A modeling method for low-frequency electromagnetic transient model of ferrite core

Abstract

A method for modeling the low-to-medium frequency electromagnetic transients of ferrite cores is proposed. First, an expression for the magnetomotive force (MTF) of the quasi-static hysteresis field of the ferrite core is established based on a continuous inverse Play model. Second, a mathematical model of its residual field and MTF is derived based on loss statistics theory. Third, an expression for the total MTF of the ferrite core at low to medium frequencies is constructed by relating the MTF to the magnetic field strength. Fourth, the permeability-capacitance analogy method is used, and the coupling equations of the ferrite core circuit and magnetic circuit are obtained through a gyroscope. Finally, the continuous inverse Play model and residual field parameters of the ferrite core are extracted to obtain the low-to-medium frequency (≤500kHz) electromagnetic transient model of the ferrite core. This invention can accurately and quickly simulate the electromagnetic transient characteristics of ferrite cores under low-to-medium frequency sinusoidal and non-sinusoidal excitation, providing theoretical and technical support for its optimized design and the overall performance improvement of its associated power electronic converter system.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic characteristic analysis and optimization design of magnetic components, specifically to a method for modeling low-frequency (≤500kHz) electromagnetic transient models in ferrite cores. Background Technology

[0002] Ferrites possess advantages such as high permeability, low loss, and low cost, making them widely used in the fabrication of magnetic cores for high-frequency magnetic components. In this context, ferrite cores typically operate under high-frequency non-sinusoidal excitation in power electronic converters, and their complex nonlinear electromagnetic properties result in complex nonlinear electromagnetic transient characteristics when interacting with power electronic devices. Therefore, accurately and efficiently simulating these electromagnetic transient characteristics of ferrite cores is crucial for their optimized design and the overall performance improvement of the power electronic converter system.

[0003] Currently, the most widely used electromagnetic transient model is the permeability-capacitance analogy method, which uses the core flux change rate d... Φ / d t Analogous to electric current i Magnetomotive force F Analogous to voltage u The magnetic permeability is analogous to that of a capacitor, and the electrical and magnetic circuits are coupled through a gyrator. However, no research has yet applied this method to the low-to-medium frequency electromagnetic transient modeling of ferrite cores, for example:

[0004] (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]. Proceedings of the CSEE, 2024, 44(13): 5420-5431. This reference considers the influence of eddy current and relaxation effects on the dynamic hysteresis characteristics of the core under high frequency conditions within the framework of the permeability-capacitance analogy method, and then establishes a dynamic hysteresis permeability model of the core based on the loss statistics theory. However, this method is aimed at good conductor materials such as nanocrystals, and the structure of such materials is quite different from that of ferrite, a non-good conductor material.

[0005] (2) Reference 2: Liu Ren, Huang Haoran, Lu Youhao, et al. Electromagnetic transient modeling method for high-frequency magnetic components considering the skin effect of the magnetic core [J]. Proceedings of the CSEE, 2026, 46(3): 1286-1298. This reference derives the analytical expression of the boundary magnetic field strength of silicon steel magnetic cores based on cosine basis functions and Galerkin method. It considers both the high-frequency skin effect and complex hysteresis constitutive relations of silicon steel magnetic cores, and uses the permeability-capacitance analogy method as the framework to build a broadband electromagnetic transient model of silicon steel magnetic cores in PLECS software. Obviously, this method is only applicable to magnetic cores made of good conductor materials and cannot be applied to magnetic cores made of non-good conductor materials such as ferrite.

[0006] Given the insulating crystalline structure within ferrite cores, their nonlinear electromagnetic properties differ significantly from those of cores made from good conductors such as silicon steel and nanocrystalline materials. Therefore, the electromagnetic transient modeling methods mentioned above cannot be directly applied to ferrite cores. In summary, there is currently no effective method for mid-to-low frequency electromagnetic transient modeling of ferrite cores. Summary of the Invention

[0007] This invention provides a method for modeling low-frequency electromagnetic transients in ferrite cores. First, an expression for the magnetomotive force of the quasi-static hysteresis field in the ferrite core is established based on a continuous inverse Play hysteresis model. Then, a mathematical model of the residual field and its magnetomotive force in the ferrite core is derived based on loss statistics theory. Subsequently, within the framework of the permeability-capacitance analogy, a method for modeling low-frequency electromagnetic transients in ferrite cores that simultaneously considers the quasi-static hysteresis field and the dynamic residual field is proposed. This method can accurately simulate the electromagnetic transient characteristics of ferrite core samples under sinusoidal rectangular wave excitation with different duty cycles, which is of great significance for improving the overall performance of the power electronic conversion system to which it belongs.

