Offline Measurement of PMSM Incremental Inductance via Geometric Fitting of Current Derivatives

Accurate incremental inductance maps of thed-andq-axes underpin model-based predictive control, sensorless operation, and fault diagnosis of permanent-magnet synchronous motors (PMSMs). This paper presents a non-invasive offline measurement technique that exploits the current-derivative transients naturally generated by inverter switching events. By reformulating the discrete switching model in a virtual-voltage-vector-oriented frame, the inductance measurement task becomes a rotor-angle-independent geometric fitting problem. A robust fitting solver with outlier rejection mitigates nonlinear effects such as sensor drift and noise. The method operates on a standard finite-control-set drive and requires no shaft lock, additional signal injection, or extra sensors, yet yields a full-range inductance map. Experimental results on an interior PMSM demonstrate that the calibrated inductance map is in close agreement with finite-element analysis, conforms to the IEEE Std 1812-2023 offline benchmark, and remains consistent with values obtained from a current-derivative-based online estimator.