A three-dimensional fast calculation method of high-frequency loss of circular litz wire

Abstract

The present application relates to circular litz wire high frequency loss calculation technology, it is especially disclosed a kind of circular litz wire high frequency loss three-dimensional fast calculation method, the method includes the following steps: step one, understand the relationship between skin effect loss, internal proximity effect loss and external proximity effect loss;Step two, based on one-dimensional electromagnetic field theory and using Tourkhani model to obtain the loss expression of any circular litz wire unit length conductor in high-frequency magnetic element window;Step three, using finite element method to establish the two-dimensional finite element equivalent model of magnetic core window, extract external magnetic field and calculate external magnetic field;Step four, construct three-dimensional loss model considering the influence of litz wire's torsion inclination angle on external magnetic field.The beneficial effects of the present application are to realize the accurate and efficient calculation of circular litz wire winding loss in a wide frequency range.

Description

Technical Field

[0001] This invention relates to the field of loss calculation for circular Litz wire windings over a wide frequency range, and in particular to a three-dimensional rapid calculation method for high-frequency losses of circular Litz wire. Background Technology

[0002] With the continuous development of power electronics technology and the energy internet, higher requirements are being placed on the power density, space utilization, and efficiency of magnetic components. High-frequency operation and miniaturization have become inevitable development trends for magnetic components such as transformers and reactors. However, as the operating frequency increases, the windings are more affected by the high-frequency skin effect and proximity effect, leading to extremely uneven current distribution within the conductor, significantly increased winding losses, and consequently, problems such as excessively high local temperature rise and reduced energy transmission efficiency. To reduce winding losses in high-frequency magnetic components, winding forms with superior high-frequency performance, such as Litz wire, are generally used.

[0003] Litz wire, due to its internal multi-strand insulated conductor periodically stranded structure, effectively reduces the effects of skin effect and proximity effect, making it a winding form that combines efficiency and cost. In high-power and high-frequency applications, conductors often require a larger current-carrying area, necessitating Litz wire with hundreds or even thousands of insulated conductors.

[0004] Existing research on the calculation methods for high-frequency losses in Litz wire can be mainly summarized into two types: numerical methods and analytical methods. While numerical methods can accurately simulate the high-frequency eddy current effect inside the conductor, the unique multi-strand stranded structure of Litz wire requires a precise three-dimensional simulation model for characterization. Therefore, the finite element model requires fine mesh generation, making it difficult to balance computational accuracy and efficiency. To address this issue, those skilled in the art have used the three-dimensional finite element method to create a detailed model of a Litz wire composed of 16 strands. However, even with the assistance of a supercomputer, such a simple Litz wire structure still requires tens of minutes of computation time. For Litz wires with more strands and a more complex structure, the required computation time is almost unimaginable. To reduce computational costs, those skilled in the art have also established an equivalent model of the Litz wire winding using two-dimensional transient finite element analysis based on a homogenized fast calculation method. However, this model cannot fully consider the influence of the stranded structure on losses and cannot obtain the actual current distribution of the Litz wire, thus having certain limitations in practical applications.

[0005] Existing analytical methods are mainly based on Dowell's one-dimensional electromagnetic field loss calculation model for copper foil windings in high-frequency transformers, established in 1966. This model utilizes the principle of area equivalence to treat Litz wire windings as equivalent to copper foil windings, making the Dowell model applicable to high-frequency loss calculations for Litz wire windings. However, Ferreira argued that the model's corrections for Litz wire windings lacked physical meaning, leading to significant errors in practical applications. To address this, Ferreira derived and proved the orthogonality between the skin effect and proximity effect in conductors in 1994, proposing a two-dimensional loss calculation model for circular Litz wires. Because it does not consider the interaction between conductors in the same layer, this model exhibits significant errors under high-frequency conditions when the windings are closely arranged. To address this problem, Tourkhani proposed a more theoretically sound loss calculation model that fully considers the internal structure of circular Litz wires by treating Litz wires as equivalent to solid circular conductors of the same diameter. This model assumes that the magnetic field in the core window region has only a longitudinal component. However, in practical applications, due to end effects, the magnetic field distribution does not strictly satisfy the one-dimensional assumption, resulting in a significant transverse component. This makes it difficult for the Tourkhani model to accurately calculate the additional losses caused by the proximity effect of the winding.

[0006] In summary, the eddy current distribution inside a Litz wire winding is extremely complex. Existing analytical calculation methods require significant simplification and approximation of the model, making it difficult to accurately characterize the high-frequency eddy current effect of the Litz wire winding. Numerical calculation methods require detailed modeling of the Litz wire, resulting in substantial computational resource consumption. Therefore, accurately and quickly calculating the losses of Litz wire windings is of great significance for the optimized design of high-frequency magnetic components. Summary of the Invention

[0007] The purpose of this invention is to solve the above-mentioned problems by designing a three-dimensional fast calculation method for high-frequency loss of a circular Litz wire.

