Number operating (n) Cumulative distribution (n) On the Development of Power Transformer Failure Models: an Australian Case Study D. Martin, J. Marks, T. Saha, O. Krause Power and Energy Systems The University of Queensland St. Lucia, Australia G. Russell, A. Alibegovic-Memisevic Powerlink Queensland Virginia, Australia Abstract Power transformers are expected to operate reliably for decades. Loading guides and models exist to estimate the functional life remaining of transformer cellulosic insulation. However, failure is essentially probabilistic and dependent on many factors, and so statistical models to ascertain the expected number of failures for a power transformer fleet are highly desirable when planning future investment. Given their low failure rate, approximately 1% per transformer year, a fleet size much larger than an individual Utility owns is required for statistically significant results. Therefore, a large study was performed on the Utilities in Australia who together operate around 6, power transformers. For this, data on 626 failures and retirements, over a fifteen year period, were collected. The Weibull distribution was used to determine failure rate for age, voltage class of transformer, and failure mode. Finally, the development of a tool to model future replacements is discussed. Index Terms-- Failure analysis, fault location, power system reliability, power transformers, reliability. I. INTRODUCTION As part of the Australian regulatory framework, the Utilities are obligated to provide an investment plan every five years, which includes forthcoming asset replacement [1]. In this plan, the Utilities identify the power transformers that they believe represent increased risk. This risk calculation is based on the probability of transformer failure for various failure modes and on future loading forecasts. This forms a list of power transformers which are recommended to be replaced, along with justification and cost. Statistical models are beneficial if the Utility can optimize the estimation of the likely number of failures on their network, into the near future, using different investment strategies. Data on the power transformer age distribution for 215/16 was collected from the Australian Utilities [2], and is presented in Figure 1. The criteria of a power transformer was one stepping the voltage down to either subtransmission or distribution medium voltage, and having a power rating 1 MVA. In general, the investigated transformers had a primary voltage ranging between 22 kv and 5 kv. Generator step-up power transformers were not included because these are normally owned by the power station, and not by a Utility. Similarly to other developed countries, a significant proportion of assets were installed in the 196s. Given that the working life of a power transformer is often assumed to be 4 to 5 years (based on n-1 planning criteria and loading guide), there are many units which have exceeded this age yet the Utility will keep them in service unless there is sufficient business reason to replace them. The aim of this research project was to develop a tool the Utilities can use to evaluate the effect of replacement strategy on the reliability of their system. Previous studies have indicated that the failure rate of a power transformer is approximately 1% per transformer year [3], [4]. Given that a Utility typically operates several hundred power transformers, only a few failures can be expected per year, and so there can be relatively few failures to analyze. Consequently, a statistical survey was performed to cover as much of the power transformer fleet, operated by the Utilities in Australia, as possible. Firstly, this study involved determining failure rates of power transformers. Then secondly, developing a tool to model how the number of failures would change into the future using different scenarios of replacement. 25 2 15 1 5 Number operating 1 5 9 1317212529333741454953576165697377818589 Cumulative distribution 1 1 1 1 1 1 This work was funded by Australian Research Council, Ausgrid, Ergon Energy, Powerlink Queensland, TransGrid and Wilson Transformer Company Figure 1. 215/16 asset age profile of Australian power transformer fleet.
