Method and device for evaluating instantaneous power and leakage inductance of circular wire type high-frequency transformer

Abstract

The present invention relates to a method for evaluating the instantaneous power and leakage inductance of a circular wire type high-frequency transformer. The leakage inductance generated by the primary winding at the current operating frequency is obtained by using a leakage inductance calculation model. The acquisition of the leakage inductance calculation model includes: equivalent the circular wire winding to a rectangular wire winding, obtain the scalar equation of the magnetic field intensity in the frequency domain of the p-th layer winding when an input alternating current is applied; obtain the expression of the magnetic field intensity distributed in the p-th layer winding; neglect the displacement current, obtain a new complex propagation constant and skin depth, and substitute them into the expression of the magnetic field intensity in the p-th layer winding to obtain an updated expression of the magnetic field intensity in the p-th layer winding; obtain the expression of the electric field intensity distributed in the p-th layer winding; calculate the instantaneous power consumed inside the p-th layer winding, and sum the instantaneous power consumed inside each layer winding to obtain an instantaneous power calculation model of the primary winding; according to the imaginary part of the instantaneous power calculation model of the primary winding and the expression of reactive power, obtain a leakage inductance calculation model of the primary winding.

Description

Technical Field

[0001] The present invention relates to the technical field of power electronics and power transmission, and particularly to a method and device for evaluating the instantaneous power and leakage inductance of a high-frequency transformer with round wire windings. Background Art

[0002] In order to reduce the volume of a switching power supply and increase its power density, power electronic converters are required to operate at a higher frequency. However, as an important component of power electronic converters, high-frequency transformers will generate additional losses due to the skin effect and proximity effect, and their leakage inductance will also decrease with the increase in frequency. Therefore, before applying the transformer to a power electronic converter, the designer should predict in advance the relationship between the leakage inductance of the transformer and the frequency.

[0003] The windings of transformers usually have two types: copper foil windings and round wire windings. Round wire windings are the preferred type of high-frequency transformers in power electronic converters. However, the magnetic field distribution of round wire windings is not as simple and intuitive as that of copper foil windings. Therefore, the research on the leakage inductance of round wire windings has become a hot issue in the scientific research field.

[0004] In 2015, M.Amin Bahmani et al. reported a method for calculating the leakage inductance of a high-frequency transformer with round wire windings. When the geometric structure parameters of the designed transformer are known, the designer can calculate the leakage inductance value of the designed round wire transformer. The expression of the method for calculating the leakage inductance of a high-frequency transformer with round wire windings is as follows:

[0005]

[0006] The existing method for calculating the leakage inductance of a high-frequency transformer with round wire windings is an improvement based on the method for calculating the leakage inductance of copper foil windings. This improvement method only simply introduces the penetration rate of round wire to replace the penetration rate of copper foil. This direct introduction of the penetration rate method has no scientific basis, no derivation process, and the calculation results are inaccurate. In addition, the existing calculation results of the leakage inductance of round wire windings are functions containing frequency and cannot give the specific value of the total leakage inductance within a power supply cycle. Therefore, when calculating the instantaneous power of a high-frequency transformer based on the leakage inductance, the calculation accuracy is poor. Summary of the Invention

[0007] Therefore, the technical problem to be solved by the present invention is to overcome the problem in the prior art that when evaluating the instantaneous power based on the leakage inductance, the leakage inductance value is calculated by directly introducing the penetration rate, resulting in inaccurate calculation results and thus inaccurate evaluation of the instantaneous power.

[0008] To solve the above technical problem, the present invention provides a method for evaluating the instantaneous power and leakage inductance of a high-frequency transformer with round wire windings, including:

[0009] Obtain the specification parameters of the primary winding of the round wire type high-frequency transformer and the operating frequency of the input alternating current, input them into the leakage inductance calculation model, and obtain the leakage inductance value generated by the primary winding at the current operating frequency;

[0010] Input the operating frequency and the specification parameters of the primary winding into the instantaneous power calculation model to evaluate the instantaneous power of the primary winding according to the current operating frequency;

[0011] The obtaining process of the leakage inductance calculation model includes:

[0012] Equivalent the round wire type primary winding to a rectangular wire primary winding with the same cross-sectional area, input the alternating current of the preset operating frequency, construct the magnetic field intensity vector equation of the p-th layer winding in the time domain, and convert it into the magnetic field intensity scalar equation in the frequency domain;

[0013] According to the relationship between the magnetic field intensity and the electric field intensity of the p-th layer winding and the curl of the electric field intensity, obtain the scalar relationship equation between the magnetic field intensity and the electric field intensity;

[0014] After obtaining the solution of the magnetic field intensity vector according to the magnetic field intensity scalar equation and the scalar relationship equation of the p-th layer winding in the frequency domain, and combining with the boundary conditions of the p-th layer winding, obtain the magnetic field intensity expression distributed in the p-th layer winding;

[0015] According to the relationship between the displacement current and the conduction current, ignoring the influence of the displacement current on the complex propagation constant and the magnetic field intensity, obtain a new complex propagation constant and calculate the new skin depth;

[0016] Substitute the new skin depth into the magnetic field intensity expression of the p-th layer winding to obtain the updated magnetic field intensity expression of the p-th layer winding;

[0017] According to the magnetic field intensity scalar equation of the p-th layer winding in the frequency domain and the updated magnetic field intensity expression, obtain the electric field intensity expression distributed in the p-th layer winding;

[0018] According to the Poynting vector of the p-th layer winding, find the first instantaneous power flowing into the outer boundary of the p-th layer winding and the second instantaneous power flowing out of the inner boundary of the p-th layer winding. Subtract the second instantaneous power from the first instantaneous power to obtain the instantaneous power consumed inside the p-th layer winding;

[0019] Sum the instantaneous power consumed inside each layer of winding to obtain a summation formula; Substitute the updated magnetic field intensity expression and the electric field intensity expression distributed in the p-th layer winding into the summation formula to obtain the primary winding instantaneous power calculation model;

[0020] According to the reactive power expression and the imaginary part of the primary winding instantaneous power calculation model, obtain the leakage inductance calculation model of the primary winding.

