METHOD AND SYSTEM FOR ASSESSMENT OF FAULT SEVERITY, RISK EXPOSURE, AND GASSING STATUS FOR LIQUID-FILLED HIGH-VOLTAGE APPARATUS

Abstract

A method for assessment of fault severity, risk exposure, and gassing status for a liquid-filled high-voltage apparatus involves taking a series of samples from a liquid-filled high-voltage apparatus at intervals over a time period and subjecting those samples to gas analysis to measure and record the concentrations of selected gases. A fault energy index is computed for each of the insulating liquid samples based upon the concentrations of the selected dissolved gases for that sample. Gassing events are identified where there is a continuous production of fault gases for a time period causing an increase in the fault energy index. A computer is used to calculate a severity of each gassing event and a cumulative severity of multiple gassing events collectively, where each severity is a based on probabilities of failure provided by a reliability model comprising a random variable representing failure-related values of the fault energy index. Risk exposure is calculated by multiplying a severity value by a cost factor such as replacement cost or MVA rating. The gassing status of an apparatus is a value suitable for ranking apparatus and is determined on the basis of the severity and timing of gassing events of the apparatus.

Claims

1. A Method for Assessment of Fault Severity, Risk Exposure, and Gassing Status for a Liquid-Filled High-Voltage Apparatus, comprising: taking a series of samples from a liquid-filled high-voltage apparatus at intervals over a time period; performing a gas analysis on each of the samples to measure concentrations of selected gases; storing in electronic form (called the database) a data record for each sample containing the gas concentration measurement values pertaining to that sample as well as information (sufficient for calculating time intervals between samples) as to when the sample was collected. programming a computer: to calculate a fault energy index value for each of any number of selected sample data records in the database based upon the gas concentrations in the data record that are required for the calculation; to search the sample data records pertaining to a selected apparatus in the database and tabulate the initial and final dates and initial and final fault energy index values of time intervals (gassing events) in which there is production of fault gas by the apparatus leading to a net increase in the fault energy index spanning the time period between the initial date and the final date; to calculate a severity of a gassing event proportional to a conditional probability of failure derived from a reliability model comprising a random variable representing failure-related values of the fault energy index; to calculate a gassing status code for the apparatus based on the time of occurrence and the severity of gassing events for that apparatus.

2. The method of claim 1, wherein the samples are representative insulating liquid samples taken from the apparatus and the gas concentrations are dissolved-gas concentrations.

3. The method of claim 1, wherein the samples are gas samples taken from a gas space of the apparatus and the gas concentrations measured for each sample are concentrations of selected gases in the gas space.

4. The method of claim 3, wherein the gas concentrations in the gas space are converted to dissolved-gas concentrations in the insulating liquid that would be expected when the gas concentrations in the gas space and the liquid are in equilibrium.

5. The method of claim 1, wherein for the selected apparatus a cumulative severity of selected gassing events is calculated, proportional to a conditional probability of failure derived from a reliability model comprising a random variable representing failure-related values of the fault energy index.

6. The method of claim 1, wherein the severity of an individual gassing event is multiplied by a predetermined cost consequence of a failure of the liquid-filled high-voltage apparatus, to calculate a risk exposure value.

7. The method of claim 5, wherein the cumulative severity of multiple gassing events is multiplied by a predetermined cost consequence of a failure of the liquid-filled high-voltage apparatus, to calculate a risk exposure value.

8. The method of claim 1, wherein the selected apparatus is assigned a gassing status code, suitable for ranking apparatus and determined on the basis of the severity and order of occurrence of selected gassing events of that apparatus.

9. The method of claim 1, wherein the computer is programmed to raise an alert if acetylene concentration increases during a time period spanned by multiple samples of an apparatus.

10. The method of claim 1, wherein the liquid-filled high-voltage apparatus is a mineral oil filled power transformer and the energy index is based on methane, ethylene, and acetylene concentrations.

11. The method of claim 10, wherein the fault energy index is also based on ethane concentration.

12. The method of claim 1, wherein the liquid-filled high-voltage apparatus is a mineral oil filled power transformer and the energy index is based on the carbon monoxide concentration.

