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This paper aims to propose an effective modeling method of dynamic hysteresis properties for soft magnetic composite (SMC) core using an equivalent circuit representation. Because the eddy currents flowing inside iron powder particles should be considered, it is well known that an accurate magnetic field analysis of the SMC core in a wide range of excitation frequency is not easy. To overcome this difficulty, a dynamic hysteresis modeling based on the standard Cauer circuit is investigated.

In the proposed method, the first inductance represents the static magnetic property of the SMC, and the latter part represents the dynamic effect because of the eddy currents. The values of the circuit elements were determined by an optimization method based on symmetric loops measured at several frequencies. To verify the validity of the proposed modeling method, finite-element analyses of a ring core inductor and an alternating current reactor were performed.

By comparing the simulated and measured magnetic properties, the necessity to consider magnetic hysteresis in the equivalent circuit model is clarified. Furthermore, the frequency-dependent inductances of practical reactors can be obtained from the finite-element analysis combined with the proposed method.

This paper demonstrates the significance of determining the circuit parameters in the equivalent circuit for dynamic hysteresis modeling based on the measured magnetic properties. The effectiveness of the proposed method is verified by comparing frequency-dependent inductances of two kinds of reactors between the simulation and measurement.

This paper aims to propose an energetic model parameter calculation method for predicting the materials’ symmetrical static hysteresis loop and asymmetrical minor loop to improve the accuracy of electromagnetic analysis of equipment.

For predicting the symmetrical static hysteresis loop, this paper deduces the functional relationship between magnetic flux density and energetic model parameters based on the materials’ magnetization mechanism. It realizes the efficient and accurate symmetrical static hysteresis loop prediction under different magnetizations. For predicting the asymmetrical minor loop, a new algorithm is proposed that updates the energetic model parameters of the asymmetrical minor loop to consider the return-point memory effect.

The comparison of simulation and experimental results verifies that the proposed parameters calculation method has high accuracy and strong universality.

The proposed parameter calculation method improves the existing parameter calculation method’s problem of relying on too much experimental data and inaccuracy. Consequently, the presented work facilitates the application of the finite element electromagnetic field analysis method coupling the hysteresis model.

The ordinary vector hysteresis stop model with constant threshold values is not able to prohibit the hysteretic property after the saturation correctly. This paper aims to develop an improved vector hysteresis stop model with threshold surfaces. This advanced anisotropic vector hysteresis stop model can represent the magnetic saturation properties and the hysteresis losses under alternating and rotating magnetizations.

By integrating anhysteretic surfaces into the elastic element of a vector hysteresis stop model, the anisotropy of the permeability of an electrical steel sheet can be represented. Instead of the commonly used constant threshold value for plastic elements of the hysteresis model, threshold surfaces are applied to the stop hysterons. The threshold surfaces can be derived directly from measured alternating major loops of the material sample. By saturated polarization, the constructed threshold surfaces are vanishing. In this way, the reversible magnetic flux density is in the same direction of the applied magnetic flux density. Thus, the saturation properties are satisfied.

Analyzing the measurements of the electrical steel sheets sample obtained from a rotational single sheet tester shows that the clockwise (CW) and counter-CW (CCW) rotational hysteresis losses decrease by saturated flux density. At this state, instead of the domain wall motion, the magnetization rotation is dominant in the material. As a result, the hysteresis losses, which are related to the domain wall motion, are vanished near the saturation. In one stop operator, the plastic element represents the hysteresis part of the model. Integrating threshold surface into the plastic element, the hysteresis part can be modified to zero near the saturation to represent the saturation properties.

The results of this work demonstrate that the presented vector hysteresis stop model allows simulation of anisotropic hysteresis effects, alternating and rotating hysteresis losses. The parameters of the hysteresis model are determined by comparing the measured and modeled minor loops in different alternating magnetization directions. With the identified parameters, the proposed model is excited with rotated excitations in CW and CCW directions. The rotated hysteresis losses, derived from the model, are then compared with those experimentally measured. The modified vector stop model can significantly improve the accuracy of representing hysteresis saturations and losses.

The purpose of this paper is to present the method which relatively easily allows to approximate the hysteresis loop of the dynamo or transformer steel sheets. The paper also looks into the formulation of an equation allowing determination of distribution of the flux density and eddy currents in cross-section of these sheets.

An exponential function was applied in the presented method relating to the approximation of the hysteresis loop. When the field strength changes its value, then, the flux density are the sum or difference of a function, describing the lower or upper hysteresis curve and some “ransient” component. On the basis of Maxwell’s equations and Amper’s law, one non-linear differential equation was formulated which allows to calculate the flux density and eddy currents in a cross-section of a transformer sheet.

The method which relatively easily allows approximation of the hysteresis loop of ferromagnetic material is presented in the paper. The paper presents the derivation of one non-linear differential equation, allowing calculation of the flux density and eddy currents in the cross-section of the transformer sheets, taking into account the hysteresis phenomenon.

The paper presents the method that can be used in modeling of the hysteresis loops of dynamo or transformer sheets, and the final non-linear differential equation can be applied in calculations of the magnetic field and eddy currents in cross-section of the transformer sheets.

The paper refers to important issues of modeling and calculations of the magnetic and eddy current field distribution in transformer steel sheets.

The purpose of this paper is to present a novel steady‐state performance analysis for the hysteresis motor whose rotor ring is made of Fe‐Cr‐Co magnet steel with magnetic anisotropy.

