Abdelazeem Hassan Shehata Atyia and Abdelrahman Mohamed Ghanim
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…
Abstract
Purpose
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.
Design/methodology/approach
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.
Findings
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.
Originality/value
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.
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Klemen Deželak, Drago Dolinar and Gorazd Štumberger
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…
Abstract
Purpose
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.
Design/methodology/approach
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.
Findings
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.
Originality/value
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.
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Long Chen, Zheyu Zhang, Ni An, Xin Wen and Tong Ben
The purpose of this study is to model the global dynamic hysteresis properties with an improved Jiles–Atherton (J-A) model through a unified set of parameters.
Abstract
Purpose
The purpose of this study is to model the global dynamic hysteresis properties with an improved Jiles–Atherton (J-A) model through a unified set of parameters.
Design/methodology/approach
First, the waveform scaling parameters β, λk and λc are used to improve the calculation accuracy of hysteresis loops at low magnetic flux density. Second, the Riemann–Liouville (R-L) type fractional derivatives technique is applied to modified static inverse J-A model to compute the dynamic magnetic field considering the skin effect in wideband frequency magnetization conditions.
Findings
The proposed model is identified and verified by modeling the hysteresis loops whose maximum magnetic flux densities vary from 0.3 to 1.4 T up to 800 Hz using B30P105 electrical steel. Compared with the conventional J-A model, the global simulation ability of the proposed dynamic model is much improved.
Originality/value
Accurate modeling of the hysteresis properties of electrical steels is essential for analyzing the loss behavior of electrical equipment in finite element analysis (FEA). Nevertheless, the existing inverse Jiles–Atherton (J-A) model can only guarantee the simulation accuracy with higher magnetic flux densities, which cannot guarantee the analysis requirements of considering both low magnetic flux density and high magnetic flux density in FEA. This paper modifies the dynamic J-A model by introducing waveform scaling parameters and the R-L fractional derivative to improve the hysteresis loops’ simulation accuracy from low to high magnetic flux densities with the same set of parameters in a wide frequency range.
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Yaqi Wang, Lin Li and Xiaojun Zhao
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…
Abstract
Purpose
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.
Design/methodology/approach
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.
Findings
Comparison of simulation and experimental results verifies that the proposed model has high accuracy and strong universality.
Originality/value
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.
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Krzysztof Chwastek, Jan Szczygłowski and Wiesław Wilczyński
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…
Abstract
Purpose
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.
Design/methodology/approach
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.
Findings
A satisfactory agreement of experimental and modelled quasi‐static and dynamic hysteresis loops is obtained.
Research limitations/implications
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.
Practical implications
The “branch‐and‐bound” optimization algorithm is a useful tool for recovery of the values of both model parameters and scaling coefficients as well.
Originality/value
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.
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José Ortega, Óscar Lahuerta, Claudio Carretero, Juan Pablo Martínez and Jesús Acero
This paper aims to apply the non-linear impedance boundary condition (IBC) for a linear piecewise B–H curve in frequency domain simulations to find the equivalent impedance of a…
Abstract
Purpose
This paper aims to apply the non-linear impedance boundary condition (IBC) for a linear piecewise B–H curve in frequency domain simulations to find the equivalent impedance of a simple induction heating system model.
Design/methodology/approach
An electromagnetic description of the inductor system is performed to substitute the effects of the induction load, for a mathematical condition, the so-called IBC. This is suitable to be used in electromagnetic systems involving high conductive materials at medium frequencies, as it occurs in an induction heating system.
Findings
A reduction of the computational cost of electromagnetic simulation through the application of the IBC. The model based on linear piecewise B–H curve simplifies the electromagnetic description, and it can facilitate the identification of the induction load characteristics from experimental measurements.
Practical implications
This work is performed to assess the feasibility of using the non-linear boundary impedance condition of materials with linear piecewise B–H curve to simulate in the frequency domain with a reduced computational cost compared to time domain simulations.
Originality/value
In this paper, the use of the non-linear boundary impedance condition to describe materials with B–H curve by segments, which can approximate any dependence without hysteresis, has been studied. The results are compared with computationally more expensive time domain simulations.
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Zbigniew Szular and Witold Mazgaj
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…
Abstract
Purpose
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.
Design/methodology/approach
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.
Findings
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.
Practical implications
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.
Originality/value
The paper refers to important issues of modeling and calculations of the magnetic and eddy current field distribution in transformer steel sheets.
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Abstract
Details
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Junan Ji, Zhigang Zhao, Shi Zhang and Tianyuan Chen
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…
Abstract
Purpose
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.
Design/methodology/approach
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.
Findings
The comparison of simulation and experimental results verifies that the proposed parameters calculation method has high accuracy and strong universality.
Originality/value
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.