13. The method of claim 12, wherein the fault energy index is also based on carbon dioxide concentration.

14. The method of claim 1, wherein multiple fault energy indexes are calculated and assessed.

15. A System for Assessment of Fault Severity, Gassing Status, and Risk Exposure for a Liquid-Filled High-Voltage Apparatus, comprising: a sampler for taking a series of samples from a liquid-filled high-voltage apparatus at intervals over a time period; a gas analyzer for measuring the concentrations of selected gases in samples; a computer database for storing sample data records comprising the gas concentration measurement values for a sample as well as information (sufficient for calculating time intervals between samples) as to when the sample was collected; a computer processor programmed: to calculate a fault energy index value for each of any number of selected samples in the database based upon the gas concentrations that are required for the calculation; to search the sample data pertaining to a selected apparatus in the database and tabulate the initial and final dates and initial and final fault energy index values of time intervals (gassing events) in which there is production of fault gas by the apparatus leading to a net increase in the fault energy index spanning the time period between the initial date and the final date; to calculate a severity of a gassing event proportional to a conditional probability of failure derived from a reliability model comprising a random variable representing failure-related values of the fault energy index.

16. The system of claim 14, wherein multiple fault energy indexes are calculated and assessed.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0049] These and other features will become more apparent from the following description in which reference is made to the appended drawings, the drawings are for the purpose of illustration only and are not intended to be in any way limiting, wherein:

[0050] FIG. 1 is a block diagram of the system of the invention.

[0051] FIG. 2 is a bar chart showing the standard enthalpies of formation of four hydrocarbon gases from n-octane.

[0052] FIG. 3 is a bar chart showing the standard enthalpies of formation of two carbon oxide gases from glucose, a model of a cellulose monomer.

[0053] FIG. 4 is a probability density chart for the lognormal random variable of failure-related values of NEI-HC.

[0054] FIG. 5 is a cumulative density (failure probability) chart for the lognormal random variable of failure-related values of NEI-HC.

[0055] FIG. 6 is a probability density chart for the lognormal random variable of failure-related values of NEI-T.

[0056] FIG. 7 is a cumulative density (failure probability) chart for the lognormal random variable of failure-related values of NEI-T.

[0057] FIG. 8 is a probability density chart for the lognormal random variable of failure-related values of NEI-CO.

[0058] FIG. 9 is a cumulative density (failure probability) chart for the lognormal random variable of failure-related values of NEI-CO.

[0059] FIG. 10 is a table of fault gas concentration data for the transformer in the example. Each row of the table corresponds to one sample.

[0060] FIG. 11 is a hydrocarbon gas NEI (NEI-HC) time series chart, with NEI-HC gsssing events marked with dashed rectangles, for the transformer in the example.

[0061] FIG. 12 is a table in which each row describes an NEI-HC gassing event shown in FIG. 11.

[0062] FIG. 13 is a carbon oxide gas NEI (NEI-CO) time series chart, with one NEI-CO gsssing event marked with a dashed rectangle and another NEI-CO gassing event marked with a dotted rectangle, for the transformer in the example.

[0063] FIG. 14 is a table in which each row describes an NEI-CO gassing event shown in FIG. 13.

DETAILED DESCRIPTION

[0064] A method and system for assessment of fault severity, risk exposure, and gassing status for liquid-filled high-voltage apparatus will now be described with reference to FIG. 1 through FIG. 14.

[0065] The method of this invention does not assume or depend on any particular units or standard conditions used for expressing gas concentrations.

Method:

[0066] The method requires that at least one fault energy index, relating to one component material of the internal insulation of the apparatus, be used.

[0067] Preferred embodiments of the method use one fault energy index for each insulation component material of the apparatusfor example, one for the liquid insulation and another one for the cellulosic (paper and wood and pressboard) insulation in a transformer.

[0068] Let A be a liquid-filled high-voltage apparatus subjected to sampling and gas analysis from time to time. The method requires that gas concentration measurement values obtained by gas analysis of a sample be recorded, along with information about when the sample was collected, in a persistent data structure, referred to as a sample data record, which in turn is recorded in a persistent data store, referred to as a database.

[0069] In preferred embodiments of the method, the database contains multiple sample data records for each of many apparatuses.

[0070] For each fault energy index E used for apparatus A, an observation of E is defined to be a value for E calculated using gas concentration measurement values in a sample data record for A. Thus, each observation of E is associated with exactly one sample data record.

[0071] An E-gassing event of a specified apparatus A is defined to be a time interval in which there is production of fault gas by the apparatus A leading to a net increase in the fault energy index E spanning the time between the initial date t.sub.1 and the final date t.sub.2 of the time interval. Correspondingly there are an initial value x.sub.1 and a final value x.sub.2 of E during that time interval.

