Search results

The accurate modeling of magnetic hysteresis in electrical steels is important in several electrical and electronic applications. Numerical models have long been known that can correctly reproduce some typical behaviours of these magnetic materials. Among these, the model proposed by Jiles and Atherton must certainly be mentioned. This model is intuitive and fairly easy to implement and identify with relatively few experimental data. Also, for this reason, it has been extensively studied in different formulations. The developments and numerical tests made on this hysteresis model have indicated that it is able to accurately reproduce symmetrical cycles, especially the major loop, but often it fails to reproduce non-symmetrical cycles. This paper aims to show the positive aspects and highlight the defects of the different formulations in predicting the minor loops of electrical steels excited by non-sinusoidal currents.

The different formulations are applied to different electrical steels, and the data coming from the simulations are compared with those measured experimentally. The direct and inverse Jiles–Atherton models, including the introduction of the dissipative factor approach, are presented, and their limitations are proposed and validated using the measurements of three non-grain-oriented materials. Only the measured major loop is used to identify the parameters of the Jiles–Atherton model. Furthermore, the direct and inverse Jiles–Atherton models were used to simulate the minor loops as well as the hysteresis cycles with direct component (DC) bias excitation. Finally, the simulation results are discussed and compared to measurements for each study case.

The paper indicates that both the direct and the inverse Jiles–Atherton model formulations provide a good agreement with the experimental data for the major loop representation; nevertheless, both models can not accurately predict the minor loops even when the modification approaches proposed in the literature were implemented.

The Jiles–Atherton model and its modifications are widely discussed in the literature; however, some limitations of the model and its modification in the case of the distorted current waveform are not completely highlighted. Furthermore, this paper contains an original discussion on the accuracy of the prediction of minor loops from distorted current waveforms, including DC bias.

The investigation was aimed at magnetically‐nonlinear dynamic model of a single‐phase transformer, where the effects of dynamic hysteresis losses are accounted for by a simplified model. Such a modelling could be applied when analyzing the transient operating conditions or the impact of nonlinear and unbalanced loads on the transformer operation and the big power systems modelling.

Secondly, an inverse form of the Jiles‐Atherton hysteresis model was applied for the hysteresis losses of a transformer defining. In that sense this paper compares and evaluates both hysteresis models, where the possible errors caused by simplified model application are exposed.

The Jiles‐Atherton model can be applied when more accurate hysteresis models are required, however, at the cost of increased model complexity and required computational effort. Apart from that the main drawback is impossible application of such a modelling, when some of the input parameters are unknown. On the other hand the simplified hysteresis model does not increase the required computational effort substantially.

Both methods have been modified in such a way that they can be used when the magnetizing curve of the iron‐core material is not available, whilst the magnetically‐nonlinear characteristic of the entire device can be determined experimentally. The aforementioned characteristic can be given in the form of an approximation polynomial or in the form of a look‐up table.

The purpose of this paper is to combine the Jiles-Atherton (J-A) hysteresis model with the field separation approach to realize the accurate simulation of dynamic magnetostrictive characteristics of silicon steel sheet.

First, the energy loss of silicon steel sheet is divided into hysteresis loss Why, classical eddy current loss Wed and anomalous loss Wan according to the statistical theory of losses. The Why is calculated by static J-A hysteresis model, Wed and Wan are calculated by the analytical formulae. Then, based on the field separation approach, the dynamic magnetic field is derived. Finally, a new dynamic magnetostrictive model is proposed by means of the quadratic domain rotation model.

Comparison of simulation and experimental results verifies that the proposed model has high accuracy and strong universality.

The proposed method improves the existing method’s problem of relying on too much experimental data, and the method ensures the calculation accuracy, parameter identification accuracy and engineering practicability. Consequently, the presented work greatly facilitates further explorations and studies on simulation of dynamic magnetostrictive characteristics of silicon steel sheet.

The aim of the paper is to present a simple approach to modelling minor hysteresis loops in grain‐oriented steel sheets under quasi‐static and dynamic conditions. The hysteresis phenomenon is described with a recently developed hybrid model, which combines ideas inherent in the product Preisach model and the Jiles‐Atherton description. The dynamic effects due to eddy currents are taken into account in the description using a lagged response with respect to the input.

It is assumed that some model parameters might be dependent on the level of relative magnetization within the material. Their dependencies could be given as power laws. The values of scaling coefficients in power laws are determined.

A satisfactory agreement of experimental and modelled quasi‐static and dynamic hysteresis loops is obtained.

The present study provides a starting point for further verification of the approach for other classes of soft magnetic materials, which could be described with the developed model. At present, the approach to model minor loops by the update of model parameters is verified for the B‐sine excitation case.

The “branch‐and‐bound” optimization algorithm is a useful tool for recovery of the values of both model parameters and scaling coefficients as well.

The recently developed hybrid description of hysteresis phenomenon can be successfully extended to take into account symmetric minor loops. The developed approach could be a framework to develop a comprehensive description of magnetization phenomena in the future.

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.

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 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.