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Dielectric loss in cable

QuickField simulation example

IEC 60287* suggests that for unfilled XLPE cables rated above the 127 kV level dielectric losses should be calculated.

Engineering question
How to find dielectric losses in XLPE cable insulation

Engineering answer
Set up a plane-parallel QuickField AC Conduction problem for an XLPE cable insulation system and evaluate dielectric losses from computed field results.

Typical applications
XLPE power cables, HV cable insulation systems, underground cable insulation

Problem Type
Plane-parallel problem of AC conduction.

Geometry
Cable length is 1 km
Dielectric loss in cable IEC 60287 suggests that for unfilled XLPE cables rated above the 127 kV level dielectric losses should be calculated Insulation Screen Sheath Conductor Ø26 mm 500 mm² Ø 66.7 mm

Given
Voltage U = 132 kV (r.m.s.), frequency f = 50 Hz.
XLPE permittivity 2.5, loss tangent tan(δ) = 0.001

Task
Calculate the capacitance and dielectric losses in the cable.

Solution
In AC conduction problem we should specify the electric potential amplitude, which is U * √2.
Electrical conductivity of materials should be set in AC conduction problems. We can take into account dielectric losses by specifying the apparent value of the conductivity**:
σ = 2πf·εε0·tan(δ) = 2*3.142*50*2.5*8.854e-12*0.001 = 6.95 pS/m.

Capacitance = charge / potential difference.

Results
Cable dielectric losses are 809 W per 1 km of the cable length.
Conductor-to-screen capacitance is C = 0.02758 / (132000* √2) = 0.148 μF per 1 km of the cable length. Reference*** value is 0.147 μF/km.
Dielectric loss in cable

References:
*IEC 60287-1-1. Electric Cables - Calculation of the current rating.
** Wikipedia, Dielectric loss.
*** XLPE Al single core 76/132 kV cable datasheet.