Finite element method-based transformer loss calculation method and structure optimization method
The finite element method calculates the transformer loss and optimizes the core structure, which solves the problems of calculation time and poor accuracy in the prior art, achieves efficient and low-cost transformer loss reduction, and improves energy efficiency and material utilization.
Patent Information
- Application Number
- CN202411078885.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-08-07
- Publication Date
- 2025-01-03
AI Technical Summary
The calculation process of existing transformer loss calculation methods is time-consuming and has poor accuracy, which is difficult to meet engineering requirements, and the method of reducing transformer loss is high or the process is complicated.
Using the transformer loss calculation method based on the finite element method, by establishing a three-dimensional model on the finite element analysis software, setting circuit and magnetic circuit constraints, using the Steinmetz model and resistance thermal model to solve the core and winding losses, and optimizing the iron according to the loss distribution The core structure, for example, is rounded with iron core columns and the outer corners of the iron yoke to reduce losses.
It improves the speed and accuracy of transformer loss calculation, reduces losses, improves energy efficiency, and saves iron core materials and reduces manufacturing costs.
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Figure CN119249783A_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to the technical field of power equipment simulation, and in particular relates to a transformer loss calculation method and a structure optimization method based on a finite element method. Background Art
[0002] Currently, the digital Southern Grid and the digital State Grid are in full swing. The digitalization of the power system has great value for the construction of the power grid. As the implementation period of the dual carbon goals is getting closer, how to achieve the dual carbon goals as soon as possible is crucial to my country's economic development. Transformers play a vital role in the power system. Their normal, reliable and safe operation is related to the safe operation of the entire power grid. In the design, production and manufacturing process of transformers, upgrading the small structural links of the transformers to comprehensively improve the overall energy efficiency of the transformers is of great significance to reducing the energy consumption and operating costs of the power grid.
[0003] Carrying out transformer loss calculation and analysis is an important part of transformer design. Transformer loss calculation methods include electrical table calculation method, using Python or Matlab to write transformer calculation program, etc. The above methods are easy to build, easy to use, and easy to understand. However, there are also problems such as long calculation process and poor calculation accuracy, which are difficult to meet engineering needs.
[0004] At the same time, in the current transformer design, there are usually two ways to reduce transformer losses. One is to reduce the no-load loss of the transformer by scientifically upgrading the core material. For example, high-performance amorphous alloy materials are applied to the transformer core to reduce iron loss, but the material cost of this method is high and the manufacturing process is difficult. On the other hand, the iron loss can be reduced by optimizing the structure of the core to make the magnetic flux distribution inside the core more uniform and reduce local magnetic flux concentration and saturation. This method is low-cost and easy to implement. Summary of the invention
[0005] The purpose of the present invention is to provide a transformer loss calculation method and a structure optimization method based on the finite element method, so as to improve the transformer loss calculation speed and accuracy, and realize low-cost transformer structure optimization to reduce transformer losses, thereby improving the energy efficiency of the transformer.
[0006] To achieve the above object, the present invention provides a transformer loss calculation method and a structure optimization method based on the finite element method, wherein the technical solution of the transformer loss calculation method based on the finite element method of the present invention comprises the following steps:
[0007] S1. Calculate the transformer parameters required for transformer loss according to the finite element method and establish a three-dimensional model of the transformer on the finite element analysis software;
[0008] S2. Setting circuit constraints and magnetic circuit constraints of the three-dimensional transformer model, coupling the circuit interface of the three-dimensional transformer model with the magnetic circuit interface of the three-dimensional transformer model, solving the core loss using the Steinmetz model, and solving the transformer winding copper loss using the resistance thermal model;
[0009] S3. Apply the physical field to the three-dimensional model of the transformer, and use the circuit interface and magnetic circuit interface of the three-dimensional model of the transformer to solve the transformer current density, volume loss density and magnetic flux density model.
[0010] Preferably, in the above technical solution, in the step S1, the transformer parameters include transformer box size, core size, core material, primary winding size and material, and secondary winding size and material.
