Statistical lifetime management for energy network components

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Statistical lifetime management for energy

network components

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Statistical lifetime management for energy

network components

Proefschrift

ter verkrijging van de graad van doctor aan de Technische Universiteit Delft,

op gezag van de Rector Magnificus prof. ir. K.C.A.M. Luyben, voorzitter van het College voor Promoties,

in het openbaar te verdedigen op donderdag 7 juni 2012 om 12.30 uur

door Rogier Andreas JONGEN elektrotechnisch ingenieur

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Prof. dr. J.J. Smit

Samenstelling promotiecommissie: Rector Magnificus, voorzitter

Prof. dr. J.J. Smit, Technische Universiteit Delft, promotor Prof. ir. L. van der Sluis, Technische Universiteit Delft

Prof. ir. W.L. Kling, Technische Universiteit Eindhoven Prof. dr. M. Muhr, Technische Universität Graz, Oostenrijk Prof. dr. ing. G. Balzer, Technische Universität Darmstadt, Duitsland Prof. dr. hab. inż. J. Maksymiuk Politechnika Warszawska, Polen

Dr. ir. P.H.F. Morshuis, Technische Universiteit Delft

Prof. dr. M. Zeman, Technische Universiteit Delft, reservelid

The investigations for this thesis were financially and technically supported by Liander N.V. (former N.V. Continuon) and the foundation Ksandr (Knowledge Sharing and Research).

ISBN: 978-94-6169-231-3

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In loving memory of my father, and to Shirley, Lieve and Norah

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Summary

Statistical lifetime management for energy network components

Utilities are faced with aged infrastructures with an upcoming unavoidable replacement wave to maintain a high reliability. In this thesis a methodology is presented for the application of statistical lifetime management for network component populations in electrical and gas networks. The methodology describes the process to use network component lifetime data to provide lifetime predictions which can be further used in the asset management decision process. In the several presented case-studies the methodology is applied to collect the data, perform the statistical analysis and eventually obtain the future predictions to be evaluated in the decision process.

The research presented in this thesis was initiated by a cooperation between Delft University of Technology and the Dutch utility Liander to search for tools and technologies supporting the asset management maintenance and replacement decision processes for service aged components. Asset populations of energy networks are subject to different failure stages, e.g. ageing. These failure modes depend highly on the specific type of network components and the application. Decisions have to be made, based on e.g. economical or reliability reasons, on the strategy for managing the network as a whole, for a population of a certain asset or for individual components. An indispensable part of the asset management decision processes is related to the problematic of asset remaining life estimation. This information is of strategic importance to trigger maintenance and replacement activities on the right moment in time.

To provide the relevant tools suitable for application within asset management, this thesis elaborates on the use of statistical analysis for the evaluation of particular asset populations. The availability and contents of the asset data, failure statistics and service life history are discussed. Furthermore,

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application of the most suitable methods on a selected number of asset populations is discussed. These populations are selected based on availability of data and criticality of the component in the network.

This thesis focuses mainly on components of the electrical infrastructure but also components of natural gas infrastructures with a comparable risk profile are investigated. These two types of infrastructures have a comparable state of the art in technology used and a similar grid structure. This thesis starts with the development of techniques used for collecting lifetime data on these network components in terms of availability, in terms of sources and which information is needed for verification and selection of data. To supply the reader with a background in the statistical tools used, an overview is given of statistical tools that are applied for the evaluation of lifetime data.

Populations of specific types of MV cable joint were chosen to investigate the analysis and its results of lifetime data. The outcomes of this investigation show examples of an ageing failure behaviour as well as early life failure behaviour. Furthermore the influence of a replacement strategy is discussed on the failure estimation. The improvement on the failure development due to an applied testing program is investigated.

In the daily practice of utilities they are confronted with relatively small population sizes or small numbers of failures. The influences of component populations with a relatively small number of occurred failures on the outcomes of the analysis in relation to the number of failures are presented based on case studies concerning a specific epoxy bushing and a population of power transformers.

Furthermore, the analysis of a relatively large population of components in a natural-gas network is investigated. The results show the influence of an incomplete dataset and the distinction that is made between two failure stages.

These specific case studies were used to investigate whether the data available within utilities is of sufficient size to find failure rate functions for groups of assets, whether statistical function could be applied in order to extrapolate the functions and whether the outcome of the analyses is of some practical relevance to evaluate in the asset management decision process. To close the gap between the statistical tools and the asset management decision process, the different case studies presented are discussed in relation to the relevant asset management questions. The outcomes of the statistical analyses can

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provide the answers with respect to typical asset management decisions. It is shown in which way the outcomes of the practical case studies have contributed in the asset management decision process. Despite the fact that the failure data for network components are often limited, incomplete and sometimes imperfect, the collected life time data in the presented case studies is appropriate to be used for statistical analysis as long as the input conditions are observed.

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1

Introduction

1.1 Asset management objectives

Nowadays, energy utilities are confronted with challenges from different perspectives. Deregulation of energy markets brings about important changes in the working environment of power utilities. As a result of competition, the network operators have to concentrate more on asset management (AM). On the one hand AM concerns to reduce costs, to postpone investments and to optimise technical management while keeping at the same time the reliability and power quality at high level. On the other hand AM has to deal with an ageing infrastructure. With a value in the order of several tens of billion Euros of electrical network infrastructure in the Netherlands and the upcoming unavoidable investment wave to replace the ageing infrastructure, investments need to be well chosen for the coming years.

