Rayleigh-Schrödinger perturbation analysis of signal propagation modes in inhomogeneous multi-conductor power cables

Locating defects in an underground cable connection can be based on the propagation of transient signals emerging from faults or weaknesses in the insulation. The accuracy depends on the precise knowledge of the propagation characteristics of high-frequency components in the signals. These characteristics are analysed for multi-conductor cables in case of non-perfect rotational symmetry. Deviations can arise from the positioning of the conductors within the cable cross section or from an inhomogeneous distribution of dielectric materials. It is investigated to what extent the signal propagation modes, applicable for a symmetric configuration, remain a suitable representation for signal interpretation when the symmetry is slightly disturbed. This is judged by means of Raleigh-Schrödinger perturbation analysis in comparison to electromagnetic field simulations. Cable designs for the medium-voltage level incorporate measures to confine the electric field in designated regions. Slight asymmetry does not lead to strongly perturbed modes. For low-voltage cables, electric field control is not needed, and the conductors are positioned within short distance of each other. Modes can change significantly upon a relatively small asymmetry. Inhomogeneous heat dissipation, e.g. from a short-circuit current upon a fault, can cause a temporarily asymmetric permittivity distribution over the cable cross section. The feasibility to detect such effect from changing signal velocities of the propagation modes is discussed.