Electrical Machines II Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

Indian Institute of Technology Madras

8.2 Rotor resistance control

The reader may recall from eqn.17 the expression for the torque of the induction machine.Clearly, it is dependent on the rotor resistance. Further, eqn.19 shows that the maximumvalue is independent of the rotor resistance. The slip at maximum torque eqn.18 is dependenton the rotor resistance. Therefore, we may expect that if the rotor resistance is changed, themaximum torque point shifts to higher slip values, while retaining a constant torque. Figure28 shows a family of torque-speed characteristic obtained by changing the rotor resistance.

0 500 1000 15000

10

20

30

40

50

60

70

speed, rpm

torq

ue, N

m

Rotor resistance variation

o1

o2

o3

r1 r

2 r

3

r3 > r

2 > r

1

Figure 28: Speed-torque curves : rotor resistance variation

Note that while the maximum torque and synchronous speed remain constant, the slipat which maximum torque occurs increases with increase in rotor resistance, and so does thestarting torque. whether the load is of constant torque type or fan-type, it is evident thatthe speed control range is more with this method. Further, rotor resistance control couldalso be used as a means of generating high starting torque.

For all its advantages, the scheme has two serious drawbacks. Firstly, in order to vary

32

Electrical Machines II Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao

Indian Institute of Technology Madras

the rotor resistance, it is necessary to connect external variable resistors (winding resistanceitself cannot be changed). This, therefore necessitates a slip-ring machine, since only inthat case rotor terminals are available outside. For cage rotor machines, there are no rotorterminals. Secondly, the method is not very efficient since the additional resistance andoperation at high slips entails dissipation.

The resistors connected to the slip-ring brushes should have good power dissipation ca-pability. Water based rheostats may be used for this. A ‘solid-state’ alternative to a rheostatis a chopper controlled resistance where the duty ratio control of of the chopper presents avariable resistance load to the rotor of the induction machine.

8.3 Cascade control

The power drawn from the rotor terminals could be spent more usefully. Apart from usingthe heat generated in meaning full ways, the slip ring output could be connected to anotherinduction machine. The stator of the second machine would carry slip frequency currents ofthe first machine which would generate some useful mechanical power. A still better optionwould be to mechanically couple the shafts of the two machines together. This sort of aconnection is called cascade connection and it gives some measure of speed control as shownbelow.

Let the frequency of supply given to the first machine be f1 , its number poles be p1, andits slip of operation be s1 . Let f2, p2 and s2 be the corresponding quantities for the secondmachine. The frequency of currents flowing in the rotor of the first machine and hence in thestator of the second machine is s1f1. Therefore f2 = s1f1. Since the machines are coupledat the shaft, the speed of the rotor is common for both. Hence, if n is the speed of the rotorin radians,

n =f1

p1

(1 − s1) = ±s1f1

p2

(1 − s2). (20)

Note that while giving the rotor output of the first machine to the stator of the second,the resultant stator mmf of the second machine may set up an air-gap flux which rotates inthe same direction as that of the rotor, or opposes it. this results in values for speed as

n =f1

p1 + p2

or n =f1

p1 − p2

(s2 negligible) (21)

The latter expression is for the case where the second machine is connected in oppositephase sequence to the first. The cascade connected system can therefore run at two possible

33