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Cable insulation optimization

Problem Type:
Plane-parallel problem of electrostatics.

Geometry:
Cable insulation optimization Determine the optimal HV conductor diameter for getting minimal electric field stress in the cable insulation at the inner conductor surface. Insulation Ground HV D dHV=?

Given:
Relative permittivity of PE insulation ε = 2.2;
Cable outer diameter D = 10 cm;
HV conductor diameter dHV = 2 cm (initial value);

Problem:
Determine the optimal HV conductor diameter dHV for getting minimal electric field stress in the cable insulation at the inner conductor surface.

Solution:
Analytical solution states that the ratio D / dHV should be equal to e (2.71828..).
Built-in LabelMover tool is used to perform the optimization. Electric field strength value is measured in the single reference point (labelled as "point") on the HV conductor surface.

Results:
LabelMover indicates that the inner conductor diameter should be scaled up 1.834 times (which is 2 cm*1.834 = 3.668 cm)
The calculated ratio of outer to inner diameter is 10 cm / 3.668 cm = 2.726 (close enough to the analytical result 2.718).
Electric field stress distribution in the insulation with optimal HV conductor dimensions is shown below

Electric field stress distribution in the insulation

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