High-frequency magnetic element electromagnetic transient characteristic calculation method considering magnetic core skin effect

Abstract

The invention relates to a high-frequency magnetic element electromagnetic transient characteristic calculation method considering a magnetic core skin effect. An expression of magnetic field intensity in a magnetic core is obtained through an integration method; a hysteresis model is utilized, a Galerkin method is introduced, a magnetic core eddy current field differential equation is obtained, and then a magnetic core boundary magnetic field intensity expression considering hysteresis and macroscopic eddy current is obtained; deducing to obtain a magnetic core lamination boundary magnetic field intensity analytical model considering the magnetic domain mesoscopic eddy current; according to the relationship between the magnetomotive force and the magnetic field intensity and the relationship between the magnetic flux and the magnetic flux density, a total magnetomotive force expression considering the magnetic core skin effect, the hysteresis constitutive relationship and the mesoscopic vortex field is obtained; obtaining a control equation of the electromagnetic transient calculation model of the high-frequency magnetic element by using a magnetic conductance-capacitance analogy method; mesoscopic vortex field parameters and hysteresis model parameters are extracted, and then an electromagnetic transient characteristic calculation model is obtained. According to the invention, the hysteresis characteristic of the magnetic core under complex PWM excitation can be accurately and rapidly simulated, and the accurate and rapid simulation of the actual performance of the high-frequency magnetic element is realized.

Description

Technical Field

[0001] The invention belongs to the field of electromagnetic characteristic analysis and optimization design of magnetic components, and specifically relates to a method for calculating electromagnetic transient characteristics of high-frequency magnetic components taking into account the skin effect of a magnetic core. Background Art

[0002] With the development of power electronics technology and the improvement of the comprehensive performance of semiconductor devices and magnetic materials, magnetic components such as transformers and inductors are gradually developing towards high frequency and miniaturization. At present, high-frequency transformers, inductors and other high-frequency magnetic components have become an important part of power electronic converters, with functions such as electrical isolation, voltage conversion, and noise filtering. High-frequency magnetic components usually work under high-frequency non-sinusoidal signal excitation, such as PWM excitation of pulse width modulation (PWM) inverters. In this power electronic excitation environment, high-frequency magnetic components will produce complex electromagnetic transient characteristics. How to accurately calculate and simulate the electromagnetic transient characteristics of high-frequency magnetic components under high-frequency non-sinusoidal excitation of power electronic converters has become the key to improving their own comprehensive performance and optimizing the design of the converters they belong to.

[0003] The existing modeling method widely used in high-frequency magnetic components is based on the permeance-capacitance analogy method. This method uses the analogies of magnetic circuit and circuit concepts such as flux change rate-current, magnetomotive force-voltage, and permeance-capacitance to equate the magnetic circuit of the magnetic component to an equivalent magnetic circuit formed by the interconnection of magnetomotive force and permeance. The magnetic circuit established based on this method can be directly coupled with the external circuit through a gyrator, so based on this coupling model, both circuit variables can be solved and magnetic circuit variables can be calculated at the same time.

[0004] However, according to existing research, the current electromagnetic transient model of high-frequency magnetic components based on the permeability-capacitance analogy method does not take into account the skin effect of the magnetic core under high-frequency excitation, and only uses simple analytical formulas to characterize the low-frequency macroscopic eddy currents of the magnetic core, such as: 1) Reference 1: Chen Bin, Cai Wenjie, Feng Yuzhang, et al. Simulation method of dynamic hysteresis characteristics of high-frequency transformer core under non-sinusoidal excitation [J / OL]. Proceedings of the CSEE [2024-05-23]. This document deduces and proposes the boundary magnetic field strength of the core to consider the eddy current effect of the magnetic components. H s Total magnetomotive force F The expression is used, and the dynamic hysteresis permeance model of the magnetic core is established on this basis. This modeling method cannot take into account the skin effect of the magnetic core under high-frequency non-sinusoidal excitation of power electronics, and it is also difficult to accurately calculate and simulate the electromagnetic transient characteristics of high-frequency magnetic components under high-frequency non-sinusoidal excitation of power electronic converters.

[0005] 2) Invention application CN202310649975.6: Chen Bin, Wang Chuanyuan, Wan Nina, et al. Modeling method of electromagnetic model of high-frequency transformer based on permeability-capacitance analogy method. The invention first divides the transformer magnetic field into multiple magnetic circuit sections, and then uses the Preisach hysteresis model to simulate the hysteresis effect of the iron core to establish an electromagnetic transient model of the high-frequency transformer. This method only considers the hysteresis effect of the iron core, but does not consider the macroscopic and mesoscopic eddy current fields, resulting in low simulation accuracy, and it cannot simulate the electromagnetic transient characteristics of high-frequency transformers under high-frequency non-sinusoidal excitation, so its application range is relatively narrow.

