Hysteresis loop simulation method, device, equipment and medium

Abstract

The application discloses a hysteresis loop simulation method, device, equipment and medium, and belongs to the technical field of transformers. The method comprises the following steps: acquiring the magnetic flux density of a ferromagnetic element and air pressure data in the environment; inputting the air pressure data into an interpolation model for interpolation processing to obtain a corresponding shape function; wherein the interpolation model is trained based on at least two air pressure data samples and shape function samples corresponding to the air pressure data samples respectively, the shape function samples are extracted from corresponding hysteresis loop samples, and the hysteresis loop samples are the hysteresis loop of the ferromagnetic element when the ferromagnetic element is in the air pressure environment matched by the corresponding air pressure data samples; determining the static magnetic field strength based on the magnetic flux density and the shape function; determining the dynamic magnetic field strength based on the static magnetic field strength; and simulating the dynamic hysteresis loop of the ferromagnetic element based on the magnetic flux density and the determined dynamic magnetic field strength.

Description

Technical Field

[0001] This application relates to the field of transformer technology, and in particular to a hysteresis loop simulation method, apparatus, equipment and medium. Background Technology

[0002] With human progress and technological development, power systems are constantly expanding in scale, capacity, and coverage, bringing numerous conveniences to people's lives. At the same time, faults can cause significant economic losses to users and society, making the safe and reliable operation of power systems paramount. Transformers are commonly used components in power systems. By analyzing the magnetic performance data of ferromagnetic components within transformers and simulating their magnetic properties, we can provide references for transformer design and optimization, thereby improving transformer performance and ensuring the safe and reliable operation of power systems.

[0003] Currently, there are some research results in the simulation of the magnetic properties of ferromagnetic components. Most of these studies focus on the simulation of magnetic properties under normal operating conditions. However, they have not considered the magnetic properties of ferromagnetic components under special operating conditions, such as high altitude and low pressure or underwater high pressure. As a result, it is impossible to simulate the magnetic properties of ferromagnetic components under special operating conditions, which leads to poor performance of the converter. Summary of the Invention

[0004] In view of the above problems, this application is made to provide a hysteresis loop simulation method, apparatus, device and medium to solve the above problems, which can realize the simulation of the magnetic properties of ferromagnetic components under special operating conditions, thereby improving the performance of the converter.

[0005] Firstly, this application provides a method for simulating hysteresis loops, including:

[0006] Obtain the magnetic flux density of the ferromagnetic element and the air pressure data of its environment;

[0007] The air pressure data is input into the interpolation model for interpolation processing to obtain the corresponding shape function;

[0008] The interpolation model is trained based on at least two air pressure data samples and shape function samples corresponding to each air pressure data sample. The shape function samples are extracted from the corresponding hysteresis loop samples. The hysteresis loop samples are the hysteresis loops of the ferromagnetic element when the ferromagnetic element is in the air pressure environment matched by the corresponding air pressure data sample.

[0009] The static magnetic field strength is determined based on the magnetic flux density and the shape function;

[0010] Based on the static magnetic field strength, determine the dynamic magnetic field strength;

[0011] Based on the magnetic flux density and the determined dynamic magnetic field strength, the dynamic hysteresis loop of the ferromagnetic element is simulated.

[0012] In one embodiment, after determining the dynamic magnetic field strength based on the static magnetic field strength, the method further includes:

[0013] The dynamic magnetic field strength and the magnetic flux density of the ferromagnetic element are input into the magnetostrictive model;

[0014] Obtain the relationship expression between air pressure data and free parameter values; based on the air pressure data and the relationship expression, determine the corresponding free parameter values; and use the free parameter values ​​as the free parameter values ​​of the magnetostrictive model.

[0015] Based on the dynamic magnetic field strength, the magnetic flux density of the ferromagnetic element, and the free parameter values, the magnetostrictive strain of the ferromagnetic element is calculated using the magnetostrictive model.

[0016] Based on the magnetostrictive strain and the magnetic flux density, the magnetostrictive loop of the ferromagnetic element is simulated.

[0017] In one embodiment, the process of constructing the relational expression includes:

[0018] Obtain at least two air pressure data samples, and free parameter value samples corresponding to each air pressure data sample;

[0019] Based on each air pressure data sample and the corresponding free parameter value sample, the relational expression is constructed using the least squares method.

[0020] In one embodiment, obtaining the free parameter samples corresponding to each pressure data sample includes:

[0021] For each air pressure data sample, obtain the strain test value corresponding to the current air pressure data sample;

[0022] Based on the current air pressure data sample, the initial stretching model is trained at least once until the training end condition is met, and the magnetostrictive model corresponding to the training end condition is obtained.

[0023] The free parameter values ​​in the magnetostrictive model trained on the current air pressure data sample are used as the free parameter value samples corresponding to the current air pressure data sample.

[0024] The training operations include:

[0025] Based on the air pressure data samples and the initial stretching model, the strain prediction values ​​are obtained;

[0026] Based on the difference between the strain prediction value and the strain test value, the free parameters of the initial scaling model are adjusted, and the initial scaling model with adjusted parameters is used as the initial scaling model for the next training.

[0027] In one embodiment, the calculation of the magnetostrictive strain of the ferromagnetic element based on the dynamic magnetic field strength, the magnetic flux density of the ferromagnetic element, and the free parameters using the magnetostrictive model includes:

[0028] Based on the dynamic magnetic field strength and the magnetic flux density of the ferromagnetic element, the magnetization intensity of the ferromagnetic element is obtained;

[0029] Based on the dynamic magnetic field strength, the magnetization intensity, and the free parameters in the magnetostrictive model, the magnetostrictive strain of the ferromagnetic element is calculated using the magnetostrictive model.

[0030] In one embodiment, determining the dynamic magnetic field strength based on the static magnetic field strength includes:

[0031] Based on the conductivity, cross-sectional area, structural characteristic parameters, preset dimensionless coefficients, and magnetic flux density change rate of the ferromagnetic element, the magnetic field strength corresponding to the abnormal loss of the ferromagnetic element is determined.

[0032] Based on the thickness of the ferromagnetic element and the rate of change of magnetic flux density, the magnetic field strength corresponding to the eddy current loss of the ferromagnetic element is determined.

[0033] The dynamic magnetic field strength is determined based on the static magnetic field strength, the magnetic field strength corresponding to abnormal losses, and the magnetic field strength corresponding to eddy current losses.

