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| Vector Hysteresis Model for Rotational Hysteresis Loss of Ferromagnetic Materials Based on Deep Belief Network Algorithm |
| Ma Yangyang1,2, Li Yongjian1, Sun He1, Yang Ming1, Dou Runtian1 |
1. State Key Laboratory of Reliability and Intelligence of Electrical Equipment Hebei University of Technology Tianjin 300130 China;
2. State Gird Cangzhou Electric Power Supply Company Cangzhou 061000 China |
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Abstract The silicon steel sheet is the core material of electrical equipment, and its magnetization characteristics directly affect the operation mechanism of equipment. So, the hysteresis modeling of ferromagnetic materials is one of the basic theoretical studies in the field of electrical engineering. In this paper, a vector hysteresis model is proposed based on the deep belief network (DBN) algorithm and hysteresis operator space theory.
The structure of the model consists of three parts: input mapping function, operator space and DBN model. In this paper, the Langevin function is used as the input mapping function to calculate the input mapping of hysteresis data, so that the data can adapt to the characteristics of hysteresis operator in the subsequent structure and can reflect the saturation characteristics of hysteresis phenomenon. Hysteresis operators in multiple directions in H space construct a hysteresis operator space. And the magnetization trajectory of the material mapped by Langevin function is projected in all directions on H space. The high-dimensional hysteresis operator data is generated by calculating hysteresis operators in all directions. Then the output of the operator space is taken as the input of the DBN model. In the construction of vector hysteresis model, DBN model is mainly used to characterize the nonlinear relationship between the high-dimensional vector data output by the operator and the magnetic induction data of the material. The parameters of the vector hysteresis model are obtained by training the magnetic induction data of training samples and the operator data generated by the training samples. The model parameters are mainly obtained by training DBN parameters. And the training process of DBN mainly consists of two parts: (1) The CD algorithm is used to the pre-training of the RBM in each layer, then the RBMs are stacked to obtain the preliminary optimization parameters of the model. (2) The parameters obtained by pre-training are taken as initial values, and the Nadam optimizer is used for global parameter tuning to obtain the final optimization parameters of the model. The obtained model is fitted under the conditions of high, middle and low magnetic density (Bm=0.5 T, 1 T, 1.5 T) respectively, and it is proved that the trajectory error between the calculated data of the model and the original magnetization data is small. In addition, the x-axis and y-axis decomposition of the calculated vector hysteresis data also prove that the proposed vector model has a relatively small error in terms of phase for hysteresis data, thus ensuring the reliability of magnetic loss calculation. So, the simulation results of hysteresis data obtained by experiment show that the model can effectively describe the nonlinear characteristics and anisotropic of ferromagnetic materials under the rotation vector excitation.
Based on the magnetic loss separation theory, an improved loss calculation model is proposed in this paper. In the magnetic loss calculation model, the deviation between the magnetic loss calculated by the data calculated by the model and the actual magnetic loss is checked by the conversion function. Thus, the independence of the magnetic loss calculation and the characterization of the magnetic characteristics of the model are effectively guaranteed. And the data obtained by the hysteresis model is applied to the dynamic loss calculation. The simulation results show that the hysteresis model can fit the actual situation effectively.
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Received: 14 May 2021
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2023, Vol. 38 
