CN112417727B - High-frequency transformer leakage inductance parameter calculation method considering end effect - Google Patents

High-frequency transformer leakage inductance parameter calculation method considering end effect Download PDF

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CN112417727B
CN112417727B CN202011314420.9A CN202011314420A CN112417727B CN 112417727 B CN112417727 B CN 112417727B CN 202011314420 A CN202011314420 A CN 202011314420A CN 112417727 B CN112417727 B CN 112417727B
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陈彬
万妮娜
陈健
唐波
黄力
袁发庭
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China Three Gorges University CTGU
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Abstract

A high-frequency transformer leakage inductance parameter calculation method considering end effect comprises determining core window structure of high-frequency transformer; dividing the total magnetic leakage energy of the high-frequency transformer model into an iron core inner part and an iron core outer part; analyzing the sensitivity of the unit length magnetic leakage energy to the structural factor of the transformer, and screening out the decisive influence factor; carrying out non-dimensionalization treatment on the screened decisive influence factors by a dimension analysis method to obtain a plurality of non-dimensionalized parameters; establishing a parameterized finite element simulation model of the high-frequency transformer, and extracting magnetic leakage energy under the condition of combination of all different dimensionless transformers; and selecting a basic fitting function, performing multivariate regression analysis, and determining a correction coefficient. The method can be applied to accurate evaluation of the leakage inductance of the multilayer winding high-frequency transformer, is suitable for calculating the winding loss of the copper foil winding, the narrow foil and the rectangular conductor under different filling rates and arrangement modes, and reduces the calculation amount and the calculation time required by the optimization design.

Description

High-frequency transformer leakage inductance parameter calculation method considering end effect
Technical Field
The invention belongs to the field of high-frequency transformer design, and particularly relates to a method for calculating leakage inductance parameters of a high-frequency transformer by considering an end effect.
Background
In order to realize Zero Voltage Switching (ZVS) technology of a high-power bidirectional full-bridge DC/DC converter, switching loss is reduced. It is generally necessary to achieve series resonance using the leakage inductance of a high frequency transformer for electrical isolation and power distribution in a bi-directional full bridge DC/DC converter as the inductance in the resonant circuit. The circuit adopts a phase-shifted full-bridge control mode, and the minimum inductance value required by realizing zero-voltage switching depends on the input and output voltage, the switching frequency, the phase shift angle and the output power of the converter. Too large a leakage inductance will reduce the efficiency of the converter output, and too small a leakage inductance will not allow zero voltage switching. Therefore, accurate calculation of the leakage inductance of the high frequency transformer is very important for the design of the entire converter.
In the calculation of the leakage inductance of the high-frequency transformer in the prior art, it is generally assumed that the magnetic field is a one-dimensional variable, and the influence of the transverse magnetic field component corresponding to the end-of-winding effect is ignored. In 2005, Robert F adopted a finite element simulation method to analyze the distribution of leakage magnetic field in the winding region under different vertical insulation distances between the winding and the yoke, and indicates that the end effect can affect the distribution of the magnetic field and the current density in the winding region. At present, scholars at home and abroad have proposed various calculation methods for leakage inductance parameters of transformers successively, such as:
(1) and the first literature: dowell P L.effects of edge currentss in transformer wires [ J ]. Proceedings of the institute of Electrical Engineers, 1966, 113 (8): 1387-1394. it is proposed to store the magnetic field energy of the foil winding in the winding conductor and to use the inductive reactance corresponding to the imaginary part of the winding impedance as a winding leakage inductance parameter. This method does not consider the leakage energy of the interlayer insulation region.
(2) And the second document: dauhajre A. modeling and evaluation of leakage phenomena in magnetic circuits [ D ]. Pasadena, California: california Institute of Technology, 1986, an analytical formula for leakage inductance parameters was derived assuming a one-dimensional linear distribution of the leakage magnetic field in the core window, but the formula does not take into account the high frequency eddy current effect of the conductor region.
(3) And document three: hurley W G, Wilcox D j.calibration of leakage inductance in transformers wires [ J ]. IEEE Transactions on Power Electronics, 1994, 9 (1): 121-126, an analytic calculation formula considering the frequency-dependent characteristic of the leakage inductance parameter is derived based on expressions of the mutual inductance and the self-inductance of the winding, but the method is only suitable for the toroidal core.
(4) And document four: wilson P R, Wilcock R. frequency dependent model of leakage index for magnetic components [ J ]. Advanced electronics, 2012, 1 (3): 99-106, a centralized parameter equivalent model of leakage inductance of the high-frequency transformer is provided, leakage inductance parameters are obtained through circuit simulation, and the method is not suitable for circuit simulation and is not capable of providing an analytic expression of the leakage inductance.
(5) And the fifth document: the method for calculating the leakage inductance parameter of the high-power intermediate frequency transformer based on the flux linkage partition [ J ] is reported in the technical and electrical science, 2016 and 31 (05): 164-169, an analytic calculation method of leakage inductance parameters of a high-power intermediate frequency transformer based on flux linkage partition is proposed, but the model only aims at wide foil windings.
