CLLC resonant circuit circular litz wire winding loss calculation method and system

Abstract

The application discloses a CLLC resonant circuit circular Litz wire winding loss calculation method and system, comprising: constructing a Litz wire internal magnetic field strength model, determining a polar coordinate expression of the circular Litz wire magnetic field strength according to the Litz wire internal magnetic field strength model; determining a primary side current effective value and a secondary side current effective value of the CLLC resonant circuit; determining a proximity effect loss expression, calculating the proximity effect loss value of the primary and secondary sides of the CLLC resonant circuit according to the polar coordinate expression, the primary side current effective value, the secondary side current effective value and the proximity effect loss expression; determining a skin effect loss expression, and calculating the skin effect loss value of the primary and secondary sides of the CLLC resonant circuit according to the polar coordinate expression, the primary side current effective value, the secondary side current effective value and the skin effect loss expression. The application improves the accuracy of the CLLC resonant circuit circular Litz wire winding loss calculation, and can be applied to the field of circuit measurement technology.

Description

Technical Field

[0001] This invention relates to the field of circuit measurement technology, and in particular to a method and system for calculating the loss of circular Litz wire windings in a CLLC resonant circuit. Background Technology

[0002] The CLLC resonant circuit, as an isolated bidirectional DC-DC converter operating at high frequencies and possessing high power density characteristics, is widely considered a promising topology for bidirectional power conversion technology due to its excellent soft-switching capability. This converter has a wide range of applications, covering many important fields such as uninterruptible power supply systems, DC distribution networks, and interconnection systems between electric vehicles and the power grid.

[0003] With advancements in power electronic control technology and continuous improvements in the performance of semiconductors and magnetic materials, the operating frequency of converters has increased significantly. This frequency increase leads to increased winding losses in transformers at higher operating frequencies, primarily due to enhanced skin and proximity effects, which in turn cause problems such as increased internal component temperature and decreased energy conversion efficiency. To effectively reduce winding losses in high-frequency transformers, higher-performance high-frequency windings, such as Litz wire, are typically selected for improvement.

[0004] Three main analytical models exist for high-frequency winding losses in Litz wires: the improved Dowell model, the Ferreira model, and the modified Tourkhani model. Initially, the Dowell model was derived based on the assumption that the long copper foil winding had an ideal one-dimensional magnetic field distribution. Some researchers improved the Dowell model by treating the Litz wire winding as a copper foil winding using the area equivalence principle, but Ferreira pointed out that this simplification method had physical limitations, leading to significant calculation errors. Therefore, Ferreira proposed a two-dimensional loss calculation model for circular Litz wires, but this model did not consider the interaction between conductors in the same layer, potentially resulting in large errors when the windings are closely arranged. To address this issue, Tourkhani equivalently treated the Litz wire as a circular solid conductor with the same diameter and proposed a loss calculation model that fully considered the internal structure. However, Tourkhani's derivation contained errors, failing to provide an accurate analytical expression for the magnetic field, leading to errors in the final model. Ren Liu discovered and pointed out this problem in 2023, providing the correct derivation process and results. However, the corrected Tourkhani model still has some problems with a maximum error of 11.25%. In actual engineering, considering the insulation requirements, the height of the transformer winding is generally smaller than the height of the core window. At this time, the winding ends will have obvious end effects, making it difficult to accurately calculate the additional losses caused by the proximity effect.

[0005] The above problems urgently need to be addressed.

[0006] Terminology Explanation:

[0007] CLLC resonant circuit: a type of power electronic converter typically used for efficient power transfer. It utilizes resonant inductors and capacitors to achieve efficient power transfer by adjusting the resonant frequencies of current and voltage.

[0008] Winding losses refer to the energy loss in a transformer or inductor caused by the heat generated by the current flowing through the conductor in the coil winding. These mainly include DC resistance losses and losses caused by the skin effect and proximity effect at high frequencies.

[0009] Skin effect: Under high-frequency current, the current tends to concentrate on the surface of the conductor rather than the entire cross-section of the conductor, resulting in a reduction in the effective conductor area, which increases the equivalent resistance of the conductor and thus increases the loss.

[0010] Proximity effect: When multiple conductors are close to each other, the current in one conductor generates a magnetic field, which affects the current distribution in nearby conductors, causing the current to concentrate on the nearby surface, thereby increasing the conductor's losses.

[0011] Litz wire is a type of conductor made up of many insulated fine wires braided or arranged in parallel, designed to reduce winding losses caused by skin effect and proximity effect. Summary of the Invention

[0012] The purpose of this invention is to at least partially solve one of the technical problems existing in the prior art.

[0013] Therefore, one objective of this invention is to provide a method for calculating the loss of a circular Litz wire winding in a CLLC resonant circuit, which improves the accuracy of the loss calculation.

[0014] Another objective of this invention is to provide a system for calculating the loss of circular Litz wire windings in a CLLC resonant circuit.

