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# Cable thermal breakdown voltage

The insulation in a DC cable is subjected to both thermal and electric stress at the same time. Defects in insulation may cause a local overheating due to leakage currents. Calculate the electric current in the faulty insulation with small defective area.

Problem Type:
A plane-parallel problem of DC conduction.

Geometry:

Given:
Electric conductivity of insulation γ - depends on temperature, as shown on the plot below;
Conductor potential U = 10 kV;
Shield potential U = 0 V;
Cable temperature T = 80 °C (353 K);
Local overheating Tmax = 120 °C (393 K).

Problem:
Calculate the electric current in the insulation.

Solution:
The model depth is taken as 10 cm (defect region length).

Results:

 Leakage current, I Without defect, Tmax=80 °C 1.24e-8 A (124 μA/km) With defect, Tmax=120 °C 1.255e-8 A

Current density distribution in the insulation close to the thermal defect.

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