A method for testing high frequency transformer loss

Abstract

The present invention belongs to the technical field of high-frequency transformer design, and specifically discloses a high-frequency transformer loss test method. It includes: calculating the skin effect loss per unit length of a single-strand conductor; expressing the skin effect loss of the entire bundle of Litz wires as the superposition of the losses caused by multiple strands of round conductors; calculating the eddy current loss of the proximity effect within a pitch; analyzing and calculating the proximity effect loss that cannot be eliminated by twisting, including the external proximity effect loss of the conductor without twisting, and the internal proximity effect caused by the magnetic field generated by the current flowing through each conductor on other conductors; based on the skin effect loss, the external proximity effect loss and the internal proximity effect, a total eddy current loss calculation model is obtained. The present invention makes a detailed distinction between eddy current losses, calculates the proximity effect loss that cannot be twisted, and performs equivalent calculations on the losses generated by the internal magnetic field, saving the amount of calculations.

Description

Technical Field

[0001] The invention relates to the technical field of high-frequency transformer design, and in particular to a high-frequency transformer loss testing method. Background Art

[0002] With the continuous development of power electronics technology and energy Internet, higher requirements are placed on the power density, space occupancy and efficiency of magnetic components. High frequency and miniaturization have become the inevitable development trend of magnetic components such as transformers and reactors. However, with the increase of operating frequency, the winding is increasingly affected by the high-frequency skin effect and proximity effect, resulting in extremely uneven current distribution inside the conductor and significantly increased winding losses, which in turn cause problems such as excessive local temperature rise in the system and reduced energy transmission efficiency. In order to reduce the winding loss of high-frequency magnetic components, winding forms with superior high-frequency performance such as Litz wire are generally used.

[0003] Litz wire is a winding form that combines efficiency and cost due to its periodic twisted structure of multiple insulated wires. In high-power and high-frequency applications, conductors often require a larger current-carrying area, which requires Litz wire to have hundreds or even thousands of insulated wires.

[0004] The prior art calculates the eddy current loss of the Litz wire by summing the losses of the skin effect and the proximity effect. In the calculation of the proximity effect loss, only the effect of the twisted structure on eliminating the magnetic field of the Litz wire is considered. There are also untwisted wires in the Litz wire harness. The loss generated by this part of the wire is also a part of the increased energy loss, which will cause physical damage to the winding. Summary of the invention

[0005] In view of the above-mentioned shortcomings of the prior art, an object of the present invention is to provide a high-frequency transformer loss testing method for improving the calculation accuracy of eddy current loss and optimizing the calculation amount and calculation time of the loss calculation process.

[0006] To achieve the above object and other related objects, the present invention provides a high-frequency transformer loss testing method.

[0007] S10. Treat each strand of the Litz wire as a solid circular conductor and calculate the skin effect loss caused by high-frequency current. Specifically,

[0008] S11. Calculate the skin effect loss per unit length of a single-strand conductor;

[0009] S12. The skin effect loss of the whole bundle of Litz wires is expressed as the superposition of the losses caused by multiple strands of round wires;

[0010] S20. Assuming that the conductor is in a uniform external magnetic field, the proximity effect loss coefficient is introduced to calculate the proximity effect loss under the influence of the proximity effect; specifically,

[0011] S21. Analyze the twisted structure of a single-strand round conductor, define a single-strand round conductor rotated 2π as a pitch, and calculate the eddy current loss of the proximity effect within a pitch;

[0012] S22. Analyze the influence of external magnetic field on the twisted structure of Litz wire. Within the pitch of a rotating circle, the proximity loss caused by the external magnetic field can be eliminated by twisting.

[0013] S23. Analyze and calculate the proximity effect loss that cannot be eliminated by twisting, including the external proximity effect loss of the wire without twisting, and the internal proximity effect caused by the magnetic field generated by the current flowing through each wire on other wires;

[0014] S30, obtaining a total eddy current loss calculation model based on the skin effect loss, the external proximity effect loss and the internal proximity effect.

