Analytical Calculation of the Slot Leakage Inductance in Fractional-Slot Concentrated-Winding Machines

This paper obtains analytical expressions for the calculation of the slot leakage inductance for fractional-slot concentrated-winding (FCSW) machines with one-, two-, or four-layer windings. The formulas are derived from solving the 2-D Poisson problem associated with the slot region, making them more accurate than classically used expressions that assume a leakage flux path parallel to the placement of the conductors in the slot. Explicit formulas are given in the case of one- and two-layer FSCWs with a number of phases ranging from 3 to 7. The obtained analytical expressions are validated by a finite-element analysis, showing excellent agreement between both calculation methods, even for large slot-opening-to-slot-pitch ratios. A brief comment with regard to the fault-tolerant capability of permanent-magnet FSCW machines with respect to the number of layers is also given.