DQ analysis of fractional-slot machines with star-delta concentrated winding

This paper presents a novel method for addressing the challenge of dq -transformation in fractional-slot machines with star-delta connected concentrated windings. These machines have no neutral point, preventing direct measurement of mutual inductance between phases. This complicates the calculation of d - and q -axis inductances, which are crucial for modern control techniques such as field-oriented and sensorless control. The proposed method derives d - and q -axis inductances as functions of individual star and delta coil inductances, which can easily be measured. Moreover, it demonstrates that the d - and q -axis inductances can be calculated using measurements from just two adjacent coils. The method begins with constructing a decomposed coil-by-coil inductance matrix, separating each phase winding into individual star and delta coil inductances. This matrix is then transformed into the dq -frame using a three-step process: firstly, summing individual flux linkages to derive line flux linkage based on circuit configuration; secondly, decomposing 3-phase abc supply currents into individual currents within the star and delta coils to address phase shift and amplitude differences; and finally, transforming line flux linkage into the dq -frame using a modified power-invariant Park transformation. The proposed method is validated by simulations and experiments on both surface mounted and interior permanent magnet machines.