[0015] Alternatively, the loss per unit length of a single round wire due to skin effect is expressed as:

[0016] (1);

[0017] In the formula, the current density inside a single round conductor is expressed by the Bessel ordinary differential equation with complex variable k in the cylindrical coordinate system, , are the standard solution functions of Bessel ordinary differential equations, which are 0th-order and 1st-order Bessel functions, respectively. is the strand radius; is an imaginary unit; is the skin depth; is the DC resistance per unit length of the strand; is the effective value of the alternating current.

[0018] Alternatively, the skin effect loss per unit length of Litz wire is expressed as The loss caused by the stranded round conductor is superimposed, that is,

[0019] (2);

[0020] In the formula, is the current flowing through the winding cross section, is the resistivity.

[0021] Alternatively, the eddy current loss due to proximity effect within one pitch is:

[0022] (3)

[0023] In the formula, is the proximity effect loss coefficient; For the Pitch cycle; , Respectively in , The magnetic field strength in the direction varies with the real independent variable The change value of; From formula (3), it can be seen that within a pitch of 2π rotation, the proximity effect loss caused by the external magnetic field can be eliminated by twisting;

[0024] When the excitation waveform is a high-frequency sine wave, is the maximum value of the magnetic field, and the magnetic field strength is Direction is represented by , formula (3) can be transformed into:

[0025] (4);

[0026] In the formula, is the speed of light; is the current frequency.

[0027] Optionally, if the eddy current effect caused by the proximity effect is expected to be zero within a pitch period of the strand, that is, the proximity effect of the external magnetic field is eliminated, the two integral values ​​of equation (4) should be zero, that is, the following equation is satisfied:

[0028] (5);

[0029] When the ratio of the product of the current frequency and the pitch to the speed of light is an integer, the proximity effect of the external magnetic field can be eliminated.

[0030] Optionally, calculate the external proximity effect loss of the entire bundle of Litz wires, where the center conductor is not twisted and cannot eliminate the external magnetic field:

[0031] (6);

[0032] In the formula, is the external magnetic field strength.

[0033] Optionally, calculate the internal proximity effect of the magnetic field generated by the current flowing through each wire in the entire litz wire bundle on other wires, including:

[0034] Through finite element analysis, the magnetic field distribution is consistent with the winding path of the wire. The magnetic field distribution generated by the current flowing through each wire is equivalent to a circular distribution, and the magnitude of the internal magnetic field is:

[0035] (7);

[0036] In the formula, is the distance between any position on the cross section of the Litz wire and the center of the cross section; is the total current amplitude of the Litz wire; is the distance between the position of the Litz wire in the entire bundle cross section and the center of the circle.

[0037] Since the influence of the internal magnetic field generated by the current flowing through the wire on other wires is similar to the skin effect characteristics, the internal proximity effect is equivalent to the skin effect of the entire bundle of Litz wires:

[0038] (8);

[0039] In the formula, Number of turns of Litz wire winding; is the electrical conductivity of the winding material; ,in, is the skin depth, is the magnetic permeability, is the current frequency; is the strand radius; and are the real and imaginary parts of the Bessel function of the first kind, respectively; and are the reciprocals of the real and imaginary parts of the Bessel function of the first kind, respectively; and are the real and imaginary parts of the second-order Bessel function of the 3π / 4 quantity respectively.

[0040] Optionally, the total eddy current loss of the entire bundle of Litz wires is calculated as follows:

[0041] (9);

[0042] In the formula, is the total eddy current loss of the whole bundle of Litz wires; is the skin effect loss; is the external proximity effect loss; is the internal proximity effect loss.

[0043] As described above, a high-frequency transformer loss test method proposed in the present invention has the following beneficial effects: the present invention derives a frequency-dependent eddy current loss model that can be used to calculate the Litz wire winding of a high-frequency transformer through the structure of the Litz wire, and calculates the skin effect loss, the proximity effect loss of the incompletely twisted part, and the proximity effect loss inside the Litz wire separately. This calculation model is an improved model based on the eddy current loss of a circular conductor, which reduces the amount of calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 A schematic diagram showing a flow chart of a high-frequency transformer loss testing method according to an embodiment of the present invention;

[0045] Figure 2 A schematic diagram showing the eddy current loss types of Litz wire according to an embodiment of the present invention;

[0046] Figure 3 A schematic diagram showing the direction of the induced electromotive force on the parallel wires after twisting according to an embodiment of the present invention; DETAILED DESCRIPTION

[0047] The following describes the embodiments of the present invention through specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention.

