NEW APPROXIMATIONS TO DEEP-UNDERGROUND CONDUCTOR IMPEDANCES.

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