Electrical Machines - Autotransformer

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An autotransformer is a one winding transformer in which a part of the winding is common to both primary and secondary windings.

An autotransformer has a single continuous winding with a tap point between the primary and secondary windings. The tap point can be adjusted to obtain the desired output voltage, hence this is an obvious advantage of the autotransformer. The main disadvantage of an autotransformer is that the secondary winding is not electrically isolated from the primary.

Theory of Autotransformer

Case 1 - Autotransformer on No-Load

The connection diagram of an unloaded autotransformer (step-down and step-up) is shown in the figure. In this, the winding 'ab' is called primary winding having N₁ turns and the winding 'bc' is called secondary winding having N₂ turns.

Here it can be noted that the primary and secondary windings are connected magnetically as well as electrically. Thus, the power from the primary winding is transferred to the secondary winding magnetically as well as conductively.

Case 2 - Autotransformer on Load

When the load is connected to the secondary of an autotransformer, then it is said to be loaded. The figure shows the circuit diagram of a loaded autotransformer (step-down and step-up).

In which the current I₁ is the primary input current and the current I₂ is the secondary output current or load current. The current in common portion of the primary and secondary windings is the difference of the currents I₁ and I₂, regardless of whether the autotransformer is stepdown or step-up.

For the step-down autotransformer the current I₂ > I₁, thus the current flowing in the common portion is

$$\mathrm{\text{Current in common portion } \: = \: I_{2} \: - \: I_{1}}$$

For the step-up autotransformer the current I₂ < I₁, thus the current in the common portion is

$$\mathrm{\text{Current in common portion } \: = \: I_{1} \: - \: I_{2}}$$

Circuit and Working Principle of Autotransformer Starter

The circuit diagram of an autotransformer starter for starting a 3-phase induction motor is shown in the figure. The autotransformer starter can be used for starting both star and delta connected 3-phase induction motors. In this method, the starting current of the motor is limited by using a 3-phase autotransformer to decrease the initial applied voltage to the stator. The autotransformer is provided with a number of tappings to obtain the variable voltage.

In the autotransformer starting method, the starter is connected to a particular tapping of the autotransformer to obtain the most suitable starting voltage. A changeover switch S is used to connect the autotransformer in the circuit for starting the motor.

When the handle (H) of the switch S is at the START position, the primary winding of the autotransformer is connected to supply line and the induction motor is connected to the secondary winding of the autotransformer. When the motor picks up the speed (about 80 % of the rated speed), then the handle H is thrown to the RUN position. Consequently, the autotransformer is isolated from the circuit and the motor is now directly connected to the supply line and gets its rated voltage.

The handle is held in the RUN position by the under-voltage relay. When the supply voltage fails or falls below a certain value, then the handle is released and comes back to the OFF position. To provide the overload protection to the motor, a thermal overload relay is used in the motor circuit.

Theory of Autotransformer Starter

The figure below shows the circuit connections for the direct switching of the motor and the autotransformer starting of the motor.

When direct switching of the motor to the supply line −

Let,

Z_e10 = Per phase equivalent impedance of motor referred to stator at standstill

V₁ = Supply voltage per phase

Thus, when the full supply voltage per phase (V₁) is applied to the motor with direct switching, then the starting line current drawn by the motor from the supply line is given by,

$$\mathrm{I_{stl} \:=\:\frac{V_{1}}{Z_{10}} \:\: \dotso \:(1)}$$

Now, with autotransformer starting, if a tapping of autotransformer with transformation ratio kis used, then the voltage available across the secondary winding terminals of the autotransformer (i.e., the voltage per phase across the motor) is kV₁. Hence, the starting current of the motor with autotransformer starting is given by,

$$\mathrm{I_{stm} \:=\: \frac{kV_{1}}{Z_{e10}} \:\: \dotso \:(2)}$$

If the no-load current of the transformer is neglected, then, the ratio of currents in a transformer is inversely proportional to the voltage ratio, i.e.,

$$\mathrm{\frac{I_{1}}{I_{2}} \:=\: \frac{V_{2}}{V_{1}}}$$

$$\mathrm{\Rightarrow \: V_{1}I_{1} \:=\: V_{2}I_{2}}$$

Thus,

$$\mathrm{V_{1}{I^{′}_{stl}} \:=\: kV_{1}I_{stm}}$$

Where, ${I^{′}_{stl}}$ is the line current drawn from the supply by the autotransformer.