[0006] In summary, there is no electromagnetic transient modeling method for high-frequency magnetic components that accurately considers the skin effect of the magnetic core in the prior art. Summary of the invention

[0007] The purpose of the present invention is to provide a method for calculating the electromagnetic transient characteristics of high-frequency magnetic components taking into account the skin effect of the magnetic core in order to solve the above problems. First, the cosine basis function is introduced to approximately expand the control equation of the eddy current field of the magnetic core laminations, and the expression of the magnetic field intensity inside the magnetic core is obtained by integration. Then, a simplified model of the eddy current field of the high-frequency magnetic component considering the hysteresis constitutive relationship, skin effect and mesoscopic eddy current is derived, and a calculation model for the electromagnetic transient characteristics of the high-frequency magnetic component is established. This method can accurately and quickly obtain the electromagnetic transient characteristics of high-frequency magnetic components under different working conditions, which has important practical significance for the optimization design and comprehensive performance improvement of itself and power electronic converters.

[0008] In order to achieve the above object, the present invention provides the following technical solutions: A method for calculating electromagnetic transient characteristics of a high-frequency magnetic component considering the skin effect of a magnetic core comprises the following steps: Step 1: Based on the eddy current field control equation of the magnetic core lamination of the magnetic component, the expression of the magnetic field strength inside the magnetic core is obtained by the integration method; Step 2: Using the hysteresis model and introducing the Galerkin method, we can obtain the differential equation of the eddy current field of the magnetic core, and then obtain the magnetic field strength of the magnetic core boundary considering only hysteresis and macroscopic eddy currents. Parsing expressions; Step 3: Derive an analytical model of the magnetic field intensity at the core lamination boundary considering the mesoscopic eddy current of the magnetic domain; Step 4: Based on the relationship between magnetomotive force and magnetic field intensity, magnetic flux and magnetic flux density, obtain the analytical expression of the total magnetomotive force considering the magnetic core skin effect, hysteresis constitutive relation and mesoscopic eddy current field; use the permeance-capacitance analogy method to obtain the control equation of the electromagnetic transient calculation model of high-frequency magnetic components; Step 5: The mesoscopic eddy current field parameters are calculated by linear regression method, and the hysteresis model parameters are calculated. Combined with the analytical expression and control equation of the total magnetomotive force obtained in step 4, the electromagnetic transient characteristic calculation model of the high-frequency magnetic component is obtained; Step 6: Use the power electronics simulation PLECS software and computer language program modules to build an electromagnetic transient calculation model for high-frequency magnetic components and calculate the winding current i ,Voltage u , magnetic field strength at the core boundary H s , average magnetic flux density B av or flux Φ .

[0009] Furthermore, in step 1, the expression of the magnetic field strength inside the magnetic core is: (1); in, (2); (3); In the formula, is the magnetic field strength inside the magnetic core of the magnetic component, h s ( t ) is the magnetic field strength at the core lamination boundary; is the conductivity; d is the thickness of the laminate; is the cosine basis function; b 0 is the average magnetic flux density, b m ( t ), m=1 ,... N -1 is the high-order magnetic flux density component; is an intermediate variable, and the cosine basis function  m ( z ) is related to the quadratic integral; z is the thickness, z ∈[- d / 2, d / 2]; t Indicates time; b m ( t ) and magnetic flux density b ( z , t ) satisfies the relationship: (4); In the formulaN Represents the number of cosine basis functions.

[0010] Furthermore, in step 2, the magnetic field strength at the core boundary that only considers hysteresis and macroscopic eddy currents is The analytical expression is: (8) In the formula, represents the magnetic field strength corresponding to the hysteresis loss; represents the cosine basis function components; represents the average magnetic flux density; in, (9) In the formula, b 1： represents the high-order magnetic flux density vector; represents the cosine basis function vector; C 00 , C 0,1: , C 1:,0 , C 1:,1: Both C The sub-matrix of C is a constant matrix with N rows and N columns.

[0011] Furthermore, in step 3, based on the loss statistics theory, the analytical model of the magnetic field intensity at the core lamination boundary considering the mesoscopic eddy current of the magnetic domain is derived as follows: (10) In the formula, represents the magnetic field intensity at the core lamination boundary considering the mesoscopic eddy current of the magnetic domain, represents the magnetic field strength corresponding to the hysteresis loss; is the conductivity; d is the thickness of the laminate; is a symbolic function, when d b / d t >0, , when d b / d t <0, ; G is the dimensionless coefficient; S is the core cross-sectional area; V 0 It is a statistical parameter related to the micromagnetic structure inside the core; B av is the average magnetic flux density of the core.

[0012] Furthermore, in step 4, the control equation of the electromagnetic transient calculation model of the high-frequency magnetic element considering the magnetic core skin effect and the hysteresis constitutive relationship is: ; (11) ; (12) In the formula, F is the magnetomotive force; u is the voltage; i is the current, represents magnetic flux; N w is the number of winding turns, H s is the magnetic field strength at the core boundary, l is the equivalent magnetic path length of the core; According to the relationship between magnetomotive force and magnetic field intensity, magnetic flux and magnetic flux density, the mesoscopic eddy current field considering magnetic domains can be obtained based on equation (10): H ex The analytical expression of the magnetic field intensity at the boundary of the core lamination is: (13) In the formula, k is the mesoscopic eddy current field coefficient; F hy , F ex and F cl are the magnetomotive force corresponding to hysteresis loss, macroscopic and mesoscopic eddy current loss, F is the total magnetomotive force.

