Environmental Engineering Reference
In-Depth Information
Figure 4.9
The Transformer. (Reproduced from Reference [1] with permission of John Wiley & Sons,
Inc.)
standing of the mode of operation of induction generators which are used extensively in wind
turbines.
The properties of an inductance are discussed in the Appendix. A current carrying inductor,
usually wound in the form of a coil, generates a magnetic fl ux. This fl ux links with the turns
of the coil or the
winding
and induces a voltage in these turns if the current and therefore the
fl ux is increased or decreased. It stands to reason that if a changing magnetic fi eld produced
by one inductor were to 'link' with the turns of wire in another adjacent inductor, it would
induce a voltage in the
unpowered
inductor. This phenomenon is called
mutual inductance
and the
transformer
is a device constructed to exploit this effect.
By having two inductors coupled together by a common magnetic fi eld path, it is possible
to transfer energy from one inductor circuit to the other. In order for this to work, the magnetic
fi eld has to be constantly changing in strength, otherwise no voltage will be induced in the
unpowered winding. Thus, the transformer is essentially an AC device. The powered winding
of a transformer is called the
primary
, while the unpowered winding is called the
secondary
.
Figure 4.9 shows a transformer in outline [1]. The primary winding is connected to
an AC supply
V
1
. The winding is wound round a substantial closed ferromagnetic core.
This provides a very low 'magnetic resistance' to the fl ow of magnetic fl ux in comparison
to the surrounding air. Because of the very low resistance to the fl ux fl ow, only a very
low current, known as the
magnetizing current
, is required from the supply to set up an
mmf that circulates a fl ux which induces a voltage in the primary that exactly balances
V
1
. For the present the effect of this low current may be disregarded. Because of the low
'magnetic resistance' of the ferromagnetic core it can be assumed that practically all of
the generated magnetic fl ux is constrained to fl ow within the core with only a small
amount of leakage fl ux taking paths in the surrounding air, which will also be disregarded
at this point. The consequence of this is that the secondary winding which is also wound
round the transformer core, links exactly the same fl ux as the primary winding. Finally,
if it is assumed that the windings consisted of large cross-section copper wire their ohmic
resistance could be disregarded. All these simplifi cations lead to the concept of the
ideal
transformer
.
In an ideal transformer the voltage induced in an inductor of
N
turns linking a fl ux varying
at d
φ
/d
t
is proportional to
N
. Hence for the transformer in Figure 4.9, we can write
