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 planeparallel 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 T_{max} = 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, 
1.24e8 A (124 μA/km) 
With defect, 
1.255e8 A 
Current density distribution in the insulation close to the thermal defect.
See the DCCond1.pbm problems in the Examples folder.