In many power generation and distribution applications, semi-conducting dielectric materials are used to reduce electrical stresses. Here, we will take a look at a simple model which highlights the key components/stages in modelling this. The figure below shows a typical bushing arrangement with an HV conductor at 10 kV (red) emerging from a grounded tank lid (yellow) with a green insulating bushing between them. The permittivity of the bushing is 5.7.
Only the dielectric and the surrounding air need to be included in the model. The model has 8-fold symmetry so can be further simplified by including only 45 degrees.
The electric field just in the air outside the insulator near the lid is close to 40 kV cm-1, as can be seen below. This can lead to breakdown as it exceeds 33 kV cm-1.
Model with stress relief
To overcome the high electric fields, a coating of stress-grading material can be applied over the insulator. The figure below shows the 45 degree section model with the stress grading material included.
The properties of the material are ϵ = 2 , σ = 10−6 S/m. The material connects the high and low voltage boundaries allowing a small current (because of the low conductivity) to flow and thus redistributes the electric field.
The current density in the lossy dielectric material can also be evaluated, as shown below.