Abstract

A mathematical model of an induction motor (IM) with a phase rotor is developed on the basis of the usual assumptions that does not use the supposition that there is an annular rotating field in its air gap and various transformations of coordinates. The model is valid for both transient and steady-state modes and with various ways of control by changing the parameters of the three-phase feeding voltage system of the IM stator coil. It is shown that the desired stationary operation mode that exists in the developed nonlinear IM model at a constant feeding voltage of the stator and load torque corresponds to the constant electromagnetic torque and spinning frequency of the rotor at sine-wave rotor and stator currents. A digital IM model is developed in the MATLAB system. An analytical solution is derived for the system of linear differential equations that describes the IM with a retarded rotor and allows evaluating the nonlinear digital model for correctness. Examples of applying the IM model in analyzing transient and steady-state operation modes of this motor are provided.

中文翻译：

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带有相位转子的三相感应电动机的数学模型

摘要

基于通常的假设，开发了具有相位转子的感应电动机（IM）的数学模型，该假设不使用在其气隙中存在环形旋转场以及各种坐标变换的假设。通过更改IM定子线圈的三相馈电电压系统的参数，该模型对于瞬态和稳态模式均有效，并具有多种控制方式。结果表明，在恒定的定子进给电压和负载转矩下，在已开发的非线性IM模型中存在的所需静态运行模式对应于正弦波转子和定子电流下转子的恒定电磁转矩和旋转频率。在MATLAB系统中开发了数字IM模型。推导了线性微分方程系统的解析解，该系统描述了带滞后转子的IM，并允许评估非线性数字模型的正确性。提供了在分析此电动机的瞬态和稳态运行模式时应用IM模型的示例。