HV cables
Capacitance of a screened cable (IEC 60287-1-1)
- where
- capacitance per phase (F/m; shown in µF/km)
- permittivity of free space, 8.854 × 10⁻¹² F/m
- relative permittivity of the insulation
- diameter over the insulation, excluding screen (mm)
- diameter over the conductor screen (mm)
Explain this equation
Works out the capacitance per phase between conductor and screen of a single-core or radial-field three-core cable. It feeds charging current, dielectric loss and earth-fault current calculations.
ε₀ is the permittivity of free space and ε_r how much the insulation raises it (about 2.5 for XLPE, 3 for EPR, 8 for PVC). Dᵢ is the diameter over the insulation and d_c the diameter over the conductor screen.
It is the coaxial capacitor formula: charge per metre divided by the voltage found by integrating the 1/x field across the insulation. IEC 60287 writes 1/(2πε₀) as 18 × 10⁹, which is the same thing rounded.
Typical MV XLPE cables are 0.2 to 0.5 µF/km; 132 kV XLPE about 0.15 to 0.25 µF/km. A thicker insulation raises the log term and lowers C; a larger conductor raises C.
Only the ratio of the diameters matters, but both must be measured on the same basis (screen to screen).
Capacitance between conductor and screen of a single-core cable or each core of a screened (radial field) three-core cable, per unit length.
Enter your values to see the result.
Good to know
IEC 60287-1-1 writes this as C = εr/(18 ln(Di/dc)) × 10⁻⁹ F/m, the 18 being 1/(2πε0) rounded (it gives about 0.14 % higher C than the exact constant used here). εr values from IEC 60287-1-1: XLPE 2.5 (unfilled), EPR 3.0, PVC 8.0, PE 2.3, impregnated paper about 3.3–4.0. Manufacturers' data sheets give C directly; use them where available.
Common mistake
Using the conductor diameter rather than the diameter over the conductor screen, or including the insulation screen thickness in Di.
Limits
Radial field cables only. Not for belted (unscreened) three-core cables, whose capacitances need the geometric factor method.
Sources
For competent high-voltage engineers. Results are calculations from the published methods shown and depend entirely on the data you enter. They are not a substitute for a system study, manufacturer data, the applicable standards and Engineering Recommendations, or your organisation’s safety rules. Never use a result to justify working on or near live HV equipment.