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• 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]

• 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]

• 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]