A method for calculating core loss of high-frequency transformer considering skin effect

Abstract

The application relates to a high-frequency transformer core loss calculation method considering skin effect, and comprises the following steps: obtaining a magnetic hysteresis loop, calculating the average magnetic flux density and the magnetic field intensity in a period; performing Fourier analysis on the average magnetic flux density, calculating the eddy current magnetic field intensity corresponding to each harmonic, and obtaining the total eddy current magnetic field intensity after superposition; constructing a dynamic J-A magnetic hysteresis model, substituting the total eddy current magnetic field intensity to obtain an improved dynamic J-A model, and identifying the parameters in the improved dynamic J-A model; simulating the magnetic hysteresis loop based on the improved dynamic J-A model, and calculating the unit volume core loss. The application introduces the skin effect and realizes the collaborative modeling of the magnetic hysteresis and the eddy current, significantly improves the authenticity of the magnetic hysteresis loop simulation and the accuracy of the core loss calculation, thereby realizing the reliable prediction of the core loss under the high-frequency non-sinusoidal excitation working condition, and providing an analysis method with more engineering value for the optimized design and performance evaluation of the high-frequency transformer.

Description

Technical Field

[0001] This invention relates to the field of power electronics and magnetic materials technology, and in particular to a method for calculating the core loss of a high-frequency transformer that takes into account the skin effect. Background Technology

[0002] Against the backdrop of rapid development in power electronics technology, high-frequency transformers have become key magnetic components in switching power supplies, electric drive systems for new energy vehicles, and photovoltaic grid-connected devices. Compared with traditional power frequency transformers, high-frequency transformers typically operate in the frequency range of several kilohertz or even higher, and their excitation signals often exhibit non-sinusoidal forms such as rectangular waves and pulse-width modulated waves. Under these operating conditions, the electromagnetic response inside the core material exhibits more complex distribution characteristics, especially the eddy current effect induced by the alternating magnetic field in the conductive magnetic material is significantly enhanced, resulting in a pronounced skin effect and causing the magnetic flux density to be distributed non-uniformly along the cross-section.

[0003] Core loss, a crucial factor affecting the efficiency and thermal performance of high-frequency transformers, is typically composed of hysteresis loss, eddy current loss, and additional losses. To describe hysteresis behavior, various hysteresis modeling methods have been proposed in existing technologies, such as the Preisach model based on statistical theory, the Energetic model based on the principle of energy conservation, and the Jiles-Atherton (JA) model with clearly defined physical parameters. Among these, the JA model, due to its relatively simple structure, fewer parameters, and ease of engineering implementation, has been widely used for modeling the hysteresis characteristics and predicting losses in magnetic materials.

[0004] However, traditional hysteresis models still have certain limitations in application under high-frequency non-sinusoidal excitation conditions. Existing dynamic JA models are usually based on the ideal assumption that the magnetic field and magnetic flux density are uniformly distributed inside the core, failing to fully reflect the electromagnetic field gradient distribution characteristics caused by the skin effect under high-frequency conditions. While this simplification helps reduce model complexity, in practical applications it leads to insufficient characterization of eddy current distribution and its coupling effect with hysteresis behavior, thus affecting the accurate assessment of core losses, especially under high-frequency, strongly nonlinear excitation conditions, where prediction errors are more pronounced.

[0005] Therefore, in view of the problem that the existing technology does not adequately describe the electromagnetic distribution inside the core under high-frequency operating conditions, it is urgent to propose a high-frequency transformer core loss calculation method that can take into account the influence of the skin effect, so as to more accurately reflect the magnetic flux distribution and its dynamic change law, thereby improving the reliability and engineering applicability of the loss prediction results. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to overcome the shortcomings of the prior art and provide a method for calculating the core loss of high-frequency transformers that takes into account the skin effect.

[0007] This invention is achieved through the following technical solution: A method for calculating the core loss of a high-frequency transformer considering the skin effect includes the following steps: S1. Obtain the hysteresis loop and calculate the average magnetic flux density B over one period. av (t) and magnetic field strength H(t); S2. Regarding the average magnetic flux density B av (t) Fourier analysis was used to calculate the eddy current magnetic field strength corresponding to each harmonic, and the total eddy current magnetic field strength H was obtained by superimposing the results. ed (t); S3. Construct a dynamic JA hysteresis model and substitute the total eddy current magnetic field strength H. ed (t) Obtain the improved dynamic JA model and identify the parameters in the improved dynamic JA model; S4. Simulate the hysteresis loop based on the improved dynamic JA model and calculate the core loss per unit volume.

