Effect of Change in Rotor Resistance on Torque

Effect of Change in Rotor Resistance on Torque    AU : May-08,11,16, Dec.-05, 08

It is known that in slip ring induction motor, externally resistance can be added in the rotor. Let us see the effect of change in rotor resistance on the torque produced.

Let     R₂ = Rotor resistance per phase

Corresponding torque,   

Now externally resistance is added in each phase of rotor through slip rings.

Let     R₂ = New rotor resistance per phase

Corresponding torque,   

Similarly the starting torque at s = 1 for R₂ and R₂ can be written as 

Key Point It can be observed that Tm is independent of R2 hence whatever may be the rotor resistance, maximum torque produced never changes but the slip and speed at which it occurs depends on R₂.

For R₂  s_m = R₂ / X₂  where T_m occurs.

For R₂  s_m = R₂ / X₂  where T_m occurs.

As R₂  > R₂, the slip s'_m > s_m. Due to this, we get a new torque-slip characteristics for rotor resistance R₂. This new characteristics is parallel to the characteristics for R₂ with same Tm but occurring at s'm. The effect of change in rotor resistance on torque-slip characteristics is shown in the Fig. 5.14.1.

It can be seen that the starting torque T_st for R₂. is more than T_st for R₂. Thus by changing rotor resistance the starting torque can be controlled.

If now resistance is further added to rotor to get resistance as R₂. and so on, it can be seen that T_m remains same but slip at which it occurs increases to sm and so on. Similarly starting torque also increases to T_st and so on.

If maximum torque T_m is required at start then s_m = 1 as at start slip is always unity, so

Key Point Thus by adding external resistance to rotor till it becomes equal to X2, the maximum torque can be achieved at start.

It is represented by point A in the Fig. 5.14.1 

If such high resistance is kept permanently in the circuit, there will be large copper losses (I²R) and hence efficiency of the motor will be very poor. Hence such added resistance is cut-off gradually and finally removed from the rotor circuit, in the normal running condition of the motor. So this method is used in practice to achieve higher starting torque hence resistance in rotor is added only at start.

Thus good performance at start and in the running condition is ensured.

Key Point This is possible only in case of slip type of induction motors as in squirrel cage due to short circuited rotor, extra rotor resistance cannot be added.

As rotor reactance X₂ is increased then the slip at which Tm occurs decreases, the magnitude of Tm decreases and starting torque also decreases. Hence the torque - slip characteristics gets modified as shown in the Fig. 5.14.2.

Example 5.14.1 A 6 pole, 50 Hz, 3-phase induction motor has a rotor resistance of 0.25 Q per phase and a maximum torque of 10 N-m at 875 r.p.m. Calculate 1) The torque when the slip is 5 % and 2) The resistance to be added to the rotor circuit to obtain 60 % of the maximum torque at starting. Explain why two values are obtained for this resistance. Which value will be used ? The stator impedance is assumed to be negligible. AU : May-08, Marks 12

Solution :

Now R_x is added to the rotor to make its resistance R'₂ and Tst = 60 % of T_max Ts

Mathematically there are two values of this resistance, one for motoring action and other for generating action. The higher of the two must be eliminated as it can produce large rotor copper losses and it gives absurd values for the slip at which maximum torque occurs. Hence smaller of the two is to be used.

Example 5.14.2 An 8 pole, 50 Hz, 3 phase induction motor is running at 4% slip when delivering full load torque. It has standstill rotor resistance of 0.1 Ω and reactance of 0.6 Ω per phase. Calculate the speed of the motor if an additional resistance of 0.5 Ω per phase is inserted in the rotor circuit. Assume full load torque remains constant. AU : Dec.-08, Marks 8

Solution : P = 8, f = 50 Hz, s = 4 % = 0.04, R2 = 0.1 Ω , X2 = 0.6 Ω

Hence the new speed of the motor is,

N’ = Ns(1-s’) = 750 (1-0.24) = 570 r.p.m

Example 5.14.3 A 40 kW, 3-phase, slip-ring induction motor of negligible stator impedance runs at a speed of 0.96 times synchronous speed at rated torque. The slip at maximum torque is four times the full-load value. If the rotor resistance of the motor is increased by 5 times, determine : a) The speed, power output and rotor copper loss at rated torque, b) The speed corresponding to maximum torque.

Solution :

Examples for Practice

Example 5.14.4 Rotor resistance and standstill reactance per phase of a 3 phase induction motor are 0.04 Ω and 0.2 Ω respectively. What should be the external resistance required at start in rotor circuit to obtain

i) Maximum torque at start ii) 50 % of maximum torque at start.

[Ans.: i) 0.16 Ω per phase ii) 0.0135 Ω per phase]

Review Questions

1. Prove that to increase the starting torque an extra resistance must be added in the rotor circuit. AU : Dec.-05, May-11, Marks 6

2. How the torque-slip characteristics of a 3 phase induction motor gets modified if

i) The rotor circuit resistance is increased ii) The rotor circuit resistance is decreased. M3 : Dec.-05, Marks 6