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This paper presents various available and new techniques for prediction of the hysteresis loop, no‐load current curve and hysteresis losses. It is shown that linearization is a convenient method to be employed for quick estimation of the hysteresis loop with acceptable accuracy. Although the third and fifth order functions for saturation curve prediction lead to more accurate results, it requires more data and also more complicated equations resulting in longer computation time. Use of various third and fifth order functions for saturation curve are the noticeable advantages of the techniques. The three proposed techniques could predict the hysteresis loop of transformers using simple experiments and iterative computer computations.

This paper aims to compare different static history-independent hysteresis models (mathematical-, behavioural- and physical-based ones) and a history-dependent hysteresis model in terms of parameter identification effort and accuracy.

The discussed models were tested for distorted-excitation waveforms to explore their predictions of complex magnetization curves. Static hysteresis models were evaluated by comparing the calculated and measured major and minor static hysteresis loops.

The analysis shows that the resulting accuracy of the different hysteresis models is strongly dependent on the excitation waveform, i.e. smooth excitations, distorted flux waveforms, transients or steady-state regimes. Obtained results show significant differences between predictions of discussed static hysteresis models.

The general aim was to identify the models on a very basic and limited set of measured data, i.e. if possible using only the measured major static loop of the material. The quasi-static major hysteresis loop was measured at B_max = 1.5 T.

The presented analysis allows selection of the most-suited hysteresis model for the sought-for application and appraisal of the individual limitations.

The presented analysis shows differences in intrinsic mechanisms to predict magnetization curves of the majority of the well-known static hysteresis models. The results are essential when selecting the most-suited hysteresis model for a specific application.

Piezoelectric actuators (PEAs) exhibit hysteresis nonlinearity in open-loop operation, which may lead to unwanted inaccuracy and limit system performance. Classical Preisach model is widely used for representing hysteresis but it requires a large number of first-order reversal curves to ensure the model accuracy. All the curves may not be obtained due to the limitations of experimental conditions, and the detachment between the major and minor loops is not taken into account. The purpose of this paper is to propose a modified Preisach model that requires relatively few measurements and that describes the detachment, and then to implement the inverse of the modified model for compensation in PEAs.

The classical Preisach model is modified by adding a derivative term in parallel. The derivative gain is adjusted to an appropriate value so that the measured and predicted hysteresis loops are in good agreement. Subsequently, the new inverse model is similarly implemented by adding another derivative term in parallel with the inverse classical Preisach model, and is then inserted in open-loop operation to compensate the hysteresis. Tracking control experiments are conducted to validate the compensation.

The hysteresis in PEAs can be accurately and conveniently described by using the modified Preisach model. The experimental results prove that the hysteresis effect can be nearly completely compensated.

The proposed modified Preisach model is an effective and convenient mean to characterize accurately the hysteresis. The compensation method by inserting the inverse modified Preisach model in open-loop operation is feasible in practice.

This paper starts with the description of a purely mathematical model of the saturation curve and the hysteresis loop based on the fundamental similarities between the Langevin function the specified T(x) function and the sigmoid shape. The T(x) function which is composed of tangent hyperbolic and linear functions with its free parameters can describe the regular anhysteretic magnetisation curve. Developed from this function the model describes not only the regular hysteresis loop but also the biased and other minor loops like the ones produced by the interrupted and reversed magnetisation process and the open “loops” created by a piecewise monotonic magnetising field input of diminishing amplitude. The remanent magnetism as the function of the interrupted field co‐ordinates is predicted by the model in this mathematical form for the first time. The model presented here is based on the principle that all processes follow the shape of the T(x) function describing the shape of the major hysteresis loop of the ferromagnetic specimen under investigation. The model is also applicable to hysteretic processes in other fields.

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 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 paper sets out to formulate the intermolecular forces leading to Barkhausen instability. In the approach the known concept of effective field is used within the framework of the T(x) model. The aim is to provide a mathematical tool to theoreticians and applied scientists in magnetism that is easier to use than those of other models. At the same time to demonstrate the easy applicability of the T(x) model to hysteretic phenomena.