Number The industry commonly takes into account the remaining life of the paper insulation of a transformer when determining replacement [5], [6], based on the tensile strength of the paper. Previous surveys have indicated many failures occurring due to the on-load tap changer (OLTC) and bushings, which are obviously independent of the winding paper condition. Thus, an algorithm to help the Utilities determine when to replace a transformer based upon its reliability is highly desirable. Several surveys have been performed. The reliability of the Australian and New Zealand (ANZ) power transformer fleet was investigated in the mid 9s, finding a low failure rate of 1% [3]. However, twenty years have passed and so improvements in technology and management may have changed the failure rate. A CIGRE study, published in 215, reviewed international failure rates for power transformers [7]. However, only data for power transformers with a primary voltage of 69 kv or above were collected. In Australia a significant proportion of power transformers operate with a line voltage of 22, 33 or 66 kv. Different regulatory environments across countries may also affect the life expectancy of a transformer. Consequently, a new review was planned. Since a Utility may withdraw a transformer due to poor condition, before failure actually occurs, information on retirements was also collected and analyzed. II. DATA COLLECTION AND PROCESSING Previous studies had used the definition of a failure being one when the transformer either tripped due to the protection, or was removed from service within 3 minutes of an alarm sounding [3]. Another definition was costly failure, where the failure had caused the Utility to incur an expense of at least 2% of the value of the transformer [3]. A Utility may then have an option to repair the transformer rather than replace it. Given that the Utilities have different cost structures, and may in the same circumstance come to a different decision on whether to repair or replace, failure was defined for this study as when the transformer had to be permanently removed from service (non-repairable). Of the twenty Utilities operating in Australia, nineteen were contacted and asked for information on power transformer failure and retirement. The twentieth Utility did not appear to own power transformers because it supplied off-grid communities in Western Australia. Data was sourced from seventeen of these Utilities, composing 97% of the Australian power transformer fleet. The Utilities were asked for the age of the transformer on failure or retirement, and the cause of the event. The Weibull distribution was applied to model the failure rate, as a function of age, using the method given in Standard BS61649:28 [8]. The probability density function (PDF) is shown in (1), where β and η are two coefficients which represent the shape and scale of the distribution, t is age. f(t) = β tβ 1 e (t η β η )β (1) According to BS61649 the data is classed as either complete or non-complete, with the distinction being whether or not all units have failed by the end of the test. Three types of data are used, censored (units are still functioning by end of test), suspended (unit was retired before failure) and failed. Thus, in addition to data on withdrawn units, information was also collected on those which were still functional. The collected data was truncated to a 15 year window (2 215), because most of the Utilities were unable to provide data prior to 2. The failure rate for a given age of transformer can be expressed as (2), where n failures and n survivors represent the numbers of transformers failing and surviving age i. F Rate = n failures (i) n survivors (i) +n failures (i) (2) The reason for failure or retirement was noted where possible and was sorted into bushings, OLTCs, windings, insulation, other and unknown failure modes (as these had been identified in previous surveys as the main modes causing failure). For retirements, the reasons were not always recorded, and so either poor condition overall or network augmentation was used. It was noted that the Utilities did not often retire (suspended by our definition) a transformer based on one problem. Usually, the unit had a number of issues making it either uneconomic to repair or of unacceptable reliability. 14 12 1 8 6 4 2 Figure 2. Age distribution of failed power transformers. The distribution of failed transformers is shown in Figure 2. Some transformers can be seen to fail early. Therefore, to model the data more than one Weibull distribution might be required, with the first representing infant mortality [11] failures and the second representing age-related problems. The number of retired units is shown in Figure 3. The number of transformers which had survived by the end of the monitoring period (215/16) is shown in Figure 4. The number of transformers surviving each year of operation was calculated keeping the 15 year observation window in mind. For instance, as long as the reporting was accurate, for a transformer installed in 2 the survey would have 15 years of operational data available. Therefore, a failure rate could be calculated for the number of units failing up to, and including, the 15 th year of operation. For the transformers surviving age 16 and older, it can obviously be stated that they had survived their first year of operation. But, it could not be determined how many of their initial population had failed before 2, and so the pre-2 survival data was omitted. For instance, for the transformers reaching 16 years in 215, only failure rate for ages 2 to 16 was calculated, and the failure rate for the
