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This article presents the modified Preisach model of hysteresis for a 3-phase medium frequency transformer in a 100 kW dual active bridge converter. The transformer magnetic core is assembled out of ferrite I-cores, which results in multiple parasitic air gaps. For this transformer, the hysteresis loops were measured and parameters of the Preisach model were determined. The Preisach distribution function is approximated with a two-dimensional Gauss function series and the feedback function is a 3rd-degree polynomial. The optimized identification of Preisach distribution function parameters was prepared. Two sets of parameters were determined based on the analysis of major and minor hysteresis loop. The developed model is used to analyze the transformer core power loss. A new set of Steinmetz equation parameters for multi air gap ferrite core MFT is proposed.

The Preisach model of hysteresis has two parts: a geometrical staircase and a density or weighting function. In typical applications, the underlying density function of hysteresis operators is estimated through partial derivatives of first order reversal curves, or a priori assumed to obey simple functional forms like Gaussian, Lorenzian etc. Here we take a more agnostic and empirical approach, and expand the density in a general form using the spectrum of the Laplace operator on a bounded triangular domain. Transforming the input to the same bounded domain, we have a nonlinear parameter fitting problem. We fit parameters to our own magnetic hysteresis data directly using complex waveforms, for both soft and hard loops. For hard loops, if the Preisach density is to be kept strictly nonnegative (as is usual), a nonlinear transformation of the Preisach output is needed. Additionally, the Preisach density is consists of a single hump for soft loops and three distinct humps for hard loops. Our fitted density function, based on a general expansion, contains several coefficients, but subsequent simulation is quick. The main contribution of this paper is a direct demonstration of fitting the density function without making a priori assumptions about the functional form.

The objective of the present paper is to generalize the vector Preisach hysteresis model to take dynamic effects into account. A comprehensive analysis of the vector behavior has been performed by a single sheet tester with a specimen of round shape. The locus of the magnetic flux density vector has been controlled by a digital measurement set up at different frequency. An inverse vector Preisach hysteresis model has been built up by viscous-type scalar models and an identification procedure has been developed to follow the measured data. Finally, the model has been inserted into a finite element procedure through the fixed point technique to simulate electrical engineering problems.

This paper presents a simple dynamic vector-play model to calculate the iron loss and describe the vector hysteresis behavior of a non-oriented (NO) electrical steel sheet (ESS) under 50 Hz rotating magnetic fields. Based on the iron loss separation theory, the proposed model is separated to the static hysteresis component and eddy current component. The static hysteresis component is constructed by vector play model, which is identified by using 1 Hz minor $B$ – $H$ loops. And two coefficients $\omega _{x}$ and $\omega _{y}$ are introduced to consider the anisotropic property of NO ESS and the excess loss of eddy-current component under 50 Hz magnetic field. The validity of the proposed dynamic vector hysteresis model is verified by comparing it with the experimental results under various 50 Hz magnetic field conditions.

An anisotropic vector hysteresis model based on the improved isotropic vector play operator has been presented to predict the magnetization behavior of anisotropic hysteresis materials. The required parameters can be identified from the major hysteresis loops in all principal axes, which can be easily measured, or are directly available from magnetic material manufacturers. The presented model, which has been successfully implemented in 2-D and 3-D transient finite-element analysis, is validated by numerical experiments and measured data cited from TEAM problem 32, and is applied to simulate a synchronous reluctance motor with an axially laminated anisotropic rotor.

This paper presents an improved identification algorithm of the scalar play model, and suggests a novel vector play model to describe the vector hysteretic behavior of a nonoriented electrical steel sheet (ESS) under rotating magnetic fields. The proposed identification algorithm gives much better numerical accuracy than a conventional one by assigning more play operators than the measured asymmetric minor loops. The vector-shape function of the suggested vector play model consists of two scalar shape functions, which are independently identified by using measured hysteresis loops under alternating magnetic fields along rolling and transverse direction of ESS, respectively. The vector play model, furthermore, employs a nonlinear coefficient, which is a function of the magnitude and direction of magnetic flux density, to increase the numerical accuracy. The validity of the suggested vector play model is verified by comparing it with experimental results under various magnetic-field conditions.

