Modeling and Analysis of Induction Machines Containing Space Harmonics Part I: Modeling and Transformation

The coupled-circuit approach is used to derive a mathematical model of a general m-n winding machine in which all MMF harmonics are taken into account. The model, which is applicable to both squirrel cage and phase- wound rotors, has provision for cage rotors with non-integral number of rotor bars per stator pole-pair. The effects of the transformations from polyphase to a-P-0 and to d-q-0 on the machine equations are analyzed. It is shown that the polyphase to a-P-0 transformation, when applied to the stator and rotor of the m-n winding machine, divides the harmonics into different groups of harmonics with possible interaction, whereupon each group of harmonics can then be represented by an a-P or a zero component circuit. This result shows that the usual assumption of representing the cage rotor by independent harmonics circuits is, in general, not valid. It is also shown that the polyphase to rotating d-q transformation is applicable when only one harmonic from each a-P component is to be considered, otherwise a new problem of separating the harmonic voltages within each a-P component is created.