**Subject :**Electrical Machines II (AC Machines)

**Unit :**Induction machines

## Maximum Torque under Running Conditions

**Maximum Torque under Running Conditions:**

The running torque of an induction motor is given as:

In order to find the value of rotor resistance that gives maximum torque under running conditions, differentiate exp. (i) w.r.t. s and equate the result to zero i.e.,

Thus for maximum torque (T_{m}) under running conditions:

**Rotor resistance/phase = Fractional slip x Standstill rotor reactance/phase**

Now, from equation of the running torque, we get,

For maximum torque, R_{2} = s X_{2}. Putting R_{2} = s X_{2} in the above expression, the maximum torque T_{m} is given by;

Slip corresponding to maximum torque, s = R_{2}/X_{2}.

It can be shown that:

It is evident from the above equations that:

(i) The value of rotor resistance does not alter the value of the maximum torque but only the value of the slip at which it occurs.

(ii) The maximum torque varies inversely as the standstill reactance. Therefore, it should be kept as small as possible.

(iii) The maximum torque varies directly with the square of the applied voltage.

(iv) To obtain maximum torque at starting (s = 1), the rotor resistance must be made equal to rotor reactance at standstill.