[0013] because h hy ( b ( z , t )) is non-uniformly distributed along the thickness direction of the laminate, so the integral term of equation (13) is solved by numerical method.

[0014] Furthermore, in step 5, the calculation formula for the core loss under low-frequency sinusoidal excitation is: (14) Among them, the analytical formula of the magnetic field intensity at the lamination boundary under low-frequency excitation is: (15) In the formula, W , W hy , W cl , W ex They are total loss, hysteresis loss, macroscopic eddy current loss and mesoscopic eddy current loss;T , f are the excitation period and frequency respectively; ρ is the magnetic core density; B p is the peak magnetic density.

[0015] According to equations (14) and (15), the difference between the total loss measurement value and the macroscopic eddy current loss calculation value is calculated. W diff = W ( B p , f )- W cl ( B p , f )and f 0.5 The mesoscopic eddy current field coefficient is obtained by the linear function relationship k .

[0016] Preferably, in step 5, three static symmetrical hysteresis loops under high, medium and low magnetic density are used to extract Play hysteresis model parameters based on the first-order rotation curve construction method and genetic algorithm.

[0017] Furthermore, step 6 includes: using the magnetic device in the magnetic domain of the PLECS simulation software to express each term on the right side of equation (13), and using its winding device based on the permeability-capacitance analogy method to realize the circuit-magnetic circuit coupling, that is, obtaining an electromagnetic transient calculation model of a high-frequency magnetic component that considers the core skin effect and the hysteresis constitutive relationship.

[0018] Specifically, the magnetomotive force related to the macroscopic eddy current loss F cl By magnetic resistance Multiply by the rate of change of magnetic flux It means that the magnetomotive force related to the mesoscopic eddy current loss is F ex By the rate of change of magnetic flux The controlled magnetomotive force represents the magnetomotive force associated with the hysteresis loss F hy Variable magnetic permeability P It is indicated that, according to the modeling method of nonlinear capacitor, the variable magnetic permeability block is modeled as a controlled magnetomotive force to consider the hysteresis characteristics of the magnetic core, thereby establishing an electromagnetic transient calculation model of high-frequency magnetic components considering the skin effect and hysteresis constitutive relationship of the magnetic core.

[0019] Compared with the prior art, the beneficial effects of the present invention include: (1) The present invention constructs the hysteresis constitutive relationship of magnetic materials under complex non-sinusoidal excitation conditions through the Play hysteresis model, and derives a simplified eddy current field model of high-frequency magnetic components considering the hysteresis constitutive relationship, skin effect and mesoscopic eddy current, thereby obtaining an electromagnetic transient calculation model of high-frequency magnetic components considering the skin effect of the magnetic core. That is, the present invention provides an electromagnetic transient modeling method for high-frequency magnetic components considering the skin effect of the magnetic core, which solves the problem of the lack of an electromagnetic transient modeling method for high-frequency magnetic components that accurately considers the skin effect of the magnetic core in the prior art.

[0020] (2) The method of the present invention can accurately and quickly simulate the hysteresis characteristics of the magnetic core under complex PWM excitation, thereby realizing accurate and rapid simulation of the actual performance of high-frequency magnetic components and the power electronic conversion system to which they belong, providing a solid theoretical and technical foundation for accurately and efficiently evaluating the energy transmission efficiency of high-frequency magnetic components, optimizing the overall design structure, and improving the comprehensive electromagnetic and thermal performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0022] Figure 1 A schematic diagram of a method for calculating electromagnetic transient characteristics of a high-frequency magnetic component taking into account the magnetic core skin effect according to an embodiment; Figure 2 A topological diagram of a single-phase bridge PWM inverter circuit of an embodiment; Figure 3 A schematic diagram of an electromagnetic transient characteristic calculation model considering the core skin effect implemented by a language program of an embodiment; Figure 4 is the carrier frequency in the embodiment f c The dynamic hysteresis loop obtained by simulating the electromagnetic transient characteristics calculation model of high-frequency magnetic components under 2.5kHz bipolar PWM wave excitation; Figure 5 is the carrier frequency in the embodiment f c The voltage and current simulation results of the electromagnetic transient characteristics calculation model of high-frequency magnetic components under 2.5kHz bipolar PWM wave excitation; Figure 6 is the carrier frequency in the embodiment f c This is the dynamic hysteresis loop obtained by simulating the electromagnetic transient characteristics calculation model of high-frequency magnetic components under 3.5kHz bipolar PWM wave excitation; Figure 7 is the carrier frequency in the embodiment f c These are the voltage and current simulation results of the electromagnetic transient characteristics calculation model of high-frequency magnetic components under 3.5kHz bipolar PWM wave excitation. DETAILED DESCRIPTION