[0011] Preferably, in the above technical solution, the step S1 also includes performing a mesh analysis on the transformer model, using a coarse mesh for the box of the three-dimensional model of the transformer, and using a free tetrahedral mesh for the core and winding of the three-dimensional model of the transformer, and the mesh density of the core and the winding is greater than the mesh density of the box.
[0012] Preferably, in the above technical solution, in step S2, the circuit constraint, when taking into account the transformer winding resistance, ignores the transformer winding skin effect; in the magnetic circuit constraint, the boundary condition of the iron core is set to magnetic insulation, and the magnetic field interface is fixed by the magnetic vector potential specification, and the magnetic vector potential specification calculation formula is:
[0013]
[0014] δE+J e =J#(3)
[0015]
[0016] In the formula, is the Hamiltonian operator, H is the magnetic field intensity, B is the current density, B is the magnetic flux density, A is the vector magnetic potential, E is the electric field intensity, δ is the conductivity, J e is the volume current density.
[0017] Preferably, in the above technical solution, in step S2, the calculation formula for solving the core loss using the Steinmetz model is:
[0018] k h (f) α (|B|) β =Q Fe #(5)
[0019] In the formula, k his the iron loss coefficient, α is the frequency index, and β is the magnetic flux density index;
[0020] The calculation formula for solving the transformer winding copper loss using the resistance thermal model is:
[0021]
[0022] In the formula, T represents the calculation cycle time, T end Indicates the calculation stop time;
[0023] Adding the core loss and the winding copper loss gives the total transformer loss:
[0024] Q cu +Q Fe =Q#(7)
[0025] Preferably, in the above technical solution, step S3 further includes setting a magnetic insulation equation:
[0026] n×A=0
[0027] In the formula, n represents the transverse component of magnetic flux, and the curl is 0;
[0028] Set up the gauge fixing equation for the magnetic vector potential:
[0029]
[0030] The coil equation of the transformer winding satisfies the following calculation formula:
[0031]
[0032] F J ×L edges =L coil #(9)
[0033] F A ×A domain =A coil #(10)
[0034] Where N represents the number of coil turns, I coil represents the current, e coil Indicates the charge of the electron, F J is the coil multiplication factor, L edges is the winding side length, L coil Indicates the coil length, F A is the coil area multiplication factor, A domain represents the average cross-sectional area of the coil, A coil Represents the cross-sectional area of the coil.
[0035] On the other hand, a transformer structure optimization method based on finite element method of the present invention comprises:
[0036] According to the flux density modulus and volume loss density of the transformer three-dimensional model calculated by the transformer loss calculation method based on the finite element method, the core structure of the transformer three-dimensional model is optimized and finite element calculation is performed. The volume loss density of the core of the transformer three-dimensional model before and after optimization is compared and analyzed, and the core structure optimization scheme of the transformer three-dimensional model is determined, that is, the outer corners of the core column and the iron yoke are rounded, or the inner corners of the core column and the iron yoke are rounded without changing the overall size of the core.
[0037] Compared with the existing technology, the present invention has the following beneficial effects:
[0038] 1. By establishing a three-dimensional transformer model on the finite element analysis software and applying multi-physics fields to the geometric model, the circuit and magnetic field interfaces are used to solve the transformer current density, volume loss density, and flux density modulus. According to the flux density modulus and volume loss density, users can understand the flux distribution and loss distribution inside the transformer in more detail. By using a coarse grid for the transformer box and a free tetrahedral grid for the transformer core and winding, the grid density is greater than the box grid density, which can ensure the accuracy of the solution and effectively improve the accuracy and speed of the solution. The transformer loss distribution is calculated based on the solution results, which greatly improves the speed and accuracy of the transformer loss solution.