With the combination of the effective and the external field the model is applied to hysteresis loops as well as to the anhysteretic state showing in both cases the local development of unstable conditions at beyond a critical point, leading to local hysteresis loops.

The paper formulates the critical conditions for the hysteretic and the anhysteretic process and calculates the susceptibility as the functions of magnetisation and the applied field.

Experimental verification will be required to prove the applicability to the various magnetic materials and to the accuracy of the model.

The paper provides an easy mathematical and visual method to show the conditions before and after the Barkhausen instability sets in during the magnetisation process.

The paper provides an easy mathematical tool for theoreticians and experimental scientists with a visual presentation of processes leading to Barkhausen instability and magnetic behaviour beyond that by using the T(x) model.

The purpose of this paper is to introduce a simplified method, based on an improvement to the actual second‐order approximation to magnetic hysteresis curves, to calculate an estimation of quasi‐static hysteresis loops of ferromagnetic materials.

The addition of a new dB(B) function is proposed to second‐order rational approximation for the upward and downward magnetic quasi‐static hysteresis loop. The new semi‐empirical approach is tested with typical cycles of commercial Ni‐ferrites (ferroxcube) and Ni standards using a vibrating sample magnetometer (VSM).

The model is simple and a fast tool to reproduce with reasonable accuracy the hysteresis loops based on appropriate parameters of materials under analysis. The proposed extension to the Rivas model has reduced the maximum difference between experimental and modeled values from 19 to 0.08 per cent in the approximation to different hysteresis cycles of the magnetic materials studied here.

This paper presents an improvement to second‐order rational functions approach for fitting of hysteresis loops with simple added functions.

The paper aims to take a critical view of the Wholfarth's assumption and the Henkel plots as the measure of molecular mean‐field interaction in magnetic materials. At the same time it seeks to formulate the effect of the molecular field interaction on the anhysteretic remanence.

Based on the recently verified Bosorth's original definition of anhysteretic state, the paper verifies Wohlfarth's conjecture. By including the molecular field interaction into the effective field expression it formulates the hysteretic and anhysteretic remanent behavior of the magnetic material.

The hysteretic and anhysteretic character of the material can be formulated up to and beyond the Barkhausen jump. The paper also points out that, the now verified, Wholfarth's conjecture is applicable to not only major hysteresis loops but also to symmetrical minor loops as well, within the same set. By doing so it removes the uncertainty surrounding its mathematical formulation.

In the light of these findings the conjecture's relation to multi‐phase magnetic materials has to be investigated in the future.

The formulation of the hyteretic and anhysteretic remanent character can provide a graphical interpretation of the materials behavior. The paper demonstrate how the Henkel plots, based on the Wholfarth's conjecture, used as an indicator of the magnitude of the molecular interaction, can be simplified to the benefit of the theoretical and practical users.

The purpose of this paper is to examine the relationships between processing conditions and magnetic properties of cores made of Soft Magnetic Composite (SMC) Somaloy 500.

The effects of compaction pressure and hardening temperature may be combined considering SMC density. This quantity may be chosen for optimization of properties of ready-made cores. In order to describe hysteresis loops the phenomenological model based on hyperbolic tangent transformation is applied.

SMC density affects substantially the shape of hysteresis loop. The paper provides a number of charts useful for checking how the parameters of the hysteresis model are affected.

The present study considers just one composition of the SMC and one type of lubricant. Future research shall be devoted to verification of the approach on a wider class of SMCs.

Material density may be a relevant quantity in optimization of magnetic properties of ready-made SMC cores. The simple hysteresis model based on the, “effective field” concept and Takács’ idea of hyperbolic tangent transformation may be useful for description of hysteresis curves of SMC cores. Model parameters are sensitive against variations of material density.

The results of the analysis may be useful for designers of magnetic circuits made of SMCs.