Two-dimensional leakage inductance model construction method and system for high-frequency transformer with tightly arranged windings

Abstract

The application relates to a two-dimensional leakage inductance model construction method and system for tightly arranging high-frequency transformers, and belongs to the technical field of high-frequency transformers. The method comprises the following steps: constructing a first relationship formula satisfied by electric field and magnetic field intensity according to the porosity of a primary winding and Maxwell equations; constructing a first intensity component relationship formula according to the first relationship formula and a magnetic field intensity component relationship formula; constructing a second relationship formula satisfied by electric field and magnetic field intensity, and constructing a second intensity component relationship formula according to an electric field intensity component relationship formula; constructing an electric field intensity expression according to the second intensity component relationship formula and the first intensity component relationship formula; constructing a two-dimensional magnetic field intensity mathematical model according to the electric field intensity expression and the second intensity component relationship formula; constructing a winding magnetic field energy model according to the two-dimensional magnetic field intensity mathematical model and winding parameters of the primary winding; and obtaining a two-dimensional leakage inductance model of the primary winding according to the winding magnetic field energy model. The application improves the calculation precision.

Description

Technical Field

[0001] This invention relates to the field of high-frequency transformer technology, and in particular to a method and system for constructing a two-dimensional leakage inductance model for a high-frequency transformer with closely spaced windings. Background Technology

[0002] High-frequency transformers are core and widely used electromagnetic components in power electronic circuits, and their performance parameters directly determine the overall operating performance of power electronic devices. With the rapid development of power electronics technology towards higher power density, higher efficiency, and miniaturization, the design accuracy requirements for high-frequency transformers continue to increase. The parasitic parameters of transformers are key factors affecting the operating efficiency, stability, and power density of power electronic circuits, and leakage inductance, as one of the core parasitic parameters, plays a crucial role in optimizing transformer design due to the high accuracy of its calculation.

[0003] Currently, the calculation methods for leakage inductance of high-frequency transformers in the industry are mainly divided into two categories: analytical calculation methods and numerical calculation methods. Compared with numerical calculation methods, analytical calculation methods have become the mainstream calculation method in the field of high-frequency transformer design due to their advantages of simple calculation process, fast calculation speed, and adaptability to iterative engineering design, and are widely used by a large number of engineering designers.

[0004] In existing technologies, the mainstream analytical calculation models for high-frequency transformer leakage inductance mainly include one-dimensional high-frequency transformer leakage inductance analytical calculation models and two-dimensional leakage inductance analytical calculation models based on the image method. Both types of models provide fundamental support for the engineering calculation of high-frequency transformer leakage inductance, but both suffer from unavoidable technical problems in practical applications, making it difficult to simultaneously meet the core requirements of calculation accuracy and efficiency. Specifically, the traditional one-dimensional leakage inductance analytical calculation model only performs a one-dimensional simplified analysis of the transformer's magnetic field. This high degree of simplification fails to fully characterize the three-dimensional structural characteristics and actual magnetic field distribution of the high-frequency transformer, resulting in inherently low calculation accuracy. The calculated results deviate significantly from the actual operating leakage inductance parameters of the transformer, failing to meet the design optimization requirements of high-precision transformers. While the two-dimensional leakage inductance analytical calculation model based on the image method overcomes the limitations of the one-dimensional model by considering the two-dimensional magnetic field distribution characteristics of the transformer, improving the accuracy of leakage inductance calculation to some extent, this model still has technical shortcomings. On the one hand, the model's computational logic is complex and the parameter solution process is cumbersome, which greatly increases computational complexity and leads to a significant reduction in computational speed. It loses the core advantage of efficient operation of analytical algorithms and is difficult to adapt to the scenario of rapid iterative design in engineering. On the other hand, existing two-dimensional leakage inductance models based on the mirror method generally adopt a correction method that introduces a single frequency factor to achieve frequency characteristic fitting when adapting to frequency variation conditions. This correction method has poor fit and limited adaptability, and cannot accurately characterize the dynamic change law of transformer leakage inductance under different operating frequencies. Ultimately, this leads to a significant limitation on the calculation accuracy of leakage inductance when the frequency condition changes, which seriously restricts the design accuracy and performance optimization effect of high-frequency transformers under wide frequency conditions. Summary of the Invention

[0005] Therefore, the technical problem to be solved by the present invention is to overcome the problems of high computational complexity, slow operation speed, poor adaptability of traditional frequency correction methods, insufficient leakage inductance calculation accuracy under wideband conditions, and inability to simultaneously take into account computational efficiency, computational accuracy and wideband adaptability performance in the prior art.

