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Plane capacitor dielectric loss

QuickField simulation example

This is an example of the plane capacitor simulation, performed with QuickField software.

Engineering question
How to find electric field in multilayer HV insulation

Engineering answer
Set up a plane-parallel QuickField AC Conduction problem for a multilayer high-voltage insulation system and evaluate electric field from computed field results.

Typical applications
multilayer HV insulation systems, cable insulation structures, bushing insulation assemblies

Problem Type
Plane-parallel problem of AC conduction.

Geometry
Plane capacitor Capacitor with non-ideal dielectric can be replaced by electric circuit with ideal capacitor and resistivity connected in parallel. 10 mm 0.1 mm 10 mm GND U Dielectric

Given
Relative permittivity of dielectric ε = 10.
Voltage U = 5 V, frequency f = 1000 kHz.
Loss tangent tan(δ) = 0.01.

Task
Calculate dielectric loss in the plane capacitor.

Solution
To calculate dielectric losses we specify effective value of electric conductivity for dielectric, that is a function of loss tangent, frequency and relative permittivity:
g = 2πf·εε0·tan(δ) = 2·3.142·1000000·10·(8.854·10-12)·0.01 = 5.56·10-6 S/m.

Results
Active power loss is PA = 0.0695 mW per 10 mm³.
Electric current vectors and electric potential distribution in plane capacitor
Electric current vectors and electric potential distribution in plane capacitor