Finite element order reduction method, system and equipment for rapidly solving stress of power transformer winding and medium

Abstract

The invention relates to the technical field of electric power, and discloses a finite element order reduction method, system, equipment and medium for rapidly solving the stress of a power transformer winding, and the method comprises the steps: obtaining the electrical physical quantity related to the power transformer winding, and carrying out the three-dimensional entity model building of a power transformer, performing spatial order reduction on the three-dimensional solid model to obtain a two-dimensional axisymmetric finite element calculation model of the power transformer; carrying out initial grid division on the solution domain, and carrying out finite element numerical calculation solution on an internal electromagnetic field of the power transformer under various operation conditions to obtain electrodynamic force density data; and solving the stress distribution of the power transformer winding under the corresponding working condition, and generating a response surface model for calculating the stress of the power transformer winding. According to the method, the effects of reducing the calculation dimension, reducing the calculation amount and saving the calculation time and CPU load can be achieved, the calculation rapidity and accuracy of the reduced-order model are proved, and a basis and an optimization thought are provided for stress analysis and solution of the power transformer.

Description

Technical Field

[0001] This invention relates to the field of power technology, and in particular to a finite element method, system, device, and medium for rapid solution of winding stress in power transformers. Background Technology

[0002] Power transformers are crucial devices in the power transmission process. Their windings are subjected to various stresses during operation, including thermal stress, mechanical stress, and environmental stress. Temperature rise in the windings leads to thermal stress due to inconsistencies in material properties, while the electromagnetic force generated by the linkage between current and leakage magnetic field causes mechanical stress. Insulating materials primarily bear thermal stress, while conductive materials primarily bear mechanical stress, which can potentially generate destructive forces under high current conditions. Therefore, studying the stresses experienced by power transformer windings is of great significance for ensuring high power supply reliability in power systems.

[0003] Currently, due to cost and testing limitations, large transformers generally cannot undergo specialized mechanical performance tests, making numerical theoretical research the dominant approach in actual transformer production. Existing research largely focuses on establishing equivalent system models of winding vibration during transformer operation, based on the characteristics of the winding structure and the mechanical properties of the insulating pads. The finite element method (FEM) is used to calculate short-circuit electromagnetic forces and winding strength, analyzing the distribution characteristics of electromagnetic forces during transformer short circuits. Numerical analysis is used to calculate the critical load for winding instability under short-circuit electrodynamic forces. However, when using FEM to simulate the magnetic field of actual transformers, especially large transformers, the simulation exhibits multi-scale spatial characteristics due to their large overall size and the relatively small size of thin structures such as silicon steel sheets. In FEM simulations, the full-order model (FOM) of the dynamic system obtained from discrete partial differential equations has a large number of geometric degrees of freedom (DoF), resulting in long solution times and high memory requirements. In the context of multi-parameter queries and real-time analysis, it is necessary to solve the full-order model multiple times for different parameter values, which puts significant pressure on CPU computation time and memory. Summary of the Invention

[0004] In view of the aforementioned existing problems, this invention is proposed. Therefore, this invention provides a finite element method for rapid solution of winding stress in power transformers, addressing the aforementioned problems.

[0005] To solve the above-mentioned technical problems, the present invention provides the following technical solution:

[0006] In a first aspect, the present invention provides a finite element method for rapid solution of winding stress in power transformers, comprising:

[0007] The electrical physical quantities related to the windings of the power transformer are obtained, a three-dimensional solid model of the power transformer is built, and the spatial order of the three-dimensional solid model is reduced to obtain a two-dimensional axisymmetric finite element calculation model of the power transformer.

[0008] Based on the two-dimensional axisymmetric finite element calculation model of the power transformer, the solution domain is initially meshed, and the electromagnetic field inside the power transformer under various operating conditions is solved by finite element numerical calculation to obtain the electrodynamic density data.

[0009] Based on the electrodynamic density data, the stress distribution of the power transformer windings under the corresponding operating conditions is solved, and a response surface model for calculating the stress of the power transformer windings is generated.

[0010] As a preferred embodiment of the finite element method for rapid solution of winding stress in power transformers as described in this invention, the construction of a three-dimensional solid model of the power transformer includes:

[0011] The windings of the power transformer are modeled as a cylinder in three dimensions.

