Method for Evaluating the Working Efficiency of a Round-Wire-Type High-Frequency Transformer Based on AC Resistance

Abstract

The present invention relates to a method for evaluating the working efficiency of a round-wire type high-frequency transformer based on AC resistance, including: obtaining the specification parameters of the round-wire type winding and the working frequency of the input AC current, inputting them into the AC resistance calculation model, and obtaining the AC resistance value generated by the primary winding at the current working frequency; obtaining the relationship between the working frequency and the AC resistance when the primary winding is working, so as to evaluate the working efficiency of the primary winding according to the current working frequency. The obtaining of the AC resistance calculation model includes equivalenting the round-wire type winding to a rectangular-wire winding, obtaining the updated magnetic field intensity expression of the p-th layer winding when the input AC current is obtained and the displacement current is ignored; obtaining the electric field intensity expression distributed in the p-th layer winding; summing the instantaneous power consumed inside each layer of winding to obtain the total instantaneous power equation of the primary winding; and obtaining the AC resistance of the primary winding according to the real part of the total instantaneous power equation of the primary winding and the thermal power formula of the resistance.

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 working efficiency of a circular wire type high-frequency transformer based on AC resistance. Background Art

[0002] A transformer is one of the most important components in a power electronic circuit. Power electronic circuits often operate at relatively high frequencies. The high operating frequency will cause the skin effect and proximity effect in the windings of the transformer, which makes the resistance of the high-frequency transformer winding change with the increase of frequency. That is to say, as the operating frequency increases, the resistance of the transformer winding will deviate from its DC resistance value and generate a higher AC resistance value. The generation of AC resistance will bring additional losses to the entire power electronic system, thus affecting the overall efficiency. Therefore, the specific relationship between the AC resistance of the transformer and the frequency change and the calculation of the AC resistance have become hot research issues today. The windings of the transformer usually have two types: copper foil windings and circular wire type windings. The circular wire type windings are the most widely used in power electronic circuits.

[0003] In 1966, P.L. Dowell reported the calculation expression for the AC resistance of a high-frequency transformer with a circular wire type winding. So far, the Dowell formula is still in use and has become the standard formula in the industry. Since 2000, many research scholars have tried to create more accurate calculation expressions for the AC resistance of high-frequency transformers, but most of the results are based on estimation and approximation, and their rigor is not as ideal as the Dowell model. The Dowell formula is expressed as:

[0004]

[0005] Among them, is the penetration rate, is the skin depth.

[0006] The existing calculation method for the AC resistance of a high-frequency transformer with a circular wire type winding, also called the Dowell method, starts from deriving the current density, and then obtains the leakage impedance by deriving the sum of the induced voltage and the resistive voltage. The real part of the leakage impedance is the obtained AC resistance. Its disadvantage is that it does not consider the proximity effect between the solenoid coils under DC power supply, resulting in inaccurate calculation results; the inaccurate AC resistance cannot accurately evaluate the working efficiency of the high-frequency transformer at the current operating frequency. Summary of the Invention

[0007] Therefore, the technical problem to be solved by the present invention is to overcome the problem that the existing technology does not consider the proximity effect between the solenoid coils when calculating the working efficiency based on the AC resistance, resulting in inaccurate calculation results of the AC resistance and affecting the evaluation of the working efficiency.

[0008] To solve the above technical problems, the present invention provides a method for evaluating the working efficiency of a circular wire type high-frequency transformer based on AC resistance, including:

[0009] Obtain the specification parameters of the circular wire type winding and the working frequency of the input AC current, input them into the AC resistance calculation model, and obtain the AC resistance value generated by the primary winding at the current working frequency;

[0010] According to different working frequencies and the corresponding AC resistance values, obtain the relationship between the working frequency and the AC resistance when the primary winding works, so as to evaluate the working efficiency of the primary winding according to the current working frequency;

[0011] The acquisition of the AC resistance calculation model includes:

[0012] Equivalent the circular wire type primary winding to a rectangular wire primary winding with the same cross-sectional area, input the AC current at the preset working 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 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 a 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 within each layer of the winding to obtain a summation formula; substitute the updated magnetic field strength expression and the electric field strength expression distributed in the p-th layer of the winding into the summation formula to obtain the total instantaneous power equation of the primary winding;

[0020] According to the real part of the total instantaneous power equation of the primary winding and the thermal power expression of the resistance, obtain the AC resistance calculation model of the primary winding.

