Electrical characteristics of polyphase transmission systems with special reference to boundary-value calculations at power-line carrier frequencies

摘要

In this paper, the matrix solution of the multiconductor line developed previously is summarised. Particular emphasis is given to a proof justifying the relatively complex approach used. This is achieved by considering the modal parameters at infinite frequency as a limiting case of the general solution and indicating that this is different from the value obtained by earlier theories using simplifying assumptions. The main purpose of the paper is to consider the results of a number of specific boundary-value calculations. The calculations are based on the concept of polyphase reflection factor and the necessary analytical procedure is set out. Although not used in this paper, the matrix four-part equations are set out as an alternative set of boundary equations. All the equations are defined in terms of matrix functions, since the results are more concise in this form. The basic parameters of four-line configurations are given, i.e. single- and twin-circuit vertical and horizontal arrangements. The general properties of the modal parameters are discussed, i.e. the increase in attenuation with frequency, presence of ground and phase modes and the asymptotic approach of phase velocity to the free-space value with increasing frequency. The particular, importance of the characteristic-impedance matrix is discussed. It is shown how the influence of the soil resistivity on circuit-breaker-recovery voltage transients is readily taken into account without recourse to elaborate boundary-value calculations. The basic parameters of a 330kV line, derived analytically, are compared with values obtained by field measurement, and the same is done for a number of specified boundary-value problems. It is shown that acceptable correlation between theory and practice is obtained. It is also shown that, in the case of power-line carrier coupling, optimum arrangements may be predicted by considering the relative, proportions of modes for various forms of energisation. It is emphasised t-nhat the low-attenuation modes should be dominant for most efficient propagation. In a further boundary-value calculation, the problem of mode cancellation is discussed. It is shown that, in certain coupling arrangements, modes with intermediate attenuation dominate at the sending end of the line. For critical frequencies, the modes which were in phase at the sending end arrive in antiphase at the receiving end of the system owing to phase-velocity differences resulting in abnormally high transmission losses. The paper concludes with a consideration of some of the problems still outstanding in the theory of multiconductor lines.