statistical dga limits for ltcs - transformers...

IEEE/PES TC WG C57.139 Apr 2009

Statistical DGA Limits for LTCs

Dr. Jim DukarmDelta-X Research Inc.Victoria BC Canada


Topics

1. Summary of LTC DGA method proposed for IEEE C57.139

2. Percent points as gas ratio DGA limits3. Interpretation of percent-point limits4. Variability of percent-point limits vs percentiles5. Outlier rejection limit U1 as alternative to C0956. Remarks about gas concentration caution limits7. Conclusions


Summary of LTC DGA methodCaution and warning limits for important gas ratios− Examples: ethylene/acetylene, TDHG/acetylene,

ethane/ethylene, methane/acetylene

Caution limits for important gas concentrations− Hydrogen, methane, ethylene, acetylene, possibly also

ethane

No limits exceeded means: no problem foundAny limit exceeded means: investigate− Resample to verify; sample further to seek evidence of

continuation or worsening; check non-DGA information


Percent-point DGA limits for gas ratiosLTC gas ratio values tend to fit a lognormal distribution when no fault is present− Single ratio, one type of LTC, one breathing type− Only calculate ratio where each gas is at least 10 ppm− Define ratio so that "worst" values are large

Do simple outlier elimination to remove fault-related ratio values before deriving limitsCalculate 95th and 99th percent point valuesaccording to a simple formulaUse as Caution and Warning DGA limits


Meaning of percent-point DGA limitsPercent-point limits are the basis for the most common kind of statistical hypothesis testThe test, for LTC DGA, says this:− A ratio value which exceeds the Caution limit is likely to

represent a faulty condition. (Warning / very likely)‏− Only about 5% of ratio values fitting the normal pattern

might exceed the Caution limit. (About 1% / Warning) ‏

Most serious LTC faults generate gas ratio values (or high gas concentrations) high enough to be detected in this way. (This justifies doing DGA).


Percent points vs. percentilesPercentiles are properties of the individual data set.Percent points are properties of a probability distribution whose shape closely fits the data set's histogram.Higher percentiles (like 95th, 99th) depend on a small part of the data set and so are highly variable from one data set to another.Percent points depend on the entire data set and so are less variable from one data set to another.The hypothesis test based on percent points is statistically more powerful than one based on corresponding percentiles.


Variability: percent points & percentilesPercent point limits and percentiles calculated from different data sets for same or similar equipment vary randomlyIt is desirable for statistically derived limits for the same kind of equipment to be consistent from one data set to anotherStatistical limits from large data sets are less variable than from small data setsPercent point limits are less variable than percentiles, for any fixed size of data set


Simulation experiment: N = 500Ten thousand data sets, each of size N = 500, were selected from a fixed lognormal distribution representing "fault free" ethylene/acetylene ratios from a single LTC type.For each of those data sets, the 95th percentile of the data was calculated, and also the 95th percent point of the data set's lognormal approximation.Based on the results for all 10000 data sets, 95% confidence intervals were calculated for the percentiles and the percent points.


Variability of limits for N = 500Red = data 95th percentile Black = 95th percent point



10000 data sets of size N=500 from same population


Simulation experiment: N = 150Ten thousand data sets, each of size N = 150, were selected from a fixed lognormal distribution representing "fault free" ethylene/acetylene ratios from a single LTC type.For each of those data sets, the 95th percentile of the data was calculated, and also the 95th percent point of the data set's lognormal approximation.Based on the results for all 10000 data sets, 95% confidence intervals were calculated for the percentiles and the percent points.


Summary and comparison of resultsN = 150 95% confidence interval

low high spreadc095 0.89 1.20 ±16.1%c099 1.31 1.90 ±20.5%

p095 0.90 1.32 ±21.3%p099 1.15 2.34 ±42.4%

N = 500 95% confidence intervallow high spread

c095 0.96 1.13 ±8.4%c099 1.45 1.77 ±10.6%

p095 1.00 1.23 ±10.8%p099 1.44 2.07 ±19.8%


Outlier rejection limit U1 as alternativeSometimes the data distribution is "pathological" and the percent point limits are clearly not useful− Very close together, extremely large or small

In all non-pathological lognormal data sets, the U1 outlier limit (Q3 + 1.5*IQR) is close to C095By its nature, U1 is designed to always be a good dividing line between usual & unusual valuesLike percent points, U1 depends on most of the data set, so is less variable than an upper percentile.


Outlier rejection limit U2 for gasesThe distributions of LTC key gas concentrations are often irregular and do not look like subsets of a lognormal or other standard distribution.The U2 outlier rejection limit (Q3 + 3*IQR) is a standard statistical dividing line between "typical" and "atypical" values in a data setU2 seems a better candidate for a Caution limit than U1, which "rejects" more valuesU2 depends on most of the data set, so is less variable than an upper percentile.


ConclusionsA percent-point limit for gas ratio DGA is the standard statistical tool for this kind of test and is statistically more likely to detect a real fault than a percentile-based limit.Percent-point limits are more consistent from one data set to another than percentile-based limitsU1 is less variable than an upper percentile, so is more appropriate as an alternative ratio limitSimilarly, U2 (for gas concentrations) is more appropriate as a Caution limit than an upper percentile.

statistical dga limits for ltcs - transformers...

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