[0039] 2. According to the calculated flux density modulus and volume loss density of the three-dimensional transformer model, it is found that the loss generated by the core of the three-dimensional transformer model is uneven, and the flux at each end corner is small. Based on this, without changing the overall size of the core and without affecting the flux performance of the core, the outer corners of the core column and the iron yoke of the three-dimensional transformer model are rounded, or the inner corners of the core column and the iron yoke of the three-dimensional transformer model are rounded, which reduces the flux distortion at the end corners of the core and reduces the no-load loss of the core. At the same time, the flux density of each part of the core tends to be evenly distributed, thereby improving the energy conversion efficiency of the transformer, increasing the utilization rate of the core per unit area, effectively reducing the transformer loss, and thus improving the energy efficiency of the transformer. By removing the edges and corners of the core, the core material is saved and the manufacturing cost of the transformer is reduced. BRIEF DESCRIPTION OF THE DRAWINGS
[0040] Figure 1 It is a flow chart of transformer loss calculation based on finite element method of the present invention.
[0041] Figure 2 It is a grid division diagram of the transformer three-dimensional model of the present invention.
[0042] Figure 3 It is the electrical connection diagram of the transformer of the present invention.
[0043] Figure 4It is the magnetic flux density model and current density diagram of the transformer of the present invention.
[0044] Figure 5 It is a three-dimensional volume loss density diagram of the transformer of the present invention.
[0045] Figure 6 It is a front view of the core loss density of the present invention.
[0046] Figure 7 It is a top view of the core loss density of the present invention.
[0047] Figure 8 It is a front view of the iron loss density after the outer corners of the iron core column and the iron yoke of the present invention are rounded.
[0048] Fig. 9 It is a top view of the iron loss density after the outer corners of the iron core column and the iron yoke are rounded.
[0049] Fig.10 It is a front view of the iron loss density after the inner corners of the iron core column and the iron yoke are rounded.
[0050] Fig.11 It is a top view of the iron loss density after the inner corners of the iron core column and the iron yoke are rounded in the present invention. Specific embodiments
[0051] The specific implementation modes of the present invention are described in detail below in conjunction with the accompanying drawings, but it should be understood that the protection scope of the invention is not limited by the specific implementation modes.
[0052] refer to Figure 1 The present invention proposes a transformer loss calculation method based on the finite element method, comprising the following steps:
[0053] S1. Calculate the transformer parameters required for transformer loss according to the finite element method and establish a three-dimensional model of the transformer on the finite element analysis software;
[0054] S2. Setting circuit constraints and magnetic circuit constraints of the three-dimensional transformer model, coupling the circuit interface of the three-dimensional transformer model with the magnetic circuit interface of the three-dimensional transformer model, solving the core loss using the Steinmetz model, and solving the transformer winding copper loss using the resistance thermal model;
[0055] S3. Apply the physical field to the three-dimensional model of the transformer, and use the circuit interface and magnetic circuit interface of the three-dimensional model of the transformer to solve the transformer current density, volume loss density, and magnetic flux density model.
[0056] refer to Figure 2, in specific implementation, the present invention uses COMSOL Multiphysics software, in step S1, the transformer parameters include transformer box size, core size, core material, primary winding size and material, secondary winding size and material, specifically, the built transformer three-dimensional model is a three-phase double-winding oil-immersed transformer with a length of 128cm, a width of 102cm, and a height of 176cm, and the core length, width, and height are set, the core material is set to silicon steel sheet, the primary and secondary winding outer diameters and inner diameters, the winding coil cross-sectional area, the height and thickness of the winding, the winding is copper, and the transformer oil flow characteristics. The transformer three-dimensional model is meshed, and since the finite element analysis needs to integrate and solve the model grids one by one, and finally perform summation calculation, the density of the grid has a greater impact on the accuracy of the solution result. According to the characteristic that the loss of the transformer is mainly in the core and winding, in order to reduce the calculation amount of the model and improve the calculation speed, a coarse grid is used for the box of the three-dimensional model of the transformer, which reduces the number of calculation grids in the box part, reduces the calculation resources used by the computer used by the finite element software, and improves the calculation speed of the volume loss density and the flux density model of the box part. The core and winding use free tetrahedral grids. The grid density of the core and winding is greater than the grid density of the box, that is, the number of grids in the core and winding is higher than the number of grids in the box, which can reflect the electromagnetic phenomena of more parts of the core and winding after the physical field is applied to the three-dimensional model of the transformer, thereby obtaining the magnetic flux density B, current density J, magnetic field intensity H, magnetic field intensity E, and winding electron charge e of more parts of the core and winding. coil and current I coil , thereby ensuring the winding copper loss Q of the core part of the transformer three-dimensional model cu and core loss Q Fe The calculation accuracy of .