[0021] In an embodiment of the present invention, for the input of an alternating current with a preset working frequency, constructing the magnetic field intensity vector equation of the p-th layer winding in the time domain includes:

[0022] According to the integration path of the p-th layer winding and the position of the origin of the x-axis, using the integral form of Maxwell, the first line integral expression of the magnetic field intensity is obtained:

[0023]

[0024] where is the conduction current density vector in the wire, is the displacement current density vector in the wire, is the electric displacement vector s c is the total cross-sectional area of the rectangular wire enclosed by the integration path; s c satisfies s represents the total area enclosed by the integration path of the p-th layer winding, and the porosity c represents the height of the p-th layer winding in the primary winding, and b represents the total height of the primary winding;

[0025] Using the total area s enclosed by the integration path of the p-th layer winding to replace the total cross-sectional area s of the rectangular wire enclosed by the integration path c , the second line integral expression of the magnetic field intensity is obtained:

[0026]

[0027] According to Stokes' theorem, the third line integral expression of the magnetic field intensity is obtained:

[0028]

[0029] According to the second line integral expression of the magnetic field intensity and the third line integral expression of the magnetic field intensity, the magnetic field intensity vector equation of the p-th layer winding in the time domain is obtained:

[0030]

[0031] In an embodiment of the present invention, obtaining the magnetic field intensity scalar equation of the p-th layer winding in the frequency domain includes:

[0032] According to the density relationship between the electric field and the current and the curl of the magnetic field intensity, the magnetic field intensity vector equation of the p-th layer winding in the time domain is converted into a magnetic field intensity scalar equation in the time domain:

[0033]

[0034] where ε is the permittivity, and the relationship between the electric field and the current density is σ represents the conductivity of the primary winding wire, represents the electric field strength vector inside the rectangular conductor, and the direction of the electric field strength is the same as the current density and is the opposite direction of the y-axis; x represents the horizontal axis coordinate in the p-th layer of the winding. Taking the leftmost edge of the p-th layer of the winding as the coordinate origin, the x-axis extends to the right of the p-th layer of the winding until the rightmost edge; for the primary winding, there is Therefore

[0035] the direction of the magnetic field strength inside the p-th layer of the winding is the positive z-axis direction, the curl of the magnetic field strength can be expressed as:

[0036]

[0037] where represents the unit vector in the y-axis direction, represents the unit vector in the z-axis direction, represents the unit vector in the x-axis direction, H z (x) and E y (x) respectively represent the instantaneous value of the magnetic field strength and the instantaneous value of the electric field strength in the time domain of the p-th layer of the winding;

[0038] According to the change of the instantaneous value of the magnetic field strength with time t and the horizontal axis x, write H z (x) as H z (t,x);

[0039] According to the scalar equation of the magnetic field strength in the time domain of the p-th layer of the winding, obtain the scalar equation of the magnetic field strength in the frequency domain of the p-th layer of the winding:

[0040]

[0041] where and respectively represent the phasor of the magnetic field strength and the phasor of the electric field strength of the p-th layer of the winding; j represents the unit of the imaginary number in the complex number, and ω represents the angular frequency, satisfying ω = 2πf, where f is the frequency of the input alternating current.

[0042] In an embodiment of the present invention, the obtaining of the scalar relationship equation between the magnetic field strength and the electric field strength according to the relationship between the magnetic field strength and the electric field strength of the p-th layer of the winding and the curl of the electric field strength includes:

[0043] According to the vector form of Maxwell's equations, obtain the relationship between the magnetic field strength and the electric field strength:

[0044]

[0045] The curl of the electric field strength is expressed as:

[0046]

[0047] The scalar relationship equation between the magnetic field strength and the electric field strength is expressed as:

[0048]

[0049] where μ cu is the magnetic permeability of the primary winding.

[0050] In an embodiment of the present invention, bringing the new skin depth into the magnetic field strength expression of the pth layer winding to obtain the updated magnetic field strength expression of the pth layer winding includes:

[0051] According to the scalar equation of the magnetic field strength in the pth layer winding in the frequency domain and the scalar relationship equation between the magnetic field strength and the electric field strength, the solution of the magnetic field strength vector is obtained:

[0052]

[0053] where k is the complex propagation constant, satisfying:

[0054]

[0055] where α is the attenuation constant, representing the attenuation of the magnetic field per unit distance; β is the phasor constant, representing the change of the phasor during the propagation of the magnetic field;

[0056] The parameters and are determined by the boundary conditions of the winding. Assuming that the magnetic permeability of the magnetic core is infinite, the boundary magnetic field strength at the right boundary of the first layer winding is:

[0057]

[0058] where, is the current passing through each wire, and Nl represents the number of turns of the wire in each layer of the winding;

[0059] The magnetic field strength expression in the pth layer winding is:

[0060]

[0061] where h represents the total thickness of the primary winding, is the modulus of the magnetic field strength, and φ H is the initial phase of the alternating current;

[0062] According to the relationship between displacement current and conduction current, ignoring the influence of displacement current on the complex propagation constant and magnetic field strength, a new complex propagation constant is obtained:

[0063] According to the new complex propagation constant, a new skin depth is obtained:

[0064]

[0065] Substituting the new skin depth into the magnetic field strength expression of the p-th layer winding, the updated magnetic field strength expression of the p-th layer winding is obtained as:

[0066]

[0067] In an embodiment of the present invention, the electric field strength distributed in the p-th layer winding is expressed as:

[0068]

[0069] In an embodiment of the present invention, the acquisition of the total instantaneous power of the primary winding includes:

[0070] The Poynting vector in the p-th layer winding of the primary winding is:

[0071]

[0072] Among them, the direction of the Poynting vector is the negative direction of the x-axis, and the instantaneous power flows in from the outer boundary of the p-th layer winding and out from the inner boundary. Therefore, the instantaneous power consumed inside the p-th layer winding is the instantaneous power flowing into the outer boundary of the p-th layer winding, which is

[0073] Subtracting the instantaneous power flowing out from the inner boundary of the p-th layer winding, which is Expressed as:

[0074]

[0075] Among them, the differential area of the inner boundary of the p-th layer winding The differential area of the outer boundary lT is the average length of each turn of the primary winding, is the power flow density at x = h in the p-th layer, is the power flow density at x = 0 in the p-th layer;

[0076] Summing the instantaneous powers of the m-layer windings in the primary winding, the summation formula is obtained:

[0077]

[0078] Substitute the updated magnetic field strength expression and the electric field strength expression into the summation formula to obtain the instantaneous power calculation model of the primary winding:

[0079]

[0080] where m represents the number of layers of the primary winding, Nl represents the number of turns per layer of the primary winding, lT represents the average length of each turn of the primary winding; σ represents the conductivity of the primary winding wire, b represents the total height of the primary winding, h represents the total thickness of the primary winding, represents the penetration rate, δ w ′ represents the skin depth.

[0081] In an embodiment of the present invention, obtaining the leakage inductance calculation model of the primary winding according to the imaginary part of the instantaneous power calculation model of the primary winding and the reactive power expression includes:

[0082] The reactive power expression;

[0083] where ω represents the angular frequency, satisfying ω = 2πf, and f is the operating frequency of the input alternating current;

[0084] The leakage inductance calculation model of the primary winding is:

[0085]

[0086] In an embodiment of the present invention, the instantaneous power of the primary winding is:

[0087]

[0088] An embodiment of the present invention also provides a device based on the method for evaluating the instantaneous power and leakage inductance of a round wire type high-frequency transformer as described above, including:

[0089] A parameter acquisition module for acquiring the number of layers, total height, total thickness, porosity, number of turns of the wire in each layer of the winding, average length of each turn of the winding, resistivity, conductivity, permeability of the round wire, and the operating frequency of the input alternating current of the round wire type primary winding;

[0090] A leakage inductance calculation module for calculating the leakage inductance value generated by the primary winding at the current operating frequency based on the parameters acquired by the parameter acquisition module using the leakage inductance calculation model;

[0091] An instantaneous power calculation module for calculating the instantaneous power at the current operating frequency according to the above parameters and the instantaneous power calculation model of the primary winding.

[0092] The above technical solutions of the present invention have the following advantages compared with the prior art:

[0093] The method for evaluating the instantaneous power and leakage inductance of a circular wire type high-frequency transformer according to the present invention evaluates the instantaneous power at different operating frequencies by using the instantaneous power calculation model of the primary winding, and calculates the leakage inductance generated by the primary winding by using the leakage inductance calculation model; the acquisition of the leakage inductance calculation model includes equivalent the circular wire into a rectangular wire with the same cross-sectional area, and deriving the scalar equation of the magnetic field intensity by using the line integral of the magnetic field intensity; according to the scalar relationship between the magnetic field intensity and the electric field intensity, obtaining the electric field intensity; when calculating the magnetic field intensity and the electric field intensity, the skin effect and the proximity effect are considered, and the influence of the displacement current, which is much smaller than the conduction current, on the magnetic field intensity is ignored, obtaining a new complex propagation constant and skin depth to calculate the magnetic field intensity and the electric field intensity; using the Poynting vector to obtain the instantaneous power consumed by the p-th layer winding by calculating the instantaneous power flowing into and out of the p-th layer winding, and calculating the leakage inductance according to the reactive power stored in the leakage inductance of the primary winding represented by the imaginary part of the total instantaneous power obtained by summation; the present invention obtains the calculation formula of the leakage inductance of the circular wire type high-frequency transformer based on direct logical derivation, and the calculated leakage inductance is a specific value, and the calculation result is more accurate. By inputting the transformer specification parameters into the leakage inductance calculation model and the instantaneous power calculation model, the leakage inductance and instantaneous power of the transformer under the current parameters can be obtained, so that the designer can accurately evaluate the leakage inductance and instantaneous power of the transformer operation according to the primary winding specification parameters. Description of the Drawings

[0094] In order to make the content of the present invention easier to be clearly understood, the following further describes the present invention in detail according to the specific embodiments of the present invention in conjunction with the drawings, where

[0095] Figure 1 is the step flow chart of the method for evaluating the instantaneous power and leakage inductance of the circular wire type high-frequency transformer provided by the present invention;

[0096] Figure 2 is the step flow chart for obtaining the leakage inductance calculation model of the circular wire type high-frequency transformer provided by the present invention;

[0097] Figure 3 is the schematic diagram of the structure of the primary winding of the circular wire type high-frequency transformer provided by the present invention on the ZX plane;

[0098] Figure 4 is the schematic diagram of the circular wire type winding provided by the present invention;

[0099] Figure 5 is the schematic diagram of the equivalent rectangular winding provided by the present invention;

[0100] Figure 6 is the schematic diagram of the integration path and the position of the origin of the x-axis in the p-th layer winding provided by the present invention;

[0101] Figure 7 It is a schematic diagram of the boundary conditions of the first layer and the p-th layer of the primary winding provided by the present invention;

[0102] Figure 8 It is a schematic diagram of the composition of the leakage inductance calculation device of the circular wire type high-frequency transformer provided by the present invention. Specific embodiments

[0103] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, so that those skilled in the art can better understand the present invention and be able to implement it, but the embodiments cited do not limit the present invention.