[0008] According to the above technical solution, preferably, step S1 includes: Waveform data of the primary side current i1(t) and secondary side voltage u2(t) of the magnetic ring were collected using a current probe and a voltage probe, respectively. The average magnetic flux density Bav(t) and magnetic field strength H(t) over one period are calculated using the following formulas: , , Where N1 is the number of turns in the primary winding; N2 is the number of turns in the secondary winding; S is the effective cross-sectional area of ​​the core; l e This is the effective magnetic circuit length of the iron core.

[0009] According to the above technical solution, preferably, step S2 includes: The average magnetic flux density B av (t)Fourier decomposition into a superposition of harmonic components; Calculate the equivalent eddy current magnetic field strength H corresponding to each harmonic. ed(n) (t); The eddy current magnetic field strength H corresponding to each harmonic ed(n) (t) superimposed, the total eddy current magnetic field strength H considering the skin effect is obtained. ed (t).

[0010] According to the above technical solution, preferably, in step S2, the average magnetic flux density Bav (t) The Fourier decomposition is a superposition of the harmonic components. , Among them, B n-max and is the amplitude and phase of the nth harmonic magnetic flux density, m is the maximum harmonic, and f is the fundamental frequency.

[0011] According to the above technical solution, preferably, in step S2, when calculating the eddy current magnetic field strength corresponding to each harmonic, under sinusoidal excitation, for a one-dimensional eddy current problem, the magnetic field strength H... hy The boundary conditions are Then the surface magnetic field strength H a for: , , Where k is a dimensionless constant, and H max ω is the amplitude of the surface magnetic field intensity, ω is the angular frequency, and d is the thickness of the magnetic ring. The expression for a one-dimensional vortex field is: , Based on the magnetic constitutive equation, the expression for magnetic flux density is derived: , , , Derive H a With H hy Relationship: , Under sinusoidal excitation, the expression for the eddy current field is: , Combining the above equations, we can derive the expression for the equivalent eddy current magnetic field strength corresponding to the nth harmonic: , in, , , .

[0012] According to the above technical solution, preferably, in step S2, the total eddy current magnetic field strength H ed The expression for (t) is: .

[0013] According to the above technical solution, preferably, in step S3, the static JA hysteresis model is: , Where M is the total magnetization, M an δ is the hysteresis-free magnetization; α is the average field parameter of the coupling within the magnetic domain; c is the reversible magnetization coefficient; δ M The limiting coefficients are introduced to prevent non-physical interpretations; δ is the direction coefficient; k is the pinning coefficient; The hysteresis-free magnetization of a soft magnetic material can be expressed as: , Among them, M s Let be the saturation magnetization; a be the shape parameter of the hysteresis-free magnetization curve; and He be the effective magnetic field strength, expressed as: , Where H is the applied magnetic field strength; α is the average field parameter of the coupling within the magnetic domain; and M is the total magnetization. δ、δ M They are represented as follows: , , The total core loss is broken down into hysteresis loss, eddy current loss, and residual loss: , Based on the field separation method, the total loss can be further expressed as: , Where W is the total loss; W hys For hysteresis loss; W ed For eddy current losses; W ex For residual losses, consider the effective hysteresis magnetic field H of the dynamic field. dyn for: , Neglecting residual losses, the effective hysteresis magnetic field H of the dynamic field will be considered. dyn The expression simplifies to: , The expression for the dynamic JA hysteresis model is: , Then the total eddy current magnetic field strength H ed (t) Substitute into the dynamic JA hysteresis model to obtain the improved dynamic JA model.

[0014] According to the above technical solution, preferably, in step S3, the PSO particle swarm optimization algorithm is used, with the root mean square error of the magnetic flux density waveform as the objective function, to identify the five parameters α, a, c, k, and M of the improved dynamic JA model. s .