An integral approach is applied based on selecting those issues where the largest cost savings will be reached. Besides this the most important risk reduction and performance improvements are achieved.

The focus can be on a system view, where the combination of the individual network components is regarded to operate as system. For this research a second approach is chosen where the particular performance of the different individual network components is evaluated. The latter implies, in case of for instance high voltage components like switchgear, power transformers or power cable systems, the implementation of optimal maintenance and replacement strategies, which are necessary to meet the expectations of all stakeholders, for example efficiency requirements imposed by the government. To be able to evaluate the overall performance of the system it is important to obtain the individual performance of the network components.

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An indispensable part of the asset management integral approach is related to the problematic of asset remaining life estimation. This information is of strategic importance to trigger the maintenance/replacement activities on time.

Asset populations of an electricity network are subject to different failure modes. These failure modes depend highly on the type of component. For example, components type specific ageing and wear-out of an asset which takes place during the asset’s whole service life could lead to different failure behaviour.

Decisions have to be made, based on e.g. economic or reliability reasons, on the strategy for managing the network as a whole, for a population of a certain asset, or for individual components. A structured approach is required to optimise the replacement of ageing assets. To support the asset management decision making, various information sources and data analysis tools are used. This can provide the information which is an integral part of the asset management framework pyramid, Figure 1.1 [1].

Strategy

Organisation Information

Process

Figure 1.1 The pyramid presenting the asset management framework [1]

In this AM framework the four main management accountabilities are presented. The figure shows that the elements have an interaction and are dependant with each other. The focus in this thesis is especially on the information part within the AM framework pyramid. This information part consists of elements like: information architecture, management information and decision support. Although these elements are closely related to each other, there often exists a gap between the available asset information from one side and the analysis of these data which eventually has to support the AM decision process.

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1.2 Failures in the MV and HV electricity network

Within operational asset management different goals are formulated, such as: • Optimisation of revenue

• Shareholder interest • Risk management

• Compliance with regulations

These goals are related to the network availability and the technical ability of supplying energy over the network. These factors are influenced by for instance the design of the network structure, the possibility of minimizing failure rates and the time of repair.

The design of the network structure in such a way that a certain availability level is obtained is a historically well described subject in literature which is found for example in [2, 3] and is not further discussed. The scope of this thesis is to obtain failure rate functions of network components and to use these to evaluate the future failure development. Furthermore is analyzed which effects maintenance and replacement strategies have on the future failure expectation. The goal is to include this information in the asset management decision process.

An important information source is life time data of network components. This data includes failure data of components. Failures of single network components are an important aspect in the power outage of the network. Depending on the location of a failure in the network a various number of customers can encounter loss of energy supply. When this occurs, the duration of the interruption is an important factor. The combination of the number of customers affected and the time duration to restore the energy supply is summarized over a year and averaged over the total number of connected customers. This result in the total minutes lost per year due to power interruptions, which is shown in Figure 1.2 for different countries in Europe [4]. From this figure it is seen that large fluctuations are present for the various years, as well large differences between the different countries.

As an example the total minutes lost for the Netherlands are taken for a more detailed overview. It is seen that the mean total minutes lost per year over a period of 5 years is 30 minutes. The Netherlands has one of the highest availabilities in the electricity supply of Europe with a mean reliability of 99.9943 over 5 years [5]. These figures are a total over all the interruptions in low-, medium- and high voltage networks. It is seen in Figure 1.3 that the

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largest contribution of minutes lost per year are assigned to the failures in the medium voltage network. A clear trend in the number of minutes lost in the past years can not be found.

0 100 200 300 400 500 600 700 800 900 1000 1999 2000 2001 2002 2003 2004 2005 2006 2007 Year M in u te s l o s t p e r y e a r r x

Estonia Hungary Iceland Italy the Netherlands Portugal Spain Sweden United Kingdom

Figure 1.2 Total minutes lost per year for different countries in Europe [4]

Furthermore it is seen that the contribution to failures in the low voltage network shows to have a stable number over the past years. In the low voltage network only a relatively small number of customers are affected.

0 10 20 30 40 2000 2001 2002 2003 2004 2005 2006 2007 Year M in u te s l o s t p e r y e a r x LV (≤ 1kV) MV (> 1kV and < 35 kV) HV (≥ 35kV)

Figure 1.3 Total minutes lost per year in the Netherlands for the low- medium and high voltage (including extra high voltage) network [5]

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In the high voltage network the outage time is more fluctuating if the numbers of the past years are compared. This is explained due to the fact that in some years external incidents occurred resulting in long outage times. Furthermore is the outage time very dependent on the number of affected customers and the time needed to restore the energy supply by means of repair or switching. Figure 1.4 shows that several causes are assigned for occurring failures in the medium voltage- and high voltage network. One of the mentioned causes is ageing / wear of network components with 11.9% for the medium voltage network and 15.3% for the high voltage network. This shows that ageing is designated as a significant failure cause in the network.

