Equivalent resistivity approximation of two-layer earth structures for earth return impedance calculations

The equivalence conditions between homogeneous and two-layer earth structures are investigated in this paper. The analysis is based on the comparison between the two-layer and the homogeneous earth return impedance relations. The aim is the derivation of a new simple formula to connect the homogeneous earth equivalent resistivity with the two-layer earth electromagnetic and geometric properties. Thus, the relatively simple expressions for the impedance calculation of the homogeneous earth case can be used for two-layer earth models. The new formula is implemented for six actual cases of two-layer earth models. The two-layer earth impedances are calculated for various configurations, including overhead transmission lines, underground cable systems and a combination of overhead line and underground conductor. The calculated impedances are compared to the corresponding for the homogeneous earth, using the equivalent resistivity given by the new formula.