[0008] The technical solution adopted in this invention is as follows: A method for modeling low-frequency electromagnetic transients in a ferrite core, comprising: S1: Based on the continuous inverse Play hysteresis model, establish the expression for the quasi-static hysteresis field magnetomotive force of the ferrite core; S2: Based on the loss statistics theory, derive the mathematical model of the residual field and magnetomotive force of the ferrite core; S3: Based on the relationship between magnetomotive force and magnetic field strength, construct an expression for the total magnetomotive force in the low-frequency range of the ferrite core; S4: Using the magnetic permeability-capacitance analogy method, and through a gyroscope, the coupling equations of the ferrite core circuit and the magnetic circuit are obtained; S5: The residual field parameters are calculated using the least squares method, and the parameters of the continuous inverse Play hysteresis model are extracted. Combined with the total magnetomotive force expression in S3 and the coupling equation in S4, the electromagnetic transient model of the ferrite core at low and medium frequencies is obtained.

[0009] In S1, the expression for the quasi-static hysteresis magnetomotive force is: ; in: ; ; In the above formula: F hy , H hy These are the magnetomotive force of the hysteresis field and the hysteresis field, respectively. l , BIndicates the magnetic circuit length and magnetic flux density; h i It is a shape function; p i , p i 0 These represent the Play operator at the current time step and the Play operator at the previous time step, respectively. This represents the magnetic flux density value as a function of time. ζ i For operator threshold, ζ i =( i -1) B max / M ,in, B max Indicates saturation magnetic flux density; M This indicates the number of Play operators.

[0010] In S2, research confirms, as recorded in the literature (Dobák S, Beatrice C, Tsakaloudi V, et al. Magnetic losses in soft ferrites[J]. Magnetochemistry, 2022, 8: 60-86.), the velocity of the 180° magnetic domain walls inside a non-conductive ferrite single crystal. satisfy: ; μ 0 represents the permeability of free space; M s , B s , H c These are the saturation magnetization, saturation magnetic flux density, and their local coercive field of the ferrite, respectively. H a The strength of the applied magnetic field; β w Indicates the spin damping coefficient; Then apply an external magnetic field strength H a Subtract the coercive field of the 180° magnetic domain wall inside the single crystal H c This is equivalent to the mesoscopic eddy current field of the 180° magnetic domain wall inside its ferrite single crystal. H W ,Right now: .

[0011] Therefore, the above equation is equivalent to: (8); Furthermore, STL (Statistical Theory of Losses) shows that, under certain simplifying assumptions, the rate of change of magnetic flux d Φ / d t With domain wall velocity The following expression applies between them: (9); In equation (9): d This represents the thickness of the region where the magnetic domain walls move; for ferrite, its non-conductive single crystal can be considered as this moving region; therefore, it is possible to... d The average grain size of all single crystals in the ferrite core is < d >; Then, by combining equations (8) and (9), the velocity of the magnetic domain walls can be eliminated. v w That is, it is possible to obtain the mesoscopic eddy current field of the 180° domain walls inside the ferrite single crystal. H W expression: (10).

[0012] In formula (10): This represents the mesoscopic eddy current field at the 180° domain wall inside a ferrite single crystal.

[0013] In S2, based on STL (Statistical Theory of Losses), the equivalent residual field of the lumped parameters of the ferrite core can be obtained. H exc Its 180° domain wall mesoscopic vortex field H W The relationship is as follows: (11).

[0014] In equation (11): Indicates the remaining field; Indicates the number of magnets.

[0015] Furthermore, for non-good conductor magnetic materials such as ferrites, the residual field H exc With the number of magnets n They satisfy an exponential function relationship: (12).

[0016] In equation (9): This indicates that the number of magnets and the residual field have a power-law relationship, with the power being 1. α proportionality coefficient k With ferrite magnetic flux density peak Bp Related; Next, by combining equations (11) and (12), the number of magnets is eliminated. n And substitute equation (10) into the elimination n In the subsequent formula, the residual field of the ferrite core is finally obtained. H exc The specific expression is: (13); Furthermore, the residual magnetomotive force of the ferrite core can be derived. F exc : (14); In S3, according to STL (Statistical Theory of Losses), the applied magnetic field strength can be divided into quasi-static hysteresis fields. H hy Macroscopic eddy field H cl and the remaining fields H exc For low- to mid-frequency ferrite cores with excitation frequencies ≤500kHz, the low conductivity results in weak macroscopic eddy currents, thus limiting the eddy current field in practical applications. H cl Negligible; applied magnetic field strength H a It can represent: (15); Multiply both sides of equation (15) by the magnetic circuit length. l Alternatively, by directly adding equation (4) and equation (14), we get: (16); In equation (13): F t It represents the total magnetomotive force of the ferrite core.