[0023] like Figure 1 As shown in FIG. 1 , the electromagnetic transient characteristic calculation method of high-frequency magnetic components considering the skin effect of the magnetic core includes the following steps: Step 1: Use the cosine basis function to approximately expand the governing equation of the eddy current field of the core laminations, and derive the expression of the magnetic field strength inside the core by the integral method, as follows: Assuming that the eddy current flows parallel to the lamination surface, the magnetic field intensity and magnetic flux density are The direction satisfies the following electromagnetic diffusion equation: (1) In the formula, h ( z , t )and b ( z , t ) are the magnetic field intensity and magnetic flux density inside the core respectively; is the conductivity; Further, by increasing the thickness of the laminate z The flux density distribution in is approximately N The truncated Fourier cosine series sum of the terms, that is, (2) In the formula, b 0 is the average magnetic flux density, b 0 = b av ; b 1 ( t ) ... b N-1 ( t ) is the high-order magnetic flux density component; is the cosine basis function, ; Substitute equation (2) into equation (1) and integrate twice to obtain the magnetic field strength inside the core: h ( z , t )Specific expression: (3) in, (4) (5) In the formula, is the magnetic field strength inside the magnetic core of the magnetic component, h s (t ) is the magnetic field strength at the core lamination boundary; is the conductivity; d is the thickness of the laminate; is the cosine basis function; b 0 is the average magnetic flux density, b m ( t ), m=1 ,... N -1 is the high-order magnetic flux density component; is an intermediate variable, and the cosine basis function The quadratic integral of is related to; t Indicates time; Step 2: Use the Play hysteresis model and introduce the Galerkin method to obtain the differential equation of the eddy current field of the magnetic core, and then obtain the magnetic field intensity at the boundary of the magnetic core Expression; specifically as follows: Using Play's hysteresis model to consider the hysteresis constitutive relationship of magnetic core magnetic materials h hy ( b ), in addition, the basic idea of ​​Galerkin method is introduced to make equation (3) and hysteresis constitutive relation h hy ( b ) in the thickness direction of the laminate satisfies the following formula: (6) Substituting equation (3) into equation (6), the following differential equations corresponding to the eddy current field of the magnetic core are derived: (7) In the formula h s ( t ) is the magnetic field strength at the core lamination boundary, represents the magnetic flux density, represents the magnetic field strength associated with hysteresis losses; are all cosine basis functions, is the average magnetic flux density, … are all magnetic flux density components; C is a constant matrix; According to formula (5), the magnetic field strength at the boundary of the core lamination is obtained: h s ( t ) and the magnetic flux density component b 1 ( t ) ... b N-1 ( t ), where the constant matrixC Elements in C mn The calculation formula is: (8) In the formula, m , n =0,…, N -1, then the constant matrix can be expressed as: (9) For the convenience of explanation, the constant matrix in equation (16) is C Divide into blocks, namely: (10) In the formula, C 00 , C 0,1: , C 1:,0 , C 1:,1: All are constant matrices C The sub-matrix of C 0,1: The matrix size is 1×( N -1), C 1:,0 The matrix size is ( N -1)×1, C 1:,1: The matrix size is ( N -1)×( N -1); Similarly, using the symbol b 1： , They represent the high-order magnetic flux density components [ b 1 ... b N-1 ] T and cosine basis functions , and finally the magnetic field strength at the core boundary can be obtained expression: (11) in, (12) Step 3: Based on the loss statistics theory, the analytical model of the magnetic field intensity at the core lamination boundary considering the mesoscopic eddy current of the magnetic domain is derived, and its expression is: (13) In the formula, represents the magnetic field intensity at the core lamination boundary considering the mesoscopic eddy current of the magnetic domain, represents the magnetic field strength corresponding to the hysteresis loss; is the conductivity; d is the thickness of the laminate; is a symbolic function, when d b / d t >0, , when d b / d t <0, ; G is the dimensionless coefficient; S is the core cross-sectional area; V 0 It is a statistical parameter related to the micromagnetic structure inside the core; B av is the average magnetic flux density of the core.

[0024] Step 4: Based on the relationship between magnetomotive force and magnetic field intensity, magnetic flux and magnetic flux density, obtain the analytical expression of the total magnetomotive force considering the core skin effect, hysteresis constitutive relation and mesoscopic eddy current field; use the permeance-capacitance analogy method to obtain the control equation of the electromagnetic transient calculation model of high-frequency magnetic components; Among them, the analytical expression of the total magnetomotive force considering the magnetic core skin effect, hysteresis constitutive relation and mesoscopic eddy current field is: (14) In the formula, k is the mesoscopic eddy current field coefficient; F hy , F ex and F cl are the magnetomotive force corresponding to hysteresis loss, macroscopic and mesoscopic eddy current loss respectively; h hy ( b ( z , t )) is non-uniformly distributed along the thickness direction of the laminate, so the integral term of equation (14) needs to be solved by numerical methods. The Gauss-Legendre quadrature formula is used in the embodiment, and its basic idea is to select appropriate integral nodes z m and weight W m , m =1 ... N , the integrand is transformed into the weighted sum of multiple Gaussian functions on the integration interval; Furthermore, the coupling of magnetic circuit and electric circuit is realized based on the permeance-capacitance analogy method, specifically: ; (15) ; (16) In the formula, F is the magnetomotive force; u is the voltage; i is the current, represents magnetic flux; N w is the number of winding turns, H s is the magnetic field strength at the core boundary, l is the equivalent magnetic path length of the core; Step 5: Use the linear regression method to calculate the mesoscopic eddy current field parameters and the hysteresis model parameters. Combined with the analytical expression and control equation of the total magnetomotive force obtained in step 4, the calculation model of the electromagnetic transient characteristics of high-frequency magnetic components is obtained.