[0015] According to the above technical solution, preferably, in step S4, the core loss per unit volume is calculated based on the improved dynamic JA model to simulate the hysteresis loop: , Where P is the core loss, V is the magnetic ring volume, and f is the frequency.

[0016] The beneficial effects of this invention are: This invention combines Fourier decomposition with magnetic constitutive relations to introduce an equivalent magnetic field composed of eddy current magnetic fields corresponding to each harmonic in the dynamic JA hysteresis model, thereby achieving an explicit characterization of the skin effect. This overcomes the limitations of traditional models based on the assumption of uniform magnetic flux density distribution and effectively solves the problem of uneven magnetic flux distribution inside the iron core under high-frequency conditions.

[0017] Meanwhile, this invention can decompose complex excitations into multi-frequency components and analyze their eddy current responses one by one for typical non-sinusoidal excitation forms such as rectangular waves and PWM waves. Then, it can accurately reconstruct the overall electromagnetic behavior by superposition, so that the model has good adaptability under different frequencies, different duty cycles and different soft magnetic materials.

[0018] In addition, by coupling the skin effect with the hysteresis characteristics in the model, the realism of the hysteresis loop simulation and the accuracy of the core loss calculation are significantly improved. This enables reliable prediction of core loss under high-frequency non-sinusoidal excitation conditions, providing a more valuable analytical tool for the optimization design and performance evaluation of high-frequency transformers. Attached Figure Description

[0019] Figure 1 This is a waveform diagram of voltage and magnetic flux density under rectangular wave excitation according to the present invention.

[0020] Figure 2 This is a schematic diagram of the vortex field of the present invention.

[0021] Figure 3 This is a comparison diagram of the hysteresis loops of the improved dynamic JA model in this invention.

[0022] Figure 4 This is a comparison chart of the errors of traditional dynamic JA and improved dynamic JA under rectangular wave excitation with f=5kHz and D=1 in this invention.

[0023] Figure 5 This is a schematic diagram illustrating the improvement of JA error in the amorphous magnetic ring under rectangular wave excitation with D=1 in this invention.

[0024] Figure 6 The amorphous magnetic ring in this invention is in B m=0.6T, an error diagram of the improved JA model under different duty cycles and frequencies.

[0025] Figure 7 This is a comparison diagram of amorphous and silicon steel magnetic rings in this invention. Detailed Implementation

[0026] To enable those skilled in the art to better understand the technical solutions of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and preferred embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0027] Example 1: The present invention includes the following steps: S1. Obtain the hysteresis loop and calculate the average magnetic flux density B over one period. av (t) and magnetic field strength H(t).

[0028] Specifically, waveform data of the primary side current i1(t) and secondary side voltage u2(t) of the magnetic ring are collected using current probes and voltage probes, respectively. The average magnetic flux density Bav(t) and magnetic field strength H(t) over one period are calculated using Faraday's law of electromagnetic induction and Ampere's circuital law. The calculation formulas are as follows: , , Where N1 is the number of turns in the primary winding; N2 is the number of turns in the secondary winding; S is the effective cross-sectional area of ​​the core; l e This is the effective magnetic circuit length of the iron core.

[0029] S2. Regarding the average magnetic flux density B av (t) Fourier analysis was used to calculate the eddy current magnetic field strength corresponding to each harmonic, and the total eddy current magnetic field strength H was obtained by superimposing the results. ed (t).

[0030] First, the average magnetic flux density B av (t) The Fourier decomposition is a superposition of the harmonic components: , Among them, B n-max and is the amplitude and phase of the nth harmonic magnetic flux density, m is the maximum harmonic, and f is the fundamental frequency.

[0031] Then, calculate the equivalent eddy current magnetic field strength H corresponding to each harmonic. ed(n) (t), under sinusoidal excitation, for a one-dimensional eddy current problem, the boundary condition for the magnetic field strength Hhy is: Then the surface magnetic field strength Ha is: , , , , Where, k, is a dimensionless constant, where Hmax is the amplitude of the surface magnetic field intensity, ω is the angular frequency, d is the thickness of the magnetic ring, and μav is the average value of the permeability in the unsaturated region under quasi-static conditions.

