Unbalanced operation of five-phase induction machines using steady state symmetrical components — Part I: Theoretical considerations

The unbalanced operation of five-phase induction machines is described using the method of steady state symmetrical components and including aspects not yet considered, such as the changes in the airgap induction. Starting from the dynamic equations, described by instantaneous symmetrical components, sequence equations are obtained in terms of steady state symmetrical components, thus establishing a clear relationship between these two methods. The sequence equations allow to determine the machine performance under any unbalanced operation in a simple and direct way. Furthermore, the approach followed here allows to analyze the machine from the point of view of positive- and negative-rotating fields, as each symmetrical component can be associated with a distinct rotating field in the airgap. Analytical expressions are derived for the mean and pulsating torque produced by each steady state symmetrical component. Further, analytical expressions of the induction in the airgap are also derived as a function of sequence currents. It is demonstrated that, besides a positive- and a negative-rotating fundamental induction wave, two additional waves with triple pole pair number are created in the airgap, rotating at 1/3 of the speed of the fundamental wave. Finally, it is shown that, similar to three-phase machines, currents with high-frequency components are induced in the rotor. The model presented is useful not only to analyze but also to design five-phase machines capable of working under unbalance. The second part of the paper presents typical applications of the model described here.