Extending mathematical model of permanent magnet synchronous motors in alpha-beta coordinate system for EKF

This paper deals with the derivation of the permanent magnet synchronous motor (PMSM) model in alpha-beta coordinate system. The exact model of PMSM is essential for rotor position and speed estimation algorithms. Information about the rotor position is necessary even to be able to control drive speed. Extended Kalman filter (EKF) was used to estimate the rotor position. Conventional algorithms based on EKF are developed using a simple model of permanent magnet synchronous motor (L
_d
= L
_q
= L
_s
), thereby they provide bad performance in the low speeds. Extended mathematical performance in the (L
_d
≠ L
_q
≠ L
_s
) makes possible for EKF to operate in low speeds, because information about rotor position is contained in changes of stator inductance.