Estimating the maximum length of water trees using extreme value statistics

The authors discuss a statistical evaluation method for water tree analysis, where only the maximum tree length found in any particular cable sample is measured. The physical justification for the use of extreme value statistics is presented. By treating the maximum tree length as a stochastic variable it is possible to estimate the most probable length of the longest tree in a given length of a cable. The validity of this method was tested on results from water-tree examination of both service and laboratory aged XLPE (cross-lined polyethylene) cables. It is stressed that, in order to obtain stochastic variables of extreme tree lengths, the examined length of a cable has to be adjusted in accordance with the width and density of the water trees. The first asymptotic and the Weibull type distribution functions have been examined. In the case when the water trees exceed about 75% of the insulation wall, the limited Weibull type of distribution may give a better extrapolation than the unlimited first asymptotic distribution function