[0034] In one embodiment, determining the static magnetic field strength based on the magnetic flux density and the shape function includes:

[0035] The magnetic flux density and the shape function are input into the inverse operator hysteresis model;

[0036] Based on the magnetic flux density, the shape function, the hysteresis operators in the inverse operator hysteresis model, and the total number of hysteresis operators, the static magnetic field strength is calculated using the inverse operator hysteresis model.

[0037] Secondly, this application provides a hysteresis loop simulation device, the device comprising:

[0038] The acquisition module is used to acquire the magnetic flux density of the ferromagnetic element and the air pressure data of the environment in which it is located;

[0039] The processing module is used to input the air pressure data into the interpolation model for interpolation processing to obtain the corresponding shape function;

[0040] The interpolation model is trained based on at least two air pressure data samples and shape function samples corresponding to each air pressure data sample. The shape function samples are extracted from the corresponding hysteresis loop samples. The hysteresis loop samples are the hysteresis loops of the ferromagnetic element when the ferromagnetic element is in the air pressure environment matched by the corresponding air pressure data sample.

[0041] The first determining module is used to determine the static magnetic field strength based on the magnetic flux density and the shape function;

[0042] The second determining module is used to determine the dynamic magnetic field strength based on the static magnetic field strength;

[0043] The simulation module is used to simulate the dynamic hysteresis loop of the ferromagnetic element based on the magnetic flux density and the determined dynamic magnetic field strength.

[0044] Thirdly, this application provides an electronic device, including: a memory and a processor, the memory and the processor being communicatively connected to each other, the memory storing computer instructions, and the processor executing the computer instructions to perform the method as described in the first aspect.

[0045] Fourthly, this application provides a computer-readable storage medium storing computer instructions for causing the computer to perform the method described in the first aspect.

[0046] The technical solutions provided in this application embodiment have at least the following technical effects or advantages: This application pre-constructs an interpolation model, which is based on at least two air pressure data samples and shape function samples corresponding to each air pressure data sample. The shape function samples are extracted from the corresponding hysteresis loop samples. The hysteresis loop samples are the hysteresis loops of the ferromagnetic element when the ferromagnetic element is in the air pressure environment matched by the corresponding air pressure data sample. After obtaining the magnetic flux density of the ferromagnetic element and the air pressure data of the environment, the air pressure data can be input into the interpolation model for interpolation. The values ​​are processed to obtain the corresponding shape function, which corresponds to the current air pressure data. Then, based on the magnetic flux density and the shape function, the static magnetic field strength is determined. Based on the static magnetic field strength, the dynamic magnetic field strength is determined. Based on the magnetic flux density and the determined dynamic magnetic field strength, the dynamic hysteresis loop of the ferromagnetic element is simulated. That is, the dynamic hysteresis loop of the ferromagnetic element under the air pressure data conditions can be modeled. Thus, when the ferromagnetic element is in a special operating environment, such as high altitude and low pressure or underwater high pressure, the magnetic properties of the ferromagnetic element can be simulated, thereby improving the transformer performance.

[0047] The above description is only an overview of the technical solution of this application. In order to better understand the technical means of this application and to implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of this application more obvious and understandable, the following are specific embodiments of this application. Attached Figure Description

[0048] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the scope of this application. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings:

[0049] Figure 1 This is a flowchart illustrating a hysteresis loop simulation method provided in an embodiment of this application;

[0050] Figure 2 This is a flowchart illustrating another hysteresis loop simulation method provided in an embodiment of this application;

[0051] Figure 3 This is a schematic diagram of the structure of a hysteresis loop simulation device provided in an embodiment of this application;

[0052] Figure 4 This is a schematic diagram of the structure of the electronic device provided in the embodiments of this application. Detailed Implementation

[0053] In practical applications, transformers operate in special environments such as high altitude and low voltage, and underwater high voltage, which can affect the magnetic properties of the transformer core. Simulating the magnetic properties of ferromagnetic materials under special operating conditions can provide theoretical support for core material selection, magnetic property prediction and evaluation, and optimized design for core vibration reduction and noise reduction, thereby optimizing transformer performance.

[0054] As mentioned above, there have been some research results on the simulation of the magnetic properties of ferromagnetic components such as silicon steel sheets and amorphous alloys. Most of these studies focus on the simulation of magnetic properties under normal operating conditions, without considering the magnetic properties of ferromagnetic components under special operating conditions. Therefore, this application proposes a simulation of the dynamic hysteresis loop and magnetostriction characteristics of ferromagnetic components in transformers under different air pressure conditions.

[0055] To make the objectives, technical solutions, and advantages of this application clearer, the embodiments of this application will be described in further detail below with reference to the accompanying drawings. It should be understood that the embodiments of this disclosure and the specific features in the embodiments are detailed descriptions of the technical solutions of this application, rather than limitations on the technical solutions of this application. Unless otherwise specified, the embodiments of this application and the technical features in the embodiments can be combined with each other.

[0056] Figure 1 This is a flowchart of a hysteresis loop simulation method provided in an embodiment of this application, such as... Figure 1 As shown, the method includes:

[0057] Step S101: Obtain the magnetic flux density of the ferromagnetic element and the air pressure data of the environment in which it is located;

[0058] Ferromagnetic elements can be the core of a transformer, and the environment in which they are located is the air pressure environment of the transformer or the ferromagnetic elements in the transformer. The air pressure data can be specific air pressure values.

[0059] Step S102: Input the air pressure data into the interpolation model for interpolation processing to obtain the corresponding shape function;

[0060] The interpolation model is constructed based on at least two air pressure data samples and shape function samples corresponding to each air pressure data sample. The shape function samples are extracted from the corresponding hysteresis loop samples. The hysteresis loop samples are the hysteresis loops of the ferromagnetic element when the ferromagnetic element is in the air pressure environment matched by the corresponding air pressure data sample.

[0061] In this embodiment, the interpolation model can be a radial basis function (RBF) interpolation model;

[0062] The static concentric hysteresis loop of the ferromagnetic element is measured under the air pressure environment matched by each air pressure data sample. The static concentric hysteresis loop is used as the hysteresis loop sample corresponding to the air pressure data sample. The shape function in the static concentric hysteresis loop is extracted to obtain the shape function sample corresponding to the air pressure data sample. The air pressure data sample and the shape function sample corresponding to the corresponding air pressure data sample are used as known quantities to train the initial interpolation model to obtain the above interpolation model.

