电枢分段供电永磁直线同步电机的非线性数学模型

Non-Linear Mathematic Model of a Segmented Powered Permanent Magnet Linear Synchronous Machine

电枢分段供电永磁直线同步电机(PMLSM)中,相邻分段铁心的存在会导致气隙磁场脉振,动子穿过电枢定子段也会引发复杂的暂态过程。为准确描述电机的动态过程,该文考虑以上两种特有的电磁特性,建立双三相分段供电PMLSM的相空间模型。首先,采用解析法分析脉振气隙磁场的成因,研究电感不平衡以及饱和效应问题,将六相电流转化到αβ坐标系下建立二维电感查询表,有效地降低了模型的运算量。其次,引入易于求导的Sigmoid函数构造随动子位置变化的耦合系数,准确描述动子通过分段过程产生的空载磁链及反电动势。依据上述方法构建电机相空间模型,与有限元模型进行对比,两者电压与推力计算结果一致。最后,在RT-Lab中搭建基于相空间模型的半实物实验平台,结果表明,该模型能够准确地体现电机的各种效应,可以替代计算成本较大的有限元模型。

Due to the segmented arrangement of windings in long primary dual-three phase permanent magnet linear synchronous machine(PMLSM),the adjacent segments will cause the off-set pulsating magnetic field,and the mover passing through the powered segment will also cause complex transient processes.In this paper,in order to describe the dynamic characteristics of the PMLSM precisely,a phase-domain mathematic model is established and the two fore-mentioned special effects are considered.The causes of off-set pulsation in the air-gap flux distribution are analyzed by the analytical method,and the unbalanced inductance and saturation effects caused by the off-set flux distribution are studied.A 2-D inductance look-up table inαβcoordinate system is established to reduce the computation consumption of the model.Then,the easy-to-derivative Sigmoid function is introduced to describe the no load flux linkage and back electromagnetic force.Finally,the mathematic model is established,the voltage and thrust are calculated by the model and verified by the finite element method.Finally,an experiment platform based on the RT-Lab is built.The results show that the model can reflect the various effects of the motor and can replace the finite element model with a large computational cost.