基于磁导-电容类比法和解析Preisach模型的铁心动态磁滞建模方法

Dynamic Hysteresis Modeling Method for Iron Core Based on Permeance-Capacitance Analogy and Analytic Preisach Model

铁磁材料的磁滞、涡流和驰豫效应对电力变压器铁心的非线性特性和功率损耗有显著的影响。为了研究电磁暂态过程中电力变压器的时域响应行为,需要准确计及铁心的动态磁化特性,在电路仿真中对电力变压器铁心进行精细建模。为此,该文首先采用考虑可逆分量的解析Preisach模型表征铁磁材料的静态磁滞效应,通过磁导-电容类比法建立了铁心的回转器-磁导模型,构建铁心静态电磁模型。其次,基于传统损耗统计理论和场分离理论,在静态电磁模型的基础上引入恒定磁阻和受控磁动势源,分别用于表征铁磁材料的涡流效应和弛豫效应对磁滞效应和损耗效应的影响,构建基于传统损耗统计理论的铁心动态电磁模型。最后,运用R-L分数阶导数对涡流损耗表达式进行修正,采用受控磁动势源表示涡流效应,对传统的铁心动态电磁模型进行改进。基于电工钢测量系统测量了硅钢铁心在不同频率、不同磁通密度下的动态磁滞回线,与实验相比改进模型的平均相对误差为6.59%,验证了所提出的改进动态模型的正确性。

With the introduction of a large number of nonlinear loads into the power system,transformers work more frequently at high frequencies,and ferromagnetic materials show strong frequency dependence under high-frequency conditions.Therefore,this paper establishes an electromagnetic loss model considering the eddy current effect and relaxation effect of ferromagnetic materials,which can simulate the voltage and current characteristics at both ends of the transformer and predict the core loss of the transformer.Firstly,the Lorentz function replaces the distribution function of the classical Preisach model.The ascending and descending branch expressions are derived with the input of the magnetic field strength Hand the output of the magnetic induction intensity B.The reversible component expression is introduced in the classical Preisach model to simulate the static hysteresis characteristics of ferromagnetic materials accurately.The characteristic parameters of the Preisach model are obtained according to static hysteresis loop data from experimental measurements and particle swarm optimization algorithm.Based on the permeance-capacitance analogy method and the analytical Preisach model,the static hysteresis permeance model of the core is established in the simulation software PLECS,which can adjust the permeance value in real-time according to the change of magnetic field strength H.According to the experimental data,the static hysteresis permeance model can simulate the static hysteresis loop of the core.Secondly,based on the traditional loss statistical theory and field separation theory,the loss of ferromagnetic materials is divided into hysteresis loss,eddy current loss,and residual loss.Constant magnetoresistive and controlled magnetomotive force sources are introduced to characterize the eddy current loss and residual loss of ferromagnetic materials.The traditional core dynamic hysteresis permeance model is established.Based on the electrical steel measurement system,the hysteresis loop and loss value of silicon steel core at different frequencies and magnetic densities aremeasured.Under high-frequency conditions,the internal magnetic flux of ferromagnetic materials is not uniformly distributed due to the skin effect.As a result,the average error of the traditional dynamic hysteresis permeance model is 14.04%compared with the experimental data.Finally,to consider the non-local,frequency,historical,and other dependent processes of eddy current loss of ferromagnetic materials,the R-L fractional derivative is used to modify the eddy current loss expression,and its parameters are extracted according to the experimental loss value and quantum genetic algorithm.The controlled magnetomotive force source characterizes the eddy current effect,and an improved core dynamic hysteresis permeability model is established.The average relative error of the improved model is 6.59%,which verifies that the improved model can shorten the error.