Auto Transformer
Auto Transformer
Auto Transformer
Sasidhara Rao
11 Auto Transformer
I1
C
T1 I2
B
V1
T2 V2 ZL
I2
A
I1
V1 : V2 = T1 : T2 (76)
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When the secondary winding delivers a load current of I2 ampere the demagnetizing ampere
turns is I2 T2 . This will be countered by a current I1 flowing from the source through the
T1 turns such that,
I1 T1 = I2 T2 (77)
A current of I1 ampere flows through the winding between B and C . The current
in the winding between A and B is (I2 − I1 ) ampere. The cross section of the wire to be
selected for AB is proportional to this current assuming a constant current density for the
whole winding. Thus some amount of material saving can be achieved compared to a two
winding transformer. The magnetic circuit is assumed to be identical and hence there is
no saving in the same. To quantify the saving the total quantity of copper used in an auto
transformer is expressed as a fraction of that used in a two winding transformer as,
This means that an auto transformer requires the use of lesser quantity of copper
given by the ratio of turns. This ratio therefore denotes the savings in copper. As the
space for the second winding need not be there, the window space can be less for an auto
transformer, giving some saving in the lamination weight also. The larger the ratio of the
voltages, smaller is the savings. As T2 approaches T1 the savings become significant. Thus
auto transformers become ideal choice for close ratio transformations. The savings in mate-
rial is obtained, however, at a price. The electrical isolation between primary and secondary
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φ
I1+I2 I1 I2
I2 V2
V1
V1+V2 ZL
I1+I2 I1
I2
has to be sacrificed.
If we are not looking at the savings in the material, even then going in for the auto
transformer type of connection can be used with advantage, to obtain higher output. This
can be illustrated as follows. Fig. 29 shows a regular two winding transformer of a voltage
ratio V1 : V2 , the volt ampere rating being V1 I1 = V2 I2 = S. If now the primary is connected
across a supply of V1 volt and the secondary is connected in series addition manner with the
primary winding, the output voltage becomes (V1 + V2 ) volt. The new output of this auto
transformer will now be
V1 V1
I2 (V1 + V2 ) = I2 V2 (1 + ) = S(1 + ) (81)
V2 V2
I2
= V1 (I1 + I2 ) = S(1 + ) (82)
I1
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V1 V1
I2 (V1 − V2 ) = I2 V2 ( − 1) = S( − 1) (83)
V2 V2
I1
r1,xl1 I1 I2
V1
r2,xl2 V2
(I2 -I1)
I1 I2
As mentioned earlier the magnetizing current can be neglected, for simplicity. Writing
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Note that the resistance r1 and leakage reactance xl1 refer to that part of the winding where
only the primary current flows. Similarly on the load side we have,
= aV2 + I1 (r1 + jxl1 + r2 + jxl2 + a2 r2 + ja2 xl2 − ar2 − ajxl2 − ar2 − jaxl2 )
Equation (85) yields the equivalent circuit of Fig. 31 where Re = r1 + (a − 1)2 r2 and
Xe = xl1 + (a − 1)2 xl2 .
The magnetization branch can now be hung across the mains for completeness. The
above equivalent circuit can now be compared with the approximate equivalent circuit of
a two winding case Re = r1 + a2 r2 and Xe = xl1 + a2 xl2 . Thus in the case of an auto
transformer total value of the short circuit impedance is lower and so also the percentage
resistance and reactance. Thus the full load regulation is lower. Having a smaller value
of short circuit impedance is sometimes considered to be a disadvantage. That is because
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Re=r1+(a-1)2r2
Re jXe Xl=xl1+(a-1)2xl2
Io
Ic Im
V1 Rc jXm V’2=aV1
the short circuit currents become very large in those cases. The efficiency is higher in auto
transformers compared to their two winding counter part at the same load. The phasor
diagram of operation for the auto transformer drawing a load current at a lagging power
factor angle of θ2 is shown in Fig. 32. The magnetizing current is omitted here again for
simplicity.
From the foregoing study it is seen that there are several advantages in going in for the
autotransformer type of arrangement. The voltage/current transformation and impedance
conversion aspects of a two winding transformer are retained but with lesser material (and
hence lesser weight) used. The losses are reduced increasing the efficiency. Reactance is
reduced resulting in better regulation characteristics. All these benefits are enhanced as
the voltage ratio approaches unity. The price that is required to be paid is loss of electri-
cal isolation and a larger short circuit current (and larger short circuit forces on the winding).
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I1x1 (I2-I1)r2
I1r1
(I2-I1)x2
V1
I2
E1
E2 (I2-I1)x2
I1
(I2-I1)r2
V2
θ2
θ1
I2
φ
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Auto transformers are used in applications where electrical isolation is not a critical
requirement. When the ratio V2 : V1 is 0.3 or more they are used with advantage. The
normal applications are motor starters, boosters or static balancers.
Variable
a.c output
V in
M oving contact
The conductor is selected based on the maximum secondary current that could be
drawn as the output voltage varies in practically continuous manner. These are used in
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voltage stabilizers, variable d.c. arrangements (with a diode bridge) in laboratories, motor
starters, dimmers etc.
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