[0048] like Figure 1 As shown, a high-frequency transformer loss test method includes the following steps:

[0049] S10. Treat each strand of the Litz wire as a solid circular conductor and calculate the skin effect loss caused by high-frequency current.

[0050] When a high-frequency alternating current flows through a conductor, eddy currents are generated in the conductor due to the electromagnetic effect, changing the current distribution on the cross section. Figure 2 As shown in (a), eddy currents enhance the current on the surface of the conductor and weaken the current at the center of the conductor, causing the transmission current to tend to flow on the surface.

[0051] The skin effect loss calculation process specifically includes the following steps:

[0052] S11. Calculate the skin effect loss per unit length of a single-strand conductor;

[0053] Among them, the loss per unit length caused by the skin effect of a single-strand round conductor is expressed as:

[0054] (1);

[0055] In the formula, the current density inside a single round conductor is expressed by the Bessel ordinary differential equation with complex variable k in the cylindrical coordinate system, 、 are the standard solution functions of Bessel ordinary differential equations, which are 0th-order and 1st-order Bessel functions, respectively. is the strand radius; is an imaginary unit; is the skin depth; is the DC resistance per unit length of the strand; is the effective value of the alternating current.

[0056] S12. The skin effect loss of the whole bundle of Litz wires is expressed as the superposition of the losses caused by multiple strands of round wires;

[0057] The skin effect loss per unit length of Litz wire is expressed as The stranded round conductor causes the superposition of losses, namely:

[0058] (2);

[0059] In the formula, is the current flowing through the winding cross section, is the resistivity.

[0060] S20, assuming that the conductor is in a uniform external magnetic field, introduce the proximity effect loss coefficient to calculate the proximity effect loss under the influence of the proximity effect;

[0061] When multiple strands of wire are wound together, as shown in Figure 2 (b), the high-frequency magnetic field generated by the high-frequency current flowing through the wire near it will induce eddy currents in other wires, thereby changing the current distribution of nearby conductors. This eddy current effect caused by the high-frequency magnetic field of adjacent conductors is called the proximity effect, and the loss caused by it is called the proximity effect loss. The size of the proximity effect loss is not only related to the frequency, but also the geometric shape, size, arrangement and spacing between the conductors will have an impact on it. The proximity loss coefficient is defined as Quantifying proximity effect losses.

[0062] Specifically, the proximity effect loss calculation includes the following steps:

[0063] S21. Analyze the twisted structure of a single-strand round conductor, define a single-strand round conductor rotated 2π as a pitch, and calculate the eddy current loss of the proximity effect within a pitch; Figure 3 As shown, the twisted wire will rotate 180° within one pitch, so the induced electromotive force generated will also be in the opposite direction and cancel each other;

[0064] (3);

[0065] In the formula, is the proximity effect loss coefficient; For the Pitch cycle; , Respectively in , The magnetic field strength in the direction varies with the real independent variable The change value of; From formula (3), it can be seen that within a pitch of 2π rotation, the proximity effect loss caused by the external magnetic field can be eliminated by twisting;

[0066] When the excitation waveform is a high-frequency sine wave, is the maximum value of the magnetic field, and the magnetic field strength is Direction is represented by , formula (3) can be transformed into:

[0067] (4);

[0068] In the formula, is the speed of light; is the current frequency.

[0069] If it is expected that the eddy current effect caused by the proximity effect of the strand is zero within one pitch period, that is, the proximity effect of the external magnetic field is eliminated, the two integral values ​​of equation (4) should be zero, that is, the following equation is satisfied:

[0070] (5);

[0071] When the ratio of the product of the current frequency and the pitch to the speed of light is an integer, the proximity effect of the external magnetic field can be eliminated.