[0017] In S4, in the permeability-capacitance analogy method, the following coupling equation is satisfied between the magnetic circuit side and the circuit side: (17); (18); In the above formula, Indicates the rate of change of magnetic flux in the magnetic core; F It is a magnetomotive force; u , i These are voltage and current, respectively; N , H This indicates the number of turns in the winding and the magnetic field strength.

[0018] In step S5, to extract the residual field parameters, the formula for the residual loss of the ferrite core sample under sinusoidal excitation was first derived: (19); In equation (19): Indicates remaining loss; S This represents the cross-sectional area of ​​the magnetic core. f , T Indicates frequency and period.

[0019] Next, take the natural logarithm of both sides of equation (19): (20); in: (twenty one); After the above operations, equation (19) is transformed into a linear form as shown in equation (20). y = A + Bx ,in: y =ln W exc , x =ln f , B =1 / (1+ α ).

[0020] Then, based on the difference between the measured total loss and the measured quasi-static hysteresis loss, the residual loss value of the ferrite core is obtained. Subsequently, based on the relationship between the above equation (20) and the frequency, the residual field parameters are determined using the least squares method. k , α ; Extracting parameters related to remaining loss, the specific extraction process is as follows: 1) First, select four peak magnetic flux density points of the sample under sinusoidal excitation. Here, we select... B p =0.1, 0.15, 0.2, 0.25T; 2) Select four frequency points under each peak magnetic flux density, obtain the corresponding measured loss, and then subtract the measured hysteresis loss under quasi-static conditions from the value to obtain the corresponding residual loss value; 3) Under each peak magnetic flux density, the slope can be obtained by using the relationship between the residual loss and frequency described by the above equation (20) and fitting it based on the least squares method. B The value is then used to determine the corresponding magnetic flux density. α value; 4) Finally, the intercept expression is used to determine the magnetic flux density under different magnetic flux density conditions. k Value. Given... α This is a material parameter, and the value is obtained from four sets of magnetic flux density. αThe average value is used to minimize the global prediction error.

[0021] For the continuous inverse Play model, only three static symmetric hysteresis loops under high, medium and low magnetic flux density are needed, and its parameters can be quickly identified based on the numerical generation method of first-order gyroscopic curves and genetic algorithm.

[0022] Introducing measured hysteresis loss W h and coercivity H c The mean squared error is defined as the objective function OF: (twenty two); in, (twenty three); (twenty four); In the above formula, W h 'and H c '' represents the simulated hysteresis loss and coercivity, respectively; hysteresis loss and coercivity are used to consider the simulation accuracy at both the overall and local critical points of the model; through the above operations, the accuracy of extracting the optimal parameters can be evaluated, thereby identifying the parameters of the continuous inverse Play model. a i,j ,in, a i,j In the continuous inverse Play model, the first element representing the shape function is... i The th polynomial in the ... j Each monomial coefficient.

[0023] Based on the extracted parameters, the total magnetomotive force expression (16), and the circuit and magnetic circuit coupling equations (17) and (18), a low-frequency electromagnetic transient model of a ferrite core can be constructed within the magnetic permeability-capacitance analogy framework.

[0024] Using the underlying modules and language of PLECS software, an electromagnetic transient model of a ferrite core at low and medium frequencies was built.

[0025] Based on the total magnetomotive force of the ferrite core F t Expression (16) uses devices such as magnetomotive force table, magnetic flux table, and controlled magnetomotive force source in the Magnetic module library of PLECS software to establish its magnetic circuit part; the circuit part is constructed using devices such as voltage source, ammeter, and voltmeter in the Electrical module library; the two parts are coupled through winding (rotator) to realize the coupling of electrical and magnetic circuits.

[0026] According to the formula: ; The total magnetomotive force of the magnetic circuit was constructed in PLECS. Then, within the magnetic permeability-capacitance analogy framework, a gyroscope was used to connect the electric and magnetic circuits, ultimately obtaining a low-frequency electromagnetic transient model of the ferrite core that simultaneously considers the quasi-static hysteresis field and the dynamic residual field.

[0027] The specific process is as follows: The residual field magnetomotive force is given by the equation: ; It can be seen that, through the rate of change of magnetic flux d Φ / d t Controlled magnetomotive force representation; The magnetomotive force of the hysteresis field is given by the following formula: ; It can be seen that in a magnetic circuit, it can be encapsulated as a sub-module to describe the hysteresis field magnetomotive force, and then coupled through a gyroscope.

