Modeling dispersion of partial discharges due to propagation velocity variation in power cables

• We proposed a new model for partial discharge propagation based on a second order polynomial in frequency to model the propagation phase.
• The relationship between the propagation velocity and frequency, as well as the peak reduction and the PD spread due to dispersion, can be now quantified.
• A new scheme is presented to estimate the dependence of the propagation delay and dispersion constant with frequency.

Existing models for partial discharge (PD) propagation based on a single attenuation constant are unable to explain how each frequency component travels with a different propagation velocity. This paper proposes a new model based on a complex propagation term whose real component does not depend on the frequency (f), and whose imaginary part is modeled with a second order polynomial in f. The proposed model explains how the PD is attenuated, delayed, and dispersed due to the fact that each frequency component is differently delayed.A closed-form expression is proposed for the PD peak value and width, and a method to derive the model parameters from a reference model existing in the bibliography. Simulation results show that the peak value and width of the propagated PD pulse are similar to those obtained with the proposed model. Additionally, the proposed model provides the velocity of each PD frequency component, which is crucial to get an accurate estimation of the PD source location.The parameters of the proposed model have been estimated using a vector network analyzer for a XLPE cable. These results have been compared to the measurement obtained in a medium voltage test bench where intentionally induced PDs have been captured and processed, confirming the results of attenuation, delay and dispersion predicted by the proposed model.