1) In a slip ring induction motor ( SRIM) , a three phase variable resistor $R_2$ can be inserted in the rotor circuit as shown in Fig 12.37 (a) . By varying the rotor circuit resistance $R_2$ . the motor torque can be controlled as shown in fig 12.37 ( b)

2) The starting torque and starting current can also be varied by controlling the rotor circuit resistance, Fig 12.37 ( b) and ( c )

3) The disadvantages of this method of speed control are

• Reduced efficiency at low speeds

• Speed changes very widely with load variation

• Unbalances in voltages and currents if rotor circuit resistances are not equal.

4) In spite of these , this method of speed control is used when speed drop is required for short time, as for example in overhead cranes, in load equalization.

5) The three phase resistor of Fig 12.37 ( a ) may be replaced by a three phase diode rectifier, chopper and one resistor as shown in Fig 12.38 ( a )

• In this figure, the function of inductor LD is to smoothen the current ID.

• GTO chopper allows the effective rotor circuit resistances to be varied for the speed control of SRIM.

• Diode rectifier converts slip frequency input power to dc at its output terminals.

6) Operation:

a) When chopper is on, $V_{dc} = V_d = 0$ and resistance R gets short circuited.

b) When chopper is off, $V_{dc} = V_d$ and resistance in the rotor circuit is R. This is shown in fig 12.38 ( b )

c) From this figure, effective external resistance $R_e$ is

$R_e=\frac{R.T_{off}}{T}=\frac{R(T-T_{on})}{T}=R(1-k)\\ where \ \ k=\frac{T_{on}}{T}= duty \ \ cycle \ \ of \ \ chopper. $

7) Analysis of induction motor with chopper control

• The equivalent circuit for 3 phase IM, diode rectifier and chopper circuit of fig 12.38

• ( a ) is as shown n Fig 12.39 (a)

• If stator and rotor leakage impedances are neglected as compared to inductor $L_D$ , equivalent circuit of Fig 12.39 ( b ) is obtained. Stator voltage $V_1$ when referred to rotor circuit gives slip – frequency voltage as

$s.\frac{V_1}{N_1}.N_2=saV_1=sE_2$

Where E2 = rotor induced emf per phase at stand – still

$V_1$ = stator voltage per phase

α = ( rotor effective turns, $N_2$ ) / ( Stator effective turns, $N_1$) = per phase turns ratio from rotor to stator

Voltage $sE_2 = sαV_1$ , after rectification by three phase diode appears as $V_d$ ( rectifier output voltage)

Substituting the value of from Eq. (1) we get

$$\omega_m=\omega_s(1-s)$$

Motor speed,

$$\omega_s\big[1-\frac{I_dR(1-k)}{2.339.aV_1}\bigg]---(5)$$

Also

$N_c=N_s\bigg[1-\frac{I_dR(1-k)}{2.339.aV_1}\bigg]---[6(a)]$

9) Torque speed characteristics with a variable rotor resistance

10) From fig 5.2, the critical slip at which motor produces maximum torque is proportional to the rotor resistance.

11) With the increase in rotor resistance the critical slip value also increase for example: for a constant load torque (TL ) , the motor operating points shift from A to B to C with change in order of resistance.

The corresponding speeds are $N1, N2 \ \ and \ \ N3 \ \ with \ \ N1 \gt N2 \gt N3$

In this way the speed of the induction motor decreases with increases in the rotor resistance.