0071 Full Paper IET IAM 2011 London R.P.Y.Mehairjan


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0071 Full Paper IET IAM 2011 London R.P.Y.Mehairjan

  1. 1. STATISTICAL LIFE DATA ANALYSIS FOR ELECTRICITY DISTRIBUTION CABLE ASSETS -An Asset Management Approach- R.P.Y. Mehairjan*†, D. Djairam†, Q. Zhuang†, J.J. Smit†, A.M. van Voorden* *Stedin B.V., Rotterdam, the Netherlands, † Delft University of Technology, High Voltage Technology & Asset Management, Delft, the Netherlands.Keywords: asset management, decision making, failure rate, asset information, utilities have progressively createdlife data analysis, ageing assets, equipment failures. databases to record asset or business data such as failure, maintenance, operation and costs. However, in practice, theAbstract available data required to track equipment reliability are not sufficiently comprehensive to provide a basis forNowadays, power utilities are adopting Asset Management as straightforward decision-making. An important reason for thistheir framework in order to cope with the challenges shortcoming is because AM is a fairly new concept and manyintroduced by the privatization and market competition in this utilities did not see a reason for collecting detailedsector. Stedin, a Dutch Distribution System Operator information to track equipment lifetimes [3]. However, inrecognized the vital role that an Asset Management system practice, it is not always possible to collect all requiredhas for its organization. Therefore, Stedin, has adopted the equipment lifetime data. Nevertheless, with AM approachpublicly available specification, BSI:PAS55, as a standard to heavily relying on asset level data to support sound AMperform the Asset Management responsibilities and tasks of decisions, there is a strong demand for methods and tools thattheir electricity and gas networks. Equipment life cycle and are able to analyse equipment lifetime data even in the oftentechnical performance activities form an integral part of the occurring case of incomplete or inconsistent data. Therefore,implementation of an Asset Management system. In this developing a systematic approach in which optimal use iscontext, Stedin felt the strong need to have access to made of the limited data is required with the aim of obtainingsystematic techniques and guidelines on how to deal with an indicator of the future failure expectancy of the assets. Oneinformation of equipment lifetimes. In this paper a systematic way to extract the essential information out of the data is to fitmethod, based on Statistical Life Data Analysis, which deals the parameters of a hypothesized failure distribution to thiswith limited or incomplete life time data of large populations data. This process is connected to the application of statisticsof assets with the aim of obtaining an indicator of the future and its mathematical analysis [4].failure expectancy is discussed. The methods and analyticaltools developed in this contribution share a basic framework 2 Methodologyfor decision-making and specify the evolution of the failuresof asset population over time. In practice, it is frequently encountered that engineers still use their experience as their primary basis for equipment lifetime1 Introduction and technical performance decisions. For making substantiated decisions, it is important to base decisions onThe increasing pressure from both customers and regulators information and facts rather than on intuition alone.to maintain and enhance service reliability, while Two commonly used options to predict the technicalsimultaneously controlling costs, has caused many utility performance of populations of components are:distribution businesses to adopt Asset Management (AM) astheir framework to balance the financial aspects with the  Statistical data analysisreliability engineering and infrastructure aspects [1].  Understanding of degradation mechanismGenerally, AM consists of data driven decision-makingprocesses with the goal of deriving the most value from the The choice of an adequate method for predicting the technicalutility assets within the available budget. Asset intensive performance of components depends on the state ofindustries rely on asset data and distilled from this the component, the available data, and the goal of analysis. Forinformation and knowledge as key enablers in undertaking this paper, the statistical data analysis is chosen, because ofboth strategic AM activities and operational activities [2]. the previously mentioned considerations. A statistical methodGood asset information (timely, reliable and accurate data) uses historical failure information to understand and predictenables better decisions to be made such as determining the future failure expectancy of populations of assets.optimal asset maintenance or renewal frequency for apopulation of assets. Because of the growing importance of 1
