution to theoretically exhibit a power-law singularity, meaning the electric field strength increases radially. ( The form of the equation approaches infinity. The gradient recovery process of the Zienkiewicz-Zhu type estimator is based on the premise that the field is sufficiently smooth. It reconstructs the continuous gradient field by performing least-squares fitting on the gradient values ​​of the surrounding elements. When the true gradient near the singular point is discontinuous and cannot be smoothed, it indicates that the fitted recovered gradient has been contaminated by the singular field. Since its value is systematically lower than the true peak value under this condition, the Zienkiewicz-Zhu error estimate is severely underestimated at the three-junction point. The adaptive algorithm misjudges that the region has converged and does not perform further refinement. This results in a considerable underestimation error in the calculation of the peak field strength by the finite element solution. Finally, the peak field strength output by the simulation is lower than the true physical value, and the insulation design margin is considered to be artificially high, leaving potential risks of partial discharge and breakdown. Summary of the Invention

[0005] To address the problem of premature termination of grid refinement and systematic underestimation of peak field strength caused by singular field contamination in the ZZ-type error estimator at the three junction points of high-voltage switchgear, this invention provides an optimization method for electric field distribution in high-voltage switchgear based on adaptive grid partitioning.

[0006] This invention provides a method for optimizing the electric field distribution of high-voltage switchgear based on adaptive grid partitioning, employing the following technical solution:

[0007] S1. Analyze the three-dimensional geometric model of the high-voltage switchgear to locate the singular junctions, extract the local geometric parameters of the singular junctions, and solve the corresponding singularity index based on the characteristic equation of the electrostatic field boundary value problem. Store the location and singularity index of the singular junctions in the singular point index table. S2. Perform finite element analysis on the three-dimensional geometric model and execute super-convergent gradient recovery to obtain the basic error index of each mesh element. Combine the singularity index in the singularity index table to determine whether the mesh element is within the singular influence domain. For mesh elements within the singular influence domain, use the singularity index to correct the basic error index upward to obtain the corrected error index. S3. Select a subset of refined elements based on the correction error index, perform adaptive mesh refinement on the subset of refined elements and re-solve the finite element problem until the maximum correction error index of the whole domain is lower than the preset termination threshold, output the final converged mesh and record the convergence file. S4. Extract the electric field numerical solution of the neighborhood of the singular junction on the final converged grid, perform singular series extrapolation in combination with the converged archive, calculate the extrapolated peak field strength estimate, and generate insulation safety margin classification label based on the extrapolated peak field strength estimate.

[0008] By introducing a correction method based on the singularity index, the errors of grid cells within the singular influence domain are corrected upwards, accurately reflecting the true error distribution that is systematically missed within the singular influence domain. This avoids the premature and erroneous termination of the adaptive densification loop at the three-junction point, allowing the grid to be continuously densified in the neighborhood of the singular point until the absolute error tolerance is met. Then, the peak field strength estimate of the three-junction point, which approaches the true value, is obtained through singular series extrapolation, thus improving the reliability of the insulation safety margin assessment.

[0009] Preferably, the three-dimensional geometric model of the high-voltage switchgear is analyzed to locate singular junctions, local geometric parameters of the singular junctions are extracted, and the corresponding singularity indices are solved based on the characteristic equation of the electrostatic boundary value problem. The locations and singularity indices of the singular junctions are stored in a singularity index table. This includes: traversing the boundary intersection nodes in the three-dimensional geometric model, selecting nodes with at least two dielectric constants and containing conductor boundaries as singular junctions; extracting the conductor wedge half-angle and the relative permittivity of the two adjacent dielectrics corresponding to the singular junctions as local geometric parameters; constructing a transcendental equation containing the conductor wedge half-angle and the relative permittivity, searching for the smallest positive real root of the transcendental equation using a numerical root-finding algorithm, and determining the smallest positive real root as the singularity index; and storing the three-dimensional coordinates, singularity index, and local geometric parameters of the singular junctions in association, ultimately forming the singularity index table.

