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

In this first paper of a two-part series, the harmonic plane decomposition is introduced, which is an extension of the vector-space decomposition. In multiphase electrical machines with variable phase-pole configurations, the vector-space decomposition leads to a varying numbers of vector spaces when changing the configuration. Consequently, the model and current control become discontinuous. The method in this paper is based on samples of each single slot currents, similarly to a discrete Fourier transformation in the space domain that accounts for the winding configuration. It unifies the Clarke transformation for all possible phase-pole configurations such that a fixed number of orthogonal harmonic planes are created, which facilitates the current control during reconfigurations. The presented method is not only limited to the modeling of multiphase electrical machines but all kinds of existing machines can be modeled. In the second part of this series, the harmonic plane decomposition will be completed for all types of machine configurations.