A dielectric response change after drying is useful evidence only when the comparison conditions are understood. The transformer may be warmer, the oil may have been processed, and the terminal boundary may differ. Those changes can alter the curve without uniquely measuring removed paper water. [1]
Match the state or quantify the mismatch
| Input | Before/after record | Why it matters |
|---|---|---|
| Temperature | Representative value, stability and gradients | Relaxation and conductivity shift |
| Connections and guarding | Same insulation boundary | Different paths produce different responses |
| Liquid condition | Replacement, filtration and conductivity evidence | Oil contribution may change |
| Prior test history | Charging and relaxation record | Initial polarization may differ |
| Analysis model | Same applicable library and definitions | Software choices may move the estimate |
Compare measured curves before fitted numbers
Inspect capacitance, loss and other retained measured quantities over the common reliable window. Examine repeatability and frequency-dependent changes. A shift at one end of the curve may be more consistent with changed conductivity or history than a uniform material interpretation.
For an illustrative difference Δy = yafter − ybefore, independent standard uncertainties combine as √(uafter² + ubefore²). Shared calibration or processing can create covariance, so independence must be justified. The uncertainty calculation does not attribute the difference to moisture.
Combine standard uncertainties with covariance where effects are correlated; repeatability alone does not include all systematic contributions. [2]
Test the significance of the matched change
Assumptions: matched 0.1 Hz results at 20 °C before and after drying are 0.020 and 0.016, with independent standard uncertainties 0.001 and 0.0015. Difference is −0.004 and uΔ = √(0.001² + 0.0015²) = 0.001803. With assumed coverage factor 2, the difference interval is −0.007606 to −0.000394, excluding zero. Treat the electrical change as resolved under that measurement model, but do not translate it directly into removed paper water. Confirm liquid processing, charging history and the reference library before making a moisture claim; correlations would require a revised interval. [2]
References
- IEEE, IEEE C57.161-2018, IEEE Guide for Dielectric Frequency Response Test.
- B. N. Taylor and C. E. Kuyatt, NIST Technical Note 1297, Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results, 1994, sections 5 and 6.