[0072] It can be seen from the above formula that only by strictly controlling the size of the pitch can the Litz wire eliminate the influence of the proximity effect by utilizing the twisted structure;

[0073] S22. Analyze the influence of external magnetic field on the twisted structure of Litz wire. Within the pitch of a rotating circle, the proximity loss caused by the external magnetic field can be eliminated by twisting.

[0074] S23. Analyze and calculate the proximity effect loss that cannot be eliminated by twisting, including the external proximity effect loss of the wire without twisting, and the internal proximity effect caused by the magnetic field generated by the current flowing through each wire on other wires;

[0075] The entire bundle of wires is not twisted near the center, and without a twisted structure, the proximity effect of the external magnetic field cannot be eliminated.

[0076] Specifically, the calculation of the external proximity effect loss of the entire bundle of Litz wires, which is not twisted and cannot eliminate the external magnetic field, is as follows:

[0077] (6);

[0078] In the formula, is the external magnetic field strength.

[0079] Considering the interior of the entire bundle of Litz wires, since current also flows through the multiple wires in the strand, the small current in each wire will also form a magnetic field, thereby forming a proximity effect on other strands of wire. Through finite element analysis, the magnetic field distribution of this part of the internal magnetic field is consistent with the winding path of the wire. With the increase of the outer layer of wires, the distribution of the wire in the cross section tends to be ideal, approximately circular distribution, so that the internal magnetic field distribution also tends to be circular distribution, so each wire will be affected by a radial vertical magnetic field. Through analytical calculation, the size of the internal magnetic field is:

[0080] (7);

[0081] In the formula, is the distance between any position on the cross section of the Litz wire and the center of the cross section; is the total current amplitude of the Litz wire; is the distance between the position of the Litz wire in the entire bundle cross section and the center of the circle.

[0082] Since the influence of the internal magnetic field generated by the current flowing through the wire on other wires is similar to the skin effect characteristics, the internal proximity effect is equivalent to the skin effect of the entire bundle of Litz wires:

[0083] (8);

[0084] In the formula, Number of turns of Litz wire winding; is the electrical conductivity of the winding material; ,in, is the skin depth, is the magnetic permeability, is the current frequency; is the strand radius; and i are the real and imaginary parts of the Bessel function of the first kind, respectively; and are the reciprocals of the real and imaginary parts of the Bessel function of the first kind, respectively; and are the real and imaginary parts of the second-order Bessel function of the 3π / 4 quantity respectively.

[0085] S30, obtaining a total eddy current loss calculation model based on the skin effect loss, the external proximity effect loss and the internal proximity effect.

[0086] The total eddy current loss of the entire bundle of Litz wires is calculated as follows:

[0087] (9);

[0088] In the formula, is the total eddy current loss of the whole bundle of Litz wires; is the skin effect loss; is the external proximity effect loss; is the internal proximity effect loss.

[0089] The above embodiments are merely illustrative of the principles and effects of the present invention, and are not intended to limit the present invention. Anyone familiar with the art may modify or alter the above embodiments without departing from the spirit and scope of the present invention. Therefore, all equivalent modifications or alterations made by a person of ordinary skill in the art without departing from the spirit and technical concept disclosed by the present invention shall still be covered by the claims of the present invention.

