A multi-winding high-frequency transformer leakage inductance analytical calculation method

Abstract

A multi-winding high-frequency transformer leakage inductance analytical calculation method, comprising: determining the number of leakage inductances of the secondary winding corresponding to different primary windings according to the number of primary and secondary windings of the multi-winding high-frequency transformer; dividing the leakage magnetic energy region corresponding to different leakage inductances into winding interlayer insulation region, winding insulation region, through-flow winding region and open-circuit winding region; deriving the magnetic field intensity of the winding interlayer insulation region and the winding insulation region; deriving the magnetic field intensity of the through-flow winding region and the open-circuit winding region based on Maxwell's equations; further integrating the corresponding leakage magnetic energy according to the magnetic field intensity of each region; calculating the leakage magnetic energy corresponding to each leakage inductance according to the different leakage magnetic energy calculation region of each leakage inductance, summing the leakage magnetic energy of the corresponding region, and then calculating the leakage inductance parameters according to the magnetic field energy method. The method considers the open-circuit winding unique in the leakage inductance calculation process of the multi-winding high-frequency transformer, and accurately calculates the leakage magnetic energy of the open-circuit winding.

Description

Technical Field

[0001] This invention relates to the field of high-frequency transformer leakage inductance calculation technology, specifically to an analytical calculation method for leakage inductance of multi-winding high-frequency transformers. Background Technology

[0002] The quadruple active bridge (QAB) converter is an extension of the dual active bridge (DAB) converter. While retaining the advantages of the latter, it reduces the number of transformers and auxiliary modules, thus lowering costs. QAB converters can be structurally divided into two types: asymmetrical quadruple active bridge (AQAB), consisting of three input bridges and one output bridge, and symmetrical quadruple active bridge (SQAB), consisting of two input bridges and two output bridges. AQAB offers higher efficiency and lower cost, making it more widely used. The multi-winding high-frequency transformer is the core component of the QAB converter. By integrating multiple isolated windings on a single magnetic core, it achieves multiple independent outputs and bidirectional power flow within the same structure, significantly improving the system's power density and integration. It also enables voltage matching and power dispatching in multi-port power conversion. Unlike two-winding transformers, multi-winding transformers have multiple leakage inductances, each corresponding to a different leakage magnetic field distribution. This characteristic is significantly different from that of two-winding transformers, making traditional methods for analyzing the leakage inductance of two-winding transformers no longer entirely applicable.

[0003] There are two main methods for calculating the leakage inductance of high-frequency transformers: numerical methods and analytical methods.

[0004] (I): In terms of numerical methods, the literature [1] (Liu Xingliang, Qiu Qi, Wang Ruoyu, et al. Leakage inductance design method of segmented winding of high frequency high voltage transformer based on finite element simulation [J]. High Voltage Engineering, 2020, 46(2): 610-617.) combines finite element simulation with the concept of segmented winding to accurately control the leakage inductance parameters.

[0005] Reference [2] (Chen Bin, Li Lin, Liu Haijun, et al. Calculation and analysis of leakage inductance and winding loss of high frequency transformer based on finite element method [J]. New Technology of Electrical Engineering and Energy, 2018, 37(01): 8-14.) uses the finite element method to analyze the influence of winding structure and different cross-transformation arrangement on frequency-varying leakage inductance.

[0006] Reference [3] (CHEN Tianyuan, ZHAO Zhigang, SHEN Zhan, et al. A homogenized FEM data-driven model for cal-culating leakage inductance of high-frequency transformer with Litz-wire winding[J]. IEEE Journal of Emerging and Selected Topics in Power Electronics, 2024,12(2):2067-2081.) uses a two-dimensional finite element model to calculate the leakage inductance of Litz wire winding at high frequencies. Considering the frequency-varying characteristics of leakage inductance, the finite element method needs to perform frequency sweep calculations at multiple frequency points in a wide frequency range, which takes a long time and has high hardware requirements for computers.

[0007] (ii) Regarding analytical methods, the one-dimensional magnetic field assumption of winding leakage magnetic field energy was first proposed in reference [4] (Dowell P L. Effects of eddy currents in transformer windings[J]. Proceedings of the Institution of Electro-ecological Engineers, 1966, 113(8): 1387-1394.). This method has high calculation accuracy for copper foil windings.

[0008] Reference [5] (Lu Fangcheng, Guo Yunxiang, Li Peng. Calculation and correction method of leakage inductance of high power medium frequency transformer [J]. High Voltage Engineering, 2016, 42(6): 1702-1707.) uses the porosity coefficient to correct the conductivity of the winding and converts other types of windings into copper foil windings with the same height as the window to calculate the leakage inductance parameters.

[0009] Reference [6] (Zhao Zhigang, Zheng Yuxuan, Chen Tianyuan, et al. Calculation model of leakage inductance of high frequency round conductor transformer based on mirror method [J]. Proceedings of the CSEE, 2023, 44(16): 6697-6706.) Considering the end effect of the winding, the leakage magnetic field of the core window region is extracted by mirror method, and the frequency correlation factor characterizing the skin effect and proximity effect is introduced to accurately calculate the leakage inductance of high frequency round conductor transformer.

[0010] Currently, the calculation of leakage inductance of high-frequency transformers mainly focuses on two-winding transformers, while there is relatively little research on the analysis and calculation of leakage inductance parameters for multi-winding transformers.

[0011] References [7] (Liang Yong. Research and Design of Multi-winding High-Frequency Transformers [D]. Shanghai: Shanghai Jiaotong University, 2017.) and [8] (Cao Hongxia. Multi-objective Design and Insulation Structure Optimization of Multi-winding Medium-Frequency Transformers [D]. Yichang: Three Gorges University, 2023.) use the finite element method to simulate the leakage inductance of multi-winding transformers, without mentioning analytical calculation methods.

[0012] Reference [9] (Wang Jiang. Research on parameter constraints and design of MMC-SST four-winding high-frequency transformer [D]. Qinhuangdao: Yanshan University, 2023.) directly applies the leakage inductance calculation method of two-winding toroidal transformer to four-winding toroidal transformer, which has a limited scope of application. Reference

[10] (Yuan Xuan. Electromagnetic characteristic analysis and optimization design method of large-capacity three-winding high-frequency transformer [D]. Beijing: North China Electric Power University (Beijing), 2021.) derives the analytical calculation formula for leakage inductance of three-winding high-frequency transformer, but the calculation of leakage magnetic energy of open-circuit winding has a large error when the number of winding layers increases. Summary of the Invention

[0013] To address the problem of precise control of leakage inductance in multi-winding high-frequency transformers in multi-active bridge converters, this invention provides an analytical calculation method for the leakage inductance of multi-winding high-frequency transformers. This method considers the open-circuit windings unique in the leakage inductance calculation process of multi-winding high-frequency transformers, accurately calculates the leakage magnetic energy of the open-circuit windings, and further derives analytical expressions for the frequency-varying leakage inductance attributed to different primary windings. This provides a theoretical basis for the structural design and leakage inductance control of multi-winding high-frequency transformers.

[0014] The technical solution adopted in this invention is as follows:

[0015] A method for analytically calculating the leakage inductance of a multi-winding high-frequency transformer includes the following steps: Step 1: Determine the number of leakage inductances of the secondary windings attributed to different primary windings based on the number of primary and secondary windings of the multi-winding high-frequency transformer. Step 2: Divide the leakage magnetic energy regions corresponding to different leakage inductances. Generally, they are divided into the interlayer insulation region, the inter-winding insulation region, the current-carrying winding region, and the open-circuit winding region. Step 3: Based on Ampere's circuital law, derive the magnetic field strength in the interlayer insulation region and the inter-winding insulation region of the winding; based on Maxwell's equations, derive the magnetic field strength in the current-carrying winding region and the open-circuit winding region. Step 4: Based on the magnetic field strength of each region, further integrate to obtain the corresponding leakage magnetic energy; Step 5: Calculate the leakage magnetic energy of each leakage inductor according to the different leakage magnetic energy calculation regions, sum the leakage magnetic energy of the corresponding regions, and then calculate the parameters of each leakage inductor according to the magnetic field energy method.