(6) And document six: yebin, lie lin, zhao bin a large-capacity high-frequency transformer leakage inductance analytical calculation method considering frequency-dependent characteristics [ J ] chinese electro-mechanical engineering newspaper, 2017, 37 (13): 3928-.
(7) And seventh document: high-frequency transformer leakage inductance and winding loss calculation and analysis based on finite element method [ J ] electrician new technology of electric energy, 2018, 37 (01): and 8-14, calculating leakage inductance parameters of the high-frequency transformer by adopting a finite element method, and analyzing the influence of winding cross transposition on the leakage inductance parameters. Although the finite element calculation method has high precision, the method is only suitable for modeling calculation in electromagnetic field simulation software, and is inconvenient for the optimization design of the high-frequency transformer.
Disclosure of Invention
Aiming at the accurate calculation of the leakage inductance of the high-frequency power transformer, the invention provides a high-frequency transformer leakage inductance parameter calculation method considering the end effect, which comprehensively considers the influences of the high-frequency eddy current effect and the end effect, provides a high-frequency loss semi-empirical calculation formula of a foil winding, a flat copper wire winding and a square winding, saves the calculation time and calculation amount of the leakage inductance, and improves the calculation accuracy.
The technical scheme adopted by the invention is as follows:
a method for calculating leakage inductance parameters of a high-frequency transformer by considering end effects comprises the following steps:
step 1: determining the core window structure of the high-frequency transformer:
parameters related to the core window structure include: foil thickness d, winding layer insulation thickness dinsThe number m of the winding layers and the horizontal distance d between the secondary winding and the iron corechPerpendicular distance d between winding and corecvAn isolation distance disoHeight h of iron core windoww；
Step 2: dividing the total leakage energy of the high-frequency transformer model into an iron core inner part and an iron core outer part, wherein each part is divided into a winding region and an isolation region; analyzing the leakage magnetic energy W per unit length by means of a controlled variable methodmScreening out a decisive influence factor for the sensitivity of the structural factor of the transformer;
and step 3: carrying out non-dimensionalization treatment on the decisive influence factors screened out in the step 2 by a dimension analysis method to obtain a plurality of non-dimensionalized parameters,
and 4, step 4: establishing a parameterized finite element simulation model of the high-frequency transformer, and extracting magnetic leakage energy under the condition of combination of all different dimensionless transformers;
and 5: and selecting a basic fitting function in a proper form, performing multivariate regression analysis, and determining a correction coefficient.
In step 2, the sensitivity calculation expression is as follows:
Figure BDA0002790873640000031
in the formula:
Figure BDA0002790873640000032
is unit length magnetic leakage energy WmRate of change for transformer structure factor x;
n is the number of equally spaced points of a single structural factor;
xitaking the value of the structure factor x at the ith interval point;
xi+1the value of the structural factor x at the (i + 1) th interval point is obtained;
WmFEM(xi) Is corresponding to xiThe magnetic leakage energy simulation value.
WmFEM(xi+1) The leakage flux energy per unit length when the structure factor x is at the (i + 1) th interval point;
in step 3, 5 non-dimensionalized parameters are determined as follows:
Figure BDA0002790873640000033
X1is a dimensionless parameter related to foil thickness; delta is the normalized thickness; d is the thickness of the foil; δ is the skin depth.
Figure BDA0002790873640000034
X2Is a dimensionless parameter related to the vertical insulation spacing; h is a total ofwIs the core window height; dcvIs the vertical spacing between the winding and the core.
Figure BDA0002790873640000041
X3Is a dimensionless parameter related to the isolation distance; h iswIs the core window height; disoIs the separation distance.
X4＝m,
X4Is a dimensionless parameter related to the number of layers; and m is the number of winding layers.
Figure BDA0002790873640000042
X5For insulating from the winding layersA thickness-related dimensionless parameter; d is a radical ofinsThe thickness of the insulation between the winding layers; h iswIs the core window height.
In the step 4, carrying out parametric modeling by adopting ANSYS/Maxwell electromagnetic field simulation software high-frequency transformer, and setting the height of an iron core window of the parametric finite element simulation model as hwSelecting current source excitation in eddy current field solver, and testing foil thickness d and winding interlayer insulation thickness d under short circuit test conditioninsThe number m of winding layers and the insulation distance d between the primary winding and the secondary windingisoPerpendicular distance d between winding and corecvAnd (4) performing parameter scanning, and calculating the leakage flux energy of each region in unit length when different setting values are calculated under the conditions of sinusoidal current excitation and equal ampere turns of primary and secondary windings.
