Inductance of a cable consist of two parts:

1. the self-inductance of the conductor
2. the mutual inductance between conductors

BICC Electrical Cables Handbook

The BICC Electric Cables Handbook, give the formuale for inductance as:

$L=\left(K+0.2\ln \frac{2S}{d}\right)\times {10}^{-6}$

where:
L - cable inductance, H.m^-1
K - conductor formation constant
S - axial spacing between conductors within a cable, mm
- axial spacing between condcutors in trefoil, mm
- 1.26 x phase spacing of flat formation conductors, mm
d - condcutor diamters, mm

For 2, 3 or 4-core circular or sector-shaped cables, multiply the above by 1.02 to obtain the inductance.  Multiply by 0.97 for 3-core oval conductors.

Typical values of K

Number of wire in conductor	K
1 (solid)	0.0500
3	0.0778
7	0.0642
19	0.0554
37	0.0528
61 and over	0.0514

Reactance

The reactance of a conductor is given by:

$X=2\pi fL$

where:

X - reactance in Ω.m-¹
L i indcutance in H.m^-1

 

CENELEC CLC/TR 50480

Equations for inductance are given by CENELEC CLC/TR 50480 "Determination of cross-sectional area of conductors and selection of protective devices".

Three-line or line to line:

 

Line to neutral:

 

where:
x - reactance per metre of conductors, mΩ.m^-1
X_c - reactance of conductor, mΩ
X_cN - 
X_cPE -
X_cPEN - 

 

IEC 60909

See