Application of Fixed Point Harmonic Finite Element Algorithm Considering Hysteresis in Asymmetric DC-Biased Magnetic Conditions
Zhao Xiaojun1, Xiao Yuchen1, Wu Xinyi2, Gao Shengze1, Yi Zhuo1
1. Department of Electrical Engineering North China Electric Power University Baoding 071003 China; 2. State Grid Shanghai Shibei Electric Power Supply Company Shanghai 200080 China
Abstract：In the frequency domain finite element analysis, considering the hysteresis properties of materials is of great significance in improving the simulation accuracy of electromagnetic characteristics of electrical equipment under DC bias excitation. Aiming at the problems of excessive number of iterations anddivergence in the frequency domain finite element calculation, this paper proposes an improved fixed point iteration strategy based on the ratio magnetic reluctivity. It is applied to the frequency domain finite element analysis under DC bias excitationbased on the loss separation model. After the problem of discontinuity point is solved, the finite element algorithm proposed in this paper has better convergence speed and higher accuracy by using the fixed-point reluctivity and the improved relaxation factor. Compared with the inverse Preisach model based on the analytical first-order reversal curves, the hysteresis model based on the concentric hysteresis loops makes more comprehensive use of the measured data, simplifies the calculation process, and achieves higher accuracy at low flux density amplitude. Therefore, this paper uses the hysteresis model based on the concentric hysteresis loops to describe the static hysteresis characteristics of the iron core. Because the excitation system of transformers and other electrical equipment mostly imposesa voltage source, this paper considers the electromagnetic coupling and solves the excitation current and magnetic vector potential in the frequency domain at the same time. When the magnetic flux density passes through zero, the corresponding ratio reluctivity often appears jumping breakpoints, which will greatly affect the following finite element iteration. To solve the problem, this paper uses density-based spatial clustering of applications with the noise algorithm to identify the discontinuities, and then uses the data close to the discontinuities to supplement the points. Because the magnetic field strength corresponding to eddy current loss and exclusive loss in the method is not directly expressed in the finite element matrix equation, which is calculated based on the iterative results of the magnetic vector potential and hysteresis model in the calculation process, the non-linear magnetic field relationship brings some disturbance to the iterative process. this paper considers using relaxation method to reduce the numerical disturbance and improve the stability and convergence speed of the algorithm. Based on the value range of gradient modulus and artificially set range of relaxation factor, the relaxation factor of each node is differentiated to improve the stability and convergence speed of the algorithm. Finally, the excitation current, magnetic field distribution and loss characteristics of the dry-type transformer model with rolled iron core excited by 400 Hz AC and DC bias excitation are tested and simulated by the finite element method. The hysteresis model based on the concentric hysteresis loops is used to describe thehysteresis characteristics of GT-100 silicon steel. The dynamic hysteresis loops simulated by the model are of high accuracy. In the two-dimensional calculation model, the limb-yoke area is selected as ancalculation domain. The calculated excitation current is compared with the measured data whose bias excitation current is 1.3 A, 2.6 A, and 5.2 A, respectively. After one period of computation, the total iron loss is calculated by integrating the dynamic hysteresis loop area of each element. Comparing the total iron loss with the measured data, the maximum relative error is less than 7%, which proves the effectiveness of the algorithm. Through the simulation analysis, the following conclusions can be obtained: (1) By analyzing the characteristics of the ratio reluctivity about the hysteresis loops, the problem of large error and unstability caused by the ratio reluctivity when the flux density crosses zero is effectively solved. (2) Compared with other relaxation methods, the local relaxation method proposed effectively improves the stability and convergence speed of the algorithm and improves the convergence speed by about 40%. (3) In this paper, the influence of the hysteresis effect on the calculation results of excitation current and iron loss is fully considered. Compared with the frequency domain finite element method using a magnetization curve, the calculation accuracy of excitation current is improved. In addition, the hysteresis model is also used to calculate the core loss, and the results are compared with the measured results to verify the effectiveness of the algorithm.
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2025, Vol. 40 