International audience; We propose an original approach to solve the coupled problem of alternative magnetic field penetration inside a toroidal soft ferromagnetic sample and frequency dependent magnetic hysteresis. Local repartition of ferromagnetic losses depends on the instantaneous material properties and on the frequency of the excitation field waveform. A correct solution to the model, with respect to this repartition, implies a higher resolution in two dimensions of the diffusion equation including local dynamic hysteresis consideration. The resulting model gives precious local information but requires complex parameter setting, high computational capacity and long simulation time. Due to the toroidal shape, a single dimension algorithm solving of the diffusion equation is clearly insufficient and it would lead to inaccurate simulation results. Consequently, a large number of discretization nodes and extended simulation time must be considered in two dimensional configurations. In our alternative solution, starting from a lumped model, we add a fractional time derivative of the dynamic hysteresis losses. It leads to an accurate formulation of the problem with a reduction in complexity and simulation times.

Preisach-based method was used to characterize a series of BaTiO3 hysteresis loops with varying external field frequencies. A stochastic adjustment of hysterons' weight was performed to obtain the Preisach densities. These densities, in representing the hysteresis responses, were characterized with three key parameters of the 3-dimensional hyperbolic-like distribution. One of the parameters relates directly to coercivity, while the other two concurrently represent polarization derivatives close to the coercivity, and emphasize an adaptability of the material to the external field around the main body of the loops. Thus, this approach can be extended to characterize other series of hysteresis loops to study changes of material responses influenced by varying external field frequency factor.

This paper deals with the models elaboration for the asymmetric three-phase transformers. The first model uses the principle of the hysteresis integration in two-dimensional finite-element method (FEM) with magnetic field calculations. This method is based on inverse Jiles–Atherton hysteresis model. The second one is a dynamic electromagnetic model (DEM) based on Tellinen hysteresis model. The DEM and FEM models used in ferromagnetic cores have been modified by replacing the anhysteretic curve by the hysteresis loop. A simulation in time domain is carried out and the simulated results are compared with those obtained experimentally to validate the proposed approach. An error calculation is performed to show the accuracy of results obtained by DEM and FEM models.

The Preisach function is considered as a product of two special one dimensional functions, which allows the closed form evaluation of the Everett integral. The deduced closed form expressions are included in Preisach models, in particular in the static model, moving model and a rate dependent hysteresis model, which can simulate the frequency dependence of the magnetization process. The details of the freely available implementations, which are available online are presented. The identification of the model parameters and the accuracy to describe the magnetization process are discussed and demonstrated by fitting measured data. Transient electric circuit simulation with hysteresis demonstrates the applicability of the developed models.

This paper deals with the implementation of an energy-consistent ferromagnetic hysteresis model in 2D finite element computations. This vector hysteresis model relies on a strong thermodynamic foundation and ensures the closure of minor hysteresis loops. The model accuracy can be increased by controlling the number of intrinsic cell components while parameters can be easily fitted on common material measurements. Here, the native h-based material model is inverted using the Newton-Raphson method for its inclusion in the magnetic vector potential formulation. Simulations are performed on a 2D T-shaped magnetic circuit exhibiting rotational flux. By way of validation, results are compared with those obtained with the dual magnetic scalar potential formulation. A very good agreement for global quantities is observed. ispartof: IEEE Transactions on Magnetics vol:52 issue:3 pages:1-4 ispartof: location:CANADA, McGill Univ, Montreal status: published

This study presents a new model using the combination of Preisach and Hyperbolic Tangent models, to predict the magnetic hysteresis of Terfenol-D at different frequencies. Initially, a proper experimental setup was fabricated and used to obtain different magnetic hysteresis curves of Terfenol-D; such as major, minor and reversal loops. Then, it was shown that the Hyperbolic Tangent model is precisely capable of modeling the magnetic hysteresis of the Terfenol-D for both rate-independent and rate-dependent cases. Empirical equations were proposed with respect to magnetic field frequency which can calculate the non-dimensional coefficients needed by the model. These empirical equations were validated at new frequencies of 100 Hz and 300 Hz. Finally, the new model was developed through the combination of Preisach and Hyperbolic Tangent models. In the combined model, analytical relations of the Hyperbolic Tangent model for the first order reversal loops determined the weighting function of the Preisach model. This model reduces the required experiments and errors due to numerical differentiations generally needed for characterization of the Preisach function. In addition, it can predict the rate-dependent hysteresis as well as rate-independent hysteresis.

