Inrush current
When a transformer is initially connected
to a source of AC voltage, there may be a substantial surge of current
through the primary winding called inrush current. This is
analogous to the inrush current exhibited by an electric motor that is
started up by sudden connection to a power source, although transformer
inrush is caused by a different phenomenon.
We know that the rate of change of
instantaneous flux in a transformer core is proportional to the
instantaneous voltage drop across the primary winding. Or, as stated
before, the voltage waveform is the derivative of the flux waveform, and
the flux waveform is the integral of the voltage waveform. In a
continuously-operating transformer, these two waveforms are
phase-shifted by 90o. Since flux (Φ) is proportional to the
magnetomotive force (mmf) in the core, and the mmf is proportional to
winding current, the current waveform will be in-phase with the flux
waveform, and both will be lagging the voltage waveform by 90o:
Let us suppose that the primary winding
of a transformer is suddenly connected to an AC voltage source at the
exact moment in time when the instantaneous voltage is at its positive
peak value. In order for the transformer to create an opposing voltage
drop to balance against this applied source voltage, a magnetic flux of
rapidly increasing value must be generated. The result is that winding
current increases rapidly, but actually no more rapidly than under
normal conditions:
Both core flux and coil current start
from zero and build up to the same peak values experienced during
continuous operation. Thus, there is no "surge" or "inrush" or current
in this scenario.
Alternatively, let us consider what
happens if the transformer's connection to the AC voltage source occurs
at the exact moment in time when the instantaneous voltage is at zero.
During continuous operation (when the transformer has been powered for
quite some time), this is the point in time where both flux and winding
current are at their negative peaks, experiencing zero rate-of-change (dΦ/dt
= 0 and di/dt = 0). As the voltage builds to its positive peak, the flux
and current waveforms build to their maximum positive rates-of-change,
and on upward to their positive peaks as the voltage descends to a level
of zero:
A significant difference exists, however,
between continuous-mode operation and the sudden starting condition
assumed in this scenario: during continuous operation, the flux and
current levels were at their negative peaks when voltage was at its zero
point; in a transformer that has been sitting idle, however, both
magnetic flux and winding current should start at zero. When the
magnetic flux increases in response to a rising voltage, it will
increase from zero upwards, not from a previously negative (magnetized)
condition as we would normally have in a transformer that's been powered
for awhile. Thus, in a transformer that's just "starting," the flux will
reach approximately twice its normal peak magnitude as it "integrates"
the area under the voltage waveform's first half-cycle:
In an ideal transformer, the magnetizing
current would rise to approximately twice its normal peak value as well,
generating the necessary mmf to create this higher-than-normal flux.
However, most transformers aren't designed with enough of a margin
between normal flux peaks and the saturation limits to avoid saturating
in a condition like this, and so the core will almost certainly saturate
during this first half-cycle of voltage. During saturation,
disproportionate amounts of mmf are needed to generate magnetic flux.
This means that winding current, which creates the mmf to cause flux in
the core, will disproportionately rise to a value easily exceeding
twice its normal peak:
This is the mechanism causing inrush
current in a transformer's primary winding when connected to an AC
voltage source. As you can see, the magnitude of the inrush current
strongly depends on the exact time that electrical connection to the
source is made. If the transformer happens to have some residual
magnetism in its core at the moment of connection to the source, the
inrush could be even more severe. Because of this, transformer
overcurrent protection devices are usually of the "slow-acting" variety,
so as to tolerate current surges such as this without opening the
circuit.
|
