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Stratified high voltage bushing - QuickField simulation example

Example prepared by Dr. Wlodzimierz Kalat

Stratified high voltage bushing is composed of several insulation layers separated with very thin "floating" conductors. Their constant but unknown potential results from the capacitive distribution of electrostatic field and may be controlled by variation of their lengths, thickness and permittivity of the dielectric layers. From the technological point of view only the lengths adjustment can be considered as reasonable way of getting the most uniform distribution of radial component Er of electric strength. It assures the best utilization of insulating material and moderates the field across the high voltage bushing.

In theory, the infinite number of free potential electrodes leads to the uniform and continuous distribution of electric field across the bushing (E(r)=const) instead of logarithmic one. In reality, only the finite number of layers can be considered, usually 10-12.

The main goal of the example is to model very simple (only 2 layers) high voltage bushing, find the E(r) distribution and compare results with some mathematical formula. The condition of Ermax equality in every layer (E1rmax = E2rmax) gives the possibility to find the length of "floating" conductor and their potential.

Engineering question

How to calculate the reduction in electric stress from floating grading foils in a high-voltage bushing?

Answer
Model the foils as floating electrodes in an axisymmetric electrostatic problem and adjust their geometry to equalize peak radial electric stress.

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Typical applications
high-voltage condenser bushings, stratified insulation bushings, capacitive graded bushings

Stratified high voltage bushing

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Simulation problem

Problem Type
An axisymmetrical problem of free potential electrode in electrostatic field. Dirichlet boundary conditions with given potential are placed at zero and high voltage electrodes.

Geometry
Stratified high voltage bushing geometry Axisymmetric cross-section: grounded barrier, two insulation layers and a floating grading electrode, with radial dimensions 0 zero potential tubular electrode high voltage tubular electrode air 2-nd Insulation layer floating electrode 1-st Insulation layer 2 1 axis of rotational symmetry C2 C1 C10 R30 mm R2 mm

Given
HV potential U = 110 kV
Relative permittivity of dielectric material (epoxy resin) ε = 5.0

Task
Verify that the length of the "floating" grading electrode equalizes the maximum electric field stress in the two insulation layers (E1rmax = E2rmax), and calculate the partial capacitances C1, C2 and C10.

Solution
The length (L) of the "floating" electrode was found analytically from the charge balance condition Q1 = Q2 + Q10 (this derivation is outside the scope of the current example).
If the length is determined correctly, E1rmax = E2rmax should hold.

Results
To compare E1 and E2, the field strength E(r) is plotted along the middle cross-section of the bushing. high voltage bushing

C10[pF] C1[pF] C2[pF] Er1[kV/cm] Er2[kV/cm] U[kV]
Theory 3.84 84.64 68.51 36.57 36.57 59.31
C = 2·W / U² 3.97 81.37 70.10 36.0 34.6 58.9
C = Q/U 3.52 79.68 75.90 - - -

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