Stator inductance matrix diagonalization algorithms for different multi-phase winding schemes of round-rotor electric machines part I. theory

The stator winding of multi-phase machines can be designed according to different schemes, which differ by either the number or the spatial arrangement of phases. For control and analysis purposes, it is often useful that the stator inductance matrix is reduced to a diagonal form. This allows for the multiphase machine to be split into independently-controllable systems and directly leads to stator harmonic impedance determination. Simple and compact diagonalization algorithms are established in this paper covering all possible multi-phase schemes of practical importance with a unified approach, under the hypothesis of uniform air-gap and negligible magnetic saturation. In a companion paper, All the proposed equations are experimentally assessed though dedicated tests on several multiphase winding schemes.