[0006] In a first aspect, to solve the above-mentioned technical problems, the present invention provides a method for constructing a two-dimensional leakage inductance model for a high-frequency transformer with closely spaced windings, comprising: S1. The high-frequency transformer includes a primary winding; based on the porosity parameter of the primary winding and Maxwell's equations, a first relationship between the electric field strength and the magnetic field strength is constructed; based on the first relationship and the magnetic field strength component relationship of the magnetic field strength, a first intensity component relationship between the magnetic field strength component and the electric field strength component is constructed. S2. Based on Maxwell's equations and the power supply angular frequency of the high-frequency transformer, obtain the second relationship between the electric field strength and the magnetic field strength; based on the second relationship and the electric field strength component relationship of the electric field strength, construct the second intensity component relationship between the magnetic field strength component and the electric field strength component. S3. Based on the second intensity component relationship and the first intensity component relationship, construct an electric field intensity expression; based on the electric field intensity expression and the second intensity component relationship, construct a two-dimensional magnetic field intensity mathematical model. S4. Construct a winding magnetic field energy model based on the two-dimensional magnetic field strength mathematical model and the winding parameters of the primary winding; S5. Based on the winding magnetic field energy model and the input current of the primary winding, obtain the two-dimensional leakage inductance model of the primary winding.

[0007] In one embodiment of the present invention, step S4, in the process of constructing the winding magnetic field energy model based on the two-dimensional magnetic field strength mathematical model and the winding parameters of the primary winding, includes: obtaining winding parameters under different winding structures based on the volume occupied by the insulation layer in the primary winding; if the volume occupied by the insulation layer is less than a threshold, the winding parameters include the average turn length, winding height, and winding thickness; otherwise, the winding parameters include the average turn length, winding height, winding thickness, and insulation layer thickness.

[0008] In one embodiment of the present invention, if the volume occupied by the insulating layer is less than a threshold, the expression for the winding magnetic field energy model is: ; If the volume occupied by the insulating layer is not less than the threshold, the expression for the winding magnetic field energy model is: ; in, This represents the energy of the winding magnetic field. Indicates permeability, Indicates the average turn length. Indicates the winding height. and Both refer to the winding thickness. Represents the magnetic field strength vector. Indicates the thickness of the insulation layer. This indicates the number of layers in the primary winding.

[0009] In one embodiment of the present invention, if the volume occupied by the insulating layer is less than a threshold, the expression of the two-dimensional leakage inductance model is: ; in, Indicates the leakage inductance value. This represents the input current of the primary winding. Indicates permeability, Indicates the average turn length. Indicates the winding height. Indicates the winding thickness. This represents the magnetic field strength vector.

[0010] In one embodiment of the present invention, if the volume occupied by the insulating layer is not less than a threshold, the expression of the two-dimensional leakage inductance model is: ; in, Indicates the leakage inductance value. This represents the input current of the primary winding. Indicates permeability, Indicates the average turn length. Indicates the winding height. Indicates the winding thickness. Represents the magnetic field strength vector. Indicates the thickness of the insulation layer. This indicates the number of layers in the primary winding.

[0011] In one embodiment of the present invention, the first relationship between the electric field strength and the magnetic field strength is: ; in, Represents the Hamiltonian operator. Represents the magnetic field strength vector. This indicates the porosity of the circular conductor winding. This indicates the conductivity of a round conductor winding. This represents the electric field intensity vector.

[0012] In one embodiment of the present invention, the second relationship between the electric field strength and the magnetic field strength is: ; in, Represents the Hamiltonian operator. Represents the electric field intensity vector. Represents the magnetic field strength vector. Indicates the imaginary part. Indicates permeability, This indicates the angular frequency of the power supply.

[0013] In one embodiment of the present invention, the expression for the electric field strength is: ; in, This represents the component of the electric field intensity along the y-axis. Indicates the imaginary part. Indicates the angular frequency of the power supply. Indicates permeability, This indicates the conductivity of a round conductor winding. This indicates the porosity of a circular conductor winding.

[0014] In one embodiment of the present invention, the relationship of the first intensity component is: ; in, This represents the magnetic field strength along the x-axis. This represents the z-axis component of the magnetic field strength. This represents the component of the electric field intensity along the y-axis. This indicates the conductivity of a round conductor winding. This indicates the porosity of a circular conductor winding.

[0015] Secondly, to solve the above-mentioned technical problems, the present invention provides a two-dimensional leakage inductance model construction system for a closely spaced high-frequency transformer, used to implement the above-mentioned method for constructing a two-dimensional leakage inductance model for a closely spaced high-frequency transformer, comprising: The first intensity component relationship construction module is used for a high-frequency transformer including a primary winding; based on the porosity parameter of the primary winding and Maxwell's equations, it constructs a first relationship between the electric field intensity and the magnetic field intensity; based on the first relationship and the magnetic field intensity component relationship of the magnetic field intensity, it constructs a first intensity component relationship between the magnetic field intensity component and the electric field intensity component. The second intensity component relationship construction module is used to obtain a second relationship between the electric field intensity and the magnetic field intensity based on the Maxwell equation and the power supply angular frequency of the high-frequency transformer; and to construct a second intensity component relationship between the magnetic field intensity component and the electric field intensity component based on the second relationship and the electric field intensity component relationship of the electric field intensity. The magnetic field strength mathematical model construction module is used to construct an electric field strength expression based on the second intensity component relationship and the first intensity component relationship; and to construct a two-dimensional magnetic field strength mathematical model based on the electric field strength expression and the second intensity component relationship. The winding magnetic field energy model construction module is used to construct a winding magnetic field energy model based on the two-dimensional magnetic field strength mathematical model and the winding parameters of the primary winding. The leakage inductance model construction module is used to construct a two-dimensional leakage inductance model of the primary winding based on the winding magnetic field energy model and the input current of the primary winding.