[0032] The expression for a one-dimensional vortex field is: , Based on the magnetic constitutive equation (B=μ) av H hy ), and derive the expression for magnetic flux density: , , , Derive H a With H hy Relationship: , Under sinusoidal excitation, the expression for the eddy current field is: , Combining the above equations, we can derive the expression for the equivalent eddy current magnetic field strength corresponding to the nth harmonic: , in, , , .

[0033] Then, the eddy current magnetic field strength H corresponding to each harmonic is... ed(n) (t) superimposed, the total eddy current magnetic field strength H considering the skin effect is obtained. ed (t): .

[0034] This application transforms complex excitation into a superposition of multiple harmonics by performing Fourier decomposition on the average magnetic flux density under non-sinusoidal excitation. Eddy current magnetic field models are then established for each harmonic, and the total eddy current magnetic field intensity is obtained by superposition. This enables a quantitative characterization of the skin effect under high-frequency operating conditions. Compared to the simplified assumption of uniform magnetic flux density distribution in traditional methods, this scheme can more realistically reflect the spatial distribution characteristics of the electromagnetic field inside the iron core, thereby improving the model's ability to describe actual operating conditions.

[0035] S3. Construct a dynamic JA hysteresis model and substitute the total eddy current magnetic field strength H. ed (t) Obtain the improved dynamic JA model and identify the parameters in the improved dynamic JA model.

[0036] The static JA hysteresis model is: , Where M is the total magnetization, M an δ is the hysteresis-free magnetization; α is the average field parameter of the coupling within the magnetic domain; c is the reversible magnetization coefficient; δ M The limiting coefficients are introduced to prevent non-physical interpretations; δ is the direction coefficient; k is the pinning coefficient; The hysteresis-free magnetization of a soft magnetic material can be expressed as: , Among them, M s Let be the saturation magnetization; a be the shape parameter of the hysteresis-free magnetization curve; and He be the effective magnetic field strength, expressed as: , Where H is the applied magnetic field strength; α is the average field parameter of the coupling within the magnetic domain; and M is the total magnetization. δ、δ M They are represented as follows: , , According to Bertotti's loss separation theory, the total core loss can be decomposed into hysteresis loss, eddy current loss, and residual loss: , Based on the field separation method, the total loss can be further expressed as: , Where W is the total loss; W hys For hysteresis loss; W ed For eddy current losses; W ex For residual losses, consider the effective hysteresis magnetic field H of the dynamic field. dyn for: , Considering that under high-frequency excitation, eddy current loss dominates the dynamic losses, and the residual losses caused by domain wall bending are negligible, the effective hysteresis magnetic field H of the dynamic field will be considered. dyn The expression simplifies to: , The expression for the dynamic JA hysteresis model is: , Then the total eddy current magnetic field strength H ed (t) Substituting the values ​​into the dynamic JA hysteresis model yields the improved dynamic JA model. The technical solution of this application introduces the constructed total eddy current magnetic field into the dynamic JA hysteresis model, corrects the effective magnetic field, and establishes a coupled model that considers both hysteresis characteristics and eddy current effects. This allows the evolution of the hysteresis loop to reflect the physical mechanism under high-frequency dynamic conditions. This improved model not only enhances the ability to characterize the nonlinear behavior of magnetic materials but also significantly improves the accuracy of core loss prediction under high-frequency, non-sinusoidal excitation conditions.

[0037] Using the Particle Swarm Optimization (PSO) algorithm, with the root mean square error of the magnetic flux density waveform as the objective function, the five parameters α, a, c, k, and M of the improved dynamic JA model are identified. s .

[0038] The core mathematical expression of the Particle Swarm Optimization (PSO) algorithm is as follows:

[0039]

[0040] In the formula, x i : Particle position, v i Particle velocity; p i : Individual optimal position, g: Global optimal position; ω: Inertia weight, c1, c2: Learning factors, r1, r2∈[0,1] random numbers.

[0041] S4. Based on the improved dynamic JA model, simulate the hysteresis loop and calculate the core loss per unit volume: , Where P is the core loss, V is the magnetic ring volume, and f is the frequency.

