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In many transformer applications, it is necessary to have a core magnetization model that takes into account both magnetic and electrical effects. This becomes particularly important in three-phase ...

A computationally efficient and robust neural network-based model to reproduce the hysteresis phenomenon for soft ferromagnetic alloys is here presented, as well as a dedicated procedure to generate a suitable training set from a minimal set of experimental data. Firstly, an accurate experimental verification has been performed for a commercial NGO electrical steel, measuring a family of hysteresis loops under sinusoidal and non-sinusoidal magnetic induction waveforms. The Preisach model of hysteresis, identified with the sinusoidal loops, has been exploited to generate a wider data set, which consists of a family of first-order reversal curves (FORCs), suitable to train the neural network. Then, a neural network-based hysteresis model, with the capability to reproduce the eventual presence of sub-loops, has been developed. The two simulation approaches have been validated taking into account the other experimental data, which consist of a family of hysteresis loops measured under different types of magnetic induction waveforms. The comparison between the Preisach model and the neural network-based model also covers the simulation of the waveforms found in magnetic systems supplied by pulse-width modulated (PWM) signals. The substantial agreement found indicates that the neural network model can replicate the behaviour of the Preisach model with a considerable advantage in terms of computational cost and memory allocation. In addition, the possibility to be quickly inverted makes the proposed method suitable for matching with FEM solvers.

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.

Amorphous ferromagnetic Fe-based microwires (MWs) have a magnetic structure consisting mainly of a single longitudinal domain and small closure domains at both ends. A rectangular hysteresis loop is then observed according to the fast domain wall propagation along the microwire. This type of material is a good physical example of the idea of a magnetic relay hysteron as described in Preisach model of hysteresis. The hysteron was defined as a mathematical operator acting on the field and producing rectangular loops whose superposition gives out the hysteresis loop. The hysteron idealization is frequently used to describe and interpret FORC (First Order Reversal Curve) diagrams by comparison with Preisach plane. The central idea of this work is to study the FORCs of a real physical sample that behaves closely to the ideal hysteron, both isolated and interacting with a twofold aim. On one hand, providing a better understanding of FORC measurements, and, on the other, analyzing the magnetization reversal processes in microwires with rectangular hysteresis loops. While for a single microwire the behaviour is that expected for a hysteron, both in the hysteresis loop and in the FORC diagram, the magnetostatic interaction between two microwires breaks with the ideal behaviour due to the change in the domain wall mobility at the end of the wires.

The measurement of core losses in machine laminations reveals a fundamental difference between rotational and pulsating types. Rotational core losses under rotating fields decrease at high flux density, while pulsating losses keep increasing steadily. Experimental analyses of loss components Px and Py in x and y directions with rotating fields show that the loss decreases in one loss component and sometimes attains negative values. Tracking the evolution of hysteresis loops along this loss component discloses a peculiar behavior of magnetic hysteresis, where the loop changes its path from counterclockwise to clockwise within a cycle of magnetization process, the so called interleaved hysteresis loop. This paper highlights a successful procedure for modeling the interleaved hysteresis loop in the measurement of rotational core losses in electrical machine laminations using the generalized Prandtl–Ishlinskii (PI) model. The efficiency of the proposed model is compared to Preisach model. Results and conclusion of this work are of importance toward building an accurate model of rotational core losses.

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.

A phenomenological constitutive model is presented to describe the magnetization curve within the context of thermodynamics. Due to the phenomenological analogy between the magnetic hysteresis and the stress hysteresis, the basic structure of the proposed model comes from rate-dependent plasticity in continuum mechanics, namely viscoplasticity. The total magnetic flux density is assumed to be the sum of reversible and irreversible parts. The model introduces the evolution laws of two internal state variables to incorporate the effect of the ever-changing internal microstructure on the current state. The conception originated from viscoplasticity enables the frequency dependence of the hysteresis curve to be modeled.

In this paper, a novel direct method of recursive identification of the Preisach hysteresis density function is proposed. Using the discrete dynamic Preisach model, which is a state-space realization of the classical scalar Preisach model, the method is designed based on the output increment error. After giving the general formulation, the identification scheme implemented for a discretized Preisach plane is introduced and evaluated through the use of numerical simulations. Two cases of Gaussian mixtures are considered for mapping the hysteresis system to be identified. The parameter convergence is shown for a low-pass filtered white-noise input. Further, the proposed identification method is applied to a magnetism-related application example, where the flux linkage hysteresis of a proportional solenoid is assumed from the measurements, and then the inverse of a standard demagnetization procedure is utilized as the identification sequence.