[0016] Compared with the prior art, the above-described technical solution of the present invention has the following advantages: (1) The present invention provides a method and system for constructing a two-dimensional leakage inductance model for a high-frequency transformer with closely spaced windings. It improves the coupling relationship of electromagnetic field components through Maxwell's equations, fully characterizing the interaction of electromagnetic fields at high frequencies and avoiding distortion in high-frequency field strength calculations. By simultaneously solving two sets of field strength relationships, the two-dimensional magnetic field model is analytically solved, eliminating the need for extensive mirror-iteration calculations, simplifying the calculation process, and balancing the rigor of the derivation with computational efficiency. The two-dimensional magnetic field model is combined with winding parameters to establish a magnetic field energy model, avoiding errors caused by approximate estimation of magnetic field energy and providing reliable intermediate quantities for leakage inductance calculation. Furthermore, the present invention obtains a two-dimensional leakage inductance model based on magnetic field energy, reducing computational complexity and shortening simulation time through analytical methods. Combining porosity, high-frequency electromagnetic characteristics, and actual winding parameters improves the model's engineering fit. Therefore, the present invention does not rely on empirical corrections, balancing modeling novelty, high computational accuracy, and high efficiency. It can accurately and quickly solve the leakage inductance of the primary winding of a high-frequency transformer, effectively improving the electromagnetic simulation and design level of devices, and demonstrating strong engineering practicality.

[0017] (2) In the modeling and derivation process of this invention, porosity parameters are introduced to fully consider the influence of the pores of the winding and core structure on the leakage magnetic field distribution, restore the leakage magnetic field distribution law under the real electromagnetic working conditions, eliminate modeling deviation in two dimensions, and obtain higher leakage inductance calculation accuracy compared with the traditional mirror method. Attached Figure Description

[0018] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings.

[0019] Figure 1 This is a flowchart of a method for constructing a two-dimensional leakage inductance model for a high-frequency transformer with closely spaced windings, according to a preferred embodiment of the present invention. Figure 2 This is a schematic diagram of a high-frequency transformer with a half-circular conductor winding and the coordinate system used in a preferred embodiment of the present invention. Figure 3 This is a schematic diagram of a tightly arranged circular conductor winding and its position in a coordinate system, according to a preferred embodiment of the present invention. Detailed Implementation

[0020] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0021] Example 1: Reference Figure 1 As shown, this invention provides a method for constructing a two-dimensional leakage inductance model for a high-frequency transformer with closely spaced windings, including but not limited to the following steps: S1. The high-frequency transformer includes a primary winding. Based on the porosity parameter of the primary winding and Maxwell's equations, a first relationship between the electric field strength and the magnetic field strength is constructed. Based on the first relationship and the magnetic field strength component relationship of the magnetic field strength, a first intensity component relationship between the magnetic field strength component and the electric field strength component is constructed. S2. Based on Maxwell's equations and the power supply angular frequency of the high-frequency transformer, the second relationship between the electric field strength and the magnetic field strength is obtained; based on the second relationship and the relationship between the electric field strength components, the second intensity component relationship between the magnetic field strength components and the electric field strength components is constructed. S3. Based on the relationship between the second intensity component and the first intensity component, construct the expression for the electric field intensity; based on the expression for the electric field intensity and the relationship between the second intensity component, construct a two-dimensional mathematical model for the magnetic field intensity. S4. Construct a winding magnetic field energy model based on the two-dimensional magnetic field strength mathematical model and the winding parameters of the primary winding; S5. Based on the winding magnetic field energy model and the input current of the primary winding, construct a two-dimensional leakage inductance model of the primary winding.