[0016] In step 1, the multi-winding high-frequency transformer used in the AQAB converter is taken as the calculation object. This multi-winding high-frequency transformer has three primary windings, P1, P2, and P3. It has one secondary winding, S1. The number of leakage inductances to be calculated is three, meaning the leakage inductance of the secondary winding S1 is respectively attributed to the primary windings P1, P2, and P3. L σ(P1,S1) , L σ(P2,S1) and L σ(P3,S1) .

[0017] In step 2, the method for dividing the leakage magnetic energy region is as follows: According to the magnetic field energy method, it is necessary to divide the calculation area for leakage magnetic energy corresponding to different leakage inductances. The relationship between leakage inductance and leakage magnetic energy is as follows: (1); In formula (1): W This refers to the leakage magnetic energy of the transformer. L σ To reduce the leakage inductance to the original side; I To calculate the effective value of the winding current on the reduced side; μ 0 represents the permeability of free space; H To calculate the magnetic field strength in the region; V This is the volume of the computational region.

[0018] The leakage magnetic energy region can be generally divided into the winding interlayer insulation region, the winding inter-insulation region, and the winding region. The winding region can be further divided into the current-carrying winding region and the open-circuit winding region. Figure 2 A schematic diagram showing the division of leakage magnetic energy regions in a multi-winding high-frequency transformer.

[0019] Calculate leakage inductance L σ(P1,S1) At that time, the area to be covered for calculating leakage magnetic energy is as follows: Figure 3 As shown, this includes: the internal region of the secondary winding S1, see... Figure 3 Number ①; Interlayer insulation region of secondary winding S1, see Figure 3 Number ②; the internal region of the primary winding P1, see Figure 3 Designation ③; Interlayer insulation region of primary winding P1, see Figure 3 Number ④; Insulation area between secondary winding S1 and primary winding P1, see Figure 3 Number ⑤; Calculate leakage inductance L σ(P2,S1) At that time, the area to be covered for calculating leakage magnetic energy is as follows: Figure 4 As shown, this includes: the internal region of the secondary winding S1, see... Figure 4 Number ①; Interlayer insulation region of secondary winding S1, see Figure 4 Number ②; the internal region of the primary winding P2, see Figure 4 Designation ③; Interlayer insulation region of primary winding P2, see Figure 4 Number ④; Internal area of ​​open winding P1, see Figure 4 Number ⑤; Interlayer insulation area of ​​open winding P1, see Figure 4 Reference number ⑥; the insulation region between the secondary winding S1 and the open winding P1, see Figure 4 Reference number ⑦; the insulation region between open winding P1 and primary winding P2, see Figure 4 Number ⑧.

[0020] Calculate leakage inductance L σ(P3,S1) At that time, the area to be covered for calculating leakage magnetic energy is as follows: Figure 5 As shown, this includes: the internal region of the secondary winding S1, see... Figure 5 Number ①; Interlayer insulation region of secondary winding S1, see Figure 5 Number ②; the internal region of the primary winding P3, see Figure 5 Designation ③; Interlayer insulation region of primary winding P3, see Figure 5 Number ④; Internal area of ​​open winding P1, see Figure 5 Number ⑤; Interlayer insulation area of ​​open winding P1, see Figure 5 Number ⑥; Internal area of ​​open winding P2, see Figure 5 Number ⑦; Interlayer insulation region of open winding P2, see Figure 5 Number ⑧; Insulation area between secondary winding S1 and open winding P1, see Figure 5 Number 9; Insulation area between open windings P1 and P2, see Figure 5 Number ⑩; Insulation area between open winding P2 and primary winding P3, see Figure 5 winning number .

[0021] In step 3, the method for calculating the magnetic field strength in each region is as follows: The magnetic field strength in the interlayer insulation region and the inter-winding insulation region of the winding is obtained from Ampere's circuital law: No. i The magnetic field strengths of the inner and outer insulation regions of the copper foil winding are: (2); (3); In the above formula: H in , H out These represent the magnetic field strengths of the inner and outer insulation regions of the winding, respectively. I This represents the effective value of the winding current.h w This refers to the height of the transformer core window. This refers to the specific number of layers in a single-layer copper foil winding.

[0022] Solving for the magnetic field strength in the current-carrying winding region and the open-circuit winding region requires the use of Maxwell's equations: No. i Copper foil winding along thickness The magnitude of the internal magnetic field strength in the direction is: (4); In equation (4): H ( x ) represents the copper foil winding along the thickness The magnitude of the internal magnetic field strength in the direction; α =(1+j) / δ , The imaginary unit, δ For skin depth; d f The thickness of each winding layer; The expression for skin depth is: (5); In formula (5): f The frequency of the applied current; σ Electrical conductivity; is the vacuum permeability.

[0023] In step 4, the method for calculating the leakage magnetic energy in each region is as follows: According to the magnetic field energy method, it is necessary to calculate the magnetic field strength of each region; the relationship between the leakage magnetic energy and the magnetic field strength of each region is as follows: (6); In formula (6): To calculate the leakage magnetic energy in the region; l To calculate the average length of the region; d To calculate the thickness of the region; The formula for calculating the leakage magnetic energy in the interlayer insulation region of the current-carrying winding is: (7); In equation (7): This refers to the leakage magnetic energy in the interlayer insulation region of the current-carrying winding; d ins This refers to the interlayer insulation distance of the current-carrying winding; m This represents the total number of layers in the current-carrying winding. This represents the effective value of the winding current.

[0024] The formula for calculating leakage magnetic energy in the insulation region between different windings is: (8); In equation (8): Leakage magnetic energy in the insulation region between different windings; d iso This refers to the insulation distance between different windings; This represents the total number of layers of the current-carrying winding within the insulation region.

[0025] The formula for calculating the leakage flux energy in the current-carrying winding region is: (9); In equation (9): W w This refers to the leakage magnetic energy in the current-carrying winding region. d f This refers to the thickness of a single-layer winding. For the first n The magnitude of the magnetic field strength inside the laminar current winding; m This represents the total number of layers in the current-carrying winding. n This refers to the specific number of layers in a single-layer current-carrying winding.

[0026] F 1 and F 2 represents the skin effect and proximity effect factors of the corresponding windings, respectively, and are calculated as follows: (10); In equation (10): Δ1 is the normalized thickness of the winding, Δ1= d f / δ ; If the magnetic field strength on the inner and outer sides of the open-circuit winding is approximately the same, then the leakage magnetic energy stored in each layer of the open-circuit winding is equal. m The formula for calculating the leakage magnetic energy stored in a two-layer open-circuit winding is: (11); In equation (11): The leakage magnetic energy stored in the open-circuit winding; They are respectively the 1st, 2nd, ... th m Leakage magnetic energy stored in two layers of open-circuit windings m 2 represents the total number of layers in the open-circuit winding; m 3 represents the total number of layers of the open-circuit winding with current-carrying winding inside; and These are the skin effect and proximity effect factors for open-circuit windings, respectively; F 1 and F In step 2, Δ1 is transformed into the normalized thickness Δ of the open-circuit winding. Ind We can then obtain, where Δ Ind = d f,Ind / δ ,d f,Ind This refers to the thickness of a single-layer open-circuit winding.

[0027] m The expression for the interlayer leakage flux energy of a two-layer open-circuit winding is: (12); In equation (12): for m Interlayer leakage magnetic energy of 2-layer open-circuit winding m 2 represents the total number of layers in the open-circuit winding; d ins,Ind This refers to the interlayer insulation distance of the open-circuit winding; m 3 represents the total number of layers of the open-circuit winding with current-carrying winding inside.

[0028] In step 5, different leakage inductors correspond to different leakage magnetic energy calculation regions. The leakage magnetic energy of the corresponding regions is summed to obtain the total leakage magnetic energy corresponding to each leakage inductor. W The leakage inductance is calculated using the total leakage magnetic energy. (13); In equation (13): It is a leakage inductance.

