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The inductance of a cable consists of two parts:
Both concepts play a role when calculating the inductance for multi-conductor systems like three-phase cables.
For single-phase cables, the inductance (L) formula aligned with IEC 60909 is:
$L=\frac{{\mu}_{0}}{2\pi}\mathrm{ln}\left(\frac{D}{r}+\frac{1}{4}\right)\u200a\text{H/m}$ Where: μ_{0} is the permeability of free space. D is the center-to-center distance between the conductors. r is the radius of the conductors.
$L=\frac{{\mu}_{0}}{2\pi}\mathrm{ln}\left(\frac{D}{r}+\frac{1}{4}\right)\u200a\text{H/m}$
Where:
For three-phase cables, the inductance matrix includes self and mutual inductance terms:
$\mathbf{L}=\begin{array}{ccc}{L}_{s}& M& M\\ M& {L}_{s}& M\\ M& M& {L}_{s}\end{array}$
When calculating the inductance of a cable, it is important to consider all factors. Some of the more common considerations include:
Mutual Inductance: In a three-core cable, the cores induce a magnetic field on each other. This can be accounted for using more complex matrix methods to define the mutual inductance between cores.
Shielding: The presence of a metallic shield can alter the inductive characteristics of the cable.
Non-uniform Arrangement: If the cores are not equally spaced, a more complex geometric mean distance (GMD) method may be required.