A Mathematical Review Study on Dynamical Models of Symmetrical Three-Phase Induction Machine in Various Reference Frames

Abstract

This paper presents dynamic models of a three-phase induction machine in various reference frames widely employed in alternating-current (ac) machine analysis. The main objective is to derive and explain the machine model in relatively basic terms by using the idea of rotating reference frame theory. Many matrix manipulations and complex frame-to-frame transformations performed to obtain an advanced model from primitive dynamical equations are presented in a more compact and easy-to-understand way. Therefore, this paper reviews a detailed, yet simple and understandable mathematical background on the dynamic models of the induction machine. Furthermore, a unified and broadly applicable simulation model is proposed for simulating the dynamic behavior of the machine in any desired reference frame. The simulation model has also a modular and user-friendly structure. For the simulation studies, Matlab/Simulink environment is preferred due to its popularity. A Simulink machine model with several subsystems is explicitly given. The simulation study is realized for a small power induction machine operating under both load and no-load conditions. The variations of three-phase currents, electromagnetic torque, and rotor mechanical speed as well as the rotor flux-linkage components are shown. The key features of each reference frame are discussed, especially through the measured rotor flux-linkage components.