[0015] To achieve the above-mentioned technical objectives, the technical solutions adopted in the embodiments of the present invention include:

[0016] In a first aspect, embodiments of the present invention provide a method for calculating the loss of a circular Litz wire winding in a CLLC resonant circuit, comprising the following steps:

[0017] Construct a model of the magnetic field strength inside the Litz line, and determine the polar coordinate expression of the magnetic field strength of the circular Litz line based on the model.

[0018] Determine the effective values ​​of the primary and secondary currents of the target CLLC resonant circuit;

[0019] The proximity effect loss expression is determined, and the proximity effect loss value of the primary and secondary sides of the target CLLC resonant circuit is calculated based on the polar coordinate expression, the effective value of the primary side current, the effective value of the secondary side current, and the proximity effect loss expression.

[0020] The skin effect loss expression is determined, and the skin effect loss values ​​of the primary and secondary sides of the target CLLC resonant circuit are calculated based on the polar coordinate expression, the effective value of the primary side current, the effective value of the secondary side current, and the skin effect loss expression.

[0021] Furthermore, in one embodiment of the present invention, the magnetic field strength model inside the Litz wire is as follows:

[0022] H = [H] ext (Δx,k)+H int [r]cosθ]·e y -H int sinθ·e x

[0023]

[0024] Where H represents the magnetic field strength at each point inside the k-th layer of the circular Litz wire, Δx represents the horizontal distance from each point inside the circular Litz wire winding to its leftmost point, r represents the distance between each point inside the circular Litz wire and the center of the circular Litz wire, θ represents the angle between the line segment connecting each point inside the circular Litz wire and the center of the circular Litz wire and the x-axis, and e x e represents the unit vector along the x-axis. y h represents the unit vector along the y-axis. w The height of the circular Litz wire winding is represented by n, where n represents the number of turns of the circular Litz wire in each layer of the winding, and d represents the height of the circular Litz wire winding. Litz The diameter of the circular Litz wire winding is represented by r. Litz The radius of the circular Litz wire winding is represented by I, and the current amplitude through the circular Litz wire is represented by I.

[0025] Furthermore, in one embodiment of the present invention, the polar coordinate expression is:

[0026]

[0027] Here, H(r,θ) represents the polar coordinates of the magnetic field strength at a point (r,θ) inside the circular Litz line.

[0028] Furthermore, in one embodiment of the present invention, the effective value of the primary side current is determined by the following formula:

[0029]

[0030] The effective value of the secondary current is determined by the following formula:

[0031]

[0032] Among them, I Lr1,rms I represents the effective value of the primary current. Lr2.rms This represents the effective value of the secondary current, V. o The output voltage of the target CLLC resonant circuit is represented by N, where N represents the transformer turns ratio and L represents the output voltage of the target CLLC resonant circuit. m R0 represents the magnetizing inductance, and f represents the load resistance. s Indicates the operating frequency of the circuit.

[0033] Furthermore, in one embodiment of the present invention, the expression for the proximity effect loss is:

[0034]

[0035] Among them, P proximity D represents the proximity effect loss value, and B represents the waveform duty cycle. p σ represents the amplitude of the sinusoidal magnetic field, f represents the frequency of the magnetic field change, l represents the length of the circular Litz wire conductor, d represents the diameter of the circular Litz wire conductor, and σ represents the conductivity of the conductor.

[0036] The expression for the skin effect loss is:

[0037]

[0038]

[0039] Among them, P skin θ represents the skin effect loss value, r represents the distance between each point inside the circular Litz line and the center of the circular Litz line, and θ represents the angle between the line segment connecting each point inside the circular Litz line and the center of the circular Litz line and the x-axis.

[0040] Furthermore, in one embodiment of the present invention, the proximity effect loss value is calculated using the following formula:

[0041]

[0042] Among them, P 1,proximity P represents the proximity effect loss value of the primary side of the target CLLC resonant circuit. 2,proximity V represents the proximity effect loss value on the secondary side of the target CLLC resonant circuit. o The output voltage of the target CLLC resonant circuit is represented by N, where N represents the transformer turns ratio and L represents the output voltage of the target CLLC resonant circuit. m R0 represents the magnetizing inductance, and f represents the load resistance. sThe circuit operating frequency is represented by μ0, and the permeability of free space is represented by h. w The height of the circular Litz wire winding is represented by n, and the number of turns of the circular Litz wire in each layer of the winding is represented by r. Litz The radius of the circular Litz wire winding is represented by , and k represents the number of layers of the circular Litz wire.

