Multiconductor transmission lines. Theory of natural modes and fourier integral applied to transient analysis

In this paper, a theoretical formulation of a method of multiconductor transient analysis is developed. The method combines the use of the modified Fourier transform and the steady-state theory of natural modes. The virtues of this particular formulation are that the frequency dependence of parameters can be taken into account irrespective of the complexity of the expressions defining their steady-state values. The paper discusses the problem of the first pole to close when a power line is being energised from a source of infinite capacity. The argument is further extended to cover simultaneous pole closure of a circuit breaker. The mathematical representation of the source-side network is covered and two alternative methods of simulation of a multiconductor-source infeed are presented. Both methods are shown to retain the distributed-parameter nature of a source infeed, or a group of such infeeds, while achieving a reduction in the computation time that would otherwise be required to meet the needs of a fairly accurate form of representation. The numerical results of a series of digital-computer studies are presented. These illustrate various cases of practical important and highlight specific aspects of the behaviour of multiconductor systems.