This paper shows that a Preisach engine, based on the classical Preisach model of hysteresis and identified using the Everett integrals and the first-order reversal curves, can be used whatever the orientation of the hysteresis loop [counterclockwise or clockwise] and whatever the monotonicity of the branches (increasing/decreasing). This is important for the use of the Preisach model in many innovative applications, such as hysteresis compensators in magnetostrictive devices and lithium-iron-phosphate rechargeable battery, as both the applications are characterized by clockwise hysteresis loops and strictly increasing loop branches. Numerical simulations of both cases, compared with experimental data, prove the validity of the approach.

© 2017 IEEE. This paper introduces a comparative study of two different hysteresis models, limiting loop model and elemental operator model. The former is regarded as a mathematical approach based on the traditional Preisach model. To circumvent the difficulty of determining the distribution function in the Preisach model, the data of the limiting hysteresis loop and a function transform on the Preisach diagram are employed. The latter is a physical method which adopts a vectorial elemental operator with biaxial anisotropy based on the magnetization mechanisms of the ferromagnetic material. These two models are analyzed and compared in terms of the underlying principle, numerical implementation, and calculation accuracy in this paper. To verify the introduced models, the magnetic properties of non-oriented silicon steel Lycore-140 and soft magnetic composite material Somaloy 500 under alternating excitations are measured and compared with simulated results, which show the validity and practicability of the models but with different calculation accuracy and speed.

Purpose – The paper presents a mathematical model for the hysteresis phenomenon in a multi-winding single-phase core type transformer. The set of loop differential equations was developed for Kth winding transformer model where the flux linkages of each winding includes a flux common Φ to all windings as function of magneto motive force Θ of all windings. The purpose of this paper is to first determine a hysteresis nonlinearity involved in Φ(Θ) function using modified Preisach theory and second to develop new analytical formula of Preisach distribution function (PDF). Design/methodology/approach – It is assumed in this paper that flux linkage characteristics Ψ(i) of each winding have nonlinear component due to the magnetization characteristic of the steel core and sum of linear components due to the self and mutual leakage fluxes. This nonlinear component of Ψ(i) characteristic can be expressed as a flux common Φ to all windings vs ampere-turns Θ of all windings. The nonlinear flux linkage characteristics...

The laminated core is tested under sinusoidal and dc-biased magnetizations. The measured data are manipulated by the proposed modified iterative method to obtain dc-biasing hysteresis loops accurately. The hysteresis model, based on a consuming function, is used to simulate the hysteresis effects of the iron core under different magnetizations. The fixed-point technique is combined with the harmonic-balanced method to compute exciting currents and magnetic fields simultaneously by considering the hysteresis effects. The global convergent strategies are presented to guarantee the convergence of harmonic solutions. The hysteretic characteristics and iron loss of the laminated core are analyzed on the basis of harmonic solutions of the magnetic field.

The paper focuses on the effect of frequency variations on the shape of modeled hysteresis loops. The concept relies on a modification of value of single parameter related to coercive field strength. The considered description is the GRUCAD model. It is a low-dimensional description based on a ordinary differential equation and some auxiliary nonlinear relationships.

this paper presents a hysteresis model for the mgb 2 using a parameterized Preisach model, in which the weighting functions is determined only based on the M-H limiting loop. The results of simulation and experiment of accuracy of the parameterized Preisach model are reported for the case of iron-sheathed MgB2 superconducting cable samples with an external magnetic field perpendicular to its surface.

History-dependent and history-independent models of magnetic hysteresis are proposed. Spline approximations to the magnetization curves make these models applicable to major loops of any shape. The H(B) representation of reversal curves permits the development of a method that generates reversal curves guaranteed to be free from nonphysical negative slopes and excursions outside the major loop. The applicability of the models to electrical steels and a powder core is illustrated.

In this paper, we present a benchmark problem for the validation of numerical models of vector magnetic hysteresis. The problem geometry and the measurement system are described. The materials considered are both oriented grain (OG) and not OG Si-Fe steels. A series of experimental data about magnetic field and magnetic induction loci under rotational magnetization are presented with the corresponding magnetic losses. The measured data can be useful as a reference for the numerical models testing, comparison, and development. In addition, we propose here a comparison of the experimental data with the numerical results computed using a vector hysteresis model based on the extension of the Preisach model in 2-D.

