488 / 2022-03-17 01:08:24

Uncertainty Analysis of Two Gas Measurement DGA Ratios for Improved Diagnostics Applications

DGA,Gas Ratios,PDF

Transformer dissolved gas values are generally measured using on-line dissolved gas analyser (DGA) instruments or through laboratory analysis via manually taken oil samples. However, the gas measurement method implies an unavoidable measurement error. For single or individual measured gas level measurements, x and y, with measurement errors s_x and s_y respectively, the gas ratio R = x/y is assumed to derive from a Gaussian probability density function (PDF), with variance that model the measurement errors. In this scenario, the conventional Gaussian statistical error combination formula is used to calculate the error s_R on the estimate of the true value R₀ = x/y_, which is given by s_R = (x² s_y² + y² s_x²)^1/2/y². In contrast, this paper derives from first principles the correct analytical gas ratio PDF for R = x/y. The correct PDF is demonstrated to be non-Gaussian in nature.


The correct PDF for R is derived and normalised using a = s_x/x₀, b = s_y/y₀ and a = R/R₀. Example PDF distributions for different values of a and b are shown in Figure 1.


It is shown that the correct PDF tends towards a conventional Gaussian PDF with maximum likelihood value R₀ and variance s_R only in the limit when individual gas measurements errors become small e.g. < 5%. For larger measurement errors, the correct PDF is a biased distribution where R is not the maximum likelihood of the PDF. For larger gas measurement variances, the PDF is also shown to have a broader variance than the standard formulae. A de-biasing method to estimate the “true” value R₀ in these circumstances is proposed.

Conclusions

For gas measurement errors greater than 5% the error on the ratio R requires to be adjusted. In addition, the value of R requires to be de-biased to provide a more accurate measurement of the true value