Question

2. A three-phase induction machine is designed to operate at a near constant speed for the compressor of an environmental control system of an aircraft. The power system to which it is connected is a standard 400Hz, 115 Vrms (phase voltage) sinusoidal AC supply. The nominal speed for the compressor is NOM_SPEED (i.e. the synchronous speed with zero slip). During manufacture, the stator resistance is measured to be Ri. During a locked-rotor test at 400Hz after assembly, the measured input power per phase is LR_INPUT_POWER and the measured phase current is LR_CURRENT when operated at standstill with a reduced stator voltage of LR_VOLTAGE. The machine as a core loss at 3% slip of CORE_LOSS. The magnetising reactance, Xm, is j300. a) Calculate the number of poles for the design to achieve the specified nominal speed. [3] b) Using the full approximate equivalent circuit, calculate the torque produced by the machine for a slip of 3%. c) Calculate the total input current at this operating point. d) Calculate the efficiency at this operating point. e) On the basis of a simplified v/f analysis, calculate the supply frequency and hence voltage which must be applied to the machine to produce the same torque as part (b) but at 60% of the rotational speed in part (b). [8]

where the values of R1=0.25, Pin=441W ,Pcore-loss=37W, LR-voltage=45Vrms ,LR-current=28 Arms ,synchronus or nominal speed =12000,

Actually that's what given in the question nothing else without the recatance values ,

Answer 1

a)  

Nomimal speed = 120 * f/P

Where, f= frequency (in Hz)

Nominal Speed in rpm

& P = no. of poles

Implying this formula we get, 12000= 120*400/P

on calculating, we get P=4

b)

Max. torque of three phase induction motor,

T = (sER2/(R+(sX2)?)) * (3/2003)