Secondary arc on ultra-high-voltage（UHV） transmission lines weakens security and stability of power system. If the secondary arc cannot be extinguished in time

single-phase automatic reclosure（SPAR） would be failed. The parameter of a transmission line is one of the main factors affecting secondary arc current and recovery voltage. It is necessary to consider the line distribution parameters for UHV long distance transmission line. Distribution characteristic of line parameter is actually a function of frequency because of skin effect. In this paper

a secondary arc parameters transmission dive equation for the UHV transmission lines with a single-phase earthing fault is established according to the frequency related parameters circuit theory. The physical process of secondary arc is analyzed in detail

the boundary conditions and initial conditions of recovery voltage and secondary arc current are given

and the variation regularities of recovery voltage and secondary arc current are obtained through calculation and analysis. The results show that: ① the electrostatic induction component of recovery voltage is independent to length of line and fault position

while the electromagnetic induction component closely relates to fault position;② the secondary arc current is composed of electrostatic induction component and electromagnetic induction component

which closely relate to fault position. This study may provide a basis for further analyzing the influences of various conditions and factors on secondary arc.