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 NOMINAL_SPEED (i.e. the synchronous speed with zero slip).During manufacture, the stator resistance is measured to be R₁. 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, X, is j3002. a) Calculate the number of poles for the design to achieve the specified nominal speed. b) Using the full approximate equivalent circuit, calculate the torque produced by the machine for a slip of 3%.fol 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).

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