A method for simulating the hysteresis characteristics of soft magnetic materials based on the analytical inverse Preisach model

Abstract

The present invention discloses a method for simulating the hysteresis characteristics of soft magnetic materials based on an analytical inverse Preisach model, comprising: first, based on the analytical positive Preisach model, using the derivation rule to derive analytical expressions for the initial magnetization curve, the ascending branch of the limiting hysteresis loop, and the descending branch of the magnetic permeability, respectively; then, based on the difference method, deriving analytical expressions for the initial magnetization curve, the ascending branch of the limiting hysteresis loop, and the descending branch of the magnetic permeability, respectively, with the current magnetic induction intensity as input and the current magnetic field intensity as output, thereby obtaining an analytical inverse Preisach model. The analytical inverse Preisach model parameters are then extracted based on a genetic algorithm and three measured hysteresis loops under high, medium, and low magnetic densities, and the hysteresis loops of the soft magnetic material under different working conditions are calculated based on the model and parameters. The analytical inverse Preisach model proposed in the present invention can not only accurately and quickly simulate the hysteresis characteristics of soft magnetic materials, but also plays an important supporting role in research work such as core loss calculation, electromagnetic multi-physics field simulation, and global structural optimization design of electrical equipment.

Description

Technical Field

[0001] The present invention relates to the field of hysteresis characteristic analysis of soft magnetic materials, and in particular to a hysteresis characteristic simulation method of soft magnetic materials based on an analytical inverse Preisach model. Background Art

[0002] Soft magnetic materials, such as silicon steel, are widely used in electrical equipment such as motors, transformers, and reactors. However, their inherent nonlinear hysteresis properties significantly impact the electromagnetic field, excitation current, and energy loss of these devices. Therefore, developing a hysteresis model that accurately simulates the hysteresis properties of soft magnetic materials is crucial. Research in areas such as global structural optimization design of electrical equipment involves numerous optimization objectives, constraints, and iterative model calculations. Therefore, electromagnetic models, such as hysteresis models, must be both highly accurate and fast; otherwise, research is difficult to conduct. Furthermore, it is important to note that magnetic field calculations for electrical equipment typically use the vector magnetic potential A as a variable. Therefore, the inverse hysteresis model, which uses magnetic flux density B as input and magnetic field intensity H as output, avoids the complex iterative computational issues associated with the positive hysteresis model (B = ▽ × A). Therefore, developing an accurate analytical inverse hysteresis model provides valuable support and guidance for research in electromagnetic multiphysics simulation and global structural optimization design of electrical equipment (the "analytic" factor ensures a fast solution speed).

[0003] The classical Preisach model is widely used due to its higher simulation accuracy and universality than other hysteresis models, but its existing inverse model is not in analytical form. For example:

[0004] (1) Literature 1: Zhao Xiaojun, Liu Xiaona, Xiao Fan, et al. Simulation of hysteresis and loss characteristics of oriented silicon steel sheets under DC bias based on Preisach model [J]. Transactions of China Electrotechnical Society, 2020, 35(09): 1849-1857. A simulation method for the loss characteristics of oriented silicon steel sheets under DC bias conditions was proposed, but the inverse Preisach model used was not an analytical model.

[0005] (2) Literature 2: Li Yiling, Li Lin, Liu Ren, et al. Identification of the distribution function of the static inverse Preisach model based on the non-uniform unit discretization method [J]. Proceedings of the CSEE, 2021, 41(15): 5340-5351. A non-uniform unit discretization method for extracting the distribution function of the inverse Preisach hysteresis model was proposed, but the design involved complex double integral numerical calculations, and the inverse Preisach model used was not an analytical model.

[0006] (3) Reference 3: Liu Ren, Du Yingxue, Li Lin, Chen Bin, Tang Bo. Derivation and correction of analytical positive Preisach hysteresis model [J / OL]. Proceedings of the CSEE: 1-10 [2022-06-17]. An accurate and universal analytical positive Preisach model was derived and proposed, but no analytical inverse Preisach model was proposed.

[0007] In summary, there is currently no analytical inverse Preisach model.

[0008] Therefore, it is of great significance to invent a method for simulating the hysteresis characteristics of soft magnetic materials based on the analytical inverse Preisach model. Summary of the Invention

[0009] The problem to be solved by the present invention is to address the deficiencies of the above-mentioned existing models and methods and to provide a method for simulating the hysteresis characteristics of soft magnetic materials based on the analytical inverse Preisach model.

