Bivariate Modeling of Normalized Energy Intensity of Oil and Paper for Determining the Health Index of In-Service Transformers and Reactors

This article aims at developing a copula model for investigating the dependence structure between normalized energy intensity of oil
$(\mathbf{NE}{\mathbf{I}}_{\mathbf{oil}})$
and normalized energy intensity of paper (
$\mathbf{NE}{\mathbf{I}}_{\mathbf{paper}}).$
The normalized energy index is a quantity that is directly related to the energy dissipated during a fault inside an oil filled transformer and reactor. The
$\mathbf{NE}{\mathbf{I}}_{\mathbf{oil}}$
and
$\mathbf{NE}{\mathbf{I}}_{\mathbf{paper}}$
are derived from real time dissolved gas analysis data of in-service transformer and reactors. Gumbel copula has been used for evaluating the conditional probabilities between the parameters. Results of the copula model indicate that for an increment of 0.5 kJ/kL in
$\mathbf{NE}{\mathbf{I}}_{\mathbf{oil}}$
there is an increment in
$\mathbf{NE}{\mathbf{I}}_{\mathbf{paper}}$
between 1.0 and 2.2 kJ/kL. It demonstrates the importance of considering
$\mathbf{NE}{\mathbf{I}}_{\mathbf{paper}}$
in addition to
$\mathbf{NE}{\mathbf{I}}_{\mathbf{oil}}$
for assessing the fault severity and evaluating the internal condition of liquid and solid insulation of transformer and reactor. Subsequently, the health index of transformers and reactors considering oil parameters,
$\mathbf{NE}{\mathbf{I}}_{\mathbf{oil}}$
and
$\mathbf{NE}{\mathbf{I}}_{\mathbf{paper}}$
have been evaluated thus making it an unique nature of study. Additionally, a range of values of
$\mathbf{NE}{\mathbf{I}}_{\mathbf{oil}}$
and
$\mathbf{NE}{\mathbf{I}}_{\mathbf{paper}}$
has been determined which can be used directly for future study. The study undertaken will help in monitoring, maintenance, and conditioning assessment of the equipment based on NEI values, thereby saving unprecedented failure of in-service transformers and reactors.