[0021] In an embodiment of the present invention, input an alternating current with a preset operating frequency to construct a magnetic field strength vector equation of the p-th layer of winding in the time domain, including:

[0022] According to the integration path of the p-th layer of 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 strength:

[0023]

[0024] 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 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 of winding, and the porosity c represents the height of the p-th layer of winding in the primary winding, and b represents the total height of the primary winding;

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

[0026]

[0027] According to Stokes' theorem, obtain the third line integral expression of the magnetic field strength:

[0028]

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

[0030]

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

[0032] 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:

[0033]

[0034] Among them, 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 intensity vector inside the rectangular conductor, and the direction of the electric field intensity 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 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

[0035] 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:

[0036]

[0037] 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 time domain of the p-th layer winding;

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

[0039] 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:

[0040]

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

[0042] In one embodiment of the present invention, obtaining 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 pth layer winding and the curl of the electric field strength includes:

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

[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 one embodiment of the present invention, substituting 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] Obtaining the solution of the magnetic field strength vector according to the magnetic field strength scalar equation of the pth layer winding in the frequency domain and the scalar relationship equation between the magnetic field strength and the electric field strength:

[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 N l represents the number of turns of the wire in each layer of the winding;

[0059] The expression for the magnetic field strength in the p-th layer winding is as follows:

[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 the displacement current and the conduction current, ignoring the influence of the displacement current on the complex propagation constant and the 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 expression for the magnetic field strength in the p-th layer winding, the updated expression for the magnetic field strength in 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] where 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 minus the instantaneous power flowing out from the inner boundary of the p-th layer winding, which is expressed as:

[0073]

[0074] where 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;

[0075] Sum the instantaneous power of the m-layer windings in the primary winding to obtain the summation formula:

[0076]

[0077] Substitute the updated magnetic field strength expression and the electric field strength expression into the summation formula to obtain the total instantaneous power equation of the primary winding:

[0078]

[0079] where m represents the number of layers of the primary winding, ρ represents the resistivity of the primary winding wire, N l represents 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, h represents the total thickness of the primary winding, represents the penetration rate, represents the skin depth.

[0080] In an embodiment of the present invention, obtaining the AC resistance of the primary winding according to the real part of the total instantaneous power equation of the primary winding and the thermal power expression of the resistance includes:

[0081] The thermal power formula of the resistance is:

[0082] The thermal power of the AC resistance is equal to the active power consumed by the resistance on the primary winding, and the equivalent AC resistance of the primary winding is:

[0083]

[0084] In an embodiment of the present invention, the working efficiency of the primary winding is:

[0085]

[0086] The embodiment of the present invention also provides a device for evaluating the working efficiency of a round wire type high-frequency transformer based on the AC resistance as described above, including:

[0087] 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, magnetic permeability of the round wire, and the operating frequency of the input alternating current of the round wire type primary winding;

[0088] An AC resistance calculation module for calculating the AC resistance value generated by the primary winding at the current operating frequency based on the parameters acquired by the parameter acquisition module using the AC resistance calculation model;

[0089] A working efficiency calculation module for calculating the working efficiency at the current operating frequency according to the AC resistance value and the total instantaneous power equation of the primary winding.

