Electrostatic Analysis of Transformer Bushing Insulator

This example shows how to compute the electric field intensity in a bushing insulator of a transformer. Bushing insulators must withstand large electric fields due to the potential difference between the ground and the high-voltage conductor. This example uses a 3-D electrostatic model to compute the voltage distribution and electric field intensity in the bushing.

Create an electromagnetic model for electrostatic analysis.

model = createpde("electromagnetic","electrostatic");

Import and plot the bushing geometry.

gmBushing = importGeometry("TransformerBushing.stl");
pdegplot(gmBushing)

Model the surrounding air as a cuboid, and position the cuboid to contain the bushing at its center.

gmAir = multicuboid(1,0.4,0.4);
gmAir.translate([0.25,0.125,-0.07]);
gmModel = addCell(gmAir,gmBushing);

Plot the resulting geometry with the cell labels.

pdegplot(gmModel,"CellLabels","on","FaceAlpha",0.25)

Include the geometry in the model.

model.Geometry = gmModel;

Specify the vacuum permittivity value in the SI system of units.

model.VacuumPermittivity = 8.8541878128E-12;

Specify the relative permittivity of the air.

electromagneticProperties(model,"Cell",1,"RelativePermittivity",1);

Specify the relative permittivity of the bushing insulator.

electromagneticProperties(model,"Cell",2,"RelativePermittivity",5);

Before specifying boundary conditions, identify the face IDs by plotting the geometry with the face labels. To see the IDs more clearly, rotate the geometry.

pdegplot(gmModel,"FaceLabels","on","FaceAlpha",0.2)
view([55 5])

Specify the voltage boundary condition on the inner walls of the bushing exposed to conductor.

electromagneticBC(model,"Face",12,"Voltage",10E3);

Specify the grounding boundary condition on the surface in contact with the oil tank.

electromagneticBC(model,"Face",9,"Voltage",0);

Generate a mesh and solve the model.

generateMesh(model);
R = solve(model)

R = 
  ElectrostaticResults with properties:

      ElectricPotential: [40952x1 double]
          ElectricField: [1x1 FEStruct]
    ElectricFluxDensity: [1x1 FEStruct]
                   Mesh: [1x1 FEMesh]

Plot the voltage distribution in the bushing.

elemsBushing = findElements(model.Mesh,"Region","Cell",2);
pdeplot3D(model.Mesh.Nodes, ...
          model.Mesh.Elements(:,elemsBushing), ...
          "ColorMapData",R.ElectricPotential);

Plot the magnitude of the electric field intensity in the bushing.

Emag = sqrt(R.ElectricField.Ex.^2 + ...
            R.ElectricField.Ey.^2 + ...
            R.ElectricField.Ez.^2);
pdeplot3D(model.Mesh.Nodes, ...
          model.Mesh.Elements(:,elemsBushing), ...
          "ColorMapData",Emag);

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