[Definition of Park transform extensions for the control of surface-mounted permanent magnet synchronous motors]

The high performance controls of surface-mounted permanent-magnet synchronous motors are based on the use of the Park transformation. This state transformation offers certain advantages, among which is the fact that, in this new reference frame, the electromagnetic torque is directly an image of the quadrature ("q") component of the stator current. This result applies only to the machines with sinusoidal flux distribution. We propose in this paper extensions of the Park's transformation to the machines with non-sinusoidal flux distribution. Two different versions are proposed and compared: a normalized version which allows to define "dq"-like axes such as the electromagnetic torque depends on the only "q"-like components of the stator current; a denormalized version such as the proportionality factor between the electromagnetic torque and the current "q"-like component is constant (does not depend on the rotor position).