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Magnet-free variable phase-pole machines are competitive alternatives in electric vehicles where torque-speed operating region, reliability, cost, and energy efficiency are key metrics. However, their modeling and control have so far relied on existing fixed-phase and pole-symmetrical models, limiting their drive capabilities especially when switching the number of poles on the fly. This paper establishes the harmonic plane decomposition theory as a space-discrete Fourier transformation interpretation of the Clarke transformation, decomposing all pole-pair fields into a fixed number of orthogonal subspaces with invariant parameters. The model remains unaltered for all phase-pole configurations, guaranteeing continuity even under phase-pole transitions. Relations of the state and input space vectors, and model parameters to those of the vector space decomposition theory used for multiphase machines are established via the use of the complex winding factor. Experiments confirm the modeling theory and demonstrate its practical usefulness by performing a field-oriented-controlled phase-pole transition. Non-trivial configurations with more than one slot/pole/phase and a fractional phase number are also demonstrated.

Enabling Variable Phase-Pole Drives with the Harmonic Plane Decomposition