When modelling electrical devices, one has to estimate quite accurately the iron losses for the sake of efficiency. The use of non-sinusoidal electrical sources increases the harmonic content in electrical systems and, consequently, increases significantly the magnetic losses in devices feed by these sources. The harmonic content adds non-centred minor hysteresis loops over the classical major one. The numerical tool used for the material modelling must be able to represent the magnetic behaviour in such conditions. Then, the use of a hysteresis model is the more suited solution, but the chosen model has to take into account correctly the minor loops. The Jiles–Atherton hysteresis model is one of the most employed, due its well-known properties, but it is not able to represent closed minor loops. In this work, we propose a simple approach based on experimental observations and empirical considerations, to improve the representation of minor loops in this model by keeping its simplicity of use and implementation in a FE calculation code. Differently to other approaches found in the literature, the previous knowledge of the magnetic field evolution is not needed. A comparison between measured and calculated curves, as well with the Preisach model, is performed to validate the model.

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.

In this paper a thermodynamic model with internal variables is presented and applied to ferromagnetic hysteresis. The out-of-equilibrium Gibbs free energy of a magnetic system is expressed as a function of the internal state of the Preisach model. Expressions for the system entropy and the entropy production are derived. By this approach it is possible to reproduce the characteristic features of the experimentally observed temperature changes (of the order of 10 - 4 K around room temperature) induced by the magnetic field along the hysteresis loop performed in iron under adiabatic condition.

In electrical engineering, study and design of electromagnetic systems require more and more accurate models. To improve the accuracy of field calculation code, hysteresis phenomenon has to be taken into account to model ferromagnetic material. This material model has to be accurate and fast. In that context, two macroscopic models are often used: the Preisach and the Jiles–Atherton (J–A) models. In this paper, both models are presented. Field calculation requires a model giving the magnetization M versus either the magnetic field H or the magnetic flux density B . Consequently, from the classical Preisach and J–A, two sub-models M ( H ) and M ( B ) are deduced. Then, we aim at comparing these models in terms of identification procedure facilities, accuracy, numerical implementation and computational effort. This study is carried out for three kinds of materials, which have different magnetic features: ferrites, FeSi sheets and a soft magnetic composite material. Then, the implementation of these models in a finite element code is presented. As example of application, a high-frequency transformer supplied by a rectangular voltage is studied.

The Jiles–Atherton (JA) theory of hysteresis has been extended in the present paper to model hysteresis in two-phase magnetic materials. Two-phase materials are those that exhibit two magnetic phases in one hysteresis cycle: one at lower fields and the other at higher fields. In magnetic hysteresis, the transition from one phase to the other i.e. low field phase to high field phase depends mainly on the exchange field. Hence, the material-dependent microstructural parameters of JA theory: spontaneous magnetization, MS, pinning factor, k, domain density, a, domain coupling, α, and reversibility factor, c, are represented as functions of the exchange field. Several cases based on this model have been discussed and compared with the measured data from existing literature. The shapes of the calculated and measured hysteresis loops are in excellent agreement.

The static 2D vector magnetic behaviour of an anisotropic silicon iron sheet is modelled by a particle which depicts its space-averaged behaviour. The magnitude of magnetization is governed by a classical Preisach operator with the projection of field strength on the magnetization direction as input. Its orientation is determined by the equilibrium between the field strength orientation and the anisotropy of the sheet.

Preisach model has enjoyed extensive applications in describing the hysteresis phenomena. An important open question in the analysis of hysteresis using Preisach models is the determination of the model parameters and is referred as the identification problem. However, no general mathematical methods appear to be available for identification and customized identification algorithms must be developed for each specific area of applications. In order to describe physical systems more closely, it becomes increasingly difficult to derive the Preisach function and its associated parameters from the experimental results as the complexity of hysteresis models increases. This paper presents a new approach — a wavelet identification of Preisach model. Since a wavelet can generate a basis for all functions with finite energy, in this application the system output and the Preisach functions are represented by using wavelet approximation. The coefficients of the wavelet approximation expansion can be obtained by a series of experimental data. The modeling and prediction of hysteresis can be done by manipulating the wavelet series. Some comparison of experimental and computational results are also presented in this paper.

A novel hysteresis model is presented which exhibits all main features of hysteresis, such as initial magnetization, saturation, coercivity, remanence and frequency-dependent losses. It consists merely of three differential equations with six parameters. Depending on the slope of the outer hysteresis loop four variants of the model are discussed.

A new mathematical model for the magnetization of ferromagnets subjected to a slowly changing weak magnetic field and severe mechanical load is suggested. The basic concept is to use the Preisach model for the hysteresis of the magnetic texture induced by the mechanical stress.

In the product model of hysteresis the magnetization was proposed to be an indirect function of the magnetic field. The reversible paramagnetic and the irreversible hysteretic contributions to the magnetization appeared together as additional terms in the argument of a sigmoid type envelope function. Recent experimental data suggest that this enveloping sigmoid should be the Brillouin function. Therefore it is proposed that the mean-field theory for the temperature dependence can be generalized for the description of the combined field and temperature dependence of magnetization processes.

