Conductor Impedance Approximations for Deep-Underground Mines

Wagner and Evan´s approximation to Carson´s equations for overhead conductors has been used to approximate the impedance of conductors buried deep within the earth such as an underground mine environment. While these equations are acceptable for overhead and shallow-buried conductors, superior approximations, retaining the same general form as the Wagner and Evans approximation, may be derived. The derivation of self-and mutual-impedance equations for conductors that are enclosed in a cylindrical dielectric and surrounded by a homogeneous earth of arbitrary permeability is presented. New approximations to modified Bessel functions are presented and used to obtain approximate impedance expressions which show superior error performance. Error performance is graphically presented for self-and mutualimpedance values over a broad range of operating conditions. Emphasis is placed on the effect of nonunity relative permeability.