Method for solving transformer core hysteresis permeability based on j-a model

Abstract

The method comprises the following steps: initializing magnetic flux density and magnetic field intensity; solving current time magnetic flux and providing the same as input quantity to a C-Script module; calculating magnetization intensity and step length of a previous time in the C-Script module based on a static J-A magnetic hysteresis model; solving differential equation groups of the static J-A magnetic hysteresis model by using a Runge-Kutta-Fehlberg method to obtain current time magnetization intensity and differential magnetization intensity; calculating output quantity magnetic field intensity and magnetic permeability of the current time in the C-Script module; calculating variable magnetic permeability and magnetic motive force and providing the same to a variable magnetic permeability module; saving the current time magnetic flux density and magnetic field intensity and continuing to repeat the above steps until the current time is greater than a set calculation time, and then ending the calculation. The method can be applied to power transformer electromagnetic transient modeling and accurate characteristic evaluation, can more accurately simulate the magnetic hysteresis effect of the core, and is more in line with the real core magnetization physical process.

Description

Technical Field

[0001] This invention belongs to the technical field of transformer core characteristic evaluation, specifically involving a method for solving transformer core hysteresis and permeability based on the JA model. Background Technology

[0002] Transformer models are mainly divided into three categories: 1) models based on circuit theory; 2) magnetic circuit models and circuit models derived from them through dual transformation; 3) gyroscope-capacitor magnetic component models based on the magnetic permeability-capacitance analogy method.

[0003] The transformer model based on circuit theory was first proposed by V. Brandwajn et al. in 1982. To account for the nonlinear saturation characteristics of the core, a nonlinear inductor is usually connected in parallel at the winding port closest to the core. However, this model does not include information such as the transformer's geometric parameters and topology, and therefore cannot obtain information such as the magnetic flux and magnetic flux density at various locations inside the core.

[0004] The transformer modeling method based on the duality principle and magnetic circuit model can use circuit elements to convert the physical magnetic circuit of the transformer into a dual circuit suitable for simulation in electromagnetic transient simulation software. This model considers the nonlinear characteristics of the iron core and the structural characteristics of the transformer, and is suitable for the study of phenomena such as inrush current, ferroresonance, and DC bias. For example, in the literature [1]: Li Jinlong, Li Jinzhong, Zhang Shuqi. Transformer topology correction transient model and its application in DC bias tolerance assessment [J]. Power System Technology, 2019, 43(9): 3439-3447. A topology correction transient model considering the structural characteristics of the transformer and the nonlinear magnetization characteristics of the iron core material is proposed using the magnetic circuit-circuit duality principle, which is used to calculate the DC bias excitation current of the transformer. This model considers the iron core topology and interphase coupling characteristics, but cannot reflect the circuit and magnetic circuit information of the transformer at the same time, which is not conducive to fully understanding the working state of the transformer and the circuit.

[0005] The Gyrator-Capacitor Model (GC model) is a magnetic component model proposed by DCHamill in 1993 based on the magnetic permeability-capacitance analogy. The model includes both electrical and magnetic circuit components. The GC model can fully represent the electrical and magnetic circuit information, making it suitable for simulating hybrid electro-magnetic systems. Furthermore, the modeling method of the GC model can be used in different circuit simulation software such as PLECS and Saber, demonstrating strong versatility. For example, reference [2]: Chen Qianhong, Xu Ligang, Li Zhujun, et al. Improved gyrator-capacitor nonlinear magnetic core simulation model [J]. Journal of Electrical Engineering, 2009, 24(4): 14-21. An improved gyrator-capacitor magnetic component model was proposed, using nonlinear resistance to simulate the hysteresis characteristics of the iron core and nonlinear capacitance to simulate the saturation characteristics; reference [3]: Zhang HY, Tian MX, Li HC, et al. Improved gyrator-capacitor model considering eddy current and excess losses based on loss separation method [J]. AIP Advances, 2020, 10(3): 035309. An improved hysteresis equivalent model of the iron core magnetic circuit considering eddy current and excess loss was proposed, but the above models cannot explain the physical process of iron core magnetization.

