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Inrush is due to the saturation of the core of the transformer.

When the highside device closes to energize the transformer, it does not always do so right at a voltage peak. The transformer core B (magnetic field) will be 90 degrees out of phase with the applied voltage, so a peak voltage close is ideal. Once it is closed, the B will continue up and down 90 degrees out of phase with the voltage. Assuming there is no residual magnetic field (B starts at zero), it will be offset by the initial non - peak close. This offset in magnetic field will cause the core to go into saturation; depending on the core design it may be further or less into saturation on different Transformers.

When the core saturates, large currents flow, and these currents (normally) have a high 2nd harmonic component which is used in protective relaying to restrain for inrush.

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Q: In-rush current phenomena in transformer
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