In this paper， the characteristics of the measuring impedance are discussed under load operation and ground fault conditions based on the distributed parameter line model due to the large shunt capacitance， the high voltage level and the long transmission radius for UHV AC transmission lines. The hyperbola function relationship between the measuring impedance and the fault distance has been established. A novel residual compensation mode for ground impedance relays is proposed and correlative issues， such as normalization and linearization of factor P， are also discussed. Theoretical analysis and case test results show that the ground impedance relay can be set based on the lumped parameter line model if the length of a UHV AC transmission line is less than 400 km. Otherwise， the directional ground impedance relay must be set based on the distributed parameter model and the residual compensation mode should be used.