[0006] Reference [4]: ​​Luo M, Dujic D, Allmeling J. Modeling frequency independent hysteresis effects of ferrite core materials using permeance-capacitance analogy for system-level circuit simulations[J].IEEE Transactions on Power Electronics, 2018, 33(12): 10055-10070. Based on the permeance-capacitance analogy, a hysteresis permeance model based on the Preisach model was established, and eddy current loss and residual loss were characterized by reluctance. However, in the electromagnetic transient simulation of transformers, the Preisach model is relatively complex and requires a large number of complex experiments to obtain model parameters. The semi-microscopic and semi-macroscopic JA hysteresis model based on the magnetization physical process of magnetic materials is an effective method for describing the hysteresis characteristics of transformer cores. Summary of the Invention

[0007] This invention provides a method for solving transformer core hysteresis and permeability based on the JA model. This method is based on the JA hysteresis model and the permeability-capacitance analogy. It uses the underlying modules and language of the power electronics simulation software PLECS to write a program to establish a JA hysteresis and permeability model with magnetic flux density B as input and magnetic field strength H as output. With the help of the semi-microscopic and semi-macroscopic JA hysteresis model, the hysteresis effect of the core can be simulated more accurately, and it is more consistent with the actual physical process of core magnetization, thus providing support for subsequent evaluation of transformer electromagnetic characteristics and structural design.

[0008] The technical solution adopted in this invention is as follows:

[0009] The method for solving the hysteresis and permeability of transformer cores based on the JA model includes the following steps:

[0010] Step 1: Initialize magnetic flux density and magnetic field strength, and give initial values ​​for magnetic flux density and magnetic field strength;

[0011] Step 2: Solve for the magnetic flux B(t) at the current time t and provide it as input to the C-Script module;

[0012] Step 3: Calculate the magnetization M(t0) and step size h(t0) at time t0 based on the static JA hysteresis model in the C-Script module;

[0013] Step 4: Solve the differential equations of the static JA hysteresis model using the Runge-Kutta-Fehlberg method to obtain the magnetization M(t) and differential magnetization dM / dB(t) at time t.

[0014] Step 5: Calculate the output magnetic field strength H at time t in the C-Script module. hy (t) and permeability μ(t);

[0015] Step 6: The magnetic field strength H obtained in Step 5 hy After processing by a gain converter, the variable permeability P(t) = μ(t)S / l and the magnetomotive force F(t) = H are obtained. hy (t)l, and provided to the variable permeability module; where: S represents the magnetic circuit area; l represents the magnetic circuit length;

[0016] Step 7: Save the magnetic flux density B(t) at time t as B(t0), and the magnetic field strength H hy (t) is saved as H hy (t0), and t is saved as t0;

[0017] Step 8: When time t is greater than the set calculation time t set When the time t is less than or equal to the set calculation time t, the calculation ends;set If the time is right, then continue repeating steps 2 through 7.

[0018] In step 1, the initial value of magnetic flux density B(t0) and magnetic field strength H hy (t0) is calculated as follows:

[0019] B(t0) = 0(T);

[0020] T represents the unit of magnetic flux density: Tesla.

[0021] H hy (t0)=1×10 -5 Unit: A / m;

[0022] t0 represents the previous simulation time.

[0023] Step 2 includes the following steps:

[0024] S2.1: The variable time step Δt is set. var Calculate the current simulation time t = t0 + Δt var ;

[0025] S2.2: Extract the rate of change of magnetic flux flowing through the variable permeability component at time t using the magnetic flux table.

[0026] A flux meter can measure the rate of change of magnetic flux in a specific magnetic circuit branch. Flux meters are existing components in the system-level power electronics simulation software PLECS, such as... Figure 2 Chinese symbol

[0027] S2.3: Then, the rate of change of magnetic flux is measured by an integrator. Integrate to obtain the magnetic flux φ(t);

[0028] S2.4: Finally, the magnetic flux density B(t) is obtained by dividing the gain by the cross-sectional area S of the magnetic circuit, and is provided as an input to the C-Script module.

[0029] The C-Script module is a programming module in the system-level power electronics simulation software PLECS, which allows programs to be written in the C language, such as... Figure 2 Chinese symbol

[0030] In step 3, the magnetization M(t0) and step size h(t0) are calculated as follows:

[0031] M(t0)=B(t0) / μ0-H hy (t0);

[0032] h(t0) = B(t) - B(t0);

[0033] In the formula: M(t0) is the magnetization intensity at time t0; B(t0) and B(t) are the magnetic flux densities at times t0 and t, respectively; h(t0) is the step size at time t0; μ0 is the free permeability.

