The paper presents a mathematical model and algorithm of the computer program to calculate the transient phenomena of burning and extinguishing of long secondary are at high voltage overhead lines. The results of investigations of selfextinguishing of secondary are under automatic single Phase reclosing (ASPR) for compact line 500 kV are given as well. Additionly the attendat factors as transient recovery voltage after are extinction and voltage at the neutral terminal of shunt reactor (in a case of four-key reactor) are determined.