21, rue d Artois, F-75008 PARIS CIGRÉ-807 2016 CIGRÉ Canada Conference http : //www.cigre.org Vancouver, BC Canada, October 17-19, 2016 TRANSFORMER RELIABILITY AND DISSOLVED-GAS ANALYSIS J. J. DUKARM 1 and M. DUVAL 2 1 Delta-X Research Inc, Victoria BC, and 2 IREQ, Varennes QC CANADA SUMMARY Dissolved-gas analysis (DGA) is widely used for transformer condition screening and assessment. Conventional DGA practice is to employ statistically derived limits for combustible gas concentrations and their increments or rates of increase for the purpose of classifying a transformer's condition as acceptable, suspicious, or abnormal. The DGA condition assessment, in the form of numeric "condition codes," is sometimes used as part of a transformer health index for prioritizing of testing and maintenance or for asset management functions such as replacement planning. The basis of this condition classification scheme is the seemingly reasonable assumption that higher fault gas levels must represent progressively worsened states of the transformer, with correspondingly reduced reliability. We show that this assumption is not supported by the data. Methods of reliability engineering statistics were applied to a large DGA database augmented with transformer failure data to obtain nonparametric and parametric models of survival probability as a function of a thermodynamic index of fault energy -- the Normalized Energy Intensity (NEI), which is based on concentrations of hydrocarbon gases dissolved in the transformer oil. Key concepts from the Probability of Failure in Service (PFS) method devised by Duval and others were adapted for the application of reliability statistics to DGA. The best-fitting parametric model of a pre-failure values distribution for NEI and also for fault gas concentrations is lognormal. From the shape of the associated failure rate curves it follows that -- except at low gas concentrations -- the instantaneous failure rate relative to NEI actually decreases as NEI increases, implying that higher NEI levels do not imply more impaired transformer reliability. Therefore, "condition codes" based on NEI are not a good basis for classifying transformer health. This conclusion was verified for hydrocarbon gas concentrations as well. While levels of NEI or fault gas concentrations in themselves cannot say whether a transformer's suitability for continued service has been compromised, the survival models show that fault severity associated with a gassing event (producing an increase in NEI over two or more consecutive samples) can be quantified in terms of failure probability, optionally multiplied by a criticality or cost factor. DGA case histories are presented to show how this approach works in practice. KEYWORDS Transformer - DGA - Severity assessment - NEI - Reliability - Risk exposure 1 j.dukarm@ieee.org
1. INTRODUCTION For power transformers, dissolved-gas analysis (DGA) is a widely used economical means of periodic screening to identify units that may need intervention or extra attention. When a possible problem is found, DGA can identify the apparent type and severity of the fault. Especially for condition-based maintenance it is very desirable to find a way to rely on DGA as the primary evidence that a transformer may be in need of maintenance. Conventional approaches to DGA screening as described in [1] and [2] are based on using high percentiles of gas concentrations as limits for the combustible gases hydrogen, methane, ethane, ethylene, acetylene, and carbon monoxide on the general principle that healthy transformers operated under normal conditions should produce very little of those gases. Experience has shown that for many transformers the gradual accumulation of combustible gas as a result of stressful events and temporary problems is such that that gas concentrations alone are not good indicators of suitability for service. Various schemes have been presented for supplementing the concentration limits with limits for gas increments and rates of increase. 2. THE PFS METHOD A method of employing transformer failure data for deriving DGA limits related to the probability of failure in service (PFS) was devised by Duval and recommended in CIGRE Technical Brochure 296 [3] as the basis of pre-failure gas concentration (PFGC) and other condition limits for combustible gases. In summary, omitting many details, the PFS method involves plotting a curve of PFS vs. gas concentration (or rate of change) for each combustible gas. At the location (gas concentration or rate) where the curve starts to rise sharply, a "pre-failure" limit for that gas concentration (or that gas rate of change) is determined. For plotting PFS curves, a database of transformer DGA histories is required, consisting of all available in-service oil sample DGA test records for a large number of transformers. For the small minority of transformers that have experienced a failure-related event (FRE) -- a forced outage related to a DGA-detectable fault -- the last in-service sample within one year of the forced outage is flagged as failure-related (FR). For each fault gas, the entire observed range of concentration of that gas is divided into about six subintervals. For each subinterval, working only with sample records for which the concentration of the designated gas falls in that interval, a PFS value is calculated as the ratio of the number of FR samples to the number of all samples for that interval. The PFS curve for a gas is constructed in a coordinate system with PFS as the vertical axis and gas concentration as the horizontal axis. For each subinterval, a point (x, y) is plotted, where x is the midpoint value of the subinterval and y is the PFS value. A smooth curve is drawn through those points. 