[0029] 1) Calculate leakage inductance L σ(P1,S1) At that time, the total leakage magnetic energy in each region is: (14); In equation (14): To calculate leakage inductance L σ(P1,S1) Total leakage magnetic energy in each region at that time; This refers to the leakage magnetic energy inside the secondary winding S1. This refers to the leakage magnetic energy inside the primary winding P1. This refers to the leakage magnetic energy in the interlayer insulation region of the secondary winding S1. This refers to the leakage magnetic energy in the interlayer insulation region of the primary winding P1; This refers to the leakage magnetic energy in the insulation region between the secondary winding S1 and the primary winding P1.

[0030] The formula for calculating the leakage inductance between the secondary winding S1 and the primary winding P1, referred to the primary winding P1 side, is as follows: (15); In equation (15): The leakage inductance between the secondary winding S1 and the primary winding P1 is referred to the primary winding P1 side; This represents the effective value of the primary winding P1 current. This refers to the number of turns in a single layer of the primary winding P1; This represents the number of layers in the primary winding P1. This refers to the number of layers in the secondary winding S1. To correct the skin depth of the secondary winding S1; δ P1 To correct the skin depth of the primary winding P1; This refers to the interlayer insulation distance of the secondary winding S1; This is the interlayer insulation distance of the primary winding P1; This is the insulation distance between the secondary winding S1 and the primary winding P1; F S,S1 and F P,S1 These are the skin effect and proximity effect factors of the secondary winding S1, respectively; F S,P1 and F P,P1 These are the skin effect and proximity effect factors of the primary winding P1, respectively. F 1 and F In step 2, Δ1 is transformed into the normalized thickness Δ of the secondary winding S1 and the primary winding P1. S1 and Δ P1 You can get it immediately.

[0031] Δ S1 = d f,S1 / δ S1 ,Δ P1 = d f,P1 / δ P1 .

[0032] in: d f,S1 The thickness of a single layer of the secondary winding S1 is [missing information]. d f,P1 The thickness of a single layer of the primary winding P1 is given.

[0033] δ S1 = δ ( η S1 ) -0.5 , η S1 is the fill factor of the secondary winding S1.

[0034] δ P1 = δ ( η P1 ) -0.5 , η P1is the fill factor of the primary winding P1.

[0035] 2) Calculate leakage inductance L σ(P2,S1) At that time, the total leakage magnetic energy in each region is: (16); In equation (16): To calculate leakage inductance L σ(P2,S1) Total leakage magnetic energy in each region at that time; This refers to the leakage magnetic energy inside the secondary winding S1. This refers to the leakage magnetic energy inside the primary winding P2; This refers to the leakage magnetic energy in the interlayer insulation region of the secondary winding S1. This refers to the leakage magnetic energy in the interlayer insulation region of the primary winding P2; This refers to the leakage magnetic energy in the insulation region between the secondary winding S1 and the open winding P1. This refers to the leakage magnetic energy in the insulation region between the open-circuit winding P1 and the primary winding P2. This refers to the leakage magnetic energy inside the open-circuit winding P1; This represents the leakage magnetic energy in the interlayer insulation region of the open-circuit winding P1.

[0036] The formula for calculating the leakage inductance between the secondary winding S1 and the primary winding P2, referred to the primary winding P2 side, is as follows: (17); In equation (17): The leakage inductance between the secondary winding S1 and the primary winding P2 is referred to the primary winding P2 side; This represents the effective value of the primary winding P2 current. This refers to the number of turns in a single layer of the primary winding P2; This refers to the number of layers in the primary winding P2. This refers to the number of layers in the secondary winding S1. To correct the skin depth of the open-circuit winding P1; This is the insulation distance between the open-circuit winding P1 and the primary winding P2.

[0037] F S,P2 and F P,P2 These are the skin effect and proximity effect factors of the primary winding P2, respectively. F 1 and F In step 2, Δ1 is transformed into the normalized thickness Δ of the primary winding P2. P2 You can get it immediately; Δ P2 = d f,P2 / δP2 , in: d f,P2 The thickness of a single layer of the primary winding P2; δ P2 To correct the skin depth of the primary winding P2, δ P2 = δ ( η P2 ) -0.5 , η P2 is the fill factor of the primary winding P2.

[0038] F Ind(S,P1) and F Ind(P,P1) These are the skin effect and proximity effect factor of the open-circuit winding P1 under the influence of the magnetic field of the adjacent winding, respectively. F Ind(S,P1) = F S,P1 , F Ind(P,P1) = F P,P1 ; F S,P1 and F P,P1 These are the skin effect and proximity effect factors of the primary winding P1, respectively.

[0039] 3) Calculate leakage inductance L σ(P3,S1) At that time, the total leakage magnetic energy in each region is: (18); In formula (18): To calculate leakage inductance L σ(P3,S1) Total leakage magnetic energy in each region at that time; This refers to the leakage magnetic energy inside the secondary winding S1. This refers to the leakage magnetic energy inside the primary winding P3; This refers to the leakage magnetic energy in the interlayer insulation region of the secondary winding S1. This refers to the leakage magnetic energy in the interlayer insulation region of the primary winding P3; This refers to the leakage magnetic energy in the insulation region between the secondary winding S1 and the open winding P1. This refers to the leakage magnetic energy in the insulation region between open-circuit windings P1 and P2. The leakage magnetic energy in the insulation region between the open-circuit winding P2 and the primary winding P3; This refers to the leakage magnetic energy inside the open-circuit winding P1; The leakage magnetic energy in the interlayer insulation region of the open-circuit winding P1; This refers to the leakage magnetic energy inside the open-circuit winding P2; This represents the leakage magnetic energy in the interlayer insulation region of the open-circuit winding P2.

[0040] The formula for calculating the leakage inductance between the secondary winding S1 and the primary winding P3, referred to the primary winding P3 side, is as follows: (19); In equation (19): The leakage inductance between the secondary winding S1 and the primary winding P3 is referred to the primary winding P3 side. To calculate leakage inductance L σ(P3,S1) Total leakage magnetic energy in each region at that time; This represents the effective value of the primary winding P3 current. This refers to the number of turns in a single layer of the primary winding P3; This refers to the number of layers in the primary winding P3. This refers to the number of layers in the secondary winding S1. To correct the skin depth of the primary winding P3; and The skin effect and proximity effect factor of open-circuit winding P1 under the influence of the magnetic field of adjacent windings; This is the insulation distance between the open-circuit winding P1 and the secondary winding S1; This is the insulation distance between open-circuit winding P1 and open-circuit winding P2; This is the insulation distance between the open-circuit winding P2 and the primary winding P3; This is the interlayer insulation distance for the open-circuit winding P1; This is the interlayer insulation distance for the open-circuit winding P2.

[0041] F S,P3 and F P,P3 These are the skin effect and proximity effect factors of the primary winding P3, respectively. F 1 and F In step 2, Δ1 is transformed into the normalized thickness Δ of the primary winding P3. P3 You can get it immediately; Δ P3 = d f,P3 / δ P3 , d f,P3 The thickness of a single layer of the primary winding P3; δ P3 To correct the skin depth of the post-winding P3, δ P3 = δ ( η P3 )-0.5 , η P3 is the fill factor for winding P3.

[0042] F Ind(S,P2) and F Ind(P,P2) These are the skin effect and proximity effect factor of the open-circuit winding P2 under the influence of the magnetic field of the adjacent winding, respectively. F Ind(S,P2) = F S,P2 , F Ind(P,P2) = F P,P2 ; F S,P2 and F P,P2 These are the skin effect and proximity effect factors of the primary winding P2, respectively.

[0043] This invention provides an analytical calculation method for the leakage inductance of a multi-winding high-frequency transformer, with the following technical advantages: 1) Step 1 of this invention systematically clarifies the analysis objective, pre-determines the number of leakage inductance parameters to be calculated based on the number of windings, transforms the complex multi-winding coupling problem into a clear mathematical model, avoids omissions in subsequent analysis, and lays a structured foundation for the entire method.

[0044] 2) Step 2 of this invention constructs a more accurate physical model by finely dividing the leakage magnetic energy region. This division specifically considers the influence of eddy currents inside the open-circuit winding at high frequencies, which is key to achieving high-precision calculations.

[0045] 3) Step 3 of this invention precisely applies the corresponding theoretical tools to the physical nature of different regions: for the non-current insulating region, the simple Ampere circuital theorem is used, while for the current-carrying conductor region, it is necessary to derive it based on Maxwell's equations. In this way, while ensuring the calculation efficiency of the insulating region, the complex magnetic field distribution inside the conductor at high frequency is strictly described.