[0090] The above technical solution of the present invention has the following advantages compared with the prior art:

[0091] The method for evaluating the working efficiency of a round wire type high-frequency transformer based on AC resistance according to the present invention evaluates the working efficiency based on the AC resistance value generated by the primary winding; the present invention calculates the AC resistance generated by the primary winding by constructing an AC resistance calculation model, equivalent the round wire to a rectangular wire with the same cross-sectional area, and uses the line integral of the magnetic field intensity to deduce the scalar equation of the magnetic field intensity; according to the scalar relationship between the magnetic field intensity and the electric field intensity, the electric field intensity is obtained; 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, and a new complex propagation constant and skin depth are obtained to calculate the magnetic field intensity and the electric field intensity; the instantaneous power consumed by the p-th layer winding is obtained by calculating the instantaneous power flowing into and out of the p-th layer winding using the Poynting vector, and the AC resistance is calculated according to the active power consumed by the resistance on the primary winding represented by the real part of the total instantaneous power; the calculation derivation of the AC resistance of the present invention is more in line with scientific logic, and the calculation result of the AC resistance of the primary winding is more accurate; therefore, using the calculated AC resistance value, the working efficiency of the current high-frequency transformer can be evaluated more accurately, so as to calculate the loss of the power electronic system. Description of the Drawings

[0092] In order to make the content of the present invention easier to be clearly understood, the following further details the present invention according to specific embodiments of the present invention and in conjunction with the drawings, where

[0093] Figure 1 is the flowchart of the steps of the method for evaluating the working efficiency of a round wire type high-frequency transformer based on AC resistance provided by the present invention;

[0094] Figure 2 is the flowchart of the steps for obtaining the AC resistance calculation model provided by the present invention;

[0095] Figure 3 is the schematic diagram of the structure of the primary winding of the round wire type high-frequency transformer provided by the present invention on the ZX plane;

[0096] Figure 4 is the schematic diagram of the round wire type winding provided by the present invention;

[0097] Figure 5 is the schematic diagram of the equivalent rectangular winding provided by the present invention;

[0098] Figure 6 It is a schematic diagram of the integration path and the position of the x-axis origin in the p-th layer winding provided by the present invention;

[0099] 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;

[0100] Figure 8 It is a schematic diagram of the composition of the AC resistance calculation model provided by the present invention. Specific Embodiments

[0101] 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 specific embodiments cited are not intended to limit the present invention.

[0102] Referring to Figure 1 as shown, the method step flow chart for evaluating the working efficiency of a round wire type high-frequency transformer based on AC resistance provided by the present invention includes:

[0103] S1: Obtain the specification parameters of the primary winding of the round wire type high-frequency transformer and the working frequency of the input AC current;

[0104] S2: Construct an AC resistance calculation model; input the specification parameters and the working frequency to obtain the AC resistance value generated by the primary winding;

[0105] S3: According to different working frequencies and the corresponding AC resistance values, obtain the relationship between the working frequency and the AC resistance when the primary winding is working, so as to evaluate the working efficiency of the primary winding according to the current working frequency.

[0106] Specifically, referring to Figure 2 as shown, it is a schematic diagram of the construction process steps of the AC resistance calculation model provided by the present invention, including:

[0107] S21: Equivalent the round wire type winding to a rectangular wire winding with the same cross-sectional area, and obtain the magnetic field intensity vector equation in the time domain of the p-th layer winding when the input AC current is applied;

[0108] Referring to Figure 3 as shown, it is a schematic diagram of the structure of the primary winding of the round wire type high-frequency transformer of the present invention in the ZX plane. The magnetic core used is an EE magnetic core. The three inner layers of coils represent the primary winding of the round wire type winding, and the two outer layers of coils represent the secondary winding of the round wire type winding. The dots in the winding represent the direction of the current flowing in, and the crosses in the winding represent the direction of the current flowing out.

[0109] Referring to Figure 4 and Figure 5As shown, the round wire winding is equivalent to a rectangular wire winding with the same cross-sectional area. In this way, gaps appear between the rectangular windings. Therefore, for the equivalent rectangular wire winding, the porosity is: where N l is the number of turns of the wire in each layer of the winding.