  2. 2. The first step is to collect available asset population (un-failed ( ) ∫ ( ) and ( ) ( )assets) and asset failure data. The second step is to performstatistical life data analysis and the third step is to use the That is, the probability that X assumes a value in the intervalstatistical results to support various AM decision-making [a, b] is the area under the density function.processes. A straightforward procedure of the appliedmethodology is shown in Figure 1. The cdf is a function F(x) of a random variable, X, and is defined for a number x by: Data Statistical AM Collection Analysis Decision ( ) ( ) ∫ ( ) ( ) The cdf is the integral of the pdf, and reflects the probabilityFigure 1. Application of statistical life data analysis. This figure illustrates that f(x) will be equal to or less than x.the procedure for performing the life data analysis.2.1 Statistical Life Data Analysis From the cdf (unreliability function) the reliability function R(t) can be determined, and is the probability of success orMethods for analysing continuous life data fall into two not failing, of a component before a specific time. With theclasses, distinguished by whether or not they make failure rate function, λ(t), the number of failures per unit ofassumptions about the distribution of the data [5]. The first is time can be determined.the method that uses distributional assumptions and is calledparametric methods. All of the commonly used parametric ( ) ( ) ( )methods assume that the data follows a chosen failure ( ) ( ) ( ) ( )distribution. Parametric methods are most appropriate for ( ) ( )large data samples.A second method is the non-parametric method, which allows The above mentioned equations (1) through (4) can bethe user to analyze data without assuming an underlying converted into each other. Therefore, they contain allfailure distribution. information about the failure process of the system underIn general, non-parametric methods are less statistically consideration. After a certain distribution is selected to fit thepowerful than their parametric counterparts, especially when data, the next step is to estimate the parameters of thisthe life data analysis is intended for creating more knowledge distribution. Subsequently, the estimates can be used towith regard to the failure behaviour of a population [6]. The construct probability functions and plots. Popular failureparametric distribution fitting method will be used in this distributions used for continuous life data analysis are normal,study for the life data analysis. This method comprises a Weibull, exponential and Gumbel distributions. Estimatednumber of steps and a straightforward procedure is depicted distribution parameters can be calculated on several methods.in Figure 2. Three methods that are often used for life data analysis are Probability Plotting (PP), Least Squares Estimation (LSE) and Maximum Likelihood Estimation (MLE) [6]. In this paper, the MLE method is used, because of its ability to take into account large numbers of suspensions (non-failed units) and large data sets. MLE is asymptotically consistent, which means that as the data sets gets larger, the estimates converge to the true value[6].Figure 2. Evaluation flowchart for life data analysis. The parametric methodis used for this study. 2.3 Goodness-of-fit Test When modelling life data, it is often desirable to diagnose the2.2 Failure Distribution Fitting and Parameter Estimation fitted model in order to assess whether the assumed modelDistribution fitting can be seen as a process that fits the data matches the data that it is supposed to represent. Thepoints from the life data with an appropriate statistical failure statistical tools that can help in deciding whether or not adistribution (probability model). The chosen probability distribution is a good choice are called Goodness-of-Fitmodels are mathematical equations allowing a large amount Tests[6]. In general, for a chosen parameter estimationof information, characteristics and behaviours to be described method there are corresponding Goodness-of-Fit Testby a small number of parameters. The basic distributions are methods. When using the MLE method to estimatethe cumulative distribution function (cdf) and the probability parameters of the distribution model, the Likelihood Value Ldensity function (pdf) and they describe the probability can be used to assess the fit to the data set. The likelihooddistribution of a random variable. The basic equations are value L can be used to compare the fit of multipledescribed briefly: distributions and the distribution with the largest L value isIf X is a continuous random variable, then the pdf, of X, is a the best fit statistically. Other methods which can be used forfunction f(x) such that for two numbers, a and b with a<b: LSE and MLE are e.g. the Kolmogorov-Smirnov (KS) test, chi-squared test, Anderson-Darling test [6, 7]. 2
  3. 3. 3 Application of Statistical Life Data Analysis continuously. As a result, the available MV failure data forfor Medium Voltage Cable Joints the period 2004 until 2009 has been consistent and could be used in a viable way for this study. The analysis takes 556 cable joint failures within the last 6 years into account. Apart3.1 Medium Voltage Power Distribution Network from information regarding the cause of failure and theIn the Netherlands, almost 100% of the distribution of power number of cable joints failed, additional information about theis realized by means of underground Medium Voltage (MV) age of the cable joints at the moment of failure is available.cable infrastructures (approximately 100.000 km). The most Most of the time, the exact age of the cable joints at thedominating component related failures (85%) are observed moment of failure is not known to the utility. To circumventfor MV cable systems (cable systems have an insulation this problem, rough estimations of the age are reported bysystem, consisting of three different types of components using age intervals (age bins). In order to perform statisticalnamely cable parts, cable terminations and cable joints) [12]. analysis, the data should have properties such as,The reliability of the cable system depends on the reliability independency and homogeneity. However, due to the lack ofof the individual components. Although the cables are far detailed recorded information, it is necessary to makemore expensive than the related cable accessories, it is usually assumptions. From a statistical point of view, it is