A 15-kVA, 230-V, two-pole, three-phase permanent-magnet synchronous motor has a maximum speed of 10,000 r/min and produces rated open-circuit voltage at a speed of 7620 r/min. It has a synchronous inductance of 1.92 mH. The motor is to be operated under field-oriented torque control.

a. Calculate the maximum torque the motor can produce without exceeding rated armature current.

b. Assuming the motor to be operated with the torque controller adjusted to produce maximum torque (as found in part (a)) and iD = 0, calculate the maximum speed at which it can be operated without exceeding rated armature voltage.

c. To operate at speeds in excess of that found in part (b), flux weakening will be employed to maintain the armature voltage at its rated value. Assuming the motor to be operating at 10,000r/min with rated armature voltage and current, calculate

(i) The direct-axis current iD.

(ii) The quadrature-axis current iQ.

(iii) The motor torque.

(iv) The motor power and power factor.