Insulation
Dielectric loss per unit length (IEC 60287-1-1)
- where
- dielectric loss per phase (W/m)
- frequency (Hz)
- capacitance per phase (µF/km)
- voltage to earth (kV)
- dielectric loss factor of the insulation
- dielectric loss of three phases (kW/km, numerically W/m)
Explain this equation
Works out the heat generated in the insulation by the alternating field, per phase per metre, as used in the IEC 60287 current rating equation.
C is the capacitance per phase, U₀ the voltage to earth and tan δ the insulation loss factor: the ratio of in-phase (loss) current to capacitive current. W_t is the sum for three phases.
The capacitive current is ωCU₀; the fraction tan δ of it is in phase with the voltage and dissipates power U₀ × ωCU₀ tan δ. The 10⁻³ converts µF/km and kV² into watts per metre, and W/m is numerically the same as kW/km.
For 132 kV XLPE (C = 0.2 µF/km, tan δ = 0.001) the loss is about 0.36 W/m per phase, small next to conductor losses of tens of W/m. For PVC at 11 kV with tan δ = 0.1 it is about 0.5 W/m, which is why PVC is not used at higher voltages.
Loss rises with the square of voltage, so it matters mainly at HV and EHV; IEC 60287 only requires it above stated voltages for each insulation type.
Heat generated in the insulation by the a.c. field, Wd = ωCU0² tan δ, as used in the IEC 60287 rating equation.
Enter your values to see the result.
Good to know
IEC 60287-1-1 gives tan δ and εr per insulation type: XLPE unfilled up to 18/30 kV 0.004, above 18/30 kV 0.001; EPR up to 18/30 kV 0.02, above 0.005; PVC 0.1; impregnated paper (solid) 0.01. The standard says dielectric loss need only be included above certain U0 values, e.g. 127 kV for unfilled XLPE and PE, 63.5 kV for EPR, 38 kV for solid paper and 6 kV for PVC. Below those it is small compared with conductor loss.
Common mistake
Using line voltage instead of U0 (triples the loss), or forgetting that tan δ rises with ageing and temperature in paper and PVC insulation.
Limits
Uses a single tan δ value at operating temperature and power frequency, as IEC 60287 does. Does not cover d.c. or harmonics.
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.