Mathematical Model for MTPA Control of Permanent-Magnet Synchronous Motor in Stator Flux Linkage Synchronous Frame

A mathematical model is proposed for the maximum torque per ampere (MTPA) control law of a permanent-magnet synchronous motor (PMSM) in the stator flux linkage synchronous frame (M-T frame). The mathematical model takes into consideration magnetic saturation and cross-magnetization effects. In taking into consideration magnetic saturation effects, most of the mathematical models in the d-q frame are complex. The M-T frame has several advantages, such as the simplicity of the flux-weakening control law and its applicability to various motors. In this paper, the control characteristics of a PMSM in the M-T frame are analyzed, and a mathematical model for estimating the MTPA control trajectory in the M-T frame is proposed. In addition, a method of simply determining the parameters for the mathematical model is proposed. The validity of the proposed model is confirmed by comparing the analytical and experimental results.