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This paper presents a modified Mayergoyz-based vector hysteresis model to describe the anisotropic material behavior of nonoriented (NO) steels over a wide range of rotational excitations. The proposed model adopts a new representation of a vector Everett function, which is actually an elliptical interpolation motivated by the real anisotropic behavior of NO steel, to deal with the uniaxial anisotropy characteristic, which is especially pronounced at low induction levels. The biaxial anisotropy occurring at high densities is described by a nonlinear coefficient, which is actually a function of the magnitude of magnetic flux density. A systematic identification algorithm is given in detail. The validity of this model is verified through comparison with experimental data under both alternating and rotational excitations. The 2-D finite element analysis (FEA) of incorporating this model into TEAM problem 32 simulation is also illustrated. [ABSTRACT FROM AUTHOR]

Extensive research and experiments have shown that rotational core loss, which usually exists in the corner joints of multi-phase transformers and behind the teeth of rotational motors, may amount to more than 50% of the total core loss. The frequency of rotational magnetic field can reach even kilohertz level in high-speed motors. In this paper, a new magnetizer of double-yoke vertical structure made of ultrathin steel sheet (0.05 mm) and the corresponding $B$ – $H$ sensing structure are proposed and constructed. Both the alternating and 2-D rotational magnetic properties for non-oriented steel B35A210 and grain-oriented steel B27R090 are measured and characterized up to kilohertz. The magnetic anisotropy of silicon steel is observed and analyzed from its origin mechanism. Moreover, the alternating, 2-D circular and elliptical rotational core losses are compared and discussed. This paper can provide a reference for core loss modeling and the calculation of electrical machines or transformers under different magnetization conditions. [ABSTRACT FROM AUTHOR]

Magnetic components in power electronic equipment usually suffer from nonsinusoidal excitations. In this paper, a brief description about the existing core loss calculation methods for nonsinusoidal excitations is given. Then calculation formulas of aforementioned methods for two typical excitation waveforms, that is, square and rectangular with variable duty cycle ${D}$ , are derived. Core loss of nanocrystalline FT-3KS, under above two nonsinusoidal excitations, is measured on an established test setup. The accuracy and applicability of each method are discussed theoretically and verified experimentally, especially in terms of different duty cycles and frequencies. It is found that the waveform coefficient Steinmetz equation (WcSE) is more applicable for the case of relatively small harmonics content of magnetic field intensity ${H}$ (normal duty cycle region), while the improved generalized Steinmetz equation (IGSE) has better precision where the harmonics count (extreme duty cycle region). In addition, the IGSE can better follow the changing trend of core loss with ${D}$ and have better frequency applicability than WcSE, which is proven to be not valid in low frequency (where the static hysteresis loss dominates). The results can provide reference for core loss prediction under nonsinusoidal excitations. [ABSTRACT FROM AUTHOR]

As the effect of factors like temperature and stress on the magnetic properties of electrical steel materials are gradually being emphasized, many research teams are carrying out related tests. Currently, most studies focus only on the effect of a single factor on the magnetic properties, while in reality, multiple factors exist simultaneously in electrical equipment. Therefore, accurate data of alternating (1D) and rotational (2D) magnetic properties under simultaneous loading of temperature and stress are very important. In this paper, a system based on a vertical rotational single sheet tester (VRSST) with temperature and stress loading parts is designed and constructed. Then, the 1D and 2D magnetic properties under many combinations of different temperatures, uniaxial and biaxial stress are measured and analyzed. [ABSTRACT FROM AUTHOR]

Magnetic materials are widely used in switching-mode power supplies (SMPS) and magnetic components in SMPS usually work under two typical rectangular excitations (with or without the period of zero voltage). Extensive experimental results have shown that there is quite a difference of core loss between sinusoidal excitations and rectangular excitations, which means the traditional core loss calculation methods are no longer applicable. In this paper, two formulas for core loss calculation under the above rectangular excitations are derived based on the Improved Generalized Steinmetz Equation (IGSE). Core loss of different magnetic materials, under both sinusoidal excitations and rectangular excitations with different frequencies and duty cycles, are measured. Experimental results show that the formulas are accurate enough and very useful to predict the core loss. [ABSTRACT FROM AUTHOR]

