The AC series arc fault of low-voltage power lines is prone to electrical fires, causing personal and property loss. Given the sudden change of fault current amplitude and the arc randomness waveform characteristics of the current change, this paper proposes a recognition method based on the absolute difference of neighboring waves and randomness of the fault current. The method is based on the change law of the current abrupt change amount before and after the fault, and the abrupt change amplitude is used as the initiation criterion. Then an arc fault existence criterion is constructed based on the arc random characteristic time domain distribution of the current change amount during the fault cycle under different load types and air gap spacing. Finally, arc fault identification is achieved through a one-dimensional convolutional neural network (1DCNN) integrated. The average detection accuracy of the method using untrained trunk circuit data is 90.97% when the load power of the faulty branch circuit accounts for 20%. Thus this can effectively detect series arc faults with good adaptability.