Cable inductance describes the magnetic coupling associated with current flowing in cable conductors. It contributes to cable reactance and therefore affects voltage drop, impedance, fault current and power-system calculations.
This article consolidates the original Inductance note with the BICC Electrical Cables Handbook formula. For the wider impedance context, see Cable Impedance.
Self and mutual inductance
- Self-inductance: the property of a conductor or circuit to oppose a change in the current flowing through it.
- Mutual inductance: the effect where a changing current in one conductor induces voltage in a neighbouring conductor.
Both effects are relevant in multicore and three-phase cable systems because the conductors are magnetically coupled.
Single-phase cable inductance
For a simple two-conductor arrangement, a commonly used inductance expression is:
| μ0 | Permeability of free space |
| D | Centre-to-centre distance between conductors |
| r | Conductor radius |
| L | Inductance, H/m |
The same relationship is also used in the more detailed impedance derivations, where conductor spacing may be replaced by an appropriate geometric mean distance.
Three-phase cable inductance
For a three-phase cable system, inductance can be represented using a matrix with self-inductance terms on the diagonal and mutual inductance terms off the diagonal:
For balanced, symmetrical arrangements this representation can be simplified. For non-uniform arrangements, such as flat formation with unequal spacing, the geometric mean distance method is used to capture the average magnetic spacing between phases.
BICC Electrical Cables Handbook formula
The BICC Electrical Cables Handbook gives the following practical cable inductance formula:
| L | Cable inductance, H/m |
| K | Conductor formation constant |
| S | Axial spacing between conductors within a cable, axial spacing in trefoil, or 1.26 times phase spacing for flat formation, mm |
| d | Conductor diameter, mm |
For two-core, three-core or four-core circular or sector-shaped cables, multiply the result by 1.02. For three-core oval conductors, multiply the result by 0.97.
Typical BICC values of K
| Number of wires in conductor | K |
|---|---|
| 1, solid | 0.0500 |
| 3 | 0.0778 |
| 7 | 0.0642 |
| 19 | 0.0554 |
| 37 | 0.0528 |
| 61 and over | 0.0514 |
Factors affecting cable inductance
- Mutual inductance: phase conductors induce magnetic fields in each other, especially in multicore and three-phase systems.
- Shielding and sheaths: metallic screens, sheaths and bonding arrangements can alter inductive behaviour.
- Conductor arrangement: trefoil, flat and non-uniform spacing arrangements produce different inductance values.
- Geometric mean distance: used where conductor spacing varies across the cable set.
For related calculations, see Geometric Mean Distance, Cable Impedance and Voltage Drop.