Magnetic field and impedance of a circuit with ground return for a two-layer overhead conductor

Abstract

For a circuit with ground return consisting of a long rectilinear overhead conductor the vector magnetic potential is introduced. Transformation of the differential equations describing the magnetic potential by means of Fourrier’s transformation yields the vector potential in the form of an analytical formula. Next, the magnetic field strength represented by improper integrals is determined. Appropriate representation of those calculations reduces them to the calculation of Laplace’s transformation, thus yielding analytical formulae describing the magnetic field in the circuit with ground return. The impedance of a circuit with ground return for a two-layer overhead conductor is represented as the total of external and internal impedances. The external impedance is determined using the vector magnetic potential to compute the induced electric field strength. The internal impedance of the conductor is determined using the solution of the Helmholtz’s equation for electric field strength. Finally a computer simulation in Delphi of the discussed question is presented.