Time-Optimal Transition Method for Six-Step Operation of PMSM via Geometric Prediction of Flux Trajectory

This article analyzes the time-optimal trajectory of the stator flux vector in a permanent-magnet synchronous motor (PMSM) under the six-step operation. In the rotor reference frame (RRF), the time-optimal trajectory of the flux vector takes the form of a detour to the target locus, which poses challenges for implementing the time-optimal trajectory with a conventional controller designed in RRF; an open-loop structure is required. On the other hand, in the stationary reference frame (SRF), the time-optimal trajectory appears as a shortcut when the flux angle increases and a detour when the flux angle decreases. Based on the analysis in SRF, this article proposes a closed-loop time-optimal transition method for the six-step operation of a PMSM. The proposed method applies a voltage vector so that the flux vector follows the time-optimal trajectory via prediction. The performance of the proposed method is verified through simulations and experiments with a 30 kW-PMSM for HEV applications.