[0034] In step 4, the Runge-Kutta-Fehlberg method (RKF45) is used to solve the differential equations of the static JA hysteresis model. This is a fourth-order method with a fifth-order error estimate, yielding the magnetization M(t) and differential magnetization dM / dB(t) at time t, as detailed below:

[0035] The equations of the static JA hysteresis model are expressed as follows:

[0036]

[0037] Where: H e B represents the effective magnetic field strength; α represents the magnetic flux density; and α represents the average field parameter of the coupling within the magnetic domain.

[0038] M an The magnetization is hysteresis-free; M s denoted as saturation magnetization; 'a' is the shape parameter of the hysteresis-free magnetization curve.

[0039] M is the magnetization intensity; c is the reversible magnetization coefficient; k is the restraint coefficient;

[0040] δ is the direction coefficient, when dH hy When / dt>0, δ=1; dH hy When / dt<0, δ=-1;

[0041] k0 is the default value for the restraint coefficient; σ is the standard deviation; H hy Indicates the static magnetic field strength;

[0042] This simply represents a common mathematical operation, where e is a natural constant in mathematics, and H... hy This represents the static magnetic field strength.

[0043] δ M The direction coefficient, defined to prevent non-physical interpretations, must satisfy the following:

[0044]

[0045] In the formula: sign(·) is the symbol parameter.

[0046] Magnetization intensity M = M rev +M irr Where: Mrev represents the reversible magnetization component, and Mirr represents the irreversible magnetization component;

[0047] Differential magnetization:

[0048] In step 5, the magnetic field strength H hy The values ​​of (t) and permeability μ(t) are calculated as follows:

[0049] H hy (t)=B(t) / μ0-M(t);

[0050] μ(t)=1 / (1 / μ0-dM / dB(t)).

[0051] In step 6, the permeability μ(t) and the magnetic field strength H hy (t) After gaining, the variable permeability P(t) = μ(t)S / l and the magnetomotive force F(t) = H are obtained. hy (t)l, and provided to the variable permeability module.

[0052] The gain unit is a multiplication and division module in the system-level power electronics simulation software PLECS, and its specific symbol is:

[0053] The variable permeability module is a variable permeability module in the system-level power electronics simulation software PLECS. It can change the magnitude of the permeability, and its specific symbol is:

[0054] In step 7, the magnetic flux density B(t) at time t is stored as B(t0), and the magnetic field strength H... hy (t) is saved as H hy (t0), and t is saved as t0;

[0055] In step 8, when time t is greater than the set calculation time t set When the time t is less than or equal to the set calculation time t, the calculation ends; set If the time is right, then continue repeating steps 2 through 7.

[0056] This invention provides a method for solving the hysteresis and permeability of transformer cores based on the JA model, with the following technical advantages:

[0057] 1) This invention combines the JA model and material characteristic parameters. Based on the concept of magnetic permeability in the gyroscope-capacitor magnetic component model, it uses the underlying modules and programming language of the power electronics simulation software PLECS to establish a nonlinear JA hysteresis permeability model with magnetic flux density B as input and magnetic field strength H as output. In each iteration step, a new differential permeability is calculated according to the magnetic field strength and the dynamic JA model, and then the permeability of each branch of the iron core is updated. The JA hysteresis model is a semi-microscopic, semi-macroscopic model, which can more accurately simulate the hysteresis effect of the iron core compared to the Energetic model and the Preisach model.

[0058] 2) The method of the present invention can be applied to electromagnetic transient modeling and accurate characteristic evaluation of power transformers, taking into account the influence of core hysteresis characteristics on transformer electromagnetic transients.

[0059] 3) Based on the JA hysteresis model, this invention establishes a hysteresis-permeability module based on the permeability-capacitance analogy, realizing the coupling between the transformer core magnetic circuit and the external circuit. The JA hysteresis model is a semi-microscopic, semi-macroscopic model, which can more accurately simulate the hysteresis effect of the core; at the same time, it is more consistent with the real physical process of core magnetization, providing support for subsequent evaluation of transformer electromagnetic characteristics and structural design. Attached Figure Description

[0060] Figure 1 This is a schematic diagram of the process of the present invention.

[0061] Figure 2 This is a model diagram of a rotary capacitor magnetic component.

[0062] Figure 3 To simulate the hysteresis loop based on the static JA hysteresis model.