[0104] Referring to Figure 1 As shown, the method step flow chart of the instantaneous power evaluation of the circular wire type high-frequency transformer provided by the present invention includes:

[0105] S1: Obtain the specification parameters of the circular wire type winding and the operating frequency of the input alternating current;

[0106] S2: Construct a leakage inductance calculation model; input the specification parameters and the operating frequency to obtain the leakage inductance value generated by the primary winding;

[0107] S3: Input the operating frequency and the specification parameters of the primary winding into the instantaneous power calculation model to evaluate the instantaneous power of the primary winding according to the current operating frequency.

[0108] Referring to Figure 2 As shown, it is the method step flow chart of the leakage inductance calculation of the circular wire type high-frequency transformer provided by the present invention, and the specific steps include:

[0109] S21: Equivalent the circular wire type winding to a rectangular wire winding with the same cross-sectional area, and obtain the magnetic field intensity vector equation of the p-th layer winding in the time domain when inputting the alternating current;

[0110] Referring to Figure 3 As shown, it is a schematic diagram of the structure of the primary winding of the circular wire type high-frequency transformer of the present invention on the ZX plane. The magnetic core used is an EE magnetic core. The three inner layers of coils represent the primary winding of the circular wire type winding, and the two outer layers of coils represent the secondary winding of the circular wire type winding. The dots in the winding represent that the direction of the current is flowing in, and the crosses in the winding represent that the direction of the current is flowing out.

[0111] Referring to Figure 4 And Figure 5 As shown, the circular wire type winding is equivalent to a rectangular wire winding with the same cross-sectional area. In this way, there are gaps between the rectangular windings. Therefore, for the equivalent rectangular wire winding, its porosity is: where Nl is the number of turns of the wire in each layer of the winding.

[0112] Reference Figure 6 Using the integral form of Maxwell's equations with respect to the integral path and the position of the origin of the x-axis as shown, the magnetic field strength The first line integral expression is obtained as follows:

[0113]

[0114] Wherein, is the conduction current density vector in the wire, is the displacement current density vector, and sc is the total cross-sectional area of the rectangular wire enclosed by the integral path; sc satisfies Wherein, s represents the total area enclosed by the integral path, and η is the porosity;

[0115] Using the total area S enclosed by the integral path to replace the total cross-sectional area sc of the rectangular wire enclosed by the integral path, the second line integral expression of the magnetic field strength is obtained:

[0116]

[0117] According to Stokes' theorem, the third line integral expression of the magnetic field strength is obtained:

[0118]

[0119] According to the first line integral expression of the magnetic field strength and the second line integral expression of the magnetic field strength, the magnetic field strength vector equation of the pth layer winding in the time domain is obtained:

[0120]

[0121] S22: According to the relationship between the curl of the magnetic field strength, the electric field strength and the current density, the magnetic field strength vector equation of the pth layer winding in the time domain is converted into the magnetic field strength scalar equation of the pth layer winding in the time domain; the magnetic field strength scalar equation of the pth layer winding in the time domain is converted into the magnetic field strength scalar equation in the frequency domain;

[0122] According to the magnetic field strength vector equation of the pth layer winding in the time domain and the relationship between the electric field and the current density, the magnetic field strength vector equation with respect to the electric field strength can be obtained:

[0123]

[0124] Wherein, ε is the permittivity, and the relationship between the electric field and the current density is σ represents the conductivity of the primary winding wire, represents the electric field strength vector inside the rectangular conductor, and the electric field strength has the same direction as the current density The same, in the opposite direction of the y-axis; x represents the horizontal axis coordinate in the p-th layer winding, with the leftmost edge of the p-th layer winding as the coordinate origin, and the x-axis extends to the right of the p-th layer winding until the rightmost edge; for the primary winding, there is Therefore

[0125] Inside the p-th layer winding, the direction of the magnetic field intensity is the positive z-axis direction. Therefore, the curl of the magnetic field intensity can be expressed as:

[0126]

[0127] Among them, represents the unit vector in the y-axis direction, represents the unit vector in the z-axis direction, represents the unit vector in the x-axis direction, H z (x) and E y (x) respectively represent the instantaneous value of the magnetic field intensity and the instantaneous value of the electric field intensity in the p-th layer winding in the time domain;

[0128] Regarding the magnetic field intensity vector equation of the electric field intensity and the curl of the magnetic field intensity, convert the magnetic field intensity vector equation in the p-th layer winding in the time domain into the magnetic field intensity scalar equation in the p-th layer winding in the time domain:

[0129]

[0130] Among them, H z (x) and E y (x) represent the instantaneous values of the magnetic field intensity and the electric field intensity in the time domain;

[0131] According to the magnetic field intensity varying with time t and the horizontal axis x, write H z (x) as H z (t,x);

[0132] According to the magnetic field intensity scalar equation in the p-th layer winding in the time domain, obtain the magnetic field intensity scalar equation in the p-th layer winding in the frequency domain:

[0133]

[0134] Among them, among them, and respectively represent the phasor of the magnetic field intensity and the phasor of the electric field intensity in the p-th layer winding; j represents the unit of the imaginary number in the complex number, ω represents the angular frequency, satisfying ω = 2πf, f is the frequency of the input alternating current; since in the frequency domain the magnetic field intensity varies with the frequency ω and the X-axis, can be written as

[0135] S23: Obtain the scalar relationship equation between the magnetic field intensity and the electric field intensity according to the relationship between the magnetic field intensity and the electric field intensity of the p-th layer winding and the curl of the electric field intensity;

[0136] Obtain the relationship between the magnetic field intensity and the electric field intensity according to the vector form of Maxwell's equations:

[0137]

[0138] The curl of the electric field intensity is expressed as:

[0139]

[0140] The scalar relationship equation between the magnetic field intensity and the electric field intensity is expressed as:

[0141]

[0142] where μ cu is the magnetic permeability of the primary winding.