[0022] This invention discloses a method for constructing a two-dimensional leakage inductance model for a high-frequency transformer with tightly arranged windings. Through a complete technical logic of layered simultaneous equations, component iterative derivation, and energy equivalent modeling, it systematically solves the industry problems of weak theoretical support, poor computational accuracy, high computational redundancy, and insufficient adaptability to actual operating conditions in traditional mirror-based leakage inductance modeling. In step S1, this invention overcomes the inherent defects of traditional leakage inductance modeling, which assumes ideal dense windings and ignores the inherent structure of winding porosity. It integrates the porosity parameter of the primary winding into Maxwell's fundamental equations in the frequency domain, constructing a field strength correlation formula that closely matches the actual winding structure. This method avoids the crude modeling approach of relying on manually introducing frequency factors and empirical formulas to correct parameters, and considers the leakage magnetic field distortion caused by winding porosity and gaps from the source of modeling. It effectively avoids the systematic deviations of traditional modeling, ensures the physical rigor of the basic modeling equations, and reduces theoretical calculation errors at the source, laying a solid foundation for the construction of high-precision leakage inductance models. In step S2, this invention derives the correlation between electric and magnetic field strengths through simultaneous derivation of Maxwell's equations, perfecting the coupling logic of each component of the electromagnetic field in the two-dimensional plane. This overcomes the shortcomings of traditional techniques that rely on single electromagnetic equations for derivation and provide only a partial representation of electromagnetic field coupling characteristics. It can fully adapt to the electromagnetic field interaction laws under the high-frequency operating conditions of high-frequency transformers, effectively avoiding the problem of field strength calculation distortion in high-frequency scenarios and significantly improving the model's adaptability to high-frequency operating conditions. In step S3, this invention uses simultaneous iteration of the field strength component relationships from the previous two steps. By first solving the electric field strength expression and then deriving the two-dimensional magnetic field strength mathematical model through a closed-loop progressive logic, it achieves a precise mathematical representation of the leakage magnetic field across the entire two-dimensional plane. Unlike the fragmented logic of traditional mirror-based modeling, which requires a large number of mirror units and repeated iterative corrections, this invention adopts a purely analytical progressive derivation method, eliminating the need for complex iterative calculations. This avoids the logical loopholes of traditional modeling and significantly simplifies the calculation process, balancing modeling rigor with computational efficiency. In step S4, based on the obtained two-dimensional magnetic field strength mathematical model, the present invention constructs a winding magnetic field energy model by combining the actual winding parameters of the primary winding. This avoids the crude processing method of simplifying the magnetic field distribution and approximating the magnetic field energy in traditional technology. It uses precise magnetic field data across the entire domain to complete the magnetic field energy calculation, realizing the accurate mapping between the theoretical calculation of magnetic field energy and the actual working condition of the winding. This solves the problems of large errors and weak adaptability in traditional energy estimation, and provides reliable and accurate core intermediate data support for the accurate construction of the final leakage inductance model.In step S5, this invention completes the final construction of the two-dimensional leakage inductance model based on the winding magnetic field energy model, forming a complete modeling closed loop. Compared with the traditional mirror method, which relies on a large number of numerical iterations and equivalent fittings to solve for leakage inductance, this invention significantly reduces the computational complexity of leakage inductance modeling through an analytical solution approach, effectively shortening the simulation calculation time. Simultaneously, it integrates porosity characteristics, high-frequency electromagnetic coupling laws, and actual winding structure parameters throughout the modeling process for correction, ensuring that the final two-dimensional leakage inductance model closely matches the actual working state of the high-frequency transformer. This solves the technical problems of low computational accuracy, poor computational efficiency, and insufficient adaptability to operating conditions inherent in traditional models. In summary, this invention, through the layered and systematic innovative modeling logic of steps S1 to S5, forms an integrated modeling system from structural correction, equation solving, field strength calculation, energy modeling to leakage inductance formation. Compared with the traditional mirror method, it achieves multiple technological breakthroughs in high computational accuracy, fast computation speed, and low computational complexity. It can efficiently and accurately complete the leakage inductance calculation of the primary winding of a high-frequency transformer, significantly improving the accuracy and efficiency of electromagnetic design and simulation analysis of high-frequency transformers, and possesses extremely high engineering application and promotional value.

[0023] Specifically, refer to Figure 2 and Figure 3 As shown, in this embodiment of the invention, a coordinate system is constructed for the closely spaced windings in a high-frequency transformer, with the origin of the coordinate system being... Located at the rightmost edge of the lowest winding in the winding region (i.e., the right end of the lowest winding), with the x-axis extending continuously to the right and the z-axis extending continuously upward; that is, the x-axis and z-axis are not limited to a single winding layer. Figure 2 The image shows a high-frequency transformer with a half-circular conductor winding and the coordinate system used. Figure 3 It shows the closely packed circular conductor windings and their position in the coordinate system.

[0024] In this embodiment of the invention, the main core idea is as follows: first, a two-dimensional magnetic field strength mathematical model is constructed (corresponding to steps S1 to S3); second, a two-dimensional leakage inductance model is constructed using the two-dimensional magnetic field strength mathematical model (corresponding to steps S4 to S5). The specific steps of the two-dimensional leakage inductance model construction method proposed in this invention are described in detail below.