[0110] Referring to Figure 6 the integral path shown and the position of the origin of the x-axis, using the integral form of Maxwell's equations, the first line integral expression of the magnetic field strength is obtained:

[0111]

[0112] where is the conduction current density vector in the wire, is the displacement current density vector, s c is the total cross-sectional area of the rectangular wire enclosed by the integral path; s c satisfies where s represents the total area enclosed by the integral path, and η is the porosity;

[0113] Using the total area S enclosed by the integral path to replace the total cross-sectional area s of the rectangular wire enclosed by the integral path c , the second line integral expression of the magnetic field strength is obtained:

[0114]

[0115] According to Stokes' theorem, the third line integral expression of the magnetic field strength is obtained:

[0116]

[0117] 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 p-th layer winding in the time domain is obtained:

[0118]

[0119] S22: According to the relationship between the curl of the magnetic field strength, the electric field strength and the current density, convert the magnetic field strength vector equation of the p-th layer winding in the time domain into the magnetic field strength scalar equation of the p-th layer winding in the time domain; convert the magnetic field strength scalar equation of the p-th layer winding in the time domain into the magnetic field strength scalar equation in the frequency domain;

[0120] According to the magnetic field strength vector equation of the p-th layer winding in the time domain and the relationship between the electric field and the current density, the magnetic field strength vector equation about the electric field strength can be obtained:

[0121]

[0122] Among them, 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 winding, with the leftmost edge of the p-th layer of winding as the coordinate origin, and the x-axis extends to the right of the p-th layer of winding until the rightmost edge; for the primary winding, there is Therefore

[0123] The direction of the magnetic field strength inside the p-th layer of winding is the positive z-axis direction, Therefore, the curl of the magnetic field strength can be expressed as:

[0124]

[0125] 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 in the time domain of the p-th layer of winding;

[0126] Regarding the magnetic field strength vector equation of the electric field strength and the curl of the magnetic field strength, the magnetic field strength vector equation in the time domain of the p-th layer of winding is converted into the magnetic field strength scalar equation in the time domain of the p-th layer of winding:

[0127]

[0128] Among them, H z (x) and E y (x) represent the instantaneous values of the magnetic field strength and the electric field strength in the time domain;

[0129] According to the magnetic field strength changing with time t and the horizontal axis x, H z (x) is written as H z (t,x);

[0130] According to the magnetic field strength scalar equation in the time domain of the p-th layer of winding, the magnetic field strength scalar equation in the frequency domain of the p-th layer of winding is obtained:

[0131]

[0132] Among them, 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, and ω = 2πf, where f is the frequency of the input alternating current; since the magnetic field intensity changes with the frequency ω and the X-axis in the frequency domain, can be written as

[0133] 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;

[0134] According to the vector form of Maxwell's equations, obtain the relationship between the magnetic field intensity and the electric field intensity:

[0135]

[0136] The curl of the electric field intensity is expressed as:

[0137]

[0138] The scalar relationship equation between the magnetic field intensity and the electric field intensity is expressed as:

[0139]

[0140] where μ cu is the magnetic permeability of the primary winding.

[0141] S24: Obtain 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 the boundary conditions of the p-th layer winding, and obtain the magnetic field intensity expression distributed in the p-th layer winding;

[0142] According to the magnetic field intensity scalar equation and the scalar relationship equation of the p-th layer winding in the frequency domain, obtain the deformed form of the magnetic field intensity scalar equation of the p-th layer winding in the frequency domain:

[0143]

[0144] The solution of the magnetic field intensity vector in the rectangular wire is:

[0145]

[0146] where k is the complex propagation constant. The complex propagation constant satisfies:

[0147]

[0148] 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;

[0149] Refer toFigure 7 As shown, it is a schematic diagram of the boundary conditions for 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:

[0150]

[0151] where, is the current passing through each wire, and N l represents the number of turns of the wire in each layer of the winding;

[0152] The first frequency-domain expression of the magnetic field intensity distributed in the p-th layer of the winding is:

[0153]

[0154] where, is the modulus of the magnetic field intensity, and φ H is the initial phase.

[0155] 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 intensity, obtain the new complex propagation constant and the skin depth; substitute the new complex propagation constant and the skin depth into the magnetic field intensity expression in the p-th layer of the winding to obtain the updated magnetic field intensity expression in the p-th layer of the winding;

[0156] Both the complex propagation constant k and the boundary magnetic field intensity H0 contain the influence of the displacement current. In the AC 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 ratio of the amplitudes of the conduction current and 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.