[0042] The improved dynamic model is used to numerically simulate the hysteresis loop and calculate the unit volume loss, which makes the evaluation process of core loss have good consistency and repeatability, and helps to provide a more reliable theoretical basis for the design optimization and performance evaluation of high-frequency transformers.

[0043] Example 2: like Figures 4-6 As shown, a 1K101 amorphous magnetic ring is used at a frequency f=5kHz, a duty cycle D=1, and a magnetic flux density amplitude B. mUnder the condition of 0.4T, the core loss was calculated according to the above steps. The results show that the loss error of the improved model is 1.0%, while the error of the traditional dynamic JA model is 1.5%. A B23R085 oriented silicon steel magnetic ring was used, and the core loss was calculated at f=5kHz, D=1, and B... m Under the condition of 0.6T, the loss error of the improved model is 0.6%, verifying the applicability of the model to different materials. At f=5kHz, B m Under the condition of 0.6T, the hysteresis loops were tested for D=0.7, 0.8, 0.9, and 1 respectively. The results show that the error of the improved model is less than 1.5% at all duty cycles, and it can accurately reflect the influence of duty cycle on loss.

[0044] By comparing amorphous and silicon steel materials, it was found that silicon steel is more sensitive to the skin effect, providing a theoretical basis for the selection of materials for high-frequency transformers. Figure 7 As shown, in B m Under the conditions of 0.6T and D=1, the core loss of the amorphous magnetic ring decreases from 28.58 J / m at f=3kHz. 3 Increased to 33.39 J / m at f=5kHz 3 The increase was 16.8%. For silicon steel magnetic rings, under the same conditions, the core loss increased from 179.44 J / m at f=3kHz. 3 Increased to 259.04 J / m at f=5kHz 3 The increase was 44.4%, a growth rate significantly higher than that of amorphous magnetic rings. Under high-frequency excitation, eddy current loss is the main component of core loss, and the skin effect primarily affects eddy current loss. This indicates that, compared to amorphous materials, eddy current loss accounts for a higher proportion of core loss in silicon steel materials, thus silicon steel materials are more susceptible to the skin effect.

[0045] In summary, this invention combines Fourier decomposition with magnetic constitutive relations to perform harmonic decomposition of magnetic flux density under non-sinusoidal excitation. Based on each harmonic, a corresponding eddy current magnetic field model is constructed. Furthermore, the additional magnetic field influence generated by the skin effect is explicitly introduced into the dynamic JA hysteresis model, overcoming the idealized assumption of uniform magnetic flux density distribution in traditional models. This effectively solves the problems of uneven magnetic flux distribution and the difficulty in accurately characterizing eddy current effects within the core under high-frequency operating conditions. Simultaneously, this method is applicable to complex non-sinusoidal excitation forms such as rectangular waves and PWM waves. Combined with a parameter identification mechanism, it achieves unified modeling and analysis of the hysteresis behavior and loss characteristics of different soft magnetic materials under different frequencies and duty cycles. This significantly improves the accuracy and applicability of high-frequency transformer core loss calculation, enabling accurate prediction of core loss under non-sinusoidal excitation conditions.

[0046] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for calculating the core loss of a high-frequency transformer considering the skin effect, characterized in that, Includes the following steps: S1. Obtain the hysteresis loop and calculate the average magnetic flux density B over one period. av (t) and magnetic field strength H(t); S2. Regarding the average magnetic flux density B av (t) Fourier analysis was used to calculate the eddy current magnetic field strength corresponding to each harmonic, and the total eddy current magnetic field strength H was obtained by superimposing the results. ed (t); S3. Construct a dynamic JA hysteresis model and substitute the total eddy current magnetic field strength H. ed (t) Obtain the improved dynamic JA model and identify the parameters in the improved dynamic JA model; S4. Simulate the hysteresis loop based on the improved dynamic JA model and calculate the core loss per unit volume.

2. The method for calculating the core loss of a high-frequency transformer considering the skin effect according to claim 1, characterized in that, Step S1 includes: Waveform data of the primary side current i1(t) and secondary side voltage u2(t) of the magnetic ring were collected using a current probe and a voltage probe, respectively. The average magnetic flux density Bav(t) and magnetic field strength H(t) over one period are calculated using the following formulas: ， ， Where N1 is the number of turns in the primary winding; N2 is the number of turns in the secondary winding; S is the effective cross-sectional area of ​​the core; l e This is the effective magnetic circuit length of the iron core.