[0063] The process of training the initial interpolation model to obtain the aforementioned interpolation model specifically includes:

[0064] For each air pressure data sample, an initial interpolation model is output from the air pressure data sample. The shape function is predicted by the initial interpolation model. The predicted shape function is compared with the shape function sample. Based on the comparison result, the parameters in the initial interpolation model are adjusted until the error between the shape function predicted by the initial interpolation model and the corresponding shape function sample is within the preset accuracy range, thus obtaining the above interpolation model.

[0065] After training the interpolation model, the current air pressure data is input into the interpolation model for interpolation processing, and the shape function of the ferromagnetic element under the air pressure environment matched by the current air pressure data is calculated.

[0066] Step S103: Determine the static magnetic field strength based on the magnetic flux density and shape function;

[0067] The magnetic flux density and shape function are input into the inverse operator hysteresis model, and the corresponding static magnetic field strength is obtained by simulating the model.

[0068] Step S104: Determine the dynamic magnetic field strength based on the static magnetic field strength;

[0069] Based on the field separation theory and the static magnetic field strength, the dynamic magnetic field strength is simulated. Based on this, the dynamic magnetic field strength of ferromagnetic components under various air pressure environments can be simulated.

[0070] Step S105: Based on the magnetic flux density and the determined dynamic magnetic field strength, simulate the dynamic hysteresis loop of the ferromagnetic element.

[0071] For different atmospheric pressure environments, based on the magnetic flux density and dynamic magnetic field strength of the ferromagnetic element under that atmospheric pressure environment, the dynamic hysteresis loop of the ferromagnetic element under that atmospheric pressure environment is simulated. The dynamic hysteresis loop is used to characterize the relationship between magnetic flux density and dynamic magnetic field strength.

[0072] As can be seen, this application can simulate the corresponding dynamic hysteresis loop for different environments. Therefore, for special atmospheric pressure environments such as high altitude and low pressure or underwater high pressure, the dynamic hysteresis loop of ferromagnetic components can be modeled, providing a reference for the design and optimization of transformers, thereby improving transformer performance.

[0073] This application pre-constructs an interpolation model based on at least two air pressure data samples and shape function samples corresponding to each air pressure data sample. The shape function samples are extracted from the corresponding hysteresis loop samples. The hysteresis loop samples are the hysteresis loops of ferromagnetic elements when they are in the air pressure environment matched by the corresponding air pressure data samples. After obtaining the magnetic flux density of the ferromagnetic element and the air pressure data of the environment, the air pressure data can be input into the interpolation model for interpolation processing to obtain the corresponding shape function. That is, the shape function corresponds to the current air pressure data. Then, based on the magnetic flux density and the shape function, the static magnetic field strength is determined. Based on the static magnetic field strength, the dynamic magnetic field strength is determined. Based on the magnetic flux density and the determined dynamic magnetic field strength, the dynamic hysteresis loop of the ferromagnetic element is simulated. That is, the dynamic hysteresis loop of the ferromagnetic element under the air pressure data conditions can be modeled. Thus, when the ferromagnetic element is in a special operating environment, such as high altitude and low pressure or underwater high pressure, the magnetic properties of the ferromagnetic element can be simulated, thereby improving the transformer performance.

[0074] In one embodiment, determining the static magnetic field strength based on the magnetic flux density and the shape function includes: inputting the magnetic flux density and the shape function into an inverse operator hysteresis model; and calculating the static magnetic field strength based on the magnetic flux density, the shape function, the hysteresis operators in the inverse operator hysteresis model, and the total number of hysteresis operators through the inverse operator hysteresis model.

[0075] In the inverse operator hysteresis model, the hysteresis operators and the total number of hysteresis operators are predefined; the inverse operator hysteresis model can be the inverse form of the play hysteresis model, where play refers to the hysteresis operator.

[0076] The expression for the inverse operator hysteresis model used to solve for the static magnetic field strength H(t) is as follows:

[0077] ;

[0078] In the formula, H ( t )and B ( t These represent the static magnetic field strength and magnetic flux density, respectively. p i For the first i One hysteresis operator; h i It is a shape function; n denoted as the number of hysteresis operators.

[0079] It should be noted that when the input magnetic flux density B ( t When the input magnetic flux density is sinusoidal, the model simulates the static magnetic field strength under the corresponding sinusoidal operating condition; when the input magnetic flux density is... B ( t When the waveform is non-sinusoidal, the model simulates the static magnetic field strength under the corresponding non-sinusoidal working condition.

[0080] In one embodiment, determining the dynamic magnetic field strength based on the static magnetic field strength includes: determining the magnetic field strength corresponding to the abnormal loss of the ferromagnetic element based on the conductivity, cross-sectional area, structural characteristic parameters, preset dimensionless coefficients, and magnetic flux density change rate of the ferromagnetic element; determining the magnetic field strength corresponding to the eddy current loss of the ferromagnetic element based on the thickness and magnetic flux density change rate of the ferromagnetic element; and determining the dynamic magnetic field strength based on the static magnetic field strength, the magnetic field strength corresponding to the abnormal loss, and the magnetic field strength corresponding to the eddy current loss.

[0081] In this embodiment, the dynamic magnetic field strength is the sum of the static magnetic field strength, the magnetic field strength corresponding to abnormal loss, and the magnetic field strength corresponding to eddy current loss; the magnetic field strength corresponding to abnormal loss refers to the magnetic field strength lost when the ferromagnetic element generates abnormal energy loss; the magnetic field strength corresponding to eddy current loss refers to the magnetic field strength lost when the ferromagnetic element generates eddy current loss.

[0082] When the static magnetic field strength is the same as that under sinusoidal conditions, the model simulates the corresponding dynamic magnetic field strength under sinusoidal conditions; when the static magnetic field strength is the same as that under non-sinusoidal conditions, the model simulates the corresponding dynamic magnetic field strength under non-sinusoidal conditions. Specifically:

[0083] When the magnetic flux density is sinusoidal, according to the field separation theory, the dynamic magnetic field strength... H sin Represented as:

[0084] ;

[0085] In the formula, , ,as well as These are the magnetic field strengths corresponding to hysteresis loss, abnormal loss, and eddy current loss of ferromagnetic elements, respectively. Specifically:

[0086] Magnetic field strength corresponding to hysteresis loss That is, the static magnetic field strength when the magnetic flux density is a sinusoidal waveform;

[0087] ;

[0088] in, The conductivity of the ferromagnetic element. S Let be the cross-sectional area of ​​the ferromagnetic element. G This is a preset dimensionless coefficient, typically set to 0.1356; V 0 represents a structural characteristic parameter, which can be a statistical parameter used to describe the microstructural characteristics of ferromagnetic components. In this application, dB / dt is the rate of change of magnetic flux density, which characterizes the change of magnetic flux density over time;

[0089] ;

[0090] in, d The thickness of the ferromagnetic element. The meanings of dB / dt will not be elaborated here. In the formula, "." represents a multiplication sign.

