Analytic expression of torque ripple by fourier coefficients of flux linkages

A major source for torque ripple is the harmonics in airgap permeance caused by stator slotting, permanent magnet (PM) flux barrier, etc. They are reflected in the flux linkages of the stator windings. In this work, we express the d and q-axis flux linkages as Fourier series after obtaining them using finite element analysis (FEA). Torque ripples are obtained analytically using the Fourier coefficients of the flux linkages, and justified by comparing the results with FEA torque. With a linear flux model in current, the ripple components are expressed explicitly in current and high order saliency. Through simulations, it is demonstrated that the ripple increases as the d-axis current increases negatively along a constant torque line.