[0010] By topologically traversing the boundary intersection nodes and combining the dielectric partition interface and conductor boundary, the geometric locations of actual field singularities are screened out, eliminating the interference of non-singular corner points. Using the conductor wedge half-angle and relative permittivity as input parameters, a quantitative singularity index is obtained by numerically finding the root of the transcendental equation, providing accurate quantitative input for subsequent error correction and series extrapolation.

[0011] Preferably, determining whether a grid cell is within a singular influence domain by combining the singularity index in the singularity index table includes: calculating the actual distance from the centroid of the grid cell to the nearest singular juncture point; obtaining the average cell size of the global grid, and calculating the critical radius of the influence domain based on the average cell size and the singularity index corresponding to the nearest singular juncture point; comparing the actual distance with the critical radius of the influence domain, and if the actual distance is less than or equal to the critical radius of the influence domain, then the grid cell is finally determined to be within a singular influence domain.

[0012] By calculating the critical radius of the influence domain and comparing it with the actual distance, the spatial range in which the singular field substantially contaminates the error estimation is accurately defined. This ensures that subsequent error correction operations can accurately apply to the grid cells that truly need compensation, preventing the waste of computational resources caused by over-correction.

[0013] Preferably, for grid cells located within the singular influence domain, the singularity index is used to correct the basic error index upwards to obtain the corrected error index. This includes: obtaining the feature size of the grid cell and the actual distance from the centroid of the grid cell to the nearest singular junction; calculating the ratio of the feature size to the actual distance, and calculating the difference between 1 and the singularity index; multiplying the ratio and the difference and adding 1 to obtain the error compensation coefficient; and multiplying the basic error index by the error compensation coefficient to finally obtain the corrected error index.

[0014] By extracting the ratio of the characteristic size of the grid cell to the actual distance and combining it with the singularity index to construct the error compensation coefficient, the relative change of the true field strength across the cell span is reflected. This effectively compensates for the error components missed by the smoothness assumption in the superconvergent gradient recovery, ensuring the objectivity and accuracy of the correction error index.

[0015] Preferably, the process of selecting a subset of refined units based on the correction error index includes: sorting all grid units in the entire domain in descending order according to the magnitude of the correction error index; calculating the sum of squares of the correction error indices of all grid units in the entire domain and multiplying it by a preset coverage ratio parameter to obtain the target error contribution; and accumulating the squares of the correction error indices of the grid units in the sorted order until the accumulated value is greater than or equal to the target error contribution for the first time, and finally classifying the grid units participating in the accumulation into the subset of refined units.

[0016] Preferably, adaptive mesh refinement is performed on the refined element subset and the finite element method is solved again until the global maximum correction error index is lower than the preset termination threshold. The final converged mesh is then output and the convergence file is recorded. This includes: for mesh elements in the refined element subset that are located within the singular influence domain, an anisotropic refinement method is used to perform mesh subdivision by setting the refinement ratio along the radial direction and the refinement ratio along the tangential direction, respectively; the finite element method is solved again on the newly meshed mesh and the correction error index is updated, and the refinement and solution process is repeated; when the updated global maximum correction error index is detected to be lower than the termination threshold, the loop is stopped and the final converged mesh is output; the feature size of the element closest to the singular junction point in the current iteration and the singular influence domain are extracted and finally recorded as the convergence file.

[0017] By adopting an anisotropic refinement method and setting the refinement ratios for the radial and tangential directions respectively, while maintaining the same effect of capturing rapid changes in field strength, the mesh distortion caused by excessive anisotropy is significantly reduced. This avoids the oscillation problem of repeated jumps in element aspect ratio due to excessive stretching under extreme conditions, and effectively controls the growth rate of the overall mesh size.

[0018] Preferably, the electric field numerical solution in the neighborhood of the singular junction point is extracted on the final converged mesh, and singular series extrapolation is performed in conjunction with the convergence archive to calculate the extrapolated peak field strength estimate. This includes: extracting the finite element electric field amplitude and corresponding radial distance at the center of several layers of elements closest to the singular junction point in the final converged mesh to form a data point set; using the first term of the singular series containing the singularity index as the basis function, performing least squares fitting on the data point set to calculate the amplitude coefficient; extracting the feature size of the element closest to the singular junction point from the convergence archive to calculate the resolvable minimum physical distance; and finally calculating the extrapolated peak field strength estimate based on the amplitude coefficient, the minimum physical distance, and the singularity index.