In step 5, the basic fitting function is as follows:
1) basic fitting function of winding area:
Figure BDA0002790873640000043
in the formula:
Figure BDA0002790873640000044
Wr *the leakage flux energy is the unit length of a winding region and is a nonlinear function of alpha, tau, beta and xi; mu is magnetic conductivity; alpha is a dimensionless parameter X1-X5A polynomial function of highest order equal to 2 as an argument; tau, beta, xi are dimensionless parameters X1-X5A polynomial function of highest order equal to 1, being an argument; let X 01, α, τ, β, ξ are expressed as follows:
Figure BDA0002790873640000051
2) and the basic fitting function of the isolation region between the original secondary side winding is as follows:
Figure BDA0002790873640000052
Figure BDA0002790873640000053
for the leakage flux energy per unit length of the isolation region, is
Figure BDA0002790873640000054
And a non-linear function of γ;
Figure BDA0002790873640000055
and gamma is a dimensionless parameter X1-X5A polynomial function of highest order equal to 2 as an argument; let X0＝1，
Figure BDA0002790873640000056
And γ is expressed as follows:
Figure BDA0002790873640000057
when the number of layers m is 1, K is 4, and the undetermined coefficients are 60; when the number m of layers is more than or equal to 2, K is 5, and the undetermined coefficients are 81.
The method further comprises step 6: expressing the leakage magnetic energy in unit length of the winding region in the step 5 as Wr *＝f1(alpha, tau, beta, xi) and isolation region unit length leakage flux energy expression
Figure BDA0002790873640000058
The application range of (2) is expanded to windings of conductors of other shapes, and the influence of turn-to-turn distance on the calculation accuracy of the semi-analytic formula is analyzed.
Dimensionless parameter X1The correction is carried out, and a semi-empirical formula can be popularized to the rectangular conductor winding:
Figure BDA0002790873640000059
in the formula: d is the thickness of the rectangular conductor; w is the width of the rectangular conductor; v is the turn-to-turn distance of adjacent rectangular conductors in the same layer; Δ' is the normalized thickness of the rectangular conductor winding; δ is the skin depth.
The invention relates to a high-frequency transformer leakage inductance parameter calculation method considering an end effect, which has the following technical effects:
the calculation method can be applied to accurate evaluation of leakage inductance of the multilayer winding high-frequency transformer, is suitable for calculation of winding loss of copper foil windings, narrow foils and rectangular conductors under different filling rates and arrangement modes, reduces calculation amount and calculation time required by optimal design, is convenient and quick, and is beneficial to engineering application.
Drawings
FIG. 1 is a flow chart of the calculation method of the present invention.
FIG. 2(a) is a diagram of a core window internal geometry factor definition;
fig. 2(b) is a diagram defining the internal geometry factor of the core window.
FIG. 3(a) is a fitted graph of the leakage magnetic energy of the winding region inside the iron core;
FIG. 3(b) is a fitted graph of magnetic leakage energy of the inner isolated region of the core;
FIG. 3(c) is a fitted graph of the leakage magnetic energy of the outer winding region of the iron core;
fig. 3(d) is a fitted graph of the leakage energy of the core outer isolation region.
FIG. 4(a) is a comparison graph of the relative deviation of magnetic leakage energy for different inter-turn distances in the winding region inside the core;
FIG. 4(b) is a comparison graph of the relative deviation of magnetic leakage energy under different turn-to-turn distances in the isolation region inside the core;
FIG. 4(c) is a graph comparing the relative deviation of magnetic leakage energy for different turn-to-turn spacings in the outer winding region of the core;
fig. 4(d) is a comparative graph of the relative deviation of the magnetic leakage energy under different turn-to-turn distances of the isolation region outside the iron core.
FIG. 5 is a two-dimensional structure diagram of a core model.
Fig. 6 is a schematic two-dimensional structure diagram of the shell model.
FIG. 7(a) is a distribution diagram of leakage magnetic field intensity of the core type high frequency transformer;
FIG. 7(b) is a distribution diagram of the leakage field intensity of the core type high frequency transformer.
Detailed Description
A method for calculating leakage inductance parameters of a high-frequency transformer by considering end effects comprises the following steps:
step 1: determining the core window structure of the high-frequency transformer:
parameters related to the core window structure include: thickness d of foil and thickness d of insulation between winding layersinsThe number m of winding layers and the horizontal distance d between the secondary winding and the iron corechPerpendicular distance d between winding and corecvAn isolation distance disoHeight h of iron core windoww。
Step 2: because the distribution of the leakage magnetic field inside and outside the transformer core window has some differences, the influence relationship of the leakage magnetic energy inside and outside the transformer core window on the sensitivity of each structural parameter and the end effect of each region of the transformer on the leakage magnetic energy is determined in order to calculate the leakage magnetic energy inside and outside the transformer core more accurately. Dividing the total leakage energy of the high-frequency transformer model into an iron core inner part and an iron core outer part, wherein each part is divided into a winding region and an isolation region; analyzing the leakage magnetic energy W per unit length by means of a controlled variable methodmAnd (4) screening out the decisive influence factors on the sensitivity of the structural factors of the transformer.
The sensitivity calculation expression is as follows:
Figure BDA0002790873640000071
in the formula:
Figure BDA0002790873640000072
is unit length magnetic leakage energy WmRate of change for transformer structure factor x;
n is the number of equally spaced points of a single structural factor;
xitaking the value of the structural factor x at the ith interval point;
xi+1the value of the structural factor x at the (i + 1) th interval point is obtained;
WmFEM(xi) To correspond to xiThe magnetic leakage energy simulation value.