[0143] S24: Obtain the solution of the magnetic field intensity vector according to the scalar equation of the magnetic field intensity of the p-th layer winding in the frequency domain and the scalar relationship equation, and obtain the expression of the magnetic field intensity distributed in the p-th layer winding in combination with the boundary conditions of the p-th layer winding;

[0144] According to the scalar equation of the magnetic field intensity of the p-th layer winding in the frequency domain and the scalar relationship equation, obtain the deformed form of the scalar equation of the magnetic field intensity of the p-th layer winding in the frequency domain:

[0145]

[0146] The solution of the magnetic field intensity vector in the rectangular wire is:

[0147]

[0148] where k is the complex propagation constant. The complex propagation constant satisfies:

[0149]

[0150] where α is the attenuation constant, representing the attenuation of the magnetic field per unit distance; β is the phasor constant, representing the change of the phasor during the propagation of the magnetic field;

[0151] Refer to Figure 7 shown, which is a schematic diagram of the boundary conditions of the first layer and the p-th layer of the primary winding. The parameters and are determined by the boundary conditions of the winding. Assuming that the magnetic permeability of the magnetic core is infinite, the boundary magnetic field intensity at the right boundary of the first layer winding is:

[0152]

[0153] Among them, is the current passing through each wire, and N l represents the number of turns of the wire in each layer of the winding;

[0154] The first frequency-domain expression of the magnetic field strength distributed in the pth layer of the winding is:

[0155]

[0156] Among them, is the modulus of the magnetic field strength, and φ H is the initial phase.

[0157] S25: According to the relationship between the displacement current and the conduction current, ignoring the influence of the displacement current on the complex propagation constant and the magnetic field strength, obtain the new complex propagation constant and the skin depth; substitute the new complex propagation constant and the skin depth into the magnetic field strength expression in the pth layer of the winding to obtain the updated magnetic field strength expression in the pth layer of the winding;

[0158] Both the complex propagation constant k and the boundary magnetic field strength H0 contain the influence of the displacement current. In the alternating current case, there are both conduction current and displacement current inside the wire. The conduction current can be expressed as The displacement current can be expressed as The amplitude ratio of the conduction current to the displacement current is J D / J = ωε / σ. However, in a copper conductor, ωε / σ << 1. Therefore, in a copper winding, compared with the conduction current, the magnitude and electromagnetic influence of the displacement current are much smaller and can be ignored.

[0159] Obtain the new complex propagation constant:

[0160] According to the new complex propagation constant, obtain the new skin depth:

[0161] The updated magnetic field strength expression in the pth layer of the winding:

[0162]

[0163] S26: According to the relationship between the magnetic field strength and the electric field strength in the pth layer of the winding and the scalar equation of the magnetic field strength in the pth layer of the winding in the frequency domain, obtain the electric field strength distributed in the pth layer of the winding:

[0164]

[0165] S27: Obtain the first instantaneous power flowing into the outer boundary of the p-th layer winding and the second instantaneous power flowing out of the inner boundary of the p-th layer winding according to the Poynting vector of the p-th layer winding, and subtract the second instantaneous power from the first instantaneous power to obtain the instantaneous power consumed inside the p-th layer winding;

[0166] The Poynting vector represents the directional instantaneous power flow density generated by the instantaneous electric field and magnetic field. The surface integral of the Poynting vector over the cross-sectional area perpendicular to the direction of the Poynting vector represents the instantaneous power flow through that area.

[0167] The Poynting vector in the p-th layer winding of the primary side coil is:

[0168]

[0169] where the direction of the Poynting vector is the negative direction of the x-axis, and the instantaneous power flows into the p-th layer winding from the outer boundary and out of the inner boundary. Refer to Figure 5 as shown, which are the inner and outer boundaries of the p-th layer winding;

[0170] The instantaneous power consumed inside the p-th layer winding is the instantaneous power flowing into the outer boundary of the p-th layer winding, which is minus the instantaneous power flowing out of the inner boundary of the p-th layer winding, which is Expressed as:

[0171]

[0172] Because there is no electric field in the air gap between turns, the surface area calculation needs to be multiplied by the porosity η; the differential area of the inner boundary of the p-th layer winding the differential area of the outer boundary l T is the average length of each turn of the winding, is the power flow density at x = h in the p-th layer, is the power flow density at x = 0 in the p-th layer;

[0173] S28: Sum the instantaneous power consumed inside each layer of the winding to obtain a summation formula; substitute the magnetic field strength and the electric field strength into the summation formula to obtain the instantaneous power calculation model of the primary winding:

[0174] Summation formula,

[0175] Instantaneous power calculation model of the primary winding:

[0176]

[0177] where m represents the number of layers of the primary winding, ρ represents the resistivity of the primary winding wire, N lrepresents the number of turns per layer of the primary winding, l T represents the average length of each turn of the winding, b represents the total height of the primary winding, and h represents the total thickness of the primary winding represents the penetration rate, δ′ w represents the skin depth

[0178] S29: Obtain the leakage inductance inside the primary winding according to the imaginary part of the reactive power expression and the primary winding instantaneous power calculation model

[0179] The imaginary part of the primary winding instantaneous power calculation model represents the reactive power stored in the leakage inductance of the round wire type winding

[0180] According to the reactive power expression The calculation expression for the leakage inductance inside the round wire type winding in the primary winding is obtained as follows

[0181]

[0182] When constructing the leakage inductance calculation model of the present invention, the round wire is equivalent to a rectangular wire with the same cross-sectional area, and the scalar equation of the magnetic field strength is derived by line integral of the magnetic field strength; according to the scalar relationship between the magnetic field strength and the electric field strength, the electric field strength is obtained; when calculating the magnetic field strength and the electric field strength, the skin effect and the proximity effect are considered, and the influence of the displacement current, which is much smaller than the conduction current, on the magnetic field strength is ignored, and a new complex propagation constant and skin depth are obtained to calculate the magnetic field strength and the electric field strength; the instantaneous power consumed by the pth layer of the winding is obtained by calculating the instantaneous power flowing into and out of the pth layer of the winding using the Poynting vector, and the leakage inductance is calculated according to the reactive power stored in the leakage inductance of the primary winding represented by the imaginary part of the total instantaneous power obtained by summation; based on direct logical derivation, the present invention obtains the calculation formula for the leakage inductance of the round wire type high-frequency transformer, and the leakage inductance calculation formula does not contain frequency, and the calculated leakage inductance is a specific value, and the calculation result is more accurate