[0025] Specifically, for the primary winding of a high-frequency transformer, assuming the current in each conductor points in the positive y-axis direction, the electric field strength also only has a component in the positive y-axis direction. Here, the electric field strength... The mathematical expression is: ,and , ; in, This represents the component of the electric field intensity along the y-axis. This represents the component of the electric field intensity along the x-axis. Let represent the component of the electric field intensity along the z-axis. This represents the unit vector along the y-axis.

[0026] Specifically, in this embodiment of the invention, the magnetic field strength of the primary winding is considered to be two-dimensionally distributed, meaning the magnetic field strength has components in both the x-axis and z-axis directions. Two-dimensional magnetic field strength distribution. The mathematical representation of is: ,and ; in, This represents the component of the magnetic field strength along the x-axis. This represents the component of the magnetic field strength along the x-axis. This represents the component of the magnetic field strength along the x-axis. Represents the unit vector along the x-axis. This represents the unit vector along the z-axis.

[0027] Specifically, in step S1, refer to Figure 3 As shown, Maxwell's equations are written. Based on the integral form of Maxwell's equations and the porosity parameter of the primary winding, we obtain: (1) in, This indicates the porosity of the circular conductor winding. Indicates the integration path The area enclosed Represents the integral loop element vector. This indicates the conductivity of a circular conductor winding.

[0028] Furthermore, according to Stokes' theorem, we obtain: (2) in, This represents the Hamiltonian operator.

[0029] Furthermore, combining formulas (1) and (2), we obtain: (3)

[0030] Furthermore, according to formula (3), the first relationship between the electric field strength and magnetic field strength containing porosity is constructed as follows: (4) in, Represents the magnetic field strength vector. This represents the electric field intensity vector.

[0031] Furthermore, based on the first relational expression and the relational expression for the magnetic field strength components, the steps to construct the first intensity component relational expression between the magnetic field strength components and the electric field strength components are as follows: Step S110: Obtain the magnetic field strength component relationship formula; wherein the magnetic field strength component relationship formula is: (5) in, This represents the rate of change of the field quantity along the x-axis in space. This represents the rate of change of the field quantity along the y-axis in space. This represents the rate of change of the field quantity along the z-axis in space.

[0032] Step S120: Combine the first relation (4) with the magnetic field strength component relation (5) to obtain: , .

[0033] The first intensity component relationship between the magnetic field intensity component and the electric field intensity component is further obtained, and its expression is: (6)

[0034] Specifically, in step S2, based on Maxwell's equations, the power supply angular frequency, and the permeability of the copper wire, insulating layer, and air, a second relationship is obtained between the electric field strength and the magnetic field strength, the expression of which is: (7) in, Represents the electric field intensity vector. Represents the magnetic field strength vector. Indicates the imaginary part. Indicates the permeability of copper wire, insulation layer, and air. This indicates the angular frequency of the power supply applied to the high-frequency transformer.

[0035] Specifically, based on the second relation and the electric field intensity component relation, the steps to construct the second intensity component relation between the magnetic field intensity component and the electric field intensity component are as follows: Step S210: Obtain the relationship between the electric field intensity components, which is expressed as follows: (8)

[0036] Step S220: Based on the second relation (7) and the electric field intensity component relation (8), the second intensity component relation between the magnetic field intensity component and the electric field intensity component is obtained as follows: (9)

[0037] Specifically, in step S3, the specific steps for constructing the two-dimensional magnetic field strength mathematical model are as follows: S310. Based on the second intensity component relationship (9), the electric field intensity and magnetic field intensity satisfy the following relationship: (10) (11)

[0038] S320. Substituting formulas (10) and (11) into the first intensity component relationship (6), we obtain the electric field intensity expression, which is as follows: (12)

[0039] S330, Solve for the electric field strength expression (12) to obtain... The specific expression for the electric field strength is obtained from the expression (12). Substituting back into formula (10), the x-axis component of the magnetic field strength can be obtained. Similarly, the electric field strength expression (12) is obtained... By substituting into formula (11), the z-axis component of the magnetic field strength can be obtained. .

[0040] Furthermore, the obtained Components and Substituting the components into the mathematical model of the two-dimensional magnetic field strength, we obtain the two-dimensional magnetic field strength. The specific expression is as follows. Specifically, the expression for the two-dimensional magnetic field strength mathematical model is: .

[0041] Based on the two-dimensional mathematical model of the magnetic field strength obtained in step S3, a two-dimensional mathematical model of the leakage inductance is further constructed.

[0042] Specifically, in step S4, the process of constructing the winding magnetic field energy model based on the two-dimensional magnetic field strength mathematical model and the winding parameters of the primary winding includes constructing the relationship satisfied by the magnetic field energy (i.e., the winding magnetic field energy model) based on the insulation layer thickness of the primary winding. If the insulation layer thickness of the primary winding is thin, its volume can be ignored; however, if the insulation layer thickness is large, the influence of the insulation layer thickness needs to be considered. Specifically, the winding parameters under different winding structures are obtained based on the volume occupied by the insulation layer in the primary winding; if the volume occupied by the insulation layer is less than a threshold, the winding parameters include the average turn length, winding height, and winding thickness; otherwise, the winding parameters include the average turn length, winding height, winding thickness, and insulation layer thickness. Among them, the judgment threshold of the insulation layer volume is determined based on the ratio of the outer diameter of the winding conductor to the insulation layer thickness.

