一种考虑动态磁滞效应的高效稳定时域有限元计算方法

An Efficient and Stable Time Domain Finite Element Method Considering Dynamic Hysteresis Effect

在时域有限元分析中,考虑铁心磁滞特性与损耗等效磁场对磁场分布的反馈作用,对精细化模拟电工装备的暂态电磁特性具有重要意义。针对耦合动态磁滞特性有限元分析中,存在计算时间长、收敛不稳定等问题,该文提出一种基于等效磁阻率的改进固定点迭代策略,并应用于耦合Preisach磁滞模型的时域有限元分析中。首先,鉴于逆Preisach模型易于数值实现且具有较高的计算精度,铁心材料的磁滞行为由逆Preisach模型进行描述,并基于解析一阶回转曲线对模型进行了参数辨识;其次,通过分析动态磁场分量对收敛性的影响,提出基于等效磁阻率的固定点迭代策略,并在有限元迭代过程中引入松弛因子以加强算法的收敛速度与稳定性;最后,以爱泼斯坦方圈为例,计算铁心中的磁场分布特性与瞬时损耗分布特性并进行实验验证。结果表明,该文所提动态磁滞有限元计算方法在具有较高精度的同时具有较好的收敛速度及稳定性。

In the time-domain finite element analysis,considering the hysteresis properties of the iron core and the feedback effect of the loss equivalent magnetic field on the magnetic field distribution is of great significance for finely simulating the transient electromagnetic characteristics of electrical equipment.Aiming at the problems of long calculation time and divergence in the finite element analysis coupled with dynamic hysteresis characteristics,this paper proposes an improved fixed point iteration strategy based on equivalent reluctivity,and applies it to time domain finite element analysis implemented with Preisach model.With the modified reluctivity and the introduced relaxation factor,the finite element algorithm proposed in this paper has good convergence speed and stability with high accuracy. Firstly, since numerical application of the inverse Preisach model is easy and has high accuracy, the hysteresis behavior of the core material is described by the inverse Preisach model. The Preisach model is established based on the analytical first order reversal curves, of which the parameters are identified by several symmetric hysteresis loops. Secondly, by analyzing the influence of the dynamic magnetic field component on the convergence,a fixed-point iterative strategy based on equivalent reluctivity is proposed, and a relaxation factor is introduced in finite element iterations to enhance the convergence speed and stability of the algorithm. Finally, taking the Epstein frame as an example, experiments and finite element calculations are carried out on the magnetic field distribution and instantaneous loss characteristics of the iron core. There are 9 analytical polynomial parameters of B30P105 electrical steel sheet, identified by Genetic Algorithm. The static hysteresis loops simulated by the Preisach model is of high accuracy. In the 2-D dimensional computation model, the triangle located at the limb-yoke region is selected as an observation spot. The calculated dynamic hysteresis loops, exciting current and instantaneous loss are compared with measured ones, under voltage excitation amplitude of 9 V and 13 V, respectively. The maximum error of the instantaneous loss is less than 6%. After one period computation, the total iron loss is calculated by integrate the area of dynamic hysteresis loop in each element. The calculated iron losses under different flux density are in substantial agreement. In order to investigate the effect of relaxation factor on the convergence property of the program, various values of relaxation factor are chosen and the results show that the average number of iterations and computation time are inversely proportional to the magnitude of the relaxation factor. However, the iteration process doesn't converge with the relaxation factor set as 0.8. The following conclusions can be drawn from the simulation analysis: (1) The Preisach hysteresis model based on analytical first order reversal curves can accurately simulate the static hysteresis characteristics of electrical steel sheets. (2) By incorporating the dynamic hysteresis effect into the improved fixed-point iteration process, the proposed finite element algorithm can realize precise calculation of low-frequency dynamic hysteresis magnetic field, with good computation speed and stability. (3) The error of the calculated instantaneous loss is small, which meets engineering application requirements.