Unified theory of torque production in switched and synchronous reluctance motors

One of the difficulties in comparing the capabilities of the switched reluctance motor with those of AC motors is the lack of a unified theory of torque production, in which the same equation can be used for both motors so that the comparison can be reduced to the comparison of coefficients. The main impediment to the development of such a theory has been the fact that the switched reluctance motor does not satisfy the necessary conditions for the dq-axis transformation, because of its double saliency. Essentially it produces torque in impulses and it is analysed by calculating the energy converted from electrical to mechanical during one stroke. This is equal to the area enclosed by the trajectory of the operating point in the phase flux-linkage versus phase-current diagram. In this paper the torque production in the synchronous reluctance motor is analysed by the same energy conversion loop method. The new concept of the ellipse diagram not only allows a direct comparison with the switched reluctance motor, but also enables the calculation of torque ripple, this not being possible using conventional dq-axis theory