Since the most faults on overhead high voltage transmission lines are transient single phase to ground faults, the successful operation of re-closing relays significantly influences stability and continuity of power systems. In order to set the dead time of usual re-closing relays or design adaptive re-closing relays, it is required to know the final extinction time of the secondary arc and variation manner of this time by different factors. Therefore, in this paper, a comprehensive investigation of various factors impact on the secondary arc extinction time is presented via simulation of various fault conditions on a test power system and analysis of the fault voltage components. For this purpose, the power system model and the non linear dynamic model of the secondary arc have been implemented in the used software. Using the studies results, the approximate sensitivity of the final extinction time of the secondary arc to related factors are presented in terms of number of power cycles.