[0183] Reference Figure 8 As shown, it is the composition of the leakage inductance calculation model of the round wire type high-frequency transformer provided by the present invention, including

[0184] The magnetic field strength acquisition module 100 equates the circular wire winding to a rectangular wire winding with the same cross-sectional area. When acquiring the input alternating current, it obtains the magnetic field strength vector equation of the p-th layer winding in the time domain and converts it into the magnetic field strength scalar equation of the p-th layer winding in the frequency domain. According to the relationship between the magnetic field strength and the electric field strength of the p-th layer winding and the curl of the electric field strength, it obtains the scalar relationship equation between the magnetic field strength and the electric field strength. According to the magnetic field strength scalar equation of the p-th layer winding in the frequency domain and the scalar relationship equation, it obtains the solution of the magnetic field strength vector, and together with the boundary conditions of the p-th layer winding, it obtains the magnetic field strength expression distributed in the p-th layer winding. Ignoring the displacement current, it obtains the new complex propagation constant and the skin depth. Substituting the new complex propagation constant and the skin depth into the magnetic field strength expression in the p-th layer winding, it obtains the magnetic field strength in the p-th layer winding.

[0185] The electric field strength acquisition module 200 obtains the electric field strength distributed in the p-th layer winding according to the relationship between the magnetic field strength and the electric field strength of the p-th layer winding and the magnetic field strength scalar equation of the p-th layer winding in the frequency domain.

[0186] The instantaneous power acquisition module 300 obtains the first instantaneous power flowing into the outer boundary of the p-th layer winding and the second instantaneous power flowing out of the inner boundary of the p-th layer winding according to the Poynting vector of the p-th layer winding, and subtracts the second instantaneous power from the first instantaneous power to obtain the instantaneous power consumed inside the p-th layer winding.

[0187] The total instantaneous power acquisition module 400 sums the instantaneous power consumed inside each layer of winding to obtain a summation formula. Substituting the magnetic field strength and the electric field strength into the summation formula, it obtains the primary winding instantaneous power calculation model.

[0188] The leakage inductance calculation module 500 obtains the leakage inductance inside the primary winding according to the reactive power expression and the imaginary part of the primary winding instantaneous power calculation model.

[0189] The leakage inductance calculation device of the circular wire type high-frequency transformer described in this embodiment is used to implement the foregoing leakage inductance calculation method of the circular wire type high-frequency transformer. Therefore, the specific implementation manners in the leakage inductance calculation device of the circular wire type high-frequency transformer can be seen in the embodiment part of the foregoing leakage inductance calculation method of the circular wire type high-frequency transformer. For example, the magnetic field strength acquisition module 100 is used to implement steps S1, S2, S3, S4, and S5 in the foregoing leakage inductance calculation method of the circular wire type high-frequency transformer; the electric field strength acquisition module 200, the instantaneous power acquisition module 300, the total instantaneous power acquisition module 400, and the leakage inductance calculation module 500 are respectively used to implement steps S6, S7, S8, and S9 in the foregoing leakage inductance calculation method of the circular wire type high-frequency transformer. Therefore, its specific implementation manners can be referred to the descriptions of the corresponding respective part embodiments and will not be elaborated here.

[0190] Based on the above embodiments, in an embodiment of the present invention, an evaluation device for the instantaneous power and leakage inductance of a round wire type high-frequency transformer is provided, including:

[0191] A parameter acquisition module, configured to acquire the number of layers, total height, total thickness, porosity, number of turns of the wire in each layer of the winding, average length of each turn of the winding, resistivity, conductivity, magnetic permeability of the round wire, and the operating frequency of the input alternating current.

[0192] A leakage inductance calculation module, configured to use a leakage inductance calculation model to calculate the leakage inductance value generated by the primary winding at the current operating frequency based on the parameters acquired by the parameter acquisition module.

[0193] An instantaneous power calculation module, configured to calculate the instantaneous power at the current operating frequency according to the leakage inductance value and the instantaneous power calculation model of the primary winding.

[0194] The evaluation method for the instantaneous power and leakage inductance of the round wire type high-frequency transformer described in the present invention uses an instantaneous power calculation model of the primary winding to evaluate the instantaneous power at different operating frequencies, and uses a leakage inductance calculation model to calculate the leakage inductance generated by the primary winding. The acquisition of the leakage inductance calculation model includes equivalent the round wire to a rectangular wire with the same cross-sectional area, and using the line integral of the magnetic field intensity to derive the scalar equation of the magnetic field intensity; according to the scalar relationship between the magnetic field intensity and the electric field intensity, obtaining the electric field intensity; when calculating the magnetic field intensity and the electric field intensity, the skin effect and proximity effect are considered, and the influence of the displacement current, which is much smaller than the conduction current, on the magnetic field intensity is ignored, to obtain a new complex propagation constant and skin depth, for calculating the magnetic field intensity and the electric field intensity; using the Poynting vector to calculate the instantaneous power consumed by the p-th layer of the winding by calculating the instantaneous power flowing into and out of the p-th layer of the winding, and calculating the leakage inductance according to the reactive power stored in the leakage inductance of the primary winding represented by the imaginary part of the total instantaneous power obtained by summation; based on direct logical derivation, the present invention obtains the calculation formula for the leakage inductance of the round wire type high-frequency transformer, and the calculated leakage inductance is a specific value, and the calculation result is more accurate. By inputting the transformer specification parameters into the leakage inductance calculation model and the instantaneous power calculation model, the leakage inductance and instantaneous power of the transformer under the current parameters can be obtained, so that designers can accurately evaluate the leakage inductance and instantaneous power of the transformer operation according to the specification parameters of the primary winding.