Iron parts of electrical machines are made of nonoriented isotropic ferromagnetic materials. The finite element method (FEM) is usually applied in the numerical field analysis and design of this equipment. The scalar Preisach hysteresis model has been implemented for the simulation of static and dynamic magnetic effects inside the ferromagnetic parts of motors. The dynamic model is an extension of the static one; an extra magnetic field intensity term is added to the output of the static inverse model. This is a viscosity-type dynamic model. The fixed point method with stable scheme has been realized to take frequency-dependent anomalous losses into account in FEM. This scheme can be used efficiently in the frame of any potential formulations of Maxwell's equations. The comparison between measured and simulated data using a toroidal core shows a good agreement. A modified nonlinear version of T.E.A.M. Problem No. 30.a is also shown to test the hysteresis model in the FEM procedure.

This paper discusses the implementation of the inverse Jiles-Atherton vector hysteresis model with 2-D finite element (FE) method for the analysis of a hysteresis motor electromechanical behavior. A differential reluctivity tensor couples the hysteresis model with the magnetic vector potential-based FE model. Simulation results are validated by experimental data obtained from a specially designed machine.

The representation of a magnetic material using the Preisach Model of hysteresis requires the determination of the Everett function through the measurement of a complete set of B-H curves. Unfortunately, this data is not available in the literature for most materials, which can be a limitation for practical engineering applications. In this paper, we propose an identification procedure of the Everett function using only the more conventional major hysteresis loop and the initial magnetization curve measurements. The B-H curves reproduced with this technique show a very good agreement with experimental data.

This paper shows the equivalence of an energy based model (EBM) of ferromagnetic hysteresis and the well-known Preisach model (PM) of hysteresis for the case of a scalar input variable. It is shown that the memories of both models have a similar representation and a simple mapping between the models is presented. It is revealed that the Preisach density functions originating from the EBM are defined only along discrete lines. This opens up a comfortable possibility to evaluate an integral over the Preisach density function. The model was applied to the diffusion equation which describes thin ferromagnetic steel sheets. Simulation results are presented. A similar interpretation of the vector valued EBM as a vector Preisach operator is possible, however it is not treated within this paper.

A new hysteresis model is developed to describe clockwise hysteresis, in which the positive saturation is achieved for positive values of the input. The model is based on the traditional (counter-clockwise) Jiles-Atherton (JA) model and describes the input-output relation in the form of a first-order differential equation. The most important characteristics such as initial susceptibility, coercive fields, remanence, thermal stability, first and higher order reversal curves are discussed. A comparison with other two clockwise hysteresis models of hysteresis (i.e., the Preisach and Bouc-Wen models) is provided. It is proven that the clockwise JA model can describe novel hysteretic behavior that cannot be reproduced by the previous two models. The novel model is also appealing due its relatively simple numerical implementation and its small number of parameters.

This paper proposes a different inverted hysteresis model with modification of the classic Preisach switch operator. By using this new switch operator, the inverted model remains the wiping out and congruency properties. It also guarantees the symmetry and total positiveness of weight function in the Preisach plane. According to the change pattern of H(B) branches, a differentiable weight function is introduced in the inverted model. The weight function performs with good continuity and symmetry. This makes it possible to implement the inverted model in numerical analysis without iterative procedure. The identification work is done by means of the measured major loops. Here the Newton method algorithm is applied to optimize the mean squared error (MSE) between the measured and simulated data. By this way, the limited number of parameters can be determined. The inverted model was verified for both soft and hard magnetic materials. Besides major hysteresis loops, minor loops and first-order reversal curves (FORCs) can also be simulated. By comparison, the simulation results produced by the inverted hysteresis model show good approximation to the measurement data.

