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Plane-parallel problem of electrostatics.
Relative permittivity of PE insulation ε = 2.2;
Cable outer diameter D = 10 cm;
HV conductor diameter dHV = 2 cm (initial value);
Determine the optimal HV conductor diameter dHV for getting minimal electric field stress in the cable insulation at the inner conductor surface.
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.
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