necessarythe accessories that affect the reliability of the cable system. to assume that cable joint constructions are comparable withA vast majority of the distribution grid outage times is due to each other and operated under equivalent conditions (i.e.failures in MV cable joints (45%) [12]. The main reasons why similar load and ambient temperature).cable joints are subjected to more failures are because [8]:  they are subjected to higher electrical, mechanical 3.3 In-Service Data and thermal stresses In-service data is defined here as information about assets  they are mounted in the field and usually under non- which did not fail at the moment the reliability of the ideal circumstances, particularly during outage population was determined. The total recorded population of situations all three types of cable joints is roughly 31700. The features  they are not subjected to expensive reliability testing captured for the cable joint data are used for analysing the age procedures like the cable itself distribution of the cable joint population. However, for a large  the quality of mounting the joints is quite sensitive to portion of the joint population the exact age (year of workmanship, experience and care of the involved installation) is not specified, as a result of missing data technician. records. Likewise, for some part of the joint population theUsing the available lifetime data of the cable joints, a corresponding joint type is unknown. Such records are oftenstatistical lifetime data analysis is performed to predict the missing for assets that were installed more than 20 to 30 yearstechnical reliability of the large populations of cable joints ago. These shortcomings are dealt with by using estimationswhich are installed in MV network of Stedin. for the missing data records, based on experience knowledge within the utility.A case study for the application of statistical life data analysiswas carried out for a particular region of 10 kV distribution 3.4 Statistical Life Data Analysisnetwork of Stedin. Three types of 10 kV cable jointpopulations were investigated. The three categories are The systematic approach, which is depicted in figure 2, isdistinguished on the principle of joint insulation used. These used for modelling the life data of three different 10 kV cablethree categories are: joint populations. The recorded failure data together with the  Mass insulated joints (liquid mixture of oil and resin) in-service data of the cable joint populations are used as input  Oil insulated joints for the parametric distribution fitting method. Based on  Synthetic insulated joints statistical test and engineering knowledge the corresponding failure distribution (probability model) are selected for eachDifferent insulating materials have different ageing of the three categories of cable joints analyzed in this study.mechanisms, which should be distinguished when performingstatistical studies (homogeneity). The number of 10 kV cable The failure rate (λ(t)) and probability density function (pdf)joint failures resulting in power delivery outages in this allow different assets to be compared with other. In figure 3region is high compared to other regions. The available and 4 the pdf curve and the failure rate curve are shown,population and failure data for this region have been recorded respectively. From figure 3, the density of failure probabilitywith more accuracy in the past, which makes it useful for can be examined for the three different cable joint groups.statistical analysis. The peak value of the pdf curve for the synthetic insulated cable joint (green) is higher then the remaining ones.3.2 Available Failure Data Typically, this illustrates that synthetic insulated cable joints have a higher probability of failure when the components ageThe Dutch utilities have been collecting outage data since is near the peak value (mean life).1976 starting with paper documentation. Since 1991, aspecific database tool is used. The failure reporting databasehas developed throughout the years and is improving 3
  4. 4. which leads to electrical discharges and may finally lead to breakdown of the component. 4 AM Decision Support for Cable Joint Failures Even when databases are found to have missing or incomplete data, it is still possible to develop sensible failure probability models. Aspects, such as, failure probability, ageing and failure frequency are important [10]. Knowledge and information of these aspects can contribute in the decision process of AM. With the results of the statistical analysis from the previous section, information regarding the failure probability and the failure frequency at a certain age of asset groups in the near future of the three types of 10 kV cable joints can be extracted. 4.1 Percentile LifeFigure 3. Probability density functions (pdf) for three different types of 10 The use of the percentile life, or B(x)-lives in engineeringkV cable joints. The probability that a specific type of cable joint will fail terminology, is encountered in almost every industry. Inwithin a certain range of age is indicated by the area under the pdf plot. general, these parameters give the estimated time when the probability of failure will reach a specific point. For instance, if 10 % of the cable joints are expected to fail by 15 years of operation, then, it can be stated that the B(10) life is 15 years. The value of the B(x)-lives can assist the asset manager in anticipating which level of reliability is acceptable and at which age this level of reliability is reached. In table 1, the B(x)-lives are shown for all three types of cable joints. Mass Insulated Cable Joint Population Component Age (year) 90 % B-Life 90 % Bound Bound B(1)-life 26 27 28 B(10)-life 43 44 45 B(25)-life 53 54 56 B(50)-life (mean life) 67 65 63 Synthetic Insulated Cable Joint PopulationFigure 4. Failure rate curves for the three different types of cable joint Component Age (year)populations. 