[0072] An observation of E is defined to be failure-related if (a) it is associated with a sample collected from A within the time span of an E-gassing event, and (b) that sample is the last one collected from A within one routine sampling interval before A experienced a forced outage due to failure or impending failure of A.

[0073] The method of this invention requires, for a specified kind of appratus and for each fault energy index E used in connection with that kind of apparatus, a means of computing failure probability F.sub.E(x) as an increasing continuous function of values x of E, where F.sub.E(x) denotes the proportion of a population of that kind of apparatus that is expected to fail with E less than or equal to the value x. Such a means can always be understood mathematically as defining F.sub.E(x) as the cumulative distribution function for a random variable X.sub.E such that F.sub.E(x)=Pr(X.sub.Ex). The random variable X.sub.E is thus a reliability model for failure-related observations of E.

[0074] According to the method of the invention, the severity of an E-gassing event in which E increases from x.sub.1 to x.sub.2 is defined to be the conditional probability

sev.sub.E(x.sub.1, x.sub.2)=Pr(x.sub.1<X.sub.Ex.sub.2|X.sub.E>x.sub.1) (4)

[0075] Since F.sub.E is the cumulative distribution function for X.sub.E, it follows that the severity (4) of a gassing event in which E increases from x.sub.1 to x.sub.2 can be calculated from F.sub.E thus:

[00003]$\begin{array}{cc}{\mathrm{sev}}_E\left(x_1,x_2\right)=\frac{F_E\left(x_2\right)-F_E\left(x_1\right)}{1-F_E\left(x_1\right)}& \left(5\right)\end{array}$

[0076] Let G.sub.1, G.sub.2, . . . , G.sub.n be a sequence of E-gassing events for apparatus A, where for each i between 1 and n the initial and final values of E.sub.i are respectively a.sub.i and b.sub.i, and where none of the events overlaps in time with any of the other events, and where G.sub.1 is the earliest event. Although a.sub.i<b.sub.i for all i, it is possible that due to gas loss from the apparatus A, b.sub.i>a.sub.i+1 for some values of i. That is, the E value ranges of some of the events may overlap if A is not gas-tight.

[0077] According to the method of the invention, the cumulative severity of a sequence G.sub.1, G.sub.2, . . . , G.sub.n of E-gassing events for apparatus A as described above is defined to be the conditional probability

csev.sub.E(a.sub.1, a.sub.2, . . . , a.sub.n; b.sub.1, b.sub.2, . . . , b.sub.n)=Pr(a.sub.1<X.sub.Eb|X.sub.E>a.sub.1) (6)

where b is:

[00004]$\begin{array}{cc}b=a_1+\underset{1in}{\overset{}{.Math.}}.Math.\left(b_i-a_i\right)& \left(7\right)\end{array}$

[0078] It follows that the cumulative severity of a sequence G.sub.1, G.sub.2, . . . , G.sub.n of E-gassing events for apparatus A as described above can be calculated thus:

csev.sub.E(a.sub.1, a.sub.2, . . . , a.sub.n; b.sub.1, b.sub.2, . . . , b.sub.n)=sev.sub.E(a.sub.1, b) (8)

where b is defined as in (7) above.

[0079] Let c be any failure cost factor (such as estimated replacement cost) for apparatus A. According to the method of the invention, the risk exposure due to an E-gassing event for A with initial value E=x.sub.1 and final value E=x.sub.2 is defined to be the product c.Math.sev.sub.E(x.sub.1, x.sub.2).

[0080] Let c be any failure cost factor (such as estimated replacement cost) for apparatus A. According to the method of the invention, the cumulative risk exposure due to a sequence of E-gassing events for A with cumulative severity s is defined to be the product c.Math.s. Note that risk exposure is not an indication of the risk of imminent failure or of increased failure rate.

[0081] The method of the invention defines the gassing status code of an apparatus A to be a code number assigned to A on the basis of the pattern and severity of the gassing events of A. Let every E-gassing event of an apparatus A, for every fault energy index E used for assessing A, be called a gassing event of A. The intention of the gassing status code is to provide a numerical ranking for apparatus with respect to the apparent degree of need for surveillance, maintenance, or mitigative action, in the style of the condition code defined in IEEE Std C57.104-2008. A gassing status code value of 0 denotes no data available; 1 denotes no significant gassing ever; 2 denotes no recent significant gassing event; and 3 denotes recent significant gassing. Optionally status value 4 can be defined as recent extreme gassing. The method does not specify how to define the significance of a gassing event. It could be based, for example, on severity or on risk exposure.