[0043] Furthermore, in one embodiment of the present invention, the skin effect loss value is calculated by the following formula:

[0044]

[0045] Among them, P 1,skin P represents the skin effect loss value of the primary side of the target CLLC resonant circuit. 2,skin V represents the skin effect loss value on the secondary side of the target CLLC resonant circuit. o The output voltage of the target CLLC resonant circuit is represented by N, where N represents the transformer turns ratio and L represents the output voltage of the target CLLC resonant circuit. m R0 represents the magnetizing inductance, and f represents the load resistance. s Indicates the circuit's operating frequency, h w The height of the circular Litz wire winding is represented by n, and the number of turns of the circular Litz wire in each layer of the winding is represented by r. Litz This indicates the radius of the circular Litz wire winding.

[0046] Secondly, embodiments of the present invention provide a system for calculating the loss of a circular Litz wire winding in a CLLC resonant circuit, comprising:

[0047] The polar coordinate expression determination module is used to construct a model of the magnetic field strength inside the Litz line and determine the polar coordinate expression of the magnetic field strength of the circular Litz line based on the model of the magnetic field strength inside the Litz line.

[0048] The current RMS value determination module is used to determine the RMS values ​​of the primary side current and the secondary side current of the target CLLC resonant circuit;

[0049] The proximity effect loss calculation module is used to determine the proximity effect loss expression and calculate the proximity effect loss value of the primary and secondary sides of the target CLLC resonant circuit based on the polar coordinate expression, the effective value of the primary side current, the effective value of the secondary side current, and the proximity effect loss expression.

[0050] The skin effect loss calculation module is used to determine the skin effect loss expression and calculate the skin effect loss value of the primary and secondary sides of the target CLLC resonant circuit based on the polar coordinate expression, the effective value of the primary side current, the effective value of the secondary side current, and the skin effect loss expression.

[0051] Thirdly, embodiments of the present invention provide a device for calculating the loss of a circular Litz wire winding in a CLLC resonant circuit, comprising:

[0052] At least one processor;

[0053] At least one memory for storing at least one program;

[0054] When the at least one program is executed by the at least one processor, the at least one processor implements the above-described method for calculating the loss of a circular Litz wire winding in a CLLC resonant circuit.

[0055] Fourthly, embodiments of the present invention also provide a computer-readable storage medium storing a processor-executable program, which, when executed by a processor, is used to perform the above-described method for calculating the loss of a circular Litz wire winding in a CLLC resonant circuit.

[0056] The advantages and beneficial effects of the present invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention:

[0057] This invention constructs a model of the internal magnetic field strength of a Litz wire, determines the polar coordinate expression of the magnetic field strength of a circular Litz wire based on this model, determines the effective values ​​of the primary and secondary currents of the target CLLC resonant circuit, determines the expression for the proximity effect loss, and calculates the proximity effect loss values ​​of the primary and secondary sides of the target CLLC resonant circuit based on the polar coordinate expression, the effective values ​​of the primary and secondary currents, and the proximity effect loss expression. It also determines the skin effect loss expression and calculates the skin effect loss values ​​of the primary and secondary sides of the target CLLC resonant circuit based on the polar coordinate expression, the effective values ​​of the primary and secondary currents, and the skin effect loss expression. This invention calculates the CLLC high-frequency transformer winding losses separately, dividing them into proximity effect losses and skin effect losses. This allows for the consideration of additional losses caused by end effects to a certain extent, thereby avoiding calculation errors due to end effects and improving the accuracy of calculating the losses of the circular Litz wire winding in the CLLC resonant circuit. Attached Figure Description

[0058] To more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the embodiments of the present invention are described below. It should be understood that the drawings described below are only for the convenience of clearly describing some embodiments of the technical solutions of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0059] Figure 1A flowchart illustrating the steps of a method for calculating the loss of a circular Litz wire winding in a CLLC resonant circuit, as provided in an embodiment of the present invention;

[0060] Figure 2 A schematic diagram of the structure of a CLLC transformer and the distribution of the magnetic field inside its circular Litz wire winding;

[0061] Figure 3 This is a schematic diagram of a CLLC resonant circuit.

[0062] Figure 4 A simplified schematic diagram of the equivalent circuit for the forward fundamental frequency.

[0063] Figure 5 This is a schematic diagram of the conductor cross-section;

[0064] Figure 6 A schematic diagram of a uniformly changing magnetic field;

[0065] Figure 7 Dimensioning diagram of the Maxwell simulation model of the CLLC high-frequency transformer;

[0066] Figure 8 A comparison chart showing the calculated, simulated, and measured values ​​of the AC resistance of the CLLC transformer windings;

[0067] Figure 9 A structural block diagram of a CLLC resonant circuit circular Litz wire winding loss calculation system provided in an embodiment of the present invention;

[0068] Figure 10 This is a structural block diagram of a CLLC resonant circuit circular Litz wire winding loss calculation device provided in an embodiment of the present invention. Detailed Implementation

[0069] The embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention. The step numbers in the following embodiments are set only for ease of explanation, and there is no limitation on the order between the steps. The execution order of each step in the embodiments can be adaptively adjusted according to the understanding of those skilled in the art.

