Conductor bundles

It is quite common for overhead lines to consist of bundles of conductors. Each bundle is held together with spacing frames, and these frames are located at regular intervals along the route. A bundle typically contains two or four conductors. The frames are ordinarily small compared with the line separation. However the potential on any conductor in a bundle is influenced by the charges on the other conductors in the bundle. The charge divides equally between the conductors. The potential on any conductor in a twin conductor bundle is then (ignoring all other bundles)

$$\phi = - \frac{1}{2 \pi \epsilon _{0}} ln \left( \sqrt{ 2 r R } \right)$$ (3)

where $r$ is the conductor radius and $R$ is the radius of the bundle circle (which contains all the centres of the conductors in that bundle). Hence the equivalent radius of a single conductor is given by

$$a _{2} = \sqrt{ 2 r R }$$ (4)

This expression should then be substituted for $a$ in the expression for the Green's function $G _{q}$ associated with charges on single conductors.

The corresponding potential for a quadruple conductor bundle is

$$\phi = - \frac{1}{2 \pi \epsilon _{0}} ln \left( \left( 4 r R ^{3} \right) ^{\frac{1}{4}} \right)$$ (5)

In this case the equivalent radius of a single conductor is given by

$$a _{4} = \left( 4 r R ^{3} \right) ^{\frac{1}{4}}$$ (6)