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The purpose of this paper is to present the vector magnetic properties of the electrical steel sheet and investigate its influences on the magnetic field and iron loss distributions for the electrical machines.

The vector magnetic property of the electrical steel sheet is measured by using a two-dimensional single sheet tester and modelled through an E&S vector hysteresis model to be applied to finite element analysis.

The magnetic field and iron loss distributions are calculated by finite element analysis combined with the E&S vector hysteresis model for the three-phase transformer and induction motor models.

The influences of the vector magnetic property on the electrical machines are verified by comparing with the numerical results from a scalar magnetic property.

The purpose of this paper is to reduce computation time of magnetic characteristic analysis considering 2D vector magnetic properties.

The paper proposes a complex E&S modelling with assumption that both flux density and field strength waveforms are sinusoidal. The computation time of the complex E&S modeling becomes 1/10 in comparison with one of the conventional E&S modeling. This modeling is applicable up to 1.4 T of the local magnetic flux density condition in the case of non‐oriented magnetic materials.

In the results of the magnetic field analyses of a linear‐induction motor model core by means of the finite element method taking account of the complex E&S modeling, the distributions of the flux density and the field strength were able to be approximately analyzed and their phase differences in space were represented. The results of the magnetic characteristic analysis of the linear‐induction motor showed that the teeth‐end shape had large influences on the thrust and cogging.

This technique helps to know approximately local vector magnetic properties in core materials. This modeling is very useful for magnetic core design taking account of the simplified 2D vector magnetic properties.

The method presented in this paper enables expression of the simplified 2D vector magnetic properties in magnetic field analyses. The computation time can be considerably reduced in comparison with the conventional method.

The purpose of this paper is to show formulation of a dynamic E&S model, which enables analysis of the effects of eddy currents under vector magnetic behavior in numerical simulations and to demonstrate its usefulness.

When a magnetic flux waveform is distorted, effects of eddy currents increase due to harmonic flux components. In such a case, the result calculated by using the conventional E&S model does not agree with the measured one. The conventional E&S model is improved by considering magnetic flux waveform distortion. The harmonic components of the magnetic field strength waveform were estimated with the classical eddy current model.

In the verification of the dynamic E&S model, it was found that the magnetic field was suppressed by the effect of the eddy current. The conventional analysis overestimates the magnetic field, because the magnetic flux waveform cannot distort. In the magnetic characteristic analysis of a three‐phase transformer model core, the correlation between the eddy currents and the flux waveform distortion are clearly demonstrated.

Both magnetic flux and field strength waveform distortions can be represented in numerical simulations. The dynamic E&S model is very useful for magnetic core design, taking account of practical 2D vector magnetic properties.

The method presented in this paper enables effects of eddy currents in the magnetic characteristic analysis to be more accurately expressed, considering the 2D vector magnetic properties.

The purpose of this paper is to present the differences in results of numerical calculations arising from different simplifications of the rotational magnetization model in typical dynamo sheets.

A comprehensive model of rotational magnetization processes in typical dynamo sheets should take into consideration the magnetic hysteresis and eddy current phenomena and also certain anisotropic properties. The chosen model of the rotational magnetization is briefly presented in this paper. A method of the inclusion of the rotational magnetization model into equations of the magnetic field distribution is described. The correctness of these equations has been verified experimentally. Numerical calculations of the rotational magnetization in two types of dynamo sheets were carried out for several simplifications of the described model.

Results of numerical calculations of the rotational magnetization with the omission of the hysteresis phenomenon or with the omission of eddy currents were compared with results obtained with the use of the comprehensive model of the rotational magnetization.

The paper presents comments and recommendations concerning the omission of both the hysteresis phenomenon and eddy currents in the analysis of the rotational magnetization in dynamo sheets and the impact of these simplifications on numerical calculation results.

The content of the paper refers to very important issues of modeling and calculations of the rotational magnetization in typical dynamo steel sheets.

A simplified method for calculating iron loss of three-phase transformer is proposed in this paper. The rotating iron loss measured from 2-D vector magnetic property measurement system of gain-oriented silicon steel sheet can be taken into account in this method. The paper aims to discuss these issues.

The finite element analysis formulation is combined with the magnetic reluctivity model expressed by diagonal tensor for 2-D nonlinear and anisotropic magnetic problem, while the iron loss is computed in terms of the interpolation of rotational loss curves measured under various loci of controlled magnetic flux density B.

The iron loss of three-phase transformer is obtained by the proposed method. And the calculating iron loss is verified with experimental results.

The method presented in this paper enables the iron loss of three-phase transformer to be more accurately calculated and more easily applied, considering the rotational iron loss.

The purpose of this paper is to introduce a chaotic harmony search (CHS) approach based on the chaotic Zaslavskii map to parameters identification of Jiles-Atherton vector hysteresis model.

In laminated magnetic cores when the magnetic flux rotates in the lamination plane, one observes an increase in the magnetic losses. The magnetization in these regions is very complex needing a vector model to analyze and predict its behavior. The vector Jiles-Atherton hysteresis model can be employed in rotational flux modeling. The vector Jiles-Atherton model needs a set of five parameters for each space direction taken into account. In this context, a significant amount of research has already been undertaken to investigate the application of metaheuristics in solving difficult engineering optimization problems. Harmony search (HS) is a derivative-free real parameter optimization metaheuristic algorithm, and it draws inspiration from the musical improvisation process of searching for a perfect state of harmony. In this paper, a CHS approach based on the chaotic Zaslavskii map is proposed and evaluated.