[0046] 4) Step 4 of this invention completes the key conversion from vector magnetic field to field energy. By performing volume integral on the magnetic field strength of each region, the distributed field quantity is converted into superimposed scalar energy. This process naturally includes the geometric dimension information of the winding, laying the foundation for the final extraction of leakage inductance.

[0047] 5) Step 5 of this invention efficiently and reasonably converts the distributed magnetic field energy into leakage inductance parameters that can be directly used in circuit design. By accurately summarizing the relevant regional energy for each target leakage inductance, this method can handle the coupling between windings, and the calculation results can be directly used for circuit simulation.

[0048] 6) This invention takes into account the open-circuit winding unique in the calculation of leakage inductance of multi-winding high-frequency transformers, accurately calculates the leakage magnetic energy of the open-circuit winding, and further derives the analytical expression of frequency-varying leakage inductance attributed to different primary windings, providing a theoretical basis for the structural design and leakage inductance control of multi-winding high-frequency transformers. Attached Figure Description

[0049] The present invention will be further described below with reference to the accompanying drawings and examples; Figure 1 This is a flowchart of the analytical calculation method for leakage inductance of a multi-winding high-frequency transformer according to the present invention.

[0050] Figure 2 A schematic diagram showing the division of leakage magnetic energy regions in a multi-winding high-frequency transformer.

[0051] Figure 3 To calculate leakage inductance L σ(P1,S1) Schematic diagram of the area covered by leakage magnetic energy.

[0052] Figure 4 To calculate leakage inductance L σ(P2,S1) Schematic diagram of the area covered by leakage magnetic energy.

[0053] Figure 5 To calculate leakage inductance L σ(P3,S1) Schematic diagram of the area covered by leakage magnetic energy.

[0054] Figure 6 This is the topology diagram of the AQAB converter.

[0055] Figure 7 This is a structural diagram of a multi-winding high-frequency transformer.

[0056] Figure 8 For the first i Magnetic field distribution diagram of copper foil winding.

[0057] Figure 9 This is a diagram showing the magnetic field distribution of an open-circuit winding.

[0058] Figure 10 For calculation L σ(P1,S1) Schematic diagram of leakage magnetic field distribution within the window of the magnetic core.

[0059] Figure 11 For calculation L σ(P2,S1) Schematic diagram of leakage magnetic field distribution within the window of the magnetic core.

[0060] Figure 12 For calculation L σ(P3,S1) Schematic diagram of leakage magnetic field distribution within the window of the magnetic core.

[0061] Figure 13(a) shows a two-dimensional simulation model of a high-frequency transformer with flat copper wire windings; Figure 13(b) shows a two-dimensional simulation model of a high-frequency transformer with a round conductor winding.

[0062] Figure 14(a) is the wiring diagram for the short-circuit test of the primary winding P1 and the secondary winding S1; Figure 14(b) shows the wiring diagram for the short-circuit test of the primary winding P2 and the secondary winding S1. Figure 14(c) shows the wiring diagram for the short-circuit test of the primary winding P3 and the secondary winding S1.

[0063] Figure 15(a) shows the current density distribution of the primary winding P1 and secondary winding S1 per unit length of the flat copper wire winding transformer under a short-circuit test. Figure 15(b) shows the current density distribution of the primary winding P2 and secondary winding S1 per unit length of the flat copper wire winding transformer under a short-circuit test. Figure 15(c) shows the current density distribution per unit length of the primary winding P3 and secondary winding S1 under a short-circuit test of a flat copper wire winding transformer.

[0064] Figure 16(a) shows the current density distribution of the primary winding P1 and secondary winding S1 per unit length of the transformer with round conductor windings under a short-circuit test.

[0065] Figure 16(b) shows the current density distribution per unit length of the primary winding P2 and secondary winding S1 under a short-circuit test of a transformer with round conductor windings.

[0066] Figure 16(c) shows the current density distribution per unit length of the primary winding P3 and secondary winding S1 under a short-circuit test of a transformer with round conductor windings.

[0067] Figure 17(a) shows the leakage magnetic field distribution inside the core window of the transformer with flat copper wire winding under a short-circuit test of the primary winding P1 and the secondary winding S1 per unit length. Figure 17(b) shows the leakage magnetic field distribution inside the core window of the transformer with flat copper wire winding under a short-circuit test of the primary winding P2 and the secondary winding S1 per unit length. Figure 17(c) shows the leakage magnetic field distribution within the core window of the transformer with flat copper wire windings under a short-circuit test of the primary winding P3 and the secondary winding S1 per unit length.

[0068] Figure 18(a) shows the leakage magnetic field distribution inside the core window of the transformer with round conductor winding under a short-circuit test of the primary winding P1 and the secondary winding S1 per unit length.

[0069] Figure 18(b) shows the leakage magnetic field distribution inside the core window of the transformer with round conductor winding under a short-circuit test of the primary winding P2 and the secondary winding S1 per unit length.

[0070] Figure 18(c) shows the leakage magnetic field distribution inside the core window of the transformer with round conductor winding under a short-circuit test of the primary winding P3 and the secondary winding S1 per unit length.

[0071] Figure 19(a) shows the calculation and simulation results of the leakage inductance per unit length of the flat copper wire winding transformer, referred to the primary winding P1, P2 and secondary winding P3. Figure 19(b) shows the calculation and simulation results of the leakage inductance per unit length of the round conductor winding transformer, referred to the primary winding P1, P2 and secondary winding P3. Detailed Implementation

[0072] A method for analytically calculating the leakage inductance of a multi-winding high-frequency transformer includes the following steps: Step 1: Based on the number of primary and secondary windings of the multi-winding high-frequency transformer, determine the number of leakage inductances of the secondary winding attributed to different primary windings. Taking a multi-winding high-frequency transformer used in an AQAB converter as the calculation object, this multi-winding high-frequency transformer has 3 primary windings, namely P1, P2, and P3. It has 1 secondary winding, S1. The number of leakage inductances to be calculated is 3, that is, the leakage inductances of the secondary winding S1 attributed to the primary windings P1, P2, and P3 respectively. L σ(P1,S1) , L σ(P2,S1) and L σ(P3,S1) The AQAB converter topology diagram is as follows: Figure 6 As shown.

[0073] Step 2: Divide the leakage magnetic energy calculation area corresponding to different leakage inductances. Generally, it is divided into the winding interlayer insulation area, the winding inter-insulation area, the current-carrying winding area, and the open-circuit winding area.

[0074] According to the magnetic field energy method, it is necessary to divide the calculation region for leakage magnetic energy corresponding to different leakage inductances. The relationship between leakage inductance and leakage magnetic energy is as follows: ; In the formula: W This refers to the leakage magnetic energy of the transformer. L σ To reduce the leakage inductance to the original side; I To calculate the effective value of the winding current on the reduced side; μ 0 represents the permeability of free space; H To calculate the magnetic field strength in the region; V This is the volume of the computational region.

[0075] Calculate leakage inductance L σ(P1,S1) At that time, the area to be covered for calculating leakage magnetic energy is as follows: Figure 3As shown, this includes: the internal region of the secondary winding S1, see... Figure 3 Designation ①. Secondary winding S1 interlayer insulation region, see... Figure 3 Reference number ②. The internal region of the primary winding P1, see... Figure 3 Designation ③. Interlayer insulation region of primary winding P1, see... Figure 3 Reference number ④. The insulation region between the secondary winding S1 and the primary winding P1, see... Figure 3 Number ⑤; Calculate leakage inductance L σ(P2,S1) At that time, the area to be covered for calculating leakage magnetic energy is as follows: Figure 4 As shown, this includes: the internal region of the secondary winding S1, see... Figure 4 Designation ①. Secondary winding S1 interlayer insulation region, see... Figure 4 Reference number ②. The internal region of the primary winding P2, see... Figure 4 Designation ③. Interlayer insulation region of primary winding P2, see... Figure 4 Number ④. The internal region of the open winding P1, see... Figure 4 Number ⑤. Interlayer insulation region of open winding P1, see... Figure 4 Reference number ⑥. The insulation region between the secondary winding S1 and the open winding P1, see... Figure 4 Reference number ⑦. The insulation region between the open-circuit winding P1 and the primary winding P2, see... Figure 4 Number ⑧.