[0195] Obviously, the above embodiments are only examples given clearly and are not limitations on the implementation manners. For those of ordinary skill in the art, other different forms of changes or variations can be made based on the above description. It is not necessary and impossible to list all the implementation manners here. And the obvious changes or variations derived therefrom are still within the protection scope of the present invention.

Claims

1. A method for evaluating the instantaneous power and leakage inductance of a circular wire type high-frequency transformer, characterized in that, Including: Obtain the specification parameters of the primary winding of the circular wire type high-frequency transformer and the operating frequency of the input alternating current. Input the leakage inductance calculation model to obtain the leakage inductance value generated by the primary winding at the current operating frequency. Input the operating frequency and the specification parameters of the primary winding into the instantaneous power calculation model to evaluate the instantaneous power of the primary winding according to the current operating frequency. The obtaining process of the leakage inductance calculation model includes: Equivalent the circular wire type primary winding to a rectangular wire primary winding with the same cross-sectional area, input the alternating current of the preset operating frequency, construct the magnetic field intensity vector equation of the p-th layer winding in the time domain, and convert it into the magnetic field intensity scalar equation in the frequency domain. According to the relationship between the magnetic field intensity and the electric field intensity of the p-th layer winding and the curl of the electric field intensity, obtain the scalar relationship equation between the magnetic field intensity and the electric field intensity. After obtaining the solution of the magnetic field intensity vector according to the magnetic field intensity scalar equation and the scalar relationship equation of the p-th layer winding in the frequency domain, and combining with the boundary conditions of the p-th layer winding, obtain the magnetic field intensity expression distributed in the p-th layer winding. According to the relationship between the displacement current and the conduction current, ignore the influence of the displacement current on the complex propagation constant and the magnetic field intensity, obtain a new complex propagation constant, and calculate the new skin depth. Substitute the new skin depth into the magnetic field intensity expression of the p-th layer winding to obtain the updated magnetic field intensity expression of the p-th layer winding. According to the magnetic field intensity scalar equation of the p-th layer winding in the frequency domain and the updated magnetic field intensity expression, obtain the electric field intensity expression distributed in the p-th layer winding. According to the Poynting vector of the p-th layer winding, obtain the first instantaneous power flowing into the outer boundary of the p-th layer winding and the second instantaneous power flowing out of the inner boundary of the p-th layer winding. Subtract the second instantaneous power from the first instantaneous power to obtain the instantaneous power consumed inside the p-th layer winding. Sum the instantaneous power consumed inside each layer of the winding to obtain a summation formula; substitute the updated magnetic field intensity expression and the electric field intensity expression distributed in the p-th layer winding into the summation formula to obtain the instantaneous power calculation model of the primary winding, expressed as: According to the reactive power expression and the imaginary part of the instantaneous power calculation model of the primary winding, obtain the leakage inductance calculation model of the primary winding, expressed as: where m represents the number of layers of the primary winding, Nl represents the number of turns per layer of the primary winding, lT represents the average length of each turn of the primary winding; σ represents the conductivity of the primary winding wire, b represents the total height of the primary winding, and h represents the total thickness of the primary winding. represents the penetration rate, and δ w ' represents the skin depth, ω represents the angular frequency, and satisfies ω = 2πf, where f is the operating frequency of the input alternating current.

2. The method for evaluating the instantaneous power and leakage inductance of a circular wire type high-frequency transformer according to claim 1, characterized in that, The construction of the magnetic field intensity vector equation of the p-th layer winding in the time domain by inputting the alternating current of the preset operating frequency includes: According to the integration path of the p-th layer winding and the position of the origin of the x-axis, use the integral form of Maxwell to obtain the first line integral expression of the magnetic field intensity: Among them, is the conduction current density vector in the wire, is the displacement current density vector in the wire, is the electric displacement vector sc is the total cross-sectional area of the rectangular wire enclosed by the integration path; sc satisfies s represents the total area enclosed by the integration path of the p-th layer winding, and the porosity c represents the height of the p-th layer winding in the primary winding, and b represents the total height of the primary winding; Use the total area s enclosed by the integration path of the p-th layer winding to replace the total cross-sectional area sc of the rectangular wire enclosed by the integration path to obtain the second line integral expression of the magnetic field intensity: According to Stokes' theorem, obtain the third line integral expression of the magnetic field intensity: According to the second line integral expression of the magnetic field intensity and the third line integral expression of the magnetic field intensity, obtain the magnetic field intensity vector equation of the p-th layer winding in the time domain:

3. The method for evaluating the instantaneous power and leakage inductance of a circular wire type high-frequency transformer according to claim 2, characterized in that, The obtaining of the magnetic field intensity scalar equation of the p-th layer winding in the frequency domain includes: According to the relationship between the electric field and the current density and the curl of the magnetic field intensity, the magnetic field intensity vector equation of the p-th layer winding in the time domain is converted into a magnetic field intensity scalar equation in the time domain: where ε is the permittivity, and the relationship between the electric field and the current density is σ represents the conductivity of the primary winding wire, represents the electric field strength vector inside the rectangular conductor, and the electric field strength has the same direction as the current density which is the opposite direction of the y-axis; x represents the horizontal axis coordinate in the p-th layer of the winding, with the leftmost edge of the p-th layer of the winding as the coordinate origin, and the x-axis extends to the right of the p-th layer of the winding until the rightmost edge; for the primary winding, there is Therefore The direction of the magnetic field intensity inside the p-th layer winding is the positive z-axis direction. The curl of the magnetic field intensity can be expressed as: Among them, represents the unit vector in the y-axis direction, represents the unit vector in the z-axis direction, represents the unit vector in the x-axis direction, H z (x) and E y (x) respectively represent the instantaneous values of the magnetic field strength and the electric field strength of the pth layer winding in the time domain; According to the fact that the instantaneous value of the magnetic field strength changes with time t and the horizontal axis x, write H z (x) as H z (t, x); According to the magnetic field intensity scalar equation of the p-th layer winding in the time domain, the magnetic field intensity scalar equation of the p-th layer winding in the frequency domain is obtained: Among them, and respectively represent the magnetic field intensity phasor and the electric field intensity phasor of the p-th layer winding; j represents the unit of the imaginary number in complex numbers, ω represents the angular frequency, satisfying ω = 2πf, and f is the frequency of the input alternating current.