[0057] In step S2, in the circuit constraints, when taking into account the transformer winding resistance, the skin effect of the transformer three-dimensional model winding is ignored;
[0058] In the magnetic circuit constraint, the boundary condition of the iron core is set to magnetic insulation. To ensure the convergence of the magnetic field interface solution, the magnetic field interface is fixed using the magnetic vector potential specification. The magnetic vector potential specification calculation formula is:
[0059]
[0060] δE+J e =J#(3)
[0061]
[0062] In the formula, is the Hamiltonian operator, H is the magnetic field intensity, J is the current density, B is the magnetic flux density, A is the vector magnetic potential, E is the electric field intensity, δ is the conductivity, J e is the volume current density.
[0063] refer to Figure 3 , connect a sinusoidal excitation voltage source U1 and a resistor R1 to the primary winding of the transformer, connect the secondary winding of the transformer to a resistor R2, and energize the transformer through the sinusoidal excitation voltage source U1, so that the transformer has electromagnetic coupling function. The calculation formula for the core loss is solved by the Steinmetz model:
[0064] k h (f) α (|B|) β =Q Fe #(5)
[0065] In the formula, k h is the iron loss coefficient, α is the frequency index, and β is the magnetic flux density index;
[0066] The calculation formula for transformer winding copper loss using the resistance thermal model is:
[0067]
[0068] In the formula, T represents the calculation cycle time, T end Indicates the calculation stop time;
[0069] Adding the core loss and the winding copper loss gives the total transformer loss:
[0070] Q cu +Q Fe =Q#(7)
[0071] Where Q is the total transformer loss.
[0072] Step S3 also includes setting the magnetic insulation equation:
[0073] n×A=0
[0074] In the formula, n represents the transverse component of magnetic flux, and the curl is 0;
[0075] Set up the gauge fixing equation for the magnetic vector potential:
[0076]
[0077] The coil equation for the transformer winding satisfies the following calculation formula:
[0078]
[0079] F J ×Ledges =L coil #(9)
[0080] F A ×A domain =A coil #(10)
[0081] Where N represents the number of coil turns, I coil represents the current, e coil Indicates the charge of the electron, F J is the coil multiplication factor, L edges is the winding side length, L coil Indicates the coil length, F A is the coil area multiplication factor, A domain represents the average cross-sectional area of the coil, A coil Represents the cross-sectional area of the coil.
[0082] refer to Figure 4-Figure 7 Through the above steps, the calculation of the core loss and winding copper loss of the transformer three-dimensional model is completed, and by applying the physical field to the transformer model and using the circuit interface and magnetic circuit interface of the transformer three-dimensional model, the transformer current density, volume loss density, and magnetic flux density model are solved.
[0083] On the other hand, the present invention proposes a transformer structure optimization method based on the finite element method. According to the calculated flux density modulus and volume loss density of the three-dimensional transformer model, it is found that the loss generated by the iron core of the three-dimensional transformer model is uneven, and the flux of each end corner is small. Without changing the overall size of the iron core and without affecting the magnetic flux performance of the iron core, the outer corners of the core column and the iron yoke are rounded, or the inner corners of the core column and the iron yoke are rounded, and the optimized core structure is calculated by the finite element method. By comparing the magnetic flux density modulus and volume loss of the core before and after optimization, the optimization method is determined. By eliminating the corners of the core, the volume loss of this part is reduced, the core material is saved, and the transformer manufacturing cost is reduced. The principle of reducing the loss of the core is as follows: the magnetic flux density modulus and volume loss density of the three-dimensional model of the transformer are calculated by the finite element method, and based on the obtained magnetic flux density modulus, the outer or inner corners of the core column and the iron yoke are rounded without changing the overall size of the core and without affecting the magnetic flux performance of the core, so that the area of the corner magnetic flux of the core deviating from the rolling direction of the silicon steel sheet is reduced. By analyzing the magnetic flux density modulus and volume loss density of the three-dimensional model of the transformer, it is found that the magnetic flux distortion at each end corner of the core is reduced, thereby reducing the no-load loss of the core, and at the same time making the magnetic flux density of each part of the core tend to be evenly distributed, thereby improving the energy conversion efficiency of the transformer and improving the utilization rate of the core per unit area.