3. NORMALIZED ENERGY INTENSITY (NEI) A thermodynamic index of fault energy can be used instead of multiple combustible gas concentrations for the assessment of fault severity, reducing the multidimensional problem of classifying several gas concentrations to a single-dimensional one [4]. The main fault gases formed by "cracking" of the transformer oil when it is exposed to heat or electrical discharges are the low molecular weight hydrocarbon gases methane, ethane, ethylene, and acetylene. The hydrocarbon gas normalized energy intensity (referred to below as NEI for brevity) for an oil sample is calculated as NEI = (77.7C CH4 + 93.5C C2H6 + 104.1C C2H4 + 278.3C C2H2 ) / 22400 (1) where C CH4, C C2H6, C C2H4, and C C2H2 respectively denote the concentrations of methane, ethane, ethylene, and acetylene in μl/l, corrected to standard temperature and pressure (0º C and 101.325 kpa). The coefficients of the gas concentrations are the respective enthalpies of formation (kj/mol) of 2
each gas from n-octane, a chemical model of a typical oil molecule. The units of NEI are kilojoules per kilolitre (kj/kl). 4. SURVIVAL ANALYSIS CONCEPTS Statistical survival analysis is widely used in reliability engineering and medical research to investigate and model processes in which designated terminal events gradually deplete some population of objects or organisms in relation to an index t of cumulative stress, wear, or ageing. Examples of such processes are: * months until relapse after a surgical procedure for cancer * hours of burn time until failure of an incandescent light bulb * number of operations until failure of a circuit breaker. The terminal event is not always failure or death, and the wear or ageing index is not always elapsed time or hours of operation. The value T of the index t at which the terminal event occurs for an individual can be regarded as a random variable. The probability distribution (often called the distribution of lifetimes) associated with T has a cumulative distribution function F T (t) = Pr(T t) expressing the probability of termination with index value no larger than a specified value t. The complementary function S T (t) = 1 - F T (t), expressing the probability of terminating with an index value larger than a specified value t, is called the survival function. The survival function describes how lucky a unit is to survive past t, but it is the hazard or failure rate function h(t) = -S T '(t)/s T (t) that describes the instantaneous rate of termination near t. The famous "bathtub curve" representing the pattern of reliability of a complex machine or system during its lifetime is a failure rate function. A classic and widely applicable reliability model is described by an exponential random variable. Its distribution of lifetimes has density function f(t) = r exp(-rt), and its survival function is S(t) = exp(-rt). In this simple case, the failure rate function h(t) has the constant value r, and the mean time to failure is 1/r. For example, it is known that the lifetime distribution of incandescent light bulbs can be modelled by an exponential random variable. A popular brand of 60-watt incandescent light bulbs is advertised as having an average lifetime of 2000 hours. That implies that the average failure rate of non-failed bulbs is r = 1/2000 = 0.0005, or 0.05% of the remaining bulbs per hour of burn time, regardless of how many hours the bulbs have already burned. The fraction of bulbs remaining from an original large batch after t hours of burn time would be approximately S(t) = exp(-t/2000). About ten percent of the bulbs will have failed by t = -2000 ln(0.90) = 210.7 hours of burn time. In this case, where the failure rate h(t) is the same for all t, would it make sense to set limits and say that a light bulb may be suspected as unreliable at t = 4600 hours and replacement should be planned at t = 6000 hours? What about in case the failure rate is decreasing as t increases? 5. TRANSFORMER RELIABILITY MODELS BASED ON DGA Key concepts from the PFS method -- failure-related event in service (FRE) and failure-related (FR) oil Figure 1: Survival probability curves for NEI -- Kaplan-Meier (black) and MLE lognormal (red). Vertical dashed lines represent the NEI 90th, 95th, and 99th percentiles in a large database. 3