In order to analyze the motor performance at synchronous pull‐out, the finite‐element method is used, where hysteresis torque is obtained from the magnetic field analysis of the hysteresis motor with the isotropic magnet. The reluctance torque due to magnetic anisotropy can be obtained by using the difference of the B‐H hysteresis‐loop area between the anisotropic and isotropic magnets.

The good agreement between computed and measured performance in an experimental motor validates the proposed analysis.

The proposed method is quite useful for the design and analysis of the hysteresis motor with magnetic anisotropy.

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).

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 Ψ(i) of the tested transformer are calculated from the set of measured terminal voltages and terminal currents. To simulate magnetic behavior of the iron core the feedback scalar Preisach model of hysteresis is proposed which gives more accurate predictions than classical model. For this hysteresis model the PDF and feedback function are needed. The intend of this paper is to find these function as an analytical formulas which are convenient for numerical simulations. For identification of the PDF and feedback function parameters of the considered iron core of tested transformer the Levenberg-Marquardt optimization algorithm was used.

The flux common to all windings is calculated by integrating the induced voltages of the appropriate windings. In this paper the PDF is proposed as a functional series including two dimensional Gauss expressions. In order to proper approximation of hysteresis nonlinearity of the tested iron core the first three terms of functional series of the PDF have been used. In the optimization algorithm only initial and descending limiting hysteresis curves Φ(Θ) were utilized. The feedback function for proposed hysteresis model is assumed as third-order polynomial. The hysteresis model has been successfully validated by comparing the calculated and measured results of Φ(Θ) hysteresis curves. This hysteresis model can be used in transient and steady state simulations of tested transformer taking into account the hysteresis phenomenon. The developed hysteresis model can be also used for analysis of the influence of remnant flux on the operation of tested transformer especially in transient states.

In this paper the feedback Preisach hysteresis model is involved in the flux common to all windings vs ampere-turns of all windings. The new PDF is proposed as functional series including two dimensional Gauss expressions. For tested transformer the three first terms of this functional series may be used for proper approximation of hysteresis nonlinearities.

The purpose of this paper is to present a Preisach model to simulate the vector hysteresis properties of ferromagnetic materials.

The vector behavior has been studied at low frequency applying a single‐sheet tester with a round‐shaped specimen, and the locus of the magnetic flux density vector has been controlled by a digital measurement system. An inverse vector Preisach hysteresis model has been developed and identified by using the measured data.

Finally, the inverse model has been inserted into a finite element procedure through the combination of the fixed point technique and the reduced magnetic scalar potential formulation. The developed single‐sheet tester measurement system has been simulated. The applicability of the realized measurement system as well as the developed model has been proven by comparing measured and simulated results.

The identification technique is original, based on a previous work of the author.

The scope of the work is to provide an identification procedure for an hysteresis model based on nonlinear circuit cells.

An identification procedure for an hysteresis model based on nonlinear circuit cells is presented. The response of elementary cell is equal to a generalized play operator. The procedure allows the identification of the limit symmetric hysteresis loop and of minor loops. The identification procedure is based on the relationship between the circuit parameters and the discretization of the first derivative of the BH curve by means of a staircase function.

The model obtained is employed for the simulation of soft magnetic composite material cores under different supply voltage waveforms. The proposed identification procedure is able to define an accurate model of an hysteretic material with a low number of elemental network cells. The identification algorithm is simple and makes use of the limit hysteresis cycle only. Symmetric minor loops are used to tune “soft” operators for the correct reconstruction of cycles which do not reach saturation.

The model is limited to scalar and static hysteresis model.

The model obtained can be used in network simulator like SPICE in order to model circuits in which magnetic devices are involved.

The circuit hysteresis model has been presented in literature, while its identification is newly proposed by the authors.

The classical Preisach model and its modifications are one of the most generally applied simulations to model the behavior of magnetic materials, to describe hysteresis phenomena and different properties, as noncongruent minor loops, frequency dependence, temperature dependence, accommodation, and so on. Artificial neural networks (NNs) are widely used in fields of research where the solution of problems with conventional methods on traditional computers is very difficult to work out, for example system identification, modeling and function approximation. NNs can be considered as universal approximation for functions based on the theorem of Kolmogorov‐Arnold. In this paper a new NN model of scalar hysteresis characteristics is introduced. The examined method is built on the function approximation and continuous interpolation capability of NNs. The anhysteretic magnetization curve and a set of the ascending and a set of the descending first order reversal branches can be stored in a system of three neural networks. Different properties of magnetic materials can be simulated by a simple knowledge‐based algorithm. Value of differential susceptibility can be expressed in analytical form. Finally hysteresis characteristics predicted by the introduced model are compared with the results of the Preisach simulation.

The increase of the accuracy of a mathematical model of hysteresis by the choice of the optimum saturation curve for a given material.

Hysteresis loops of typical soft magnetic materials are approximated with the help of the Taka´cs magnetization model using different saturation curves. The quality of approximations is determined by the deviation of computed magnetic induction amplitudes, iron losses, apparent remanences and coercivities from the measured values.

By the proper choice of saturation curve, the relative inaccuracy of approximations can be reduced with reference to the original model based on tangent hyperbolic function.

The accuracy of approximations worsens close to saturation because of the excessive rise of magnetization due to the linear term of the model. This effect should be minimized by the application of complex saturation curves using greater number of parameters.

Owing to the convenient analytical form and increased accuracy, the model equations can be used in simpler practical evaluations of hysteresis effects and for teaching purposes.

Presented form of model equations enables approximation of hysteresis loops and the evaluation of main characteristics of magnetic materials on the basis of any saturation curve.