$$\mathrm{\Rightarrow I^{′}_{stl} \:=\: kI_{stm} \:\: \dotso \:(3)}$$

Substituting the value of I_stm from eqn. (2) in eq. (3), we get,

$$\mathrm{ I^{′}_{stl} \:=\: k\left(\frac{kV_{1}}{Z_{e10}}\right) \:=\: \frac{k^{2}V_{1}}{Z_{e10}} \:\: \dotso \:(4)}$$

Therefore,

$$\mathrm{\frac{\text{Starting Current with Autotransformer Starter}\:(I′_{stl} )}{\text{Starting current with direct switching } \: (I_{stl})} \:=\: \frac{\frac{k^{2}V_{1}}{Z_{e10}}}{\frac{V_{1}}{Z_{e10}}} \:=\: k^{2}}$$

$$\mathrm{\therefore \: \text{ Starting Current with Autotransformer Starter } \:=\: k^{2} \: \times \: \text{ Starting Current with Direct Switching } \:\: \dotso \:(5)}$$

Since the torque developed in an induction motor is directly proportional to the square of the applied voltage. Thus, the torque with direct switching of the motor is,

$$\mathrm{\tau_{std} \: \propto \: V_{1}^{2} \:\: \dotso \:(6)}$$

And, the torque developed with the autotransformer starter is,

$$\mathrm{\tau_{sta} \: \propto \: k^{2} V_{1}^{2} \:\: \dotso \:(7)}$$

Hence,

$$\mathrm{\frac{\text{Starting Torque with Autotransformer Starter } \: (\tau_{sta})}{\text{Starting Torque with Direct Switching } \: (I_{std})} \:=\: \frac{k^{2}V_{1}^{2}}{V_{1}^{2}} \:=\: k^{2}}$$

$$\mathrm{\therefore \: \text{ Starting Torque with Autotransformer Starter } \:=\: k^{2} \: \times \: \text{ Starting Torque with Direct Switching} \:\: \dotso \:(8)}$$

From the eqns. (5) and (8), it is clear that with an autotransformer starter, the starting current of the motor drawn from the main supply line and the starting torque are reduced to k² times of their corresponding values with the direct switching starting of the motor.

Advantages of Autotransformer

The advantages of an autotransformer are given as follows −

• An autotransformer has smaller core and copper losses and hence higher efficiency as compared to an ordinary 2-winding transformer.
• Autotransformer requires less conductor material as compared to the 2-winding transformer.
• It has better voltage regulation due to reduced voltage drops in resistance and leakage reactance.
• It has smaller size and cheaper than a 2-winding transformer.
• It requires smaller excitation current.
• An autotransformer can produce variable output voltage.

Disadvantages of Autotransformer

The disadvantages of an autotransformer are given as follows −

• There is a direct connection between the primary and secondary sides. In case of an open circuit in the common portion bc of the windings, the full primary voltage would be applied to the load on the secondary side. This may damage the equipment connected to the secondary side.
• An autotransformer has reduced internal impedance as compared to a 2-winding transformer which results in a larger short circuit current.
• The autotransformer is not electrically isolated, thus cannot be used to isolate two circuits electrically.

Applications of Autotransformer

The autotransformer is mainly used in following applications −

• The autotransformers are used for boosting of supply voltage to compensate the voltage drops in distribution systems.
• Autotransformers are used for interconnection of power systems of different voltage levels.
• The autotransformers with tapings are used for starting induction motors and synchronous motors.
• The autotransformers are used as variac (variable AC) in the situations where a continuous variable voltage over a wide range is required.