[0082] A preferred embodiment of the method defines the gassing status of an apparatus A as follows. [0083] 1. No significant gassing event ever. [0084] 2. There was at least one significant gassing event, but none recently (where the preferred meaning of recently for this purpose is within one routine sampling interval). [0085] 3. There is a recent gassing event of low to moderate severity (severity less than a predefined limit such as 2 [0086] 4. There is a recent gassing event of high severity (severity equal to or exceeding a predefined limit as above).

System:

[0087] Because of the large volume of data that must be interpreted to assess the results of periodic gas analysis testing of a fleet of liquid-filled high-voltage apparatus in an electric utility or an industrial plant, for example, it is necessary to have an organized system to acquire and organize the data, perform the assessment according to the method, and generate summary results for review by experts such as maintenance engineers and asset managers.

[0088] Referring to FIG. 1, the system used to implement the method includes a means of sampling apparatus 10, a gas analyzer 20 to perform the gas analysis on each sample collected, a database 30 for recording the analysis data, and a computer processor 40 programmed to calculate outputs 50, comprising the energy indexes, tabulated gassing events, gassing event severities and cumulative severities, and E-status of the apparatus for each fault energy index E employed. Based on those calculations, the computer can provide notifications and summary and detail results to the expert users.

Working ExampleFault Energy Indexes

[0089] For the case of power transformers filled with mineral oil, three fault energy indexes are useful:

[0090] The hydrocarbon gas normalized energy intensity (NEI-HC) is defined as

[00005]$\begin{array}{cc}\mathrm{NEI}.Math.\text{-}.Math.\mathrm{HC}=\frac{77.7\left[{\mathrm{CH}}_4\right]+93.5\left[C_2.Math.H_6\right]+104.1\left[C_2.Math.H_4\right]+278.3\left[C_2.Math.H_2\right]}{22400}& \left(9\right)\end{array}$

[0091] The Duval triangle gas normalized energy intensity (NEI-T) is defined as

[00006]$\begin{array}{cc}\mathrm{NEI}.Math.\text{-}.Math.T=\frac{77.7\left[{\mathrm{CH}}_4\right]+104.1\left[C_2.Math.H_4\right]+278.3\left[C_2.Math.H_2\right]}{22400}& \left(10\right)\end{array}$

[0092] The hydrocarbon gas normalized energy intensities for mineral oil defined in formulas (9) and (10) were introduced in a paper by F. Jakob and J. Dukarm titled Thermodynamic estimation of transformer fault severity and published in IEEE Transactions on Power Delivery in 2015.

[0093] The carbon oxide gas normalized energy intensity (NEI-CO) is defined as

[00007]$\begin{array}{cc}\mathrm{NEI}.Math.\text{-}.Math.\mathrm{CO}=\frac{101.4\left[\mathrm{CO}\right]+30.2\left[{\mathrm{CO}}_2\right]}{22400}& \left(11\right)\end{array}$

[0094] In each of the three formulas above, the bracketed gas names denote dissolved-gas concentrations (L/L) in mineral oil, measured in the same sample and expressed at standard temperature and pressure (for example, 273.15 K and 101.325 kPa). (For this example, concentrations in free gas would need to be converted to corresponding dissolved-gas concentrations by multiplying them by the respective partition coefficients.) The numeric coefficients of the gas concentrations in the formulas are the respective standard enthalpies of formation (kJ/mol), from n-octane (C.sub.8H.sub.16, a model for a typical mineral oil molecule) for the hydrocarbon gases (see FIG. 2), and from glucose (C.sub.6H.sub.12O.sub.6, a model for the monomer of cellulose) for the carbon oxide gases (see FIG. 3). The denominator of 22400 in each case is a units conversion factor converting from (kJ/mol).Math.(L/L) to kJ/kL or, equivalently, kJ.Math.m.sup.3.

[0095] In situations where all of the gas concentrations required for both NEI-HC and NEI-CO are provided, NEI-HC is used for assessment of faults affecting the insulating oil, and NEI-CO is used for the assessment of faults affecting the solid (cellulosic) insulation.

[0096] NEI-T is used instead of NEI-HC for transformers that are suspected of ethane stray gassing, i.e., production of excessive amounts of ethane gas under moderate operating temperatures where no abnormality is suspected. In those cases, NEI-T is used for assessment of faults affecting the insulating oil, and NEI-CO is used for the assessment of faults affecting the solid (cellulosic) insulation.