The proposed CHS presents an efficient strategy to improve the search performance in preventing premature convergence to local minima when compared with the classical HS algorithm. Numerical comparisons with results using classical HS, genetic algorithms (GAs), particle swarm optimization (PSO), and evolution strategies (ES) demonstrated that the performance of the CHS is promising in parameters identification of Jiles-Atherton vector hysteresis model.

This paper presents an efficient CHS approach applied to parameters identification of Jiles-Atherton vector hysteresis model.

The purpose is to implement and compare different approaches for modelling the magnetostriction phenomenon in iron sheet used in rotating electrical machines.

In the force-based approach, the magnetostriction is modelled as a set of equivalent forces, which produce the same deformation of the material as the magnetostriction strains. These forces among other magnetic forces are computed from the solution of the finite element (FE) field computation and used as loads for the displacement-based mechanical FE analysis. In the strain-based approach, the equivalent magnetostrictive forces are not needed and an energy-based model is used to define magnetomechanically coupled constitutive equations of the material. These equations are then space-discretised and solved with the FE method for the magnetic field and the displacements.

It is found that the equivalent forces method can reproduce the displacements and strains of the structure but it results in erroneous stress states. The energy-based method has the ability to reproduce both the stress and strains correctly; thus enabling the analysis of stress-dependent quantities such as the iron losses and the magnetostriction itself.

The investigated methods do not account for hysteresis and other dynamic effects. They also require long computation times. With the available computing resources, the computation time does not present any problem as far as they are not used in everyday design procedures but the modelling of dynamic effect needs to be elaborated.

The developed and implemented methods are verified with measurements and simulation experiments and applied to as complex structure as an electrical machine. The problems related to the different approaches are investigated and explained through simulations.

The purpose of this paper is to propose the speed-up of the fixed-point method by updating the reluctivity at each iteration (this is called a modified fixed-point method).

A modified fixed-point method, which updates the derivative of reluctivity at each iteration, is proposed. It is shown that the formulation of the fixed-point method using the derivative of reluctivity is almost the same as that of the Newton-Raphson method. The convergence characteristic of the newly proposed fixed-point method is compared with those of the Newton-Raphson method.

The modified fixed-point method has an advantage that the programming is easy and it has a similar convergence property to the Newton-Raphson method for an isotropic nonlinear problem.

This paper presents the formulation and convergence characteristic of the modified fixed-point method are almost the same as those of the Newton-Raphson method.

Due to existence of skin effect under rotational excitation, especially to high-frequency motors and power transformers run at the frequency of hundreds or even thousands of hertz, core losses will increase significantly, which may cause local overheating damage, and the efficiency and longevity will be decreased. The purpose of this paper is to accurately calculate the rotational anomalous loss in electrical steel sheets.

The influence of skin effect to rotational anomalous loss coefficient is described in detail. Based on the rotational core losses calculation approach, the transformed coefficient and parameters of rotational anomalous loss are determined in accordance with experimental data obtained by using 3D magnetic properties testing system. Then, a variable loss coefficient calculation model of rotational anomalous loss is built. Meanwhile, a separation of the total 2D elliptical rotation experimental core losses is worked out.

The two methods are analysed and compared qualitatively. It should be noted that the novel calculation model can be more effectively presented anomalous loss features. Moreover, quantitative comparisons between 2D elliptical rotation and alternating core losses have achieved beneficial conclusions.

Transformed rotational anomalous loss coefficient and parameters of electrical steel sheets considering skin effect are determined. Based on that, a novel calculation model evaluating 2D elliptical rotation anomalous loss is presented and verified based on the experimental measurement and the separation of the total 2D elliptical rotation core losses. The 2D elliptical rotation core losses separation method and quantitative comparison with alternating excitation are helpful to engineering application.

The magnetic characterization of electrical steel is typically examined by measurements under the condition of unidirectional sinusoidal flux density at different magnetization frequencies. A variety of iron loss models were developed and parametrized for these standardized unidirectional iron loss measurements. In the magnetic cross section of rotating electrical machines, the spatial magnetic flux density loci and with them the resulting iron losses vary significantly from these unidirectional cases. For a better recreation of the measured behavior extended iron loss models that consider the effects of rotational magnetization have to be developed and compared to the measured material behavior. The aim of this study is the adaptation, parametrization and validation of an iron loss model considering the spatial flux density loci is presented and validated with measurements of circular and elliptical magnetizations.

The proposed iron loss model allows the calculation and separation of the different iron loss components based on the measured iron loss for different spatial magnetization loci. The separation is performed in analogy to the conventional iron loss calculation approach designed for the recreation of the iron losses measured under unidirectional, one-dimensional measurements. The phenomenological behavior for rotating magnetization loci is considered by the formulation of the different iron loss components as a function of the maximum magnetic flux density B_m, axis ratio f_Ax, angle to the rolling direction (RD) θ and magnetization frequency f.

The proposed formulation for the calculation of rotating iron loss is able to recreate the complicated interdependencies between the different iron loss components and the respective spatial magnetic flux loci. The model can be easily implemented in the finite element analysis of rotating electrical machines, leading to good agreement between the theoretically expected behavior and the actual output of the iron loss calculation at different geometric locations in the magnetic cross section of rotating electrical machines.

Based on conventional one-dimensional iron loss separation approaches and previously performed extensions for rotational magnetization, the terms for the consideration of vectorial unidirectional, elliptical and circular flux density loci are adjusted and compared to the performed rotational measurement. The presented approach for the mathematical formulation of the iron loss model also allows the parametrization of the different iron loss components by unidirectional measurements performed in different directions to the RD on conventional one-dimensional measurement topologies such as the Epstein frames and single sheet testers.