[0012] The key dimensional parameters of the power transformer are associated with the geometric features of the three-dimensional solid model.

[0013] As a preferred embodiment of the finite element method for rapid solution of winding stress in power transformers as described in this invention, the method for obtaining a two-dimensional axisymmetric finite element calculation model of the power transformer includes:

[0014] By introducing the boundary conditions of the governing equations for symmetric boundary conditions and impedance boundary conditions, and by converting the three-dimensional model to two-dimensional analysis and setting boundary conditions, the spatial order of the three-dimensional solid model is reduced by half, resulting in a two-dimensional symmetric finite element calculation model of the power transformer.

[0015] The advantages of this preferred solution are that it can reduce the computational scale of the model, improve the solution speed, and retain the key physical field characteristics.

[0016] As a preferred embodiment of the finite element method for rapid solution of winding stress in power transformers as described in this invention, the initial mesh generation of the solution domain includes:

[0017] The solution domain is initially meshed and then solved to calculate the electromagnetic field energy;

[0018] The electromagnetic field energy is compared with a preset convergence threshold to determine whether the current grid accuracy meets the standard.

[0019] If convergence has been achieved, then the current mesh accuracy has met the standard.

[0020] If convergence is not achieved, the current mesh accuracy is not up to standard. Based on the gradient of electromagnetic field quantity change, the region with drastic field quantity change is located, the mesh in the region is automatically refined, and the solution and evaluation are performed again. The above process is repeated until convergence is achieved.

[0021] The advantages of this preferred scheme are that it efficiently achieves mesh optimization within the solution domain, automatically adjusts the mesh density according to the stress gradient, and ensures the accuracy of electromagnetic field numerical calculations.

[0022] As a preferred embodiment of the finite element method for rapid solution of winding stress in power transformers as described in this invention, the method for obtaining electrodynamic density data includes:

[0023] The internal magnetic field of the transformer is calculated using the finite element method, introducing vector magnetic potential A and scalar potential. Solve Maxwell's equations, perform finite element numerical calculations to solve the internal electromagnetic field of power transformers under no-load, light-load and rated load operating conditions, visualize the spatial leakage magnetic field using cloud maps, and derive the electrodynamic density calculation results.

[0024] Assuming all field quantities vary sinusoidally with a fixed angular frequency ω over time, the governing equations and various boundary conditions for solving the magnetic field distribution inside the transformer are obtained, expressed as follows:

[0025]

[0026] Where v represents magnetoresistivity, σ represents conductivity, ω represents angular frequency, j is the imaginary unit, and H t Γ1 and Γ2 represent the first and second type boundaries, respectively, and A0 represents the magnitude of the magnetic potential vector on the boundary.

[0027] As a preferred embodiment of the finite element method for rapid solution of power transformer winding stress according to the present invention, the solution of the power transformer winding stress distribution under the corresponding operating condition includes:

[0028] The electromagnetic force direction of the transformer winding magnetic field is determined by importing the electrodynamic density data through grid mapping and interpolation, and the electromagnetic force value is calculated.

[0029] Based on the electromagnetic force values, the winding stress distribution and winding stress values ​​are obtained by solving.

[0030] As a preferred embodiment of the finite element method for rapid solution of winding stress in power transformers as described in this invention, the obtained winding stress distribution and winding stress values ​​include:

[0031] Based on the leakage magnetic field and current density of the transformer winding, the electromagnetic force df borne by the differential unit dV is expressed as:

[0032] df=J×BdV

[0033] Where J represents current density and B represents magnetic flux density;

[0034] Integrating the electromagnetic force formula, the force on the entire winding V is obtained, expressed as:

[0035] F=∫ V (J×B)dV

[0036] Where F represents the force on the entire winding.

[0037] Secondly, the present invention provides a finite element order reduction system for rapid solution of winding stress in power transformers, comprising:

[0038] The model building module is used to acquire electrical physical quantities related to the windings of the power transformer, build a three-dimensional solid model of the power transformer, and perform spatial order reduction on the three-dimensional solid model to obtain a two-dimensional axisymmetric finite element calculation model of the power transformer.

[0039] The first calculation module is used to perform initial meshing of the solution domain based on the two-dimensional axisymmetric finite element calculation model of the power transformer, and to perform finite element numerical calculation to solve the electromagnetic field inside the power transformer under various operating conditions, so as to obtain the electrodynamic density data.