[0076] Calculate leakage inductance L σ(P3,S1) At that time, the area to be covered for calculating leakage magnetic energy is as follows: Figure 5 As shown, this includes: the internal region of the secondary winding S1, see... Figure 5 Designation ①. Secondary winding S1 interlayer insulation region, see... Figure 5 Reference number ②. The internal region of the primary winding P3, see... Figure 5 Designation ③. Interlayer insulation region of primary winding P3, see... Figure 5 Number ④. The internal region of the open winding P1, see... Figure 5 Number ⑤. Interlayer insulation region of open winding P1, see... Figure 5 Number ⑥. Internal region of open winding P2, see... Figure 5 Number ⑦. Interlayer insulation region of open winding P2, see... Figure 5 Reference number ⑧. The insulation region between the secondary winding S1 and the open winding P1, see... Figure 5 Number 9. Insulation region between open windings P1 and P2, see... Figure 5 Number ⑩. The insulation region between the open-circuit winding P2 and the primary winding P3, see... Figure 5 winning number .

[0077] Multi-winding high-frequency transformer structure, such as Figure 7 As shown.

[0078] Step 3: Derive the magnetic field strength of the interlayer insulation region and the inter-winding insulation region based on Ampere's circuital theorem, and derive the magnetic field strength of the current-carrying winding region and the open-circuit winding region based on Maxwell's equations.

[0079] The magnetic field strength in the interlayer insulation region and the inter-winding insulation region of the winding is obtained using Ampere's circuital law. For example... Figure 8 As shown, the first i The magnetic field strengths of the inner and outer insulation regions of the copper foil winding are: ; ; In the formula: I This represents the effective value of the winding current. h w This refers to the height of the transformer core window.

[0080] Solving for the magnetic field strength in the current-carrying winding region and the open-circuit winding region requires the use of Maxwell's equations. i Copper foil winding along thickness Magnitude of internal magnetic field in the direction H ( x )for: ; In the formula: α =(1+j) / δ , The imaginary unit; H in , H out These represent the magnetic field strengths inside and outside the winding, respectively. δ For skin depth; d f Let be the thickness of each winding layer. The skin depth expression is: ; In the formula, f The frequency of the applied current; σ Electrical conductivity; μ 0 is the vacuum permeability Step 4: Based on the magnetic field strength of each region, further integrate to obtain the corresponding leakage magnetic energy.

[0081] According to the magnetic field energy method, it is necessary to calculate the magnetic field strength of each region and the leakage magnetic energy of each region. W and the magnetic field strength in this region H ( x The relationship is: ; In the formula: l To calculate the average length of the region; d To calculate the thickness of the region.

[0082] Leakage magnetic energy in the interlayer insulation region of the current-carrying winding W ins The calculation formula is: ; In the formula: d ins This refers to the interlayer insulation distance of the current-carrying winding; m This represents the total number of layers in the current-carrying winding.

[0083] Leakage magnetic energy in insulation regions between different windings W iso The calculation formula is: ; In the formula: d iso This refers to the insulation distance between different windings. This represents the total number of layers of the current-carrying winding within the insulation region.

[0084] Leakage magnetic energy in the current-carrying winding region W w The calculation formula is: ; In the formula: d f The thickness of a single-layer current-carrying winding; For the first n The magnitude of the magnetic field strength inside the laminar current winding; m This represents the total number of layers in the current-carrying winding. n This refers to the specific number of layers in a single-layer current-carrying winding.

[0085] F 1 and F 2 represents the skin effect and proximity effect factors of the corresponding winding, calculated as follows: ; In the formula: Δ1 is the normalized thickness of the winding, Δ1= d f / δ .

[0086] If the magnetic field strength on the inner and outer sides of an open-circuit winding is approximately the same, then the leakage magnetic energy stored in each layer of open-circuit winding is equal. For example... Figure 9 As shown, m Leakage magnetic energy stored in 2 layers of open-circuit windings W Ind The calculation formula is: ; In the formula: They are respectively the 1st, 2nd, ... th m Leakage magnetic energy stored in two layers of open-circuit windings; m 2 represents the total number of layers in the open-circuit winding; m 3 represents the total number of layers of the open-circuit winding with current-carrying winding inside; F Ind,S and F Ind,P These are the skin effect and proximity effect factors for open-circuit windings, respectively. F 1 and F In step 2, Δ1 is transformed into the normalized thickness Δ of the open-circuit winding. Ind This can be obtained, where Δ Ind = d f,Ind / δ .

[0087] m Interlayer leakage magnetic energy of 2-layer open-circuit winding W ins,Ind The expression is: ; In the formula: m 2 represents the total number of layers in the open-circuit winding; d ins,Ind This refers to the interlayer insulation distance of the open-circuit winding; m 3 represents the total number of layers of the open-circuit winding with current-carrying winding inside.

[0088] Step 5: Calculate the leakage magnetic energy of each leakage inductor according to the different leakage magnetic energy calculation regions, sum the leakage magnetic energy of the corresponding regions, and then calculate the parameters of each leakage inductor according to the magnetic field energy method.

[0089] Figure 10 For calculation L σ(P1,S1) The leakage magnetic field distribution within the core window, and the total leakage magnetic energy in each region. W (P1,S1) for: ; In the formula: This refers to the leakage magnetic energy inside the secondary winding S1. This refers to the leakage magnetic energy inside the primary winding P1. This refers to the leakage magnetic energy in the interlayer insulation region of the secondary winding S1. This refers to the leakage magnetic energy in the interlayer insulation region of the primary winding P1; This refers to the leakage magnetic energy in the insulation region between the secondary winding S1 and the primary winding P1.

[0090] The leakage inductance between S1 and P1 on the primary winding P1 side is considered as follows: L σ(P1,S1)The calculation formula is: ; In the formula: This represents the effective value of the primary winding P1 current. This refers to the number of turns in a single layer of the primary winding P1; This represents the number of layers in the primary winding P1. This refers to the number of layers in the secondary winding S1. To correct the skin depth of the secondary winding S1; δ P1 To correct the skin depth of the primary winding P1; This refers to the interlayer insulation distance of the secondary winding S1; This is the interlayer insulation distance of the primary winding P1; This is the insulation distance between the secondary winding S1 and the primary winding P1. F S,S1 and F P,S1 These are the skin effect and proximity effect factors of the secondary winding S1, respectively; F S,P1 and F P,P1 These are the skin effect and proximity effect factors of the primary winding P1, respectively. F 1 and F In step 2, Δ1 is transformed into the normalized thickness Δ of the secondary winding S1 and the primary winding P1. S1 and Δ P1 That will give you Δ. S1 = d f,S1 / δ S1 ,Δ P1 = d f,P1 / δ P1 .

[0091] in: d f,S1 The thickness of a single layer of the secondary winding S1 is [missing information]. d f,P1 The thickness of a single layer of the primary winding P1 is given.

[0092] δ S1 = δ ( η S1 ) -0.5 , η S1 The fill factor for the secondary winding S1 is... δ P1 = δ ( η P1) -0.5 , η P1 is the fill factor of the primary winding P1.

[0093] Figure 11 For calculation L σ(P2,S1) Distribution of leakage magnetic field within the core window. Total leakage magnetic energy in each region. W (P2,S1) for: ; In the formula: This refers to the leakage magnetic energy inside the secondary winding S1. This refers to the leakage magnetic energy inside the primary winding P2; This refers to the leakage magnetic energy in the interlayer insulation region of the secondary winding S1. This refers to the leakage magnetic energy in the interlayer insulation region of the primary winding P2; This refers to the leakage magnetic energy in the insulation region between the secondary winding S1 and the open winding P1. This refers to the leakage magnetic energy in the insulation region between the open-circuit winding P1 and the primary winding P2. This refers to the leakage magnetic energy inside the open-circuit winding P1; This represents the leakage magnetic energy in the interlayer insulation region of the open-circuit winding P1.

