DC-Current Injection With Minimum Torque Ripple in Interior Permanent-Magnet Synchronous Motors

Several proposals based on dc-current injection have been reported for estimating the stator winding resistance in induction machines, and recently extended for synchronous machines. Tracking this resistance can be very useful, e.g., for thermal monitoring or preserving control dynamics. In surface-mounted permanent-magnet synchronous machines (PMSMs), it is possible to inject a dc component in the $d$-axis, without perturbing the torque. However, it has been claimed that, for synchronous machines with saliency, it is not possible to avoid the torque ripple due to such injection. This letter proposes optimum reference currents to impose dc current in three-phase interior PMSMs while minimizing to practically zero its associated torque ripple. Namely, the dc signal is injected in combination with a suitable second-order harmonic so that the stator current space vector follows the constant-torque locus, while the fundamental is set according to the maximum-torque-per-ampere strategy. Experimental results validate the theory.