Harmonic Plane Decomposition: An Extension of the Vector-Space Decomposition - Part II

In this paper the harmonic plane decomposition from part I is completed. Multiphase electrical machines with independently controlled stator coils benefit from a fixed amount of current controllers and unified models. In part I, the foundation for such models was laid. This paper shows that the choice of the base case has to fulfill certain criteria to properly represent vector-space quantities. More specifically, phase-pole configurations with an even number of pole pairs need adapted base cases with reduced rank as compared to the odd base case. Continuous modeling and control requires retention of the dimensionality of Clarke matrices. A different number of stator and rotor slots can lead to aliasing in the transformation, when keeping the dimension consistent. Therefore, a specific Clarke transformation for rotor quantities based on the developed theory is elaborated. Finally, it is demonstrated how the harmonic plane decomposition can be used to model each harmonic plane of an arbitrary phase-pole configuration with conventional machine equivalent circuits, e.g. the T-equivalent or inverse-Γ models.