Number ln(ln(1/(1-median Rank))) Number Instantaneous failure rate Number first year of operation was omitted. The number of survivors as a function of age, omitting pre-2 data, is given in Figure 5. Using (2) the failure rate, shown in Figure 6 was calculated (omitting retirements). The instantaneous failure rate (IFR) calculated using the Weibull distribution is also shown for comparison, along with its ± 95% confidence interval (CI), which will be discussed in the next paragraphs. 35 3 25 2 15 1 5 implying distinctly separate infant mortality and aging related failure modes. The change in mode occurred at approximately 2 years. The ± 95% confidence intervals for the β and η coefficients were calculated using the technique given in BS61649, based on work published by Bain and Engelhardt [9] and [1]. The β and η coefficients determined using the line characteristics, shown in Figure 7, and their ± 95% confidence intervals, were then used to calculate the instantaneous failure rate λ (3) shown in Figure 6. As can be seen, there is good agreement between the two methods to calculate the failure rate, although the ± 95% confidence interval should be used to capture the peaks in failure rate. λ(t) = β tβ 1 η β (3) Figure 3. 25 2 15 Age distribution of retired power transformers. 3.% 2.5% 2.% 1.5% 1.%.5% Non-parametric Weibull IFR Weibull IFR + 95% CI 1 5 25 2 15 1 5 Figure 5. Figure 4. Age distribution of censored transformers. Number of transformers in population surviving each year of age, omitting pre-2 data. The coefficients required for use by the Weibull distribution were determined graphically. As discussed in BS61649 [8], plotting ln (ln(1 (1 Median rank))) against ln (age) will give a straight line if the data follows a Weibull distribution. The coefficients of this line are then used to determine the β and η values, where β is the gradient of the line, and η = e (yintercept β). When the median ranks of the failure data were plotted, shown in Figure 7, it was evident that two distributions were present,.% Figure 6. -1-2 -3-4 -5-6 -7-8 -9 2 4 6 8 Instantaneous failure rate of investigated power transformers. y =.4939x - 7.27 R² =.9199 y = 3.354x - 15.82-1 -3-2 -1 1 2 3 4 5 Figure 7. III. Finding coefficients ln(age) Determining coefficients for Weibull distributions. MODELLING FAILURE MODES AND DIFFERENT VOLTAGE CLASSES Since previous research has indicated the failure mode differs depending on the voltage class of the transformer [3], the data was split into three voltage bins, 66 kv, 66 < kv 275 and > 275 kv. These bins were chosen for the following reasons. Firstly, there had to be a sufficiently large number of failures in each bin not to reduce the confidence interval; at least 2 failures is suggested by BS61649 [8]. Secondly, the Utilities had to report the number of transformers in operation to the industry Regulator in prescribed voltage levels. It was
not possible to distinguish between certain voltage levels. Data on transformers operating at either 22 or 275 kv were combined with 11 and 132 kv units, rather than higher voltage classes, because the failure mode appeared more consistent with the lower voltage units. Weibull distributions for 66 kv, 66 < kv 275 and >275 kv are shown in Figures 8 to 1. For the 66 and 66 < kv 275 populations both the probability of retirement and failure is given. There has been only a small number of > 275 kv transformers retired since 2, and so there was insufficient data on which to fit a distribution. Only one distribution was used to model this voltage class because, otherwise, the confidence interval would become very large from there being only two small sets of data. The 66 kv and 66 < kv 275 populations are similar because agerelated failures seem to begin at around 2 years old, similar failure modes may be responsible. The probability of a unit failing is higher than the probability of it being retired over the first few decades of operation (approximately 4 years for 66 kv and 6 years for 66 < kv 275). This implies that failure can catch the industry unaware. Once the transformer reaches its later years the industry may be more likely to retire it based on poor condition, rather than retiring due to the manifestation of a specific fault which was thought to be leading to failure. If fewer transformers are replaced, more resource may be required by the industry to manage the aging units. Figure 9. Weibull distributions for failure and retirement for 66 < kv 275 transformers. Figure 1. Weibull distribution for failure of > 275 kv transformers. Figure 8. Weibull distributions for failure and retirement for 66 kv transformers. The failure mode for these transformers was also investigated, shown in Figures 11 and 12. Winding related problems were the predominant mode of failure for transformers 275kV, while higher voltage transformers had a more mixed-mode of failure. Winding-related faults are often by lightning or downstream surges [7], where the resultant mechanical force distorts the conductors forming a winding. Figure 11. Weibull distributions for failure and retirement for 66 kv transformers.