• A single-sheet tester to measure electrical steel loss under uniaxial magnetisation. • Transverse magnetisation is shown to occur in grain-oriented silicon steel. • Losses due to transverse fields are not detected in conventional test methods. • Transverse losses depend on grain size and mis- orientation in grain oriented steel. • Transverse loss is not normally of practical importance in electrical machine cores. A modified rotational single-sheet tester, in which a circular sample can be rotated to be magnetised along arbitrary directions, was used to study the transverse magnetisation and associated losses in grain-oriented electrical steel (GOES). Longitudinal and transverse components of flux density B and magnetic field H in a sample of commercial GOES were measured under alternating excitation at angles from −90° to +90° to the rolling direction (RD) at peak flux densities up to 1.5 T over a magnetising frequency range of 20–400 Hz. The loss due to the transverse components of B and H, referred to as the transverse loss, was evaluated. At 1.5 T, 20 Hz, the transverse loss was less than 0.1 mW/kg when magnetised along either the RD or the transverse direction but it rose to around 5 mW/kg when magnetised at 30° to the RD. It was found to be magnetising direction, frequency and flux density dependent. The transverse loss was a simple function of the angle of magnetisation with respect to the RD but it differed when magnetised along directions on either side of to the RD dependent on the grain structure in the measurement region. The basic phenomenon is explained with the aid of simple magnetic domain and magnetisation models. The difficulty of quantifying its absolute effect in GOES and non-oriented electrical steel is discussed. It appears that transverse magnetisation in GOES is not normally large enough to have any practical effect on measurements obtained using IEC Standard loss testers or on the prediction of electrical machine core losses. A preliminary series of tests showed that transverse loss also occurs in non-oriented electrical steel but it is difficult to quantify. [ABSTRACT FROM AUTHOR]

With the increase in power electronic equipment in power system, the excitation of ferromagnetic materials often involves a large number of harmonics. Therefore, it is necessary to construct an accurate dynamic hysteresis model to adapt to this complicated operating state of electrical equipment. In this paper, a Hybrid Dynamic Hysteresis Model (HDHM), which can effectively characterize the harmonic excitation of materials is studied based on the Preisach model and Stacked Auto-Encoder (SAE) model. The static part of this model takes the form of the inverse Preisach model. And the Multiple Dynamic Hysteresis Model Set (MDHMS) is constructed by multiple dynamic models of eddy currents and excess characteristics of the ferromagnetic materials. The dynamic part of the HDHM takes the form of the model structure combining the Stacked Auto-encoder and the MDHMS. The calculation results of the hysteresis loop and ferromagnetic loss in the harmonic condition of silicon steel sheet proves the validity of this model. Moreover, compared with the conventional dynamic hysteresis model, the HDHM has better accuracy and generalization ability. [ABSTRACT FROM AUTHOR]

• A single-sheet tester is built to measure alternating and rotational magnetostriction of electrical steel. • Selection considerations of resistance strain gauges are summarized. • Ignoring magnetostriction anisotropy and rotational magnetostriction will cause errors in electromagnetic analyses. • The research can provide data support for electromagnetic design under different magnetizations. Extensive numerical analyses and experimental tests have shown that while major regions of magnetic cores in electromagnetic devices, such as transformers and rotating electric machines, are dominated by the alternating magnetic fields, the rotating magnetic fields exist in the corner joints of multi-phase transformers and the yoke area behind the teeth of rotating electric machines. These magnetic fields cause core losses due to hysteresis and eddy currents, mechanical vibration and acoustic noises due to magnetostriction. Many studies have been reported in the literature on alternating and rotational core losses and alternating magnetostriction, but not so much on rotational magnetostriction, especially in non-oriented (NO) silicon steel sheets. The vibration and noise caused by rotational magnetostriction are much higher than those caused by alternating magnetostriction. This paper reports the development of a magnetostriction measurement system consisting of a 2D symmetrical single sheet tester (SST) and resistance strain gauges. The selection considerations of resistance strain gauges are summarized. The alternating and rotational magnetostriction characteristics of a NO silicon steel, B35A300 (0.35 mm), are measured. Because the rotating magnetic field in the stator is not always ideally circular but more often elliptical, the magnetostriction under elliptical magnetizations with different axis ratios is also measured. The magnetostriction anisotropy of the NO steel sheet is observed and analyzed. The elongation and contraction under alternating, circular and elliptical rotating magnetizations with different axis ratios are discussed. The results can provide data support for calculating and designing multi-phase transformers and rotating electric machines under different types of magnetizations. The research can provide theoretical and practical guidance for mitigating mechanical vibration and acoustic noise caused by magnetostriction. [ABSTRACT FROM AUTHOR]

