Cableizer ®

Inductance conductor i

Definition according to 'Kabel und Leitungen für Starkstrom' by L. Heinhold, 5th Ed. 1999, chap. 24.

Symbol
$L_{i}$
Unit
H/m
Formulas
$\frac{\mu_{0}}{2\pi} \left(\ln\left(\frac{\sqrt{a_{12} a_{31}}}{GMR_{c}}\right)+j \sqrt{3} \ln\left(\frac{S_{ab}}{S_{ac}}\right)\right)$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
Related
$a_{12}$
Distance phases 1—2 [mm]
$a_{23}$
Distance phases 2—3 [mm]
$a_{31}$
Distance phases 3—1 [mm]
$GMD$
Geometric mean distance between phases of the same system [m]
$GMR_{c}$
Geometric mean radius conductor [m]
$\mu_{0}$
Vacuum permeability [H/m]
$\pi$
Archimedes' constant $\pi$
$S_{ab}$
Distance phases a—b [m]
$S_{ac}$
Distance phases a—c [m]
$S_{bc}$
Distance phases b—c [m]