[0097] NEI-T is also used instead of NEI-HC when the source of gas analysis data is an online gas monitor that measures the concentrations of methane, ethylene, and acetylene but not ethane.

[0098] NEI-CO can be used only when the concentrations of both carbon monoxide and carbon dioxide are being measured.

Working ExampleReliability Model for a Fault Energy Index

[0099] A data set was compiled from gas analysis and transformer failure data supplied by two large USA electric utilities, comprising 7151 sample data recordsone for each of 7151 transformersof the form (x, t.sub.x), where x is the last observed in-service value of NEI-HC (defined above in formula (9), and t.sub.x=1 if (a) the respective transformer experienced a failure-related forced outage within one year of the date of the sample and (b) the sample was part of an NEI-HC gassing event. Otherwise, t.sub.x=0. Of the 7151 sample records, 101 were terminal, i.e., had t.sub.x=1.

[0100] A standard statistical procedure called maximum likelihood estimation (MLE) was used to fit various random variable types (including exponential, Weibull, and lognormal) to the data to estimate the type and parameters for the best-fitting probability models for the failure-related values of NEI-HC. The MLE procedure takes into account both the terminal (t.sub.x=1) and the nonterminal (t.sub.x=0) observed values to obtain the best fit of a specified type of random variable to the data. For NEI-HC the best fitting type of random variable for the data was lognormal.

[0101] For the fault energy indexes NEI-T (formula (10)) and NEI-CO (formula (11)), respective data sets were compiled as described for NEI-HC above. For both NEI-T and NEI-CO, MLE showed that the best fitting type of random variable for the data was lognormal.

[0102] If X is a lognormal random variable, then ln(X) is a normal random variable. Conventionally the parameters (mean) and (standard deviation) of that associated normal random variable are used as the parameters to describe the lognormal random variable. The probability density function for a lognormal random variable X with parameters and in that sense is

[00008]$\begin{array}{cc}{f}_X\left(x\right)=\frac{1}{.Math..Math.x}.Math.\left(\frac{\ln \left(x\right)-}{}\right)& \left(12\right)\end{array}$

where x >0 and is the density function of the standard normal random variable. The cumulative distribution function (also called the failure probability function or reliability function in the context of reliability statistics) for a lognormal random variable X with parameters and is

[00009]$\begin{array}{cc}{F}_X\left(x\right)=\mathrm{Pr}\left(Xx\right)={}_0^x.Math.f_X\left(t\right).Math.\mathrm{dt}=\left(\frac{\ln \left(x\right)-}{}\right)& \left(13\right)\end{array}$

where x>0 and is the cumulative distribution function of the standard normal random variable.

[0103] The parameters of the fitted lognormal random variables found by MLE were =4.507 and =2.231 for NEI-HC; =4.119 and =2.235 for NEI-T; and =6.334 and =1.321 for NEI-CO. The corresponding probability density graphs are shown in FIG. 4 for NEI-HC, FIG. 6 for NEI-T, and FIG. 8 NEI-CO. The corresponding failure probability graphs are shown in FIG. 5 for NEI-HC, FIG. 7 for NEI-T, and FIG. 9 for NEI-CO.

Working ExampleAssessment of a Power Transformer

[0104] FIG. 10 is a table showing the gas analysis data, one row per oil sample, for a 140 MVA mineral-oil-filled power transformer. For this transformer the NEI-HC cumulative severity is 3.39% based on two NEI-HC gassing events. The NEI-CO cumulative severity is 0.23% based on two NEI-CO gassing events. The gassing status of the transformer is 3 because there is at least one recent gassing event. In all the gassing events noted, the apparent fault type is T1 (overheating below 300 degrees Celsius). The risk exposure based on NEI-HC cumulative severity and the MVA rating is (0.0339)(140)=4.67 MVA. Risk exposure based on NEI-HC cumulative severity and an assumed $5 million cost of failure is (0.0339)(5000000)=$169,500an amount sufficient to warrant an investigation and possible mitigative action.

[0105] FIG. 11 is a time series graph showing NEI-HC vs. time for the transformer. The dashed boxes superimposed on the graph mark NEI-HC gassing events. FIG. 12 is a table, each row of which describes an event indicated in FIG. 11.

[0106] Similarly, FIG. 13 is a time series graph showing NEI-CO vs. time for the same transformer. A dashed box indicates an NEI-CO gassing event, and a dotted box indicates another NEI-CO gassing event of marginal significance (with severity less than 0.1 percent). FIG. 14 is a table, each row of which describes an event indicated in FIG. 13.