WmFEM(xi+1) The leakage flux energy per unit length when the structure factor x is at the (i + 1) th interval point;
the screened out decisive influence factors comprise the thickness d of the foil and the thickness d of the insulation between the winding layersinsThe number m of winding layers and the vertical distance d between the winding and the iron corecvAn isolation distance disoHeight h of iron core windoww。
And step 3: and (3) carrying out non-dimensionalization treatment on the decisive influence factors screened out in the step (2) by a dimension analysis method to obtain a plurality of non-dimensionalized parameters. The method comprises the following steps:
5 dimensionless parameters were determined as follows:
Figure BDA0002790873640000073
X1is a dimensionless parameter related to foil thickness; delta is the normalized thickness; d is the thickness of the foil; δ is the skin depth.
Figure BDA0002790873640000074
X2Is a dimensionless parameter related to the vertical insulation spacing; h iswIs the core window height; dcvIs the vertical spacing between the winding and the core.
Figure BDA0002790873640000081
X3To be dimensionless in relation to the separation distanceChanging parameters; h iswIs the core window height; disoIs the separation distance.
X4＝m；
X4Is a dimensionless parameter related to the number of layers; and m is the number of winding layers.
Figure BDA0002790873640000082
X5Is a dimensionless parameter related to the insulation thickness between winding layers; dinsThe thickness of the insulation between the winding layers; h iswIs the core window height.
In order to ensure the practicability of the semi-empirical formula, the value range of the dimensionless parameter should be able to satisfy the design requirements of the high-voltage high-frequency transformer under different application backgrounds. In the process of optimally designing the power electronic converter, when the thickness of a foil winding of the internal magnetic element is approximately equal to the skin depth, the influence of the skin effect can be reduced, and the d/delta is approximately equal to or slightly smaller than 1. The non-sinusoidal load current in the converter contains more odd harmonic components, the amplitudes of the 3 rd order, 5 th order and other low-order harmonics are larger, and the amplitudes of the other various order harmonics are smaller and can be ignored. Thus, the parameter X1The lower limit of (2) is set to 0.5, and the upper limit is set to 6, so that the design requirement of the high-frequency transformer winding can be met. According to the insulation requirement of the transformer design, the dimensionless parameter (h)w-2dcv)/hw、diso/hwAnd dins/hwThe value ranges of the transformer are set to be 0.4-1, 0.02-0.14 and 0.01-0.04 respectively, and the insulation design of the high-frequency transformer can be met.
And 4, step 4: and establishing a parameterized finite element simulation model of the high-frequency transformer, and extracting the magnetic leakage energy under the condition of different dimensionless transformer combinations.
Adopting ANSYS/Maxwell electromagnetic field simulation software high-frequency transformer to carry out parametric modeling, and setting the height of an iron core window of a parametric finite element simulation model as hwSelecting a current source for excitation in an eddy current field solver, wherein the current frequency is 5kHz, and under the condition of a short-circuit test,thickness d of counter foil and thickness d of insulation between winding layersinsThe number m of winding layers and the insulation distance d between the primary winding and the secondary windingisoPerpendicular distance d between winding and corecvAnd (4) performing parameter scanning, and calculating the leakage flux energy of each region in unit length when different setting values are calculated under the conditions of sinusoidal current excitation and equal ampere turns of primary and secondary windings.
And 5: and selecting a basic fitting function in a proper form, performing multivariate regression analysis, and determining a correction coefficient.
The basis fit function is as follows:
1) basic fitting function of winding area:
Figure BDA0002790873640000091
in the formula:
Figure BDA0002790873640000092
Wr *the leakage flux energy is the unit length of a winding region and is a nonlinear function of alpha, tau, beta and xi; mu is magnetic conductivity; alpha is a dimensionless parameter X1-X5A polynomial function of highest order equal to 2 as an argument; tau, beta, xi are dimensionless parameters X1-X5A polynomial function of highest order equal to 1, being an argument; let X 01, α, τ, β, ξ are expressed as follows:
Figure BDA0002790873640000093
2) and a basic fitting function of an isolation area between the original secondary winding:
Figure BDA0002790873640000094
Figure BDA0002790873640000095
for the leakage flux energy per unit length of the isolation region, is
Figure BDA0002790873640000096
And a non-linear function of γ;
Figure BDA0002790873640000097
and gamma is a dimensionless parameter X1-X5A polynomial function of highest order equal to 2 as an argument; let X0＝1，
Figure BDA0002790873640000098
And γ is expressed as follows:
Figure BDA0002790873640000099
when the number of layers m is 1, K is 4, and the undetermined coefficients are 60; when the number m of layers is more than or equal to 2, K is 5, and the undetermined coefficients are 81.
Step 6: expressing the leakage magnetic energy in unit length of the winding region in the step 5 as Wr *＝f1(alpha, tau, beta, xi) and isolation region unit length leakage flux energy expression
Figure BDA0002790873640000101
The application range of the method is expanded to windings of conductors in other shapes, such as rectangular flat copper wires, squares and the like, and the influence of turn-to-turn distance on the calculation accuracy of the semi-analytic formula is analyzed.
