Environmental Engineering Reference
In-Depth Information
V
V
N
N
1
1
=
(4.10)
2
2
Suppose that the secondary is connected to a resistor that draws current
I
2
with the
consequence that power
V
2
I
2
is extracted from the secondary. The energy conservation
principle requires that this power is supplied from the source to which the primary is
connected. It follows that a primary current
I
1
is established the value of which can be
determined from:
VI
=
V I
(4.11)
11
2 2
and from Equation (4.10)
I
I
N
N
1
2
=
(4.12)
2
1
Note that an open circuit or a short circuit on the secondary winding of an ideal transformer
are seen as an open or short circuit respectively on the primary side.
An ideal transformer with identical primary and secondary windings would manifest equal
voltage and current in both sets of windings. In a perfect world, transformers would transfer
electrical power from primary to secondary as effi ciently as though the load were directly
connected to the primary power source, with no transformer there at all, but it will be found
later that this ideal goal cannot be realized in practice. Nevertheless, transformers are highly
effi cient power transfer devices with no moving parts achieving effi ciencies in the high
nineties.
The transformer has made long distance transmission of electric power a practical reality,
as AC voltage can be 'stepped up' and current 'stepped down' for reduced ohmic resistance
losses along power lines connecting generating stations with loads. A transformer that
increases voltage from primary to secondary (more secondary winding turns than primary
winding turns) is called a
step - up
transformer. Conversely, a transformer designed to do just
the opposite is called a
step - down
transformer.
4.3.2 The Transformer Equivalent Circuit
The next task is to develop an equivalent circuit capable of representing realistically the
behaviour of a transformer in studies aimed at determining the fl ow of power in electrical
systems. Figure 4.10 shows how such an equivalent circuit can be built up starting with the
ideal transformer in the hatched box. The small but fi nite current required to set up the fl ux
in the core is simulated by the presence of the shunt inductance
L
m
, the
magnetizing induc-
tance
, which has a large value in henries.
Next, the fi nite resistance of the two transformer windings can be simulated by the series
resistors
R
1
and
R
2
. To keep losses low, these have low numerical values. Finally, any mag-
netic fl ux not contained in the core is free to store and release energy rather than transfer it
from one coil to the other. Any energy thus stored by this
uncoupled
fl ux manifests itself as
an inductance in series with the relevant winding. This stray inductance is called
leakage
inductance
and is represented in the equivalent circuit by
L
1
and
L
2
both having numerical
values much smaller than
L
m
.