[0157] Obtain the new complex propagation constant:

[0158] According to the new complex propagation constant, obtain the new skin depth:

[0159] The updated magnetic field intensity expression in the p-th layer of the winding:

[0160]

[0161] S26: Obtain 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 scalar equation of the magnetic field strength of the p-th layer winding in the frequency domain:

[0162]

[0163] 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. Subtract the second instantaneous power from the first instantaneous power to obtain the instantaneous power consumed inside the p-th layer winding;

[0164] 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 this area.

[0165] The Poynting vector in the p-th layer winding of the primary side coil is:

[0166]

[0167] 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, for the inner boundary and outer boundary of the p-th layer winding;

[0168] 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 is minus the instantaneous power flowing out of the inner boundary of the p-th layer winding is Expressed as:

[0169]

[0170] 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;

[0171] 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 total instantaneous power equation of the primary winding:

[0172] Summation formula,

[0173] Total instantaneous power equation of the primary winding:

[0174]

[0175] Where, m represents the number of layers of the primary winding, ρ represents the resistivity of the wire of the primary winding, N l represents 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, h represents the total thickness of the primary winding, represents the penetration rate, δ w ′ represents the skin depth.

[0176] S29: Obtain the AC resistance of the primary winding according to the real part of the total instantaneous power equation of the primary winding and the thermal power formula of the resistance.

[0177] The total instantaneous power equation of the primary winding includes the power consumed by the resistance on the primary winding and the instantaneous power stored in the leakage inductance of the primary winding; the real part of the equation represents the active power consumed by the resistance on the primary winding; then the AC resistance of the primary winding can be calculated by the real part of the equation;

[0178] Thermal power formula of the resistance:

[0179] AC resistance of the primary winding:

[0180]

[0181] In the construction process of the AC resistance calculation model described in 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 deduced by using the 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; the instantaneous power consumed by the p-th layer of the winding is obtained by calculating the instantaneous power flowing into and out of the p-th layer of the winding by using the Poynting vector, and according to the active power consumed by the resistance on the primary winding represented by the real part of the total instantaneous power, the AC resistance is calculated, so that the derivation of the AC resistance is more in line with scientific logic and the calculation result of the AC resistance of the primary winding is more accurate.

[0182] The working efficiency of the primary winding is: Based on the calculated value of the AC resistance, substituting it into the thermal power expression of the AC resistance and the total instantaneous power equation of the primary winding, the working efficiency of the primary winding at the current operating frequency can be calculated.

[0183] Reference Figure 8As shown in the figure, it is an AC resistance calculation model of a round wire type high-frequency transformer provided by an embodiment of the present invention, including:

[0184] A magnetic field strength acquisition module 100, which equates the round wire type winding to a rectangular wire winding with the same cross-sectional area. When obtaining 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 combines it with the boundary conditions of the p-th layer winding to obtain the magnetic field strength expression distributed in the p-th layer winding; ignoring the displacement current, it obtains a new complex propagation constant and skin depth; substituting the new complex propagation constant and skin depth into the magnetic field strength expression in the p-th layer winding to obtain an updated magnetic field strength expression in the p-th layer winding;

[0185] An electric field strength acquisition module 200, which 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] An instantaneous power acquisition module 300, which 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] A total instantaneous power acquisition module 400, which sums up 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 to obtain the total instantaneous power equation of the primary winding;

[0188] An AC resistance calculation module 500, which obtains the AC resistance of the primary winding according to the real part of the total instantaneous power equation of the primary winding and the thermal power formula of the resistance.

[0189] The circular wire type high-frequency transformer AC resistance calculation device described in this embodiment is used to obtain the aforementioned circular wire type high-frequency transformer AC resistance calculation model. Therefore, the specific implementation in the circular wire type high-frequency transformer AC resistance calculation device can be seen in the embodiment part of the circular wire type high-frequency transformer AC resistance calculation model. For example, the magnetic field strength acquisition module 100 is used to implement steps S1, S2, S3, S4, and S5 in the above-mentioned circular wire type high-frequency transformer AC resistance calculation model; the electric field strength acquisition module 200, the instantaneous power acquisition module 300, the total instantaneous power acquisition module 400, and the AC resistance calculation module 500 are respectively used to implement steps S6, S7, S8, and S9 in the above-mentioned circular wire type high-frequency transformer AC resistance calculation model. Therefore, its specific implementation can refer to the descriptions of the corresponding individual 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 working efficiency of a circular wire type high-frequency transformer based on AC resistance 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 circular wire type primary winding, average length of each turn of the winding, resistivity, conductivity, magnetic permeability of the circular wire, and the working frequency of the input alternating current.

