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.
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.
Specify the relative permittivity of the bushing insulator.
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.
Specify the grounding boundary condition on the surface in contact with the oil tank.
Generate a mesh and solve the model.
generateMesh(model); R = solve(model)
R = ElectrostaticResults with properties: ElectricPotential: [40956x1 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);