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Main >> Applications >> Sample problems >> Cable insulation optimization

**Problem Type:**

Plane-parallel problem of electrostatics.

**Geometry:**

**Given:**

Relative permittivity of PE insulation ε = 2.2;

Cable outer diameter *D* = 10 cm;

HV conductor diameter *d*_{HV} = 2 cm (initial value);

**Problem:**

Determine the optimal HV conductor diameter *d*_{HV} for getting minimal electric field stress in the cable insulation at the inner conductor surface.

**Solution:**

Analytical solution states that the ratio *D* / *d*_{HV} 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