[0019] Preferably, generating insulation safety margin classification markers based on extrapolated peak field strength estimation includes: obtaining the breakdown field strength limit of the insulating medium in high-voltage switchgear; comparing the extrapolated peak field strength estimate with the breakdown field strength limit; and finally generating insulation safety margin classification markers corresponding to singular junctions based on the preset range of the comparison result.

[0020] The extrapolated peak field strength estimate is numerically compared with the insulation dielectric breakdown field strength limit, and a three-level classification label is generated based on the preset interval in which the ratio falls. This explicit classification exposes the risk of local field strength exceeding the limit to insulation designers in an intuitive form, transforming complex numerical results into clear engineering decision signals, and providing a basis for design intervention measures such as adjusting the position of the equalizing ring, modifying the profile of the insulator end, and embedding metal inserts at the three-junction point.

[0021] Preferably, adaptive mesh refinement is performed on the refined unit subset and the finite element solution is re-performed until the maximum correction error index of the whole domain is lower than the preset termination threshold. This includes: obtaining the breakdown field strength design specification of the insulating medium in the high voltage switchgear; determining the uniform field breakdown strength according to the breakdown field strength design specification; calculating the uniform field breakdown strength according to the preset allowable numerical error ratio, and finally obtaining the termination threshold for driving mesh refinement termination.

[0022] Preferably, after outputting the final converged grid and recording the convergence profile, the method further includes: overlaying the extrapolated peak field strength estimate with the standard global field distribution map; generating and outputting a complete electric field distribution dataset containing the peak correction results of singular points for final use in insulation design verification.

[0023] The present invention has the following technical effects: 1. To address the systematic failure of the error estimator at the three connection points of high-voltage switchgear, a dual-channel posterior error estimator based on singular sensing is constructed. This estimator combines grid geometric statistics with the depth of the characteristic equation solution, effectively overcoming the defect of traditional adaptive algorithms that terminate prematurely in the neighborhood of singular points. This method not only ensures repeatability under different equipment models and media combinations but also controls the overall grid size while improving local accuracy through anisotropic refinement.

[0024] 2. Under the practical engineering constraints where the finite element mesh cannot be infinitely refined, the peak field strength estimate at the three-junction point is obtained by using singular series extrapolation correction to approximate the true value, explicitly exposing the risk of local field strength exceeding limits. This provides accurate numerical basis for design intervention measures such as adjusting the position of the equalizing ring and modifying the profile of the insulator end, transforming the insulation safety margin assessment from a rough assessment relying on direct readings from finite element nodes to a precise verification based on physically convergent extrapolated values. Attached Figure Description

[0025] Figure 1 This is a flowchart of the electric field distribution optimization method for high-voltage switchgear based on adaptive grid partitioning, as described in this invention.

[0026] Figure 2 This is a schematic diagram of the mesh encryption space distribution around singular junctions using existing methods.

[0027] Figure 3 This is a schematic diagram of the spatial distribution of the grid encryption around the singular junction point using the method of the present invention. Detailed Implementation

[0028] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0029] This invention discloses a method for optimizing the electric field distribution of high-voltage switchgear based on adaptive grid partitioning, referring to... Figure 1 This includes the following steps: S1. Analyze the three-dimensional geometric model to locate singular junctions.

[0030] In an optional embodiment, a three-dimensional geometric model of the high-voltage switchgear is read in. Based on the topological relationships, all boundary intersection nodes in the model are traversed, and nodes that simultaneously satisfy the following conditions are selected as a candidate set of singular junctions: the node contains at least two dielectric partition interfaces with different dielectric constants, and at least one of these partitions must be a conductor partition with a Dirichlet boundary condition applied. It should be noted that there are many other ways in the art to read in and parse the topological relationships of a three-dimensional geometric model. Those skilled in the art can choose different parsing interfaces according to actual needs, and this invention does not limit this.

