Comparing Open-Loop and Closed-Loop Operation of a Synchronous Motor
This Demonstration compares open-loop and closed-loop operation of a non-salient pole synchronous motor. Non-salient implies that the reactance is equal along every axis due to the uniform airgap between stator and rotor. The voltage vectors and the current vector in the - coordinate system are shown for the case of open-loop and closed-loop operation. The motor torque is proportional to the component of the current vector . In the case of closed-loop operation the current vector is always parallel to the axis.
The current of a non-salient pole synchronous motor fulfills the equation
In this equation is the supply voltage, is the back-EMF, is the resistance, is the reactance, and is the imaginary unit.
The voltages , , , and are represented by phasors in the - coordinate system. The axis, which is the imaginary axis, is parallel to the phasor of the back-EMF . The axis, which is the real axis, is perpendicular to the phasor of the back-EMF .
 J.R. Hendershot and T.J.E. Miller, Design of Brushless Permanent-Magnet Motors, Hillsboro, OH: Magna Physics Publications, 1994.