Dimensionless parameter X1The correction is carried out, and a semi-empirical formula can be popularized to the rectangular conductor winding:
Figure BDA0002790873640000102
in the formula: d is the thickness of the rectangular conductor; w is the width of the rectangular conductor; v is the turn-to-turn distance of adjacent rectangular conductors in the same layer; Δ' is the normalized thickness of the rectangular conductor winding; δ is the skin depth.
Example (b):
the invention relates to a method for calculating leakage inductance parameters of a high-frequency transformer by considering end effects, which has the application range that the method can not be limited by specific types of winding structures, such as: rectangular flat copper strips, square conductors, single-layer or multi-layer conductors, different fill ratios, and the like. In addition, the input variables should be a set of non-dimensionalized parameters. The flow of establishing the semi-empirical formula of the leakage inductance parameter considering the end effect influence proposed by the present invention is shown in fig. 1.
A semi-empirical formula is established under the following assumptions:
firstly, the primary and secondary windings are composed of straight foils which are parallel to each other and have equal thickness;
secondly, the distance between the end part of the primary and secondary windings and the upper and lower iron yokes is equal, and the primary and secondary windings are wound on the iron core with high magnetic conductivity;
thirdly, the ampere turns of the primary and secondary windings are equal;
the secondary winding is positioned between zero magnetomotive force and maximum magnetomotive force;
fifthly, the primary side is a single-layer conductor, such as a rectangular solid wire or a foil.
Step one, screening of decisive influence factors:
the undetermined coefficients of semi-empirical formulas and the complexity of multivariate regression analysis are completely dependent on the number of independent variables. Therefore, the influence rule of the iron core window geometric structure on the leakage magnetic energy W needs to be systematically analyzed, and a decisive influence factor is screened out. The primary and secondary windings of the high-frequency transformer core window are all formed by single-turn foils. The core window structure may be defined by: the thickness d of the foil; insulation thickness d between winding layersins(ii) a The number m of winding layers; horizontal spacing d between secondary winding and iron corech(ii) a Perpendicular spacing d between winding and corecv(ii) a Separation distance diso(ii) a Height h of iron core windoww。
Because there are some differences in the distribution of the leakage magnetic field inside and outside the transformer core window, in order to calculate the leakage magnetic energy inside and outside the transformer core more accurately, and to clarify the influence relationship of the leakage magnetic energy of each region of the transformer to the sensitivity of each structural parameter and the end effect on the leakage magnetic energy of each region, the total leakage magnetic energy of the transformer model is divided into two parts, namely the inside of the core and the outside of the core, and each part can be divided into a winding region and an isolation region, as shown in fig. 2(a) and 2 (b).
The leakage energy of the foil winding depends on the frequency f and the structural parameters of the transformer. Analyzing the leakage magnetic energy W per unit length by means of a controlled variable methodmSensitivity to the transformer form factor. Notably, the sensitivity analysis was at f ═ 5kHz and hwAt a frequency f and core window height h of 100mmwWhen the sensitivity of the leakage magnetic energy to the structural factor is changed, the screening result of the decisive influence factor is not influenced. Establishing a two-dimensional simulation model of the high-frequency transformer shown in the figures 2(a) and 2(b) by adopting ANSYS/Maxwell electromagnetic field simulation software, calculating the leakage flux energy of a single structural factor at each equal interval point by using a finite element method, keeping the other structural factors unchanged, and calculating
Figure BDA0002790873640000111
Average value of (a). The calculation expression for sensitivity is as follows:
Figure BDA0002790873640000112
in the formula: n is the number of equally spaced points of a single structural factor; x is the number ofiTaking the value of the structural factor x at the ith interval point; wmFEM(xi) To correspond to xiThe magnetic leakage energy simulation value.
dchIs the geometric variable with the least influence, so the structure factor can be eliminated.
Step two, dimensionless parameters and effective ranges thereof:
the leakage energy of each region is closely related to the structural parameters of the transformer, and in order to simplify the equation form, the influence of the original variable dimension is eliminated. Carrying out non-dimensionalization treatment on the decisive influence factors screened out in the step one by means of a dimension analysis method, and finally determining 5 non-dimensionalized parameters as follows:
Figure BDA0002790873640000113
Figure BDA0002790873640000114
the core window structure shown in fig. 2 can be uniquely determined using the 5 non-dimensionalized parameters.
In order to ensure the practicability of the semi-empirical formula, the value range of the dimensionless parameter should be able to satisfy the design requirements of the high-voltage high-frequency transformer under different application backgrounds. In the process of optimally designing the power electronic converter, when the thickness of a foil winding of the internal magnetic element is approximately equal to the skin depth, the influence of the skin effect can be reduced, and the d/delta is approximately equal to or slightly smaller than 1. The non-sinusoidal load current in the converter contains more odd harmonic components, the amplitudes of the 3 rd order, 5 th order and other low-order harmonics are larger, and the amplitudes of the other various order harmonics are smaller and can be ignored. Thus, the parameter X1The lower limit of (2) is set to 0.5, and the upper limit is set to 6, so that the design requirement of the high-frequency transformer winding can be met. According to the insulation requirement of the transformer design, the dimensionless parameter (h)w-2dcv)/hw、diso/hwAnd dins/hwThe value ranges of the transformer are set to be 0.4-1, 0.02-0.14 and 0.01-0.04 respectively, and the insulation design of the high-frequency transformer can be met. Finally, the valid ranges of the determined non-dimensionalized parameters are shown in table 1.
