Irregular wave propagation characteristics in underground transmission cables

Wave propagation characteristics of overhead lines and underground cables are usually determined using the well known theory of natural modes of propagation. The paper shows that some special circumstances may inhibit the use of such methods of analysis, since the matrix diagonalisation involved in that procedure cannot always be carried out. A critical non-diagonalisable situation is presented with a configuration as simple as a single buried underground coaxial cable. For this irregular case, the wave propagation characteristics are described, and the correct solution is shown not to consist of a superposition of natural exponential modes. Furthermore, the paper alerts the reader to the fact that modal analysis in general, and eigenvalue calculation in particular, may not be so straightforward as it is usually thought, meaning that some surprises may arise with modal analysis computer programs currently in use. Besides informing the reader of the possibility of irregular non-diagonalisable cases the paper also points out two alternative methods of overcoming the difficulties associated with such cases.