Linear power networks with distributed constants

The study of power networks with localized constants is based on an approximation that becomes less valid the higher the frequency of the power sources. This approximation can no longer be used in the case of power transmission networks, which are made up of long overhead lines or buried cables, supplied at a frequency of 50 Hz.

However, the efficiency of the methods used to study the various networks with localized constants encourages us to seek, in the case of networks with distributed constants, a model using localized elements.

Consider a single-phase line, made up of two conductors AC and BD (figure 1 ), supplied by a source S and loaded by a load Ch.

As the conductors in the line are resistive, they are subject to Joule effect losses. Together, they form a large loop, which means that magnetic energy is stored. What's more, the two conductors are insulated from each other. There is therefore a capacitive and possibly resistive effect across the board. All these effects are uniformly distributed along the line.

The aim of the article is to present a general model for a set of n conductors, to show how the various parameters can be determined as a function of the geometry of each conductor, to look at the exploitation of the model obtained and, finally, to extend it to the tricky case where the materials run along a cylinder of magnetic material.