[0031] For each singular junction in the candidate set, local geometric parameters are extracted. Specific local geometric parameters include: conductor wedge half-angle. The relative permittivity of the two adjacent media and Based on the characteristic equation of the boundary value problem of electrostatic field in two-dimensional polar coordinates, the singularity index is determined by the smallest positive real root of the following transcendental equation. :

[0032] The formula is constructed based on eigenvalue analysis when both the tangential and normal electric displacement conditions are simultaneously satisfied at the wedge-shaped domain interface, and then adapted to the typical geometric constraints of the GIS three-way junction. Read directly from the model's geometric quantities. and The values ​​are assigned to the corresponding medium parameters in the material library. The smallest positive real root of the transcendental equation is searched using a numerical root-finding algorithm, and the smallest positive real root is determined as the singularity index.

[0033] in, This represents the singularity intensity. A smaller value indicates a faster divergence rate of the electric field strength near the junction point, resulting in a stronger singularity; a larger value indicates a slower divergence rate, resulting in a weaker singularity. Since the singularity intensity fluctuates with the dielectric constant ratio and the wedge angle, accurately determining the intensity at each junction point is crucial. The value is a prerequisite for subsequent error estimation. For numerical root finding of transcendental equations, the bisection method or Newton's iteration method is used. Search for the smallest positive real root within the interval to ensure convergence to a solution that meets the tolerance requirements under engineering accuracy requirements.

[0034] Complete each singular junction After solving, the 3D coordinates, singularity index, and local geometric parameters of all singular junctures are associated and stored, ultimately forming a singularity index table, which serves as the basic data structure for subsequent error estimation and correction. The index table uses the juncture number as the primary key and records the 3D coordinates, singularity index, and local geometric parameters of all singular junctures. The values ​​and local wedge angle parameters facilitate the rapid retrieval of the nearest singular point information corresponding to each grid cell based on distance relationships during subsequent iterations.

[0035] Thus, through a systematic topological traversal and root-finding of the characteristic equation of the three-dimensional geometric model, the positions of all singular junctions within the device and their respective singularity intensities are determined in specific ways. The values ​​are recorded in full, providing accurate input parameters for the correction channel in the subsequent dual-channel error estimation.

[0036] S2. Determine the singular influence domain and calculate the correction error index.

[0037] In an optional embodiment, after the standard finite element method is solved, conventional Zienkiewicz-Zhu type superconvergent gradient recovery is performed on the global mesh to obtain the mesh elements. Basic error index .

[0038] For mesh cells within the influence domain of singular juncture points, an error correction channel based on the singularity index is introduced. The actual distance from the centroid of the mesh cell to the nearest singular juncture point is calculated. Obtain the average cell size of the global mesh. And based on average cell size The singularity index corresponding to the nearest singular junction Calculate the critical radius of the influence domain. Compare the actual distance with the critical radius of the influence domain. When the actual distance... satisfy When the condition is met, it indicates that the grid cell is within the influence domain, and the processor ultimately determines that the grid cell is within the singular influence domain.

[0039] In the formula, This represents the actual distance from the centroid of the mesh cell to the nearest singular junction. The average cell size of the initial global mesh. The singularity index is the singularity index corresponding to the singular junction closest to the unit. This represents the singularity index corresponding to the nearest singular junction. Since grid cells can no longer distinguish continuous changes in the singular field within this scale, the smoothness assumption will inevitably fail if superconvergent gradient recovery continues to be used, leading to distorted error estimation.

[0040] Furthermore, for grid cells within the singular influence domain, the singularity index is used to correct the basic error index upwards, resulting in a corrected error index. The error index of the original Zienkiewicz-Zhu estimator is:

[0041] in, This is the basic error index for grid cell i. For superconvergent gradient recovery field, For finite element solutions, Indicates the first grid cells Take the space area occupied Norm. Because the superconvergent gradient recovery field systematically underestimates the true gradient change due to the failure of the smoothness assumption within the singular influence domain, this discrepancy will make the directly calculated actual error smaller. Therefore, a correction error index is introduced to correct the error index upward.

