电机模型中牵连运动及其动生电动势的数理表达  

Mathematical Description of Entrainment Motion of Reference Frame and Its Electromotive Force in Motor Modeling

作　　者：钟再敏[1] 王业勤 ZHONG Zaimin;WANG Yeqing(School of Automotive Engineering,Tongji University,Shanghai 201804,China)

机构地区：[1]同济大学汽车学院,上海201804

出　　处：《电机与控制应用》2023年第1期30-34,共5页Electric machines & control application

基　　金：国家自然科学基金项目(51575392)。

摘　　要：引入恰当的运动参考系可以简化交流电机模型推导和分析。一般地,运动参考系下空间矢量电压方程的推导分两步:(1)在“线圈固结坐标系”中运用法拉第电磁感应定律建立电压平衡式;(2)通过坐标变换的方式推导运动坐标系下的电压方程。该过程数学推导严谨,但是,对于记忆和理解运动坐标系下的电压方程的物理意义有难度。参考力学系统中“惯性参考系”的概念,根据法拉第电磁感应定律是否直接适用,引入所谓的“法拉第参考系”概念,对运动坐标系和线圈固结坐标系加以区分。对“非法拉第参考系”,借鉴“非惯性参考系”中引入“惯性力”的做法,引入附加“牵连运动电动势”,以此表征运动参考系引入的牵连运动效果。For the analysis of the AC electrical machines, it is common to introduce rotational reference frames for the simplified analysis of AC electrical machines. Traditionally, the deduction of the governing equation under the rotational reference frames involve two steps. Step1 is constructing the voltage governing equation based on Faraday’s law under the “winding-fixed reference frame”. Step2 is using the coordinate transformation to deduce of the governing equations under the rotational reference frame. The deduction processes are mathematically rigorous. However, it is difficult to understand and remember the physical meanings behind these mathematical equations. Inspired by the “inertial frame of reference” in the mechanical system, depending on whether Faraday’s law of electromagnetic induction applies, a kind of so-called “Faraday reference frame” is introduced. It is specially used to distinguish the governing equations under the winding-fixed coordinate frame from the rotational reference frame. In this way, an additional “entrainment electromotive force” should be introduced for “non-Faraday reference frames” to characterize the effect of entrainment motion, motivated by the “inertia force” in the non-inertial frame of reference.

关 键 词：电机模型 法拉第电磁感应定律 法拉第参考系 牵连运动电动势 

分 类 号：TM34[电气工程—电机]