[0070] In the description of this invention, "multiple" means two or more. The use of "first" and "second" is for distinguishing technical features only and should not be construed as indicating or implying relative importance, or implicitly indicating the number of indicated technical features, or the order of the indicated technical features. Furthermore, unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art.

[0071] Reference Figure 1 This invention provides a method for calculating the loss of a circular Litz wire winding in a CLLC resonant circuit, specifically including the following steps:

[0072] S101. Construct a model of the magnetic field strength inside the Litz line, and determine the polar coordinate expression of the magnetic field strength of the circular Litz line based on the model.

[0073] As a further optional implementation, the model for the magnetic field strength inside the Lids line is as follows:

[0074] H = [H] ext (Δx,k)+H int [r]cosθ]·e y -H int sinθ·e x

[0075]

[0076] Where H represents the magnetic field strength at each point inside the k-th layer of the circular Litz wire, Δx represents the horizontal distance from each point inside the circular Litz wire winding to its leftmost point, r represents the distance between each point inside the circular Litz wire and the center of the circular Litz wire, θ represents the angle between the line segment connecting each point inside the circular Litz wire and the center of the circular Litz wire and the x-axis, and e x e represents the unit vector along the x-axis. y h represents the unit vector along the y-axis. w The height of the circular Litz wire winding is represented by n, where n represents the number of turns of the circular Litz wire in each layer of the winding, and d represents the height of the circular Litz wire winding. Litz The diameter of the circular Litz wire winding is represented by r. Litz The radius of the circular Litz wire winding is represented by I, and the current amplitude through the circular Litz wire is represented by I.

[0077] As a further optional implementation, the polar coordinate expression is:

[0078]

[0079] Here, H(r,θ) represents the polar coordinates of the magnetic field strength at a point (r,θ) inside the circular Litz line.

[0080] Specifically, before deriving the analytical model, it is assumed that each strand of the circular Litz wire is coated with insulating varnish and isolated from each other, and that each strand passes continuously through every point on the cross-section of the circular Litz wire. Therefore, it can be assumed that the current in the circular Litz wire is uniformly distributed across each strand, i.e., the current in each strand is the same.

[0081] exist Figure 2 The diagram illustrates the magnetic field distribution of the circular Litz wire. Each point inside the winding is affected not only by the magnetic field strength Hext generated by currents from other windings, but also by the magnetic field strength Hint generated by currents from other internal strands. Hext can be considered a one-dimensional distribution along the y-axis, meaning the core-guided leakage magnetic field is distributed axially.

[0082] The magnetic field strength H at each point inside the k-th layer of the circular Litz wire is expressed as:

[0083]

[0084] In the formula: θ represents the angle between the line segment connecting each point to the center of the circular Litz line and the x-axis. Each point The direction is the tangent direction of the circle with radius r that passes through all points. H ext and H int They represent and The modulus. In formula (1), H ext and H int This can be represented by formulas (2) and (3) respectively:

[0085]

[0086] In the formula: x is the horizontal distance from any point inside the circular Litz wire winding to its leftmost point; h w The height of the circular Litz wire winding; n is the number of turns of the circular Litz wire in each layer of the winding; d Litz r Litz Let be the diameter and radius of the circular Litz wire winding, respectively; and I be the current amplitude passing through the circular Litz wire. Using formulas (1), (2), and (3), the polar coordinate expression for the magnetic field strength H at any point (r, θ) of the j-th circular Litz wire conductor in the k-th layer of the transformer can be obtained as follows:

[0087]

[0088] S102. Determine the effective values ​​of the primary and secondary currents of the target CLLC resonant circuit.

[0089] As a further optional implementation, the effective value of the primary side current is determined by the following formula:

[0090]

[0091] The effective value of the secondary current is determined by the following formula:

[0092]

[0093] Among them, I Lr1,rms I represents the effective value of the primary current. Lr2.rms This represents the effective value of the secondary current, V. o The output voltage of the target CLLC resonant circuit is represented by N, where N represents the transformer turns ratio and L represents the output voltage of the target CLLC resonant circuit. m R0 represents the magnetizing inductance, and f represents the load resistance. s Indicates the operating frequency of the circuit.

[0094] Specifically, Figure 3 , Figure 4 These are the schematic diagram of a CLLC resonant circuit and the simplified equivalent circuit of the forward fundamental wave, respectively. The dead-time mode and three-element resonant mode (which occupy a very small proportion of the time) of the CLLC during operation are ignored. The primary current of the transformer at this time is:

[0095]

[0096] In the formula, I Lr1,rms is i Lr1(t) The effective value of ω r =2πf r f r The first resonant frequency is given by φ, which is the phase difference relative to the input voltage. o This is the output voltage of the CLLC circuit.

[0097]

[0098]

[0099] According to formulas (5), (7), and (8), we can obtain I. Lr1,rms as follows:

[0100]

[0101] In the formula, N is the transformer turns ratio, L m R is the magnetizing inductance, and R0 is the load resistance.

