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The rotor speed (N_{r}) of an induction motor is given by,

$$\mathrm{𝑁_𝑟 = (1 − 𝑠)𝑁_𝑠}$$

And the synchronous speed is given by,

$$\mathrm{𝑁_𝑠 =\frac{120𝑓}{𝑃}… (1)}$$

Therefore, the rotor speed of the motor is given by,

$$\mathrm{𝑁_𝑟 = (1 − 𝑠) (\frac{120𝑓}{𝑃}) … (2)}$$

It is clear from eqn. (2) that the speed of the induction motor can be changed by varying the frequency (*f*), number of poles (*P*) or slip (*s*).

From the eqns. (1) and (2), it can be seen that the synchronous speed and hence the speed of the motor can be controlled by changing the supply frequency.

The EMF induced in the stator of the induction motor is given by,

$$\mathrm{𝐸_𝑠 = 4.44 𝑘_{𝑤𝑠} 𝑓\varphi 𝑁_1 … (3)}$$

Eqn. (3) shows that, if the supply frequency is changed, the stator EMF E_{s} will also change to maintain the same flux in the air gap of the motor. If the stator voltage drop is neglected, then the applied terminal voltage V_{s} is equal induced EMF E_{s}.

In order to minimise the losses and to avoid the saturation of the core, the motor is operated at rated air gap flux by changing the terminal voltage (V_{s}) with the supply frequency (f) so as to maintain the (V/f) ratio constant at the rated value. For this reason, this type of speed control is also known as *constant volt per hertz control*.

Thus, from the above discussion it is clear that the speed control of an induction motor using the variable frequency supply requires a variable voltage supply source. In order to obtain the variable frequency supply, the following converters are used −

**Voltage Source Inverter**– An inverter is a circuit that converts a fixed voltage DC into a fixed or variable voltage AC with variable frequency.**Current Source Inverter**– The current source inverter converts the input direct current into an alternating current. The output voltage of the CSI is independent of the load.**Cycloconverter**– A cycloconverter converts a fixed voltage and fixed frequency AC supply into a variable voltage and variable frequency AC supply. The variable frequency will be lower than the fixed frequency. The cycloconverter controlled induction motor drives are suitable only for large power drives and to obtain low speeds.

The speed control by the variable frequency control allows good running and transient performance to be obtained from a squirrel cage induction motor.

The rotor resistance control method of speed control is used for varying the speed of slip-ring induction motors. This method is not applicable to squirrel cage induction motors. In this method, the speed of slip-ring or wound rotor induction motor is controlled by connecting external resistance in the rotor circuit through slip rings (as shown in the figure).

The maximum torque of the induction motor is independent of the rotor resistance. The greater the value of rotor resistance R_{2}, greater is the value of slip at which maximum torque occurs. When the rotor resistance is increased, the pull-out speed of the motor decreases, but the value of maximum torque remains constant. Therefore, using rotor resistance method, the speed control is provided from the rated speed to the lower speeds.

The rotor resistance method of speed control is very simple. With this method, it is possible to have high starting torque, low starting current and large breakdown or pull-out torques at small values of slip.

The primary disadvantage of the rotor resistance control method is that the efficiency of the motor is poor due to additional I^{2}R losses in the external resistors connected in the rotor circuit.

This method of speed control is used in cranes, Ward-Leonard Ilgener drives and other intermittent load applications.

In the rotor resistance speed control method of induction motor, the slip power in the rotor circuit is wasted as *I ^{2}R* loss during the low speed operation of the motor. Consequently, the efficiency of the motor by this method of speed control is reduced.

The slip power from the rotor circuit can be recovered and fed back to the AC supply source. Thus, the overall efficiency of the motor can be increased. The principle of slip-energy recovery is to connect an external source of EMF of slip frequency to the rotor circuit. The figure shows the circuit arrangement for recovering the slip-energy.

The method of slip-energy recovery shown in the figure is known as *static Scherbius drive*. It provides the control of a slip-ring induction motor below the synchronous speed. In this method, the slip power is converted into DC supply by a diode bridge rectifier and the rectified current is smoothed with the help of a filter circuit (smoothing reactor). The output of the rectifier is then fed to the inverter, which inverts this DC power to the AC power and feeds back to the AC supply source. The inverter used is a controlled rectifier operated in the inversion mode.

The slip-energy recovery method of speed control is used in large power applications where variation of speed over a wide range involves a large amount of slip power.

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