BUNDLED CONDUCTORS INVOLVING CAPACITANCE

Figure 4.10 shows a bundled-conductor line for which we can write an equation for the voltage from conductor a to conductor b. The conductors of any one bundle in parallel, and we can assume the charge per bundle divides equally between the conductors of the bundle since the separation between bundles is usually more than 15 times the spacing between the conductors of the bundle. Also, since D12 is much greater than d, we can use D12 is place of distances D12-d and D12+d make other similar substitutions of bundle separation distances instead of using the more exact expressions that occur in finding Vab. The difference due to this approximation cannot be detected in the final result for usual spacing even when the calculation is carried to five or six significant figures.

If the charge on phase a is qa, conductors a and a' each have the charge qa/2; similar division of charge is assumed for phase b and c. Then








The letters under each logarithmic term indicate the conductor whose charge is accounted for by that therm. Combining terms gives




The is the same as for a two conductor bundle except that r has replaced Ds. This leads us to the very important conclusion that a modified GMD method applies to calculation of capacitance of bundled-conductor three phase line having two conductors per bundle. The modification is that we are using outside radius in place of the GMR of a single conductor.

It is logical to conclude that the modified GMD method applies to other bundling configurations. If we let D stand for the modified GMR to be used in capacitance calculations to distinguish it from D used in inductance calculations, we have


Then for a two-strand bundle


for a three-strand bundle


and for a four-strand bundle