[0091] When the magnetic flux density is a non-sinusoidal waveform, according to the field separation theory, the dynamic magnetic field strength... Hhar Represented as:

[0092] ;

[0093] The magnetic field strength corresponding to the hysteresis loss of the ferromagnetic element is given by... The magnetic field strength corresponding to abnormal losses The magnetic field strength corresponding to eddy current loss;

[0094] Magnetic field strength corresponding to hysteresis loss That is, the static magnetic field strength when the magnetic flux density is a non-sinusoidal waveform;

[0095] The explanations of the parameters in the formula are similar to those in the corresponding parts above. middle The magnetic flux density of the ferromagnetic element under non-sinusoidal operating conditions;

[0096] The explanations of the parameters in the formula are similar to those in the corresponding parts above. middle It also refers to the magnetic flux density of ferromagnetic components under non-sinusoidal operating conditions;

[0097] As can be seen, the above embodiments detail how to simulate the dynamic magnetic field strength of ferromagnetic components under different air pressures, thereby simulating the dynamic hysteresis loop under different air pressure environments and improving transformer performance.

[0098] This application can simulate not only the dynamic hysteresis loop of ferromagnetic components under different air pressure environments, but also the magnetostrictive loop of ferromagnetic components under different air pressure environments. Specifically:

[0099] In one embodiment, after determining the dynamic magnetic field strength based on the static magnetic field strength, the method further includes: inputting the dynamic magnetic field strength and the magnetic flux density of the ferromagnetic element into the magnetostrictive model; obtaining the relationship expression between the air pressure data and the free parameter values; determining the corresponding free parameter values ​​based on the air pressure data and the relationship expression; using the free parameter values ​​as the free parameter values ​​of the magnetostrictive model; calculating the magnetostrictive strain of the ferromagnetic element through the magnetostrictive model based on the dynamic magnetic field strength, the magnetic flux density of the ferromagnetic element, and the free parameter values; and simulating the magnetostrictive hysteresis loop of the ferromagnetic element based on the magnetostrictive strain and the magnetic flux density.

[0100] In this embodiment, the magnetostrictive model may have only one free parameter or multiple free parameters. For example, the magnetostrictive model may include the magnetoelastic coupling coefficient. b Magnetic coupling coefficient a and magnetic coupling coefficient These three free parameters, for any one of them: the free parameter value in the magnetostrictive model varies depending on the current air pressure data. For all three free parameters, it is necessary to determine the free parameter value in the magnetostrictive model for different air pressure data. Specifically, let's take determining the free parameter value of a certain free parameter as an example:

[0101] This application pre-constructs a relational expression between air pressure data and free parameter values. Specifically, it uses a function containing air pressure data to represent the free parameter values. Thus, for air pressure data under the current air pressure environment, the free parameter values ​​corresponding to the air pressure data under the current air pressure environment can be determined based on the air pressure data and the pre-constructed relational expression, and these free parameter values ​​can be used as the free parameter values ​​of the magnetostrictive model.

[0102] For example, the value of the free parameter b varies depending on the air pressure data; similarly, for the free parameter... For different air pressure data, The values ​​of the free parameters are different; For different air pressure data, The values ​​can be different.

[0103] In this embodiment, the magnetostrictive model can be the Sablik magnetostrictive model. Based on the dynamic magnetic field strength, the magnetic flux density of the ferromagnetic element, and the free parameter values, the magnetostrictive strain of the ferromagnetic element is calculated using the magnetostrictive model. The specific implementation process is as follows:

[0104] Based on the magnetoelastic coupling coefficient, Poisson's ratio, Young's modulus, and magnetic energy density of the ferromagnetic element, the magnetostrictive strain of the ferromagnetic element is calculated using a magnetostrictive model. The model expression for the magnetostrictive model is as follows:

[0105] ;

[0106] denoted as γ, where γ is the magnetostrictive strain of the ferromagnetic element; b is the magnetoelastic coupling coefficient; v and Y are the Poisson's ratio and Young's modulus of the ferromagnetic element, respectively. It is the magnetic energy density;

[0107] Magnetic energy density can be obtained based on the magnetization, free permeability, average field coefficient of coupling within magnetic domains, magnetic coupling coefficient, dynamic magnetic field strength, and hysteresis-free magnetization of ferromagnetic elements. Specifically:

[0108] ;

[0109] M The magnetization of a ferromagnetic element μ 0 represents the permeability of free space; aThe average field coefficient of the coupling within the magnetic domain; and All are magnetic coupling coefficients; This refers to the dynamic magnetic field strength. M an It is the hysteresis-free magnetization intensity.

[0110] Similarly, ;

[0111] The saturation magnetization of the ferromagnetic element is given. The definitions of other parameters are similar to those in the above embodiments and will not be repeated here.

[0112] The hysteresis-free magnetization is calculated based on the shape factor of the hysteresis-free magnetization curve, the effective magnetic field strength, and the saturation magnetization of the ferromagnetic element. Specifically, it is solved using the Langevin function:

[0113] ;

[0114] The shape factor of the hysteresis-free magnetization curve; H e The effective magnetic field strength; The saturation magnetization of the ferromagnetic element;

[0115] The effective magnetic field strength is calculated based on the dynamic magnetic field strength, the average field coefficient of intradomain coupling, and the magnetization. Specifically:

[0116] ;

[0117] The average field coefficient of the coupling within the magnetic domain and denoted as magnetization intensity.

[0118] Intradomain coupling average field coefficient These are not free parameters and need to be calculated using the following formula:

[0119] ;

[0120] in, The calculation formula is: ;

[0121] The definitions of the parameters in the calculation formula are the same as those in the above embodiments, and will not be repeated here.

[0122] It should be noted that H in the formulas of this application refers to the dynamic magnetic field strength.