90 % B-life 90 % Bound BoundFrom figure 4, it can be seen that the failure behaviour is B(1)-life 17 19 21different for each population of cable joints. For all three B(10)-life 30 31 33populations, their failure rates rise over years according to the B(25)-life 38 40 42increasing right wing of the bathtub curve. Additionally, it B(50)-life (mean life) 45 48 52can be seen that the populations age quite similarly, however,the rate of rise of the failure rate with equipment age differs Oil Insulated Cable Jointfrom each other. Subsequently, the failure behaviour of oil Populationinsulated joints (red line) and of mass insulated joints (blue Component Age (year) 90 % B-life 90 %line) differs from each other, even though they belong to the Bound Boundgroup of filled cable joints. An important reason why the B(1)-life 18 19 20failure rates for the oil insulated cable joints are higher can be B(10)-life 33 35 37the result of lower liquid levels in the oil type joints. As B(25)-life 42 44 46mentioned in [9], a lowered liquid level in joints filled with B(50)-life (mean life) 51 54 57viscous material is often due to thermal heat cycles as resultof daily load cycles. Basically, a lowered liquid levels results Table 1. B(x)-lives of synthetic, mass and oil insulated 10 kV cable joints. The corresponding upper and lower 90 % confidence bounds are also listed.in a impaired electrical breakdown strength of the component, 4
  5. 5. With the statistical information from table 1, the asset the synthetic insulated cable joint population together with themanager can assess and compare the reliability of the three 90 % confidence levels. With these predictions the assetcable joint population with each other. Additionally, the B(x)- manager can determine whether the expected numbers oflives can be used to assess how many cable joints are actually future failures based on statistics are acceptable, or, whetherolder than a certain chosen B(x) level. The level of B(x)-life structural replacement is necessary in the coming years. Forwhich the asset manager can choose for a certain population instance, in the same figure the effect on the expected numberof component, depends on the network type, component, of failure after replacement of 5 % of the oldest units in 2010impact of failure, etc. If, for example, the asset manager is and 2011 are shown (green line). It can be seen that theinterested in knowing how many cable joints of each number of synthetic cable joints failures decreases in 2011 enpopulation are older than the B(10)-life, then the calculated 2012. Consider that the replacement program is stopped afterB(10)-life together with the in-service cable joints can be 2012, we then see that the number of failure gradually start toused for this. In table 2, the percentage of cable joints older increase, however are considerably lower than in case of nothan the B(1) and B(10) life are listed for each type 10 kV replacement. Similar analyses are conducted for the oil andcable joint. mass insulated cable joints. Accordingly, the cost/benefit analysis for replacements can be performed using these % of % of % of population population population results. older for older for mass older for oil synthetic joints joints 40 joints 35B(1)-Life 35% 46% 23% 30B(10)-Life # of failures 21% 5% 2% 25 20Table 2. The level of reliability for a given population together with the % ofcable joints which are older than the related B(x)-life. The asset manager can 15decide which level of reliability criteria to set for each population. 10 5For instance, it is found from table 2 that 21 % (app. 410 0 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016joints) of the synthetic insulated cable joints is older that theB(10)-life, while 5 % (app. 640 joints) of the mass insulatedcable joints is older that the B(10)-life. For the oil insulated 10 kV Synthetic joint failurescable joints, the value is 2 % (app. 125 joints). The total Year Predicted Number of Failures Upper Conf. Levelpopulation for the synthetic, mass and oil insulated joints are Lower Conf. Levelapproximately, 1950, 14460 and 15340, respectively. Based Trend Checkon these analytical results, the asset manager can decide Trend Check Upper Conf. Levelwhich portion of the population is in the end of life given the Trend Check Lower Conf. Level 5 % Replacement in 2010 and 2011selected level of reliability. In the way forward, the assetmanager can prepare maintenance or replacement policies in Figure 5. Estimation of the number of total expected failures for the comingorder to deal with the portion of the population which has six years for 10 kV synthetic insulated joints. The red line gives the numberexceeded the required reliability criteria. of predicted failures starting at 2010 until 2016. The corresponding 90 % confidence levels are also shown. In the period 2004-2009 the actual number of failures (dark blue line) is compared to the estimated number of failures4.2 Predicting Future Cable Joint Failures for that period.Ultimately, the asset manager is interested in anticipating howfailure rates of certain assets will develop in the future. 