[0040] The second calculation module is used to solve the stress distribution of the power transformer winding under the corresponding operating conditions based on the electrodynamic density data, and generate a response surface model for calculating the stress of the power transformer winding.

[0041] Thirdly, the present invention provides a computer device, comprising:

[0042] Memory and processor;

[0043] The memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions. When the computer-executable instructions are executed by the processor, they implement the steps of the finite element order reduction method for rapid solution of winding stress of power transformers.

[0044] Fourthly, the present invention provides a computer-readable storage medium storing computer-executable instructions that, when executed by a processor, implement the steps of the finite element reduction method for rapid solution of winding stress in power transformers.

[0045] Compared with existing technologies, the beneficial effects of this invention are as follows: This invention reduces the order of the model to provide a low-dimensional approximate description of the multidimensional physical process that changes over time, achieving optimization in the sense of capturing system energy. This reduces the computational dimensionality, computational load, and saves computation time and CPU load. This invention reduces the order of the finite element full-order model for winding stress analysis based on the response surface method, and the speed and accuracy of the reduced-order model calculation are demonstrated through multiple simulation comparisons. This invention can provide a basis and optimization ideas for stress analysis and solution of power transformers. Attached Figure Description

[0046] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0047] Figure 1 This is a schematic diagram of the overall process of a finite element method for rapid solution of winding stress in power transformers according to an embodiment of the present invention.

[0048] Figure 2 This is a schematic diagram of a Simulink model for calculating electrical physical quantities of an in-operation transformer, based on a finite element method for rapid solution of winding stress in power transformers according to an embodiment of the present invention.

[0049] Figure 3 This is a schematic diagram of a three-phase power transformer prototype using the finite element method for rapid solution of winding stress in a power transformer, as described in an embodiment of the present invention.

[0050] Figure 4 This is a schematic diagram of the model space preprocessing for rapid solution of winding stress in power transformers according to an embodiment of the present invention.

[0051] Figure 5 This is a diagram showing the results of the adaptive mesh generation technique of the finite element order reduction method for rapid solution of winding stress in power transformers according to an embodiment of the present invention.

[0052] Figure 6 This is a cloud map of the main magnetic field distribution of the iron core in a finite element method for rapid solution of winding stress in power transformers, as described in an embodiment of the present invention.

[0053] Figure 7 This is a spatial leakage magnetic field distribution cloud map of a finite element reduced-order method for rapid solution of winding stress in power transformers, as described in an embodiment of the present invention.

[0054] Figure 8 This is a magnetic field distribution cloud map of a finite element method for rapid solution of winding stress in power transformers, as described in an embodiment of the present invention.

[0055] Figure 9 This is an electrodynamic density distribution cloud map of the finite element order reduction method for rapid solution of winding stress in power transformers according to an embodiment of the present invention.

[0056] Figure 10 This is a contour plot of the normal stress on the winding of a finite element method for rapid solution of winding stress in a power transformer, as described in an embodiment of the present invention.

[0057] Figure 11 This is a shear stress cloud diagram of the winding of a finite element reduced-order method for rapid solution of winding stress in a power transformer, as described in an embodiment of the present invention.

[0058] Figure 12 This is a schematic diagram of the winding stress solution response surface model of the finite element order reduction method for rapid solution of winding stress in power transformers according to an embodiment of the present invention. Detailed Implementation

[0059] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of the present invention.

[0060] Example 1

[0061] Reference Figure 1 As an embodiment of the present invention, a finite element method for rapid solution of winding stress in power transformers is provided, such as... Figure 1 As shown, it includes:

[0062] S101: Obtain the electrical physical quantities related to the windings of the power transformer, build a three-dimensional solid model of the power transformer, and reduce the spatial order of the three-dimensional solid model to obtain a two-dimensional axisymmetric finite element calculation model of the power transformer.

[0063] S102, based on the two-dimensional axisymmetric finite element calculation model of power transformer, the solution domain is initially meshed, and the electromagnetic field inside the power transformer under various operating conditions is solved by finite element numerical calculation to obtain the electrodynamic density data.

[0064] S103, based on electrodynamic density data, solves the stress distribution of the power transformer windings under the corresponding operating conditions, and generates a response surface model for calculating the stress of the power transformer windings.