[0063] Figure 4 This is a schematic diagram of a platform for measuring the magnetic properties of ferromagnetic materials.

[0064] Figure 5 This is a diagram of the internal structure of the JA hysteresis and magnetic permeability module.

[0065] Figure 6 This is a comparison chart of the simulation results and the measured results of the static hysteresis loop. Detailed Implementation

[0066] A method for solving transformer core hysteresis and permeability based on the JA model is proposed. In order to consider the hysteresis effect of the core in the transformer core magnetic circuit model, it is necessary to use the underlying modules and language of power electronics simulation software to write programs and establish a static JA hysteresis and permeability module.

[0067] According to the expression for magnetic permeability in the gyroscope-capacitor magnetic component model, the magnetic permeability P of the iron core is related to the magnetic circuit area S, the magnetic circuit length l, and the magnetic permeability μ, where the differential magnetic permeability μ = dB / dH. hy The magnetic flux density B and magnetic field strength H can be established based on the static JA hysteresis model. hy The nonlinear relationship between them is obtained, i.e., BH hy The slope of the curve at the magnetic flux density B. For example, in Figure 3 Position 2 in the middle.

[0068] By combining the static JA hysteresis model and material characteristic parameters, the differential permeability μ was solved using computer C language programming in the PLECS C-Script module. The rate of change of magnetic flux through the permeability component, extracted in real time from the flux density table, is integrated using an integrator to obtain the magnetic flux φ. Then, it is divided by the magnetic circuit area S using a gain converter to obtain the magnetic flux density B, which is provided as input to the C-Script module. At each simulation step, the program iteratively calculates the new differential permeability μ(B) and magnetic field strength H based on the magnetic flux density B and the static JA hysteresis model. hy Then update the magnetic permeability P and magnetomotive force F of the iron core. The solution process is as follows: Figure 1 As shown.

[0069] Step 1: Initialize the magnetic flux density and magnetic field strength, as follows:

[0070] Initialize the two variables, magnetic flux density and magnetic field strength, by giving initial values ​​B(t0) and H for each variable. hy (t0). Initialize each variable, giving each variable an initial value:

[0071] B(t0)=0(T),H hy (t0)=1×10 -5 (A / m)

[0072] In the formula: B(t0) and H hy (t0) represents the magnetic flux density and magnetic field strength at the previous simulation time, respectively.

[0073] Step 2: Calculate the magnetic flux at the current moment and provide it as input to the C-Script module, as follows:

[0074] The variable time step Δt is set. var Calculate the current simulation time t = t0 + Δt var The rate of change of magnetic flux flowing through the variable permeability component at time t is extracted using a magnetic flux table. The magnetic flux is then obtained by integrating it through an integrator, and finally the magnetic flux density B(t) is obtained by dividing it by the cross-sectional area S of the magnetic circuit through a gain converter. This is then provided as an input to the C-Script module.

[0075]

[0076] In the formula: B(t) is the magnetic flux density at the current simulation moment; S is the cross-sectional area of ​​the magnetic circuit; is the rate of change of magnetic flux.

[0077] Step 3: In the C-Script module, based on the static JA hysteresis model, calculate the magnetization intensity and step size of the previous time step, as follows:

[0078] In the C-Script module, the magnetization intensity M(t0) and step size h(t0) at time t0 are calculated based on the static JA hysteresis model.

[0079] M(t0)=B(t0) / μ0-H hy (t0)

[0080] h(t0) = B(t) - B(t0)

[0081] In the formula: M(t0) is the magnetization intensity at time t0; B(t0) and B(t) are the magnetic flux densities at times t0 and t, respectively; h(t0) is the step size at time t0; μ0 is the free permeability.

[0082] Step 4: Using the Runge-Kutta-Fehlberg method, solve the differential equations of the static JA hysteresis model to obtain the magnetization and differential magnetization at the current moment, as follows:

[0083] The Runge-Kutta-Fehlberg method (RKF45) was used to solve the differential equations of the static JA hysteresis model. It is a fourth-order method with a fifth-order error estimate, and the magnetization M(t) and differential magnetization dM / dB(t) at time t were obtained.

