Chapter 4, Problem 4.27P

Figure 4.34 shows double-circuit conductors' relative positions in segment I of transposition of a completely transposed three-phase overhead transmission line. The inductance is given by $L=2\times {10}^{-7}\ln \frac{\text{GMD}}{\text{GMR}}\text{H/m/phase}$

Where $GMD={\left(D_{AB}{}_{{}_{eq}}{D}_{B{C}_{eq}}{D}_{A{C}_{eq}}\right)}^{1/3}$

With mean distances defined by equivalent spacings

$\begin{array}{l}{D}_{A{B}_{eq}}={\left(D_{12}{D}_{1\text{'}2\text{'}}{D}_{12\text{'}}{D}_{1\text{'}2}\right)}^{1/4}\\ D_{B{C}_{eq}}={\left(D_{23}{D}_{2\text{'}3\text{'}}{D}_{23\text{'}}{D}_{1\text{'}3}\right)}^{1/4}\\ D_{A{C}_{eq}}={\left(D_{13}{D}_{1\text{'}3\text{'}}{D}_{1\text{'}3}\right)}^{1/4}\end{array}$

And $GMR={\left[{\left(GMR\right)}_A{\left(GMR\right)}_B{\left(GMR\right)}_C\right]}^{1/3}$ with phase GMRs defined by ${\left(GMR\right)}_A={\left[r\text{'}{D}_{11\text{'}}\right]}^{1/2};{\left(GMR\right)}_B={\left[r\text{'}{D}_{22\text{'}}\right]}^{1/2};{\left(GMR\right)}_C={\left[r\text{'}{D}_{33\text{'}}\right]}^{1/2}$ and $r\text{'}$ is the GMR of phase conductors.

Now consider a 345-kV, three-phase, double-circuit line with phase-conductor’s GMR of 0.0588 ft and the horizontal conductor configuration shown in Figure 4.35.

1. Determine the inductance per meter per phase in Henries (H).
2. Calculate the inductance of just one circuit and then divide by 2 to obtain the inductance of the double circuit.