A Quadratic-Programming Approach to the Design Optimization of Fractional-Slot Concentrated Windings for Surface Permanent-Magnet Machines

Fractional-slot concentrated windings (FSCW) are becoming more and more popular in the design of permanent magnet electric machines. A well-known drawback of their adoption is the occurrence of large magneto-motive force (MMF) harmonics, which produce eddy-current losses in rotor permanent magnets. The use of a multi-layer design, with coils of different phases wound around the same tooth, is a possible countermeasure to mitigate the problem. In this paper, a new general systematic methodology is proposed to optimize the multilayer FSCW design in the form of a multi-objective quadratic programming problem. The maximization of the MMF fundamental and the minimization of total rotor losses are taken as properly weighed objective functions. Constraints are imposed to guarantee the physical feasibility and the electric symmetry of the winding. An application example to a 9-slot 8-pole machine is presented, together with extensive validations by comparison with finite element analysis (FEA) simulations, to prove the effectiveness of the proposed technique.