INDUCTANCES AND AIRGAP FLUX DENSITY OF A SYNCHRONOUS RELUCTANCE MACHINE USING THE ACTUAL MACHINE GEOMETRY

Abstract

This paper reports the direct utilization of the actual rotor and stator geometry and winding placement patterns of a cageless synchronous reluctance machine to calculate its radial airgap flux density distribution and inductances. Analytical expressions representing machine winding functions and non-uniform airgap are derived in detail. The new method of computing the inductances and airgap flux density using this actual geometry and windings are based on the old concept of winding functions (WF). The procedure developed here does not rely on Fourier series expressions for airgap or winding, therefore complicated integrations are avoided. The effects of stator slots are included by considering them as added airgaps in its actual shapes and position not approximated forms that use Carter's coefficients. The rotor pole faces are modeled in the tapered manner in which they are made, considering the airgap along the pole arc as not being uniform. The inductances obtained are transformed to d-q-0 reference frame and the results are seen to compare favorably with finite- element (FE) calculations and measurements. Cross-coupling effects between the d-axis and q-axis inductances which finite element or the traditional measuring techniques are unable to identify are readily yielded by the proposed direct WF method.