[0102] The secondary current of the transformer is obtained using the same method:

[0103]

[0104] S103. Determine the proximity effect loss expression. Calculate the proximity effect loss values ​​of the primary and secondary sides of the target CLLC resonant circuit based on the polar coordinate expression, the effective value of the primary current, the effective value of the secondary current, and the proximity effect loss expression.

[0105] S104. Determine the skin effect loss expression. Calculate the skin effect loss values ​​of the primary and secondary sides of the target CLLC resonant circuit based on the polar coordinate expression, the effective value of the primary current, the effective value of the secondary current, and the skin effect loss expression.

[0106] As a further optional implementation, the proximity effect loss expression is:

[0107]

[0108] Among them, P proximity D represents the proximity effect loss value, and B represents the waveform duty cycle. p σ represents the amplitude of the sinusoidal magnetic field, f represents the frequency of the magnetic field change, l represents the length of the circular Litz wire conductor, d represents the diameter of the circular Litz wire conductor, and σ represents the conductivity of the conductor.

[0109] The expression for skin effect loss is:

[0110]

[0111] Among them, P skin θ represents the skin effect loss value, r represents the distance between each point inside the circular Litz line and the center of the circular Litz line, and θ represents the angle between the line segment connecting each point inside the circular Litz line and the center of the circular Litz line and the x-axis.

[0112] As a further optional implementation, the proximity effect loss value is calculated using the following formula:

[0113]

[0114]

[0115] Among them, P 1,proximity P represents the proximity effect loss value of the primary side of the target CLLC resonant circuit. 2,proximity V represents the proximity effect loss value on the secondary side of the target CLLC resonant circuit. o The output voltage of the target CLLC resonant circuit is represented by N, where N represents the transformer turns ratio and L represents the output voltage of the target CLLC resonant circuit. m R0 represents the magnetizing inductance, and f represents the load resistance. s The circuit operating frequency is represented by μ0, and the permeability of free space is represented by h. w The height of the circular Litz wire winding is represented by n, and the number of turns of the circular Litz wire in each layer of the winding is represented by r. LitzThe radius of the circular Litz wire winding is represented by , and k represents the number of layers of the circular Litz wire.

[0116] As an optional implementation, the skin effect loss value is calculated using the following formula:

[0117]

[0118] Among them, P 1,skin P represents the skin effect loss value of the primary side of the target CLLC resonant circuit. 2,skin V represents the skin effect loss value on the secondary side of the target CLLC resonant circuit. o The output voltage of the target CLLC resonant circuit is represented by N, where N represents the transformer turns ratio and L represents the output voltage of the target CLLC resonant circuit. m R0 represents the magnetizing inductance, and f represents the load resistance. s The operating frequency of the circuit, h w The height of the circular Litz wire winding is represented by n, and the number of turns of the circular Litz wire in each layer of the winding is represented by r. Litz This indicates the radius of the circular Litz wire winding.

[0119] Specifically, the relationship between duty cycle and proximity effect loss is first calculated.

[0120] When adjacent conductors both carry high-frequency currents, each conductor is not only in the magnetic field generated by its own high-frequency current, but also in the magnetic field generated by the currents in other conductors. Changes in the magnetic fields of adjacent conductors lead to the generation of induced electromotive force, which in turn induces eddy currents in the conductors, causing energy loss. This loss is called proximity loss. When a cylindrical copper conductor with diameter *d* and length *l* is placed in an alternating magnetic field, assuming the magnetic field is uniform and perpendicular to the conductor, and the cross-section of the conductor is as follows... Figure 5 As shown.

[0121] The expression for proximity loss is as follows, where σ is the conductor conductivity.

[0122]

[0123] At this point, the calculation of the proximity effect loss depends on the waveform of the magnetic field. When the waveform of the magnetic field (and other periodic waveforms are similar) is as follows... Figure 4 As shown, the duty cycle can be used for calculation. Figure 6 Taking the magnetic field waveform shown as an example, Ts is the period of the magnetic field waveform, and D is the duty cycle of the waveform, which is the proportion of the positive half period to the whole period. For a complete period, it can be divided into two time periods, 0-DT and DT-T, for calculation. Formula (12) and (13) can be obtained from formula (11).

[0124]

[0125] In the formula, B p Let f be the amplitude of the sinusoidal magnetic field, and f be the frequency of the magnetic field change. Combining equations (12) and (13), the expression for the proximity effect loss can be obtained as follows:

[0126]

[0127] Combining formulas (4), (9), (10), and (14), the relationship between the proximity effect loss of the primary and secondary sides of the CLLC resonant circuit and the magnetic field duty cycle can be obtained as follows:

[0128]

[0129] In the formula, μ0 is the vacuum permeability.

[0130] Secondly, the loss caused by the skin effect is calculated.

