Hand written explanation required

Q6. A 2-pole, 3000 rev/min, A-connected synchronous turbo-motor is driven by a conventional space-vector-pulse-width-modulated inverter. The motor has a synchronous reactance of 25 2 at rated speed, and it can be assumed ideal for convenience of analysis. (a) Determine the line current and torque this motor can develop when consuming 10 KW at an induced voltage (emf) of 500 V, and the inverter output voltage of 400 V, 30 Hz. (10 marks) (b) The desired (reference) voltage vector ( Vref ) to be applied across the motor terminals over a fixed control interval (7z) is orientated as depicted in Figure Q6. If the two adjacent active voltage vectors of the inverter are V1 = Vm and V2 = Vm e/7/3, derive the following general expressions for the switching time durations of V1 and V2: Vref sin (7 / 3- a) Vref sin (a) T1 = Tz Vm sin(7 / 3) T2 = Tz' Vm sin (7 / 3)