[0025] Mesoscopic eddy current coefficient k The difference between the total core loss measured under low-frequency sinusoidal excitation and the macroscopic eddy current loss calculated can be f 0.5 Extraction of linear function relationships.

[0026] To extract the mesoscopic eddy current coefficient k , the following formula for calculating the core loss under low-frequency sinusoidal excitation is required: (17) Among them, the analytical formula of the magnetic field intensity at the lamination boundary under low-frequency excitation is: (18) In the formula, W , W hy , W cl , W ex They are total loss, hysteresis loss, macroscopic eddy current loss and mesoscopic eddy current loss; T , f are the excitation period and frequency respectively; ρ is the magnetic core density.

[0027] According to formula (17), the coefficient k The difference between the total loss measurement and the macroscopic eddy current loss calculation can be W diff = W ( B p , f )- W cl ( B p , f )and f 0.5 Extraction of linear function relationships.

[0028] The specific method for extracting the Play hysteresis model parameters in the embodiment refers to the Play hysteresis model parameter extraction method disclosed in the paper “Inverse RheologicalHysteresis Model and Its Efficient Parameter Identification Method” by Liu R, Lu Y et al. published in the 3rd issue of “IEEE Transactions on Magnetics” in 2024.

[0029] The parameters of the Play hysteresis model can be quickly extracted by using only three static symmetrical hysteresis loops under high, medium and low magnetic flux density, and based on the first-order rotation curve construction method and genetic algorithm. In the embodiment, the magnetic flux density amplitudes of the three static symmetrical hysteresis loops of the magnetic core sample are selected. B p They are 1.5, 0.9, and 0.3 T respectively. The genetic algorithm achieves parameter optimization through selection, mutation, and crossover. It has strong robustness, parallelism, and global search capabilities, avoiding the problem of falling into the local optimal solution, and is suitable for solving optimization problems of nonlinear multi-objective functions. In order to evaluate the accuracy of the optimal parameters extracted by the genetic algorithm, hysteresis loss and coercive force error are used as reference standards for the optimization algorithm: the former represents the area of ​​the hysteresis loop under static conditions, and the latter is the reverse magnetic field value added when the magnetic flux density is corrected to 0 after the external magnetic field is removed. The two take into account the simulation accuracy of the overall and local key points of the model respectively, and the calculation formula is as follows: (19) in, and is the calculated value of the hysteresis loop simulated using the proposed model.

[0030] The mean-square error, which is sensitive to errors, is introduced as the evaluation function of the optimization algorithm, that is, the objective function Fit In addition, in order to take into account the accuracy of the simulated hysteresis loop under different magnetic flux densities, the mean square error of the three hysteresis loops of the silicon steel sample under high, medium and low magnetic flux densities is set as the benchmark, and the objective function expression is as follows: (20) In the formula, W h and H c They represent the hysteresis loss and coercive force of the measured hysteresis loop respectively.

[0031] Through the above steps, the proposed parameter identification method only requires three symmetrical hysteresis loops under high, medium and low magnetic densities to identify the Play hysteresis model parameters.

[0032] Based on the model parameters extracted above and combined with the analytical expression of the total magnetomotive force of the magnetic core skin effect, hysteresis constitutive relation and mesoscopic eddy current field, namely equation (14) and the permeance-capacitance analogy model, namely equation (15) and equation (16), a new calculation model of electromagnetic transient characteristics of high-frequency magnetic components can be obtained. u Generally, it is a known parameter generated by the power electronic circuit, so using this known input parameter u The other three unknown parameters can be obtained based on the electromagnetic transient characteristics calculation model of high-frequency magnetic components, namely, equations (14), (15), and (16): i , H s , B av or Φ .

[0033] Step 6: Use the underlying modules and language programs of the power electronics simulation PLECS software to build a calculation model for the electromagnetic transient characteristics of high-frequency inductors.

[0034] In the PLECS simulation software, there is a special magnetic domain containing magnetic devices such as windings, constant magnetic resistance and variable magnetic permeance. Based on the magnetic devices in the magnetic domain, the equivalent circuit of magnetic components of any physical structure can be constructed, and the simulation speed is relatively fast. Therefore, by using the magnetic devices in the magnetic domain of the software to express each item on the right side of equation (14), and based on the magnetic permeance-capacitance analogy method, the coupling of the circuit-magnetic circuit is realized by using its winding devices, and the electromagnetic transient calculation model of high-frequency magnetic components considering the core skin effect and the hysteresis constitutive relationship can be obtained.