[0043] Furthermore, if the volume occupied by the insulating layer is less than the threshold, the expression for the constructed winding magnetic field energy model is: (13) If the volume occupied by the insulating layer is not less than the threshold, the expression for the constructed winding magnetic field energy model is: (14) in, This represents the energy of the winding magnetic field. Indicates the permeability of copper wire, insulation layer, and air. Indicates the average turn length. Indicates the winding height; and Both refer to the winding thickness. Represents the magnetic field strength vector. Indicates the thickness of the insulation layer. This indicates the number of layers in the primary winding. It should be noted that this setting is used when the volume occupied by the insulation layer is negligible. Indicates the winding thickness; when the volume occupied by the insulation layer is not negligible, it is set to... This indicates the winding thickness.

[0044] Specifically, in step S5, the magnetic field energy in the winding magnetic field energy model (13) or (14) is... Substituting these values ​​into the leakage inductance expression, the primary leakage inductance of the high-frequency transformer under two different winding conditions can be calculated; the two-dimensional leakage inductance model expression is as follows: (15) in, Indicates the leakage inductance value. This represents the energy of the winding magnetic field. express.

[0045] Furthermore, the mathematical expression for the two-dimensional leakage inductance model that ignores the thickness of the insulation layer is: (16) in, The value is the two-dimensional magnetic field strength obtained in step S3.

[0046] Furthermore, the mathematical expression for the two-dimensional leakage inductance model considering the insulation layer thickness is as follows: (17) in, The same applies to the two-dimensional magnetic field strength obtained in step S3.

[0047] Specifically, high-frequency transformers also include secondary windings. (Refer to...) Figure 2 and Figure 3As shown in the figure, red represents the primary winding and blue represents the secondary winding. The method for constructing the two-dimensional leakage inductance model of the secondary winding is similar to steps S1 to S5, only requiring the addition of the two-dimensional leakage inductance model (16) Replace with secondary winding width ; in the two-dimensional leakage inductance model (17) Replace with secondary winding width , Replace with the width of the secondary insulation layer This allows us to calculate the leakage inductance value of the secondary side in both cases. .

[0048] The leakage inductance value obtained by the above method takes into account the two-dimensional distribution of the magnetic field strength and is applicable to cases where the primary and secondary windings are closely arranged. The specific application steps of the method described in this embodiment are given below: Step 1: Solve the electric field intensity expression (12) and obtain the solution result. Specifically, by substituting the operating frequency of the high-frequency transformer, the conductivity of the copper wire, the magnetic permeability of the vacuum, and the porosity of the conductor into the solution of the electric field strength expression (12), the electric field strength values ​​at different locations of the transformer are obtained.

[0049] Step 2: Obtain the obtained Substituting the values, the permeability of vacuum, and the operating frequency of the transformer into formula (10), the x-axis component of the magnetic field strength is obtained. The obtained The value, the permeability of vacuum, and the operating frequency of the transformer are substituted into formula (11) to obtain the z-axis component of the magnetic field strength. .

[0050] Step 3: Obtain the calculated Components and Substitute the components into the following categories: The two-dimensional magnetic field strength was further obtained. The specific expression.

[0051] Step 4: Specific details of the two-dimensional magnetic field strength Substituting the values ​​of the two-dimensional magnetic field strength, winding thickness, winding height, winding turn length, and vacuum permeability into formula (16), the leakage inductance value with negligible insulation thickness can be calculated. For windings where insulation thickness cannot be ignored, it is only necessary to calculate the leakage inductance value with negligible insulation thickness. The leakage inductance of the transformer considering the insulation layer thickness can be calculated by substituting the values, winding thickness, insulation layer thickness, number of winding layers, winding height, winding turn length, and vacuum permeability into the proposed formula (17).

[0052] Furthermore, compared with existing technologies that use the traditional mirror method to construct leakage inductance models, the two-dimensional leakage inductance model construction method described in this embodiment of the invention has the following significant advantages: First, the overall modeling approach of this invention differs from the traditional mirror method. Instead of directly introducing frequency factors to characterize the correlation between the model and frequency, it uses the frequency domain Maxwell equations to complete a complete and rigorous theoretical derivation, thus avoiding the inherent limitations of the traditional mirror method that relies on empirical factors to correct frequency-varying characteristics.

