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.
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.
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.