Statistical Analysis of Breakdown Voltages in Virgin and Aged LDPE Using Johnson S<sub>B</sub> and Weibull Distribution

Abstract

Polymeric material such as low density polyethylene (LDPE) has been used for decades as insulating material. Any polymeric material will experience degradation after prolonged application of high electrical stresses. Deeper understanding of the long term electrical degradation of the insulating material is necessary to predict the life of high voltage cable. Electroluminescence method (EL) is used to detect the breakdown voltages of thin film LDPE. This method utilizes a Peltier cooled electron multiplying charge coupled device (EMCCD) camera to detect the breakdown of the sample. Statistical distribution of the AC breakdown voltages of 100μm virgin and aged LDPE has been analysed. Comparison for the best fitted distribution was made for Weibull distribution and Johnson SB distribution using Anderson-Darling (A2) goodness-of-fit and Kolmogorov-Smirnov (D) goodness-of-fit (GOF). Johnson SB is rarely used in high voltage engineering application. The probability density function (PDF) and the cumulative density function (CDF) for both distributions are defined in this article. The statistical parameters used are estimated based on Maximum Likelihood Estimation (MLE) for both distributions. Based on the statistical analysis, it is observed that Johnson SB provide better fitting than Weibull distribution with lower fitting error and that 3-parameter Weibull is much better fitting than 2-parameter Weibull distribution for most cases. It is also found that the median breakdown voltage of LDPE samples decreases with increasing aging temperature.