[0065] In this embodiment, the Matlab / Simulink software, a visualization simulation platform, is used to simulate and analyze various operating conditions of the power transformer, and to obtain time-varying current data flowing through each side of the power transformer windings, providing input conditions for subsequent electromagnetic field analysis.

[0066] In a preferred embodiment, building a three-dimensional solid model of a power transformer includes:

[0067] The windings of the power transformer are modeled as a cylinder in three dimensions.

[0068] The key dimensional parameters of the power transformer are correlated with the geometric features of the three-dimensional solid model.

[0069] Specifically, based on the geometric design parameter table, including parameters such as power transformer, capacity, connection group, low-voltage coil radial direction, high-voltage coil radial direction, core diameter, and core column center distance, a three-dimensional solid model of the power transformer prototype is built using modeling tools (such as SpaceClaim). First, the two-dimensional outlines of the main components such as the core, windings, and tank are drawn using the sketching function. Then, the two-dimensional model is converted into a three-dimensional solid, and the assembly modeling of each component is completed through operations such as moving and combining. To improve modeling efficiency, a parametric modeling method is adopted, which associates key dimensional parameters with the geometric features of the model to achieve rapid model updates when design changes occur, ensuring model accuracy.

[0070] In a preferred embodiment, the spatial complexity of the finite element analysis model is reduced to obtain a two-dimensional axisymmetric finite element calculation model for a power transformer, including:

[0071] By introducing symmetric boundary conditions and impedance boundary conditions into the governing equations, and through three-dimensional to two-dimensional analysis and setting boundary conditions, the spatial order of the three-dimensional solid model is reduced by half, resulting in a two-dimensional symmetric finite element calculation model of the power transformer.

[0072] It should be noted that symmetric boundary conditions can utilize the axisymmetry of the transformer structure to simplify the three-dimensional model into a two-dimensional axisymmetric model, while impedance boundary conditions can simplify the electromagnetic boundaries of the core and windings, reduce the computational degrees of freedom, and overall reduce the computational scale of the model, improve the solution speed, and at the same time retain the key physical field characteristics.

[0073] In an alternative implementation, spatial reduction of the three-dimensional solid model can also be achieved through the dynamic substructure method, in which windings are defined as substructures in ANSYS, boundary nodes are preserved, and then super elements are generated and assembled into the global model.

[0074] In a preferred embodiment, initial mesh generation of the solution domain includes:

[0075] The solution domain is initially meshed and then solved to calculate the electromagnetic field energy;

[0076] The electromagnetic field energy is compared with a preset convergence threshold to determine whether the current grid accuracy meets the standard.

[0077] If convergence has been achieved, then the current mesh accuracy has met the standard.

[0078] If convergence is not achieved, the current mesh accuracy is not up to standard. Based on the gradient of electromagnetic field quantity change, the region with drastic field quantity change is located, the mesh in the region is automatically refined, and the solution and evaluation are performed again. This process is repeated until convergence is achieved.

[0079] Specifically, in certain analysis types, to control errors caused by mesh generation, a posterior error estimation method is used to evaluate the calculation results. First, an initial mesh is generated for the solution domain and the solution is solved. The calculated electromagnetic field energy is compared with a preset convergence threshold to determine if the current mesh accuracy meets the standard. If convergence is not achieved, regions with drastic field changes are located based on the electromagnetic field gradient, and the mesh in these regions is automatically refined. The solution is then solved and evaluated again, and this process is repeated until the convergence criterion is met. This efficiently optimizes the mesh within the solution domain, automatically adjusting the mesh density based on the stress gradient to ensure the accuracy of the electromagnetic field numerical calculation.

[0080] In one alternative implementation, mesh generation can also be performed using a regularized Cartesian mesh or deep learning. The regularized Cartesian mesh locally refines the winding region while using a coarse mesh in other regions, and simultaneously handles surface boundaries to complete automatic mesh generation. The training data for deep learning is the stress gradient distribution in historical simulations, which is then used to generate a mesh size field to guide ANSYS in adaptive mesh generation.