[0008] The technical solution of the present invention to achieve the above objectives is a three-dimensional fast calculation method for high-frequency loss of a circular Litz wire, which includes the following steps:

[0009] Step 1: Divide the eddy current loss inside the Litz line into three categories: skin effect loss, internal proximity effect loss, and external proximity effect loss, and understand the relationship between skin effect loss, internal proximity effect loss, and external proximity effect loss.

[0010] Step 2: Assuming that the current distribution between each strand is uniform, and by introducing porosity, the Litz wire is equivalent to a solid circular conductor with the same diameter. Based on the one-dimensional electromagnetic field theory and using the Tourkhani model, the loss expression of any circular Litz wire conductor per unit length within the high-frequency magnetic element window is obtained.

[0011] Step 3: Based on the derivation process of the Tourkhani model, the Litz wire is equivalent to a solid circular wire of the same diameter. A two-dimensional finite element equivalent model of the magnetic core window is established using the finite element method, and the external magnetic field is extracted and calculated.

[0012] Step 4: Based on the influence of the three-dimensional stranded structure of the Litz wire on winding losses, construct a three-dimensional loss model that considers the influence of the torsional tilt angle of the Litz wire on the external magnetic field.

[0013] In step one, to understand the relationship between skin effect loss, internal proximity effect loss, and external proximity effect loss, it is assumed that the conductor cross-sectional current only exists. z Directional component, at this time xy The current density in the plane is:

[0014] (1)

[0015] In the formula, J For conductor current density, w Let be the angular frequency of the alternating current waveform; at this time, the conductor loss per unit length is:

[0016] (2)

[0017] In the formula, S Let be the cross-sectional area of ​​the conductor. T Let ρ be the period of the alternating current, and ρ be the resistivity; when the waveform of the alternating current is a standard sine wave,

[0018] (3)

[0019] The current densities for the skin effect and proximity effect are respectively used as J s and J p Indicate, then

[0020] (4)

[0021] When the external magnetic field is not present z When the direction component is used, J s It is an even function. J p Since it is an odd function, equation (4) can be transformed into:

[0022] (5)

[0023] In the formula, P ls This is due to skin effect loss; P lpThis is the proximity effect loss; from equation (5), it can be seen that when the external magnetic field... H ext When uniformly distributed across the conductor cross-section, the skin effect and the proximity effect are orthogonal. Therefore, the three different loss components corresponding to the skin effect, the internal proximity effect, and the external proximity effect can be calculated separately.

[0024] In step two, the high-frequency magnetic element window... k Magnetic field strength at any point within the layer winding H Size:

[0025] (6)

[0026] In the formula, q For the point in the Leeds Line and x The angle between the axes; in equation (6), the first... k Any point within the layer winding H ext and H int for:

[0027] (7)

[0028] (8)

[0029] In the formula, ∆ x This is the horizontal distance between this point and the left side of the Leeds Line. n The number of turns in the winding within the window. r This is the distance from the point to the center of the conductor. I This represents the total current amplitude of the Leeds line. h w The height of each winding layer within the window. r s Let be the radius of the Litz wire winding; according to the above formula, the magnetic field strength at any point within the winding can be obtained. H for:

[0030] (9)

[0031] When a conductor is subjected to a time-varying magnetic field, the loss generated per unit length of conductor is:

[0032] (10)

[0033] in

[0034] (11)

[0035] In the formula, ρ is the resistivity of the conductor. d0 represents the diameter of the Litz wire strand; according to equation (11), the power dissipation density of the conductor is:

[0036] (12)

[0037] In the formula, b The fill rate of the circular Litz line. r 0 represents the radius of the Leeds line. d For deep skin care, I 0 represents the peak value of the current in the Liz wire strands, where I 0= I / N 0; N 0 represents the number of Leeds Line strands;

[0038] magnetic field strength H The square of the modulus is:

[0039] (13)

[0040] The loss expression for any circular Litz wire conductor per unit length within the window of a high-frequency magnetic element can be obtained as follows:

[0041] (14)

[0042] Through derivation, we can obtain:

[0043] (15).

[0044] In step three, a two-dimensional finite element equivalent model of the magnetic core window is established using the finite element method, and an average selection is made at the edge of each turn of the conductor. n At any point on the edge, there are [number] points. i external magnetic field H ext for:

[0045] (16)

[0046] In the formula, H tot，i for i The total magnetic field strength at the point, H int，i for i The magnetic field inside the point conductor, H tot，i and H int，i The size can be calculated using equation (3);

[0047] To simplify vector calculations, the magnetic field strength at each point is decomposed into a rectangular coordinate system. x direction and y Different components in the direction, and solve for the core window ( k,t The average value of the external magnetic field of the conductor at position is:

[0048] (17)

[0049] (18)

[0050] In the formula, H ext,x and H ext,y They are respectively external magnetic fields x Components and y Component; the magnetic field strength at any point within the winding at this time. H for:

[0051] (19).

