Rotating core loss model for motor considering skin effect and dynamic hysteresis effect

Abstract: In order to improve the efficiency of agricultural electrical equipment and reduce energy consumption, many scholars attempt to estimate the iron loss accurately. The analysis of finite element showed that in rotational electric machines total core loss comprised alternating core loss and rotational core loss. Precise measured value and modeling of rotational core loss in electrical steel sheets and rotating electrical machines is very important to design and optimize the kind of agricultural motor. According to the separated core loss model under alternative excitation, the core loss can be separated into hysteresis loss, eddy current loss and excess loss. As for alternating core loss, the specific core loss with a circular magnetic flux density can also be separated into 3 portions: the rotational hysteresis loss, the rotational classical eddy-current loss and the rotational excess loss. By means of fourier analysis, the rotating core loss model which considered the influence of alternating and rotating magnetic field, skin effect, dynamic hysteresis loop and minor hysteresis loop was proposed in this paper. Actually, the static hysteresis loop and the dynamic hysteresis loop are different, when the flux density is in saturation, the hysteresis loop shape will be changed. In order to consider the complex behavior of dynamic hysteresis, variable coefficient hysteresis loss was used in the model. The classic exponential coefficient were chosen to be substituted in to the 3 parameters polynomial and fitted out the rotational hysteresis loss with the logarithm. Considering the impact of skin effect at high frequencies, eddy-current loss coefficient were corrected in the paper. Minor hysteresis loop generated by the massive harmonic components leaded the inaccurate prediction of the core loss, the influence of minor hysteresis loop was described by the modified coefficient in the improved formulations, and the modified coefficient was related to the ratio of local flux density to flux density amplitude. By applying orthogonal decomposition technology, 2 mutually orthogonal magnetic flux field was used to describe elliptical rotating magnetic field and replace the rotating loss data. Taking an object affected by the elliptical flux density as an example, the applied magnetic field intensity might not be an elliptical vector because of the nonlinear magnetic flux density-magnetic field intensity relationship and magnetic anisotropy, when it was expanded into a fourier series, however, it shown that the higher harmonics of magnetic field intensity did not contribute to the total core loss as long as magnetic flux density only contains the basic components, the total core loss under the elliptical flux was the summation of alternating core loss and rotating core loss. In order to verify the accuracy of the improved model, a new 3D magnetic properties measurement system was used to measure the rotating core loss of electrical sheet steels. The 3D excitation structure consisted of 3 orthogonal C-shaped cores, 6 multilayer excitation coils which were wound around core poles, a sensing box with built-in core material was placed in the center of 3D magnetic properties measurement device, 6 thin pieces, named as protective layer of uniform magnetic field were fixed around the specimen to make the measured field more uniform at the surface of specimen. Experimental results showed that compared with the classical model and the improved model considering the single factor of skin effect or hysteresis loops only, the accuracy of core loss calculation value of the proposed model was increased by 25.32% and 9.16%, respectively, especially under the condition of high flux density and high frequency. When the frequency was 50 Hz, compared with the classical model, the accuracy of core loss calculation value of the proposed model was increased by 9.21%, and the accuracy was increased by 39.76% at 200 Hz. The comparison of measured value between alternating core loss and rotational core loss showed that the energy of magnetic domain could not accumulated to the maximum in a fixed direction that would lead to irreversible magnetic domain conversion under alternating excitation, which resulted in the increase of hysteresis loss with the increase of magnetic density. The research results can provide reference for the design and optimization of agricultural electrical equipment.