[0028] A low-frequency electromagnetic transient model for a ferrite core includes the following modules: Magnetomotive force calculation module for magnetic core hysteresis field: Based on the continuous inverse Play model, the magnetomotive force of the magnetic core hysteresis field is calculated; The core residual field magnetomotive force calculation module: Based on STL, the expression of the low-frequency residual field in the ferrite core is derived, and then the residual field magnetomotive force components are obtained; The total magnetomotive force calculation module for the magnetic core: Based on the relationship between magnetic field strength and magnetomotive force, the expression for the total magnetomotive force that simultaneously considers the quasi-static hysteresis field and the dynamic residual field is obtained; and using the magnetic permeability-capacitance analogy method, the coupling equations of the ferrite core circuit and the magnetic circuit are obtained through the gyroscope. Ferrite core electromagnetic transient calculation model module: By using the circuit and magnetic circuit coupling equations to establish the relationship between the two, the electromagnetic transient characteristics of the ferrite core can be obtained.

[0029] This invention provides a method for modeling low-frequency electromagnetic transients in ferrite cores, with the following technical advantages: 1) This invention obtains the quasi-static hysteresis magnetomotive force of ferrite core through the continuous inverse Play model, and then derives the mathematical model of its residual field and residual field magnetomotive force based on STL. Furthermore, within the framework of the permeability-capacitance analogy method, a method for modeling the low-frequency electromagnetic transients of ferrite core that simultaneously considers the quasi-static hysteresis field and the dynamic residual field is obtained, which solves the problem of the lack of a method for modeling the low-frequency (≤500kHz) electromagnetic transients of ferrite core in the prior art.

[0030] 2) The method of the present invention can accurately simulate the electromagnetic transient characteristics of ferrite cores under sinusoidal, square, and rectangular wave excitation with arbitrary duty cycle, and the core loss error under sinusoidal excitation is only 12.91%, providing a solid theoretical basis for the optimized design of its converter and the evaluation of the energy transmission efficiency of magnetic components. Attached Figure Description

[0031] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments: Figure 1 This is a schematic diagram of a low-frequency electromagnetic transient modeling method for a ferrite core, as an example.

[0032] Figure 2 This is a schematic diagram of the 180° magnetic domain wall movement inside the ferrite single crystal in the embodiment.

[0033] Figure 3 This is a schematic diagram of the low-frequency electromagnetic transient model in the ferrite core of the embodiment.

[0034] Figure 4 The hysteresis loop is the simulation result of the low-frequency electromagnetic transient model in the ferrite core under sinusoidal excitation with a magnetic flux density peak of 0.1T in the embodiment.

[0035] Figure 5 The primary side current curve is simulated by a low-frequency electromagnetic transient model in a ferrite core under sinusoidal excitation at a frequency of 100kHz in the embodiment.

[0036] Figure 6 The hysteresis loop is the simulation result of the low-frequency electromagnetic transient model in the ferrite core under square wave excitation with a magnetic flux density peak of 0.1T in the embodiment.

[0037] Figure 7 The primary side current curve is simulated by the low-frequency electromagnetic transient model of the ferrite core under square wave excitation at a frequency of 100kHz in the embodiment.

[0038] Figure 8 For the example f =100kHz D Hysteresis loop simulated by low-frequency electromagnetic transient model in ferrite core under rectangular wave excitation of 0.3.

[0039] Figure 9 For the example f =100kHz D The primary side current curve simulated by a low-frequency electromagnetic transient model in a ferrite core under rectangular wave excitation of 0.3. Detailed Implementation

[0040] like Figure 1 As shown, a method for modeling low-frequency electromagnetic transients in a ferrite core includes the following steps: Step 1: Based on the continuous inverse Play model, the expression for the hysteresis field is obtained, and then the magnetomotive force of the hysteresis field of the ferrite core is obtained, as follows: According to the Play hysteresis model proposed by foreign scholars, each Play operator can be expressed as a function of magnetic flux density. B Related monotonic functions: (1); In equation (1), p i , p i 0 This represents the Play operator at the current time step compared to the Play operator at the previous time step. ζ i Indicates the operator threshold. ζ i =( i -1) B max / M ,in, B max Indicates saturation magnetic flux density; M Indicates the number of Play operators; Based on the Play operator mentioned above, superimposed M The shape function corresponding to each operator h i The magnetic field strength of the corresponding material can then be obtained. H hy ( t ): (2); The shape function of the continuous inverse Play model can be represented as a polynomial consisting of a superposition of several odd-degree monomials: (3); In the formula, a i,j Indicates the first i The th polynomial in the ... j Each monomial coefficient; D i Indicates the first i The number of terms in a polynomial; Further, the magnetomotive force of the hysteresis field of the ferrite core was obtained. F hy : (4); In the formula, l This represents the length of the magnetic circuit.