[0081] In a preferred embodiment, obtaining the electrodynamic density data includes:

[0082] The internal magnetic field of the transformer is calculated using the finite element method, introducing vector magnetic potential A and scalar potential. The frequency domain method is used to solve Maxwell's equations. Finite element numerical calculations are performed on the internal electromagnetic field of power transformers under no-load, light-load, and rated-load operating conditions. The spatial leakage magnetic field is visualized using cloud maps, and the electrodynamic density calculation results are derived.

[0083] Assuming all field quantities vary sinusoidally with a fixed angular frequency ω over time, the governing equations and various boundary conditions for solving the magnetic field distribution inside the transformer are obtained, expressed as follows:

[0084]

[0085] Where v represents magnetoresistivity, σ represents conductivity, ω represents angular frequency, j is the imaginary unit, and H t Γ1 and Γ2 represent the first and second type boundaries, respectively, and A0 represents the magnitude of the magnetic potential vector on the boundary.

[0086] In this embodiment, the electromagnetic field finite element analysis module Maxwell 2D of the Ansys Electronics Desktop software, an electromagnetic simulation platform, is used to perform finite element numerical calculations to solve the internal electromagnetic field of the power transformer under operating conditions such as no-load, light-load, and rated load. The spatial leakage magnetic field is visualized using cloud maps, and the electrodynamic density calculation results are exported. Specifically, the winding current excitation obtained from the Simulink platform is imported, and a large-scale algebraic equation system assembled after being discretized by the finite element method is solved to obtain the corresponding distribution cloud maps of the main magnetic field and spatial leakage magnetic field in the core, as well as the schematic diagram of magnetic field lines. The electrodynamic density is then calculated, which can evaluate the mechanical strength of the winding under electrodynamic conditions and prevent insulation breakage or deformation failure.

[0087] In a preferred embodiment, solving for the stress distribution of the power transformer windings under the corresponding operating condition includes:

[0088] Electrodynamic density data is imported using mesh mapping and interpolation to determine the direction of the electromagnetic force in the transformer winding magnetic field and to calculate the electromagnetic force value.

[0089] Based on the electromagnetic force values, the winding stress distribution and the winding stress values ​​are obtained by solving.

[0090] In a preferred embodiment, the process of obtaining the winding stress distribution and the numerical values ​​of the winding stress includes:

[0091] Based on the leakage magnetic field and current density of the transformer winding, the electromagnetic force df borne by the differential unit dV is expressed as:

[0092] df=J×BdV

[0093] Where J represents current density and B represents magnetic flux density;

[0094] Integrating the electromagnetic force formula, the force on the entire winding V is obtained, expressed as:

[0095] F=∫ V (J×B)dV

[0096] Where F represents the force on the entire winding.

[0097] In this embodiment, the structural field of the three-phase power transformer is analyzed using the structural engineering finite element analysis software Ansys Mechanical, based on the simulation integration platform AnsysWorkbench. Electrodynamic loads are imported using mesh mapping and interpolation methods to obtain the winding stress distribution and magnitude, thus realizing the multi-physics coupling of electromagnetism and force. When current flows through the transformer windings, a leakage magnetic field is generated around the windings. Under the combined action of the current and the leakage magnetic field, the winding conductors will generate an electromagnetic force. The magnitude of the electromagnetic force can be calculated using the Biot-Savart law, and the direction of the electromagnetic force can be determined using the left-hand rule.

[0098] In this embodiment, a polynomial form is selected to approximate the implicit actual response function. Then, a series of experimental points are used to determine the undetermined parameters (coefficients in the polynomial approximation function) in the approximation function. Experimental points refer to the data points used for fitting, typically based on sampling of design variables. The sampling method can employ uniform distribution or Latin hypercube sampling to cover the variable space. By reasonably selecting experimental points and an iteration strategy—that is, by using the least squares method or other optimization methods—the polynomial coefficients are solved based on the experimental point data. The selection strategy must ensure a reasonable distribution of experimental points. During iteration, residual analysis can be used to adjust the points until the approximation function converges, ensuring that the approximate response function converges to the true implicit response function. This generates a response surface model for calculating the winding stress of a power transformer. The model takes the winding current amplitude as input and outputs the conductor stress state. The polynomial of the response function refers to selecting a polynomial to approximate the implicit response function that cannot be directly analyzed. Its form can be:

[0099] f(x) = a0 + a1x + a2x + ... + a n x

[0100] Where a0, a1, ..., a n are undetermined coefficients, and n is the order of the polynomial.