TABLE 1 dimensionless parameters and their effective ranges
Figure BDA0002790873640000121
Step three, parametric modeling and finite element simulation:
the high-frequency transformers shown in fig. 2(a) and 2(b) were parametrically modeled using ANSYS/Maxwell electromagnetic field simulation software. The height of the iron core window of the two-dimensional finite element model is set as hwThe current source excitation is selected in the eddy current field solver, and the current frequency is 5 kHz. Under the condition of short circuit test, the thickness d of the foil and the thickness d of the insulation between the winding layersinsThe number m of winding layers and the insulation distance d between the primary winding and the secondary windingisoPerpendicular distance d between winding and corecvAnd (4) performing parameter scanning, and calculating the leakage flux energy of each region in unit length at different setting values under the conditions of sinusoidal current excitation and equal ampere turns of primary and secondary windings. Because the skin effect exists in the lead area, the encryption subdivision is carried out on the skin effect layer, the grids below the skin effect layer can be relatively sparse, the number of subdivision layers with the penetration depth is set to be 6, and the other areas are subjected to self-adaptive subdivision.
The parameterized variables in the finite element model correspond to the decisive influence factors (d, d) in step onecv,diso,m,dins) The variation ranges of the respective parameters are shown in table 1. For example, for non-dimensionalized parameter X1The value range is 0.5-6 (12 values in total), the method can be realized by changing the thickness d of the foil, and the frequency f and the skin depth delta are kept unchanged (f is 5 kHz). Similarly, the height of the core window is kept constant (h)w100mm), change dcv、diso、dinsImplementation of X2、X3、X5Values within the respective effective ranges. Through the parameter scanning calculation, a finite element simulation value of unit-length magnetic leakage energy under 20592 groups of different winding structures is finally obtained.
Step four, fitting a function and performing regression analysis:
in this step, a basic fitting function is determined, and the fitting function is approximated to a simulation value by a multivariate regression analysis method. Because the influence of the skin effect and the proximity effect is considered in the traditional magnetic flux leakage energy analysis expression, the equation has certain physical significance and relates to the number m of winding layers and the normalized thicknesses delta and dins/hwAnd diso/hwFour non-dimensionalized parameters. After multiple regression analysis, the finally determined basic fitting function is as follows:
1) basis fit function of winding area:
Figure BDA0002790873640000131
in the formula
Figure BDA0002790873640000132
2) Basic fitting function of the isolation region between the original secondary side windings:
Figure BDA0002790873640000133
from the equations (3) and (4), the semi-empirical equations of the leakage magnetic energy are α, τ, β, ξ, xi,
Figure BDA0002790873640000137
And γ is a non-linear function of the independent variables as follows:
Figure BDA0002790873640000134
let alpha, tau, beta, xi,
Figure BDA0002790873640000135
And gamma is a dependent variable, dimensionless parameter X1-X5For independent variables, the semi-empirical formula can now take into account the influence of the respective decisive influencing factor. Alpha, in consideration of the calculation accuracy and the complexity of the fitting function,
Figure BDA0002790873640000136
And γ selects a polynomial function with the highest order equal to 2, and τ, β, and ξ selects a polynomial function with the highest order equal to 1. When m is 1, K is 4, and the undetermined coefficients are 60; when m is larger than or equal to 2, K is 5, and the undetermined coefficients are 81. Let X0＝1，α、τ、β、ξ、
Figure BDA0002790873640000141
And γ is expressed asThe following:
Figure BDA0002790873640000142
on the basis of the parameter scanning result, the undetermined coefficient Pij,Qi，Ji、Ti、FijAnd GijIt can be obtained by least squares fitting, where the sum of squares of the differences between the fitted values and the finite element simulated values is minimal.
Figure BDA0002790873640000143
Fitting the basic fitting function for multiple times in the effective range of the non-dimensionalized parameter by using fitting software, wherein finally the sum of squares of residuals (SSE) is less than 1, the correlation coefficients (R) are more than 99.9%, and the fitting curves of the leakage magnetic energy of the four regions are shown in fig. 3(a) to 3 (d).
Step five, calculating precision of the discontinuous conductor:
the semi-empirical formula for single-foil windings has been derived previously and can be generalized to windings of other shapes of conductors, such as rectangular, square, etc., by adjusting the fill rate of each layer. The leakage magnetic energy of the tightly wound conductor winding is different from that of the sparsely wound conductor winding. Therefore, when applying the semi-empirical formula to the porous conductor layer, the influence of the inter-turn distance needs to be considered. Dimensionless parameter X1The semi-empirical formula can be generalized to a rectangular conductor winding, modified according to equation (8).
