General Model of a Five-Phase Induction Machine Allowing for Harmonics in the Air Gap Field

This paper presents a general mathematical model of a five-phase induction machine including the effects of higher space and time harmonics in the air gap field. These harmonic waves play a decisive role in the behavior of machines with more than three phases. Mathematical expressions for the calculation of the self and mutual inductances are presented, and results are compared with values obtained by finite element analysis and measurements. Based on the air gap field distribution produced by the stator and rotor, all the field harmonics are included in a direct and simple way in the self-inductances. The mutual inductances are obtained from a Fourier series description of the air gap field, resulting in a different inductance for each harmonic field. The machine equations are then simplified using coordinate transformations, which result in equivalent d-q models and equivalent circuits for given harmonic groups. In their final form, the equations are appropriated for the simulation of the machine behavior and developing new control strategies including higher space and time harmonics. Finally, practical results of a prototype machine are compared with simulations demonstrating the accuracy of the model