[0101] It should be noted that this invention uses model order reduction (MOR) to approximate the time-varying multidimensional physical process in a lower dimension, achieving optimization in the sense of capturing system energy. This reduces the computational dimensionality, computational load, and saves computation time and CPU load. This invention uses the response surface methodology to reduce the order of the full-order finite element model for winding stress analysis, and multiple simulations have demonstrated the speed and accuracy of the reduced model calculation. It effectively solves the problem of low solution efficiency in finite element models due to large computational scale, and has good engineering application prospects. It can provide a basis and optimization ideas for stress analysis and solution of power transformers based on finite element analysis.

[0102] The above is a schematic scheme of a finite element order reduction method for rapid solution of power transformer winding stress according to this embodiment. It should be noted that the technical solution of this finite element order reduction system for rapid solution of power transformer winding stress belongs to the same concept as the technical solution of the finite element order reduction method for rapid solution of power transformer winding stress described above. Details not described in detail in the technical solution of the finite element order reduction system for rapid solution of power transformer winding stress in this embodiment can be found in the description of the technical solution of the finite element order reduction method for rapid solution of power transformer winding stress described above.

[0103] Example 2

[0104] This embodiment provides a finite element method for rapid solution of winding stress in power transformers, including:

[0105] The model building module is used to acquire electrical physical quantities related to the windings of power transformers, build a three-dimensional solid model of the power transformer, and perform spatial order reduction on the three-dimensional solid model to obtain a two-dimensional axisymmetric finite element calculation model of the power transformer.

[0106] The first calculation module is used to perform initial meshing of the solution domain based on the two-dimensional axisymmetric finite element calculation model of the power transformer, and to perform finite element numerical calculation of the internal electromagnetic field of the power transformer under various operating conditions to obtain electrodynamic density data.

[0107] The second calculation module is used to solve the stress distribution of the power transformer windings under the corresponding operating conditions based on the electrodynamic density data, and generate a response surface model for calculating the stress of the power transformer windings.

[0108] This embodiment also provides a computer device suitable for finite element method reduction for rapid solution of winding stress in power transformers, including:

[0109] The memory and processor are used to store computer-executable instructions and execute the computer-executable instructions to implement the finite element order reduction method for rapid solution of winding stress of power transformers as proposed in the above embodiments.

[0110] This embodiment also provides a storage medium storing a computer program that, when executed by a processor, implements the finite element method for rapid solution of winding stress in power transformers as proposed in the above embodiments.

[0111] The storage medium proposed in this embodiment and the finite element order reduction method for rapid solution of winding stress in power transformers proposed in the above embodiments belong to the same inventive concept. Technical details not described in detail in this embodiment can be found in the above embodiments, and this embodiment has the same beneficial effects as the above embodiments.

[0112] Based on the above description of the implementation methods, those skilled in the art can clearly understand that the present invention can be implemented using software and necessary general-purpose hardware, and of course, it can also be implemented using hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as a computer floppy disk, read-only memory (ROM), random access memory (RAM), flash memory, hard disk, or optical disk, etc., including several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods of the various embodiments of the present invention.

[0113] Example 3

[0114] Reference Figures 2-12 Tables 1 and 2, which are embodiments of the present invention, provide a finite element method for rapid solution of winding stress in power transformers. To verify its beneficial effects, scientific demonstration is carried out through economic benefit calculations and simulation experiments.

[0115] Using an SG-4000 / 10 dry-type transformer as a prototype, this paper theoretically derives the currents in each winding of a three-phase power transformer under various operating conditions by employing an impedance network and numerical calculation methods. The influence of system impedance is also considered. Simulations of the operating power transformer are then performed using the Matlab / Simulink visualization simulation platform. Figure 2 As shown.

[0116] To simplify calculations while ensuring the accuracy of simulation data, the following operations were performed during transformer modeling and preprocessing:

[0117] 1) Ignoring structural components such as clamps, oil tanks, corner rings, end rings, and magnetic shielding, the model includes iron core, copper windings, pads, and support bars;

[0118] 2) Without considering the winding distribution of copper wires inside the winding, each coil is cylindrical and the number of coil turns is evenly distributed.