Claims

1. A high-frequency transformer loss test method, characterized in that: include: S10. Treat each strand of the Litz wire as a solid circular conductor and calculate the skin effect loss caused by high-frequency current. Specifically, S11. Calculate the skin effect loss per unit length of a single-strand conductor ： （1）; In the formula, the current density inside a single round conductor is expressed by the Bessel ordinary differential equation with complex variable k in the cylindrical coordinate system, 、 are the standard solution functions of Bessel's ordinary differential equation, which are 0th-order and 1st-order Bessel functions respectively; is the strand radius; is an imaginary unit; is the skin depth; is the DC resistance per unit length of strand; is the effective value of the alternating current; S12. The skin effect loss of the whole bundle of Litz wires is expressed as the superposition of the losses caused by multiple strands of round wires; S20. Assuming that the conductor is in a uniform external magnetic field, the proximity effect loss coefficient is introduced to calculate the proximity effect loss under the influence of the proximity effect; specifically, S21. Analyze the twisted structure of a single-strand round conductor, define a single-strand round conductor rotated 2π as a pitch, and calculate the eddy current loss of the proximity effect within a pitch; S22. Analyze the influence of external magnetic field on the twisted structure of Litz wire. Within the pitch of a rotating circle, the proximity loss caused by the external magnetic field can be eliminated by twisting. S23. Analyze and calculate the proximity effect loss that cannot be eliminated by twisting, including the external proximity effect loss of the wire without twisting, and the internal proximity effect caused by the magnetic field generated by the current flowing through each wire on other wires; S30, obtaining a total eddy current loss calculation model based on the skin effect loss, the external proximity effect loss and the internal proximity effect.

2. A high frequency transformer loss testing method according to claim 1, characterized in that: The skin effect loss per unit length of Litz wire is expressed as The loss caused by stranded round conductors is superimposed: （2）; In the formula, is the current flowing through the winding cross section, is the resistivity.

3. A high frequency transformer loss testing method according to claim 2, characterized in that: The eddy current loss of the proximity effect within one pitch is: （3）; In the formula, is the proximity effect loss coefficient; For the Pitch cycle; , Respectively in , The magnetic field strength in the direction varies with the real independent variable The change value of; From formula (3), it can be seen that within a pitch of 2π rotation, the proximity effect loss caused by the external magnetic field can be eliminated by twisting; When the excitation waveform is a high-frequency sine wave, is the maximum value of the magnetic field, and the magnetic field strength is Direction is represented by , formula (3) can be transformed into: （4）; In the formula, is the speed of light; is the current frequency.

4. A high frequency transformer loss testing method according to claim 3, characterized in that: If the eddy current effect caused by the proximity effect is expected to be zero within a pitch period of the strand, the two integral values ​​of equation (4) should be zero, that is, the following equation is satisfied: （5）; Then, when the ratio of the product of the current frequency and the pitch to the speed of light is an integer, the eddy current effect caused by the proximity effect is zero.

5. A high frequency transformer loss testing method according to claim 4, characterized in that: Calculate the external proximity effect loss when the center conductor of the entire bundle of Litz wires is not twisted and cannot eliminate the external magnetic field: （6）; In the formula, is the external magnetic field strength.

6. A high frequency transformer loss testing method according to claim 5, characterized in that: Calculate the internal proximity effect of the magnetic field generated by the current flowing through each wire in the entire litz wire bundle on other wires, including: Through finite element analysis, the magnetic field distribution is consistent with the winding path of the wire. The magnetic field distribution generated by the current flowing through each wire is equivalent to a circular distribution, and the magnitude of the internal magnetic field is: （7）; In the formula, is the distance between any position on the cross section of the Litz wire and the center of the cross section; is the total current amplitude of the Litz wire; is the distance between the position of the Litz wire in the cross section of the whole bundle and the center of the circle; Since the influence of the internal magnetic field generated by the current flowing through the wire on other wires is similar to the skin effect characteristics, the internal proximity effect is equivalent to the skin effect of the entire bundle of Litz wires: （8）; In the formula, Number of turns of Litz wire winding; is the electrical conductivity of the winding material; ,in, is the skin depth, is the magnetic permeability, is the current frequency; is the strand radius; and i are the real and imaginary parts of the Bessel function of the first kind, respectively; and are the reciprocals of the real and imaginary parts of the Bessel function of the first kind, respectively; and are the real and imaginary parts of the second-order Bessel function of the 3π / 4 quantity respectively.

7. A high frequency transformer loss testing method according to claim 6, characterized in that: The total eddy current loss of the entire bundle of Litz wires is calculated as follows: + （9）; In the formula, is the total eddy current loss of the whole bundle of Litz wires; is the skin effect loss; is the external proximity effect loss; is the internal proximity effect loss.

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