Figure BDA0002790873640000144
Wherein d is the thickness of the rectangular conductor; w is the width of the rectangular conductor; v is the turn pitch of adjacent rectangular conductors in the same layer.
In the uniformly wound layered winding, the turn-to-turn distance is kept unchanged, the turn-to-turn distance v is 5% -20% of the half thickness of the rectangular conductor, and the thickness of the wire self-insulation is 2 times of the thickness of the wire self-insulationAnd (4) degree. Therefore, setting 2v/d to 0.05-0.2 can meet design requirements. Expression (X) of the remaining dimensionless parameters1～X5) And its value range is the same as that of the foil conductor.
In order to research the influence of the turn pitch v on the calculation accuracy of the semi-empirical formula, a high-frequency transformer simulation model is established, wherein a primary winding is a single-layer rectangular solid wire, and a secondary winding is a four-layer rectangular solid wire. The value range of the turn pitch is 0-0.1 d. The remaining geometry of the core window is as follows: d/delta is 0.5-6; number of turns per layer Nt＝4；dcv＝8mm；dins＝2mm；diso＝10mm；h w100 mm. With the simulation results as reference, fig. 4(a) to 4(d) show the relative deviation of the semi-empirical formula of each region, and the results show that:
1): as can be seen from fig. 4(a) and 4(c), the change in turn pitch has an influence on the leakage flux energy in the winding region, and when the conductor turn pitch is large and the conductor lines are sparsely arranged, the relative deviation is smaller;
2): as can be seen from fig. 4(b) and 4(d), the leakage flux energy in the inner and outer isolation regions of the iron core is less affected by the change in the turn-to-turn pitch;
3): as can be seen from fig. 4(a), 4(b), 4(c) and 4(d), the calculation accuracy of the generalized semi-empirical formula for the primary and secondary side winding isolation regions is higher than that of the winding regions, which may be due to the introduced filling rate being not accurate enough.
Aiming at one core type high-frequency transformer model and one shell type high-frequency transformer model, a new semi-empirical method, a traditional analytic calculation method, a finite element simulation method and an experimental measurement method are respectively adopted to extract leakage inductance parameters of the two high-frequency transformers, and the leakage inductance parameters are used for researching the calculation accuracy of a new method. The iron cores of the two transformer models are made of nanocrystalline alloy, primary and secondary windings are formed by winding rectangular flat copper wires, the capacity is 10kW, the voltage level is 0.54kV/0.54kV, and the working frequency is 5 kHz. The two-dimensional structure diagram and the physical diagram of the core type high-frequency transformer are shown in fig. 5, the two-dimensional structure diagram and the physical diagram of the shell type high-frequency transformer are shown in fig. 6, and the main parameters are shown in table 2.
TABLE 2 core and Shell high-frequency Transformer model principal parameters
Figure BDA0002790873640000161
And performing time-harmonic electromagnetic field simulation calculation on the high-frequency transformer by using electromagnetic field analysis software. The three-dimensional simulation may describe the geometry of the transformer better than the two-dimensional finite elements, so the three-dimensional finite element model has a higher accuracy in the leakage inductance simulation. In addition, the three-dimensional simulation model can accurately reflect the winding bending part and the leakage magnetic field of the winding end part in the region outside the window. Fig. 7(a) shows a leakage magnetic field simulation cloud chart of the core-type high-frequency transformer, and fig. 7(b) shows a leakage magnetic field simulation cloud chart of the shell-type high-frequency transformer.
And measuring leakage inductance parameters of the high-frequency transformer test model by using an Agilent 4294A high-precision impedance analyzer. The measuring frequency range is 40 Hz-100 kHz, and open-short circuit calibration is carried out before measurement, so that the accuracy of the measuring result is improved. A low level current is applied during the measurement to ensure that the transformer operates in the linear region. As the secondary winding of the test model is short-circuited, the measured inductance of the core type and shell type transformers is the equivalent inductance reduced to the primary winding.
Table 3 lists leakage inductance parameters of core-down and shell-type high frequency transformer models with frequency of 5kHz, obtained by semi-empirical formula, finite element simulation and experimental measurement method. As can be seen from table 3, the semi-empirical formula and the finite element simulation values have a small deviation from the measured values with respect to the measured values.