[0119] 3) While ensuring that the size relationship between the pad and the coil is the same as the actual transformer size relationship, the number of winding layers is reduced proportionally.

[0120] Design parameters for the SG-4000 / 10 transformer were collected, as shown in Table 1. A 3D model of the power transformer was created using the SpaceClaim modeling tool. Duplicate faces, lines, or points were automatically detected and deleted, and redundant information in the 3D transformer model was removed. The modeling results are shown below. Figure 3 As shown, by applying symmetric boundary conditions and other methods to reduce the spatial computational scale, a result is formed as follows: Figure 4 The two-dimensional electromagnetic calculation model shown.

[0121] Table 1: Electrical and Structural Parameters of Transformers

[0122] parameter numerical values model SG-4000 / 10 Transformer capacity (kVA) 4000 Connection Group Dyn11 Low voltage coil radial direction / mm 100 High voltage coil radial direction / mm 100 Iron core diameter / mm 664.65 Center distance of the heart column / mm 1500

[0123] Finite element analysis of the electromagnetic field distribution of a two-winding three-phase power transformer was performed using the electromagnetic field finite element analysis software ANSYS Maxwell 2D. By setting the automatic mesh generation function of the eddy current solver, the local mesh was iteratively refined. The final mesh generated on the transformer core and windings is shown below. Figure 5 As shown. The winding current excitation obtained from solving the problem in the Simulink platform is imported, and the large-scale algebraic equation system formed by discretization and assembly using the finite element method is solved. This yields the corresponding distribution cloud maps of the main magnetic field and spatial leakage magnetic field within the iron core, as well as schematic diagrams of magnetic field lines, as shown below. Figure 6 , Figure 7 and Figure 8 As shown, the electrodynamic density was calculated.

[0124] The electromagnetic field solution results are imported into the Ansys Mechanical steady-state structural field analysis system. The results of the load import are as follows: Figure 9 As shown, after completing the material creation, mechanical property addition, and assignment to the corresponding solid model in the steady-state structural field analysis system, fixed constraint boundary conditions are added, and then the structural field calculation is performed to obtain the distribution cloud map of normal stress and shear stress of the power transformer winding under steady-state operation under the corresponding working condition. Figure 10 and Figure 11 As shown.

[0125] By running the design optimization application Ansys DesignXplorer in the Ansys Workbench environment and calling the Design of Experiments (DoE) component, sampling of design points is completed based on the central complex design (CCD) method. This not only reduces the number of sampling points required but also improves the accuracy of the response surface obtained from the sampling results. Combined with built-in mathematical statistical functions, the Response Surface Methodology (RSM) component is used to generate a response surface model for calculating the stress of power transformer windings, such as... Figure 12 As shown in Table 2, the power transformer data under three randomly set operating conditions were processed and calculated using the obtained response surface model. The results demonstrate that the model can infer the stress condition of the power transformer winding based on the input electrical physical quantities with almost no time delay, and the calculation results meet the accuracy requirements of engineering practice.

[0126] Table 2: Calculation results of response surface model

[0127]

[0128] In summary, the multi-physics coupling calculation method based on electro-magnetic-structural fields proposed in this invention improves the accuracy and reliability of simulation. The method for rapid solution of power transformer winding stress based on response surface methodology solves the problems of complex parameter settings and excessive calculation time in the finite element method.

[0129] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A finite element method for rapid solution of winding stress in power transformers, characterized in that, include: The electrical physical quantities related to the windings of the power transformer are obtained, a three-dimensional solid model of the power transformer is built, and the spatial order of the three-dimensional solid model is reduced to obtain a two-dimensional axisymmetric finite element calculation model of the power transformer. Based on the two-dimensional axisymmetric finite element calculation model of the power transformer, the solution domain is initially meshed, and the electromagnetic field inside the power transformer under various operating conditions is solved by finite element numerical calculation to obtain the electrodynamic density data. Based on the electrodynamic density data, the stress distribution of the power transformer windings under the corresponding operating conditions is solved, and a response surface model for calculating the stress of the power transformer windings is generated.

2. The finite element method for rapid solution of winding stress in power transformers as described in claim 1, characterized in that, The construction of a three-dimensional solid model of the power transformer includes: The windings of the power transformer are modeled as a cylinder in three dimensions. The key dimensional parameters of the power transformer are associated with the geometric features of the three-dimensional solid model.

