Model of a five-phase induction machine allowing for harmonics in the air-gap field. Part I. Parameter determination and general equations

This paper presents the mathematical model of a five-phase induction machine including the effects of higher space and time harmonics in the air-gap field. It is well known that these harmonic waves play a decisive role in the behavior of machines with more than three phases. This first part of a two-part paper discusses the calculation of the main parameters where these are derived analytically, and results are compared with values obtained by finite element analysis. The main parameters used in deriving the model are the self and mutual stator and rotor inductances. Based on the field distribution produced by 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. A discussion of the general equations for the induction machine follows. In the second part of the paper, these equations are simplified using known axis transformations, which result in equivalent d-q models and circuits for given harmonic groups. In their final form, the equations and corresponding equivalent circuits are well suited for purposes of simulation of five-phase machine behavior and developing new control strategies including higher space and time harmonics.