[0094] Leakage inductance between S1 and P2 on the primary winding P2 side L σ(P2,S1) The calculation formula is: ; In the formula: This represents the effective value of the primary winding P2 current. This refers to the number of turns in a single layer of the primary winding P2; This refers to the number of layers in the primary winding P2. This refers to the number of layers in the secondary winding S1. To correct the skin depth of the open-circuit winding P1; This is the insulation distance between the open-circuit winding P1 and the primary winding P2.

[0095] F S,P2 and F P,P2 These are the skin effect and proximity effect factors of the primary winding P2, respectively. F 1 and F In step 2, Δ1 is transformed into the normalized thickness Δ of the primary winding P2. P2 That is, Δ P2 = d f,P2 / δ P2 ,in: df,P2 The thickness of a single layer of the primary winding P2; δ P2 To correct the skin depth of the primary winding P2, δ P2 = δ ( η P2 ) -0.5 , η P2 is the fill factor of the primary winding P2.

[0096] F Ind(S,P1) and F Ind(P,P1) These are the skin effect and proximity effect factor of the open-circuit winding P1 under the influence of the magnetic field of the adjacent winding, respectively. F Ind(S,P1) = F S,P1 , F Ind(P,P1) = F P,P1 ; F S,P1 and F P,P1 These are the skin effect and proximity effect factors of the primary winding P1, respectively.

[0097] Figure 12 For calculation L σ(P3,S1) Distribution of leakage magnetic field within the core window. Total leakage magnetic energy in each region. W (P3,S1) for: ; In the formula: This refers to the leakage magnetic energy inside the secondary winding S1. This refers to the leakage magnetic energy inside the primary winding P3; This refers to the leakage magnetic energy in the interlayer insulation region of the secondary winding S1. This refers to the leakage magnetic energy in the interlayer insulation region of the primary winding P3; This refers to the leakage magnetic energy in the insulation region between the secondary winding S1 and the open winding P1. This refers to the leakage magnetic energy in the insulation region between open-circuit windings P1 and P2. The leakage magnetic energy in the insulation region between the open-circuit winding P2 and the primary winding P3; This refers to the leakage magnetic energy inside the open-circuit winding P1; The leakage magnetic energy in the interlayer insulation region of the open-circuit winding P1; This refers to the leakage magnetic energy inside the open-circuit winding P2; This represents the leakage magnetic energy in the interlayer insulation region of the open-circuit winding P2.

[0098] The leakage inductance between S1 and P3 on the primary winding P3 side is considered as follows: L σ(P3,S1) The calculation formula is: ; In the formula: This represents the effective value of the primary winding P3 current. This refers to the number of turns in a single layer of the primary winding P3; This refers to the number of layers in the primary winding P3. This refers to the number of layers in the secondary winding S1. To correct the skin depth of the primary winding P3; and The skin effect and proximity effect factor of open-circuit winding P1 under the influence of the magnetic field of adjacent windings; This is the insulation distance between the open-circuit winding P1 and the secondary winding S1; This is the insulation distance between open-circuit winding P1 and open-circuit winding P2; This is the insulation distance between the open-circuit winding P2 and the primary winding P3; This is the interlayer insulation distance for the open-circuit winding P1; This is the interlayer insulation distance for the open-circuit winding P2. F S,P3 and F P,P3 These are the skin effect and proximity effect factors of the primary winding P3, respectively. F 1 and F In step 2, Δ1 is transformed into the normalized thickness Δ of the primary winding P3. P3 That is, Δ P3 = d f,P3 / δ P3 , d f,P3 The thickness of a single layer of the primary winding P3; δ P3 To correct the skin depth of the post-winding P3, δ P3 = δ ( η P3 ) -0.5 , η P3 is the fill factor for winding P3. F Ind(S,P2) and F Ind(P,P2) These are the skin effect and proximity effect factor of the open-circuit winding P2 under the influence of the magnetic field of the adjacent winding, respectively. F Ind(S,P2) = FS,P2 , F Ind(P,P2) = F P,P2 ; F S,P2 and F P,P2 These are the skin effect and proximity effect factors of the primary winding P2, respectively.

[0099] The basic flowchart of the analytical calculation method for leakage inductance of multi-winding high-frequency transformers proposed in this invention is as follows: Figure 1 As shown.

[0100] To demonstrate the accuracy of the analytical calculation method for leakage inductance of multi-winding high-frequency transformers proposed in this invention, two-dimensional simulation models of four-winding high-frequency transformers with two different winding shapes (flat copper wire and round conductor) were established in finite element software, as shown in Figures 13(a) and 13(b). The main simulation parameters are shown in Tables 1 and 2.

[0101]

[0102]

[0103] With the frequency set to 100kHz and a peak current of 1A applied to the primary winding, the finite element method was used to calculate the winding current density and leakage magnetic field strength in the core window of a four-winding high-frequency transformer with two different winding shapes (flat copper wire and round conductor) under different short-circuit tests. This demonstrated the influence of the location of the open-circuit winding on the winding current density and the leakage magnetic field strength in the core window. Figures 14(a) to 1 4 (c) are the short-circuit test wiring circuits for the leakage inductance referred to the primary winding P1, P2 and P3 sides respectively.

[0104] Figures 15(a) to 1 5 (c) and Figures 16(a) to 1 Figure 6(c) shows the current density distribution per unit length for flat copper wire winding transformers and round conductor winding transformers under different short-circuit tests. Figures 15(a) to 1 5 (c) and Figures 16(a) to 1 As shown in 6(c), when the open-circuit winding is located between the winding to be calculated and the winding to be calculated, although no current flows through the open-circuit winding, its current density is not zero due to the eddy current effect of proximity. This conclusion holds true when the winding shape is flat copper wire or round conductor.

[0105] Figures 17(a) to 17(b) 7 (c) and Figures 18(a) to 18(b) Figure 8(c) shows the leakage magnetic field distribution per unit length in the core window of a transformer with flat copper wire windings and a transformer with round conductor windings under different short-circuit tests. Figures 17(a) to 17(b) 7 (c) and Figures 18(a) to 18(b)As shown in 8 (c), when the open-circuit winding is located between the winding to be calculated and the winding to be calculated, due to the influence of the proximity effect eddy current, the magnetic field strength inside the open-circuit winding is not 0, and the total leakage magnetic energy needs to be included in the calculation. Moreover, the magnitudes of the magnetic field strengths inside and outside the open-circuit winding are approximately equal. This conclusion holds true when the winding shape is flat copper wire or round conductor.

[0106] The leakage inductance in the frequency range of 10kHz to 100kHz was calculated comparatively using the finite element method and analytical methods, with a step size of 5kHz. This demonstrates that the analytical method can accurately calculate the leakage inductance of a four-winding high-frequency transformer. Using the results of two-dimensional finite element simulation (FEM) as a reference, the relative deviation calculation formula given below was used to analyze the deviation of the calculation results.

[0107] ; In the formula: W ( i () represents the analytical calculation result; W FEM ( i () represents the finite element simulation results.

[0108] The calculation and simulation results of the leakage inductance per unit length referred to the primary winding sides P1, P2, and P3 of transformers with flat copper wire windings and round conductor windings are shown in Figures 19(a) and 19(b). When the winding is flat copper wire, the average relative deviation between the calculated and simulated values ​​of the leakage inductance referred to the primary winding sides P1, P2, and P3 is shown. AUD The percentages were 2.87%, 2.1%, and 1.7%, respectively, with the largest relative deviation. UD max The percentages are 3.56%, 2.81%, and 2.25%, respectively. When the windings are round conductors, the average relative deviations between the calculated and simulated values ​​of the leakage inductance referred to the primary windings P1, P2, and P3 sides are... AUD The percentages were 5.53%, 5.56%, and 5.23%, respectively, with the largest relative deviation. UD max They were 7.52%, 8.55%, and 8.25%, respectively.

[0109] Overall, since the analytical calculation method takes into account factors such as the leakage magnetic energy of the open-circuit winding, it can accurately calculate the total leakage magnetic energy. The analytical calculation results are in good agreement with the two-dimensional simulation results, proving that the present invention can accurately calculate the leakage inductance of multi-winding high-frequency transformers.

