Fixed-point Frequency Domain Finite Element Algorithm Combined With Preisach Model

Transformers and other electrical equipment are made of ferromagnetic materials,and the hysteresis characteristic is one of the inherent properties of ferromagnetic materials.The study of the magnetic field distribution inside electrical equipment is of great significance to the manufacture and optimization of electrical equipment.Sponsored by the National Natural Science Foundation of China "Effective simulation and experimental verification of vibration behavior of large gap iron core reactor based on in-service characteristics of key materials and components"(51777073),this article adopts the fixed-point harmonic balance finite element method,and uses the loss separation model to comprehensively account for the effect of hysteresis.Under the condition of sinusoidal excitation,the one-dimensional nonlinear field in the silicon steel sheet and the two-dimensional nonlinear field in the transformer lamination core are calculated respectively.Studying the hysteresis characteristics of ferromagnetic materials is an important part of analyzing the internal nonlinear field of ferromagnetic materials.According to the static limit hysteresis loops under sine excitation and magnetic bias excitation,the corresponding first-order reversal curve is generated respectively,and then the inverse Everett function is generated,so as to use the Preisach hysteresis model to realize the fitting of the static hysteresis characteristics of ferromagnetic materials.Through comparison with experimental measurement results,the rationality of the Preisach hysteresis model is verified.The proposed loss separation model solves the problem of fitting the dynamic hysteresis characteristics,and the comparison with the experimental measurement results shows the rationality of the model.According to Maxwell's equations,the fixed-point harmonic balance finite element method is used to form the frequency-domain finite element equation of the nonlinear field.At the same time,the loss separation model is used to accurately account for the effect of hysteresis,solving the one-dimensional nonlinear field in the silicon steel sheet and the two-dimensional nonlinear field in the laminated core.With the introduction of fixed-point method,the coefficient matrix of the finite element equation is transformed from a variable coefficient matrix to a constant coefficient matrix,which greatly simplifies the solving process of the equation.In the twodimensional case,since electrical equipment such as transformers are excited by voltage and the excitation current is unknown,a field-circuit coupling relationship is established,and the two-dimensional nonlinear magnetic field and excitation current in the laminated core are solved as the quantities to be sought at the same time.