Abstract: Since the combustion of secondary arcs in UHV transmission lines is long, if these arcs can't be extinguished in time, the single phase automatic reclosure would be failed, thus having bad effect on the supply security and system stability. As a result, it is necessary to study the secondary arc currents on UHV transmission lines.On the base of establishing lumped parameter model of the transmission system, the calculation formulas of capacitance, inductance and total secondary arc currents are deduced by using the circuit theory. The formulas with consideration of arc resistance can calculate the secondary arc current of any fault point on lines under different compensation schemes (shunt reactor without or with the fourth reactor). The formulas can accurately compute the secondary arc current on short distance single circuit transmission lines. According to the formulas, the secondary arc current of the Huainan Shanghai UHV transmission project which is under construction in China is calculated. The influence of the compensation scheme, location of fault point, arc resistance on the secondary arc current are analyzed.