Insulation
Insulation resistance of a cable
- where
- insulation resistance of the length (MΩ)
- volume resistivity of the insulation (Ω·m)
- diameter over the insulation (mm)
- diameter over the conductor or conductor screen (mm)
- cable length (m)
- insulation resistance constant (MΩ·km)
Explain this equation
Gives the theoretical insulation resistance between conductor and screen from the volume resistivity of the insulation, for a given length and per kilometre.
ρ is the volume resistivity of the insulation, Dᵢ and d_c the diameters over and under the insulation, and l the length. R_k is the insulation resistance referred to 1 km.
Leakage current flows radially through a thin cylindrical shell at each radius; adding the shells gives ln(Dᵢ/d_c)/(2πl). Resistance falls with length because the parallel leakage paths add up. The 10⁻⁶ converts ohms to megohms.
XLPE at 10¹⁴ Ω·m with a 1.34 diameter ratio gives about 4600 MΩ for 1 km and twice that for 500 m. Field IR readings are often lower because of terminations and surface leakage.
Resistivity is very sensitive to temperature and moisture, so compare readings at similar temperatures and corrected to the same length.
Theoretical insulation resistance between conductor and screen from the insulation volume resistivity. Insulation resistance falls in inverse proportion to length.
Enter your values to see the result.
Good to know
R = ρ ln(Di/dc)/(2πl) for a coaxial insulation. Volume resistivity is highly temperature dependent and, for XLPE, often 10¹⁴–10¹⁶ Ω·m at 20 °C; IEC 60502-2 sets a minimum volume resistivity or insulation resistance constant Ki for type tests (with R = Ki log10(D/d) MΩ·km). Field readings with an IR tester are usually dominated by terminations and surface leakage, so treat this as an upper bound.
Common mistake
Comparing a field reading with a per-km value without correcting for length (longer cables read lower) or temperature.
Limits
Homogeneous insulation at a uniform temperature; d.c. steady state after absorption currents have decayed. Ignores semiconducting screens, terminations and surface leakage.
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.