Core saturation
Transformers are also constrained in
their performance by the magnetic flux limitations of the core. For
ferromagnetic core transformers, we must be mindful of the saturation
limits of the core. Remember that ferromagnetic materials cannot support
infinite magnetic flux densities: they tend to "saturate" at a certain
level (dictated by the material and core dimensions), meaning that
further increases in magnetic field force (mmf) do not result in
proportional increases in magnetic field flux (Φ).
When a transformer's primary winding is
overloaded from excessive applied voltage, the core flux may reach
saturation levels during peak moments of the AC sinewave cycle. If this
happens, the voltage induced in the secondary winding will no longer
match the wave-shape as the voltage powering the primary coil. In other
words, the overloaded transformer will distort the waveshape from
primary to secondary windings, creating harmonics in the secondary
winding's output. As we discussed before, harmonic content in AC power
systems typically causes problems.
Special transformers known as peaking
transformers exploit this principle to produce brief voltage pulses
near the peaks of the source voltage waveform. The core is designed to
saturate quickly and sharply, at voltage levels well below peak. This
results in a severely cropped sine-wave flux waveform, and secondary
voltage pulses only when the flux is changing (below saturation levels):
Another cause of abnormal transformer
core saturation is operation at frequencies lower than normal. For
example, if a power transformer designed to operate at 60 Hz is forced
to operate at 50 Hz instead, the flux must reach greater peak levels
than before in order to produce the same opposing voltage needed to
balance against the source voltage. This is true even if the source
voltage is the same as before.
Since instantaneous winding voltage is
proportional to the instantaneous magnetic flux's rate of change
in a transformer, a voltage waveform reaching the same peak value, but
taking a longer amount of time to complete each half-cycle, demands that
the flux maintain the same rate of change as before, but for longer
periods of time. Thus, if the flux has to climb at the same rate as
before, but for longer periods of time, it will climb to a greater peak
value.
Mathematically, this is another example
of calculus in action. Because the voltage is proportional to the flux's
rate-of-change, we say that the voltage waveform is the derivative
of the flux waveform, "derivative" being that calculus operation
defining one mathematical function (waveform) in terms of the
rate-of-change of another. If we take the opposite perspective, though,
and relate the original waveform to its derivative, we may call the
original waveform the integral of the derivative waveform. In
this case, the voltage waveform is the derivative of the flux waveform,
and the flux waveform is the integral of the voltage waveform.
The integral of any mathematical function
is proportional to the area accumulated underneath the curve of that
function. Since each half-cycle of the 50 Hz waveform accumulates more
area between it and the zero line of the graph than the 60 Hz waveform
will -- and we know that the magnetic flux is the integral of the
voltage -- the flux will attain higher values:
Yet another cause of transformer
saturation is the presence of DC current in the primary winding. Any
amount of DC voltage dropped across the primary winding of a transformer
will cause additional magnetic flux in the core. This additional flux
"bias" or "offset" will push the alternating flux waveform closer to
saturation in one half-cycle than the other:
For most transformers, core saturation is
a very undesirable effect, and it is avoided through good design:
engineering the windings and core so that magnetic flux densities remain
well below the saturation levels. This ensures that the relationship
between mmf and Φ is more linear throughout the flux cycle, which is
good because it makes for less distortion in the magnetization current
waveform. Also, engineering the core for low flux densities provides a
safe margin between the normal flux peaks and the core saturation limits
to accommodate occasional, abnormal conditions such as frequency
variation and DC offset.
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