• The HIHM has the better structure and higher precision than traditional models. • The magnetization state vector is used to characterize the specific magnetization of materials. • The modeling of HIHM can reduce the requirement of hysteresis data. • The HIHM can overcome this unreasonableness in the modeling of Preisach. • To the parameter identification of the J-A model, the training of HIHM taken less time. The hysteresis modeling of ferromagnetic materials in electrical equipment is one of the basic theoretical studies in the field of electrical engineering. Long training time and poor accuracy are the main challenges of the traditional hysteresis models. In this paper, a Hybrid Intelligent Hysteresis Model (HIHM) is proposed by combining the hysteresis operator space theory and Deep Belief Networks-Deep Neural Network (DBN-DNN) algorithm. The Preisach Fusion Operator (PFO) is constructed by fusing multiple traditional Preisach operators with coefficients satisfying the Gaussian distribution. And multiple PFOs are used to construct an operator space to create the high-dimensional operator data. By the operator space, the nonlinear hysteresis relationship in the hysteresis data is transformed into a nonlinear mapping between the operator data and the output of the model. The DBN-DNN model is used to characterize this nonlinear mapping. The structure of the HIHM is determined by taking the output of the operator space as the input of the DBN model. The generation of first-order reversal curve proves that the model has certain practicality. In addition, the validity and generalization of this model is verified through the simulation with experimental data of non-orientation (NO) silicon steel B35A210 at quasi-static frequency. [ABSTRACT FROM AUTHOR]

There are many magnetic inductors, such as filter inductors used in power electronic devices, being subjected in square waveform excitation together with DC bias. This paper proposes an improved core loss separation model to calculate the core loss of the magnetic materials under square waveform excitation together with DC bias. The core loss of the magnetic material with such excitation is calculated, and compare with the results using other models. The comparison shows that the improved model is more accurate than the other model. The discussion also shows that the improved model can identify the hysteresis loss and eddy loss. The results demonstrate that the improved model can optimize the design of inductors to improve the performance of the power electronic applications. [ABSTRACT FROM AUTHOR]

Accurate magnetic properties measurement of the silicon steel plays an increasingly important role in electromagnetic devices design and optimization. However, with the 2D circular and elliptical magnetization, which usually exist in the corner joint of three-phase transformer and behind the teeth of AC rotating machines, there is lack of experimental data result in the difficulty of reaching high frequency induction at kilohertz range. In this paper, a novel two-dimensional (2-D) magnetic tester with ultra-thin silicon steel sheets is designed and analyzed. In order to improve the measurement precision, a combined B-H sensing structure is designed to avoid the local inhomogeneity of magnetic field distribution caused by drilling holes. Both the alternating and 2D rotating magnetic properties of non-oriented silicon steel M210-35A are systematically measured at a wide range of frequency and magnetic flux density. [ABSTRACT FROM AUTHOR]

• Based on the white-box model theory, the Stacked Auto-Encoder is used to identify the relevant parameters of this model. • The anisotropy compensation coefficient is introduced into the model structure to reduce the model error. • The phase angle compensation parameters are calculated by the magnetic loss data to improve the loss calculation accuracy. • The Neural Networks construct the mapping between model structure and the output of hysteresis data. • The median iterative algorithm is used to search the corresponding compensation angle values. The construction of the vector hysteresis model is significant for the electromagnetic characteristics analysis of electrical equipment. With a deep learning parameter identification algorithm, this paper presents a modeling method of the inverse vector hysteresis model. The vector Everett function is obtained by the alternating hysteresis data. In order to reduce the error of the vector Everett function, the anisotropy compensation coefficient is introduced into the model structure. Based on the white-box model theory, the Stacked Auto-Encoder (SAE) model is used to identify the relevant parameters of the inverse vector hysteresis model. And the parameters of the phase angle compensation function are calculated by the magnetic loss data to further improve the magnetic loss calculation accuracy of the vector model. Compared with the experimental data of rotating magnetization, the fitting result proves the accuracy of the model in a wide range. In addition, the validity of the model is verified by calculating the dynamic magnetic loss. [ABSTRACT FROM AUTHOR]