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The impedance algorithm in distance protection for high voltage (HV) and extra high voltage (EHV) lines, although neglecting the influence of shunt capacitance, is able to produce satisfactory performance. However, the accuracy of the algorithm is significantly reduced when applying to ultra high voltage (UHV) lines due to the larger P.U. line shunt capacitance and longer transmission radius. Therefore, the distributed parameter model should be adopted, and the relay should be set based on the hyperbola function between measuring impedance and the fault distance. However, how to define and set the indexes in relay ever defined with lumped parameters, such as the residual compensation coefficient, is still unresolved. In response to this question, the paper models the UHV system with distributed parameters and introduces the concept of virtual equivalent line length controlled by zero sequence system impedance, and then proposes a novel residual compensation coefficient. Case studies and RTDS tests show that the relay with proposed coefficient offers good performance for the simulated cases. The results also can be extended into other applications, such as the design of zero sequence reactance relay, fault location, fault phase selection, power swing blocking, and load blocking components.