[0052] In step four, the torsional angle of the Litz line is considered. j External magnetic field H ext The three-dimensional loss model of the influence assumes an external magnetic field on the Litz wire winding. H ext Uniformly distributed longitudinally, due to the twisting angle j The existence of this makes the external magnetic field H ext At the strand level, there are both vertical and parallel components. We can assume that the Litz line has a layered structure, that is, the distance between the center of the strand circle and the center of the Litz line circle. r Keeping it unchanged, we can obtain the tilt angle at this point. j for:

[0053] (20)

[0054] In the formula: p The pitch of the Leeds wire is the axial distance of one turn of the Leeds wire strands. Within one pitch... j The range of values ​​for is (0, 2π].

[0055] When the external magnetic field H ext When parallel to the direction of the Lids line section, H ext Decomposable parallel to the direction of the strand H ext,‖ Perpendicular to the direction of the strand H ext,⊥ ,Right now

[0056] (twenty one)

[0057] For any strand of the conductor cross-section, we can obtain H ext， / / and Hext,⊥ The square of the modulus is:

[0058] (twenty two)

[0059] (twenty three)

[0060] In the formula: q The center of the strand is located at the cross section of the Lids line and the external magnetic field. H ext The angle corresponding to the direction,

[0061] In a linear medium, for a parallel external magnetic field H ext,‖ and vertical external magnetic field H ext,⊥ The following relationship exists in the calculation of the external proximity effect loss of the conductor:

[0062] (twenty four)

[0063] In the formula, G ⊥ and G ‖ These are the AC resistivity coefficients for the vertical external proximity effect and the parallel external proximity effect, respectively, for the Tourkhani model. G ⊥ and G ‖ They are respectively:

[0064] (25)

[0065] (26)

[0066] Because of the orthogonal relationship between the skin effect and the proximity effect of the Litz line, the core window can be obtained ( k, t Position of Litz wire winding, one pitch p The internal loss is:

[0067] (27)

[0068] After derivation, we can obtain:

[0069] (28)

[0070] According to equation (28) and the AC resistance calculation formula R ac =2 P k / I 2It can be seen that the AC resistance per unit length of the circular Litz wire winding in the core window of the high-frequency magnetic component is... R ac for:

[0071] (29)

[0072] DC resistance per unit length of Litz wire winding R dc，p It can be represented as:

[0073] (30)

[0074] Further derivation yields a simplified model of the magnetic core window region at any position ( k,t The AC resistivity of the winding is:

[0075] (31)

[0076] According to equation (31), the overall loss of the high-frequency transformer can be obtained as follows:

[0077] (32)

[0078] In the formula, I rms This represents the effective value of the Litz line current. R dc This represents the total DC resistance of the winding.

[0079] Compared with the prior art, the present invention has the following beneficial effects:

[0080] 1) This method analyzes the loss mechanism of Litz wire windings in high-frequency magnetic components and establishes a three-dimensional calculation model for the loss of circular Litz wire windings. This model combines the advantages of traditional analytical methods and the finite element method, using a two-dimensional homogenized finite element model to calculate the external magnetic field of the conductor, replacing the traditional Dowell one-dimensional electromagnetic field theory. The model fully considers the influence of the core window end effect on the magnetic field distribution between windings, improving the accuracy of the external magnetic field calculation and achieving accuracy optimization of the Tourkhani model.

[0081] 2) This method introduces Lids strands and an external magnetic field. H ext Hinge angle j This invention achieves a detailed characterization of the three-dimensional stranded structure of Litz wire windings and accurately describes the influence of the stranded structure on external proximity effects. Compared with traditional finite element models, the model in this application reduces computational costs while maintaining computational accuracy.

[0082] 3) This method designs and fabricates two high-frequency transformer models of different types. The calculated AC resistance values ​​of the model in this application are compared with the measurement results, the two-dimensional finite element simulation model, and the calculation results of the traditional Tourkhani model. The global relative average errors are 7.8% and 8.0%, respectively. Through comparative analysis, it can be seen that the three-dimensional calculation model of circular Litz wire winding loss proposed in this application can accurately characterize the skin effect and proximity effect of Litz wire, and realize accurate prediction of winding loss of high-frequency magnetic components in a wide frequency range. Attached Figure Description

[0083] Figure 1 This is a flowchart of a three-dimensional fast calculation method for high-frequency loss of a circular Litz wire as described in this invention;

[0084] Figure 2 This is the current density distribution diagram of the Litz wire cross section at a frequency of 60kHz as described in this invention;

[0085] Figure 3 This is a diagram showing the structure of the high-frequency magnetic element described in this invention and the internal magnetic field distribution of its Litz wire winding;

[0086] Figure 4 This is a diagram illustrating the equivalent process of Litz line homogenization described in this invention.

