# Mehran University College Of Engineering & Technology, Khairpur Mir’s ENGR. AHSANULLAH MEMON LECTURER DEPARTMENT OF ELECTRICAL ENGINEERING MUCET KHAIRPUR.

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Mehran University College Of Engineering & Technology, Khairpur Mir’s ENGR. AHSANULLAH MEMON LECTURER DEPARTMENT OF ELECTRICAL ENGINEERING MUCET KHAIRPUR MIRS WORKING PRINCIPLE, SLIP AND TORQUE OF IM

WORKING PRINCIPLE  When three phase supply is given to the stator of three phase induction motor, a rotating magnetic field is produced which rotates with synchronous speed.  The flux passes through the air gap and cuts the rotor conductors which are stationary.  Due to relative speed between rotating flux and stationary conductors. An emf is induced according to faradays laws of electromagnetic induction.  Since the rotor bars or conductors forms a closed circuit, rotor current is produced whose direction is given by lenz law.  Hence current in rotor will produce its own flux and to reduce relative speed, the rotor starts to running in same direction as that of rotating flux and tries to catch up with rotating flux.

Slip  In practice, the rotor can never reach the speed of stator flux. If it did, there would be no relative speed between the stator field and rotor conductors, no induced rotor currents and, therefore, no torque to drive the rotor.  The friction and windage would immediately cause the rotor to slow down. Hence, the rotor speed (N) is always less than the suitor field speed (Ns).  The difference between the synchronous speed Ns of the rotating stator field and the actual rotor speed N is called slip. It is usually expressed as a percentage of synchronous speed

Rotor Current Frequency  The frequency of a voltage or current induced due to the relative speed between a windings and a magnetic field is given by the general formula.

Rotor emf and reactance under running conditions  When s=1,rotor induced emf is maximum because relative speed between rotor and revolving stator flux is maximum.  When motor start running, relative speed is decreased and emf which is directly proportional to relative speed is also decreased.

ROTOR CURRENT  If rotor e.m.f./phase and roto reactance/phase are s E2 and sX2 respectively.  The rotor resistance/phase is R2 and is independent of frequency and, therefore, does not depend upon slip.  Likewise, stator winding values R1 and X1 do not depend upon slip.

Mehran University College Of Engineering & Technology, Khairpur Mir’s ENGR. AHSANULLAH MEMON LECTURER DEPARTMENT OF ELECTRICAL ENGINEERING MUCET KHAIRPUR MIRS TORQUE IN 3 PHASE IM

ROTOR TORQUE  As studied in DC motors that power torque of DC motor depends upon flux and rotor current, hence in AC motors torque depend upon these two factors along with power factor also.

Starting Torque (Ts)  The rotor circuit of an induction motor has low resistance and high inductance.  At starting, the rotor frequency is equal to the stator frequency (i.e., 50 Hz) so that rotor reactance is large compared with rotor resistance.  Therefore, rotor current lags the rotor e.m.f. by a large angle, the power factor is low and consequently the starting torque is small.  When resistance is added to the rotor circuit, the rotor power factor is improved which results in improved starting torque.  As rotor bars of squarel cage rotors are permanently short- circuited, it is not possible to add any external resistance in the rotor circuit at starting. Consequently, the starting torque of such motors is low.  The resistance of the rotor circuit of wound rotor motors can be increased through the addition of external resistance. By inserting the proper value of external resistance (so that R2 = X2), maximum starting torque can be obtained.

Starting Torque (Ts)

Condition for maximum starting torque  Starting torque will be maximum when rotor resistance/phase is equal to standstill rotor reactance/phase.

Under the condition of maximum starting torque, = 45° and rotor power factor is 0.707 lagging Effect of Change of Supply Voltage

Torque Under Running Conditions

Maximum Torque under Running Conditions

Torque-Slip Characteristics

At s=1 the term increases very rapidly so that may be neglected as compared to.

Problem (H.W) Consider a 6-pole, 3-phase, 50 Hz induction motor. If the full-load speed of the motor is 960 r.p.m.Standstill rotor emf / phase is 220v and rotor reactance is 100 ohm. i)Calculate rotating field speed. ii)Calculate the slip. iii)Rotor emf / phase iv)Rotor frequency v)Rotor reactance / phase

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