3. The finite element method for rapid solution of winding stress in power transformers as described in claim 2, characterized in that, The obtained two-dimensional axisymmetric finite element calculation model of the power transformer includes: By introducing symmetric boundary conditions and impedance boundary conditions into the governing equations, and through three-dimensional to two-dimensional analysis and setting boundary conditions, the spatial order of the three-dimensional solid model is reduced by half, resulting in a two-dimensional symmetric finite element calculation model of the power transformer.

4. The finite element method for rapid solution of winding stress in power transformers as described in claim 1, characterized in that, Initial mesh generation of the solution domain includes: The solution domain is initially meshed and then solved to calculate the electromagnetic field energy; The electromagnetic field energy is compared with a preset convergence threshold to determine whether the current grid accuracy meets the standard. If convergence has been achieved, then the current mesh accuracy has met the standard. If convergence is not achieved, the current mesh accuracy is not up to standard. Based on the gradient of electromagnetic field quantity change, the region with drastic field quantity change is located, the mesh in the region is automatically refined, and the solution and evaluation are performed again. This process is repeated until convergence is achieved.

5. The finite element method for rapid solution of winding stress in power transformers as described in claim 4, characterized in that, The obtained electrodynamic density data include: The internal magnetic field of the transformer is calculated using the finite element method, introducing vector magnetic potential A and scalar potential. Solve Maxwell's equations, perform finite element numerical calculations to solve the internal electromagnetic field of power transformers under no-load, light-load and rated load operating conditions, visualize the spatial leakage magnetic field using cloud maps, and derive the electrodynamic density calculation results. Assuming all field quantities vary sinusoidally with a fixed angular frequency ω over time, the governing equations and various boundary conditions for solving the magnetic field distribution inside the transformer are obtained, expressed as follows: Where v represents magnetoresistivity, σ represents conductivity, ω represents angular frequency, j is the imaginary unit, and H t Γ1 and Γ2 represent the first and second type boundaries, respectively, and A0 represents the magnitude of the magnetic potential vector on the boundary.

6. The finite element method for rapid solution of winding stress in power transformers as described in claim 5, characterized in that, Solving for the stress distribution of the power transformer windings under the corresponding operating conditions includes: The electromagnetic force direction of the transformer winding magnetic field is determined by importing the electrodynamic density data through grid mapping and interpolation, and the electromagnetic force value is calculated. Based on the electromagnetic force values, the winding stress distribution and winding stress values ​​are obtained by solving.

7. The finite element method for rapid solution of winding stress in power transformers as described in claim 6, characterized in that, The obtained winding stress distribution and winding stress values ​​include: Based on the leakage magnetic field and current density of the transformer winding, the electromagnetic force df borne by the differential unit dV is expressed as: df=J×BdV Where J represents current density and B represents magnetic flux density; Integrating the electromagnetic force formula, the force on the entire winding V is obtained, expressed as: F=∫ V (J×B)dV Where F represents the force on the entire winding.

8. A finite element order reduction system for rapid solution of winding stress in power transformers, employing the finite element order reduction method for rapid solution of winding stress in power transformers as described in any one of claims 1 to 7, characterized in that, include: The model building module is used to acquire electrical physical quantities related to the windings of the power transformer, build a three-dimensional solid model of the power transformer, and perform spatial order reduction on the three-dimensional solid model to obtain a two-dimensional axisymmetric finite element calculation model of the power transformer. The first calculation module is used to perform initial meshing of the solution domain based on the two-dimensional axisymmetric finite element calculation model of the power transformer, and to perform finite element numerical calculation to solve the electromagnetic field inside the power transformer under various operating conditions, so as to obtain the electrodynamic density data. The second calculation module is used to solve the stress distribution of the power transformer winding under the corresponding operating conditions based on the electrodynamic density data, and generate a response surface model for calculating the stress of the power transformer winding.

9. A computer device, characterized in that, include: Memory and processor; The memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions. When the computer-executable instructions are executed by the processor, they implement the steps of the finite element order reduction method for rapid solution of winding stress of power transformers as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, It stores computer-executable instructions, which, when executed by a processor, implement the steps of the finite element reduction method for rapid solution of winding stress in power transformers as described in any one of claims 1 to 7.

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