[0010] In order to achieve the above technical effects, the technical solution adopted by the present invention is:

[0011] A method for simulating the hysteresis characteristics of soft magnetic materials based on an analytical inverse Preisach model comprises the following steps:

[0012] S1, based on the analytical positive Preisach model B(H), the analytical expressions of the permeability dB / dH of the initial magnetization curve, the rising branch and the falling branch of the limiting hysteresis loop are derived using the derivation rule, as follows:

[0013]

[0014]

[0015]

[0016] Where E represents the Everett function, tanh represents the hyperbolic tangent function, and H m is the magnetic field intensity corresponding to a turning point on the hysteresis loop; and F i The calculation formula of (H) is as follows:

[0017]

[0018]

[0019] Where, α i , β i , γ i , k1, k2, k3 are model parameters;

[0020] S2, using the current magnetic induction intensity B(t+Δt) as input and the current magnetic field intensity H(t+Δt) as output, uses the difference method to derive analytical expressions for the initial magnetization curve, the rising branch, and the falling branch of the limiting hysteresis loop, thereby obtaining the analytical inverse Preisach model H(B);

[0021] S3, based on the genetic algorithm and three measured hysteresis loops at high and low magnetic flux densities in soft magnetic materials, extracts the parameters of the analytical inverse Preisach model of soft magnetic materials;

[0022] S4, using the analytical inverse Preisach model H(B) obtained in S2 and the model parameters obtained in S3, calculate the hysteresis loop of the soft magnetic material under different working conditions.

[0023] Preferably, the difference method is used in step S2, and the specific expression is:

[0024]

[0025] Where H(t) and B(t) are the magnetic field intensity and magnetic flux density at time t, respectively; H(t+Δt) and B(t+Δt) are the magnetic field intensity and magnetic flux density at time t+Δt, respectively; and dB(t) / dH(t) is a function of H(t).

[0026] Preferably, the analytical inverse Preisach model H(B) derived in step S2 is:

[0027]

[0028] Where n is the number of terms in the Everett function.

[0029] Preferably, in step S3, the root mean square error is introduced to evaluate the accuracy of the genetic algorithm solution, and three measured hysteresis loops under high, medium and low magnetic densities are selected to extract the model parameter α in the formula of step S2. i , β i , γ i , k1, k2, k3.

[0030] Preferably, in step S4, the calculation method of the hysteresis loop of the soft magnetic material under different working conditions is as follows:

[0031] S401, the state of the soft magnetic material when it is not magnetized, that is (H t =0, B=0, H m =0) as the starting point of the calculation, and input the magnetic flux density B(t) and model parameter α at each moment in the magnetization period 0~T. i , β i , γ i , k1, k2, k3 are known coefficients;

[0032] S402, calculating and outputting the magnetic field strength H(t+Δt) at any current time t by analyzing the inverse Preisach model;

[0033] S403, judgment Is it true? If it is true, assign it to H m =H(t);

[0034] S404, let t = t + Δt, and repeat the calculation until t ≥ period T; and obtain the hysteresis loops under different working conditions.

[0035] The present invention has the following beneficial effects:

[0036] The model derived and proposed in the present invention is currently the only analytical inverse Preisach model; the method for simulating the hysteresis characteristics of soft magnetic materials based on this model is highly practical. The model also has high accuracy and a fast solution speed, which can meet the research fields such as the global structural optimization design of electrical equipment, involving repeated calculations of numerous optimization objectives, constraints and models, thereby realizing accurate and rapid simulation of the hysteresis loop of soft magnetic materials, and laying a solid theoretical and technical foundation for research work such as core loss calculation, electromagnetic transient and electromagnetic thermal multi-physics field simulation, and global structural optimization design of electrical equipment. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 This is a framework diagram of the method for simulating the hysteresis characteristics of soft magnetic materials based on the analytical inverse Preisach model;

[0038] Figure 2 Schematic diagram of the process of simulating the hysteresis loop of soft magnetic materials based on the analytical inverse Preisach model;

[0039] Figure 3 Comparison results of simulated and measured hysteresis loops of oriented silicon steel samples at different magnetic flux densities;

[0040] Figure 4 Comparison results between simulated and measured hysteresis loops of non-oriented silicon steel samples under different magnetic densities. DETAILED DESCRIPTION

[0041] Example 1:

[0042] like Figure 1 As shown, a method for simulating the hysteresis characteristics of soft magnetic materials based on the analytical inverse Preisach model includes the following steps:

[0043] S1, based on the analytical positive Preisach model B(H), the analytical expressions of the permeability dB / dH of the initial magnetization curve, the rising branch and the falling branch of the limiting hysteresis loop are derived using the derivation rule, as follows:

[0044]

[0045]

[0046]

[0047] Where E represents the Everett function, tanh represents the hyperbolic tangent function, and H m is the magnetic field intensity corresponding to a turning point on the hysteresis loop; and F i The calculation formula of (H) is as follows:

[0048]

[0049]

[0050] Where, α i , β i , γ i , k1, k2, k3 are model parameters;

[0051] S2, using the current magnetic induction intensity B(t+Δt) as input and the current magnetic field intensity H(t+Δt) as output, uses the difference method to derive analytical expressions for the initial magnetization curve, the rising branch, and the falling branch of the limiting hysteresis loop, thereby obtaining the analytical inverse Preisach model H(B);

[0052] S3, based on the genetic algorithm and three measured hysteresis loops at high and low magnetic flux densities in soft magnetic materials, extracts the parameters of the analytical inverse Preisach model of soft magnetic materials;

[0053] S4, using the analytical inverse Preisach model H(B) obtained in S2 and the model parameters obtained in S3, calculate the hysteresis loop of the soft magnetic material under different working conditions.

[0054] Preferably, the difference method is used in step S2, and the specific expression is:

[0055]

[0056] Where H(t) and B(t) are the magnetic field intensity and magnetic flux density at time t, respectively; H(t+Δt) and B(t+Δt) are the magnetic field intensity and magnetic flux density at time t+Δt, respectively; and dB(t) / dH(t) is a function of H(t).

[0057] Preferably, the analytical inverse Preisach model H(B) derived in step S2 is:

[0058]

[0059] Where n is the number of terms in the Everett function.

[0060] Preferably, in step S3, the root mean square error is introduced to evaluate the accuracy of the genetic algorithm solution, and three measured hysteresis loops under high, medium and low magnetic densities are selected to extract the model parameter α in the formula of step S2. i , β i , γ i , k1, k2, k3.

[0061] Furthermore, in order to accurately evaluate the accuracy of the genetic algorithm, the fitting standard deviation, which is extremely sensitive to errors, is introduced as the evaluation index of the algorithm, that is, the objective function (fitness value), thereby transforming the problem of extracting the parameters of the analytical inverse Preisach model into an optimization problem of minimizing the objective function; the objective function is shown in the following formula:

[0062]

[0063] Where, Fitness is the root mean square error value; H mea is the measured value of magnetic field intensity; H cal is the calculated value obtained by substituting the optimized model parameters into the analytical inverse Preisach model; N is the number of experimental sampling points. Three measured hysteresis loops at high, medium, and low magnetic densities are selected to ensure the global simulation effect of the analytical inverse Preisach model. When the root mean square error (RMS) value reaches a minimum during the genetic algorithm optimization of the analytical inverse Preisach model parameters, the optimal parameters of the analytical inverse Preisach model are obtained.

[0064] like Figure 2 As shown, preferably, in step S4, the calculation method of the hysteresis loop of the soft magnetic material under different working conditions is as follows:

[0065] S401, the state of the soft magnetic material when it is not magnetized, that is (H t =0, B=0, H m =0) as the starting point of the calculation, and input the magnetic flux density B(t) and model parameter α at each moment in the magnetization period 0~T. i , β i , γ i , k1, k2, k3 are known coefficients;

[0066] S402, calculating and outputting the magnetic field strength H(t+Δt) at any current time t by analyzing the inverse Preisach model;

[0067] S403, judgment Is it true? If it is true, assign it to H m =H(t);

[0068] S404, let t = t + Δt, and repeat the calculation until t ≥ period T; and obtain the hysteresis loops under different working conditions.

[0069] Furthermore, the state of the soft magnetic material when it is not magnetized (H=0, B=0, H m =0) as the starting point for calculation; if H and H at a certain moment are known m , then this moment can also be used as the starting point for calculation; in addition, when calculating the magnetic field strength H(t+Δt) at any current moment t+Δt, the magnetic field strength H(t) at the previous moment t and the previous magnetization reversal point H m are all known parameters, so H(t), H m They are all regarded as known coefficients, and the input and output are H(t+Δt) and B(t+Δt) at the current time t+Δt respectively.