[0084] The equations of the static JA hysteresis model can be expressed as:

[0085]

[0086] Where: M an The magnetization is hysteresis-free; M s is the saturation magnetization; a is the shape parameter of the hysteresis-free magnetization curve; H e dH is the effective magnetic field strength; α is the average field parameter of the coupling inside the magnetic domain; M is the magnetization; k is the restraint coefficient; δ is the direction coefficient, when dH hyWhen / dt>0, δ=1; dH hy When / dt<0, δ=-1; c is the reversible magnetization coefficient; k0 is the default value of the restraint coefficient; σ is the standard deviation; δ M The direction coefficient, defined to prevent non-physical interpretations, must satisfy the following:

[0087]

[0088] In the formula: sign(·) is the symbol parameter.

[0089] Step 5: Calculate the output magnetic field strength and permeability of the C-Script module at the current moment, as follows:

[0090] Calculate the output magnetic field strength H at time t in the C-Script module. hy (t) and permeability μ(t).

[0091] H hy (t)=B(t) / μ0-M(t)

[0092] μ(t)=1 / (1 / μ0-dM / dB(t))

[0093] Step Six: Calculate the variable permeability and magnetomotive force, and provide them to the variable permeability module, as follows:

[0094] Permeability μ(t) and magnetic field strength H hy (t) After gaining, the variable permeability P(t) = μ(t)S / l and the magnetomotive force F(t) = H are obtained. hy (t)l, and provided to the variable permeability module.

[0095] Step 7: Save the current magnetic flux density and magnetic field strength, and continue to repeat the above steps until the current time is greater than the set calculation time, then end the calculation.

[0096] Store the magnetic flux density B(t) at time t as B(t0), and the magnetic field strength H hy (t) is saved as H hy (t0), and t is saved as t0. Then, steps two through seven are repeated. When time t is greater than the set calculation time t... set Then the calculation ends.

[0097] To verify the correctness of the proposed modeling and solution method for iron core hysteresis and magnetic permeability, a nanocrystalline magnetic ring was used as a magnetic circuit segment to establish... Figure 4 The simulation model shown.

[0098] The magnetic ring is made of 1K107B type iron-based nanocrystalline alloy strip wound together, with a strip thickness of 20μm and a fill factor of K. cThe magnetic hysteresis characteristics of the nanocrystalline magnetic ring were measured using a computer-aided sampling voltammetry method. The ring's outer diameter, inner diameter, and height were 40 mm, 31 mm, and 10 mm, respectively, with a magnetic circuit length of 1 m (111.5 mm) and a mass of 30.34 g. The hysteresis characteristics of the nanocrystalline magnetic ring were measured using a computer-aided sampling voltammetry method. A magnetic circuit was constructed as follows: Figure 4 The experimental measurement platform shown.

[0099] Compiled using ArbExpress Application software, the AFG1062 signal generator can produce voltage waveforms of arbitrary frequency and shape. It is connected to the primary side of a 1:1 turns ratio transformer via an ATA-3040 power amplifier. The transformer is used to filter out DC signals and prevent DC bias, thus avoiding its influence on the measurement results. The secondary side of the transformer is connected to the magnetic ring under test. The induced voltage u2(t) of the magnetic ring can be obtained using a TBS1152B oscilloscope with a TPP0201 voltage probe, while the excitation current i1(t) can be measured using an SRS6050 high-frequency current probe. Recording... Figure 4 The data for i1(t) and u2(t) are given, and the relationships between i1(t) and magnetic field strength H(t), and between u2(t) and magnetic flux density B(t) are given as follows:

[0100]

[0101]

[0102] In the formula: N1 and N2 are the number of turns of the magnetic ring excitation coil and the induction coil, respectively; l m K is the equivalent magnetic circuit length of the magnetic ring; c A is the fill factor of the magnetic ring; c Let be the cross-sectional area of ​​the magnetic ring.

[0103] Using the hysteresis loop measurement results of the nanocrystalline magnetic ring at a frequency of 100Hz as an approximation of the quasi-static hysteresis loop, the static JA hysteresis model parameters of the nanocrystalline magnetic ring were extracted by using a hybrid algorithm of simulated annealing and Levenberg-Marquardt. The extraction results of the hysteresis model parameters of the nanocrystalline magnetic ring are detailed in Table 1.

[0104] Table 1. Results of parameter extraction for the iron core hysteresis model

[0105]

[0106] use Figure 5 The simulation results obtained by the JA hysteresis permeability module at a frequency of 100Hz and different magnetic flux density amplitudes are shown below. Figure 6 It can be seen that the simulated curve of the hysteresis loop is basically consistent with the measured curve.