[0041] Step 2: Based on the loss statistics theory, the expressions for the residual field and magnetomotive force of the ferrite core are derived as follows: Existing research has demonstrated the velocity of the 180° magnetic domain walls within a non-conductive ferrite single crystal. Satisfy the following expression: (5); For ferrites, the magnetic field strength H Typically much smaller than the internal magnetization. M Therefore, its magnetic flux density B = μ 0( H + M )≈ μ 0 M Therefore, equation (5) above is transformed into: (6); in, (7); In the formula, M s , B s , H c These are the saturation magnetization, saturation magnetic flux density, and their local coercive field of the ferrite, respectively. H a The strength of the applied magnetic field; β w , γ, α LL These are the spin damping coefficient, gyromagnetic ratio, and damping constant, respectively. η , μ 0 represents the domain wall width and the vacuum permeability, respectively.

[0042] Furthermore, external application site H a Subtract the coercive field of the 180° magnetic domain wall inside the single crystal H c This is equivalent to its dynamic field. However, in the low-to-mid-frequency range, the macroscopic eddy current field of the ferrite core can be ignored. Therefore, the total dynamic field is only the mesoscopic eddy current field of the 180° magnetic domain wall. H W Equation (6) can be equivalent to: (8); If we assume that the 180° magnetic domain walls inside the ferrite single crystal have a thickness of... d The interior of a cuboid region of infinite length and infinite width along x Rigid body motion along the axial direction, such as Figure 2 As shown; when the internal structure and thickness of the domain walls are ignored, the rate of change d of the magnetic flux in this cuboid region is... Φ / d t With domain wall velocity v w The following expression applies between them: (9); In the formula, d This indicates the thickness of the cuboid region; for ferrite, the thickness of this region can be... d The average grain size of all single crystals in the ferrite core is < d >; Eliminating domain wall velocity by combining equations (8) and (9) v w You can get H W Specific expression: (10); Next, based on STL, the equivalent residual field of the lumped parameters of the ferrite core is calculated. H exc Its 180° domain wall mesoscopic vortex field H W satisfy: (11); In the formula, n This indicates the number of magnets; however, for non-good conductor magnetic materials such as ferrites... H exc ( n The relationship between them also satisfies an exponential function: (12); Among them, the proportionality coefficient k With ferrite magnetic flux density peak B p Related; α Material parameters; Then, by combining equations (11) and (12), the number of magnets can be eliminated. n Substituting equation (10) into the equation, the residual field of the ferrite core can be derived. H exc expression: (13); Then the residual magnetomotive force of the ferrite core is obtained. F exc : (14); Step 3: Based on the relationship between magnetomotive force and magnetic field strength, or by superimposing the magnetomotive forces corresponding to the above two steps, obtain the expression for the total magnetomotive force in the low-frequency range of the ferrite core; use the magnetic permeability-capacitance analogy method to obtain the coupling equation between the circuit and the magnetic circuit. According to STL, the applied magnetic field strength can be divided into quasi-static hysteresis fields. H hy Macroscopic eddy field H cl and the remaining fields H exc For ferrite cores with excitation frequencies ≤500kHz, the low conductivity results in weak macroscopic eddy currents, thus limiting the eddy current field in practical applications. H cl Negligible; that is, the strength of the applied magnetic field. H a It can be represented as: (15); Multiply both sides of equation (15) by the magnetic circuit length. l Alternatively, equation (4) and equation (14) can be directly added together to obtain the total magnetomotive force. F t expression: (16); Furthermore, in the permeability-capacitance analogy method, the variables on the magnetic circuit and circuit sides satisfy the following relationship: (17); (18); In the formula, F It is a magnetomotive force; u , i These are voltage and current, respectively; N , H This indicates the number of turns in the winding and the magnetic field strength.

[0043] Step 4: Calculate the remaining field parameters using the least squares method and extract the parameters of the continuous inverse Play model. Combine the total magnetomotive force expression and coupling equation from Step 3 to obtain the low-frequency electromagnetic transient model in the ferrite core. To extract the residual field parameters, the formula for the residual loss of the ferrite core sample under sinusoidal excitation was first derived: (19); In the formula, S This represents the cross-sectional area of ​​the magnetic core. f , T Indicates frequency and period; Next, take the natural logarithm of both sides of equation (19): (20); in, (twenty one); After the above operations, equation (19) is transformed into a linear form as shown in equation (20). y = A + Bx ,in y =ln W exc , x =ln f , B =1 / (1+ α The specific extraction process is as follows: 1) First, select four peak magnetic flux density points of the sample under sinusoidal excitation. Here, we select... B p =0.1, 0.15, 0.2, 0.25T; 2) Select four frequency points under each peak magnetic flux density, obtain the corresponding measured loss, and then subtract the measured hysteresis loss under quasi-static conditions from the value to obtain the corresponding residual loss value. 3) Under each peak magnetic flux density, the slope can be obtained by using the relationship between the residual loss and frequency described by equation (20) above and fitting it using the least squares method. B The value is then used to determine the corresponding magnetic flux density. α value; 4) Finally, the intercept expression is used to determine the magnetic flux density under different magnetic flux density conditions. k Value. Given... α This is a material parameter, and the value is obtained from four sets of magnetic flux density. α The average value is used to minimize the global prediction error.