TABLE 3 leakage inductance parameter table for core and shell type high-frequency transformer model
Figure BDA0002790873640000162
Figure BDA0002790873640000171

Claims (5)

1. A method for calculating a leakage inductance parameter of a high-frequency transformer considering an end effect, comprising the steps of:
step 1: determining the core window structure of the high-frequency transformer:
parameters related to the core window structure include: foil thickness d, winding layer insulation thickness dinsThe number m of winding layers and the horizontal distance d between the secondary winding and the iron corechPerpendicular distance d between winding and corecvAn isolation distance disoHeight h of iron core windoww；
Step 2: dividing the total leakage energy of the high-frequency transformer model into an iron core inner part and an iron core outer part, wherein each part is divided into a winding region and an isolation region; analyzing the leakage magnetic energy W per unit length by means of a controlled variable methodmScreening out a decisive influence factor for the sensitivity of the structural factor of the transformer;
and step 3: carrying out non-dimensionalization treatment on the decisive influence factors screened out in the step 2 by a dimension analysis method to obtain a plurality of non-dimensionalized parameters;
and 4, step 4: establishing a parameterized finite element simulation model of the high-frequency transformer, and extracting magnetic leakage energy under the condition of combination of all different dimensionless transformers;
and 5: selecting a basic fitting function with a proper form, performing multivariate regression analysis, and determining a correction coefficient;
the basis fit function in step 5 is as follows:
1) basic fitting function of winding area:
Figure FDA0003551985700000011
in the formula:
Figure FDA0003551985700000012
Wr *the leakage flux energy is the unit length of a winding region and is a nonlinear function of alpha, tau, beta and xi; mu is magnetic conductivity; alpha isBy dimensionless parameter X1-X5A polynomial function of highest order equal to 2 as an argument; tau, beta, xi are dimensionless parameters X1-X5A polynomial function of highest order equal to 1, being an argument; let X01, α, τ, β, ξ are expressed as follows:
Figure FDA0003551985700000021
2) and the basic fitting function of the isolation region between the original secondary side winding is as follows:
Figure FDA0003551985700000022
Figure FDA0003551985700000023
for the leakage flux energy per unit length of the isolation region, is
Figure FDA0003551985700000024
And a non-linear function of γ;
Figure FDA0003551985700000025
and gamma is a dimensionless parameter X1-X5A polynomial function of highest order equal to 2 as an argument; let X0＝1，
Figure FDA0003551985700000026
And γ is expressed as follows:
Figure FDA0003551985700000027
2. the method of calculating a leakage inductance parameter of a high frequency transformer considering an end effect according to claim 1, wherein: in step 2, the sensitivity calculation expression is as follows:
Figure FDA0003551985700000028
in the formula:
Figure FDA0003551985700000029
is unit length magnetic leakage energy WmRate of change for transformer structure factor x;
n is the number of equally spaced points of a single structural factor;
xitaking the value of the structural factor x at the ith interval point;
xi+1the value of the structural factor x at the (i + 1) th interval point is obtained;
WmFEM(xi) To correspond to xiThe magnetic leakage energy simulation value is obtained;
WmFEM(xi+1) Is the unit length leakage flux energy when the structure factor x is at the (i + 1) th interval point.
3. The method for calculating leakage inductance parameters of a high-frequency transformer considering the end effect as claimed in claim 1, wherein: in step 3, 5 non-dimensionalized parameters are determined as follows:
Figure FDA0003551985700000031
X1is a dimensionless parameter related to foil thickness; Δ is the normalized thickness; d is the thickness of the foil; delta is skin depth;
Figure FDA0003551985700000032
X2is a dimensionless parameter related to the vertical insulation spacing; h iswIs ironHeart window height; dcvThe vertical distance between the winding and the iron core;
Figure FDA0003551985700000033
X3is a dimensionless parameter related to the isolation distance; h iswIs the core window height; disoIs an isolation spacing;
X4＝m,
X4is a dimensionless parameter related to the number of layers; m is the number of winding layers;
Figure FDA0003551985700000034
X5is a dimensionless parameter related to the insulation thickness between winding layers; dinsThe thickness of the insulation between the winding layers; h iswIs the core window height.
4. The method of calculating a leakage inductance parameter of a high frequency transformer considering an end effect according to claim 1, wherein: in the step 4, carrying out parametric modeling by adopting ANSYS/Maxwell electromagnetic field simulation software high-frequency transformer, and setting the height of an iron core window of the parametric finite element simulation model as hwSelecting current source excitation in eddy current field solver, and testing foil thickness d and winding interlayer insulation thickness d under short circuit test conditioninsThe number m of winding layers and the insulation distance d between the primary winding and the secondary windingisoPerpendicular distance d between winding and iron corecvAnd (4) performing parameter scanning, and calculating the leakage flux energy of each region in unit length when different setting values are calculated under the conditions of sinusoidal current excitation and equal ampere turns of primary and secondary windings.
5. The method of calculating a leakage inductance parameter of a high frequency transformer considering an end effect according to claim 1, wherein: the method further comprises step 6: winding area unit in step 5Length leakage energy expression Wr *＝f1(alpha, tau, beta, xi) and isolation region unit length leakage flux energy expression
Figure FDA0003551985700000041
The application range of the method is expanded to windings of conductors with other shapes, and the influence of turn-to-turn distance on the calculation accuracy of a semi-analytic formula is analyzed;
dimensionless parameter X1The correction is carried out, and a semi-empirical formula can be popularized to the rectangular conductor winding:
Figure FDA0003551985700000042
in the formula: d is the thickness of the rectangular conductor; w is the width of the rectangular conductor; v is the turn-to-turn distance of adjacent rectangular conductors in the same layer; Δ' is the normalized thickness of the rectangular conductor winding; δ is the skin depth.
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