[0123] As can be seen, in this embodiment, the values ​​of the free parameters of the magnetostrictive model are different for different air pressure data. Therefore, the magnetostrictive strain of the ferromagnetic element is calculated based on the magnetostrictive model, and then the magnetostrictive loop of the ferromagnetic element is simulated. This can realize the magnetostrictive loop of the ferromagnetic element under different air pressure environments. In this way, the magnetostrictive loop of the ferromagnetic element can also be simulated under high altitude and low pressure or underwater high pressure environments. This provides theoretical support for the selection of magnet elements, prediction and evaluation of magnetic properties, and optimization design of core vibration reduction and noise reduction, thereby improving the performance of transformers.

[0124] Similarly, for the relational expressions in the above embodiments, taking the determination of the relational expression corresponding to any free parameter as an example, it can be obtained based on least squares fitting, specifically:

[0125] In one embodiment, the process of constructing the relational expression includes: obtaining at least two air pressure data samples and free parameter value samples corresponding to each air pressure data sample; and constructing a relational expression based on each air pressure data sample and the corresponding free parameter value samples using the least squares method.

[0126] By fitting the free parameter value samples using the least squares method, they are expressed as functions of the corresponding air pressure data samples. Thus, based on a large number of air pressure data samples and the corresponding free parameter value samples for each air pressure data sample, a relationship expression between the free parameter value and the air pressure data can be fitted for a specific free parameter. Therefore, for a given free parameter... b This allows us to obtain the relationship expression between the air pressure data and the values ​​of the free parameter b; for the free parameter... This allows us to obtain air pressure data and free parameters. The expression relating the values ​​of the free parameters; This allows us to obtain air pressure data and free parameters. The relationship expression between the values ​​of .

[0127] This embodiment specifically introduces the construction of the relationship expression between air pressure data and free parameter values ​​by using the least squares method, thereby determining the free parameter values ​​corresponding to different air pressure data, and thus simulating the magnetostrictive hysteresis loop under different air pressure data.

[0128] For any given free parameter, it is necessary to obtain free parameter value samples corresponding to multiple air pressure data samples. Taking obtaining free parameter value samples for any given free parameter as an example:

[0129] In one embodiment, obtaining the free parameter samples corresponding to each pressure data sample includes: for each pressure data sample, obtaining the strain test value corresponding to the current pressure data sample; performing at least one training operation on the initial stretching model based on the current pressure data sample until the training termination condition is met, obtaining the magnetostrictive model corresponding to the training termination condition; using the free parameter values ​​in the magnetostrictive model trained on the current pressure data sample as the free parameter value sample corresponding to the current pressure data sample; the training operation includes: obtaining the strain prediction value based on the pressure data sample and the initial stretching model; adjusting the free parameters of the initial stretching model based on the difference between the strain prediction value and the strain test value, and using the adjusted initial stretching model as the initial stretching model for the next training.

[0130] In this implementation, the initial stretching model needs to be trained at least once until the training termination condition is met. The training termination condition is that the difference between the strain prediction value obtained based on the initial stretching model and the strain test value corresponding to the current air pressure data sample is within a preset difference range.

[0131] In this embodiment, the magnetostrictive model that meets the training termination condition can be used as the magnetostrictive model mentioned above. At the same time, the free parameters in the magnetostrictive model that meets the training termination condition can be used as the free parameter value samples corresponding to the current air pressure data samples. In this way, by changing the air pressure data samples and using each air pressure data sample as the current air pressure data sample, the free parameter value samples corresponding to each air pressure data sample can be obtained.

[0132] Each training operation specifically includes:

[0133] Determining the dynamic magnetic field strength corresponding to the air pressure data sample is similar to the above embodiment and will not be described in detail here.

[0134] The dynamic magnetic field strength corresponding to the air pressure data sample is input into the initial stretching model to obtain the corresponding magnetostrictive strain. The specific implementation is similar to the above embodiment, and will not be repeated here. The obtained corresponding magnetostrictive strain is used as the strain prediction value for this training.

[0135] Then, based on the difference between the strain prediction value obtained in this training and the actual measured strain test value, the free parameters of the initial stretching model are adjusted. The strain test value is the magnetostrictive strain of the ferromagnetic element actually measured under the current air pressure environment. The initial stretching model with adjusted parameters is used as the initial stretching model for the next training.

[0136] In the next training iteration, the current air pressure data sample remains unchanged. Similarly, based on the current air pressure data sample and the initial stretching model, a new magnetostrictive strain is obtained as the strain prediction value for this training. Then, based on the difference between the strain prediction value obtained in this training and the actual measured strain test value (i.e., the actual measured strain test value remains unchanged in each training iteration), the free parameters of the initial stretching model are adjusted.

[0137] In this embodiment, the initial scaling model can be a particle swarm optimization (PSO) model, with any type of free parameter ( b , , or The free parameter value samples of the magnetostrictive model need to be extracted by the particle swarm optimization algorithm, with the goal of minimizing the error between the strain measurement and prediction values.

[0138] In this embodiment, the source of the free parameter value samples corresponding to each air pressure data sample is explained. It can be seen that this application can first determine the free parameter value samples through the PSO model. As the air pressure data samples are different, the free parameter value samples are also different. Then, based on the air pressure data samples and the corresponding free parameter value samples, the relationship expression is constructed by the least squares method. Thus, for different air pressure data, the corresponding free parameter values ​​can be determined, and the magnetostriction loop under different air pressure data can be simulated. In this way, the magnetostriction loop of ferromagnetic components can also be simulated in environments such as high altitude low pressure or underwater high pressure.

[0139] Magnetostriction models are generally based on magnetization. M The input quantity is the voltage, but in actual engineering, the physical quantity output from the transformer port is generally voltage. Faraday's law of electromagnetic induction yields magnetic flux density, and the excitation applied to the ferromagnetic element should be magnetic flux density. B Therefore, it is also necessary to adjust the magnetic field strength. M Converted to magnetic flux density B， With magnetic flux density B Input the magnetostrictive model to the input quantity to achieve B - λ Simulation of the dynamic magnetostrictive hysteresis loop (i.e., the aforementioned magnetostrictive hysteresis loop). Specifically:

[0140] In one embodiment, the step of calculating the magnetostrictive strain of the ferromagnetic element based on the dynamic magnetic field strength, the magnetic flux density of the ferromagnetic element, and the free parameters using the magnetostrictive model includes: obtaining the magnetization of the ferromagnetic element based on the dynamic magnetic field strength and the magnetic flux density of the ferromagnetic element; and calculating the magnetostrictive strain of the ferromagnetic element using the magnetostrictive model based on the dynamic magnetic field strength, the magnetization, and the free parameters in the magnetostrictive model.

