Dynamism of interconnected channels in water treed polyethylene under a constant voltage

As the ac loss current containing higher order harmonic waves is able to be detected even in a non-penetrated water treed sample, the detection of the 3rd harmonic wave has a potential for the diagnosis of CV cables. The authors have presented a model where current density j through channels interconnecting micro-voids is assumed to depend on electric field E asj=(σ₀/h)·sinh (h·E), where h is a parameter which characterizes the electric field dependence of j and σ₀ is the conductivity in low electric fields. Currents of the fundamental and 3rd harmonic waves estimated by Fourier analysis have been numerically calculated by solving a non-linear differential equation of the equivalent circuit based on the model. The numerical results give a good agreement with the changes of the observed magnitudes of fundamental and 3rd harmonic waves, I₁ and I ₃ and their phase angles θ₁ and θ ₃, respectively, for the application of a constant voltage. It has been concluded that the length of interconnected channels in the water treed region grows with time after the application of a constant voltage