[0044] Furthermore, the parameter extraction process of the continuous inverse Play model is described in the reference: Liu R, Lu Y. Inverse Rheological Hysteresis Model and Its Efficient Parameter Identification Method[J]. IEEE Transactions on Magnetics, 2024, 60(3): 1-4. Art no. 7300204.

[0045] This extraction method requires only three static symmetrical hysteresis loops under high, medium, and low magnetic flux density conditions, and can be rapidly extracted based on a first-order gyroscopic curve numerical generation method and a genetic algorithm; it also incorporates measured hysteresis loss... W h and coercivity H c The mean squared error is defined as the objective function OF: (twenty two); in, (twenty three); (twenty four); In the formula, W h 'and H c ′ represents the simulated hysteresis loss and coercivity, respectively; the simulation accuracy at key points of the model, both overall and locally, is considered using hysteresis loss and coercivity; through the above operations, the accuracy of extracting the optimal parameters can be evaluated, and the parameters of the continuous inverse Play model can be identified.

[0046] Based on the extracted parameters, the total magnetomotive force expression (16), and the circuit and magnetic circuit coupling equations (17) and (18), a low-frequency electromagnetic transient model of a ferrite core can be constructed within the magnetic permeability-capacitance analogy framework.

[0047] Step 5: Use the PLECS software's underlying modules and programming language to build a low-frequency electromagnetic transient model of the ferrite core; Based on the total magnetomotive force of the ferrite core F t Expression (16) uses magnetomotive force meters, flux meters, and controlled magnetomotive force sources from the Magnetic module library in PLECS software to establish its magnetic circuit part; the circuit part is constructed using voltage sources, ammeters, voltmeters, and other devices from the Electrical module library; the two parts are coupled through windings (rotators) to achieve electrical and magnetic circuit coupling, such as... Figure 3 As shown.

[0048] The specific implementation process of the magnetomotive force model is as follows: The rate of change of magnetic flux d Φ / d t By inputting the data into the C-Script module compiled by equation (14), the residual magnetomotive force of the ferrite core can be obtained. F exc ( t ); while the hysteresis magnetomotive force of the ferrite core F hy The solution is obtained through the following process: ① The rate of change of magnetic flux d Φ / d t The signal is transmitted to the gain unit g1 (the gain is the cross-sectional area of ​​the magnetic core). S The reciprocal of the magnetic flux density is used to obtain the rate of change d. B / d t Then, the integrator is used to obtain the magnetic flux density value. B ( t ); ② B ( tThe input is fed into a C-Script module compiled using a continuous inverse Play model, which then outputs the hysteresis field of the ferrite core. H hy ( t ); ③ Next, use the gain converter g2 (the gain is the length of the magnetic flux path) l ) to obtain the hysteresis magnetomotive force F hy It should be noted that the above-mentioned hysteresis field magnetomotive force can be... F hy The solver module is encapsulated as a magnetic circuit submodule, such as Figure 3 As shown in the blue dashed box.

[0049] To verify the accuracy of the low-frequency electromagnetic transient modeling method for ferrite cores proposed in this invention, the dynamic hysteresis loop and primary winding current of ferrite core samples under sinusoidal and rectangular wave excitation with different duty cycles were simulated; and these simulation results were compared with measured data, such as... Figures 4-9 As shown. By Figures 4-9 It can be seen that its electromagnetic transient characteristics are in high agreement with the measured values, and the core loss error under sinusoidal excitation is only 12.91% at most.

[0050] The system described above for a low-frequency electromagnetic transient modeling method in a ferrite core includes: Magnetomotive force calculation module for magnetic core hysteresis field: Based on the continuous inverse Play model, the magnetomotive force of the magnetic core hysteresis field is calculated; The core residual field magnetomotive force calculation module: Based on STL, the expression of the low-frequency residual field in the ferrite core is derived, and then the residual field magnetomotive force components are obtained; The total magnetomotive force calculation module for the magnetic core: Based on the relationship between magnetic field strength and magnetomotive force, the expression for the total magnetomotive force that simultaneously considers the quasi-static hysteresis field and the dynamic residual field is obtained; and using the magnetic permeability-capacitance analogy method, the coupling equations of the ferrite core circuit and the magnetic circuit are obtained through the gyroscope. Ferrite core electromagnetic transient calculation model module: By using the circuit and magnetic circuit coupling equations to establish the relationship between the two, the electromagnetic transient characteristics of the ferrite core can be obtained.

