A General Approach to the Design of Multi-Layer Fractional-Slot Concentrated Windings With Arbitrary Number of Slots, Poles, and Phases

Multiphase Fractional Slot Concentrated Windings (FSCWs) are an attractive potential solution in the design of permanent-magnet synchronous machines as they combine the advantages of multiphase windings, such as power segmentation and fault tolerance, with the benefits of FSCWs, like high manufacturability and short end coils. The adoption of multiphase FSCWs is limited by the fact that, according to the existing literature, their symmetrical implementation is possible only for specific sets of slot-pole combinations. The main contribution of the paper is to set forth a method which, resorting to multi-layer arrangements (wherein multiple coils belonging to different phases may be wound on the same tooth), makes it possible to design a symmetrical multiphase FSCW with a theoretically arbitrary number of slots, poles and phases. To this end, an innovative design procedure, based on linear programming and simplex method, is presented as an alternative to the conventional star-of-slot technique to achieve a symmetrical FSCW with any number of slots, poles and phases. For illustration purposes, the proposed procedure is applied to design both a six-phase (dual three-phase) FSCW and a five-phase FSCW for a surface-mounted permanent magnet machine with 9 slots and 8 poles. Both the FSCWs are considered as not feasible according to the present literature and cannot be designed using the star-of-slot technique. The paper shows that, adopting the new proposed approach, the two windings can be designed in a symmetrical form achieving reasonably high winding factors (0.967 and 0.959 in the six-phase and five-phase case, respectively). The results are validated through Finite Element Analysis (FEA) simulations, whose accuracy and reliability are preliminarily assessed by comparison against experimental tests on a laboratory prototype.