In order to precisely describe the behavior of ferromagnetic materials in rotating magnetic fields, vector hysteresis models are necessary. The extension of the Preisach model with vector methods is well known. Much research in this field is based on the Mayergoyz vector hysteresis model. The drawback of this kind of model is the computational effort for the additional integral in the vectorial Preisach operator. Therefore, much effort is being put into the development of efficient vector models. For the reason of computational efficiency, models have been developed that differ from the Preisach approach and are, for example, based on rotationally coupled step functions. We have proposed a very efficient Preisach based model before, which we called the rotational vector Preisach model. Here, we propose an extension of the rotational switching function of the mentioned model, which improves the model characteristics for arbitrary H-field trajectories. We also introduce a set of special vectorial minor loops for the general validation and comparison of vector models. We apply those H-field trajectories to isotropic materials like FeCo thin films as used in our micromechanical systems. The vectorial minor loops can readily be utilized to evaluate the model output and the results agree well with vectorial measurements.

In this paper, a study on the demagnetization of ferromagnetic materials is conducted based on both experiments with magnetic treatment facility (MTF), which is a miniaturized experimental model, and numerical analysis methods in which the static magnetic finite-element method and Preisach model are combined. The magnetic hysteresis phenomenon inside ferromagnetic materials is effectively mimicked by means of Preisach model. However, owing to the use of $M\hbox{-}H$ variables, Preisach model generally bears numerical instability during repetitive computations. A Preisach model with $M\hbox{-}B$ variables is proposed in this paper to resolve the numerical instability. From the proposed Preisach model with $M\hbox{-}B$ variables, analysis results that were tantamount to those from the general Preisach model with $M\hbox{-}H$ variables were obtained. Numerical instability was also resolved by the proposed model. Furthermore, the discrepancy was practically negligible between the experimental result from a practical demagnetization process and the numerical analysis result from the proposed Preisach model with $M\hbox{-}B$ variables, under the same conditions.

The modeling of dynamic hysteresis loops of soft magnetic materials is carried out using extended hyperbolic model. The extension is based on pure phenomenological approach and consists in elliptical component addition. This component features rounded shapes of dynamic hysteresis loops at low intensities of magnetization and it needs two parameters only. Fitting parameters for each loop are searched individually, and their dependences are then approximated by rational functions. The final model operates with approximated parameters. Proposed model was tested for the material FeNi47Cu5 at sinusoidal excitation at frequency 50 Hz.

In this paper, the identification of soft magnetic B - H characteristics when using the single measured hysteresis loop and fitting the discrete dynamic Preisach (DDP) model is addressed. The magnetic measurements with primary and secondary windings are performed to obtain the magnetostatic system response. The constrained least-squares estimation of the Preisach density function yields the global solution even for limited hysteresis data. The uncertainties detected during the measurement and computation of B and H values are discussed.

This paper introduces a differential approach to model scalar hysteresis based on the Preisach theory. This model can generate hysteresis trajectories for both symmetrical and asymmetrical minor loops and keep the memory of a material in a proper manner. It can easily be inverted, it has a simple algorithm with suitable computational speed, and is not memory consuming. Also, the obtained results of the model are in very good agreement with measurements.

This paper deals with the modeling of vector fields that exhibit hysteresis. A general class of models of vector magnetizations with hysteresis that form a natural extension of the Classical Scalar Preisach Model is defined. Although the modeling was done for the 2-d case, the same theory can be extended to the 3-d case as well. After reviewing some general properties of conservative fields, the specific case of unit magnitude vector fields is discussed. The paper focuses on discussing the properties of a general vector hysteresis operator (hysteron). The mathematical approach followed here can be applied not only to the magnetic hysteresis, but also to any hysteresis process. Some examples of vector hysterons, deduced from the general definition, are presented and their properties analyzed.

It is necessary to describe the hysteresis characteristics of magnetic material precisely for the analysis or design of system with ferromagnetic materials. Although Preisach model is regarded as the most accurate method to describe the hysteresis characteristics, it is not widely applied to the real systems because of some difficulties. The conventional Preisach model shows the numerical instabilities during the iterative computations because the density distribution obtained from the sets of M-H curves are strongly localized. To remove such numerical instabilities, M-B instead of M-H is adopted as an implementation variable in normal Preisach modeling. The two dimensional computations with hysteresis characteristics by using normal Preisach modeling are tested and the result showed that the modeling by using M-B variables showed better stabilities than M-H variables.

Hysteresis Modeling Using a Preisach OperatorThe aim of this paper is to present the analysis and modeling of the hysteresis phenomenon using a Preisach operator. The fundamentals of parameterized hysteresis modeling are introduced, by utilizing three probability density functions. Then, the Preisach operator and its characteristics are defined. Subsequently, results of simulations obtained by means of the aforementioned functions are presented and compared to the ones obtained by other authors.

