Vector space decomposition algorithm for asymmetrical multiphase machines

Benefits of modelling a multiphase machine by use of a Vector Space Decomposition (VSD) are decoupled machine model and unique mapping of all odd-order harmonics within the resulting subspaces. This is achieved by multiplying machine phase variables with VSD matrix. However, creation of VSD matrix is usually considered only for a specific machine configuration, i.e. symmetrical or asymmetrical. Moreover, available research on VSD modelling techniques produces the same or very similar VSD matrix for a considered machine type. This paper proposes a simple algorithm for creation of VSD matrix for asymmetrical machines. It is further extended to cover symmetrical configurations as well. Examples are provided for some of the most frequently used asymmetrical multiphase machines, 6-, 9-and 12-phase. In addition, as a special case, a 15-phase machine has been considered as well. Its stator windings can consist of five 3-phase winding sets or three 5-phase ones. Obtained transformations are verified by comparison with those found in the literature and confirmed using numerical simulations and experimental results.