[0141] According to magnetic flux density B Dynamic magnetic field strength H and magnetization M The constitutive relation between them is B = μ0.(H+M), where “.” is a multiplication sign, so that the magnetic field strength M can be converted into magnetic flux density B. Then, the dynamic magnetic field strength and magnetization are input into the magnetostrictive model. Based on the dynamic magnetic field strength, magnetization and free parameters in the magnetostrictive model, the magnetostrictive strain of the ferromagnetic element is calculated through the magnetostrictive model.

[0142] See attached document Figure 2 The specific implementation of this application will be explained below with reference to specific data:

[0143] S1, the static concentric hysteresis loops corresponding to the measured air pressures P1 and P2, respectively;

[0144] S2, the shape functions corresponding to P1 and P2;

[0145] S3. Predicting arbitrary air pressure P based on radial basis function interpolation method x The corresponding shape function;

[0146] The concentric hysteresis loops of the ferromagnetic element at air pressures P1 and P2 were measured respectively, and their corresponding shape functions were extracted and denoted as h. P1 and h p2； h P1 and h p2 Using known data, a radial basis function interpolation model is constructed, and other air pressures P are obtained through interpolation calculations. x The corresponding shape function h px .

[0147] S4. Calculate the static magnetic field strength under arbitrary air pressure based on the Play static hysteresis model;

[0148] Any air pressure refers to the air pressure of the current atmospheric pressure environment, where h is... px Substituting into the inverse operator hysteresis model, we obtain arbitrary air pressure P. x The corresponding static magnetic field strength. The model expression for the inverse operator hysteresis model is as described above and will not be repeated here.

[0149] S5. Calculate the dynamic magnetic field strength under any air pressure.

[0150] Based on field separation theory, the dynamic magnetic field strength under arbitrary air pressure is calculated. This dynamic magnetic field strength is then obtained by combining the static magnetic field strength with the magnetic field strength corresponding to abnormal losses and eddy current losses. The expression for calculating the dynamic magnetic field strength is as described above and will not be repeated here.

[0151] When the excitation is a non-sinusoidal waveform, the corresponding dynamic magnetic field strength is H. har； When the excitation is a sinusoidal waveform, the corresponding dynamic magnetic field strength H sin .

[0152] S6, Simulated dynamic hysteresis loop;

[0153] The dynamic magnetic field strength of ferromagnetic elements under different air pressures can be simulated, thereby achieving... B - H Simulation of dynamic hysteresis loop.

[0154] S7. Determine the free parameter value corresponding to the current air pressure data;

[0155] Parameter b , , All are free parameters. For any type of free parameter, such as b, , or Particle swarm optimization algorithm is needed to find the optimal solution for magnetostrictive strain. λ The optimization objective is to minimize the error between the measured and predicted values. The free parameter values ​​in the magnetostrictive model trained on the current air pressure data sample are determined, and these free parameter values ​​are extracted as the free parameter value samples corresponding to the current air pressure data sample.

[0156] For the free parameter b (or or Based on the free parameter value samples extracted under known air pressures P1 and P2, The value of the free parameter The pressure P is fitted using the least squares method. x The function can be used to predict any air pressure P. x The corresponding free parameter values.

[0157] S8. Based on the dynamic magnetic field strength, the magnetic flux density of the ferromagnetic element, and the free parameter values, the magnetostrictive strain of the ferromagnetic element is calculated using a magnetostrictive model.

[0158] Substituting the dynamic magnetic field strength obtained above into the Sablik magnetostrictive model allows for the simulation of the magnetostrictive characteristics of ferromagnetic components. The model expression of the Sablik magnetostrictive model is as described above and will not be repeated here.

[0159] S9, Simulated dynamic magnetostrictive loop.

[0160] The magnetic flux density B was obtained through simulation. and Magnetostrictive strain The relationship curve between λ, thus realizing B - λ Simulation of dynamic magnetostrictive hysteresis loop.

[0161] This application combines the static Play hysteresis model, field separation theory, and Sablik magnetostrictive model to simulate the dynamic hysteresis loop and magnetostrictive loop under different air pressures and sinusoidal or non-sinusoidal excitation conditions.

[0162] Based on the same concept, embodiments of the present invention also provide a hysteresis loop simulation device. Figure 3 This is a structural block diagram of a hysteresis loop simulation device 300 provided in an embodiment of this application, as shown below. Figure 3 As shown, the device 300 includes:

[0163] The acquisition module 301 is used to acquire the magnetic flux density of the ferromagnetic element and the air pressure data of the environment in which it is located;

[0164] Processing module 302 is used to input the air pressure data into the interpolation model for interpolation processing to obtain the corresponding shape function;

[0165] The interpolation model is trained based on at least two air pressure data samples and shape function samples corresponding to each air pressure data sample. The shape function samples are extracted from the corresponding hysteresis loop samples. The hysteresis loop samples are the hysteresis loops of the ferromagnetic element when the ferromagnetic element is in the air pressure environment matched by the corresponding air pressure data sample.

[0166] The first determining module 303 is used to determine the static magnetic field strength based on the magnetic flux density and the shape function;

[0167] The second determining module 304 is used to determine the dynamic magnetic field strength based on the static magnetic field strength;

[0168] The simulation module 305 is used to simulate the dynamic hysteresis loop of the ferromagnetic element based on the magnetic flux density and the determined dynamic magnetic field strength.

[0169] In one embodiment, the device includes a magnetostrictive loop simulation model, used after the second determining module determines the dynamic magnetic field strength based on the static magnetic field strength, to input the dynamic magnetic field strength and the magnetic flux density of the ferromagnetic element into the magnetostrictive model; to obtain a relational expression between air pressure data and free parameter values, to determine the corresponding free parameter values ​​based on the air pressure data and the relational expression, and to use the free parameter values ​​as the free parameter values ​​of the magnetostrictive model; to calculate the magnetostrictive strain of the ferromagnetic element through the magnetostrictive model based on the dynamic magnetic field strength, the magnetic flux density of the ferromagnetic element, and the free parameter values; and to simulate the magnetostrictive loop of the ferromagnetic element based on the magnetostrictive strain and the magnetic flux density.