[0035] The specific idea is as follows: Magnetomotive force related to macroscopic eddy current loss F cl By magnetic resistance Multiply by the rate of change of magnetic flux It means that the magnetomotive force related to the mesoscopic eddy current loss is F ex By the rate of change of magnetic flux The controlled magnetomotive force represents the magnetomotive force associated with the hysteresis loss F hy Variable magnetic permeability P According to the modeling method of nonlinear capacitor, the variable permeability block is modeled as a controlled magnetomotive force to consider the hysteresis characteristics of the magnetic core, such as Figure 3 As shown. Thus, an electromagnetic transient calculation model of high-frequency magnetic components is established considering the core skin effect and hysteresis constitutive relationship.

[0036] like Figure 3As shown in the figure, C-Script 1 module, C-Script 2 module, and C-Script 3 module are all hysteresis model program modules implemented in C language. The magnetomotive force related to hysteresis loss F hy The specific calculation process is as follows: 1) First, in the initialization interface of the PLECS simulation environment, the number of cosine basis function terms in equation (2) is given: N , in order to determine the Gaussian integration point z m , weight W m , cosine basis function and the constant matrix C , and initialize the average magnetic flux density, giving its initial value b 0 ( t 0 ).

[0037] 2) According to the set variable time step Calculate the current time , extract the current time through the magnetic flux table t The rate of change of magnetic flux , and then through the gain s 1 Divide by the magnetic circuit cross-sectional area S The average magnetic flux density change rate d is obtained b 0 / d t , and then through the gain s 2 Multiply C 1:,0 get C 1:,0 d b 0 / d t Then add the output items of C-Script 1 module, C-Script 2 module, and C-Script 3 module h hy ( z , t ) and obtained by Gaussian integral method , and finally through the gain s 3 Multiply Get the high-order flux change rate component d b 1: / d t .

[0038] 3) Use the signal multiplexer to convert the magnetic flux change rate component d b 0 / dt... d b N-1 / d t Combined, through the amplifier s 4 Multiply by cosine basis function , and then the magnetic flux density is obtained through the integrator b ( z m , t ), so that each Gaussian integration point z m Using the hysteresis model, b ( z m , t ) is provided as input to the C-Script 1 module, C-Script 2 module, and C-Script 3 module.

[0039] 4) Compile the C language program of the Play hysteresis model in the C-Script 1 module, C-Script 2 module, and C-Script 3 module to calculate t Magnetic field strength at the time h hy ( z m , t ).

[0040] 5) Using the amplifier s 5 ~ s 7 The magnetic field strength at each Gaussian integration point h hy ( z m , t ) N Item, and then through the amplifier s 8 Multiply get , and then through the gain s 9 Multiply by the weight of the corresponding integral point W m Finally, the signal selector and summer are used to obtain the magnetic field strength related to the hysteresis loss. h hy ( t ) and the integral term .

[0041] 6) Magnetic field strength H hy ( t ) through the amplifier s11 The calculation results in the magnetomotive force related to the hysteresis loss. F hy , and the integral term Transmitted to step 3) for calculating the high-order flux change rate component d b 1: / d t .

[0042] 7) t The average magnetic flux density at the time b 0 ( t )Save as b 0 ( t 0 ), the magnetic field strength related to hysteresis loss h hy ( t )Save as h hy ( t 0 ),at the same time t Save as t 0 That is, update the initial value, and then continue to repeat steps 2) to 7). If at the moment t Greater than the set simulation time T set The calculation ends.

[0043] In PLECS, small system modules are used to Figure 3 By encapsulating the internal structure of the magnetomotive force related to hysteresis loss, an electromagnetic transient calculation model of high-frequency magnetic components considering the skin effect of the magnetic core can be obtained.

[0044] In order to verify the correctness of the electromagnetic transient modeling method considering the skin effect proposed in the present invention, a high-frequency inductor sample was simulated at the fundamental frequency. f The carrier frequency is 500Hz. f c is the complex dynamic hysteresis loop in the core and the voltage and current characteristics of its ports under the excitation of 2.5kHz and 3.5kHz bipolar PWM waves. The excitation circuit of the high-frequency inductor is as follows: Figure 2 As shown; and compared with the corresponding measured results, the results are as follows Figure 4-7 As shown. Figure 4-7 It can be seen that the dynamic hysteresis loop of the electromagnetic transient calculation model considering the core skin effect of the present invention has a high degree of consistency with the voltage and current waveforms and the corresponding measured data.

[0045] The system of the method for calculating electromagnetic transient characteristics of high-frequency magnetic components considering the skin effect of the magnetic core comprises: The magnetic field strength calculation module of the magnetic core boundary is used to establish the functional relationship between the magnetic flux density and the magnetic field strength of the magnetic core boundary when considering the hysteresis and macroscopic eddy current, and calculate the magnetic field strength of the magnetic core boundary considering the hysteresis and macroscopic eddy current; The module for calculating the magnetic field strength at the boundary of the core considering the mesoscopic eddy current field is used to derive the relationship between the magnetic field strength at the boundary of the core lamination and the magnetic flux density considering the hysteresis, macroscopic and mesoscopic magnetic domains and mesoscopic eddy currents according to the loss statistics theory, and calculate the magnetic field strength at the boundary of the core lamination considering the mesoscopic eddy current field; The total magnetomotive force calculation module of the magnetic core is used to obtain the analytical expression of the total magnetomotive force considering the skin effect of the magnetic core, the hysteresis constitutive relationship and the mesoscopic eddy current field according to the relationship between the magnetomotive force and the magnetic field intensity, the magnetic flux and the magnetic flux density, so as to establish a connection with the magnetic circuit; and use the permeance-capacitance analogy method to obtain the control equation of the electromagnetic transient calculation model of the high-frequency magnetic component; High-frequency magnetic component electromagnetic transient calculation model module, used to calculate the winding current according to the control equation of the high-frequency magnetic component electromagnetic transient calculation model i ,Voltage u , magnetic field strength at the core boundary H s , average magnetic flux density B av Or magnetic flux Φ.