sample -- permit the application of reliability engineering statistical methods to DGA, using NEI as the index of aging or usage. For our study [5] two methods were used for deriving survival curves relating NEI to transformer survival probability. The Kaplan-Meier product limit survival probability estimator [6] is a nonparametric method that produces a survival function in the form of a step function. Maximum likelihood estimation (MLE) [7] uses the same data with additional information as to the form of the distribution of pre-failure values in order to approximate the parameters of that distribution and define a smooth survival curve. The data used for reliability modelling in [5] consisted of the latest in-service DGA records for each of 7151 transformers. Of those 7151 records, 101 were designated as failure-related (FR). The Kaplan- Meier and lognormal MLE curves fit to the data are shown in Figure 1. The MLE fit has lognormal parameters μ = 4.507 and σ = 2.231. Agreement between the two curves is very good, especially within the NEI range of most interest for DGA interpretation -- from zero to the 99th percentile. The equation of the lognormal survival curve is (2) where mu and sigma are as stated above and capital phi is the cumulative distribution function of the standard normal distribution. A similar Kaplan-Meier curve, based on early exploratory work on the same data, was shown in [8] Figure 1. It was limited to the portion corresponding to survival probability between 0.95 and 1.0. For computational convenience in translating between NEI and estimated survival probability, ordinary least-squares regression was used to fit a segment of a quadratic curve to the points provided by the Kaplan-Meier method for plotting the step function. It was realized only later that it was possible to use MLE with all the raw data to estimate the parameters of the pre-failure values ("lifetime") distribution and plot a smooth survival curve. 6. USE OF THE SURVIVAL ANALYSIS RESULTS 6.1 Condition code limits and failure rate Our original intention in pursuing DGA survival analysis was, following the example of the PFS method, to use the NEI survival curve to locate NEI limits for condition assessment. Following that idea, Table I of [8] uses NEI values corresponding to survival probabilities of 0.99, 0.97, and 0.95 as DGA condition assessment limits. Surprisingly, however, work subsequent to the publication of [8] demonstrated that condition codes based on gas concentration or NEI limits do not represent degrees of deterioration of the transformer. That conclusion, hinted at by the question at the end of the Survival Analysis Concepts section above, is based on inspection of the graph (Figure 2) of the lognormal failure rate function h(t) = -S'(t)/S(t) plotted using the parameters μ and σ (see above) of the lognormal distribution discovered by MLE. The NEI-based failure rate h(t) rises sharply from zero to 0.024 per unit of NEI increment at its peak, where Figure 2: Failure rate function h(t) plotted using the parameters μ and σ of the lognormal distribution discovered by MLE. Note that above the NEI 90th percentile the failure rate is decreasing. 4
NEI is approximately 0.68 (very near the 82nd percentile). For all NEI > 0.68 the failure rate decreases as NEI increases. To confirm that this is not just a peculiar property of NEI, the Kaplan Meier and MLE survival probability modelling was done for all hydrocarbon gas concentrations, where failure-related samples were limited to those with fault types mainly responsible for producing the particular gas. The gas concentration and associated quantile rank for the peak failure rate are shown for each gas in Table I. Table I -- MLE lognormal parameters and peak failure rates for NEI and hydrocarbon gases Fault Types μ σ Peak h(t) t at peak Quantile NEI (All) 4.51 2.23 0.0240 0.681 0.82 Methane PD, T1 12.00 3.09 0.0001 11.6 0.52 Ethane T1, T2 11.34 2.98 0.0001 11.9 0.52 Ethylene T3 9.96 2.25 0.0001 147 0.94 Acetylene DT, D1, D2 7.79 2.28 0.0010 14.2 0.98 For NEI, methane concentration, and ethane concentration, the maximum failure rate occurs at well below the 90th percentile. Within the range of values relevant for conventional condition code limits, the failure rate is decreasing as NEI or the gas concentration increases. For ethylene and acetylene, the peak failure rate occurs inside the range of concentrations conventionally used for defining DGA limits. Consequently, over part of that range the failure rate is increasing or flat, and near the top of the range the failure rate is starting to decrease. In summary, hydrocarbon gas concentration limits conventionally defined as high percentiles do not necessarily represent progressive degrees of deterioration of transformer reliability. Transformers with high NEI or hydrocarbon fault gas concentration are not in general more likely to fail during a further small increase than transformers with lower NEI or gas concentrations. In fact, for all hydrocarbon gas concentrations near and above the 98th percentile, the respective failure rate decreases as the gas concentration increases. Recalling the question asked at the end of the Section 4, we must ask this one. Does it make sense to consider a transformer more unreliable or suspicious just because it has a high value of NEI (or a high hydrocarbon gas concentration), considering that the failure rate (in response to NEI or gas increase) for such transformers may be lower than for transformers with a more moderate NEI (or gas concentration)? In the absence of active fault gas formation and without evidence from physical and