Number (n) lightning or simply due to the inherent mechanical weakness tested by number of close through faults. Using a Weibull distribution to model failure was similar to when a non-parametric distribution was used. Consequently, basing an algorithm to predict the likely number of failures into the future on the Weibull distribution is suitable. As evident from the Weibull distribution, a change in failure mode appears to occur around twenty years. Using one Weibull distribution to model early failures, and another to model age-related ones, appears effective. Figure 12. Weibull distributions for failure and retirement for 66 < kv 275 kv transformers. IV. TOOL DEVELOPMENT Based on these failure rates, an algorithm is being developed to help the industry to better predict the number of failures and retirements of power transformers into the near future. This will be beneficial because the Utilities have to justify their investment plans to the Australian Energy Regulator every five years. The failure rates determined from this study are being used to estimate the number of failures and retirements expected to occur in Australia over the next ten years (Figure 13). The assumptions considered valid for this modelling are that a withdrawn unit is replaced with a new one (it is recognized that a Utility may choose not to replace), and that the criteria to retire a unit does not change. The dashed lines indicate the number of events calculated using ±95% confidence intervals. The upward trend in the traces is a result of the fleet becoming older. This algorithm is being evaluated and will be reported on in due course, for instance the effect of maintenance is being studied. Future work for this algorithm includes: (a) investigating using condition of transformer rather than solely age, (b) using spares as replacement rather than new units, and (c) using network topology to relate failures to frequency and duration of customer outages. Asset condition has not been investigated so far because the Utilities have different methods to test and process data. Whereas some Utilities have used a health index, there is still no consensus on which method is optimal. Thus, health index scores across different Utilities cannot be easily compared. V. CONCLUSIONS Nearly half of all power transformer failures over the past fifteen years were caused by winding problems, likely to have been initiated by surges from downstream faults or by Replacements Failures Retirements Replacement & CI Failure & CI Retirements & CI 9 8 7 6 5 4 3 2 1 217 219 221 223 225 227 Year Figure 13. Estimation of future failures and retirements, for Australian power transformers, along with their confidence intervals (CI). In the first few decades, a transformer is more likely to fail than be retired. After either 4 years, for 66 kv units, or 6 years for 66 < kv 275 ones, a transformer is more likely to be retired than to fail. Also, if design related issues / weaknesses exist, they will usually become evident earlier in the transformer s life. REFERENCES [1] Australian Energy Regulator, Electricity Network Service Providers Replacement Model Handbook, Australia, December 211. [2] J. Marks, D. Martin, T. Saha, O. Krause, A. Alibegovic-Memisevic, G. Russell, G. Buckley, S. Chinnarajan, M. Gibson, T. MacArthur, An Analysis of Australian Power Transformer Failure Modes, and Comparison with International Surveys, IEEE AUPEC, Australia, Sep. 216. [3] Australian / New Zealand transformer reliability survey, Western Power, Australia, 1996. [4] A. Petersen and P. L. Austin, Impact of Recent Transformer Failures and Fires Australian and New Zealand Experiences, CIGRE, 22. [5] IEC 676-7, Power transformers - Part 7: Loading guide for oil immersed power transformers, IEC Standard, Switzerland, 25. [6] IEEE Guide for Loading Mineral-Oil-Immersed Transformers and STP-Voltage Regulators, IEEE Standard C57.91 211, 212. [7] Working group A2.37, Transformer Reliability Survey, Cigre brochure 642, France, 215. [8] BS EN 61649:28, Weibull analysis, BSI, UK, 28. [9] L. J. Bain and M. Engelhardt, Simple Approximate Distributional Results for Confidence and Tolerance Limits for the Weibull Distribution Based on Maximum Likelihood Estimators, Technometrics, vol. 23, no. 1, pp. 15-2, 1981. [1] L. J. Bain and M. Engelhardt, Approximate Distributional Results Based on the Maximum Likelihood Estimators for the Weibull Distribution, Journal of Quality Technology, vol. 18, no. 3, pp. 174-181, 1986. [11] J. Moubray, Reliability-Centered Maintenance, Industrial Press, New York, NY, 1997.