[0131] When alternating current or an alternating electromagnetic field is present, the current distribution inside the conductor is non-uniform. The current is mainly concentrated in a thin layer on the surface of the conductor. The current density is higher near the surface of the conductor, while the current is actually lower inside the conductor. This leads to an increase in the resistance of the conductor, which in turn increases the power loss, and this loss is called skin loss. The polar coordinate relationship between the current density and the magnetic field strength in the conductor is shown in Equation (19).

[0132]

[0133] Integrating the current density over the conductor yields the formula for skin effect loss per unit length:

[0134]

[0135] Combining formulas (4), (9), (10), (19), and (20), the skin effect loss expression of the primary and secondary sides of the CLLC resonant circuit can be obtained as follows:

[0136]

[0137] The method steps of the embodiments of the present invention have been described above. The embodiments of the present invention will be further described below with reference to simulation experiments.

[0138] like Figure 7 The figure shows the dimensioned diagram of the Maxwell simulation model of the CLLC high-frequency transformer. The parameters of the CLLC high-frequency transformer used in the simulation are shown in Table 1. To verify the CLLC winding loss calculation model proposed in this invention, a high-frequency wound transformer on a 100W CLLC resonant circuit was used as the test and analysis object. Its AC resistance was measured using a bode100 vector network analyzer, and the results were verified using Ansys Maxwell simulation.

[0139] Table 1

[0140]

[0141] Before testing, the secondary side of the transformer is short-circuited to eliminate the influence of the magnetic core, and the bode100 vector network analyzer must be calibrated with open circuit, short circuit and load.

[0142] Comparison of calculated, simulated, and measured values ​​of AC resistance of the circular Litz wire winding of the CLLC resonant circuit transformer. Figure 8 As shown. At a resonant frequency of 50.9 kHz, the measured value of the Bode 100 is 40.01 mΩ, the simulated value of the model of this invention is 36.41 mΩ, and the simulated value of the modified Tourkhani model is 36.31 mΩ. Figure 8 The following results can be obtained: ① For the CLLC resonant circuit test transformer, the model proposed in this invention is closer to the experimental measurement value and Maxwell simulation value than the modified Tourkhani model in the entire frequency range; ② For the CLLC resonant circuit test transformer, at the resonant frequency point, the error of the modified Tourkhani model is 9.25%, while that of the model proposed in this invention is 8.99%. In the range of 0 to 100 kHz, the error of the modified Tourkhani model is the largest at 9.90%, while that of the model proposed in this invention is 9.10%.

[0143] In summary, after verification by Ansys Maxwell simulation and the construction of a high-frequency transformer AC resistance measurement platform, the measurement results were compared with the calculation results of the model of this invention and the modified Tourkhani model. The results show that the Litz wire winding loss model of the CLLC resonant circuit transformer proposed in this invention can accurately calculate the Litz wire winding loss of the CLLC resonant circuit transformer, and realize the accurate prediction of the Litz wire winding loss of the CLLC resonant circuit transformer.

[0144] It is understood that this embodiment of the invention calculates the winding losses of CLLC high-frequency transformers separately, dividing them into proximity effect losses and skin effect losses. This allows for the consideration of additional losses caused by end effects to a certain extent. End effects are mainly manifested as non-uniformity in magnetic field distribution. When end effects are significant, directly calculating the total loss will lead to errors because the calculation does not consider the non-uniformity of the magnetic field caused by end effects. This embodiment of the invention calculates these two effects separately, which allows for better consideration of local changes in the magnetic field during their respective calculation processes. It also allows for more detailed analysis and processing of end effects, thereby avoiding errors in loss calculation caused by end effects and improving the accuracy of loss calculation for circular Litz wire windings in CLLC resonant circuits.

[0145] Reference Figure 9This invention provides a system for calculating the loss of a circular Litz wire winding in a CLLC resonant circuit, comprising:

[0146] The polar coordinate expression determination module is used to construct the internal magnetic field strength model of the Litz line and determine the polar coordinate expression of the magnetic field strength of the circular Litz line based on the internal magnetic field strength model of the Litz line.

[0147] The current RMS value determination module is used to determine the RMS values ​​of the primary side current and the secondary side current of the target CLLC resonant circuit;

[0148] The proximity effect loss calculation module is used to determine the proximity effect loss expression. Based on the polar coordinate expression, the effective value of the primary current, the effective value of the secondary current, and the proximity effect loss expression, the proximity effect loss value of the primary and secondary sides of the target CLLC resonant circuit is calculated.

[0149] The skin effect loss calculation module is used to determine the skin effect loss expression. Based on the polar coordinate expression, the effective value of the primary side current, the effective value of the secondary side current, and the skin effect loss expression, the skin effect loss value of the primary and secondary sides of the target CLLC resonant circuit is calculated.

