Induction motor:Condition for Maximum Torque Under Running Conditions.

Condition for Maximum Torque Under Running Conditions

The torque of a rotor under running conditions is

The condition for maximum torque may be obtained by differentiating the above expression with respect to slip s and then putting it equal to zero. However, it is simpler to put Y = 1/T and then differentiate it.

Hence, torque under running condition is maximum at that value of the slip s which makes rotor reactance per phase equal to rotor resistance per phase. This slip is sometimes written as sb and the maximum torque as Tb.

Slip corresponding to maximum torque is s = R2/X2

Putting R2 = sX2 in the above equation for the torque, we get

From the above, it is found

1. that the maximum torque is independent of rotor resistance as such.

2. however, the speed or slip at which maximum torque occurs is determined by the rotor resistance. As seen from above, torque becomes maximum when rotor reactance equals its resistance. Hence, by varying rotor resistance (possible only with slip-ring motors) maxi- mum torque can be made to occur at any desired slip (or motor speed).

3. maximum torque varies inversely as standstill reactance. Hence, it should be kept as small as possible.

4. maximum torque varies directly as the square of the applied voltage.

5. for obtaining maximum torque at starting (s =1), rotor resistance must be equal to rotor reactance.

Example 34.11. A 3-phase, slip-ring, induction motor with star-connected rotor has an induced e.m.f. of 120 volts between slip-rings at standstill with normal voltage applied to the stator. The rotor winding has a resistance per phase of 0.3 ohm and standstill leakage reactance per phase of 1.5 ohm.

Calculate (i) rotor current/phase when running short-circuited with 4 percent slip and (ii) the slip and rotor current per phase when the rotor is developing maximum torque.

(Elect. Engg.-II, Pune Univ. 1989)