[0170] In one embodiment, the apparatus further includes a construction module, the construction process of the relational expression being performed by the construction module, which is specifically used for:

[0171] Obtain at least two air pressure data samples, and free parameter value samples corresponding to each air pressure data sample;

[0172] Based on each air pressure data sample and the corresponding free parameter value sample, the relational expression is constructed using the least squares method.

[0173] In one embodiment, when the construction module acquires the free parameter samples corresponding to each air pressure data sample, it is specifically used for:

[0174] For each air pressure data sample, obtain the strain test value corresponding to the current air pressure data sample;

[0175] Based on the current air pressure data sample, the initial stretching model is trained at least once until the training end condition is met, and the magnetostrictive model corresponding to the training end condition is obtained.

[0176] The free parameter values ​​in the magnetostrictive model trained on the current air pressure data sample are used as the free parameter value samples corresponding to the current air pressure data sample.

[0177] The training operations include:

[0178] Based on the air pressure data samples and the initial stretching model, the strain prediction values ​​are obtained;

[0179] Based on the difference between the strain prediction value and the strain test value, the free parameters of the initial scaling model are adjusted, and the initial scaling model with adjusted parameters is used as the initial scaling model for the next training.

[0180] In one embodiment, the magnetostrictive loop simulation model, when calculating the magnetostrictive strain of the ferromagnetic element based on the dynamic magnetic field strength, the magnetic flux density of the ferromagnetic element, and the free parameters, is specifically used for:

[0181] Based on the dynamic magnetic field strength and the magnetic flux density of the ferromagnetic element, the magnetization intensity of the ferromagnetic element is obtained;

[0182] Based on the dynamic magnetic field strength, the magnetization intensity, and the free parameters in the magnetostrictive model, the magnetostrictive strain of the ferromagnetic element is calculated using the magnetostrictive model.

[0183] In one embodiment, when determining the dynamic magnetic field strength based on the static magnetic field strength, the second determining module is specifically used for:

[0184] Based on the conductivity, cross-sectional area, structural characteristic parameters, preset dimensionless coefficients, and magnetic flux density change rate of the ferromagnetic element, the magnetic field strength corresponding to the abnormal loss of the ferromagnetic element is determined.

[0185] Based on the thickness of the ferromagnetic element and the rate of change of magnetic flux density, the magnetic field strength corresponding to the eddy current loss of the ferromagnetic element is determined.

[0186] The dynamic magnetic field strength is determined based on the static magnetic field strength, the magnetic field strength corresponding to abnormal losses, and the magnetic field strength corresponding to eddy current losses.

[0187] In one embodiment, the first determining module is specifically used to: input the magnetic flux density and the shape function into the inverse operator hysteresis model; and calculate the static magnetic field strength based on the magnetic flux density, the shape function, the hysteresis operators in the inverse operator hysteresis model, and the total number of hysteresis operators through the inverse operator hysteresis model.

[0188] It is understood that the device provided in the above embodiments is only illustrated by the division of the above functional modules. In actual applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure of the device can be divided into different functional modules to complete all or part of the functions described above.

[0189] like Figure 4 The present invention also provides an electronic device, which may include a processor 402 and a memory 401, wherein the processor 402 and the memory 401 can communicate with each other through a bus or other means.

[0190] The processor 402 may be a central processing unit (CPU), or an application specific integrated circuit (ASIC), or one or more integrated circuits that can be configured to implement the embodiments of this application, or it may be other general-purpose processors, digital signal processors (DSPs), application specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, or other chips, or combinations of the above types of chips.

[0191] Memory 401 may include mass storage for data or instructions. For example, and not limitingly, memory may include a hard disk drive (HDD), floppy disk drive, flash memory, optical disk, magneto-optical disk, magnetic tape, or Universal Serial Bus (USB) drive, or a combination of two or more of these. Where appropriate, memory may include removable or non-removable (or fixed) media. Where appropriate, memory may be internal or external to an electronic device. In a particular embodiment, memory may be non-volatile solid-state memory.

[0192] In one instance, memory 401 may be read-only memory (ROM). In one instance, the ROM may be a mask-programmed ROM, a programmable ROM (PROM), an erasable PROM (EPROM), an electrically erasable PROM (EEPROM), an electrically rewritable ROM (EAROM), or flash memory, or a combination of two or more of these.

[0193] The processor 402 implements any of the hysteresis loop simulation methods in the above embodiments by reading and executing computer program instructions stored in the memory.

[0194] In one example, the electronic device may further include a communication interface and a bus. The processor, memory, and communication interface are connected via the bus to communicate with each other. The communication interface is primarily used to enable communication between the various modules, devices, units, and / or equipment in the embodiments of this application. Where appropriate, the bus may include one or more buses.

[0195] Furthermore, in conjunction with the hysteresis loop simulation method in the above embodiments, this invention can be implemented using a computer-readable storage medium. This computer-readable storage medium stores computer program instructions; when executed by a processor, these computer program instructions implement any of the hysteresis loop simulation methods described in the above embodiments.

[0196] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, it can include the processes of the embodiments of the methods described above. The storage medium can be read-only memory (ROM), random access memory (RAM), flash memory, hard disk drive (HDD), or solid-state drive (SSD), etc.; the storage medium can also include combinations of the above types of memory.

[0197] Numerous specific details are set forth in the specification provided herein. However, it will be understood that embodiments of the invention may be practiced without these specific details. In some instances, well-known methods, structures, and techniques have not been shown in detail so as not to obscure the understanding of this specification.

[0198] Similarly, it should be understood that, in order to simplify this disclosure and aid in understanding one or more of the various aspects of the invention, in the above description of exemplary embodiments of the invention, various features of the invention are sometimes grouped together in a single embodiment, figure, or description thereof. However, this method of disclosure should not be construed as reflecting an intention that the claimed invention requires more features than are expressly recited in each claim. Rather, as reflected in the following claims, inventive aspects lie in fewer than all features of a single foregoing disclosed embodiment. Therefore, the claims following the detailed description are hereby expressly incorporated into this detailed description, wherein each claim itself is a separate embodiment of the invention.

