A unified model for transformer core saturation is developed. The flux saturation resulting from the changes in voltage

including amplitude change and angle change

is the fundamental cause of inrush current. And the flux saturation is correlated with the moment of voltage leap

the angle difference and the amplitude. Voltage angle changes may also lead to inrush current while the voltage amplitude decreases

hence the reducing of voltage amplitude cannot be used to assert that there's no inrush current. Proceeding from the root causes of inrush current

a kind of iron core saturation criterion based on voltage integration is put forward. The proposed method can produce excitation inrush current because of transformer core saturation

which is caused by no-load closing

fault clearance

sympathetic inrush current

system fault or operation

and other abrupt changes in voltage. This criterion provides an effective and fast method for differential protection without inrush current atresia and will greatly accelerate the operation of differential protection of transformer when internal fault occurs.