[0042] Specifically, obtaining the feature size of the grid cell And the actual distance from the centroid of the mesh cell to the nearest singular junction. ; Calculate the ratio of the feature dimension to the actual distance. And calculate the difference between 1 and the singularity index. Multiply the ratio by the difference and add 1 to obtain the error compensation coefficient. ;The basic error index Multiplying by the error compensation coefficient, the final corrected error index is obtained. :

[0043] in, This indicates the correction error index. Indicates the basic error index. The singularity index is the singularity index corresponding to the singular junction closest to the unit. The characteristic size of the mesh cell, This is the actual distance from the centroid of the grid cell to the nearest singular junction.

[0044] The construction of this relation is based on the power singular field. according to After differentiation, the relative increment is taken to extract the relative change of the true electric field strength across the element span. That is, the absolute value of the exponent. The smaller the value, the greater the potential change in field strength within the unit scale, and the greater the error component missed by the smoothness assumption in superconvergent gradient recovery. A larger value indicates a smaller potential change in field strength within a single unit scale, resulting in fewer missed error components. Since superconvergent gradient recovery misses error components proportional to this relative change, it can... The omission is compensated by multiplying by the error compensation factor.

[0045] When a cell enters the boundary of a singular influence domain, it indicates that... At this point, the processor sets the linear approximation condition to... Because under this condition, the element size within the singular influence domain remains smaller than [a certain value] after adaptive encryption. This ratio is always less than or equal to 1, and It holds true consistently throughout the entire influence domain, ensuring that the truncation error of the linear approximation is within the acceptable range for engineering applications.

[0046] In response to the element being within a non-singular influence region, the error index is maintained. All parameters in the correction error index are derived from the grid geometric statistics ( , and ) and the solution to the characteristic equation ( This ensures the repeatability of the method under different equipment models and different media combinations.

[0047] Thus, by introducing an error correction channel with the singularity index as its core to supplement the conventional Zienkiewicz-Zhu estimation channel, the error components missed by the smoothness assumption in the superconvergent gradient recovery are accurately compensated, thus avoiding premature and erroneous termination of adaptive encryption at the three junction points.

[0048] S3. Filter and refine the subset of cells to perform adaptive mesh refinement.

[0049] In an optional embodiment, all grid cells across the entire domain are adjusted according to the error correction index. The values ​​are sorted in descending order, the sum of squares of the correction error indices of all grid cells in the entire domain is calculated, and then multiplied by a preset coverage ratio parameter. Obtain the target error contribution. Accumulate the squares of the correction error indices of the grid cells sequentially according to their order, until the accumulated value first exceeds or equals the target error contribution. Then, classify the grid cells involved in the accumulation into the final refinement subset. Thus, a subset of units satisfying the following relation is obtained. :

[0050] Among them, parameters The value is determined based on the balance between the target convergence rate and the computational cost per iteration. For example, The value can be 0.5; This refers to all grid cells in the entire domain.

[0051] The termination criterion for mesh reinforcement is given by the insulation dielectric breakdown field strength design specification. The breakdown field strength design specification for the insulation dielectric in high-voltage switchgear is obtained, and the uniform field breakdown field strength is determined based on this specification. Taking SF6 gas as an example, its uniform field breakdown field strength at a filling pressure of 0.4 MPa is approximately 8 MV / m. According to a preset allowable numerical error ratio and the numerical accuracy requirements for insulation design verification, the uniform field breakdown field strength is calculated, ultimately yielding the termination threshold that drives mesh reinforcement. For example, the allowable numerical error ratio can be taken as 1% of the breakdown field strength, corresponding to a termination threshold of 80 kV / m for SF6 gas at 0.4 MPa. Controlling the mesh refinement process requires comprehensive parameter control. and absolute error upper limit threshold .

