A 50 kW induction motor is operated at a lagging power factor of 0.8, the source voltage being 230 V rms. a) Find the complex power Sm that this motor is using. b) In order to get lower electricity bill it is desired to connect a parallel compensator to the motor so as to get pf=0.95 lagging and still provide the 50kW real power for the motor. Determine the total complex power S7= Sm+ Sc that will achieve the desired pf, where Sc is the power of the compensator c) Determine the complex power Sc of the compensator and the value of the parallel compensator impedance. What type of circuit element should be the compensator?

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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.