Ageing / wear 15.3% Internal defect 10.5% Different known causes 22.7% Digging 30.9% Other 14.7% Soil movement 5.9% Control 5.5% Protection 7.3% Other external 11.0% Ageing / wear 11.9% Internal defect 8.3% Different known causes 11.0% Unknown despite investigation 8.3% Digging 10.1% Weather influence 14.7% Other 11.9%

Figure 1.4 Failure causes in the Netherlands for the medium voltage network (left) and the high voltage network (right) [5]

In [7,8] it is shown that failures due to ageing network components will increase in coming years. This can even cause a replacement wave, due to the replacement of large parts of the network which will reach the ageing zone on their end of life.

Altogether, this makes it valuable to use the failure data of components, or particular in a broader sense, the life time data of components. To obtain information from these data analytical tools are used.

1.3 Failures and the application of statistical tools

Asset management of electrical utilities concerns the fundamental question about repair or replacement of network components, such as cables, switchgear and transformers. For support in drawing conclusions about the selected strategy, one applies the knowledge from past experiences (e.g. expertise obtained on the failure behaviour of a certain component), post

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mortem research (e.g. failure investigation) and predictive tools to evaluate possible future behaviour. On the other hand applied tools to support in the decision making are in particular [15]:

• Diagnostic measurements performed on the components during service life.

• Analysis of failure data obtained from the selected components for investigation.

Practical considerations have to be taken into account when using statistical failure analyses of service aged components, for instance the mathematical and physical background. Finally the analysis is used to draw conclusions to be used for further decision making.

In order to be able to use statistical analysis, the proper data needs to be collected. Life time data are gathered during the whole life of given technical components, starting from the moment of installation. However for older equipment these data are not always available due to e.g. missing or lost documentation. It has been experienced that due to the introduction of electronic databases more data becomes available and that various processes are implemented to increase the quality of these data.

F

a

il

u

re

r

a

te

,

λ

(t

)

t

I

II

III

Figure 1.5 Example of a bathtub curves and typical phases during the service life of components.

A prime role in statistical analysis plays to the so called bathtub curve, as shown in Figure 1.5. This curve describes the development of the failure rate, λ(t) according to the age of the component. The bathtub curve describes the

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failure rate during the three stages of life of the power components. The shape of such a curve in region I is characterized by a decreasing trend of the failure rate, indicating early failure or childhood disease. The so called useful life (II), in the restricted time region, shows a constant failure rate indicating random failure behaviour. The practically useful life until the end of the service life (III), stretched for over 15 to 50 years of exploitation, is connected practically with the presence of different wear-out and ageing processes.

Asset data needs to be evaluated to determine the stage of life (a part of) the component population is in. If a large amount of statistical information of asset data is available then accurate statistical tools are used. However this is often not the case and only partial information is available [62]. Studying the influences and constraints connected with the given random events (failures) offers the possibility of a better understanding of the nature of failures under discussion. Further, it allows the application of formalized statistical procedures for obtaining conclusions in a proper way [6].

1.4 Objectives of this thesis

The objective of this thesis is the development of a structured method to bridge the gap between the available information on one side and asset management decision processes of network components on the other side by application statistical analysis.

This thesis focuses on the application of statistical data analysis tools on lifetime data of energy network components to determine and to evaluate statistical distributions. The obtained distributions are used to evaluate the effect certain replacement and maintenance strategies can have on the development of the future failure estimation of network components. The emphasis is placed on the analysis of authentic data of selected energy network components like cable joints, switchgear, transformers and natural gas network components.

The evaluation of lifetime data of energy network components encounters the challenges of for instance the small number of populations and number of occurring failures, the collection of a homogenous dataset and the required expertise for the data evaluation. The requirements on the data are further discussed in chapter 2.

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1. The collection of the available and suitable data, 2. The application of statistical tools on the data,

3. Verification of the obtained results and application of statistics,

4. The evaluation of future failure development based on the extrapolation of the statistical distribution,

5. The application of the obtained information for asset management decision support.

The presented research in this thesis is divided in the following topics:

• Analysis and evaluation of particular asset populations with the focus on the availability and contents of the asset data, failure statistic and service life history.

• Practical evaluation of possible statistical methods used for data analysis of assets.

• Application of the most suitable methods on a selected number of asset populations. The populations are selected based on availability of data and criticality of the component in the network. Various methods are applied and the statistical outputs are practical evaluated. In particular, the failure predictability is obtained for the selected methods and assets under consideration.

• Evaluation of the obtained information from the statistical analysis out-come and the integration of using this information in the AM decision system.

1.5 Structure of this thesis

Chapter 2 describes the experiences of collecting lifetime data in terms of availability and sources and what information is valuable to be included in the data collected.

In chapter 3 an overview is given of statistical tools which are applied for the evaluation of lifetime data.

Chapter 4 discusses the analysis and the results of lifetime data of relative large component populations with a relative large amount of failures. The outcomes show examples of an ageing failure behaviour as well as early life

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failure behaviour. Furthermore the influence of a replacement strategy is discussed on the failure estimation. The improvement due to the applied testing program, on the failure development is investigated.

