At present

researches on the adaptive reclosure lack an analytic expression for beat frequency current about whether the beat frequency current definitely exists and the range of amplitude of the current in adaptive reclosure. The amplitude may be nonexistent or too small when the single-phase transient fault disappears

which will affect the reliability of reclosing determination. The beat frequency current in the shunt reactor is not only affected by sound phase voltage but also by the initial state of components of transmission line when fault disappears. Based on the superposition principle

the complete expression of beat frequency current is obtained

by an analysis of which the minimum beat frequency current and conditions for its occurrence are obtained. It is concluded that the beat frequency current being zero belongs to small probability event. The current is affected by fault time

arc duration

arc resistance

phase angle difference and fault location that make the amplitude obvious. If the amplitude is too small

it will affect the reliability of the reclosing determination. The paper gives the range of amplitude of the beat frequency current on 500 kV transmission lines using the method of the orthogonal experiment in mathematical statistics

proving the beat frequency current can be applied to engineering. This work is supported by National Natural Science Foundation of China(No. 50877062).