[0150] The content of the above method embodiments is applicable to this system embodiment. The specific functions implemented in this system embodiment are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those achieved in the above method embodiments.

[0151] Reference Figure 10 This invention provides a device for calculating the loss of a circular Litz wire winding in a CLLC resonant circuit, comprising:

[0152] At least one processor;

[0153] At least one memory for storing at least one program;

[0154] When the above-mentioned at least one program is executed by the above-mentioned at least one processor, the above-mentioned at least one processor implements the above-mentioned method for calculating the loss of circular Litz wire winding in a CLLC resonant circuit.

[0155] The content of the above method embodiments is applicable to the device embodiments. The specific functions implemented by the device embodiments are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0156] This invention also provides a computer-readable storage medium storing a processor-executable program that, when executed by a processor, performs the aforementioned method for calculating the loss of a circular Litz wire winding in a CLLC resonant circuit.

[0157] This invention provides a computer-readable storage medium that can execute a method for calculating the loss of a circular Litz wire winding in a CLLC resonant circuit, as provided in the method embodiments of this invention. It can execute any combination of the implementation steps of the method embodiments and possesses the corresponding functions and beneficial effects of the method.

[0158] This invention also discloses a computer program product or computer program, which includes computer instructions stored in a computer-readable storage medium. A processor of a computer device can read the computer instructions from the computer-readable storage medium, and the processor executes the computer instructions, causing the computer device to perform... Figure 1 The method shown.

[0159] In some alternative embodiments, the functions / operations mentioned in the block diagrams may not occur in the order shown in the operation diagrams. For example, depending on the functions / operations involved, two consecutively shown blocks may actually be executed substantially simultaneously, or the aforementioned blocks may sometimes be executed in reverse order. Furthermore, the embodiments presented and described in the flowcharts of this invention are provided by way of example to provide a more comprehensive understanding of the technology. The disclosed methods are not limited to the operations and logic flows presented herein. Alternative embodiments are contemplated in which the order of various operations is changed and sub-operations described as part of a larger operation are executed independently.

[0160] Furthermore, although the invention has been described in the context of functional modules, it should be understood that, unless otherwise stated, one or more of the aforementioned functions and / or features may be integrated into a single physical device and / or software module, or one or more functions and / or features may be implemented in a separate physical device or software module. It is also understood that a detailed discussion of the actual implementation of each module is unnecessary for understanding the invention. Rather, given the properties, functions, and internal relationships of the various functional modules in the apparatus disclosed herein, the actual implementation of the module will be understood within the scope of conventional skill of an engineer. Therefore, those skilled in the art can implement the invention as set forth in the claims using ordinary techniques without excessive experimentation. It is also understood that the specific concepts disclosed are merely illustrative and not intended to limit the scope of the invention, which is determined by the full scope of the appended claims and their equivalents.

[0161] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0162] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device.

[0163] More specific examples of computer-readable media (a non-exhaustive list) include: electrical connections (electronic devices) having one or more wires, portable computer disk drives (magnetic devices), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Furthermore, computer-readable media can even be paper or other suitable media on which the aforementioned program can be printed, because the aforementioned program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or, if necessary, processing in other suitable ways, and then stored in computer memory.

[0164] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0165] In the foregoing description of this specification, references to terms such as "one embodiment," "another embodiment," or "some embodiments" indicate that a specific feature, structure, material, or characteristic described in connection with an embodiment or example is included in at least one embodiment or example of the present invention. In this specification, illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0166] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

[0167] The above is a detailed description of the preferred embodiments of the present invention. However, the present invention is not limited to the above embodiments. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of the present invention. All such equivalent modifications or substitutions are included within the scope defined by the claims of this application.