Claims

1. A method for solving the hysteresis and permeability of transformer cores based on the JA model, characterized in that... Includes the following steps: Step 1: Initialize magnetic flux density and magnetic field strength, and give initial values ​​for magnetic flux density and magnetic field strength; Step 2: Solve for the current time step t magnetic flux And provide it as input to the C-Script module; Step 3: Calculate based on the static JA hysteresis model in the C-Script module magnetization intensity at time and step length ; Step 4: Solve the differential equations of the static JA hysteresis model using the Runge-Kutta-Fehlberg method to obtain... magnetization intensity at time and differential magnetization ; Step 5: Calculate the C-Script module Output magnetic field strength at time t H hy ( t and permeability ; Step 6: Magnetic field strength obtained in Step 5 H hy ( t and permeability After gain calculation, variable permeability is obtained. and magnetomotive force F ( t )= H hy ( t ) l And provided to the variable permeability module; wherein: Indicates the magnetic circuit area; Indicates the length of the magnetic circuit; Step 7: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the full magnetic flux density at time Save as magnetic field strength H hy ( t Save as H hy ( t 0), at the same time Save as ; Step 8: At time Greater than the set calculation time When the time is reached, the calculation ends; when the time is reached... Less than or equal to the set calculation time If so, continue repeating steps 2 through 7; In step 4, the Runge-Kutta-Fehlberg method is used to solve the differential equations of the static JA hysteresis model. This is a fourth-order method with a fifth-order error estimate, yielding the following results. magnetization intensity at time and differential magnetization The details are as follows: The equations of the static JA hysteresis model are expressed as follows: ； In the formula: H e The effective magnetic field strength; Indicates magnetic flux density; These are the average field parameters of the coupling within the magnetic domains; M an It is a hysteresis-free magnetization intensity; M s The saturation magnetization; a The shape parameters of the hysteresis-free magnetization curve; M The magnetization intensity; c It is the reversible magnetization coefficient; k This is the restraining coefficient; For direction coefficients, when d H hy / d t When >0, ;d H hy / d t When <0, ; k 0 is the default value for the restraint coefficient; The standard deviation; H hy H represents the static magnetic field strength. hy This refers to the static magnetic field strength. The direction coefficient, defined to prevent non-physical interpretations, must satisfy the following: ； In the formula: For symbolic parameters.

2. The method for solving transformer core hysteresis and permeability based on the JA model according to claim 1, characterized in that: In step 1, the initial value of the magnetic flux density B ( t 0) Magnetic field strength H hy ( t 0) The calculation is as follows: (T)； T represents the unit of magnetic flux density; Unit: A / m; This indicates the previous simulation time.

3. The method for solving the hysteresis and permeability of transformer cores based on the JA model according to claim 1, characterized in that: Step 2 includes the following steps: S2.1: The set variable time step Calculate the current simulation time ; S2.2: Extract using the flux table Rate of change of magnetic flux flowing through the variable permeability component at any time ; S2.3: Then, the rate of change of magnetic flux is measured by an integrator. Integrate to obtain the magnetic flux. ; S2.4: Finally, divide by the cross-sectional area of ​​the magnetic circuit through the gain converter. Obtain magnetic flux density And provide it as input to the C-Script module.

4. The method for solving the hysteresis and permeability of transformer cores based on the JA model according to claim 1, characterized in that: In step 3, the magnetization intensity and step length The calculation is as follows: ； ； In the formula: for The magnetization intensity at time; and They are respectively and t Magnetic flux density at time; for The step size of time; is the vacuum permeability.

5. The method for solving transformer core hysteresis and permeability based on the JA model according to claim 1, characterized in that: magnetization Where: Mrev represents the reversible magnetization component, and Mirr represents the irreversible magnetization component; Differential magnetization: 。 6. The method for solving transformer core hysteresis and permeability based on the JA model according to claim 1, characterized in that: In step 5, the magnetic field strength H hy ( t and permeability The calculation is as follows: ； 。 7. The method for solving transformer core hysteresis and permeability based on the JA model according to claim 1, characterized in that: In step 6, the magnetic permeability and magnetic field strength H hy ( t The variable permeability is obtained after calculation using a gain converter. and magnetomotive force F ( t )= H hy ( t ) l And provide it to the variable permeability module.

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