Claims

1. A method for modeling low-frequency electromagnetic transients in a ferrite core, characterized in that... include: S1: Based on the continuous inverse Play hysteresis model, establish the expression for the quasi-static hysteresis field magnetomotive force of the ferrite core; S2: Based on the loss statistics theory, derive the mathematical model of the residual field and magnetomotive force of the ferrite core; S3: Based on the relationship between magnetomotive force and magnetic field strength, construct an expression for the total magnetomotive force in the low-frequency range of the ferrite core; S4: Using the magnetic permeability-capacitance analogy method, the coupling equations of the ferrite core circuit and the magnetic circuit are obtained; S5: The residual field parameters are calculated using the least squares method, and the parameters of the continuous inverse Play hysteresis model are extracted. Combined with the total magnetomotive force expression in S3 and the coupling equation in S4, the electromagnetic transient model of the ferrite core at low and medium frequencies is obtained.

2. The method for modeling low-frequency electromagnetic transients in a ferrite core according to claim 1, characterized in that: In S1, the expression for the quasi-static hysteresis magnetomotive force is: ； in: ； ； In the above formula: F hy , H hy These are the magnetomotive force of the hysteresis field and the hysteresis field, respectively. l , B Indicates the magnetic circuit length and magnetic flux density; h i It is a shape function; p i , p i 0 These represent the Play operator at the current time step and the Play operator at the previous time step, respectively. This represents the magnetic flux density value as a function of time. ζ i For operator threshold, ζ i =( i -1) B max / M ,in, B max Indicates saturation magnetic flux density; M This indicates the number of Play operators.

3. The method for modeling a low-frequency electromagnetic transient model in a ferrite core according to claim 2, characterized in that: In S2, the velocity of the 180° magnetic domain walls inside the ferrite non-conductive single crystal satisfy: ； μ 0 represents the permeability of free space; M s , B s , H c These are the saturation magnetization, saturation magnetic flux density, and their local coercive field of the ferrite, respectively. H a The strength of the applied magnetic field; β w Indicates the spin damping coefficient; Then apply an external magnetic field strength H a Subtract the coercive field of the 180° magnetic domain wall inside the single crystal H c This is equivalent to the mesoscopic eddy current field of the 180° magnetic domain wall inside its ferrite single crystal. H W ,Right now: ; Therefore, the above equation is equivalent to: （8）； In addition, the rate of change of magnetic flux d Φ / d t With domain wall velocity The following expression applies between them: （9）； In equation (9): d This represents the thickness of the region where the magnetic domain walls move; for ferrite, its non-conductive single crystal can be considered as this moving region; therefore, it is possible to... d The average grain size of all single crystals in the ferrite core is < d >; Then, by combining equations (8) and (9), the velocity of the magnetic domain walls can be eliminated. v w That is, it is possible to obtain the mesoscopic eddy current field of the 180° domain walls inside the ferrite single crystal. H W expression: （10）； In formula (10): This represents the mesoscopic eddy current field at the 180° domain wall inside a ferrite single crystal.

4. The method for modeling low-frequency electromagnetic transients in a ferrite core according to claim 3, characterized in that: In S2, based on STL (Statistical Theory of Losses), the equivalent residual field of the lumped parameters of the ferrite core can be obtained. H exc Its 180° domain wall mesoscopic vortex field H W The relationship is as follows: （11）； In equation (11): Indicates the remaining field; Indicates the number of magnets; Furthermore, for non-good conductor magnetic materials such as ferrites, the residual field H exc With the number of magnets n They satisfy an exponential function relationship: （12）； In equation (9): This indicates that the number of magnets and the residual field have a power-law relationship, with the power being 1. α ; proportionality coefficient k With ferrite magnetic flux density peak B p Related; then Combine equations (11) and (12) to eliminate the number of magnets. n And substitute equation (10) into the elimination n In the subsequent formula, the residual field of the ferrite core is finally obtained. H exc The specific expression is: （13）； Furthermore, the residual magnetomotive force of the ferrite core can be derived. F exc : （14）。 5. The method for modeling a low-frequency electromagnetic transient model in a ferrite core according to claim 4, characterized in that: In S3, the applied magnetic field strength can be divided into a quasi-static hysteresis field. H hy Macroscopic eddy field H cl and the remaining fields H exc For low- to mid-frequency ferrite cores with excitation frequencies ≤500kHz, the low conductivity results in weak macroscopic eddy currents, thus limiting the eddy current field in practical applications. H cl Negligible; applied magnetic field strength H a It can represent: （15）； Multiply both sides of equation (15) by the magnetic circuit length. l Alternatively, by directly adding equation (4) and equation (14), we get: （16）； In equation (13): F t It represents the total magnetomotive force of the ferrite core.