Claims

1. A method for calculating the loss of a circular Litz wire winding in a CLLC resonant circuit, characterized in that, Includes the following steps: Construct a model of the magnetic field strength inside the Litz line, and determine the polar coordinate expression of the magnetic field strength of the circular Litz line based on the model. Determine the effective values ​​of the primary and secondary currents of the target CLLC resonant circuit; The proximity effect loss expression is determined, and the proximity effect loss value of the primary and secondary sides of the target CLLC resonant circuit is calculated based on the polar coordinate expression, the effective value of the primary side current, the effective value of the secondary side current, and the proximity effect loss expression. The skin effect loss expression is determined, and the skin effect loss values ​​of the primary and secondary sides of the target CLLC resonant circuit are calculated based on the polar coordinate expression, the effective value of the primary side current, the effective value of the secondary side current, and the skin effect loss expression. The expression for the proximity effect loss is: in, This represents the proximity effect loss value. D Indicates the waveform duty cycle. B p This represents the amplitude of the sinusoidal magnetic field. f The frequency representing the change in the magnetic field, Indicates the length of the circular Litz wire conductor. σ represents the diameter of the circular Litz wire conductor, and σ represents the conductivity of the wire. The expression for the skin effect loss is: in, This represents the skin effect loss value. r This represents the distance between each point inside the circular Litz line and the center of the circular Litz line. 𝜃 This represents the angle between the line segment connecting each point inside the circular Litz line to the center of the circular Litz line and the x-axis. The proximity effect loss value is calculated using the following formula: in, This represents the proximity effect loss value of the primary side of the target CLLC resonant circuit. This represents the proximity effect loss value on the secondary side of the target CLLC resonant circuit. This represents the output voltage of the target CLLC resonant circuit. N Indicates the transformer turns ratio. L m Indicates the magnetizing inductance. R 0 indicates the load resistance. Indicates the circuit's operating frequency. Represents the permeability of free space. h w This indicates the height formed by the circular Litz wire winding. n This indicates the number of turns of the circular Litz wire in each layer of the circular Litz wire winding. r Litz This indicates the radius of the circular Litz wire winding. k Indicates the number of layers in a circular Litz line; The skin effect loss value is calculated using the following formula: in, This represents the skin effect loss value of the primary side of the target CLLC resonant circuit. This represents the skin effect loss value on the secondary side of the target CLLC resonant circuit. This represents the output voltage of the target CLLC resonant circuit. N Indicates the transformer turns ratio. L m Indicates magnetizing inductance. R 0 indicates the load resistance. Indicates the circuit's operating frequency. h w This indicates the height formed by the circular Litz wire winding. n This indicates the number of turns of the circular Litz wire in each layer of the circular Litz wire winding. r Litz This indicates the radius of the circular Litz wire winding.

2. The method for calculating the loss of a circular Litz wire winding in a CLLC resonant circuit according to claim 1, characterized in that, The model for the magnetic field strength inside the Lids line is as follows: in, Indicates the first k The magnetic field strength at various points inside the circular Litz wire. This represents the horizontal distance from each point inside the circular Litz wire winding to its leftmost point. r This represents the distance between each point inside the circular Litz line and the center of the circular Litz line. 𝜃 This represents the angle between the line segment connecting each point inside the circular Litz line to the center of the circular Litz line and the x-axis. The unit vector representing the x-axis. The unit vector representing the y-axis. h w This indicates the height formed by the circular Litz wire winding. n This indicates the number of turns of the circular Litz wire in each layer of the circular Litz wire winding. d Litz This indicates the diameter of the circular Litz wire winding. r Litz This indicates the radius of the circular Litz wire winding. I This indicates the magnitude of the current passing through the circular Litz wire.

3. The method for calculating the loss of a circular Litz wire winding in a CLLC resonant circuit according to claim 2, characterized in that, The polar coordinate expression is: in, Represents the points inside the circular Lids line The polar coordinates of the magnetic field strength.

4. The method for calculating the loss of a circular Litz wire winding in a CLLC resonant circuit according to claim 1, characterized in that, The effective value of the primary current is determined by the following formula: The effective value of the secondary current is determined by the following formula: in, This represents the effective value of the primary current. This represents the effective value of the secondary current. This represents the output voltage of the target CLLC resonant circuit. N Indicates the transformer turns ratio. L m Indicates magnetizing inductance. R 0 indicates the load resistance. Indicates the operating frequency of the circuit.

5. A system for calculating the loss of a circular Litz wire winding in a CLLC resonant circuit, characterized in that, A method for calculating the loss of a circular Litz wire winding in a CLLC resonant circuit as described in any one of claims 1 to 4 includes: The polar coordinate expression determination module is used to construct a model of the magnetic field strength inside the Litz line and determine the polar coordinate expression of the magnetic field strength of the circular Litz line based on the model of the magnetic field strength inside the Litz line. The current RMS value determination module is used to determine the RMS values ​​of the primary side current and the secondary side current of the target CLLC resonant circuit; The proximity effect loss calculation module is used to determine the proximity effect loss expression and calculate the proximity effect loss value of the primary and secondary sides of the target CLLC resonant circuit based on the polar coordinate expression, the effective value of the primary side current, the effective value of the secondary side current, and the proximity effect loss expression. The skin effect loss calculation module is used to determine the skin effect loss expression and calculate the skin effect loss value of the primary and secondary sides of the target CLLC resonant circuit based on the polar coordinate expression, the effective value of the primary side current, the effective value of the secondary side current, and the skin effect loss expression.

6. A device for calculating the loss of a circular Litz wire winding in a CLLC resonant circuit, characterized in that, include: At least one processor; At least one memory for storing at least one program; When the at least one program is executed by the at least one processor, the at least one processor implements a method for calculating the loss of a circular Litz wire winding in a CLLC resonant circuit as described in any one of claims 1 to 4.

7. A computer-readable storage medium storing a processor-executable program, characterized in that, The processor-executable program, when executed by the processor, is used to perform a method for calculating the loss of a circular Litz wire winding in a CLLC resonant circuit as described in any one of claims 1 to 4.

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