We
have seen the speed torque characteristic of the machine. In the stable region
of operation in the motoring mode, the curve is rather steep and goes from zero
torque at synchronous speed to the stall torque at a value of slip s = ŝ.
Normally ŝ may be such that stall torque is about three times that of the rated
operating torque of the machine, and hence may be about 0.3 or less. This means that in the entire loading range
of the machine, the speed change is quite small. The machine speed is quite stiff with respect
to load changes. The entire speed
variation is only in the range ns to (1
− ŝ)ns, ns being dependent on supply
frequency and number of poles.

The
foregoing discussion shows that the induction machine, when operating from
mains is essentially a constant speed machine.
Many industrial drives, typically for fan or pump applications, have
typically constant speed requirements and hence the induction machine is
ideally suited for these. However,the induction machine, especially the
squirrel cage type, is quite rugged and has a simple construction. Therefore it is good candidate for variable
speed applications if it can be achieved.

### Speed control by changing applied voltage

From
the torque equation of the induction machine given we can see that the torque depends on the
square of the applied voltage. The variation of speed torque curves with
respect to the applied voltage is shown in fig. These curves show that the slip
at maximum torque ŝ remains same, while the value of stall torque comes down
with decrease in applied voltage. The speed range for stable operation remains
the same.

Voltage
control may be achieved by adding series resistors (a lossy, inefficient
proposition), or a series inductor / autotransformer (a bulky solution) or a
more modern solution using semiconductor devices. A typical solid state circuit
used for this purpose is the AC voltage controller or AC chopper. Another use
of voltage control is in the so-called ‘soft-start’ of the machine. This is
discussed in the section on starting methods.

### 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, shows that the
maximum value is independent of the rotor resistance. The slip at maximum
torque is dependent on the rotor resistance. Therefore, we may expect that if
the rotor resistance is changed, the maximum torque point shifts to higher slip
values, while retaining a constant torque. a family of torque-speed
characteristic obtained by changing the rotor resistance.

For all its advantages, the scheme has two serious
drawbacks. Firstly, in order to vary the
rotor resistance, it is necessary to connect external variable resistors
(winding resistance itself cannot be changed).
This, therefore necessitates a slip-ring machine, since only in that
case rotor terminals are available outside. For cage rotor machines, there are
no rotor terminals. Secondly, the method
is not very efficient since the additional resistance and operation at high
slips entails dissipation. The resistors connected to the slip-ring brushes
should have good power dissipation capability. Water based rheostats may be
used for this. A ‘solid-state’ alternative to a rheostat is a chopper
controlled resistance where the duty ratio control of of the chopper presents a
variable resistance load to the rotor of the induction machine.

### Stator frequency control

The expression for the synchronous speed
indicates that by changing the stator frequency also it can be changed. This
can be achieved by using power electronic circuits called inverters which
convert dc to ac of desired frequency. Depending on the type of control scheme
of the inverter, the ac generated may be variable-frequency-fixed-amplitude or
variable-frequency- variable-amplitude type. Power electronic control achieves
smooth variation of voltage and frequency of the ac output. This when fed to
the machine is capable of running at a controlled speed. However, consider the
equation for the induced emf in the induction machine.

*V =4.44Nφmf*
where
N is the number of the turns per phase, φm is the peak flux in the air gap and
f is the frequency. Note that in order to reduce the speed, frequency has to be
reduced. If the frequency is reduced while the voltage is kept constant,
thereby requiring the amplitude of induced emf to remain the same, flux has to
increase. This is not advisable since the machine likely to enter deep
saturation. If this is to be avoided, then flux level must be maintained constant
which implies that voltage must be reduced along with frequency. The ratio is
held constant in order to maintain the flux level for maximum torque
capability. Actually, it is the voltage across the magnetizing branch of the
exact equivalent circuit that must be maintained constant, for it is that which
determines the induced emf. Under conditions where the stator voltage drop is
negligible compared the applied voltage,

In
this mode of operation, the voltage across the magnetizing inductance in the
’exact’ equivalent circuit reduces in amplitude with reduction in frequency and
so does the inductive reactance. This implies that the current through the
inductance and the flux in the machine remains constant. The speed torque characteristics at any
frequency may be estimated as before. There is one curve for every excitation
frequency considered corresponding to every value of synchronous speed. The
curves are shown below. It may be seen that the maximum torque remains
constant.