3. The method for calculating high-frequency transformer core losses considering the skin effect according to claim 1, characterized in that, Step S2 includes: The average magnetic flux density B av (t)Fourier decomposition into a superposition of harmonic components; Calculate the equivalent eddy current magnetic field strength H corresponding to each harmonic. ed(n) (t); The eddy current magnetic field strength H corresponding to each harmonic ed(n) (t) superimposed, the total eddy current magnetic field strength H considering the skin effect is obtained. ed (t).

4. The method for calculating the core loss of a high-frequency transformer considering the skin effect according to claim 3, characterized in that, In step S2, the average magnetic flux density B av (t) The Fourier decomposition is a superposition of the harmonic components. ， Among them, B n-max and is the amplitude and phase of the nth harmonic magnetic flux density, m is the maximum harmonic, and f is the fundamental frequency.

5. The method for calculating the core loss of a high-frequency transformer considering the skin effect according to claim 3 or 4, characterized in that, In step S2, when calculating the eddy current magnetic field strength corresponding to each harmonic, under sinusoidal excitation, for a one-dimensional eddy current problem, the magnetic field strength H... hy The boundary conditions are Then the surface magnetic field strength H a for: ， ， Where k is a dimensionless constant, and H max ω is the amplitude of the surface magnetic field intensity, ω is the angular frequency, and d is the thickness of the magnetic ring. The expression for a one-dimensional vortex field is: ， Based on the magnetic constitutive equation, the expression for magnetic flux density is derived: ， ， ， Derive H a With H hy Relationship: ， Under sinusoidal excitation, the expression for the eddy current field is: ， Combining the above equations, we can derive the expression for the equivalent eddy current magnetic field strength corresponding to the nth harmonic: ， in, , , 。 6. The method for calculating high-frequency transformer core losses considering the skin effect according to claim 5, characterized in that, In step S2, the total eddy current magnetic field strength H ed The expression for (t) is: 。 7. The method for calculating the core loss of a high-frequency transformer considering the skin effect according to claim 1, characterized in that, In step S3, the static JA hysteresis model is: ， Where M is the total magnetization, M an δ is the hysteresis-free magnetization; α is the average field parameter of the coupling within the magnetic domain; c is the reversible magnetization coefficient; δ M The limiting coefficients are introduced to prevent non-physical interpretations; δ is the direction coefficient; k is the pinning coefficient; The hysteresis-free magnetization of a soft magnetic material can be expressed as: ， Among them, M s Let be the saturation magnetization; a be the shape parameter of the hysteresis-free magnetization curve; and He be the effective magnetic field strength, expressed as: ， Where H is the applied magnetic field strength; α is the average field parameter of the coupling within the magnetic domain; and M is the total magnetization. δ、δ M They are represented as follows: ， ， The total core loss is broken down into hysteresis loss, eddy current loss, and residual loss: ， Based on the field separation method, the total loss can be further expressed as: ， Where W is the total loss; W hys For hysteresis loss; W ed For eddy current losses; W ex For residual losses, consider the effective hysteresis magnetic field H of the dynamic field. dyn for: ， Neglecting residual losses, the effective hysteresis magnetic field H of the dynamic field will be considered. dyn The expression simplifies to: ， The expression for the dynamic JA hysteresis model is: ， Then the total eddy current magnetic field strength H ed (t) Substitute into the dynamic JA hysteresis model to obtain the improved dynamic JA model.

8. The method for calculating high-frequency transformer core losses considering the skin effect according to claim 7, characterized in that, In step S3, the PSO (Particle Swarm Optimization) algorithm is used, with the root mean square error of the magnetic flux density waveform as the objective function, to identify the five parameters α, a, c, k, and M of the improved dynamic JA (Rapid Aspect Reduction) model. s .

9. The method for calculating the core loss of a high-frequency transformer considering the skin effect according to claim 1, characterized in that, In step S4, the hysteresis loop is simulated based on the improved dynamic JA model, and the core loss per unit volume is calculated: ， Where P is the core loss, V is the magnetic ring volume, and f is the frequency.

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