4. The method for evaluating the instantaneous power and leakage inductance of a round-wire type high-frequency transformer according to claim 3, characterized in that, The scalar relationship equation of the magnetic field intensity and the electric field intensity is obtained according to the relationship between the magnetic field intensity and the electric field intensity of the p-th layer winding and the curl of the electric field intensity, including: According to the vector form of Maxwell's equations, the relationship between the magnetic field intensity and the electric field intensity is obtained: The curl of the electric field intensity is expressed as: The scalar relationship equation of the magnetic field intensity and the electric field intensity is expressed as: Among them, μ cu is the magnetic permeability of the primary winding.

5. The method for evaluating the instantaneous power and leakage inductance of a round-wire type high-frequency transformer according to claim 4, characterized in that, The new skin depth is brought into the magnetic field intensity expression of the p-th layer winding to obtain the updated magnetic field intensity expression of the p-th layer winding, including: According to the magnetic field intensity scalar equation of the p-th layer winding in the frequency domain and the scalar relationship equation of the magnetic field intensity and the electric field intensity, the solution of the magnetic field intensity vector is obtained: Among them, k is the complex propagation constant, which satisfies: Among them, α is the attenuation constant, representing the attenuation of the magnetic field per unit distance; β is the phasor constant, representing the change of the phasor during the propagation of the magnetic field; Parameter and are determined by the boundary conditions of the winding. Assuming that the magnetic permeability of the magnetic core is infinite, the boundary magnetic field strength at the right boundary of the first-layer winding is as follows: Among them, is the current passing through each wire, and N l represents the number of turns of the wire in each layer of the winding; The magnetic field intensity expression in the p-th layer winding is: where h represents the total thickness of the primary winding, is the magnitude of the magnetic field strength, and φ H is the initial phase of the alternating current; According to the relationship between displacement current and conduction current, ignoring the influence of displacement current on the complex propagation constant and magnetic field strength, a new complex propagation constant is obtained: According to the new complex propagation constant, a new skin depth is obtained: The new skin depth is brought into the magnetic field intensity expression of the p-th layer winding to obtain the updated magnetic field intensity expression of the p-th layer winding, which is:

6. The method for evaluating the instantaneous power and leakage inductance of a round-wire type high-frequency transformer according to claim 5, characterized in that, The electric field intensity distributed in the p-th layer winding is expressed as:

7. The method for evaluating the instantaneous power and leakage inductance of a round-wire type high-frequency transformer according to claim 1, characterized in that, According to the Poynting vector of the p-th layer winding, the first instantaneous power flowing into the outer boundary of the p-th layer winding and the second instantaneous power flowing out of the inner boundary of the p-th layer winding are obtained. The first instantaneous power minus the second instantaneous power is used to obtain the instantaneous power consumed inside the p-th layer winding, including: The Poynting vector in the p-th layer winding of the primary winding is: Among them, the direction of the Poynting vector is the negative direction of the x-axis. The instantaneous power flows into the outer boundary of the p-th layer winding and out of the inner boundary. Therefore, the instantaneous power consumed inside the p-th layer winding is the instantaneous power flowing into the outer boundary of the p-th layer winding, which is minus the instantaneous power flowing out of the inner boundary of the p-th layer winding, which is expressed as: Among them, the differential area of the inner boundary of the p-th layer winding The differential area of the outer boundary l T is the average length of each turn of the primary winding, is the power flow density at x = h in the p-th layer, is the power flow density at x = 0 in the p-th layer.

8. The method for evaluating the instantaneous power and leakage inductance of a round-wire type high-frequency transformer according to claim 7, wherein, The acquisition of the total instantaneous power of the primary winding includes: The instantaneous powers of the m-layer windings in the primary winding are summed to obtain a summation formula: The updated magnetic field intensity expression and the electric field intensity expression are brought into the summation formula to obtain the instantaneous power calculation model of the primary winding:

9. The method for evaluating the instantaneous power and leakage inductance of a round-wire type high-frequency transformer according to claim 7, wherein, According to the imaginary part of the primary winding instantaneous power calculation model and the reactive power expression, the leakage inductance calculation model of the primary winding is obtained, including: The reactive power expression; The reactive power expression is equivalent to the imaginary part of the primary winding instantaneous power calculation model, and the leakage inductance calculation model of the primary winding is obtained as:

10. An apparatus based on the method for evaluating the instantaneous power and leakage inductance of a round-wire type high-frequency transformer according to any one of claims 1 to 9, wherein, Including: A parameter acquisition module for acquiring the number of layers, total height, total thickness, porosity, number of turns of the wire in each layer of the winding, average length of each turn of the winding, resistivity, conductivity, permeability of the round wire, and the operating frequency of the input alternating current of the round wire type primary winding; A leakage inductance calculation module for calculating the leakage inductance value generated by the primary winding at the current operating frequency based on the parameters acquired by the parameter acquisition module by using the leakage inductance calculation model; An instantaneous power calculation module for calculating the instantaneous power at the current operating frequency according to the above parameters and the primary winding instantaneous power calculation model.

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