Please show a complete solution to the problem 6. A 540 V, 50 Hz, 3-phase circuit takes 31 A at a lagging power factor of 0.88. A synchronous motor is used to raise the power factor to unity. Calculate the numerical value of the power factor, in per unit, of the synchronous motor when driving a mechanical load of 7.7 kW. The motor has an efficiency of 85%. Give your final answer in 3 decimal places.   Correct Answer:  0.550 ± 0.001

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Synchronous Motor

The synchronous motor is an AC electric type motor where at a steady-state the shaft rotation is synchronized with the supply current variable-frequency. To an integral number of AC cycles, the rotation period is exactly equal. The stator of the motor in the synchronous motor contains multi-phase AC electromagnets due to which a magnetic field is created that rotates in time with the oscillation of the line current. The rotor contains a permanent magnet and the rotor rotates in synchronization with the stator field at the same rate and provides the second synchronized magnetic field which is rotating in nature as a result. When the synchronous motor is supplied with independently excited multi-phase AC electromagnets on both the rotor and the stator, it is termed as a doubly-fed machine. The most widely used AC-type motors are the synchronous AC motor and the induction AC motors.