When a transformer is taken off-line, there will be a certain amount of residual flux that can remain in the core due to the properties of the magnetic core material.
The residual flux can be as much as 50 to 90% of the maximum operating flux, depending on the type of core steel. When voltage is reapplied to the transformer, the flux introduced by this source voltage will build upon that which already exists in the core.
In order to maintain this level of flux in the core, which can be well into the saturation range of the core steel, the transformer can draw current well in excess of the transformer’s rated full load current.
Depending on the transformer design, the magnitude of this current inrush can be anywhere from 3.5 to 40 times the rated full load current. The waveform of the inrush current will be similar to a sine wave, but largely skewed towards the positive or negative direction. This inrush current will experience a decay, partially due to transformer losses, which will provide a dampening effect; however, the current can remain well above rated current for many cycles.
Decent approximations of the inrush current require detailed information regarding the transformer design which may be available from the manufacturer but is not typically available to the user.
Actual inrush currents will also depend upon where in the source voltage wave the switching operations occur, the moment of opening effecting the residual flux magnitude, and the moment of closing effecting the new flux.
Resource: James H. Harlow – Harlow Engineering Associates