[0087] Figure 5 This is a magnetic field distribution diagram of the core window region of the transformer model described in this invention;

[0088] Figure 6 This is a schematic diagram of the magnetic field distribution outside and across the cross-section of the Litz wire described in this invention;

[0089] Figure 7 This is a schematic diagram of the Litz wire stranded structure described in this invention;

[0090] Figure 8 It is the 0.2 described in this invention. mm 60 and 0.1 mm Actual image of 80 Liz Line;

[0091] Figure 9 This is a physical image of the experimental device for measuring the loss of the Litz wire winding of the high-frequency transformer described in this invention;

[0092] Figure 10 This is a diagram showing the magnetic core window and winding structure parameters of the high-frequency transformer model described in this invention;

[0093] Figure 11 This is a comparison chart of the calculated and measured values ​​of winding loss in Model I of the present invention, and the results of two-dimensional finite element simulation.

[0094] Figure 12 This is a comparison chart of the calculated and measured values ​​of the winding loss of Model I described in this invention, and the results of two-dimensional finite element simulation. Detailed Implementation

[0095] The present invention will now be described in detail with reference to the accompanying drawings, such as... Figure 1-12 As shown;

[0096] The winding losses of high-frequency magnetic components can be divided into two parts: resistive losses and eddy current losses. Resistive losses do not cause uneven current distribution, so Ohm's law can be used to solve them. Eddy current losses within the Litz wire can be roughly divided into three categories:

[0097] 1) Skin effect loss: Under high-frequency excitation, an induced current opposite to the excitation current is generated at the center of the conductor, causing the current to concentrate on the surface conductor distribution, resulting in additional losses, such as... Figure 2 As shown in (a).

[0098] 2) Internal proximity effect loss: The magnetic field generated by each strand within the Lids wire is called the internal magnetic field. H int This magnetic field causes a proximity effect at the level of the Liz line strands, and the resulting additional loss is called the internal proximity effect loss.

[0099] 3) External proximity effect loss: At the winding level, losses are caused by external magnetic fields generated by other Litz wires within the core window. H ext The influence of this will produce a proximity effect at the conductor level, causing uneven current distribution within the conductor, such as... Figure 2 As shown in (c).

[0100] like Figure 2 As shown in (d), the current in the conductor cross section only exists z Directional component, at this time xy The current density in the plane is

[0101] (1)

[0102] In the formula, J The current density in the conductor; w Let be the angular frequency of the alternating current waveform. At this point, the conductor loss per unit length is...

[0103] (2)

[0104] In the formula, S The cross-sectional area of ​​the conductor; T ρ is the period of the alternating current; ρ is the resistivity. When the waveform of the alternating current is a standard sine wave...

[0105] (3)

[0106] The current densities for the skin effect and proximity effect are respectively used asJ s and J p Indicate, then

[0107] (4)

[0108] When the external magnetic field is not present z When the direction component is used, J s It is an even function. J p Since it is an odd function, equation (4) can be transformed into

[0109] (5)

[0110] In the formula, P ls This is due to skin effect loss; P lp This is due to proximity effect loss.

[0111] From equation (5), it can be seen that when the external magnetic field H ext When uniformly distributed across the conductor cross-section, the skin effect and proximity effect are orthogonal. Therefore, the three different loss components corresponding to the skin effect, internal proximity effect, and external proximity effect can be calculated separately.

[0112] The Tourkhani model assumes that the current distribution is uniform among the strands and, by introducing porosity, equates the Litz wire to a solid circular conductor with the same diameter.

[0113] The magnetic field distribution of the circular Litz wire winding inside the core window is as follows: Figure 3 As shown. Each point inside the winding is subject to an external magnetic field. H ext In addition to external influences, it is also affected by the internal magnetic field generated by other strands within the conductor. H int The influence of this. Based on the one-dimensional electromagnetic field theory, it can be considered that... H ext It is distributed in one dimension along the y-axis.

[0114] Based on the above analysis, the first core window k Magnetic field strength at any point within the layer winding H Size is

[0115] (6)

[0116] In the formula, q For the point in the Leeds Line and x The included angle along the axial direction. In equation (6), the first... k Any point within the layer windingH ext and H int for

[0117] (7)

[0118] (8)

[0119] In the formula, ∆ x The horizontal distance between this point and the left side of the Leeds Line, such as Figure 3 As shown; n This refers to the number of turns in the winding within the window. r This is the distance from the point to the center of the conductor; I This represents the total current amplitude of the Leeds line; h w The height of each winding layer within the window; r s The radius of the Litz wire winding is given.