The application of statistical analysis on lifetime data of component populations with a relatively small number of occurred failures is described in chapter 5. In this chapter the influences on the outcomes of the analysis in relation to the number of failures are presented

The above mentioned cases concern components in the electrical network, however in chapter 6 the analysis of a relatively large population of components in a natural-gas network is discussed. This chapter shows the influence of an incomplete dataset and the distinction that is made between two failure modes.

Chapter 7 on the application of statistical analysis in the decision support describes where analyses can provide answers to typical asset management questions. Also is discussed in what way the obtained outcomes contribute in the asset management decisions.

Chapter 8 provides the conclusions of the presented research and recommendations for further investigation.

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2

Lifetime data information sources

and formats

Information about network components is of great importance for asset management decision making [1, 15]. This information is needed as input for the AM decision process to come to a decision. To be able to extract the requested information, analysis and evaluation are needed. This continuous decision process in the asset management is shown in Figure 2.1. To be able to follow this process the first step is the collection of the requested information. In this chapter the information sources, which we used for the research, are discussed. Decision process Evaluation Analysis Information Decision

Figure 2.1 Representation of the continuous AM decision process [1, 15]

Information related to network components is becoming more and more available within utilities. The information is stored in information systems like NESTOR [16], GIS, etcetera. These databases are used for digital archiving of information in such a way that it is used for information storage, operational consult and maintenance usage. In addition, the information as available in such a database can also be used to obtain the life time data (LTD) of the network components.

These life time data can exist of e.g.:

• In service time of a component or the time to failure • Condition data of a component

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• Maintenance data of a component

In the past years investments have been made in the implementation of new databases and for the extension of existing databases. These investments are driven by the need of collecting more information which is initiated by the utility itself or by regulations of the regulator [16]. Data is defined as the factual information (as measurements or statistics) used as a basis for reasoning, discussion, or calculation. In this case these are the failure data and the data of components in service. In particular, this could be the specific input data used for statistical LTD analysis. The data are the building blocks to perform analyses which eventually results in information for decision making [61]. In this chapter the following topics concerning data are discussed:

• Which information should the data analysis lead to from an asset management point of view? (section 2.1)

• What are typical information databases where data can be obtained? (section 2.2)

• What are the needs for information and data, suitable for statistical LTD analysis? (section 2.3)

• How to collect data and judge the data to obtain a homogenous dataset? (section 2.4)

• What is the minimal required information to make LTD suitable for the input of statistical analysis? (section 2.5)

2.1 Asset Management information approach

Asset Management of a utility is dealing with the following aspects [15]: • Organisation

• Information • Processes • Strategy

All the relevant information should be directed in a proper way to the asset management in order to prepare the correct decision, see Figure 2.2. This decision should be based on an impact assessment and concerns:

When, what, how and by whom a maintenance, re-investment or refurbishment activity should be executed.

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Decision processes Asset management analytical tools Data source Maintain Refurbish (re)-invest Asset management cockpit Contolling proces Preparing decisions based on information Statisitcal analysis of lifetime data FMECA Risk assessment Condition data network components Asset database Economical data External data Societal aspects Decision support system

Figure 2.2 Asset Management information flowchart

For these decisions, past, present and expected information about assets is indispensable. An asset database, which contains the relevant object data, should be provided. All the relevant costs like investment, depreciation, maintenance and operational activities should be linked to the objects in order to be informed about the life cycle costs up till the moment of decision making. Besides information about redundancy in the network and the design principles of the network, Several information sources are necessary for a thorough decision making process as shown in de first column ‘data sources’ of Figure 2.2:

1. An asset database of an utility, including all the standard and static information about the assets. It is of great importance that all the information related to the asset involved is “following” the asset if replaced in the network including the links to the information source as mentioned under 2. Moreover dynamical information mainly related to protection systems and connection circuits should be stored in this data source.

2. The condition data provides information about the (expected) asset behaviour. This data source should provide information about maintenance actions and failure occurrence and the history of the functionality of the asset involved. Further more the health index of a component can be included. This is the overall condition of a network component which is based on various condition data parameters.

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3. Economical data related to network planning and long term estimated changing of the grid. These information is dealing e.g. with expansion of network parts of with the reduction and or the phasing out of network parts or components. Economical data is related to constraint costs and results from regulator negotiations concerning in which way availability/cost ratio information has to be provided.

4. Data regarding external and societal aspects. This information deals with the acceptability or (economic) consequences of interruptions in power supply related to environmental or personal safety, possibility of customer loss or even consequences at governmental level (large industry losses, unacceptable number of outage minutes, safety issues, etcetera). These utility specific information is often described in the business values and the key performance indicators (KPI’s)

All this data has to be evaluated together in an asset management decision support system. In this system the correct relations between the different data will be used to evaluate the possible actions. The asset management cockpit function provide the basis for controlling the information coming in, judging the advice given by the expert system and deciding and managing the action to be taken based on the risk level.

The data sources mentioned under points 1 and 2 are especially of interest to provide the suitable information which is used for the input for statistical life time data analysis.

2.2 Databases for obtaining data of in-service components

If we consider the statistical analysis of life time data, information regarding the network component population is needed. This life time data consist of failure data of the components on one hand but it is of importance to include the data of the total population of components in service on the other hand. This information has to contain at least the basic information, e.g. type of equipment, year of installation. However we have observed that the availability of more detailed information gives the ability to obtain a more structured and consistent estimation. The extra information available makes it for example possible to exclude certain data if it does not meet the definitions which have been set out in advance. The extra information can also provide the possibility to divide the dataset in smaller datasets. In this way a more detailed analysis of the data is performed on e.g. a sub-population level.