[0052] Primarily targeting physical environments where the radial decay rate of the field intensity gradient is much faster than the tangential rate in singular fields, the system employs an anisotropic refinement method instead of conventional isotropic refinement to mitigate the risk of condition number degradation in finite element solutions. For mesh elements within singular influence domains in the refined element subset, the radial and tangential refinement ratios are determined based on the ratio of the radial to tangential field intensity gradient decay rates. This significantly reduces mesh distortion caused by excessive anisotropy while maintaining the same ability to capture rapid changes in field intensity. For example, the radial refinement ratio can be 1 / 4, and the tangential refinement ratio can be 1 / 2. For refined elements in ordinary regions, conventional isotropic bipartite refinement is used. Compared to the abrupt change in a globally uniform refinement ratio, this method provides a gradual transition when handling gradients in different directions, avoiding the oscillation problem of repeated jumps in element aspect ratio due to overstretching under extreme conditions.

[0053] After each round of refinement, the finite element method is solved again on the newly generated mesh, and the error index is updated and corrected. The refinement and solution process is repeated iteratively. The process terminates when the maximum global correction error index does not fall below the termination threshold. Continue executing the next round of the mark-refinement loop; when the updated global maximum correction error metric is detected to be below the termination threshold... When the loop stops, extract the current iteration number. and the feature size of the nearest unit to the singular junction within the singular influence domain. The final record is the convergence file, and the final convergence mesh is output.

[0054] Thus, by combining anisotropic refinement with the absolute error termination criterion, the growth of the overall grid size can be controlled within a reasonable range while effectively capturing rapid changes in the singular field.

[0055] S4. Perform singular series extrapolation and generate insulation safety margin classification labels.

[0056] In an optional embodiment, the numerical solutions of the electric field in the neighborhood of each singular junction are extracted on the final convergence grid. Within the final convergence grid, the distance to the singular junction is extracted. Finite element electric field amplitude at the center of the nearest several layers of elements and its corresponding radial distance , constitute a data point set The first term is a singular series containing the singularity index. The amplitude coefficients are calculated by performing least-squares fitting on the data point set using the basis functions. .

[0057] Extract the feature size of the nearest unit to the singular junction from the convergent archive. ,Will Half of it is determined as the minimum resolvable physical distance. This represents the smallest resolvable physical distance at the current finest grid scale. Based on the amplitude coefficient... Minimum physical distance and the singularity index The singular junction point was finally calculated. Extrapolated peak field strength estimation at:

[0058] in, Represents singular junctions The extrapolated peak field strength at that location Represents singular junctions Amplitude coefficient at that point, Indicates the smallest distinguishable physical distance. Represents singular junctions The singularity index at the location.

[0059] It should be noted that if If the value is much smaller than the actual surface roughness characteristic scale of the conductor (which is determined by the equipment manufacturing process specifications), the extrapolation result will enter the non-physical region of singular series divergence, losing its engineering significance. In this case, it should be considered in conjunction with the actual manufacturing process specifications. The lower limit is constrained.

[0060] Furthermore, the breakdown field strength limit of the insulating medium in the high-voltage switchgear is obtained, and the extrapolated peak field strength is estimated. The direct reading values ​​of finite element nodes are used as input for design verification. The values ​​are compared with the breakdown field strength limit. Based on the preset range of the comparison results, the insulation safety margin classification mark of the corresponding singular junction is finally generated, which is divided into three levels: sufficient margin, critical margin, and insufficient margin.

[0061] The extrapolated peak field strength estimate is overlaid with the standard global field distribution map to generate and output a complete electric field distribution dataset containing singular point peak correction results for final use in insulation design verification. Since the original uniform grid simulation process masks the risk of local field strength exceeding limits due to the failure of the Zienkiewicz-Zhu estimator, the extrapolated peak field strength is introduced to explicitly expose this risk, providing accurate numerical basis for design interventions such as adjusting the equipotential ring position, modifying the insulator end profile, and embedding metal inserts at three connection points. It should be noted that there are many other least-squares solutions in this field that can achieve singular series fitting; those skilled in the art can choose different numerical fitting libraries or solvers according to actual needs. This invention does not limit the specific implementation method.

