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A novel distance protection algorithm for the first-zone distance relay of parallel transmission lines is proposed for cross-country grounded faults. The algorithm calculates the fault impedance using one-end sampling voltages and currents from a single line. The theoretical basis of the proposed algorithm is described in this paper, which is based on the symmetrical component method for parallel lines. And an attempt is made to express the zero-sequence current of the adjacent parallel line at the relay location by the zero-sequence current of the concerned line in combination with the fault characteristics of the system model, by which the impact of the mutual coupling between the lines can be eliminated. And, thus, the distance algorithm for cross-country grounded faults is presented. The simulations show that the proposed algorithm can obtain the accurate fault reactance when cross-country bolted faults occur, which is superior to the existing distance protection algorithm based on one-end data from a single line.