Condenser bushing field grading

QuickField simulation example

The bushing is used to pass the conductor into the oil-filled tank of the transformer. Typically there are two areas where electric field stress is high: at the conductor surface and near the tank wall. We use the bushing condenser to redistribute electric potential more uniformly and reduce electric field stress in the insulation.

Problem Type
Axisymmetric problem of AC conduction.

Geometry

Given
Relative permittivity of porcelain 5.8, oil-impregnated paper 3.6, oil 2.2.
Rated voltage U~ = 72.9 kV (r.m.s.), frequency f = 50 Hz.

Task
Calculate the electric field stress distribution and C1 and C2 capacitances.

Solution
The aluminium foil is placed between the oil impregnated paper layers. The foil thickness (0.025 mm) is much lower than the spacing between foil layers (~1 mm). The aluminium foil is represented by the edge with a floating potential boundary condition assigned.
The condenser grading is designed to maintain the same capacitance between foil layers. It is achieved by varying the foil layers length and the spacing between the foil layers. The last foil layer in the condenser grading is grounded. The layer before the last is used to connect that diagnostic tap. This layer has a thickness of 0.13 mm and is modelled as is.

Normally the tap foil layer is grounded. To measure the capacitance we should repeat the on site experiment: connect the voltage source and measure the current. The C1 capacitance is measured between the diagnostic tap and the conductor. The C2 capacitance is measured between diagnostic tap and the flange.
We calculate the capacitance using the stored electric field energy value: Capacitance = 2 * Energy / (Potential difference) ²

In AC problems we should specify magnitude |U| of the sinusoidal voltage that is root mean square value U~ times square root of 2: |U| = U~ * √2.

Results

The maximum value of electric field stress in the insulation is 2.1 kV/mm.

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