When a temporary single-phase fault occurs on shunt reactor compensated EHV or UHV transmission lines， the voltage of the opened phase conductor and the current of the shunt reactor contain resonant component and power frequency component after the secondary arc is extinguished. While for a permanent single-phase fault， the above voltage and current only contain power frequency component. Based on the analysis of the circuit in which the faulted phase is opened， the method of calculating the resonant frequency is deduced. A new criterion based on the orthogonality of sine functions is proposed to detect the resonant component and determine the fault nature quickly. The proposed criterion can reduce the time to distinguish between permanent and temporary faults. The criterion is simple with high sensitivity. Simulation results show that the proposed conclusions are correct.