[0120] Based on the above formula, the magnetic field strength at any point within the winding can be obtained. H for

[0121] (9)

[0122] When a conductor is subjected to a time-varying magnetic field, the loss generated per unit length of conductor is:

[0123] (10)

[0124] in

[0125] (11)

[0126] In the formula, ρ is the resistivity of the conductor; d 0 represents the diameter of the Litz wire strand. According to equation (11), the power dissipation density of the conductor is...

[0127] (12)

[0128] In the formula, b The fill rate of the circular Litz line; r 0 represents the radius of the Leeds line strand; d For deeper skin penetration; I 0 represents the peak value of the current in the Liz wire strands, where I 0= I / N 0; N 0 represents the number of Leeds Line strands.

[0129] magnetic field strength H The square of the modulus is

[0130] (13)

[0131] The loss expression for any circular Litz wire conductor per unit length within the window of a high-frequency magnetic element can be obtained as follows:

[0132] (14)

[0133] It can be derived that

[0134] (15)

[0135] Based on the above analysis, it can be concluded that the external magnetic field of the Tourkhani model... H ext The calculations are based on Dowell's one-dimensional electromagnetic field model, and therefore must satisfy the three assumptions of the one-dimensional model: the core permeability is assumed to be infinite; the copper foil winding is wound parallel to the core column; and the winding height is equal to the window height. In this case, it can be assumed that there is no end effect within the core window, and the external magnetic field... H ext Only along y The magnetic field is distributed along the axial direction. However, high-frequency magnetic components using Litz wire as the winding material cannot fully satisfy the three assumptions of one-dimensional electromagnetic field theory, leading to an imbalance in the magnetic field outside the core window. H ext exist x The axial direction component. This causes the Tourkhani model to have a large error in practical applications.

[0136] Finite element method (FEM) simulation can perform detailed simulation modeling of the magnetic field distribution in the core window of high-frequency magnetic components based on the actual structural parameters of the components, fully considering the end effects of the windings in the window region. High-frequency transformers and other magnetic components generally have three-dimensional rotationally symmetric or axisymmetric structures; therefore, dimensionality reduction can be performed during finite element modeling. Simulating the magnetic field distribution in the transformer core window region using a two-dimensional model can reduce the modeling difficulty and computational load while maintaining computational accuracy.

[0137] While two-dimensional finite element models can significantly reduce simulation difficulty, the actual calculation process still requires substantial computational resources for Litz wire windings with a large number of strands. Therefore, we can refer to the derivation process of the Tourkhani model, equating the Litz wire winding to circular solid conductors of the same diameter and current amplitude, and further simplifying it to multiple parallel turns of circular solid conductors. The equivalence process is as follows: Figure 4 As shown.

[0138] In the simplified winding model, the current flow direction (including source current, eddy current, and displacement current) is perpendicular to the conductor cross-section. At this point, the magnetic field within the window can be considered to exist only within... xy It is planar and lacks a longitudinal magnetic field. To verify... Figure 4 To verify the correctness of the homogenization process shown, this application uses ANSYS / Maxwell 2D finite element simulation software to establish a two-dimensional simulation model of the transformer core window. The current amplitudes of the Litz wire and the circular solid conductor are both set to 1A. The magnetic field distribution in the window region is as follows. Figure 5 As shown.

[0139] Depend on Figure 5 A comparison of (a) and (b) shows that, under the same current excitation, the magnetic field distribution in the core window region obtained by the two methods is basically the same. In conclusion, the method of equating the Litz wire with a circular solid conductor of the same diameter and extracting the external magnetic field is feasible.

[0140] The magnetic field at each point on the Litz wire cross section is composed of an internal magnetic field. H int With external magnetic field H ext Superimposed, such as Figure 6 As shown in (b). In practical applications, since the diameter of the Litz wire is small, an external magnetic field can be assumed. H ext The magnetic field is uniformly distributed across the cross-section. To calculate the external magnetic field of the conductor, this application uses the finite element method to establish a two-dimensional finite element equivalent model of the core window, and selects an evenly distributed core window at the edge of each turn of conductor. n At any point on the edge, there are [number] points. i external magnetic field H ext for

[0141] (16)

[0142] In the formula, H tot，i for i The total magnetic field strength at the point; H int，i for i Magnetic field inside a point conductor.

[0143] To simplify vector calculations, the magnetic field strength at each point is decomposed into a rectangular coordinate system. x direction and y Different components in the direction. And solve for the components within the core window ( k,t The average value of the external magnetic field of the conductor at position is

[0144] (17)

[0145] (18)

[0146] In the formula, H ext,x and H ext,y They are respectively external magnetic fields x Components and y Component. The magnetic field strength at any point within the winding at this time. H for

[0147] (19);

[0148] Since the two-dimensional finite element equivalent model described above assumes that the strands of the Litz wire are parallel to each other, it does not consider the influence of its three-dimensional stranded structure on winding losses. To solve this problem, this application proposes a method that considers the torsional tilt angle of the Litz wire. j External magnetic field H ext A three-dimensional loss model of the impact.