In this paper we present a model for hysteretic nonlinearities with non-local memories. This model can be applied to describe hysteretic material behavior. Common applications are ferromagnetic or ferroelectric materials. Our model consists of an analytic function and a Preisach operator. We define a continuous Preisach weight function and introduce a method for the identification of the model parameters. The model parameters are customized to a set of symmetric hysteresis curves. We verify our model for a soft magnetic material, a hard magnetic material and the ferroelectric behavior of some piezoelectric material. After that, non-symmetric curves like the virgin curve are predicted very well by the model. It is especially useful, if forced magnetization or polarization, that appears beyond technical saturation, come into account.

The paper deals with an analytical model for hysteresis cycle representation. The hysteresis curve is decomposed in a series of arcs of circles and segments of lines. Each arc of circle or segment of line is expressed using analytical geometry as a function of some given parameters or calculated ones. The easiness of the model proposed is given by the small amount of input data needed to represent the hysteresis cycle in a satisfactory way. Using an inverse mapping function from major hysteresis branches the minor cycles, reversal curve of the first kind or curve of first magnetization can be obtained. Finally a comparison between the measured data and modelled ones was made.

In this work an approach for modeling a transformer core taking into account magnetic hysteresis is presented. For this purpose, the inverse vector Jiles-Atherton hysteresis model is incorporated in a 2D finite element code. This model allows writing naturally the differential reluctivity tensor which can be directly used in the magnetic field equations. A three-phase transformer is modeled. The excitation characteristics of the transformer, as well as hysteresis loops at specific points, are presented. The proposed model was verified with obtained experimental data.

We consider a model system describing the two-dimensional flow of a conducting fluid surrounded by a ferromagnetic solid under the influence of the hysteretic response of the surrounding medium. We assume that this influence can be represented by the Preisach hysteresis operator. Existence and uniqueness of solutions for the resulting system of PDEs with hysteresis nonlinearities is established in the convexity domain of the Preisach operator.

This paper presents a new 3-D finite-element method for taking account of vector hysteresis and anisotropy. The proposed method combines the improved scalar Preisach model with the lagging angle between magnetic flux density and magnetic field intensity to solve vector hysteresis problem. Magnetic material's curves with any other directions to rolling direction are obtained by interpolating the measured curves to solve anisotropy problem. The method enables us to solve vector hysteresis and anisotropy problem simply. In order to validate the algorithm presented, TEAM problem32 has been analyzed using 3-D FEM as an example.

The paper deals with the numerical analysis of a rotational single sheet tester with round-shaped specimen (RRSST) which is now under construction. The measurement setup consists of an induction motor the rotor of which has been removed, and its windings have been replaced to a special two phase one which can generate homogeneous magnetic field inside the motor. The two orthogonal components of the magnetic field intensity and of the magnetic flux density vectors can be measured by H -coils and B -coils, respectively. The Finite Element Method (FEM) with the T , Φ–Φ potential formulation has been applied in the simulations. The vector hysteresis property of the specimen has been approximated by the vector Preisach model. Finally, the nonlinear problem has been solved by the fixed-point technique. The aim of the present work is to focus on the design aspects of this kind of measurement system.

This work proposes a method of efficiently modeling the hysteresis of ferroelectric materials. Our approach includes the additive combination of a reversible and an irreversible portion of the polarization and strain, respectively. Whereas the reversible parts correspond to the common piezoelectric linear equations, the irreversible parts are modeled by hysteresis operators. These operators are based on Preisach and Jiles-Atherton hysteresis models which are well-established tools in ferromagnetic modeling. In contrast to micromechanical approaches, a Preisach or a Jiles-Atherton hysteresis operator can be efficiently numerically evaluated. A comparison of the resulting simulations to measured data concludes the article.

An identification technique for the parameters of phenomenological models of hysteresis is presented. The basic idea of our technique is to set up a system of equations for the parameters of the model as a function of known quantities on the major or minor hysteresis loops (e.g. coercive force, susceptibilities at various points, remanence), or other magnetization curves. This system of equations can be either over or underspecified and is solved by using the conjugate gradient method. Numerical results related to the identification of parameters in the Energetic, Jiles–Atherton, and Preisach models are presented.