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In most cases, it has been observed during the research that the dataset for the input of the statistical analysis could not be extracted from one database source. To obtain the basic needed information and more additional information for e.g. data verification, different information databases were needed. In some cases it was needed to combine the information from the different databases by means of queries. In this way the appropriate data was selected and the lifetime datasets were obtained. In this section various databases used are described.

2.2.1 Nestor

The main source for failure data as used in this thesis is obtained for electrical network components from the failure database called Nestor Electricity (Nestor-E) and for gas components in Nestor Gas. The failure registration in Nestor-E was already started in 1976.

Nestor is used to register failure in the low voltage-, medium voltage, high voltage and extra high voltage range. The last one is since 2007 added in Nestor-E. For the gas network a separate failure registration database is created Nestor Gas. The data in Nestor is owned by the regional utilities in the Netherlands and is used internally by the utilities, yearly reporting to Office of Energy Regulation (Energiekamer), as well for yearly reliability benchmarking. From 2000 there exists a legally required failure registration for utilities in the Netherlands. Nestor-E is an integral failure database used by every utility, to enter occurring failures in the network irrespectively if the failure leads to a disruption in energy supply. Nevertheless, it took till 2004 that the failures concerning all connected customers are reported, providing a 100% coverage. Figure 2.3 shows how failures are collected in the Nestor database. The entry of a failure starts with fault indication. This is for instance a message from a customer who reports an outage, or a message from the substation automation. The fault indication will result in an action to rectify the fault. After restoration of the fault, the details of the fault are registered in a form based application and subsequently entered in the database system Nestor. The data stored in Nestor is further used for reporting, data extraction and analysis.

The data entries in the Nestor database have been adapted over the years in particular to comply with new regulations and to improve the quality of the failure registration. This resulted in an increase of the data quality as well an increase in the availability of additional information regarding failures. We

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observed that the database structure makes is relatively easy to obtain the failure data of a network components by making queries. After extracting the data from the database there is still a need to manually analyse the individual data entries. In this way it is verified that each failure meets the predetermined conditions and if the entry should be included in the input dataset for further analysis.

Network Component Observed failure Failure cause Age (interval) Failure duration Customer minutes lost

etc… Fault indication Fault rectification Describe fault details Completeness check Nestor Reporting Data extraction

Figure 2.3 Flowchart indicating the registration process in Nestor in case of a network component failure

2.2.2 Geographic information system

A geographic information system (GIS), is an information database system to obtain, store, analyse and presenting data which are linked to a component at a certain location in the network. From GIS databases data is retrieved and statistically analysed for decision making. The failure data can be obtained from mobile GIS applications. With the widespread adoption of GPS, GIS has been used to capture and integrate failure data from the engineers in the field, who deal with the actual failures.

GIS applications are software tools that allow users to create interactive queries (user created searches), analyze spatial information, edit data, maps, and present the results of all these operations.

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Geographic information system technology is very useful for data analysis and asset management. In case of an energy network, a GIS database system contains the circuit model topology, which shows where components are geographically located, how they are interconnected and component information [13].

In this research the utility GIS databases are used to obtain missing information from the failure database Nestor. In one of the case studies described in this thesis, the failure data did not contain the year of installation of the components while in GIS this was (partly) available. By means of applying queries the data of the two databases could be linked and the missing information was obtained. The quality of the data available in the Utility database is increasing over the years by entering more network data and the verification of entered data.

2.2.3 International Financial Reporting Standards

The International Financial Reporting Standards (IFRS) [18] is a combination of standards that lay down in which way companies present their annual report. The reporting according to IFRS is based on fair value or actual value of e.g. assets. Although IFRS is more based on financial issues it can help to complete databases of in service components because the asset population has to be described. This database contained for example valuable information regarding the ages of components in services which was used to obtain a complete life time dataset.

2.2.4 Enterprise resource planning

Enterprise resource planning (ERP) is the planning of how business resources (components, materials, employees, customers etc.) are available. Several ERP systems are commercially available. Well known ERP based applications are e.g. SAP and PeopleSoft. An ERP system supports most of the business processes within an organisation. It is a system that maintains in an automated database the data needed for a variety of business functions such as Manufacturing, Supply Chain Management, Financials, Projects, Human Resources and Customer Relationship Management.

The discussed different databases were in this research used to obtain the necessary information and data. This list is not complete and it is known that more information databases are used within different utilities. Various data sources were needed to form the datasets for statistical life time analysis. The

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implementation of statistical life time data analysis in the asset management decision process could result in the adaption of the databases and database structures. However, often the direct underlying thoughts of the database structures are not providing input data for the application of statistical life time analysis. On the other hand is the adaption of databases an iterative process which needs a tremendous effort and time.

2.3 Needs for life time data

The available information from the different utility databases is used for [9]: - quality monitoring,

- ascertaining compliance with safety requirements, - system availability evaluation,

- economic criteria - legislation restrictions

It is of importance that the data fulfils the basic needs for the application of statistical analysis [10]. In Figure 2.4 the fundamental information required of the data is shown in the basic information level. This level consists of information regarding the (sub) component that failed. The age of the failed component and what kind of failure occurred.