[0199] It should be noted that the above embodiments are illustrative of the invention and not restrictive, and that those skilled in the art can devise alternative embodiments without departing from the scope of the appended claims. In the claims, any reference signs placed between parentheses should not be construed as limiting the claims. The word "comprising" does not exclude the presence of components or steps not listed in a claim. The word "a" or "an" preceding a component does not exclude the presence of a plurality of such components. The invention can be implemented by means of hardware comprising several different components and by means of a suitably programmed computer. In the unit claims enumerating several means, several of these means may be embodied by the same item of hardware. The use of the words first, second, and third, etc., does not indicate any order. These words can be interpreted as names.

Claims

1. A hysteresis loop simulation method characterized by, The method comprises: obtaining the magnetic flux density of the ferromagnetic element and the air pressure data in the environment; inputting the air pressure data into an interpolation model for interpolation processing to obtain a corresponding shape function; wherein the interpolation model is trained based on at least two air pressure data samples and shape function samples corresponding to each air pressure data sample, the shape function samples are extracted from corresponding magnetic hysteresis loop samples, and the magnetic hysteresis loop samples are the magnetic hysteresis loop of the ferromagnetic element when the ferromagnetic element is in the air pressure environment matched by the corresponding air pressure data sample; inputting the magnetic flux density and the shape function into an inverse operator magnetic hysteresis model to determine the static magnetic field strength through the inverse operator magnetic hysteresis model, wherein the inverse operator magnetic hysteresis model is the inverse form of the play magnetic hysteresis model; simulating the dynamic magnetic field strength based on the field separation theory and the static magnetic field strength; simulating the dynamic magnetic hysteresis loop of the ferromagnetic element based on the magnetic flux density and the determined dynamic magnetic field strength.

2. The method of claim 1, wherein, After simulating the dynamic magnetic field strength based on the field separation theory and the static magnetic field strength, the method further comprises: inputting the dynamic magnetic field strength and the magnetic flux density of the ferromagnetic element into a magnetostrictive model; obtaining a relationship expression between the air pressure data and the free parameter value, determining the corresponding free parameter value based on the air pressure data and the relationship expression, and taking the free parameter value as the free parameter value of the magnetostrictive model; calculating the magnetostrictive strain of the ferromagnetic element through the magnetostrictive model based on the dynamic magnetic field strength, the magnetic flux density of the ferromagnetic element, and the free parameter value; simulating the magnetostrictive hysteresis loop of the ferromagnetic element based on the magnetostrictive strain and the magnetic flux density.

3. The method of claim 2, wherein, The construction process of the relationship expression comprises: obtaining at least two air pressure data samples and free parameter value samples corresponding to each air pressure data sample; constructing the relationship expression through the least square method based on each air pressure data sample and the corresponding free parameter value sample.

4. The method of claim 3, wherein, Obtaining the free parameter sample corresponding to each air pressure data sample comprises: for each air pressure data sample, obtaining a strain test value corresponding to the current air pressure data sample; performing at least one training operation on the initial magnetostrictive model based on the current air pressure data sample until a training end condition is met to obtain a magnetostrictive model corresponding to the training end condition; taking the free parameter value in the magnetostrictive model trained for the current air pressure data sample as the free parameter value sample corresponding to the current air pressure data sample; The training operation comprises: obtaining a strain prediction value based on the air pressure data sample and the initial magnetostrictive model; adjusting the free parameter of the initial magnetostrictive model based on the difference between the strain prediction value and the strain test value, and taking the initial magnetostrictive model after adjusting the parameter as the initial magnetostrictive model for the next training.

5. The method of claim 2, wherein, The calculation of the magnetostrictive strain of the ferromagnetic element through the magnetostrictive model based on the dynamic magnetic field strength, the magnetic flux density of the ferromagnetic element, and the free parameter comprises: obtaining the magnetization of the ferromagnetic element based on the dynamic magnetic field intensity, the magnetic flux density of the ferromagnetic element; calculating the magnetostriction strain of the ferromagnetic element by the magnetostriction model based on the dynamic magnetic field intensity, the magnetization, and the free parameters in the magnetostriction model.

6. The method according to any one of claims 1 to 5, characterized in that, The dynamic magnetic field intensity is simulated based on the field separation theory and the static magnetic field intensity, including: determining the magnetic field intensity corresponding to the anomalous loss of the ferromagnetic element based on the conductivity, cross-sectional area, structural feature characteristic parameter, preset dimensionless coefficient, and magnetic flux density change rate of the ferromagnetic element; determining the magnetic field intensity corresponding to the eddy current loss of the ferromagnetic element based on the thickness and magnetic flux density change rate of the ferromagnetic element; determining the dynamic magnetic field intensity based on the static magnetic field intensity, the magnetic field intensity corresponding to the anomalous loss, and the magnetic field intensity corresponding to the eddy current loss.

7. The method according to any one of claims 1 to 5, characterized in that, The static magnetic field intensity is determined by inputting the magnetic flux density and the shape function into the inverse operator hysteresis model, including: inputting the magnetic flux density and the shape function into the inverse operator hysteresis model; calculating the static magnetic field intensity by the inverse operator hysteresis model based on the magnetic flux density, the shape function, the hysteresis operator in the inverse operator hysteresis model, and the total number of hysteresis operators.

8. A hysteresis loop simulation device, characterized by The device includes: An acquisition module is configured to acquire the magnetic flux density of a ferromagnetic element and air pressure data in an environment of the ferromagnetic element. A processing module is configured to input the air pressure data into an interpolation model to perform interpolation processing and obtain a corresponding shape function. The interpolation model is trained based on at least two air pressure data samples and shape function samples corresponding to the air pressure data samples. The shape function samples are extracted from corresponding hysteresis loop samples of the ferromagnetic element in a corresponding air pressure environment matched by the air pressure data samples. A first determination module is configured to input the magnetic flux density and the shape function into an inverse operator hysteresis model to determine a static magnetic field intensity by the inverse operator hysteresis model. The inverse operator hysteresis model is an inverse form of a play hysteresis model. A second determination module is configured to simulate a dynamic magnetic field intensity based on a field separation theory and the static magnetic field intensity. An simulation module is configured to simulate a dynamic hysteresis loop of the ferromagnetic element based on the magnetic flux density and the determined dynamic magnetic field intensity.

9. An electronic device, comprising: The memory and the processor are communicatively connected, and the memory stores computer instructions. The processor executes the computer instructions to perform the method in any one of claims 1-7. The computer readable storage medium stores computer instructions for causing the computer to perform the method in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, ​

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