MODELING AND ANALYSIS OF INDUCTION MACHINES CONTAINING SPACE HARMONICS

The couped-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 a squirrel cage or phase-wound rotor has provision for non-integral number of rotor bars per stator pole-pair. A general polyphase to (alpha)-(beta)-0 components transformation is described. When applied to the stator and rotor of the m-n winding machine, the polyphase to (alpha)-(beta)-0 transformation divides the harmonics into different groups of harmonics with possible interaction, whereupon each group of harmonics can then be represented by an (alpha)-(beta) or a zero component circuit. This result shows that the usual assumption of representing the cage rotor by independent harmonics circuits is not valid in general. It is also shown that the polyphase to rotating d-q transformation is applicable when only one harmonic from each (alpha)-(beta) component is to be considered, otherwise a new problem of separating the harmonic voltages within each (alpha)-(beta) component is created. As a special case of the transformation the three phase squirrel cage induction machine is considered. In addition the steady-state equations for asynchronous and synchronous action of a polyphase squirrel cage induction machine are derived. The conditions for synchronous action between two harmonics are identified. It is concluded that every pair of harmonics belonging to the same set of (alpha)-(beta) components produces synchronous action, conversely every pair of harmonics which produces synchronous action belongs to the same set of (alpha)-(beta) components. This confirms that the harmonics of each set of (alpha)-(beta) components are not separable. Finally, the effects of MMF harmonics on the steady-state and transient behaviors of three sample squirrel cage induction machines with rotors designed to give varying amounts of asynchronous and synchronous torques are studied. The influence of slot opening on the MMF, skew and skin effects are taken into account in the derivation of the parameters for these machines. The computational requirement for the solution of the original phase equations is compared with those of the (alpha)-(beta) and d-q component equations