[0053] Secondly, unlike the complex iterative calculation logic of the traditional mirror method, this invention directly solves the leakage inductance parameters analytically based on the frequency domain electromagnetic field equations, eliminating the need for a large number of mirror unit superposition and repeated iterative solution steps, effectively reducing the overall computational complexity, significantly shortening the time spent solving the leakage inductance parameters, and greatly improving computational efficiency. It can meet the needs of rapid simulation and batch parameterized design of high-frequency electromagnetic equipment.

[0054] Third, this invention improves the accuracy of leakage inductance calculation. On the one hand, this invention relies on the Maxwell equations in the frequency domain to achieve a precise mathematical representation of frequency characteristics, avoiding the empirical errors caused by directly introducing frequency factors in the traditional image method. On the other hand, the porosity parameter is introduced in the modeling and derivation process to fully consider the influence of the porosity of the winding and core structure on the leakage magnetic field distribution, restoring the leakage magnetic field distribution law under real electromagnetic conditions. This dual-dimensional elimination of modeling deviations results in higher leakage inductance calculation accuracy compared to the traditional image method.

[0055] In summary, this invention addresses the two core shortcomings of the traditional image method—high computational complexity and low computational accuracy—through frequency domain analytical modeling. It also boasts multiple advantages, including novel modeling theory, low computational complexity, fast operation speed, and high numerical solution accuracy. This invention provides high-precision and high-efficiency leakage inductance calculation support for the electromagnetic design and simulation analysis of electromagnetic devices such as high-frequency transformers and inductors, demonstrating significant engineering application value.

[0056] Example 2: Based on the same inventive concept, this embodiment provides a two-dimensional leakage inductance model construction system for a high-frequency transformer with closely arranged windings. The principle of solving the problem is similar to the two-dimensional leakage inductance model construction method for a high-frequency transformer with closely arranged windings provided in Embodiment 1, and the repeated parts will not be described again.

[0057] This embodiment provides a two-dimensional leakage inductance model construction system for a closely spaced high-frequency transformer, used to implement the two-dimensional leakage inductance model construction method for a closely spaced high-frequency transformer described in Embodiment 1, including: The first intensity component relationship construction module is used for high-frequency transformers including primary windings; based on the porosity parameter of the primary winding and Maxwell's equations, it constructs a first relationship between electric field intensity and magnetic field intensity; based on the first relationship and the magnetic field intensity component relationship of the magnetic field intensity, it constructs a first intensity component relationship between the magnetic field intensity component and the electric field intensity component. The second intensity component relationship construction module is used to obtain the second relationship between electric field intensity and magnetic field intensity based on Maxwell's equations and the power supply angular frequency of the high-frequency transformer; and to construct the second intensity component relationship between magnetic field intensity component and electric field intensity component based on the second relationship and the electric field intensity component relationship of electric field intensity. The magnetic field strength mathematical model construction module is used to construct the electric field strength expression based on the second intensity component relationship and the first intensity component relationship; and to construct a two-dimensional magnetic field strength mathematical model based on the electric field strength expression and the second intensity component relationship. The winding magnetic field energy model construction module is used to construct a winding magnetic field energy model based on the two-dimensional magnetic field strength mathematical model and the winding parameters of the primary winding. The leakage inductance model construction module is used to construct a two-dimensional leakage inductance model of the primary winding based on the winding magnetic field energy model and the input current of the primary winding.

[0058] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0059] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0060] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0061] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0062] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A method for constructing a two-dimensional leakage inductance model for a high-frequency transformer with closely spaced windings, characterized in that, include: S1. The high-frequency transformer includes a primary winding; based on the porosity parameter of the primary winding and Maxwell's equations, a first relationship between the electric field strength and the magnetic field strength is constructed; based on the first relationship and the magnetic field strength component relationship of the magnetic field strength, a first intensity component relationship between the magnetic field strength component and the electric field strength component is constructed. S2. Based on Maxwell's equations and the power supply angular frequency of the high-frequency transformer, obtain the second relationship between the electric field strength and the magnetic field strength; based on the second relationship and the electric field strength component relationship of the electric field strength, construct the second intensity component relationship between the magnetic field strength component and the electric field strength component. S3. Based on the second intensity component relationship and the first intensity component relationship, construct an electric field intensity expression; based on the electric field intensity expression and the second intensity component relationship, construct a two-dimensional magnetic field intensity mathematical model. S4. Construct a winding magnetic field energy model based on the two-dimensional magnetic field strength mathematical model and the winding parameters of the primary winding; S5. Based on the winding magnetic field energy model and the input current of the primary winding, construct a two-dimensional leakage inductance model of the primary winding.

2. The method for constructing a two-dimensional leakage inductance model for a closely spaced high-frequency transformer according to claim 1, characterized in that, In step S4, the process of constructing the winding magnetic field energy model based on the two-dimensional magnetic field strength mathematical model and the winding parameters of the primary winding includes: obtaining winding parameters under different winding structures based on the volume occupied by the insulation layer in the primary winding; if the volume occupied by the insulation layer is less than a threshold, the winding parameters include the average turn length, winding height, and winding thickness; otherwise, the winding parameters include the average turn length, winding height, winding thickness, and insulation layer thickness.

