Energy losses
When transformers transfer power, they do
so with a minimum of loss. As it was stated earlier, modern power
transformer designs typically exceed 95% efficiency. It is good to know
where some of this lost power goes, however, and what causes it to be
lost.
There is, of course, power lost due to
resistance of the wire windings. Unless superconducting wires are used,
there will always be power dissipated in the form of heat through the
resistance of current-carrying conductors. Because transformers require
such long lengths of wire, this loss can be a significant factor.
Increasing the gauge of the winding wire is one way to minimize this
loss, but only with substantial increases in cost, size, and weight.
Resistive losses aside, the bulk of
transformer power loss is due to magnetic effects in the core. Perhaps
the most significant of these "core losses" is eddy-current loss,
which is resistive power dissipation due to the passage of induced
currents through the iron of the core. Because iron is a conductor of
electricity as well as being an excellent "conductor" of magnetic flux,
there will be currents induced in the iron just as there are currents
induced in the secondary windings from the alternating magnetic field.
These induced currents -- as described by the perpendicularity clause of
Faraday's Law -- tend to circulate through the cross-section of the core
perpendicularly to the primary winding turns. Their circular motion
gives them their unusual name: like eddies in a stream of water that
circulate rather than move in straight lines.
Iron is a fair conductor of electricity,
but not as good as the copper or aluminum from which wire windings are
typically made. Consequently, these "eddy currents" must overcome
significant electrical resistance as they circulate through the core. In
overcoming the resistance offered by the iron, they dissipate power in
the form of heat. Hence, we have a source of inefficiency in the
transformer that is difficult to eliminate.
This phenomenon is so pronounced that it
is often exploited as a means of heating ferrous (iron-containing)
materials. The following photograph shows an "induction heating" unit
raising the temperature of a large pipe section. Loops of wire covered
by high-temperature insulation encircle the pipe's circumference,
inducing eddy currents within the pipe wall by electromagnetic
induction. In order to maximize the eddy current effect, high-frequency
alternating current is used rather than power line frequency (60 Hz).
The box units at the right of the picture produce the high-frequency AC
and control the amount of current in the wires to stabilize the pipe
temperature at a pre-determined "set-point."
The main strategy in mitigating these
wasteful eddy currents in transformer cores is to form the iron core in
sheets, each sheet covered with an insulating varnish so that the core
is divided up into thin slices. The result is very little width in the
core for eddy currents to circulate in:
Laminated
cores like the one shown here are standard in almost all low-frequency
transformers. Recall from the photograph of the transformer cut in half
that the iron core was composed of many thin sheets rather than one
solid piece. Eddy current losses increase with frequency, so
transformers designed to run on higher-frequency power (such as 400 Hz,
used in many military and aircraft applications) must use thinner
laminations to keep the losses down to a respectable minimum. This has
the undesirable effect of increasing the manufacturing cost of the
transformer.
Another, similar technique for minimizing
eddy current losses which works better for high-frequency applications
is to make the core out of iron powder instead of thin iron sheets. Like
the lamination sheets, these granules of iron are individually coated in
an electrically insulating material, which makes the core nonconductive
except for within the width of each granule. Powdered iron cores are
often found in transformers handling radio-frequency currents.
Another "core loss" is that of magnetic
hysteresis. All ferromagnetic materials tend to retain some
degree of magnetization after exposure to an external magnetic field.
This tendency to stay magnetized is called "hysteresis," and it takes a
certain investment in energy to overcome this opposition to change every
time the magnetic field produced by the primary winding changes polarity
(twice per AC cycle). This type of loss can be mitigated through good
core material selection (choosing a core alloy with low hysteresis, as
evidenced by a "thin" B/H hysteresis curve), and designing the core for
minimum flux density (large cross-sectional area).
Transformer energy losses tend to worsen
with increasing frequency. The skin effect within winding conductors
reduces the available cross-sectional area for electron flow, thereby
increasing effective resistance as the frequency goes up and creating
more power lost through resistive dissipation. Magnetic core losses are
also exaggerated with higher frequencies, eddy currents and hysteresis
effects becoming more severe. For this reason, transformers of
significant size are designed to operate efficiently in a limited range
of frequencies. In most power distribution systems where the line
frequency is very stable, one would think excessive frequency would
never pose a problem. Unfortunately it does, in the form of harmonics
created by nonlinear loads.
As we've seen in earlier chapters,
nonsinusoidal waveforms are equivalent to additive series of multiple
sinusoidal waveforms at different amplitudes and frequencies. In power
systems, these other frequencies are whole-number multiples of the
fundamental (line) frequency, meaning that they will always be higher,
not lower, than the design frequency of the transformer. In significant
measure, they can cause severe transformer overheating. Power
transformers can be engineered to handle certain levels of power system
harmonics, and this capability is sometimes denoted with a "K factor"
rating.
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