Claims

1. A method for calculating electromagnetic transient characteristics of high-frequency magnetic components considering the skin effect of the magnetic core, characterized in that: The following steps are involved: Step 1: Based on the eddy current field control equation of the magnetic core lamination of the magnetic component, the expression of the magnetic field strength inside the magnetic core is obtained by the integration method; Step 2: Using the hysteresis model and introducing the Galerkin method, the differential equation of the eddy current field of the magnetic core is obtained, and then the analytical expression of the magnetic field intensity at the boundary of the magnetic core considering hysteresis and macroscopic eddy current is obtained; Step 3: Derive an analytical model of the magnetic field intensity at the core lamination boundary considering the mesoscopic eddy current of the magnetic domain; Step 4: Based on the relationship between magnetomotive force and magnetic field intensity, magnetic flux and magnetic flux density, obtain the analytical expression of the total magnetomotive force considering the magnetic core skin effect, hysteresis constitutive relation and mesoscopic eddy current field; use the permeance-capacitance analogy method to obtain the control equation of the electromagnetic transient calculation model of high-frequency magnetic components; Step 5: Use the linear regression method to calculate the mesoscopic eddy current field parameters and the hysteresis model parameters. Combined with the analytical expression and control equation of the total magnetomotive force obtained in step 4, the calculation model of the electromagnetic transient characteristics of high-frequency magnetic components is obtained.

2. The method for calculating electromagnetic transient characteristics of high-frequency magnetic components considering the magnetic core skin effect according to claim 1 is characterized in that: The method further comprises step 6: using power electronics simulation PLECS software and computer language program modules to construct an electromagnetic transient calculation model of high-frequency magnetic components and calculate the primary winding current i 1. Secondary winding voltage u 2. Magnetic field strength at the core boundary H s , average magnetic flux density B av or flux Φ .

3. The method for calculating electromagnetic transient characteristics of high-frequency magnetic components considering the magnetic core skin effect according to claim 1 or 2, characterized in that: In step 1, the expression of the magnetic field strength inside the magnetic core is: ；(1) in, ；(2) ；(3) In the formula, is the magnetic field strength inside the magnetic core of the magnetic component, h s ( t ) is the magnetic field strength at the core lamination boundary; is the conductivity; d is the thickness of the laminate; is the cosine basis function; b 0 is the average magnetic flux density, b m ( t ), m=1 ,... N -1 is the high-order magnetic flux density component; is an intermediate variable, and the cosine basis function  m ( z ) is related to the quadratic integral; z is the thickness, z ∈[- d / 2, d / 2]; t Indicates time; b m ( t ) and magnetic flux density b ( z , t ) satisfies the relationship: ；(4) In the formula N Represents the number of cosine basis functions.

4. The method for calculating electromagnetic transient characteristics of high-frequency magnetic components considering the core skin effect according to claim 3 is characterized in that: In step 2, the differential equation corresponding to the eddy current field of the magnetic core considering the hysteresis constitutive relation of the magnetic material of the magnetic core is: ； (5) In the formula, h s ( t ) is the magnetic field strength at the core lamination boundary, represents the magnetic flux density, represents the magnetic field strength associated with hysteresis losses; are all cosine basis functions, is the average magnetic flux density, … are all magnetic flux density components; C is a constant matrix; According to formula (5), the magnetic field strength at the boundary of the core lamination is obtained: h s ( t ) and the magnetic flux density component b 1( t ) ... b N-1 ( t ), where the constant matrix C Elements in C mn The calculation formula is: ； (6) In the formula m =0… N -1, n =0… N -1; represents pi; is the conductivity; d is the thickness of the laminate; The constant matrix C Divide into blocks, namely: ； (7) In the formula C 00 , C 0,1: , C 1:,0 , C 1:,1: All are constant matrices C The sub-matrix of C 0,1: The matrix size is 1×( N -1), C 1:,0 The matrix size is ( N -1)×1, C 1:,1: The matrix size is ( N -1)×( N -1).

5. The method for calculating electromagnetic transient characteristics of high-frequency magnetic components considering the magnetic core skin effect according to claim 4, characterized in that: In step 2, only the magnetic field strength of the core boundary of hysteresis and macroscopic eddy current is considered. The analytical expression is: ； (8) In the formula, represents the magnetic field strength corresponding to the hysteresis loss; represents the cosine basis function components; represents the average magnetic flux density; in, ； (9) In the formula, b 1： represents the high-order magnetic flux density vector; represents the cosine basis function vector; C 00 , C 0,1: , C 1:,0 , C 1:,1: Both C The sub-matrix of C is a constant matrix with N rows and N columns.

