Definition according to the book 'Kabel und Leitungen für Starkstrom' by L. Heinhold, 5th edition 1999, chapter 24.
$\frac{\mu_0}{2\pi} \left(\ln\left(\frac{\sqrt{a_{12} a_{31}}}{GMR_c}\right)+j \sqrt{3} \ln\left(\frac{S_{ab}}{S_{ac}}\right)\right)$ | Three-phase system, individual, phase 1 |
$\frac{\mu_0}{2\pi} \left(\ln\left(\frac{\sqrt{a_{23} a_{12}}}{GMR_c}\right)+j \sqrt{3} \ln\left(\frac{S_{bc}}{S_{ab}}\right)\right)$ | Three-phase system, individual, phase 2 |
$\frac{\mu_0}{2\pi} \left(\ln\left(\frac{\sqrt{a_{31} a_{23}}}{GMR_c}\right)+j \sqrt{3} \ln\left(\frac{S_{ac}}{S_{bc}}\right)\right)$ | Three-phase system, individual, phase 3 |
$\frac{\mu_0}{2\pi} \ln\left(\frac{GMD}{GMR_c}\right)$ | Three-phase system, trefoil |
$\frac{\mu_0}{2\pi} \left(\ln\left(\frac{\sqrt{2} S_{ab}}{GMR_c}\right)-j \sqrt{3} \ln\left(\sqrt{2}\right)\right)$ | Three-phase system, flat equal distance |
$\frac{\mu_0}{2\pi} \ln\left(\frac{GMD}{GMR_c}\right)$ | Multi-core cables |