Modeling of split-phase machines in Park´s coordinates. Part I: Theoretical foundations

A split-phase machine is a special electric machine whose stator winding is split into multiple (N) three-phase sets. The possibility to supply it through N independent inverters makes it attractive especially when high power and reliability are required. So far, the dq0 refeence frame representation, originally introduced for three-phase machines, has been applied in detail to split-phase configurations in the N=2 case only. In this paper, the extension to an arbitrary number of stator sets is investigated from an analytical viewpoint. In particular, the paper shows that when N exceeds two, the d-axis and q-axis stator voltage equations are no more decoupled, in general, as it happens for N=1 and N=2. Such d-q cross-coupling is explained in terms of mutual leakage inductances, regardless of possible rotor saliencies and magnetic saturation. The implications of these results in terms of equivalent circuit representation will be presented in a companion paper (Part II).