Determination of self- impedances and mutual impedances in multi-wire systems containing underground wires

Abstract

Modeling the modes of electrical networks, which include multi-wire elements with overhead and underground wires, has a number of specific features: the location of some of the wires in underground cavities, resulting in the absence of capacitive coupling with above- ground conducting wires; increased values of self-capacitive parameters of underground wires; the possible presence of active conductivity “wire – ground”, leading to the need for mandatory consideration of parameter distribution. The article proposes a method for determining self- impedances and mutual impedances of wires in a multi-wire system containing underground wires. When developing models of multi-wire elements with underground wires, the following positions were used: wires are parallel to the surface of a flat homogeneous earth with a given specific conductivity; intersections of wires in one element are not allowed; when using chain concepts of self-impedances and mutual resistances, it is assumed that they are determined through the longitudinal electromotive force induced in the wire-ground circuit; underground wires are located inside one or more cylindrical cavities in the ground; capacitive coupling exists only between wires located in the same cavity; mutual inductive coupling takes place between all wires of the element. When considering the capacitive couplings of a group of underground wires, the method of conformal mappings was used, which gives an acceptable accuracy of modeling while respecting the relationship between the radii of the wires and their distances to the boundaries of the cavity in the ground. The verification of the correctness of the developed algorithm was carried out by comparing the linear capacitance of a cylindrical capacitor with the formulas, as well as the capacitance of a single wire located above the ground at a high altitude. Verification of the accuracy of determining the mutual resistance for non-parallel wires is performed by comparing the results of the following calculations: by approximate formulas; for an almost parallel convergence and a parallel convergence. The obtained results showed an acceptable accuracy in determining self-impedances and mutual resistances in multi-wire systems containing underground wires.