This list is not exhaustive and extra information can be added to meet specific needs, e.g. for a particular component. In the figure the first three blocks show the questions which have to lead to the basic level of information which is required to be able to perform statistical life time data analysis.

2.3.1 Data types

We have shown in the previous section that life time datasets are often obtained from several information databases. Due to the dependability of the information structure of a database, data is available with different contents of information.

The availability of the different information levels within the dataset determines in which way the statistical analysis with a certain nature of detail can be performed. With that the type of data is of importance. Some of the available formats are discussed here [15,17].

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Figure 2.4 Requested information on life time data with the most basic information level and more extensive information levels

2.3.1.1 Complete data

When the failure time of each component is known, the data are called complete data. All the components in the group have failed and the time of failure is known. In Figure 2.5 a total of n components are considered, which failed all at known times.

N o . o f C o m p o n e n t n 5 4 3 2 1 Time (t) failed Age

Figure 2.5 Example of a complete data set with only failures Life time data What (sub) components Failed? When did it fail, e.g. at which age?

How did it fail?

Why did it fail, e.g. special Circumstances? Is it a: major failure (MF) minor failure (mf) Is a failure Investigation performed? What Corrective action Was taken? …? Final data format Basic infor -mationlevel Extensive information levels

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This type of data is often present when a population of components are all run or tested until failure. This is especially the case when laboratory experiments are analyzed. This type of data is often not applicable for in service components, while not all components are used until failure.

2.3.1.2 Censored data

Life time data of network components contain components that did not all fail, or for which the exact times-to-failure are unknown. This type of data is often known as censored data. When a range of components consists of failed units as well of units that are still in service, this is called right censored data or suspended data. This is schematically displayed in Figure 2.6. Characteristic for lifetime data in practice is that the components are installed at different years, as shown in the figure.

When the exact time-to-failure is not known, but it was known that the component was functioning on a certain time and it had failed between that time and a later time, e.g. the inspection time, this is defined as interval censored data or inspection data.

The data can also be left censored. This is quite similar to the interval censored data. The moment of a failure is only to be known before a certain time.

N o . o f C o m p o n e n t n 5 4 3 2 1 Time (t) t_present In service failed Age

Figure 2.6 Example of a right censored data set with failures and suspensions

2.3.2 Judgement of life time data

In the process of collecting life time data, an important aspect is the judgement of this data. The available data of in service components is

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evaluated and analyzed if it reflects the total component population. This means for instance that the data is evaluated with questions like:

• Is the desired information available, e.g. age of failed components, age of in-service components?

• Is the database complete? Is it possible to obtain the required information of the components under consideration?

• Is specific information estimated, e.g. years of installation/ages? This of relevance for the confidence of the performed analysis.

For this thesis the required information has been obtained by analyzing the database and by consulting databases and if more component specific information was needed, component experts were consulted.

For failure data the judgement of the information deals with the analysis of the available data and to obtain the failures which fall under the pre-defined failure description. This means that in the first step it has to be defined which components, failure modes and failure causes are evaluated. As a second the data records of the failure database are reviewed to distinguish the failures which are of interest [14].

2.4 Basic demands on information in databases

As mentioned before, to be able to use statistical analysis, care has to be taken by collecting the appropriate data for the analysis. This implies that the data should have the following properties [12]:

• Randomness, • Independency, • Homogeneity,

• Minimal number of data.

In general the failure data of the whole life of a component population is not available within the utility. Although this implies that it is not possible to obtain all life stages of a component population we showed how to use the available data for statistical analysis and to derive the current life stage, e.g. random failure behaviour or ageing failure behaviour.

To be able to perform proper statistical analysis representing the failure behaviour of a population which shows a correct relation of the age at failure, it is important that the available data contains:

- Known type of (sub) component - Uniformity of failure data

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- Distinction of failure causes/modes - Year of installation of the component - Date/year of occurrence of the failure

Figure 2.7 The basic needs of life time data used as input data for statistical analysis

The basic needs and suggested information content of the life time data used as input for statistical analysis is shown in Figure 2.7. In this figure the minimum requirements for data are shown to be able to perform the statistical analysis.

2.5 Conclusions

Data selection and collection are the basis to be able to perform the statistical analysis. For this it is of great importance to provide a reliable and consistent dataset. From this point of view the following conclusions are drawn:

1) To be able to perform statistical analysis, the basic needs for the life data require to be fulfilled. This means that for a specific component and failure mode under consideration, the ages of in-service- and failed components need to be known. With more additional information available about components and failures, a more reliable data selection and in-depth analysis is possible. In service data Life time data Failure data Component

type Age Number

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2) Available databases within the utility, e.g. Nestor, GIS-databases, ERP-based databases, are used to obtain the data. Information of different databases is combined to obtain the right needed information.

3) Historical data before the introduction database like e.g. Nestor are found in utility specific databases, which contain often the requested data from 20 – 30 years ago.

4) The life time data (LTD) obtained from the information databases needs to be evaluated en judged to guarantee the consistency for the data.

