The traditional DGA (Dissolved Gas Analysis) diagnosis method does not consider the dependence between fault characteristic gases and uses the relationship between gas ratio coding and fault type to make the decision. As a tool of the dependence mechanism between variables, a copula function can effectively analyze the correlation between variables when it cannot determine whether the linear correlation coefficient can correctly measure the correlation between variable relationships. In this paper, the edge variable of a copula function is selected from the fault characteristic gas of a transformer, and the distribution type of the edge variable is fitted at the same time. Then, Bayesian estimation with the Gaussian residual likelihood function is used to fit the parameters of a copula function and a copula function is selected to describe the optimal dependence of the fault characteristic gas of transformer. The relationship between a copula function and the state of transformer is studied. The results show that the copula function boundary with hydrocarbon gas as edge variable can divide the transformer as healthy or defective state. When the cumulative distribution probability (CDF) value of the dissolved gas in the oil in the copula function is close to 0.8, the fluctuation of its gas concentration leads to a sharp change in the probability. Therefore, the analysis of dissolved gas in oil based on a copula function can be used as a powerful technical solution for oil-immersed power transformer fault diagnosis.

A moisture sensing technique for real-time monitoring of the moisture content in transformer oil based on an S-taper fiber structure, is proposed and experimentally demonstrated, with the advantages of high sensitivity, excellent repeatability, simple fabrication, compact structure and resistance to ambient temperature variation. By analyzing the physical model of the S-taper fiber, the quantitative relationship between the wavelength change of the transmission dip in the transmission spectrum of the S-taper fiber and the moisture content is established. Then the S-taper fibers with different structural parameters, such as the waist diameter and the axial offset, were fabricated in the lab, and actual measurements in transformer oil samples with different moisture content are carried out. The results show that the transmission dip experiences a red-shifts with decreasing moisture, which could be used to correlate/trace moisture content. It is demonstrated that the S-taper fiber achieves higher detection sensitivity with a decreasing waist diameter or increasing axial offset. For the Staper fiber with a waist diameter of 50 μm and an axial offset of 110 μm, the sensitivity and the lower detection limit reach up to 0.48 nm/ppm and 2.19 ppm, respectively. Therefore, the S-taper fiber sensor could effectively in-situ monitor the moisture content in the transformer oil in real-time, which helps to detect the insulation damp problem in the early stage of the transformer in time and ensure its long-term safe operation.

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