6. The method for calculating electromagnetic transient characteristics of high-frequency magnetic components considering the magnetic core skin effect according to claim 5, characterized in that: In step 3, based on the loss statistics theory, the analytical model of the magnetic field intensity at the core lamination boundary considering the mesoscopic eddy current of the magnetic domain is derived as follows: ； (10) In the formula, represents the magnetic field intensity at the core lamination boundary considering the mesoscopic eddy current of the magnetic domain, represents the magnetic field strength corresponding to the hysteresis loss; is the conductivity; d is the thickness of the laminate; is a symbolic function, when d b / d t >0, , when d b / d t <0, ; G is the dimensionless coefficient; S is the core cross-sectional area; V 0 is a statistical parameter related to the micromagnetic structure inside the core; B av is the average magnetic flux density of the core.

7. The method for calculating electromagnetic transient characteristics of high-frequency magnetic components considering the magnetic core skin effect according to claim 6, characterized in that: In step 4, the control equation of the electromagnetic transient characteristic calculation model of the high-frequency magnetic component considering the magnetic core skin effect and the hysteresis constitutive relationship is: ；(11) ； (12) In the formula, F is the magnetomotive force; u is the voltage; i is the current, represents magnetic flux; N w is the number of winding turns, H s is the magnetic field strength at the core boundary, l is the equivalent magnetic path length of the core; According to the relationship between magnetomotive force and magnetic field intensity, magnetic flux and magnetic flux density, the mesoscopic eddy current field considering magnetic domains can be obtained based on equation (10): H ex The analytical expression of the magnetic field intensity at the boundary of the core lamination is: ； (13) In the formula, k is the mesoscopic eddy current field coefficient; F hy , F ex and F cl are the magnetomotive force corresponding to hysteresis loss, macroscopic and mesoscopic eddy current loss, F is the total magnetomotive force; because h hy ( b ( z , t )) is non-uniformly distributed along the thickness direction of the laminate, so the integral term of equation (13) is solved by numerical method.

8. The method for calculating electromagnetic transient characteristics of high-frequency magnetic components considering the magnetic core skin effect according to claim 7, characterized in that: In step 5, the magnetic flux density amplitude is used B p =1.5T, B p =0.9T, B p =0.3T, and the Play hysteresis model parameters were extracted based on the first-order rotation curve construction method and genetic algorithm.

9. The method for calculating electromagnetic transient characteristics of high-frequency magnetic components considering the core skin effect according to claim 7 or 8, characterized in that: In step 6, the electromagnetic transient calculation model of the high-frequency magnetic component is constructed using the power electronics simulation PLECS software and the computer language program module: Magnetomotive force related to macroscopic eddy current losses F cl By magnetic resistance Multiply by the rate of change of magnetic flux It means that the magnetomotive force related to the mesoscopic eddy current loss is F ex By the rate of change of magnetic flux The controlled magnetomotive force represents the magnetomotive force associated with the hysteresis loss F hy Variable magnetic permeability P It is indicated that, according to the modeling method of nonlinear capacitor, the variable magnetic permeability block is modeled as a controlled magnetomotive force to represent the hysteresis characteristics of the magnetic core, thereby establishing an electromagnetic transient calculation model of high-frequency magnetic components considering the skin effect and hysteresis constitutive relationship of the magnetic core.

10. The system of the method for calculating electromagnetic transient characteristics of high-frequency magnetic components according to claim 1, 2, 4, 5, 6, 7 or 8, characterized in that: The system comprises: The magnetic field strength calculation module of the magnetic core boundary is used to establish the functional relationship between the magnetic flux density and the magnetic field strength of the magnetic core boundary when considering the hysteresis and macroscopic eddy current, and calculate the magnetic field strength of the magnetic core boundary considering the hysteresis and macroscopic eddy current; The module for calculating the magnetic field strength at the boundary of the core considering the mesoscopic eddy current field is used to derive the relationship between the magnetic field strength at the boundary of the core lamination and the magnetic flux density considering the hysteresis, macroscopic and mesoscopic magnetic domains and mesoscopic eddy currents according to the loss statistics theory, and calculate the magnetic field strength at the boundary of the core lamination considering the mesoscopic eddy current field; The total magnetomotive force calculation module of the magnetic core is used to obtain the analytical expression of the total magnetomotive force considering the skin effect of the magnetic core, the hysteresis constitutive relationship and the mesoscopic eddy current field according to the relationship between the magnetomotive force and the magnetic field intensity, the magnetic flux and the magnetic flux density, so as to establish a connection with the magnetic circuit; and use the permeance-capacitance analogy method to obtain the control equation of the electromagnetic transient calculation model of the high-frequency magnetic component; High-frequency magnetic component electromagnetic transient calculation model module, used to calculate winding current and voltage according to the control equations of the high-frequency magnetic component electromagnetic transient calculation model u , magnetic field strength at the core boundary H s , average magnetic flux density B av or flux Φ .

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