Bivariate Modelling of Normalized Energy Intensity of Oil and Paper for Accessing the Fault Severity of Transformer and Reactors

This paper aims at developing a copula model for investigating the dependence structure between normalized energy intensity of oil $(\mathrm{N}\mathrm{E}\mathrm{I}_{\mathrm{o}\mathrm{i}1})$ and normalized energy intensity of paper $(\mathrm{N}\mathrm{E}\mathrm{I}_{\mathrm{p}\mathrm{a}\mathrm{p}\mathrm{e}\mathrm{r}})$. The $\mathrm{N}\mathrm{E}\mathrm{I}_{\mathrm{o}\mathrm{i}1}$ and $\mathrm{N}\mathrm{E}\mathrm{I}_{\mathrm{p}\mathrm{a}\mathrm{p}\mathrm{e}\mathrm{r}}$ are derived from real time dissolved gas analysis data of in-service transformer and reactors having age more than a decade. Considering the positive correlation and goodness-of-fit, Gumbel copula is found to be most suitable for modeling the bivariate joint distribution. Results of the copula model indicate that for an increment of $0.5\mathrm{k}\mathrm{J}/\mathrm{k}\mathrm{L}$ in $\mathrm{N}\mathrm{E}\mathrm{I}_{\mathrm{o}\mathrm{i}1}$ there is an increment in $\mathrm{N}\mathrm{E}\mathrm{I}_{\mathrm{p}\mathrm{a}\mathrm{p}\mathrm{e}\mathrm{r}}$ between 1.0 and $2.2\mathrm{k}\mathrm{J}/\mathrm{k}\mathrm{L}$. It demonstrates the importance of considering $\mathrm{N}\mathrm{E}\mathrm{I}_{\mathrm{p}\mathrm{a}\mathrm{p}\mathrm{e}\mathrm{r}}$ in addition to $\mathrm{N}\mathrm{E}\mathrm{I}_{\mathrm{o}\mathrm{i}1}$ for assessing the fault severity and evaluating the internal condition of liquid and solid insulation of transformer and reactor. The study undertaken will help in monitoring, maintenance, and conditioning assessment of the equipment based on the NEI values, which will further help in saving unprecedented failure of in-service transformer and reactors.