Refining bushing power factor and capacitance analysis through statistics
Power factor and capacitance are two types of tests employed in diagnostic analysis of high-voltage bushings. The former is mainly used to measure the dielectric losses of the bushing insulation, which are related to contamination and deterioration of the solid and liquid insulating materials. Meanwhile, the latter is used to detect physical problems such as shorted capacitance layers and oil leaks.
Historically, the limits employed in diagnostic analysis of high-voltage bushings rely on general rules. They include a comparison of test results with a benchmark value (e.g., the nameplate or the first measurement), the use of absolute limits, and trending of empirical data over time. This approach, while useful, has its limitations. It relies on similar or the same limits being applied across different types of bushings. For example, some manufacturers recommend that the power factor value corrected to 20 °C should not exceed the value of two or three times the benchmark. Meanwhile, a limit of power factor ≤ 0.5 % is given in IEEE Std C57.19.01TM-2017 for oil-impregnated paper-insulated bushings. For capacitance, a 5 – 10 % increase / decrease in measured values over the benchmark value is used as an action limit by most users.
Typical approach for the diagnostic analysis of the high-voltage bushings uses power factor and capacitance measurements; obtained values are then compared with the benchmark data
Doble’s bushing statistical analysis tool is available in the web version of the Doble Test Assistant (DTAWeb) application, which uses statistics to open the door to a significant enhancement of the existing approach. The tool is used to tailor limits by determining what is statistically normal for a specific type, manufacturer, and voltage rating of a bushing. This is accomplished by having access to the Doble’s database of more than 6 million tests. More precisely, the tool computes the deviations of power factor and capacitance from a benchmark value for a particular population of specific bushing types based on a DTAWeb query. It is followed by the determination of the probability distribution that best fits the selected test data. Once the data is characterized by probability, the limits can be applied by using common statistics. This includes deriving the mean, and standard deviation followed (if needed) by zooming in on the region(s) of higher data concentration where the latter depends on the shape of the best probability distribution. The tool also allows the determination of the probability (i.e., ‘likelihood’) for a given bushing type to have changes in power factor or capacitance falling within a certain range.
2. Basic concepts of probability and statistics
Before discussing the statistical treatment of the empirical (observed) data, it is instructive to revisit the basic probability and statistical concepts. This, in turn, allows for a meaningful interpretation of the observed data as presented in the case studies.