Claims

1. A method for analytical calculation of leakage inductance of a multi-winding high-frequency transformer, characterized in that... Includes the following steps: Step 1: Determine the number of leakage inductances of the secondary windings attributed to different primary windings based on the number of primary and secondary windings of the multi-winding high-frequency transformer. Step 2: Divide the leakage magnetic energy regions corresponding to different leakage inductances into the winding interlayer insulation region, winding inter-insulation region, current-carrying winding region, and open-circuit winding region; Step 3: Based on Ampere's circuital law, derive the magnetic field strength in the interlayer insulation region and the inter-winding insulation region of the winding; Based on Maxwell's equations, the magnetic field strength in the current-carrying winding region and the open-circuit winding region is derived. Step 4: Based on the magnetic field strength of each region, further integrate to obtain the corresponding leakage magnetic energy; Step 5: Calculate the leakage magnetic energy of each leakage inductor according to the different leakage magnetic energy calculation regions, sum the leakage magnetic energy of the corresponding regions, and then calculate the parameters of each leakage inductor according to the magnetic field energy method.

2. The analytical calculation method for leakage inductance of a multi-winding high-frequency transformer according to claim 1, characterized in that: In step 1, the multi-winding high-frequency transformer used in the AQAB converter is taken as the calculation object. The multi-winding high-frequency transformer has three primary windings, namely P1, P2, and P3; and one secondary winding, namely S1. The number of leakage inductances to be calculated is three, that is, the leakage inductance of the secondary winding S1 is respectively attributed to the primary windings P1, P2, and P3. L σ(P1,S1) , L σ(P2,S1) and L σ(P3,S1) .

3. The analytical calculation method for leakage inductance of a multi-winding high-frequency transformer according to claim 2, characterized in that: In step 2, the method for dividing the leakage magnetic energy region is as follows: According to the magnetic field energy method, it is necessary to divide the calculation area for leakage magnetic energy corresponding to different leakage inductances. The relationship between leakage inductance and leakage magnetic energy is as follows: （1）； In formula (1): W This refers to the leakage magnetic energy of the transformer. L σ To reduce the leakage inductance to the original side; I To calculate the effective value of the winding current on the reduced side; μ 0 represents the permeability of free space; H To calculate the magnetic field strength in the region; V To calculate the volume of the region; The leakage magnetic energy region is divided into the winding interlayer insulation region, the winding inter-insulation region, and the winding region. The winding region can be further divided into the current-carrying winding region and the open-circuit winding region.

4. The analytical calculation method for leakage inductance of a multi-winding high-frequency transformer according to claim 3, characterized in that: Calculate leakage inductance L σ(P1,S1) When calculating leakage flux energy, the areas to be covered include: the internal region of the secondary winding S1; the interlayer insulation region of the secondary winding S1; the internal region of the primary winding P1; the interlayer insulation region of the primary winding P1; and the insulation region between the secondary winding S1 and the primary winding P1. Calculate leakage inductance L σ(P2,S1) The areas to be covered in the leakage flux energy calculation include: the internal region of the secondary winding S1; the interlayer insulation region of the secondary winding S1; the internal region of the primary winding P2; the interlayer insulation region of the primary winding P2; the internal region of the open-circuit winding P1; the interlayer insulation region of the open-circuit winding P1; the insulation region between the secondary winding S1 and the open-circuit winding P1; and the insulation region between the open-circuit winding P1 and the primary winding P2. Calculate leakage inductance L σ(P3,S1) The areas to be covered in the leakage flux energy calculation include: the internal region of the secondary winding S1; the interlayer insulation region of the secondary winding S1; the internal region of the primary winding P3; the interlayer insulation region of the primary winding P3; the internal region of the open-circuit winding P1; the interlayer insulation region of the open-circuit winding P1; the internal region of the open-circuit winding P2; the interlayer insulation region of the open-circuit winding P2; the insulation region between the secondary winding S1 and the open-circuit winding P1; the insulation region between the open-circuit winding P1 and P2; and the insulation region between the open-circuit winding P2 and the primary winding P3.

5. The analytical calculation method for leakage inductance of a multi-winding high-frequency transformer according to claim 4, characterized in that: In step 3, the method for calculating the magnetic field strength in each region is as follows: The magnetic field strength in the interlayer insulation region and the inter-winding insulation region of the winding is obtained from Ampere's circuital law: No. i The magnetic field strengths of the inner and outer insulation regions of the copper foil winding are: （2）； （3）； In the above formula: H in , H out These represent the magnetic field strengths of the inner and outer insulation regions of the winding, respectively. I This represents the effective value of the winding current. h w This refers to the height of the transformer core window. This refers to the specific number of layers in a single-layer copper foil winding. The magnetic field strength in the current-carrying winding region and the open-circuit winding region is solved using Maxwell's equations: No. i Copper foil winding along thickness The magnitude of the internal magnetic field strength in the direction is: （4）； In equation (4): H ( x ) represents the copper foil winding along the thickness The magnitude of the internal magnetic field strength in the direction; α =(1+j) / δ , The imaginary unit, δ For skin depth; d f The thickness of each winding layer; The expression for skin depth is: （5）； In formula (5): f The frequency of the applied current; σ Electrical conductivity; is the vacuum permeability.

6. The analytical calculation method for leakage inductance of a multi-winding high-frequency transformer according to claim 5, characterized in that: In step 4, the method for calculating the leakage magnetic energy in each region is as follows: The magnetic field strength of each region is calculated using the magnetic field energy method; the relationship between the leakage magnetic energy and the magnetic field strength of each region is as follows: （6）； In formula (6): To calculate the leakage magnetic energy in the region; l To calculate the average length of the region; d To calculate the thickness of the region; The formula for calculating the leakage magnetic energy in the interlayer insulation region of the current-carrying winding is: （7）； In equation (7): This refers to the leakage magnetic energy in the interlayer insulation region of the current-carrying winding; d ins This refers to the interlayer insulation distance of the current-carrying winding; m This represents the total number of layers in the current-carrying winding. This represents the effective value of the winding current. The formula for calculating leakage magnetic energy in the insulation region between different windings is: （8）； In equation (8): Leakage magnetic energy in the insulation region between different windings; d iso This refers to the insulation distance between different windings; This represents the total number of layers of the current-carrying winding within the insulation region. The formula for calculating the leakage flux energy in the current-carrying winding region is: （9）； In equation (9): W w This refers to the leakage magnetic energy in the current-carrying winding region. d f This refers to the thickness of a single-layer winding. For the first n The magnitude of the magnetic field strength inside the laminar current winding; m This represents the total number of layers in the current-carrying winding. n This specifies the number of layers in a single-layer current-carrying winding. F 1 and F 2 represents the skin effect and proximity effect factors of the corresponding windings, respectively, and are calculated as follows: （10）； In equation (10): Δ1 is the normalized thickness of the winding, Δ1= d f / δ ; If the magnetic field strength on the inner and outer sides of the open-circuit winding is approximately the same, then the leakage magnetic energy stored in each layer of open-circuit winding is equal. m The formula for calculating the leakage magnetic energy stored in a two-layer open-circuit winding is: （11）； In equation (11): The leakage magnetic energy stored in the open-circuit winding; They are respectively the 1st, 2nd, ... th m Leakage magnetic energy stored in two layers of open-circuit windings m 2 represents the total number of layers in the open-circuit winding; m 3 represents the total number of layers of the open-circuit winding with current-carrying winding inside; and These are the skin effect and proximity effect factors for open-circuit windings, respectively; F 1 and F In step 2, Δ1 is transformed into the normalized thickness Δ of the open-circuit winding. Ind We can then obtain, where Δ Ind = d f,Ind / δ , d f,Ind The thickness is for a single-layer open-circuit winding; m The expression for the interlayer leakage flux energy of a two-layer open-circuit winding is: （12）； In equation (12): for m Interlayer leakage magnetic energy of 2-layer open-circuit winding m 2 represents the total number of layers in the open-circuit winding; d ins,Ind This refers to the interlayer insulation distance of the open-circuit winding; m 3 represents the total number of layers of the open-circuit winding with current-carrying winding inside.