[0084] Specifically, before optimization, the volume density of the transformer 3D model is as follows: Figure 6 and Figure 7 As shown, the minimum and maximum points of the volume density of the transformer three-dimensional model are shown in Table 1:
[0085] Table 1
[0086] X Y Z <![CDATA[Volume loss density (W / m 3 ) <!-- 5 -->]]> 1121.9 -98.322 529.25 <![CDATA[7.2940e -42 ]]> -1182.5 423.85 -315.05 <![CDATA[7.3962e 7 ]]>
[0087] In Table 1, at the point (1121.9, -98.322, 529.25) of the transformer 3D model, the minimum volume density value is 7.2940e -42 W / m 3 At the point (-1182.5,423.85,-315.05), the maximum volume density is 7.3962e 7 W / m 3 .
[0088] Without changing the overall size of the core and without affecting the core magnetic flux performance, the outer corners of the core column and the iron yoke are rounded, the area of the small magnetic flux density area is reduced, and the electromagnetic field analysis is performed to solve the problem. The loss is significantly reduced, and the material processing cost is also reduced accordingly. The optimized transformer volume density is as follows Figure 8 and Fig. 9 As shown, the minimum and maximum points of the volume density of the transformer three-dimensional model are shown in Table 2:
[0089] Table 2
[0090] X Y Z <![CDATA[Volume loss density (W / m 3 )]]> -1300.0 650.00 741.00 0 472.55 -16.005 -27.756 1.0510
[0091] In Table 2, at the point (-1300.0, 650.00, 741.00) of the transformer 3D model, the minimum volume density value is 0W / m 3 At the point (472.55,-16.005,-27.756), the maximum volume density is 1.051W / m 3 .
[0092] Without changing the overall size of the core and without affecting the core magnetic flux performance, the inner corners of the core column and the iron yoke are rounded, the area of the large magnetic flux density area is increased, and the electromagnetic field analysis is performed. The transformer loss is also reduced. The optimized transformer volume density is as follows Fig.10 and Fig.11 As shown, the minimum and maximum points of the volume density of the transformer three-dimensional model are shown in Table 3:
[0093] Table 3
[0094] X Y Z <![CDATA[Volume loss density (W / m 3 )]]> -1300.0 650.00 741.00 0.0000 472.55 -16.005 -27.756 1.0485
[0095] In Table 3, at the point (-1300.0, 650.00, 741.00) of the transformer 3D model, the minimum volume density value is 0W / m3 At the point (472.55,-16.005,-27.756), the maximum volume density is 1.0485W / m 3 .
[0096] In summary, the present invention establishes a three-dimensional transformer model on finite element analysis software, analyzes the internal loss of the transformer, uses circuit and magnetic field interfaces to solve the distribution of electromagnetic fields inside the transformer, and calculates the transformer loss distribution based on the solution results, thereby improving the transformer loss solution calculation speed and accuracy. And based on the calculated volume loss density of the three-dimensional transformer model, without changing the overall size of the core and without affecting the core magnetic flux performance, the core column and the outer corners of the yoke of the three-dimensional transformer model are rounded, or the core column and the inner corners of the yoke of the three-dimensional transformer model are rounded. After simulation calculation, it is proved that the transformer loss can be effectively reduced, thereby improving the transformer energy efficiency, while saving the core material and reducing the transformer manufacturing cost.