[0070] Example 2:

[0071] like Figures 3 and 4 As shown in the figure, a method for simulating the hysteresis characteristics of soft magnetic materials based on the analytical inverse Preisach model of the present invention simulates the hysteresis loops of oriented and non-oriented silicon steel samples under different magnetic densities, and compares them with the corresponding measured hysteresis loops. It can be seen from the figure that the hysteresis loops simulated by the method proposed in the present invention are relatively consistent with the measured hysteresis loops, and the maximum error is only 8.52%, which verifies the accuracy of the method.

[0072] The above embodiments are merely preferred technical solutions of the present invention and should not be construed as limiting the present invention. The embodiments and features in the embodiments of this application may be arbitrarily combined with each other unless they conflict. The scope of protection of the present invention shall be the technical solutions described in the claims, including equivalent alternatives to the technical features of the technical solutions described in the claims. Equivalent alternatives and improvements within this scope are also within the scope of protection of the present invention.

Claims

1. A method for simulating the hysteresis characteristics of soft magnetic materials based on an analytical inverse Preisach model, characterized by: The following steps are involved: S1, to analyze the positive Preisach model B ( H ) is used as the basis, and the permeability d of the initial magnetization curve, the rising branch and the falling branch of the limiting hysteresis loop are derived respectively by using the derivation rule. B / d H The analytical expression is as follows: ； ； ； Where, E represents the Everett function, tanh represents the hyperbolic tangent function, H m is the magnetic field intensity corresponding to a turning point on the hysteresis loop; and The calculation formula is as follows: ； ； Where, α i 、 β i 、 γ i 、 k 1. k 2. k 3 is the model parameter; S2, with the current magnetic induction intensity B ( t +Δ t ) is the input, the current magnetic field strength H ( t +Δ t ) is output, and the analytical expressions of the initial magnetization curve, the rising branch and the falling branch of the limiting hysteresis loop are derived by the difference method, thereby obtaining the analytical inverse Preisach model H ( B ); S3, based on the genetic algorithm and three measured hysteresis loops of soft magnetic materials at high, medium and low magnetic densities, extracts the parameters of the analytical inverse Preisach model of soft magnetic materials; S4, analytical inverse Preisach model obtained using S2 H ( B ) and the model parameters obtained by S3 to calculate the hysteresis loop of the soft magnetic material under different working conditions.

2. The method for simulating the hysteresis characteristics of soft magnetic materials based on the analytical inverse Preisach model according to claim 1, characterized in that: In step S2, the difference method is used, and the specific expression is: ； Where, H ( t ), B ( t ) are respectively t The magnetic field strength and magnetic induction strength at the moment, H ( t +Δ t ), B ( t +Δ t ) are respectively t +Δ t The magnetic field strength and magnetic induction intensity at the moment d B ( t ) / d H ( t ) is about H ( t ) function.

3. The method for simulating the hysteresis characteristics of soft magnetic materials based on the analytical inverse Preisach model according to claim 1, characterized in that: The analytical inverse Preisach model derived in step S2 H ( B )for: ； Where, n is the number of terms of the Everett function; B m is the magnetic induction intensity corresponding to a turning point on the hysteresis loop, H ( t ), B ( t ) are the current t The magnetic field strength and magnetic induction intensity at the moment d B ( t ) / d H ( t ) is the current t Differential permeability of the hysteresis loop at time t.

4. The method for simulating hysteresis characteristics of soft magnetic materials based on the analytical inverse Preisach model according to claim 1, characterized in that: In step S3, the root mean square error is introduced to evaluate the accuracy of the genetic algorithm solution, and three measured hysteresis loops under high, medium and low magnetic densities are selected to extract the model parameters in step S2. α i 、 β i 、 γ i 、 k 1. k 2. k 3.

5. The method for simulating hysteresis characteristics of soft magnetic materials based on the analytical inverse Preisach model according to claim 1, characterized in that: In step S4, the calculation method of the hysteresis loop of the soft magnetic material under different working conditions is as follows: S401, the state of the soft magnetic material when it is not magnetized, that is, H =0, B =0, H m =0 as the starting point of calculation, input magnetization period 0~ T Magnetic induction intensity at each moment B (t) and model parameters α i 、 β i 、 γ i 、 k 1. k 2. k 3 as a known coefficient; S402, by analyzing the inverse Preisach model, calculate and output any current t Magnetic field strength at the moment H ( t +Δ t ) ; S403, judgment Is it established? If it is established, assign it to H m = H(t); S404, order t=t +Δ t， Calculate repeatedly until t≥period T; The hysteresis loops under different working conditions are obtained.

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