[0149] First, assume the external magnetic field of the Litz wire winding. H ext Evenly distributed in the longitudinal direction, such as Figure 6 As shown in (a). Therefore, for a single-stranded circular Litz wire, the incident direction of its external magnetic field is not perpendicular to the strands, as... Figure 7 As shown. Due to the twist angle j The existence of this makes the external magnetic field H ext At the strand level, both vertical and parallel components exist. In practical applications, the number of strands in a single-stranded Litz wire is typically tens to hundreds. We can assume that the Litz wire has a layered structure, meaning the distance between the center of each strand and the center of the Litz wire is... r Keep it unchanged. At this point, the tilt angle can be obtained. j for

[0150] (20)

[0151] In the formula: p The pitch of the Leeds wire is the axial distance of one turn of the Leeds wire strands. Within one pitch... j The range of values ​​for is (0, 2π).

[0152] like Figure 7 As shown in (b), when the external magnetic field H ext When parallel to the direction of the Lids line section, H ext Decomposable parallel to the direction of the strand H ext,‖ Perpendicular to the direction of the strand H ext,⊥ ,Right now

[0153] (twenty one)

[0154] For any strand of the conductor cross-section, we can obtain H ext， / / and H ext,⊥ The square of the modulus is

[0155] (twenty two)

[0156] (twenty three)

[0157] In the formula: q The center of the strand is located at the cross section of the Lids line and the external magnetic field. H ext The included angle corresponding to the direction, such as Figure 7 As shown in (a).

[0158] In a linear medium, for a parallel external magnetic field H ext,‖ and vertical external magnetic field H ext,⊥ The calculation of external proximity effect loss of conductors has the following relationship.

[0159] (twenty four)

[0160] In the formula, G ⊥ and G ‖ These are the AC resistivity coefficients of the vertical external proximity effect and the AC resistivity coefficients of the parallel external proximity effect, respectively.

[0161] For the Tourkhani model G ⊥ and G ‖ They are respectively:

[0162] (25)

[0163] (26)

[0164] Since there is an orthogonal relationship between the skin effect and the proximity effect of the Litz line, and combining the above derivation, the core window can be obtained ( k,t Position of Litz wire winding, one pitch p Internal losses are

[0165] (27)

[0166] After derivation, we can obtain

[0167] (28)

[0168] According to equation (28) and the AC resistance calculation formula R ac =2 P k / I 2 It can be seen that the AC resistance per unit length of the circular Litz wire winding in the core window of the high-frequency magnetic component is... R ac for

[0169] (29)

[0170] DC resistance per unit length of Litz wire winding R dc，p It can be represented as

[0171] (30)

[0172] Further derivation yields the following results: Figure 4 (c) Simplify the model's core window region at any position ( k,t The AC resistivity of the winding is

[0173] (31)

[0174] According to equation (31), we can obtain Figure 3 The overall loss of the high-frequency transformer shown

[0175] (32)

[0176] In the formula, I rms This represents the effective value of the Litz line current. R dc This represents the total DC resistance of the winding. Example

[0177] To verify the correctness of the Litz wire winding loss calculation model proposed in this application, experimental verification was conducted using high-frequency transformer models made with two different types of Litz wire. The two Litz wire structures are as follows: Figure 8 As shown in the figure. The experiment used a Tonghui TH2840B high-precision impedance analyzer to measure the AC resistance of the model. The instrument, utilizing automatic balancing bridge technology, achieves a wide-band measurement range of 20Hz-1MHz, with a maximum accuracy of 0.08%. To eliminate the influence of core loss, the secondary winding of the model needs to be short-circuited. The experimental setup and schematic diagram are shown below. Figure 9 As shown in Table 1, the high-frequency transformer model is designed as a shell structure, with specific structural parameters as shown in Table 1. Figure 10As shown, the magnetic core uses EC4220 ferrite. Table 1 is the structural parameter table of the experimental high-frequency transformer model, and its specific contents are as follows:

[0178] Structural parameters Model I Model II Winding layer ratio 1：1 1：1 Number of turns per layer 12：12 18：18 <![CDATA[Number of turns of single - strand Litz wire ( N 0)]]> 60 80 <![CDATA[Diameter of strand of litz wire ( d 0)]]> 0.2 0.1 <![CDATA[Diameter of Litz wire ( d c )]]> 2.0 1.5 Pitch ( ) 50 50