4.3 Failure Count DiagramPredicting future performance is a very important objectivefrom an AM point of view. With the developed failure rate With a failure count diagram, it will be possible to assess themodels for each population and the number of components in impact that typical increasing failure rates have on theoperation, the asset manager can anticipate the development installed equipment base. In practice, it is usually encounteredof future cable joint failures. Besides predicting the future that utilities do not know the exact age of a component at thenumber of failures, an additional analysis is performed in moment of failure, and make estimations of the age in theorder to assess whether the developed failure rate model is in failure records. With the failure count diagram it can beagreement with the actual historic failures. This is shown in calculated, in relative terms, how many components of anfigure 5 for the synthetic insulated cable joints. From figure 5, installed population of a particular age contribute to failuresit can be seen that the estimated number of failures (light blue [11]. The failure count diagram for the synthetic insulatedline) based on the analysis are comparable with the actual cable joints is shown in figure 6.number of failures in the period 2004-2009 (dark blue line).Resulting from this, it can be concluded that the developedfailure rate model reasonably describes the failure behaviourof the considered population. Furthermore, the expectednumber of future failures (red line) till 2016 is predicted for 5
  6. 6. Acknowledgements This research has been performed in close collaboration with, and financially supported, by the Dutch Distribution System Operator (DSO) Stedin B.V. The authors thankfully acknowledge their fruitful discussions and willingness to provide valuable data of their assets for this study. References [1] R.E. Brown. “Business Essentials For Utility Engineers”, CRCFigure 6. Shows the total number of failures occurring each year for the Pres Taylor & Francis Group, (2010).synthetic insulated cable joints. The maximum is reached at age 47, when thecombination of high failure rate and high number of remaining units peak. [2] Cigre WG D1.17. “Generic guidelines for Life Time Condition Assessment of HV Assets and Related Knowledge Rules”,When considering the failure rate curves shown in figure 4, it Cigre, (2010).can be seen from the failure count diagram (figure 6) thatfailures in intermediate years are the actual cause of the [3] EPRI. “Guidelines for Intelligent Asset Replacement:system reliability problem. More than half of the failures Underground Distribution Cables” EPRI, Palo Alto, CA:occur in the range of 21 and 51 years. The very old cable 2005.1010740.joints (older than 50 years) indeed have a higher failure rate.However, there are usually too few of these old cable joints to [4] R.A. Jongen, et al. “Application of Statistical Methods forgenerate a high total failure count. The failure count diagram Making Maintenance Decisions within Power Utilities”, Deis,is a representation of the relative contribution to failures of IEEE Electrical Insulation Magazine, Nov/Dec (2006).synthetic joints as function of their age. This diagram can be [5] Altman, G. Douglas, J.M. Bland. “Parametric vs. Non-seen as an important tool in managing reliability and parametric methods for data analysis”, BMJ, 339, (2009).replacement policies. Similar analyses have been performedfor the oil and mass insulated joints, showing that each [6] Reliasoft Corporation. “Life Data Analysis (Weibull Analysis)population has unique failure count behaviours. Reference Book”, Reliasoft.5 Conclusions [7] Nelson, Wayne. “Applied Life Data Analysis”, New York: John Wiley & Sons, (1982).With the information and tools, which has now been [8] J.G. Slootweg, A. Postma, E.F. Steennis. “A Practicaldeveloped for each joint population, the asset manager can Approach Towards Estimating Remaining MV Cable Life”,better determine which level of reliability is acceptable, better 0221, CIRED, (2007).knowledge of how failure rates develop in time and whichpart of the population has a high failure probability and thus [9] F. Wester. “Condition Assessment of Power Cables usingdeteriorates the utilities quality of service. The maximum age Partial Discharge Diagnosis at Damped AC Voltages”, PhDof certain components in relation to the requested reliability Dissertation Delft University of Technology, (2004).and the failure expectation gives valuable information to theasset manager. [10] R.A. Jongen, J.J. Smit, A.L.J. Janssen. “Application of Statistical Analysis in the Asset Management Decision Process”, International Conference on Condition MonitoringBasically, resulting from the analysis, it can be concluded that and Diagnosis, (2008).even though data was either missing or incomplete, it was stillpossible to develop sensible probability methods in order to [11] H. Lee Willis. “Power Distribution Planning Reference Book”,provide the asset manager with useful information which can 2nd edition Revised and Expanded, New york: Marcel Dekkerhelp indicate future failure expectancies and support AM Inc., (2004).decision-making processes. [12] R.P.Y. Mehairjan. “Application of Statistical Life DataUnderground cable systems, in particular, and power system Analysis for cable joints in MV Distribution Networks –Aninfrastructures, in general, will be characterized by increasing Asset Management Approach-”, MSc Thesis Report, Delft University of Technology: Electrical Engineering (2010).failure rates and will eventually result in higher costs foroperation and repair and customer costs for degraded systemperformance. Presently, most approaches are reactive and arenot able to strictly address the fact that cable system failurerates will rise in the future years. Probabilistic failure ratemodelling can help utilities to better predict failures and assetmanager in their decision support regarding replacement,maintenance and cost-effective budget plans. 6