[0097] The principles and implementation methods of the present invention are described in this article using specific examples. The description of the above examples is only used to help understand the method and core ideas of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made to the present invention without departing from the principles of the present invention, and these improvements and modifications also fall within the scope of protection of the claims of the present invention.
Claims
1. A transformer loss calculation method based on finite element method, characterized in that: The following steps are involved: S1. Calculate the transformer parameters required for transformer loss according to the finite element method and establish a three-dimensional model of the transformer on the finite element analysis software; S2. Setting circuit constraints and magnetic circuit constraints of the three-dimensional transformer model, coupling the circuit interface of the three-dimensional transformer model with the magnetic circuit interface of the three-dimensional transformer model, solving the core loss using the Steinmetz model, and solving the transformer winding copper loss using the resistance thermal model; S3. Apply the physical field to the three-dimensional model of the transformer, and use the circuit interface and magnetic circuit interface of the three-dimensional model of the transformer to solve the transformer current density, volume loss density and magnetic flux density model.
2. The transformer loss calculation method based on finite element method according to claim 1 is characterized in that: In the step S1, the transformer parameters include transformer box size, core size, core material, primary winding size and material, and secondary winding size and material.
3. The transformer loss calculation method based on finite element method according to claim 2 is characterized in that: The step S1 also includes performing a mesh analysis on the three-dimensional model of the transformer, using a coarse mesh for the box of the three-dimensional model of the transformer, and using a free tetrahedral mesh for the core and winding of the three-dimensional model of the transformer, wherein the mesh density of the core and the winding is greater than the mesh density of the box.
4. The transformer loss calculation method based on finite element method according to claim 1 is characterized in that: In step S2, the circuit constraint, when taking into account the transformer winding resistance, ignores the transformer winding skin effect; in the magnetic circuit constraint, the boundary condition of the iron core is set to magnetic insulation, and the magnetic field interface is fixed by the magnetic vector potential specification, and the magnetic vector potential specification calculation formula is: δE+J e =J#(3) In the formula, is the Hamiltonian operator, H is the magnetic field intensity, B is the current density, B is the magnetic flux density, A is the vector magnetic potential, E is the electric field intensity, δ is the conductivity, J e is the volume current density.
5. The transformer loss calculation method based on finite element method according to claim 4 is characterized in that: In step S2, the calculation formula for solving the core loss using the Steinmetz model is: k h (f) α (|B|) β =Q Fe #(5) In the formula, k h is the iron loss coefficient, α is the frequency index, and β is the magnetic flux density index; The calculation formula for solving the transformer winding copper loss using the resistance thermal model is: In the formula, T represents the calculation cycle time, T end Indicates the calculation stop time; Adding the core loss and the winding copper loss gives the total transformer loss: Q cu +Q Fe =Q#(7) Where Q is the total transformer loss.
6. The transformer loss calculation method based on finite element method according to claim 1 is characterized in that: The step S3 also includes setting the magnetic insulation equation: n×A=0 In the formula, n represents the transverse component of magnetic flux, and the curl is 0; Set up the gauge fixing equation for the magnetic vector potential: The coil equation of the transformer winding satisfies the following calculation formula: F J ×L edges =L coil #(9) F A ×A domain =A coil #(10) Where N represents the number of coil turns, I coil represents the current, e coil Indicates the charge of the electron, F J is the coil multiplication factor, L edges is the winding side length, L coil Indicates the coil length, F A is the coil area multiplication factor, A domain represents the average cross-sectional area of the coil, A coil Represents the cross-sectional area of the coil.
7. A transformer structure optimization method based on finite element method, which is implemented by any one of claims 1 to 6, characterized in that: According to the flux density modulus and volume loss density of the transformer three-dimensional model calculated by the transformer loss calculation method based on the finite element method, the core structure of the transformer three-dimensional model is optimized and finite element calculation is performed. The volume loss density of the core of the transformer three-dimensional model before and after optimization is compared and analyzed, and the core structure optimization scheme of the transformer three-dimensional model is determined, that is, the outer corners of the core column and the iron yoke are rounded, or the inner corners of the core column and the iron yoke are rounded without changing the overall size of the core.
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