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Peak inrush current results from core saturation. If at turn off of excitation the residual core flux density is high in the positive direction, and when next turned on the voltage phase is such as to create further magnetization in the same direction, then the core is driven far into saturation. This requires a lot more magnetizing current and therefore large inrush current. Whether this occurs and its magnitude is a random function dependent on where in the cycle the transformer is turned off, and where it is turned on.
On my web site at
http://www.beta-a2.com/EE-photos.html
I have photos of inrush current for a typical iron core transformer. See photos P6 thru P8. This transformer uses E-I laminations and probably uses a very standard transformer steel.
Edit.
The full load RMS input to this transformer is about 1.5 A. Thus, peak inrush to RMS full load is about 26 to 1.
End edit.
Materials with a more square loop hysteresis curve would show a higher peak current, especially wound on a toroid.
Magnetizing current is very non-sinusoidal and therefore 1.732 is not a good predictor of the peak to RMS ratio.
A magnetically tripped breaker may be more peak sensitive than RMS. An electronically tripped breaker can have almost any desired trip characteristic. In work I did for Mechanical Products in the early 1960s we developed an electronic breaker that could tolerate any reasonable inrush current and yet trip at, for example, 1% above the set-point. Further, the set-point could be compensated for line voltage or any other desired input.
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