Improved Maximum-Torque-Per-Ampere Algorithm Accounting for Core Saturation, Cross-Coupling Effect, and Temperature for a PMSM Intended for Vehicular Applications

This paper presents an improved method of deriving the ideal maximum-torque-per-ampere (MTPA) angle for a permanent-magnet synchronous machine (PMSM). The algorithm accounts for core saturation and cross coupling of the direct- and quadrature-axis magnetic flux. In addition, the impact of various temperatures is also investigated. The algorithm is demonstrated to provide a
$d{-}q$
current reference angle that is very close to the real MTPA-angle for the whole operating range. It is found that if the current dependency of the equivalent circuit machine parameters such
$L_d$
,
$L_q$
, and
$\Psi_m$
is updated for each optimization iteration step in an MTPA algorithm rather than being accounted for directly in the optimization, the MTPA angle is predicted up to 7° too low for the investigated machine. However, with the proposed MTPA-angle method here, this discrepancy is eliminated. Moreover, the consequence of utilizing the derived improved algorithm here is that the losses at the peak torque operating point is 6% lower than without the full optimization. This leads to an enhanced take-off ability by increasing the torque at the rated current by up to 3.6%.