Consider a symmetrical bundle with \(N\) subconductors arranged in a circle of radius A. The inductance of a single-phase symmetrical bundleconductor line is given by

\(\mathrm{L}=2 \times 10^{-7} \ln \frac{\mathrm{GMD}}{\mathrm{GMR}} \mathrm{H} / \mathrm{m}\)

Where GMR is given by \(\left[N r^{\prime}(\mathrm{A})^{N-1}ight]^{1 / N} r^{\prime}=\left(e^{-1 / 4} right), r\) being the subconductor radius, and GMD is approximately the distance D between the bundle centers. Note that \(A\) is related to the subconductor spacing \(S\) in the bundle circle by \(\mathrm{S}=2 \mathrm{~A} \sin (\Pi / N)\)

Now consider a \(965-\mathrm{kV}\), single-phase, bundle-conductor line with eight subconductors per phase, phase spacing \(\mathrm{D}=20 \mathrm{~m}\), and the subconductor spacing \(\mathrm{S}=45.72 \mathrm{~cm}\). Each subconductor has a diameter of \(4.572 \mathrm{~cm}\). Determine the line inductance in \(\mathrm{H} / \mathrm{m}\).