The inductance of a cable consists of two parts:

1. Self-inductance (L): The property of a conductor (or circuit) to oppose a change in current flowing through it.
2. Mutual inductance (M): The phenomenon where a change in current in one conductor induces a voltage in a neighbouring conductor.

Both concepts play a role when calculating the inductance for multi-conductor systems like three-phase cables.

Single-Phase Cables: The Standard Formula

For single-phase cables, the inductance (L) formula aligned with IEC 60909 is:

$L=\frac{{\mu }_0}{2\pi }\ln \left(\frac{D}{r}+\frac{1}{4}\right) \text{H/m}$

Where:

• μ₀​ is the permeability of free space.
• D is the center-to-center distance between the conductors.
• r is the radius of the conductors.

Three-Phase Cables: The Complexity of Multiple Conductors

For three-phase cables, the inductance matrix includes self and mutual inductance terms:

$\mathbf{L}=\begin{array}{ccc}{L}_s& M& M\\ M& L_s& M\\ M& M& L_s\end{array}$

Factors to Consider

When calculating the inductance of a cable, it is important to consider all factors.  Some of the more common considerations include:

1. 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.

2. Shielding: The presence of a metallic shield can alter the inductive characteristics of the cable.

3. Non-uniform Arrangement: If the cores are not equally spaced, a more complex geometric mean distance (GMD) method may be required.