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3

Statistical tools for the analysis of

lifetime data

Reliability evaluation of components and systems is still a growing field of interest from a research point of view as well as industry point of view. The performance of components and sub-components in the network is of increasing interest within the asset management of utilities. As discussed in the previous chapter the amount of data available is increasing tremendously in the last era. This makes it necessary to reduce data in processing the data for decision making. When considering lifetime data of components in the energy network a large variation in data formats and quantities are available. Evaluation of lifetime data by means of statistical tools is a very suitable form providing valuable information, which is applied for decision making.

In this chapter a selection is made of the statistical tools used. In Figure 3.1 the flowchart shows the steps we used for statistical analysis of lifetime data. In this chapter the non- parametric and parametric methods for continuous random variables are described. The following issues are described in this chapter:

1. The use of parametric statistical functions, adapted in descriptive statistics for lifetime data analysis.

2. Important analytical functions used to derive the failure behaviour. 3. Methods which are used to estimate the statistical parameters and to

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In section 3.1 the important basic statistical stochastic variables used as input for obtaining the suitable statistical function are discussed. In this section the functions will be discussed which will be applied for the lifetime data analysis. In section 3.2 the statistical available distributions are evaluated for their suitability for lifetime data analysis, especially for utility specific data. Various methods exist for parameter estimation of a statistical distribution. As a next step the goodness-of-fit of a distribution has to be determined which helps to obtain the best fitting distribution. Finally methods to determine the confidence bounds are evaluated, which needs especially attention in the case of small sample sizes. These topics are discussed in respectively section 3.3, 3.4 and 3.5.

3.1 Important statistical variables and functions

3.1.1 Random variables

Failure time data of energy network components consists of time-to-failures which represents the time span until the occurrence of a defined event, e.g. electrical breakdown of the insulation of a (sub) component. These events are assumed to occur randomly, independently and homogenously spread in time and space across the component population [35]. In the case of time-to-failure data, the random variable X can take on a value in the range of zero to infinity representing the age of a failed component.

A random variable can have a discrete or continuous character. When the random variable can only take discrete values this is a discrete random variable. In the case of lifetime data the random variables have a continuous character, where the age at failure can take on a value in a certain range.

Discrete random variables Continuous random variables Parametric method Non-parametric method Distributions e.g. Normal, Log-normal, Exponential, Weibull Distributions e.g. Binomial, Poisson Descriptive statistics Goodness-of-fit tests Confidence bounds Further analysis Data

Figure 3.1 General flowchart for

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3.1.2 Probability density function (PDF)

The probability density function (PDF) is used to describe the probability of occurrence for random variables having a continuous character of possible values, as well as for discrete random variables. If the random variable is denoted by X, its probability density function f(x) has the property that:

(

≤ ≤

)

=

_∫

b ≥

a f x dx with f x forall x

b X a

P ( ) ( ) 0 3-1

For every interval between the times a and b [a, b]; i.e., the probability that a random variable X falls in the region [a, b] is given the integral of the graph of f(t) between values a and b. This area is indicated in Figure 3.1 under the PDF plot between a time a and b.

Figure 3.2 Example of a probability density function

As a target age indicated with t is required, as shown in Figure 3.2, than is the area under the PDF plot until this time t the probability that a failure will occur in this time. The remaining part under the PDF after the time t is indicating the probability that a failure will occur after the age t.

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3.1.3 Cumulative distribution function (Unreliability function)

The cumulative failure distribution function F(X), or cumulative distribution function, gives the probability of a failure occurring before or at any time, t. This function is also known as the unreliability function.

In probability theory and statistical analysis, the cumulative distribution function (CDF), completely describes the probability distribution of a real-valued random variable X. For every real number x, the CDF of X is given by:

' ) ' ( ) ( ) (

∫

∞ − = ≤ =P X x x f x dx x F 3-2

F(x) represents the probability that the random variable X takes on a value less than or equal to x, as shown in Figure 3.2. The probability that X lies in the interval [a, b] is F(b) minus F(a) if a < b.

3.1.4 Reliability function

The reliability function displays the average between the age of a component and the probability that a component survives up to that age.

Reliability is defined as [10]: The conditional probability at a given confidence level, that the components will perform their intended functions satisfactorily or without failure, at a given age, for a specified length of time (mission time), when used under the specified application and operation conditions, with certain stress levels.

The reliability of a component up to an age t is obtained with:

)

(

1 '

)

'

(

)

(

)

(

x

P

X

t

f

x

dx

F

x

R

t

=

−

=

≥

=

∫

∞ 3-3

The graphical presentation of the reliability in relation to the probability density function is shown in Figure 3.2.

3.1.5 Failure rate function

The failure rate or hazard rate represents the frequency of failures of a component, expressed as the number of failures per time unit, for example per year [10, 21]. It is often denoted by the Greek letter lambda as a function of time, λ(t). The failure rate is usually time dependent, and the rate can change over time versus the expected life cycle of a component population.

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The failure rate function is obtained from the probability density function and reliability function by:

)

(

)

(

)

(

t

R

t

f

t

=

λ

3-4

3.1.6 Mean life function

The mean life is the average time of operation of a component to a failure. It is also known as the mean time to failure (MTTF) for not repairable components, which is the mean time before a failure occurs. The mean life function is defined as:

∫

∞

=

∞

=

0 0

t

f

(

t

)

dt

R

(

t

)

dt

MTTF

t

3-5

The relations between the analytical functions as discussed in previous subsections are summarized in the conversion table of Table 3.1. In this table the time t is taken for the random variable.

