The fault current contains the inherent frequencies components when the arc faults occur in UHV transmission lines with shunt reactors, which can offer effective fault information. In the primary arc, secondary arc and recovery voltage periods in the case of an arc fault with shunt reactors, the three free oscillation circuits are formed by the energy storage elements in the different periods, which will produce different inherent oscillation frequency components based on the different network. After phase-mode transformation, the free oscillation circuits in mode components are obtained and the inherent frequencies are captured, the characteristics of inherent frequency components are used to recognize the condition of a arc fault, offering a theoretical basis for the new protection principle based on inherent frequencies. PSCAD simulation results show the correctness of the theoretical analysis on the inherent，provides a good theoretical basis for the line protection and reclosing scheme by using characteristics of inherent frequency.