This paper presents the scalar dynamic magnetic hysteresis model based on the Preisach theory. The important role in this theory played hysteresis operator states. The changes of these operators' states are not immediate in the dynamic model but they are a function of time and parameter k representing the magnetic properties of the material. In this paper the transient state of the hysteresis operator is defined by the nonlinear first order differential equation. The implementation of the dynamic hysteresis is additionally associated with feedback hysteresis model. This allows for obtaining a more accurate model for low and high magnetization frequencies. The material parameter k was determined for the toroidal tape wound core made of anisotropic sheet steel ET114-27. This paper presents the magnetic hysteresis loop simulation results for the different magnetization frequencies.

In this paper a new vector hysteresis model is constructed on the basis of a scalar hysteresis model. The advantages of the scalar model are its easy identification, past memory representation and numerical simplicity. The accommodation property of the model comes from the construction philosophy of the model. The feasibility of the extrapolation is defined by the turning points. The convenience of this model is its efficiency in reduction of the calculation time. The model parameters, the modification vector fields, derived from the permeability vector can be determined from the measured data points. The vector model can approximate the behavior of the vector hysteresis characteristics of ferromagnetic materials. In this paper the main question of the vector model, the definition of the initial values of components in the selected directions is solved.

This paper introduces a simplified vector model based on the Preisach approach that intrinsically satisfies loss and saturation properties. It is able to reproduce isotropic and nonisotropic behavior. The main idea is to compute the magnetization vector in two steps independently, amplitude and phase. The first one is computed by means of a scalar Preisach model with a distribution depending on the angle of the applied field with respect to a fixed direction. The phase is computed by means of a phase diagram and a simple function that take into account the history of the angle between magnetization and applied field. The proposed formulation allows fast computation of rotational and alternative vector magnetization, the computational time is of the order of two times the scalar Preisach model

The Preisach distribution function in electrical steel at different magnetizing frequencies has been studied by the combination of the experimental measurements in an Epstein frame and the numerical identification by the method of centered cycles. The dynamic Preisach distribution function is mostly distributed in the discretized elements along the alpha=-beta axis and the neighboring axis of the alpha=beta axis in the Preisach plane. The least-squares method has been employed to determine the dependence of the values of the distribution function in those specific elements on the magnetizing frequency. The simulated results show that the method in this paper provides another way of calculating the dynamic hysteresis loops

The possibility of considering dynamic effects in three vector hysteresis models is investigated. The friction model of oriented Preisach operators which rotate due to the torque exerted by the external field, the coercive spheres model, the 3D analogue of the classical Preisach model, and a further collective model based on micromagnetic analogy are considered. Furthermore, the “external” dynamic generalization of the static hysteresis models is introduced for the vector case.

PurposeTo analyze the Jiles and Atherton hysteresis model used for hysteresis losses estimation in soft magnetic composite (SMC) material.Design/methodology/approachThe Jiles and Atherton hysteresis model parameters are optimized with genetic algorithms (GAs) according to measured symmetric hysteresis loop of soft magnetic composite material. To overcome the uncertainty, finding the best‐optimized parameters in a wide predefined searching area is done with the proposed new approach. These parameters are then used to calculate the hysteresis losses for the modeled hysteresis. The asymmetric hysteresis loops are also investigated.FindingsThe classical GAs are good optimization methods when a pre‐defined possible set of solutions is known. If no assumption on solutions is present and a wide searching area range for parameter estimation is selected then the use of the new approach with nested GAs gives good results for symmetric hysteresis loops and further for the estimation of hysteresis losses.Research limitations/implicationsThe use of the Jiles and Atherton hysteresis model for asymmetric hysteresis must be explored further. Only one set of optimized Jiles and Atherton hysteresis model parameters used for estimation of hysteresis losses gives good results for only symmetric hysteresis loops. These parameters have limitations for asymmetric hysteresis loops.Practical implicationsNested GAs are a useful method for optimization when a wide searching area is used.Originality/valueThe originality of the paper is in the establishment of nested GAs and their application in Jiles and Atherton hysteresis model parameters optimization. Also, original is the use of the Jiles and Atherton hysteresis model for hysteresis loop description of soft‐magnetic composite material.