Using the ‘Universal Relaxation Law’ to characterise water tree degradation in XLPE insulated cables

In order to access the severity of degradation in a water tree affected cable, it is necessary to obtain a physical representation of the insulation. This is especially the case when trying to determine the risk of failure of the cable, or the remaining life, which is dependant on the length of the longest water tree in the insulation. Generally, there has not been a large effort found in published materials regarding the modelling of polarisation in water tree affected insulation. In fact, in the cases where modelling has been attempted, the extended Debye model is often used. However, as will be discussed in this paper, the Debye model and its electrical circuit equivalent has limited physical relevancy in its standard uses. An alternative polarisation model is the Universal Relaxation Law (URL). This paper will attempt to construct a starting point whereby a direct physical-based polarisation model can proceed from. This approach will invoke the URL to interpret polarisation mechanisms seen in frequency domain measurements on new and field aged cables, and it will also involve the use of a distributed Debye type model, with a physical link, to describe non-interacting, ionic “dipoles” which are likely to be active in water tree structures.