electrical tests of deterioration, a transformer that is still doing its job in service after suffering the amount of stress required to produce a high NEI value may be more hardy and reliable than those that failed with lower NEI. 6.2 Assessment of gassing events If NEI limits are not useful for ranking transformer condition, how should DGA results be interpreted to support condition-based maintenance? First, the main object of attention should be gassing events, i.e., sequences of consecutive samples where NEI is greater in each sample than in the previous sample. The probability of failure with NEI between the initial NEI value t 1 and the final value t 2 of a gassing event, provided that the transformer is in service when NEI = t 1, is a suitable measure of event severity. It is easy to calculate the event severity using the survival probability values for t 1 and t 2 : (3) 5
The apparent fault type associated with a gassing event can be determined by applying the Duval Triangle (or other suitable fault identification method) to the fault gas increments over the event. If the transformer has a numeric criticality rating or an expected cost of forced outage, event risk exposure is the product of the event severity and the transformer criticality. This quantity provides a basis for prioritizing transformers for maintenance or additional testing in response to a gassing event that is very recent or in progress. EventRiskExposure = (EventSeverity)(TransformerCriticality) (4) Evaluation of DGA results should include an overview of significant gassing events to determine whether there may be evidence of incipient, recurring, or ongoing trouble. If so, is the apparent fault type consistent, or is it evolving to a higher energy type? Is the severity of the events constant or changing? Is there a regular pattern of occurrence? How recent was the latest event? Are acetylene or carbon oxide gases being produced during the events? DGA assessment of a gassing event cannot in itself say whether the transformer's reliability is compromised. Supplementary physical and electrical testing may be appropriate in response to severe or very prolonged events to determine the transformer's condition and suitability for continued service. In the absence of active gassing, DGA by itself says nothing about the transformer's current condition (other than that there appears to be no change), regardless of how high the NEI or fault gas concentrations may be. 6.3 Summary assessment In addition to an event-by-event assessment, a cumulative or summary assessment is highly desirable. Cumulative event severity and risk exposure, while not an indication of the transformer's condition or suitability for service, does provide an indication of how much drama has been associated with the transformer to date. A colourful past could suggest increased likelihood of future events and call attention to the transformer's history of test results and repairs. The cumulative severity of a series of gassing events can be represented by the sum of the severities of the individual events. The cumulative risk exposure can then be calculated as the product of the criticality and the cumulative severity. As remarked above in the discussion of failure rate, a transformer's fitness for continued service ultimately must be judged not from DGA data, but from physical test results, operational records, and incident data such as through-fault counts. For triage in connection with periodic DGA screening, in lieu of a DGA "condition" code, a "status" code can be assigned to transformers as follows: 1 - No significant gassing events. 2 - Significant gassing has occurred in the past, but not within the latest DGA screening interval. 3 - A moderate gassing event is in progress as of the latest DGA sample. 4 - A severe gassing event is in progress as of the latest DGA sample. A reasonable requirement for considering a gassing event to be significant could be, for example, that its severity be at least 0.001, which would ensure that related economic risk exposure would typically be on the order of a few hundred or a few thousand dollars. A suggested criterion for classifying a gassing event as severe versus moderate would be whether its severity exceeds 0.02, which is close to the 90th percentile event severity for all significant events in several large electric utility databases. 6
7. CASE HISTORIES 7.1 Example 1 A twelve-year-old three-phase 230 kv 235 MVA generator step-up transformer containing 39750 L of oil has been producing combustible gas in a T1 (mild overheating) pattern for several years, correlated with increasing carbon monoxide and carbon dioxide. The boxes superimposed on the NEI graph in Figure 3 indicate gassing events. The MLE lognormal parameters μ and σ mentioned in Section 5 were used to calculate the survival probabilities S(t 1 ) and S(t 2 ) corresponding to the beginning and end of each gassing event. Table II summarizes the assessments of the three gassing events, and Table III shows the gas concentrations and NEI values for the six samples that are the starting and ending points for the events. FT is the apparent fault type, as determined by applying the Duval Triangle to the increments of