Mathematical Model of a PM Brushless Motor with Different Stator-Rotor Pole Pairs Number

The paper presents a mathematical model of Permanent Magnet AC brush less machines (PMSM) having a number of stator poles-obtained via the distribution of the three-phase winding- different from the rotor one, realized by the displacement of the permanent magnets. For these so-called ´Fractional-Slot´ motors (where few total slots generate high equivalent number of poles) the available mathematical models appear partial and/or incomplete, despite of numerous designing considerations made in literature. In this paper an analytical approach is developed to point out an instantaneous-values mathematical model with concentrated parameters, that can be suitable for control architecture systems when some simplification hypotheses are added. The model takes into account a general distribution of the armature magneto motive force field, and the total harmonic content of the rotor flux density. The whole MMF harmonic content is then properly reduced and the result is compared to a traditional PMSM model.