Modelling of the permanent magnet synchronous motor (PMSM) torque ripple and PMSM current harmonics controlling technology are important branches of PMSM research. Based on the existing linear PMSM model derived from magnetic co-energy, this study considers the variation of PMSM parameters (inductance, permanent magnet flux and cogging torque) caused by magnetic saturation. Then, the harmonic coupling models including flux–current coupling model, voltage–current coupling model and torque–current coupling model are deduced. In these harmonic coupling models, the PMSM parameters no longer vary with rotor position but only with current amplitude and phase. Based on the torque–current coupling model, a novel method of obtaining the required injecting currents which could suppress torque ripple is proposed. The validity of the harmonic coupling models and the injecting current solution method is verified by finite-element method.