[0192] An AC resistance calculation module, configured to use the AC resistance calculation model to calculate the AC resistance value generated by the primary winding at the current working frequency based on the parameters acquired by the parameter acquisition module.

[0193] A working efficiency calculation module, configured to calculate the working efficiency at the current working frequency according to the AC resistance value and the total instantaneous power equation of the primary winding.

[0194] The evaluation method for the working efficiency of the circular wire type high-frequency transformer based on the AC resistance according to the present invention evaluates the working efficiency based on the AC resistance of the primary winding; the circular wire is equivalent to a rectangular wire with the same cross-sectional area, and the scalar equation of the magnetic field intensity is derived by the line integral of the magnetic field intensity; according to the scalar relationship between the magnetic field intensity and the electric field intensity, the electric field intensity is obtained; 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, and a new complex propagation constant and skin depth are obtained to calculate the magnetic field intensity and the electric field intensity; the instantaneous power consumed by the p-th layer winding is obtained by calculating the instantaneous power flowing into and out of the p-th layer winding using the Poynting vector, and the AC resistance is calculated according to the active power consumed by the resistance on the primary winding represented by the real part of the total instantaneous power; when calculating the AC resistance in the present invention, a more scientifically logical derivation is used, so that the calculation result of the resistance value of the primary winding AC resistance is more accurate; the working efficiency of the current high-frequency transformer is evaluated more accurately using the calculated AC resistance value, so as to calculate the loss of the electronic power system.

[0195] Those skilled in the art should understand that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0196] The present application is described with reference to the flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or block in the flowchart and / or block diagram, and the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing devices generate a device for realizing the functions specified in Figure 1 one process or multiple processes and / or blocks Figure 1 one block or multiple blocks.

[0197] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer-readable memory generate a manufactured article including an instruction device, and the instruction device realizes the functions in the process Figure 1 one process or multiple processes and / or blocks Figure 1The functions specified in one or more boxes.

[0198] These computer program instructions can also be loaded onto a computer or other programmable data processing device, so that a series of operation steps are executed on the computer or other programmable device to generate a computer-implemented process. Thus, the instructions executed on the computer or other programmable device provide for implementing the steps of the functions specified in Figure 1 One process or more processes and / or boxes Figure 1 The steps of the functions specified in one box or more boxes.

[0199] Obviously, the above embodiments are only examples for clear illustration and are not limitations on the implementation manners. For those of ordinary skill in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to enumerate all the implementation manners here. And the obvious changes or modifications derived therefrom are still within the protection scope of the present invention.

Claims

1. A method for evaluating the working efficiency of a round wire type high-frequency transformer based on AC resistance, characterized in that, Including: 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 the alternating current resistance calculation model to obtain the resistance value of the alternating current generated by the primary winding at the current operating frequency. According to different operating frequencies and the corresponding alternating current resistance values, obtain the relationship between the operating frequency and the alternating current resistance when the primary winding is working, so as to evaluate the working efficiency of the primary winding according to the current operating frequency. The obtaining of the alternating current resistance calculation model includes: 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. 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 of the p-th layer winding in the frequency domain and the scalar relationship equation, and combining 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, 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. 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 up 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 total instantaneous power equation of the primary winding. According to the real part of the total instantaneous power equation of the primary winding and the thermal power expression of the resistance, obtain the alternating current resistance calculation model of the primary winding: Among them, m represents the number of layers of the primary winding, ρ represents the resistivity of the primary winding wire, N l represents 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, h represents the total thickness of the primary winding, represents the penetration rate, δ′ w represents the skin depth.