[0179] The calculated AC resistance values ​​of the model in this application are compared with the measurement results, the two-dimensional finite element simulation, and the traditional Tourkhani model. The results are shown in Figures (11) and (12), where the frequency is set to a wide frequency range of 20Hz-1MHz. When the frequency is less than 10kHz, the diameter of the Litz wire strand is much smaller than the skin depth of the conductor, and the influence of the skin effect is almost negligible. The AC resistance is approximately equal to the DC resistance, and the calculation accuracy of the three methods is very high at this time. When the frequency is from 10kHz to 100kHz, the skin depth of the conductor decreases, and the influence of the skin effect and the internal proximity effect becomes obvious, and the AC resistance gradually increases. The traditional Tourkhani model does not consider the influence of the end effect of the core window winding, and the calculation error gradually increases in this frequency range. At this time, the influence of the external proximity effect is very small, so whether or not the three-dimensional torsion structure is considered has little impact on the calculation results of eddy current loss. When the frequency is from 100kHz to 1MHz, the AC resistance increases rapidly. This is because as the frequency increases, the proportion of external proximity loss caused by the external magnetic field gradually increases, which makes the AC resistance of the Litz wire winding increase rapidly. At this point, the calculation accuracy of the improved model considering the three-dimensional structure is higher than that of the two-dimensional finite element simulation model.

[0180] As the frequency increases, the errors of the traditional Tourkhani model and the two-dimensional finite element model gradually increase. The relative error of the traditional Tourkhani model at high frequencies can even exceed 100%, while the error of the two-dimensional finite element model, although within an acceptable range, requires a large amount of computational resources, which undoubtedly increases the cost of optimizing the design of high-frequency magnetic components. In contrast, the global relative average error of the improved three-dimensional model is 7.8% and 8.0%, respectively, and its computational accuracy and cost are both superior to those of the traditional Tourkhani model and the finite element model. Table 2 is a comparison table of the computational costs of the improved three-dimensional model and the two-dimensional finite element model, the details of which are as follows:

[0181]

[0182] All calculation results in this application were obtained on a server-class computer with an E5-2690V3 2.6GHz CPU and 64GB RAM. Table 2 shows a comparison of the computational costs between the improved 3D model and the 2D finite element model. Compared to the detailed 2D finite element modeling, the model in this application, using Litz wire winding homogenized finite element modeling, can more accurately characterize the high-frequency proximity effect loss caused by the external magnetic field and effectively reduce computational costs.

[0183] It should be noted that in this application, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, the phrase "comprising an element defined as..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0184] The above technical solutions only embody the preferred technical solutions of the present invention. Any modifications that may be made by those skilled in the art to certain parts thereof embody the principles of the present invention and fall within the protection scope of the present invention.

Claims

1. A method for rapid three-dimensional calculation of high-frequency loss of a circular Litz wire, characterized in that, The method includes the following steps: Step 1: Divide the eddy current loss inside the Litz line into three categories: skin effect loss, internal proximity effect loss, and external proximity effect loss, and understand the relationship between skin effect loss, internal proximity effect loss, and external proximity effect loss. Step 2: Assuming that the current distribution between each strand is uniform, and by introducing porosity, the Litz wire is equivalent to a solid circular conductor with the same diameter. Based on the one-dimensional electromagnetic field theory and using the Tourkhan i model, the loss expression of any circular Litz wire conductor per unit length within the high-frequency magnetic element window is obtained. Step 3: Based on the derivation process of the Tourkhani model, the Litz wire is equivalent to a solid circular wire of the same diameter. A two-dimensional finite element equivalent model of the magnetic core window is established using the finite element method. The external magnetic field is extracted and calculated. Step 4: Based on the influence of the three-dimensional stranded structure of the Litz wire on winding losses, construct a three-dimensional loss model that considers the influence of the torsional tilt angle of the Litz wire on the external magnetic field. Considering the torsional angle of the Lids line external magnetic field H ext The three-dimensional loss model of the influence assumes an external magnetic field H on the Litz wire winding. ext Uniformly distributed longitudinally, due to the twisting angle The presence of the external magnetic field H ext At the strand level, there are both vertical and parallel components. We can assume the Litz line has a layered structure, meaning the distance *r* between the center of the strand circle and the center of the Litz line circle remains constant. In this case, the inclination angle can be obtained. for: In the formula: p is the pitch of the Leeds wire, that is, the axial distance of one turn of the Leeds wire strands. Within one pitch, The range of values ​​for is (0, 2π).

2. The method for rapid three-dimensional calculation of high-frequency loss of a circular Litz wire according to claim 1, characterized in that, In step one, to understand the relationship between skin effect loss, internal proximity effect loss, and external proximity effect loss, it is assumed that the current in the conductor cross-section has only a z-direction component. At this time, the current density in the xy plane is: J(x,y,t)=J(x,y)cos(ωt) (1) In the formula, J is the conductor current density, and ω is the angular frequency of the alternating current waveform; the conductor loss per unit length is: In the formula, S is the cross-sectional area of ​​the conductor, T is the period of the alternating current, and ρ is the resistivity; when the waveform of the alternating current is a standard sine wave, The current densities for the skin effect and proximity effect are respectively expressed in J. s and J p It means, that is, J s For the skin effect current density, J p Given the proximity effect current density, then When the magnetic field outside the window has no z-direction component, J s J is an even function. p Since it is an odd function, equation (4) can be transformed into: In the formula, P λs For skin effect loss; P λp This is the proximity effect loss; from equation (5), it can be seen that when the external magnetic field H ext When uniformly distributed across the conductor cross-section, the skin effect and the proximity effect are orthogonal. Therefore, the three different loss components corresponding to the skin effect, the internal proximity effect, and the external proximity effect can be calculated separately.

