HV cables
Electric stress in a screened single-core cable
- where
- electric stress at radius x (kV/mm)
- rated voltage to earth (kV)
- radius at which stress is wanted (mm)
- radius over the insulation, under the insulation screen (mm)
- radius over the conductor screen (mm)
- maximum stress, at the conductor screen (kV/mm)
- minimum stress, at the insulation screen (kV/mm)
Explain this equation
Gives the radial electric stress anywhere in the insulation of a screened cable, and its maximum at the conductor screen and minimum at the insulation screen. Use it to check a design stress or to compare insulation thicknesses.
U₀ is the voltage across the insulation, conductor to earthed screen. r_c and Rᵢ are the radii of the inner and outer semiconducting screens, which act as smooth electrodes. x is any radius between them.
The field between coaxial cylinders falls as 1/x, because the same charge per metre spreads over a larger circumference further out. Integrating 1/x from r_c to Rᵢ gives ln(Rᵢ/r_c), which ties the stress to the applied voltage.
An 11 kV cable (U₀ = 6.35 kV) with 3.4 mm of XLPE over a 20 mm conductor screen gives about 2.2 kV/mm at the conductor screen and 1.6 kV/mm at the outside. HV XLPE designs run at several kV/mm. Doubling U₀ doubles every stress.
Use radii, not diameters, in the x, r_c and Rᵢ terms, and the radius over the conductor screen rather than the bare strands.
Radial electric field in the insulation of a cable with a conductor screen and an insulation screen (coaxial cylinder field). Use it to check design stresses or compare insulation thicknesses.
Enter your values to see the result.
Good to know
Stress falls as 1/x from the conductor screen to the insulation screen. Use the radius over the semiconducting conductor screen, not the bare conductor, because the screen smooths the strands and is the true inner electrode. Typical design maximum stresses at U0 are roughly 2–4 kV/mm for MV XLPE and higher for HV/EHV XLPE cables with super-clean insulation; take the actual limit from the manufacturer.
Common mistake
Using the conductor radius instead of the radius over the conductor screen, or entering diameters rather than radii (the ratio is unaffected but the stress is halved).
Limits
Ideal coaxial field: smooth concentric electrodes, homogeneous insulation, a.c. at power frequency (capacitive grading). Not valid for belted three-core cables, at terminations or joints, or for d.c. cables where the resistive stress distribution depends on temperature.
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.