Unipolar charge transport in oil-pressboard systems with planar, coaxial cylindrical and concentric spherical electrode geometries

One-dimensional migration-ohmic unipolar analysis of charge transport phenomena in series, two-region, oil-pressboard composite dielectric systems are presented in planar, coaxial cylindrical and concentric spherical electrode geometries with a step current source. Space charge limited injection solutions are presented in the steady state and transients using the method of characteristics to convert the governing partial differential equations into a set of ordinary differential equations that allow analytical solutions as a function of time and space for volume and interfacial surface charge densities, charge trajectories in the oil region, and electric field and voltage drop in oil and pressboard regions. Analytical solutions are compared with some COMSOL Multiphysics numerical solutions as a way of gaining confidence in the correctness and accuracy of our numerical solutions.