6. The method for modeling a low-frequency electromagnetic transient model in a ferrite core according to claim 5, characterized in that: In S4, in the permeability-capacitance analogy method, the following coupling equation is satisfied between the magnetic circuit side and the circuit side: （17）； （18）； In the above formula, This represents the rate of change of magnetic flux in the magnetic core; F It is a magnetomotive force; u , i These are voltage and current, respectively; N , H This indicates the number of turns in the winding and the magnetic field strength.

7. The method for modeling a low-frequency electromagnetic transient model in a ferrite core according to claim 6, characterized in that: In step S5, to extract the residual field parameters, the formula for the residual loss of the ferrite core sample under sinusoidal excitation was first derived: （19）； In equation (19): Indicates remaining loss; S This represents the cross-sectional area of ​​the magnetic core. f , T Indicates frequency and period; Next, take the natural logarithm of both sides of equation (19): （20）； in: （21）； After the above operations, equation (19) is transformed into a linear form as shown in equation (20). y = A + Bx ,in: y =ln W exc , x =ln f , B =1 / (1+ α ); Extracting parameters related to remaining loss, the specific extraction process is as follows: 1) First, select four peak magnetic flux density points of the sample under sinusoidal excitation; 2) Select four frequency points under each peak magnetic flux density, obtain the corresponding measured loss, and then subtract the measured hysteresis loss under quasi-static conditions from the value to obtain the corresponding residual loss value. 3) Under each peak magnetic flux density, the slope can be obtained by using the relationship between the residual loss and frequency described by the above equation (20) and fitting it based on the least squares method. B The value is then used to determine the corresponding magnetic flux density. α value; 4) Finally, the intercept expression is used to determine the magnetic flux density under different magnetic flux density conditions. k Value; given α This is a material parameter, and the value is obtained from four sets of magnetic flux density. α The average value is used to minimize the global prediction error.

8. The method for modeling a low-frequency electromagnetic transient model in a ferrite core according to claim 7, characterized in that: Introducing measured hysteresis loss W h and coercivity H c The mean squared error is defined as the objective function OF: （22）； in, （23）； （24）； In the above formula, W h 'and H c '' represents the simulated hysteresis loss and coercivity, respectively; hysteresis loss and coercivity are used to consider the simulation accuracy at both the overall and local critical points of the model; through the above operations, the accuracy of extracting the optimal parameters can be evaluated, thereby identifying the parameters of the continuous inverse Play model. a i,j ,in, a i,j In the continuous inverse Play model, the first element representing the shape function is... i The th polynomial in the ... j Each monomial coefficient; Based on the extracted parameters, the total magnetomotive force expression (16), and the circuit and magnetic circuit coupling equations (17) and (18), a low-frequency electromagnetic transient model of a ferrite core can be constructed within the magnetic permeability-capacitance analogy framework.

9. The method for modeling a low-frequency electromagnetic transient model in a ferrite core according to claim 8, characterized in that: Using the PLECS software's underlying modules and programming language, a low-frequency electromagnetic transient model of a ferrite core was constructed: According to the formula: ； The total magnetomotive force of the magnetic circuit is constructed in PLECS. Then, the electric and magnetic circuits are connected by a gyroscope within the magnetic permeability-capacitance analogy framework. Finally, a low-frequency electromagnetic transient model of the ferrite core that simultaneously considers the quasi-static hysteresis field and the dynamic residual field is obtained. The specific process is as follows: The residual field magnetomotive force is given by the equation: ； It can be seen that, through the rate of change of magnetic flux d Φ / d t The controlled magnetomotive force is represented by the controlled magnetomotive force; The magnetomotive force of the hysteresis field is given by the following formula: ； It can be seen that in a magnetic circuit, it can be encapsulated as a sub-module to describe the hysteresis field magnetomotive force, and then coupled through a gyroscope.

10. A low-frequency electromagnetic transient model in a ferrite core, characterized in that... Includes the following modules: Magnetomotive force calculation module for magnetic core hysteresis field: Based on the continuous inverse Play model, the magnetomotive force of the magnetic core hysteresis field is calculated; The core residual field magnetomotive force calculation module: Based on STL, the expression of the low-frequency residual field in the ferrite core is derived, and then the residual field magnetomotive force components are obtained; The total magnetomotive force calculation module for the magnetic core: Based on the relationship between magnetic field strength and magnetomotive force, the expression for the total magnetomotive force that simultaneously considers the quasi-static hysteresis field and the dynamic residual field is obtained; and using the magnetic permeability-capacitance analogy method, the coupling equations of the ferrite core circuit and the magnetic circuit are obtained through the gyroscope. Ferrite core electromagnetic transient calculation model module: By using the circuit and magnetic circuit coupling equations to establish the relationship between the two, the electromagnetic transient characteristics of the ferrite core can be obtained.

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