Pole-Transition Control of Variable-Pole Machines Using Harmonic-Plane Decomposition

Abstract

Variable phase-pole machines have the potential to extend the operational range to higher speeds through magnetic pole changes. The state-of-the-art vectorspace decomposition cannot model the transient behavior of the pole change for any possible phase-pole configuration as it creates a discontinuity. The proposed harmonicplane decomposition theory solves this issue by generalizing the vector-space decomposition to the fullest extend by using its discrete Fourier transformation interpretation. The theory for indirect rotor field-oriented control is developed using the harmonic-plane decomposition. A controlled, loaded pole change on a wound independently-controlled stator-coils machine using two transition strategies shows the harmonic-plane decomposition-based controller's ability to maintain torque in the transition. Additionally, the proposed controller accomplishes real harmonic injection and balanced steady-state operation.

Enabling Variable Phase-Pole Drives With the Harmonic Plane Decomposition

“…it is related to the degrees of freedom in the drive. On the contrary, the rank of the Clarke matrix in the HPD is always higher than m s , meaning that vector spaces ν distribute over the harmonic planes h. The relation between h and ν in ( 14) from [10] describes this vector-space distribution for a balanced [m s , p] PPC. To make notations compact, we introduce h ν as the set of harmonic planes h, which contains the same vector space, ν. Conversely, ν h is the vector space ν, that hosts the harmonic plane, h. Note that one vector space may distribute over several harmonic planes.…”

“…A shortcoming is that the number of vector spaces, ⌈ ms /2⌉, increases with the number of phases, m s . As a result, the number of controllers in an MPM with phase-changing capabilities ought to change with the number of phases [10]. That the number of subspaces depends on the number of phases stems from the fact that the VSD assumes m s fixed magnetic axes.…”

“…On the contrary, VPPMs do not necessarily generate equal and opposite currents in the slots shifted by π rad electrically. For instance, this is the case for toroidally-wound VPPMs by their construction [2], [10]. Such VPPMs provide the highest torque density among different winding types, according to [11].…”

“…In summary, the VSD does not offer a straightforward way to actively control the currents in adjacent slots belonging to the same phase belt, especially during PPC transitions. A generalized VSD, termed the harmonic plane decomposition (HPD), was introduced in [10]. It establishes a model with a fixed number of subspaces which in practice results in a fixed number of current controllers.…”

“…This paper aims to give an in-depth and machineindependent derivation of the HPD presented in [10], including some theoretical interpretations missing in previous articles, and highlight the differences to the VSD; especially when adopting the two decomposition methods to VPPMs. Section II derives the HPD from the discrete Fourier transformation (DFT) theory and juxtaposes it to the VSD.…”