[0062] In this way, the peak field strength that cannot be distinguished by the finite element mesh can be explicitly estimated by extrapolating the singular series, so that the insulation safety margin assessment is transformed from relying on the direct reading value of the finite element node to the accurate verification based on the physically converged extrapolated value.

[0063] The technical effects of this invention can also be illustrated in conjunction with the accompanying drawings. Figure 2 This is a schematic diagram illustrating the spatial distribution of mesh refinement around singular junctions using existing methods. Figure 3 This is a schematic diagram of the mesh encryption space distribution around the singular junction point using the method of the present invention, in comparison. Figure 2 and Figure 3 It can be intuitively observed that the method of the present invention forms a significantly denser colored grid cluster in the near-field of singular junctions, indicating that the method of the present invention can continuously drive the grid to deepen and densify into high singular gradient regions, while existing methods result in sparse near-field grids due to premature termination.

[0064] The above are all preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Therefore, all equivalent changes made in accordance with the structure, shape and principle of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A method for optimizing the electric field distribution of high-voltage switchgear based on adaptive grid partitioning, characterized in that, Including the following steps: S1. Analyze the three-dimensional geometric model of the high-voltage switchgear to locate the singular junctions, extract the local geometric parameters of the singular junctions, and solve the corresponding singularity index based on the characteristic equation of the electrostatic field boundary value problem. Store the location and singularity index of the singular junctions in the singular point index table. S2. Perform finite element analysis on the three-dimensional geometric model and execute super-convergent gradient recovery to obtain the basic error index of each mesh element. Combine the singularity index in the singularity index table to determine whether the mesh element is within the singular influence domain. For mesh elements within the singular influence domain, use the singularity index to correct the basic error index upward to obtain the corrected error index. S3. Select a subset of refined elements based on the correction error index, perform adaptive mesh refinement on the subset of refined elements and re-solve the finite element problem until the maximum correction error index of the whole domain is lower than the preset termination threshold, output the final converged mesh and record the convergence file. S4. Extract the electric field numerical solution of the neighborhood of the singular junction on the final converged grid, perform singular series extrapolation in combination with the converged archive, calculate the extrapolated peak field strength estimate, and generate insulation safety margin classification label based on the extrapolated peak field strength estimate.

2. The method for optimizing the electric field distribution of high-voltage switchgear based on adaptive grid partitioning according to claim 1, characterized in that, The location and singularity index of singular junctions are stored in a singularity index table, including: traversing the boundary intersection nodes in the 3D geometric model, selecting nodes with at least two dielectric constants and containing conductor boundaries as singular junctions; extracting the conductor wedge half-angle and the relative permittivity of the two adjacent dielectrics corresponding to the singular junctions as local geometric parameters; constructing a transcendental equation containing the conductor wedge half-angle and the relative permittivity, searching for the smallest positive real root of the transcendental equation using a numerical root-finding algorithm, and determining the smallest positive real root as the singularity index; and storing the 3D coordinates, singularity index, and local geometric parameters of the singular junctions together to finally form the singularity index table.

3. The method for optimizing the electric field distribution of high-voltage switchgear based on adaptive grid partitioning according to claim 1, characterized in that, Determining whether a grid cell is within a singular influence domain by combining the singularity index in the singularity index table includes: calculating the actual distance from the centroid of the grid cell to the nearest singular juncture point; obtaining the average cell size of the global grid, and calculating the critical radius of the influence domain based on the average cell size and the singularity index corresponding to the nearest singular juncture point; comparing the actual distance with the critical radius of the influence domain, and if the actual distance is less than or equal to the critical radius of the influence domain, then the grid cell is finally determined to be within the singular influence domain.