The hysteresis models are currently classified in two categories: physical and phenomenological models. A new model-type, referred to as mixed-type model, is introduced. In mixed-type models starting from the hysteresis loop model for the ferromagnetic particles as well as from their distributions as a function of orientation, anisotropy and interaction field, an equivalent distribution of pseudo-particles is computed. Each pseudo-particle is associated to a certain small zone of the Preisach plane. Since in the first stage the model is a physical-type model and in the second it becomes similar to a phenomenological Preisach-type model, it was named mixed-type model. An efficient numerical implementation of the static generalized interacting particle system (IPS) model is presented. A comparison of experimental and simulated data is provided.

A new internal variable hysteresis model is proposed, in which bulging of the pinned walls and evolution of the global domain configuration are considered as distinct phenomena. Minor loops being closed for the considered FeSi lamination, the field history is memorised as in the Preisach approach, but the resulting model is simpler. Reported results show the accuracy of the model.

A new two-dimensional Preisach particle is proposed to describe domain wall motion mechanisms under uniaxial or rotating exciting field. It is coupled to the coherent magnetization rotation Stoner Wohlfarth model adapted to a biaxial particle. The model is tested under uniaxial and rotating excitation and can be applied to both cubic textured or non-oriented materials.

The product Preisach model removes the non-real congruency property of the traditional Preisach model. Delaying its input with respect to the actual field strength variation by means of a supplementary variable, frequency-dependent effects of classical Eddy currents and domain wall displacement can be taken into account.

A new two-dimensional vector model of ferromagnetic hysteresis, which we have designated the UB model, is presented in this paper. Two types of entities constitute the model: u niaxial particles, having an energy per unit volume according to the Stoner-Wohlfarth (SW) theory, and b iaxial particles that differ from the former in the magnetocrystalline energy term. The equilibrium distribution of magnetisation corresponds to an energy minimum for all particles that constitute the model. A description of the model identification is also reported. The process, although essentially different, bears some resemblance to the one used to identify the simplified Preisach model [1] (all the Preisach surface contents concentrated along the two axes of the plane) and requires knowledge of the major hysteresis loops of the specimen under study along the x and y directions. The relationship between experimental values and model parameters is obtained taking into consideration the link that is established between an SW-type particle and Preisach entities. The paper ends with examples where UB model performances are displayed.

The Preisach model successfully describes cyclic hysteresis phenomena in a conceptually simple and mathematically elegant way. In this paper the model is extended to noncyclic magnetization processes like the first magnetization from the demagnetized state. Our experiments reveal that the Preisach function in the noncyclic case is different from that of the cyclic case, a hitherto unknown phenomenon. The change is demonstrated by a comparison of the Preisach functions of the cyclic and noncyclic case and discussed considering the real magnetic structure in the specimen. Secondly, the noncyclic case turns out to be very sensitive to mechanical stresses. It is shown that after a special ac-demagnetization with a small number of cycles the initial curve reveals mechanical influences which cannot be seen in the cyclic case.

The main reason for the recent interest in the Preisach model is the endeavour to stimulate the magnetization processes in various magnetic materials, or, in other words, to identify the model which gives the best correlation between computed and experimentally observed results. In this paper the possibilities and limits of the scalar Preisach model are summarized. A few partial problems connected with the estimation of the Preisach matrix in the moving model, the inconsistency in modeling of accomodation and with the correct representation of reversible processes are discussed and illustrated by relating results of computer experiments.

The consequent identification of the Preisach function requires a knowledge of the correct hypothetical field, allowing the transformation of measured first-order reversal curves from external to internal field dependencies. In the present paper we discuss the difficulties we met during the application of theoretically correct algorithm to soft magnetic materials with Preisach function concentrated near macroscopic coercivity and with relatively low non-congruency.

We define an effective hysteresis model of two-dimensional magnetic properties for the magnetic field analysis. Our hysteresis model is applicable to both alternating and rotating flux conditions. Moreover, we compare the calculated results with the measured ones, and verify the accuracy of this model. We can calculate iron losses in the magnetic materials exactly. As a result, it is shown that the hysteresis model is generally applicable to two-dimensional magnetic properties of some kinds of magnetic materials.

This paper describes a statistical model of bulk ferromagnetic hysteresis with emphasis on hysteresis relative to arbitrary rotating field sequences similar to those which occur during magnetic recording. The model allows a qualitatively correct description of both reversible and irreversible magnetization, complex minor loop behaviour and anhysteresis in a more general setting than is customary. It is shown that partially magnetized states can be described by phase diagrams which extend the oft-cited Preisach diagrams to the vectorial case. The model is also shown to compare favourably with two prevailing vector hysteresis models.