3. The method for constructing a two-dimensional leakage inductance model for a closely spaced high-frequency transformer according to claim 2, characterized in that, If the volume occupied by the insulating layer is less than the threshold, the expression for the winding magnetic field energy model is: ； If the volume occupied by the insulating layer is not less than the threshold, the expression for the winding magnetic field energy model is: ； in, This represents the energy of the winding magnetic field. Indicates magnetic permeability, Indicates the average turn length. Indicates the winding height. and Both refer to the winding thickness. Represents the magnetic field strength vector. Indicates the thickness of the insulation layer. This indicates the number of layers in the primary winding.

4. The method for constructing a two-dimensional leakage inductance model for a closely spaced high-frequency transformer according to claim 3, characterized in that, If the volume occupied by the insulating layer is less than the threshold, the expression for the two-dimensional leakage inductance model is: ； in, Indicates the leakage inductance value. This represents the input current of the primary winding. Indicates magnetic permeability, Indicates the average turn length. Indicates the winding height. Indicates the winding thickness. This represents the magnetic field strength vector.

5. The method for constructing a two-dimensional leakage inductance model for a closely spaced high-frequency transformer according to claim 3, characterized in that, If the volume occupied by the insulating layer is not less than the threshold, the expression for the two-dimensional leakage inductance model is: ； in, Indicates the leakage inductance value. This represents the input current of the primary winding. Indicates permeability, Indicates the average turn length. Indicates the winding height. Indicates the winding thickness. Represents the magnetic field strength vector. Indicates the thickness of the insulation layer. This indicates the number of layers in the primary winding.

6. The method for constructing a two-dimensional leakage inductance model for a closely spaced high-frequency transformer according to claim 1, characterized in that, The first relationship between the electric field strength and the magnetic field strength is: ； in, Represents the Hamiltonian operator. Represents the magnetic field strength vector. This indicates the porosity of the circular conductor winding. This indicates the conductivity of a round conductor winding. This represents the electric field intensity vector.

7. The method for constructing a two-dimensional leakage inductance model for a closely spaced high-frequency transformer according to claim 1, characterized in that, The second relationship between the electric field strength and the magnetic field strength is: ； in, Represents the Hamiltonian operator. Represents the electric field intensity vector. Represents the magnetic field strength vector. Indicates the imaginary part unit. Indicates permeability, This indicates the angular frequency of the power supply.

8. The method for constructing a two-dimensional leakage inductance model for a closely spaced high-frequency transformer according to claim 1, characterized in that, The expression for the electric field strength is: ； in, This represents the component of the electric field intensity along the y-axis. Indicates the imaginary part unit. Indicates the angular frequency of the power supply. Indicates magnetic permeability, This indicates the conductivity of a round conductor winding. This indicates the porosity of a circular conductor winding.

9. The method for constructing a two-dimensional leakage inductance model for a closely spaced high-frequency transformer according to claim 1, characterized in that... The first intensity component relationship is: ； in, This represents the magnetic field strength along the x-axis. This represents the z-axis component of the magnetic field strength. This represents the component of the electric field intensity along the y-axis. This indicates the conductivity of a round conductor winding. This indicates the porosity of a circular conductor winding.

10. A system for constructing a two-dimensional leakage inductance model for a closely spaced high-frequency transformer, used to implement the method for constructing a two-dimensional leakage inductance model for a closely spaced high-frequency transformer as described in any one of claims 1 to 9, characterized in that, include: The first intensity component relationship construction module is used for a high-frequency transformer including a primary winding; based on the porosity parameter of the primary winding and Maxwell's equations, it constructs a first relationship between the electric field intensity and the magnetic field intensity; based on the first relationship and the magnetic field intensity component relationship of the magnetic field intensity, it constructs a first intensity component relationship between the magnetic field intensity component and the electric field intensity component. The second intensity component relationship construction module is used to obtain a second relationship between the electric field intensity and the magnetic field intensity based on the Maxwell equation and the power supply angular frequency of the high-frequency transformer; and to construct a second intensity component relationship between the magnetic field intensity component and the electric field intensity component based on the second relationship and the electric field intensity component relationship of the electric field intensity. The magnetic field strength mathematical model construction module is used to construct an electric field strength expression based on the second intensity component relationship and the first intensity component relationship; and to construct a two-dimensional magnetic field strength mathematical model based on the electric field strength expression and the second intensity component relationship. The winding magnetic field energy model construction module is used to construct a winding magnetic field energy model based on the two-dimensional magnetic field strength mathematical model and the winding parameters of the primary winding. The leakage inductance model construction module is used to construct a two-dimensional leakage inductance model of the primary winding based on the winding magnetic field energy model and the input current of the primary winding.

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