3. The method for rapid three-dimensional calculation of high-frequency loss of a circular Litz wire according to claim 2, characterized in that, In step two, the magnitude of the magnetic field strength H at any point within the k-th layer winding of the high-frequency magnetic element window is: H=H ext +H int =(H ext +H int cosθ)e y -H int sinθe x (6) In the formula, θ is the angle between the point on the Lids line and the x-axis direction, and e x e is a unit vector along the x-axis. y Let H be the unit vector along the y-axis; in equation (6), H is the vector at any point within the k-th layer winding. ext With H int for: In the formula, Δx is the horizontal distance between the point and the left side of the Litz line, r is the distance from the point to the center of the conductor, I is the total current amplitude of the Litz line, and h w r is the height of each winding layer within the window. s Let be the radius of the Litz wire winding; according to the above formula, the magnetic field strength H at any point inside the winding can be obtained as: When a conductor is subjected to a time-varying magnetic field, the loss generated per unit length of conductor is: in In the formula, ρ is the resistivity of the conductor, and d0 is the diameter of the Litz strand; according to formula (11), the power dissipation density of the conductor is: In the formula, β is the fill ratio of the circular Litz wire, r0 is the radius of the Litz wire strand, δ is the skin depth, I0 is the peak value of the Litz wire strand current, where I0=I / N0; N0 is the number of Litz wire strands; The square of the magnetic field strength H modulus is: The loss expression for any circular Litz wire conductor per unit length within the window of a high-frequency magnetic element can be obtained as follows: Through derivation, we can obtain:

4. The method for rapid three-dimensional calculation of high-frequency loss of a circular Litz wire according to claim 3, characterized in that, In step three, a two-dimensional finite element equivalent model of the magnetic core window is established using the finite element method, and n points are selected on average at the edge of each turn of the conductor. At this time, the external magnetic field H at any point i at the edge is... ext for: H ext,i =H tot,i -H int,i (16) In the formula, H tot，i H is the total magnetic field strength at point i. int Let i be the magnetic field inside the conductor at point i, and H be the magnetic field inside the conductor at point i. tot， i and H int The value of i can be calculated from equation (3); To simplify vector calculations, the magnetic field strength at each point is decomposed into different components in the x and y directions of a rectangular coordinate system, and the average external magnetic field of the conductor at position (k,t) within the core window is calculated as follows: In the formula, H ext,x With H ext,y Let x and y be the x and y components of the external magnetic field, respectively; then the magnetic field strength H at any point within the winding is: H=H ext +H int =(H ext，y +H int cosθe y )+(H ext，x -H int sinθ)e x (19)。 5. The method for rapid three-dimensional calculation of high-frequency loss of a circular Litz wire according to claim 4, characterized in that, In step four, when the external magnetic field H ext When parallel to the direction of the Litz line section, H ext H can be decomposed parallel to the direction of the strand. ext, / / H perpendicular to the direction of the strand ext,⊥ ,Right now H ext =H ext， / / +H ext，⊥ (21) For any strand of the conductor cross-section, we can obtain H. ext， / / and H ext,⊥ The square of the modulus is: In the formula: θ is the distance between the center of the strand and the Lids line cross section and the external magnetic field H. ext The angle corresponding to the direction, In a linear medium, for a parallel external magnetic field H ext, / / and the vertical external magnetic field H ext,⊥ The following relationship exists in the calculation of the external proximity effect loss of the conductor: In the formula, G ⊥ With G / / These are the AC resistivity coefficients of the vertical external proximity effect and the parallel external proximity effect, respectively, for the Tourkhani model, G. ⊥ With G / / They are respectively: Since there is an orthogonal relationship between the skin effect and the proximity effect of the Litz wire, the loss of the Litz wire winding within one pitch p at the core window position (k,t) can be obtained as follows: After derivation, we can obtain: According to equation (28) and the AC resistance calculation formula R ac =2P k / I 2 It can be seen that the AC resistance R per unit length of the circular Litz wire winding in the core window of the high-frequency magnetic component is... ac for: The DC resistance R per unit length of the Litz wire winding dc，p It can be represented as: Further derivation yields the following AC resistivity coefficient of the winding at any position (k,t) in the core window region of the simplified model: According to equation (31), the overall loss of the high-frequency transformer can be obtained as follows: In the formula, I rms R is the effective value of the Litz line current. dc This represents the total DC resistance of the winding.

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