7. The analytical calculation method for leakage inductance of a multi-winding high-frequency transformer according to claim 6, characterized in that: In step 5, different leakage inductors correspond to different leakage magnetic energy calculation regions. The leakage magnetic energy of the corresponding regions is summed to obtain the total leakage magnetic energy corresponding to each leakage inductor. W The leakage inductance is calculated using the total leakage magnetic energy. （13）； In equation (13): It is a leakage inductance.

8. The analytical calculation method for leakage inductance of a multi-winding high-frequency transformer according to claim 7, characterized in that: Calculate leakage inductance L σ(P1,S1) At that time, the total leakage magnetic energy in each region is: （14）； In equation (14): To calculate leakage inductance L σ(P1,S1) Total leakage magnetic energy in each region at that time; This refers to the leakage magnetic energy inside the secondary winding S1. This refers to the leakage magnetic energy inside the primary winding P1. This refers to the leakage magnetic energy in the interlayer insulation region of the secondary winding S1. This refers to the leakage magnetic energy in the interlayer insulation region of the primary winding P1; This refers to the leakage magnetic energy in the insulation region between the secondary winding S1 and the primary winding P1. The formula for calculating the leakage inductance between the secondary winding S1 and the primary winding P1, referred to the primary winding P1 side, is as follows: （15）； In equation (15): The leakage inductance between the secondary winding S1 and the primary winding P1 is referred to the primary winding P1 side; This represents the effective value of the primary winding P1 current. This refers to the number of turns in a single layer of the primary winding P1; This represents the number of layers in the primary winding P1. This refers to the number of layers in the secondary winding S1. To correct the skin depth of the secondary winding S1; δ P1 To correct the skin depth of the primary winding P1; This refers to the interlayer insulation distance of the secondary winding S1; This is the interlayer insulation distance of the primary winding P1; This is the insulation distance between the secondary winding S1 and the primary winding P1; F S,S1 and F P,S1 These are the skin effect and proximity effect factors of the secondary winding S1, respectively; F S,P1 and F P,P1 These are the skin effect and proximity effect factors of the primary winding P1, respectively. F 1 and F In step 2, Δ1 is transformed into the normalized thickness Δ of the secondary winding S1 and the primary winding P1. S1 and Δ P1 You can get it immediately; D S1 = d f,S1 / δ S1 ,D P1 = d f,P1 / δ P1 ; in: d f,S1 The thickness of a single layer of the secondary winding S1 is [missing information]. d f,P1 The thickness of a single layer of the primary winding P1; δ S1 = δ ( η S1 ) -0.5 , η S1 This is the fill factor for the secondary winding S1; δ P1 = δ ( η P1 ) -0.5 , η P1 is the fill factor of the primary winding P1.

9. The analytical calculation method for leakage inductance of a multi-winding high-frequency transformer according to claim 8, characterized in that: Calculate leakage inductance L σ(P2,S1) At that time, the total leakage magnetic energy in each region is: （16）； In equation (16): To calculate leakage inductance L σ(P2,S1) Total leakage magnetic energy in each region at that time; This refers to the leakage magnetic energy inside the secondary winding S1. This refers to the leakage magnetic energy inside the primary winding P2; This refers to the leakage magnetic energy in the interlayer insulation region of the secondary winding S1. This refers to the leakage magnetic energy in the interlayer insulation region of the primary winding P2; This refers to the leakage magnetic energy in the insulation region between the secondary winding S1 and the open winding P1. The leakage magnetic energy in the insulation region between the open-circuit winding P1 and the primary winding P2; This refers to the leakage magnetic energy inside the open-circuit winding P1; The leakage magnetic energy in the interlayer insulation region of the open-circuit winding P1; The formula for calculating the leakage inductance between the secondary winding S1 and the primary winding P2, referred to the primary winding P2 side, is as follows: （17）； In equation (17): The leakage inductance between the secondary winding S1 and the primary winding P2 is referred to the primary winding P2 side; This represents the effective value of the primary winding P2 current. This refers to the number of turns in a single layer of the primary winding P2; This refers to the number of layers in the primary winding P2. This refers to the number of layers in the secondary winding S1. To correct the skin depth of the open-circuit winding P1; This is the insulation distance between the open-circuit winding P1 and the primary winding P2; F S,P2 and F P,P2 These are the skin effect and proximity effect factors of the primary winding P2, respectively. F 1 and F In step 2, Δ1 is transformed into the normalized thickness Δ of the primary winding P2. P2 You can get it immediately; D P2 = d f,P2 / δ P2 , in: d f,P2 The thickness of a single layer of the primary winding P2; δ P2 To correct the skin depth of the primary winding P2, δ P2 = δ ( η P2 ) -0.5 , η P2 The fill factor for the primary winding P2; F Ind(S,P1) and F Ind(P,P1) These are the skin effect and proximity effect factor of the open-circuit winding P1 under the influence of the magnetic field of the adjacent winding, respectively. F Ind(S,P1) = F S,P1 , F Ind(P,P1) = F P,P1 ; F S,P1 and F P,P1 These are the skin effect and proximity effect factors of the primary winding P1, respectively.

10. The analytical calculation method for leakage inductance of a multi-winding high-frequency transformer according to claim 9, characterized in that: Calculate leakage inductance L σ(P3,S1) At that time, the total leakage magnetic energy in each region is: （18）； In formula (18): To calculate leakage inductance L σ(P3,S1) Total leakage magnetic energy in each region at that time; This refers to the leakage magnetic energy inside the secondary winding S1. This refers to the leakage magnetic energy inside the primary winding P3; This refers to the leakage magnetic energy in the interlayer insulation region of the secondary winding S1. This refers to the leakage magnetic energy in the interlayer insulation region of the primary winding P3; This refers to the leakage magnetic energy in the insulation region between the secondary winding S1 and the open winding P1. This refers to the leakage magnetic energy in the insulation region between open-circuit windings P1 and P2. The leakage magnetic energy in the insulation region between the open-circuit winding P2 and the primary winding P3; This refers to the leakage magnetic energy inside the open-circuit winding P1; The leakage magnetic energy in the interlayer insulation region of the open-circuit winding P1; This refers to the leakage magnetic energy inside the open-circuit winding P2; The leakage magnetic energy in the interlayer insulation region of the open-circuit winding P2; The formula for calculating the leakage inductance between the secondary winding S1 and the primary winding P3, referred to the primary winding P3 side, is as follows: （19）； In equation (19): The leakage inductance between the secondary winding S1 and the primary winding P3 is referred to the primary winding P3 side. To calculate leakage inductance L σ(P3,S1) Total leakage magnetic energy in each region at that time; This represents the effective value of the primary winding P3 current. This refers to the number of turns in a single layer of the primary winding P3; This refers to the number of layers in the primary winding P3. This refers to the number of layers in the secondary winding S1. To correct the skin depth of the primary winding P3; and The skin effect and proximity effect factor of open-circuit winding P1 under the influence of the magnetic field of adjacent windings; This is the insulation distance between the open-circuit winding P1 and the secondary winding S1; This is the insulation distance between open-circuit winding P1 and open-circuit winding P2; This is the insulation distance between the open-circuit winding P2 and the primary winding P3; This is the interlayer insulation distance for the open-circuit winding P1; This refers to the interlayer insulation distance of the open-circuit winding P2; F S,P3 and F P,P3 These are the skin effect and proximity effect factors of the primary winding P3, respectively. F 1 and F In step 2, Δ1 is transformed into the normalized thickness Δ of the primary winding P3. P3 You can get it immediately; Δ P3 = d f,P3 / δ P3 , d f,P3 The thickness of a single layer of the primary winding P3; δ P3 To correct the skin depth of the post-winding P3, δ P3 = δ ( η P3 ) -0.5 , η P3 This is the fill factor for winding P3; F Ind(S,P2) and F Ind(P,P2) These are the skin effect and proximity effect factor of the open-circuit winding P2 under the influence of the magnetic field of the adjacent winding, respectively. F Ind(S,P2) = F S,P2 , F Ind(P,P2) = F P,P2 ; F S,P2 and F P,P2 These are the skin effect and proximity effect factors of the primary winding P2, respectively.

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