4. The method for optimizing the electric field distribution of high-voltage switchgear based on adaptive grid partitioning according to claim 1, characterized in that, For mesh cells within the singular influence domain, the singularity index is used to correct the basic error index upwards, resulting in a corrected error index. This process includes: obtaining the feature size of the mesh cell and the actual distance from the centroid of the mesh cell to the nearest singular junction; calculating the ratio of the feature size to the actual distance, and calculating the difference between 1 and the singularity index; multiplying the ratio and the difference by 1 to obtain the error compensation coefficient; and multiplying the basic error index by the error compensation coefficient to finally obtain the corrected error index.

5. The method for optimizing the electric field distribution of high-voltage switchgear based on adaptive grid partitioning according to claim 1, characterized in that, The process of selecting a subset of refined cells based on the correction error index includes: sorting all grid cells in the entire domain in descending order according to the magnitude of the correction error index; calculating the sum of squares of the correction error indices of all grid cells in the entire domain and multiplying it by a preset coverage ratio parameter to obtain the target error contribution; and accumulating the squares of the correction error indices of the grid cells in the sorted order until the accumulated value is greater than or equal to the target error contribution for the first time, and finally classifying the grid cells participating in the accumulation into the subset of refined cells.

6. The method for optimizing the electric field distribution of high-voltage switchgear based on adaptive grid partitioning according to claim 1, characterized in that, Adaptive mesh refinement is performed on the refined element subset, and the finite element method is solved again until the global maximum correction error index is lower than the preset termination threshold. The final converged mesh is then output and the convergence file is recorded. This process includes: for mesh elements in the refined element subset that are within the singular influence domain, an anisotropic refinement method is used, and the refinement ratios along the radial and tangential directions are set for mesh generation; the finite element method is solved again on the newly generated mesh and the correction error index is updated, and the refinement and solution process is repeated; when the updated global maximum correction error index is detected to be lower than the termination threshold, the loop is stopped and the final converged mesh is output; the feature size of the element closest to the singular junction point in the current iteration and the singular influence domain are extracted and finally recorded as the convergence file.

7. The method for optimizing the electric field distribution of high-voltage switchgear based on adaptive grid partitioning according to claim 1, characterized in that, Numerical solutions of the electric field in the neighborhood of singular junctions are extracted on the final converged grid. Singular series extrapolation is then performed using the convergence archive to calculate the extrapolated peak field strength estimate, including: In the final converged mesh, the finite element electric field amplitudes and corresponding radial distances at the centers of several layers closest to the singular junctions are extracted to form a data point set. The data point set is fitted with least squares using the first term of the singular series containing the singularity index as the basis function to calculate the amplitude coefficients. The feature size of the cell closest to the singular junction is extracted from the converged archive to calculate the resolvable minimum physical distance. Based on the amplitude coefficients, the minimum physical distance, and the singularity index, the extrapolated peak field strength estimate is finally calculated.

8. The method for optimizing the electric field distribution of high-voltage switchgear based on adaptive grid partitioning according to claim 1, characterized in that, The method for generating insulation safety margin classification markers based on extrapolated peak field strength estimation includes: obtaining the breakdown field strength limit of the insulating medium in high-voltage switchgear; comparing the extrapolated peak field strength estimate with the breakdown field strength limit; and finally generating insulation safety margin classification markers corresponding to singular junctions based on the preset range of the comparison result.

9. The method for optimizing the electric field distribution of high-voltage switchgear based on adaptive grid partitioning according to claim 1, characterized in that, Adaptive mesh refinement is performed on the refined element subset and the finite element solution is re-performed until the maximum correction error index of the entire domain is lower than the preset termination threshold. This includes: obtaining the breakdown field strength design specification of the insulating medium in high-voltage switchgear; determining the uniform field breakdown strength according to the breakdown field strength design specification; calculating the uniform field breakdown strength according to the preset allowable numerical error ratio, and finally obtaining the termination threshold for driving mesh refinement termination.

10. The method for optimizing the electric field distribution of high-voltage switchgear based on adaptive grid partitioning according to claim 1, characterized in that, After outputting the final converged grid and recording the convergence profile, the process also includes: overlaying the extrapolated peak field strength estimate with the standard global field distribution map; generating and outputting a complete electric field distribution dataset containing the peak correction results for singular points, for final use in insulation design verification.

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