0195136047.pdf

492 MAGNETIC CIRCUITS AND TRANSFORMERS

11.6 Autotransformers

In contrast to a two-winding transformer, the autotransformer is a single-winding transformer

having a tap brought out at an intermediate point. Thus, as shown in Figure 11.6.1,a–cis the

singleN 1 -turn winding wound on a laminated core, andbis the intermediate point where the tap

is brought out such thatb–chasN 2 turns. The autotransformer may generally be used as either

a step-up or a step-down operation. Considering the step-down arrangement, as shown in Figure

11.6.1, let the primary applied voltage beV 1 , resulting in a magnetizing current and a core fluxφm.

Voltage drops in the windings, exciting current, and small phase-angular differences are usually

neglected for the analysis. Then it follows that

V 1

V 2

=

I 2

I 1

=

N 1

N 2

=a (11.6.1)

in whicha>1 for step-down,a<1 for step-up transformers.

The input apparent power isS 1 =V 1 I 1 , while the output apparent power is given by

S 2 =V 2 I 2. The apparent power transformed by electromagnetic induction (or transformer action)

isSind=V 2 I 3 =(V 1 −V 2 )I 2. The output transferred by electrical conduction (because of the direct

electrical connection between primary and secondary windings) is given byScond=V 2 I 2 −V 2 I 3 =

V 2 I 1.

For the same output the autotransformer is smaller in size, weighing much less than a two-

winding transformer, and has higher efficiency. An important disadvantage of the autotransformer

is the direct copper connection (i.e., no electrical isolation) between the high- and low-voltage

sides. A type of autotransformer commonly found in laboratories is the variable-ratio autotrans-

former, in which the tapped pointb(shown in Figure 11.6.1) is movable. It is known as thevariac

(variable ac). Although here, for the sake of simplicity, we have considered only the single-phase

autotransformer, three-phase autotransformers, which are available in practice, can be modeled

on a per-phase basis and also analyzed just as the single-phase case.

V 2

b

c

V 1

+

−

I 3 = I 2 − I 1

I 2

I 1

a

+

−

Figure 11.6.1Single-phase step-down auto-

transformer.

EXAMPLE 11.6.1

The single-phase, 50-kVA, 2400:240-V, 60-Hz, two-winding distribution transformer of Example

11.3.1 is connected as a step-up autotransformer, as shown in Figure E11.6.1. Assume that the

240-V winding is provided with sufficient insulation to withstand a voltage of 2640 V to ground.

(a) FindVH,VX,IH,IC, andIXcorresponding to rated (full-load) conditions.