2. The method for evaluating the working efficiency of a round wire type high-frequency transformer based on AC resistance according to claim 1, characterized in that, The input of the alternating current of the preset operating frequency to construct the magnetic field intensity vector equation of the p-th layer winding in the time domain 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 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; Use 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 conductors enclosed by the integration path c , and obtain the second line integral expression of the magnetic field strength: 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 working efficiency of a round wire type high-frequency transformer based on AC resistance 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 density relationship between the electric field and the current and the curl of the magnetic field intensity, convert the magnetic field intensity vector equation of the p-th layer winding in the time domain into the 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 is in 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 strength inside the p-th layer winding is the positive z-axis direction. The curl of the magnetic field strength can be expressed as: Among them, Indicates 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 p-th layer winding in the time domain; According to the instantaneous value of the magnetic field strength changing with time t and the horizontal axis x, write H z (x) as H z (t, x); According to the scalar equation of the magnetic field intensity of the p-th layer winding in the time domain, obtain the scalar equation of the magnetic field intensity of the p-th layer winding in the frequency domain: Among them, and respectively represent the magnetic field strength phasor and the electric field strength 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 working efficiency of a round wire type high-frequency transformer based on the AC resistance according to claim 3, wherein, The obtaining of the scalar relation 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 includes: According to the vector form of Maxwell's equations, obtain the relationship between the magnetic field intensity and the electric field intensity: The curl of the electric field intensity is expressed as: The scalar relation equation between the magnetic field intensity and the electric field intensity is expressed as: where μ cu is the magnetic permeability of the primary winding.

5. The method for evaluating the working efficiency of a round wire type high-frequency transformer based on the AC resistance according to claim 4, wherein, The substituting the new skin depth into the magnetic field intensity expression in the p-th layer winding to obtain the updated magnetic field intensity expression of the p-th layer winding includes: According to the scalar equation of the magnetic field intensity of the p-th layer winding in the frequency domain and the scalar relation equation between the magnetic field intensity and the electric field intensity, obtain the solution of the magnetic field intensity vector: Where k is the complex propagation constant, satisfying: 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 is 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 modulus 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, obtain the new skin depth: Substitute the new skin depth into the magnetic field intensity expression in 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 working efficiency of a round wire type high-frequency transformer based on the AC resistance according to claim 5, wherein, The electric field intensity distributed in the p-th layer winding is expressed as:

7. The method for evaluating the working efficiency of a round wire type high-frequency transformer based on the AC resistance according to claim 1, wherein, The obtaining of the total instantaneous power of the primary winding includes: 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; Sum the instantaneous powers of the m layer windings in the primary winding to obtain the summation formula: Substitute the updated magnetic field intensity expression and the electric field intensity expression into the summation formula to obtain the total instantaneous power equation of the primary winding: Among them, m represents the number of layers of the primary winding, ρ represents the resistivity of the primary winding wire, N l represents 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, h represents the total thickness of the primary winding, represents the penetration rate, δ′ w represents the skin depth.

8. The method for evaluating the working efficiency of a round wire type high-frequency transformer based on AC resistance according to claim 7, wherein, The obtaining of the AC resistance of the primary winding according to the real part of the total instantaneous power equation of the primary winding and the thermal power expression of the resistance includes: The thermal power formula of the resistor is as follows: The thermal power of the AC resistance is equal to the active power consumed by the resistance on the primary winding, and the equivalent AC resistance of the primary winding is:

9. The method for evaluating the working efficiency of a round wire type high-frequency transformer based on AC resistance according to claim 8, wherein, The working efficiency of the primary winding is:

10. An apparatus for a method for evaluating the working efficiency of a round wire type high-frequency transformer based on AC resistance 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 winding, average length of each turn of the winding, resistivity, conductivity, permeability of the round wire, and the working frequency of the input alternating current of the round wire type primary winding; An AC resistance calculation module for using the AC resistance calculation model to calculate the value of the AC resistance generated by the primary winding at the current working frequency based on the parameters acquired by the parameter acquisition module; A working efficiency calculation module for calculating the working efficiency at the current working frequency according to the AC resistance value and the total instantaneous power equation of the primary winding.

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