A 3-D moving vectorial model of hysteresis for media consisting of uniaxial interacting particles is described by the standard deviations of anisotropy fields, interaction fields and easy axes angular distributions, the mean value of the anisotropy fields 〈 H k 〉 and the moving parameter α. A systematic identification procedure leading to a good agreement of the model in a limited number of cycles is proposed.

Two hysteresis models commonly used in numerical simulations of the recording process are the Preisach model and the particle assembly model. A combination of these models is presented which includes the mean field approach of the moving Preisach model. It is shown how the model can be tailored to enable an efficient numerical implementation. Comparison of the results with different experimental loops of a metal particle tape and a barium ferrite floppy disc reveals that this model has good vector properties and reproduces the different remanence loops well. The different interaction terms in the model are investigated separately. It is shown that the narrow switching field distribution of barium ferrite and the typical interaction phenomena reported by other authors can both be ascribed to a mean field interaction parallel to the particle axis.

In the energetic model the magnetic state of the material is represented by the minima of the total energy function. The model describes hysteretic curves from the demagnetized state up to saturation. At an arbitrary point of magnetization reversal, however, the distribution of the distances between domain walls and pinning centers has to be considered with respect to the magnetic history, which is important for the calculation of minor hysteresis loops.

A scheme for the computation of minor hysteresis loops from measured major loops based on Hodgdon's model is presented. The latter is regarded as a solution of the model's differential equation from which other follow. It is shown that the model's parameter (α) is a function of flux density amplitude depending on the major loop and the initial permeability.

The elements of a vector Preisach model for unoriented thin-film media are described. The implementation consists of adding a biaxial anisotropy switching function to the classic Preisach algorithm. The model was developed to simulate high-squareness thin-film recording media. The utility of the model is demonstrated by the simulations of the usual VSM curves: the major loop, forward and reverse remanence loops, and the δM curve, as well as the response to rotating fields. These results are compared with experimental measurements made on an unoriented thin-film hard disk material.

A vector hysteresis model based on the moving Preisach model, that exhibits accommodation, is discussed. It is a vector generalization of the scalar Preisach accommodation model, and is applicable to a wide variety of recording media. Its rotational remanence properties are in agreement with experimentally observed vector accommodation phenomena.

In this paper the hysteretic behaviour of an iron core inductor is described by means of a new model based on a sequential algorithm. This model has been applied to study a series ferroresonant circuit. The simulations obtained using the proposed model are in good agreement with experimental results, as well as with the predictions of the classical Preisach model; nevertheless the latter may be computationally more cumbersome.

A simple lattice model that allows hysteresis loops with exchange bias to be reproduced is presented. The model is based on the metastable Random Field Ising model, driven by an external field, with synchronous local relaxation dynamics. The key ingredient of the model is that a certain fraction $f$ of the exchange constants between neighbouring spins is enhanced to a very large value $J_E$. The model allows the dependence of several properties of the hysteresis loops to be analyzed as a function of different parameters and we have carried out an analysis of the first-order reversal curves., 2 pages, 3 figures

A model system of a regular square lattice of epitaxial garnet particles was used to investigate the magnetization process in two dimensions. Switching statistics of particles are treated in terms of the classical Preisach model of magnetic hysteresis. The dispersion of the coercivity, controlled by the technology of preparation of the medium, and the distribution of the magnetostatic interaction fields of the system of particles determine the hysteresis loop. However, the interaction fields depend on the magnetization distribution itself, i.e. on the actual information in a recording medium, and the non-ellipsoidal shape and size of the particles have a strong effect on the switching process.

Measurements of static hysteresis loops in the temperature range from 20 to 500°C are presented. The measured hysteresis curves are described by the moving Preisach model, and the model parameters are discussed in relation to the temperature dependence of magnetization processes.

A vector hysteresis model, combining the classical Preisach and Stoner-Wohlfarth models, has been developed. It is derived by superposition of Preisach models with axes dispersed in a plane. The Preisach planes are modified, defined by the actual particles' switching fields. They are calculated by the SW astroid, shifted along the easy axis to account for interactions. Both reversible and irreversible changes are considered. The model performs well in simulating experimental data.

The question of the existence of a unique demagnetized state arose when several M = 0 magnetic states at H = 0 have been observed for epitaxial garnet films having simple stripe domain structures. The Preisach model of the magnetic hysteresis is capable of describing different demagnetizing processes. A recent vector moving model of the hysteresis properties of particulate magnetic materials predicts that, depending on the demagnetizing process, the demagnetized states are different. Measurements of the initial magnetization process after ac and dc demagnetization of particulate recording media have been perfomed and compared to the predictions of the vector moving model.