methane, ethylene, and acetylene during each event. Severity is calculated according to (3) and (2). Table II - Event assessments for Example 1 Event FT Severity Days Start Day End Day Start NEI End NEI Increment 1 T1 0.0103 963 0 963 0.0069 0.5199 0.5130 2 T1 0.0179 1617 1140 2757 0.5156 1.2763 0.7608 3 T1 0.0104 251 3582 3833 0.8795 1.3228 0.4433 Table III - DGA sample data at the beginning and end of each Example 1 gassing event Days Oil Temp H2 CH4 C2H6 C2H4 C2H2 CO CO2 O2 N2 NEI 0 19 36 2 0 0 0 70 211 2770 16936 0.0069 963 35 122 95 20 23 0 347 2019 1191 12194 0.5199 1140 26 71 90 22 24 0 300 2040 3895 26924 0.5156 2757 110 238 59 44 0 457 2969 11766 51303 1.2763 3582 38 43 158 46 30 0 304 3129 12841 52344 0.8795 3833 32 103 247 66 41 0 514 3640 1059 24985 1.3228 These three gassing events represent prolonged episodes of T1 overheating with associated production of carbon oxide gases, indicating possible fault-related degradation of insulating paper. The cumulative severity of the three gassing events, one of which included the most recent sample, is 0.0386. Since event 3 is ongoing and has moderate severity, the status code is 3. Based on the cumulative severity and a rough estimate of 3 million dollars replacement value for this transformer, the cumulative risk exposure represented by gassing activity so far is (0.0386)($3 million) = $115,800. Other considerations may require other measures of criticality. For example, an index of cumulative risk exposure due to failure-related loss of production could be based on the MVA rating: (0.0386) (235 MVA) = 9.1 MVA. Likewise, an index of cumulative risk exposure due to potential failure-related oil spillage could be based on the main tank oil capacity: (0.0386)(39750 L) = 1534 L. Figure 3: NEI history of 235 MVA GSU contains three gassing events as indicated by the boxes. 7
7.2 Example 2 A twenty-year-old three-phase 230 kv 280 MVA autotransformer containing 66600 L of oil experienced several moderate gassing events, each of one or two years duration in a T1 or T2 pattern, consistent with overheating at temperatures just above and below 300º C. The last significant event (#4) ended about 14 years before the most recent oil sample. The cumulative severity of the four events shown in Figure 4 is 0.0305. Because the transformer has not had recent significant gassing activity, its status code as suggested in section 6.3 would be 2. 8. CONCLUSIONS The Duval/CIGRE PFS method of combining transformer failure data with dissolved-gas analysis introduced the key concepts of a failure related event in service (FRE) and of a failure-related sample. That and the recent introduction of the Normalized Energy Intensity (NEI), which reduced DGA fault severity assessment to a one-dimensional problem, made possible an effective application of reliability statistics to transformer DGA. Standard methods of reliability statistics can be used to fit a lognormal "lifetime" distribution to the data and derive a curve representing the relationship between NEI and survival probability. The failure rate function associated with the survival curve is decreasing for all NEI above the 82nd percentile of NEI, showing that increasing NEI does not imply deterioration of transformer reliability. Failure rate functions based on hydrocarbon gas concentrations show that the failure rate starts declining before or within the 90th to 99th percentile range in which conventional DGA condition code limits are defined. This casts doubt upon the advisability of using DGA "condition codes" as transformer health metrics. Reliability-centred DGA interprets gassing events instead of individual samples. Event severity is defined in terms of conditional probability of failure, defined by (3), and risk exposure (4). Cumulative versions of those and a status code scheme provide a useful engineering-oriented means of summarizing DGA results and prioritizing transformers for testing, repairs, or mitigative treatment. BIBLIOGRAPHY Figure 4: NEI history of a large transformer. Of the four moderate T1 or T2 gassing events, the last ends 14 years before the most recent sample. [1] Mineral Oil Impregnated Electrical Equipment in Service Guide to the Interpretation of Dissolved and Free Gases Analysis (IEC 60599, 2007). [2] IEEE Guide for the Interpretation of Gases Generated in Oil-Immersed Transformers (IEEE Std C57.104-2008, Feb. 2009). [3] Joint Task Force D1.01/A2.11 CIGRE, Recent Developments in DGA Intrepretation (CIGRE Technical Bulletin 296, Jun 2006). [4] F. Jakob and J. J. Dukarm, "Thermodynamic Estimation of Transformer Fault Severity" (IEEE Transactions on Power Delivery, vol. 30, no. 4, pp. 1941-1948, Aug. 2015, doi: 10.1109/TPWRD.2015.2415767). [5] J. J. Dukarm and M. Duval, "Transformer DGA Survival Analysis" (submitted to IEEE Transactions on Power Delivery in September 2016). [6] E. L. Kaplan and P. Meier, Nonparametric estimation from incomplete observations (J. Amer. Statist. Assn., vol. 53, pp. 457 481, 1958). [7] W. Q. Meeker and L. A. Escobar, Statistical Methods for Reliability Data (John Wiley & Sons, Inc., 1998). [8] J. J. Dukarm, Cluster Assessment for Online DGA Monitoring (paper CIGRE-692, 2015 CIGRE Canada Conference, Winnipeg MB, Sep 2015). 8