Table 3.1 Analytical statistical function conversion table

As a function of Func- tion f(t) F(t) R(t) λ(t) f(t)=

f

( t

)

dt

t

dF

(

)

dt

t

dR

(

)

−

_













−

⋅

∫

T

dt

t

0

)

(

exp

)

(

λ

F(t)=

∫

t dt t f 0 ) (

F

( t

)

1 −

R

( t

)

_













−

∫

T

dt

t

0

1 exp

λ

(

)

R(t)= −

∫

t dT t f 0 1 ( )

)

( t

F

−

1 R

( t

)

_













−

∫

T

dt

t

0

)

(

exp

λ

λ(t)=

∫

− t dt t f t f 0 1 ( ) ) ( ) ( ) ( t F dt t dF −

1

dt t dR t R ) ( ) (

1

−

λ

( t

)

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3.2 Parametric statistical distributions

In this section a selection of the applied statistical distributions which are suitable for lifetime data analysis are discussed. There are many distributions available and there will be a few mentioned here. These are often used for lifetime data but this is not an exhaustive list. The distributions are discussed in more detail in Appendix A.

3.2.1 The exponential distribution

The exponential distribution is a very wide used statistical distribution. It provides a first approach to analyze the lifetime data based on a constant failure rate. The exponential distribution describes the times to failure of components which have a constant failure rate characteristic in relation to the component age [10, 20]. The distribution has the property to be without memory and it is well-suited to model the constant failure rate interval of the bathtub curve, as described in paragraph 3.2.4.

3.2.2 The Normal and Lognormal distribution

The Normal distribution or Gaussian distribution is a widely used distribution with many fields of application [21, 34]. It is a symmetrical distribution. Because the left limit of the normal distribution can goes to negative infinity it is questioned if this distribution is suitable for modelling lifetime data of network assets. However if the mean of the distribution is relatively large with a relatively small standard deviation this issue is negligible [21].

The Lognormal distribution is another commonly used distribution. This distribution has similarities with the Normal distribution. When the logarithm of the random variable is normally distributed the random variable is considered log-normally distributed [10, 21, 34]. In contrast with the Normal distribution is the Lognormal distribution always asymmetric.

3.2.3 The Weibull distribution

In 1937 Waloddi Weibull presented for the first time the Weibull distribution. In 1951 he published about the distribution [19]. Nowadays it is one of the most commonly used distributions in reliability engineering. The reason for this is that the extreme value distribution is applicable to the weakest link failures which often occur in technical systems. Because of this the distribution can

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model a lot of different data and life characteristics. This distribution has a wide applicability in life time data analysis.

With the Weibull distribution three different failure modes can be described. Depending on the value of shape β the following modes are distinguished: • Initial failures or infant mortality: For 0 < β < 1 the failure rate is decreasing

with time. This is the case when a component fails in the early life. This can occur due to the use of poor materials, poor workmanship or manufacturing faults.

• Random failures: For β = 1 the failure rate is constant in time. The Weibull PDF becomes equal to the exponential function. These failures are occurring randomly during the lifetime of a component and are not associated with initial or wear out failures.

• Wear out failures: For β >1 the failure rate is increasing with time. The components are ageing and the failure rate will increase due to this. These different regions are shown in the bathtub curve of Figure 3.3.

3.2.4 Mixed Weibull distribution

Times-to-failure obtained from field data can represent various failure modes. Each failure mode has a distinct Weibull distribution with different parameters [21, 22]. During the different life periods several different failure modes, as described in the previous section, may occur. The proportions of times-to-failure which fall in one times-to-failure mode have to be determined and what the contribution to the reliability is, has to be quantified.

Depending on the quantity of subpopulations the following equation for the mixed Weibull PDF is given:

1

3 2 1 3 2 1 t = p⋅ f t +q⋅ f t +r⋅ f t with p+q+r = f _, _, ( ) ( ) ( ) ( ) 3-6 Or written fully:

∑

= −               −       = S i i i i i i S i i t t N N t f 1 1 , , 1 ( ) exp β β

η

β

K 3-7

Here is S the number of the subpopulations (S = 2...4).

The different analytical functions from this Weibull distribution are derived according to Table 3.1. When the failure rate of a component is plotted which

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contains failure modes of early failures, random failures and wear-out failures, a bath-tub curve is acquired, as shown in Figure 3.3.

0 0.003 0.006 0.009 0.012 0.015 0 5 10 15 20 25 30 35 40 45 50 55

Age [years]

F

a

il

u

re

r

a

te

β < 1 β = 1 β > 1

Figure 3.3 Example of a bath tube curve (mixed Weibull failure rate function) with regions of infant mortality, random failures and wear-out failures.

The difficulty with Mixed Weibull analyses is to split the failure data in the correct subpopulations. The application of Bayes’ Theorem provides an elaborate technique to accomplish this [23].

3.2.5 Competing failure modes

In a component population, more than one failure mode can be present. Competing failure modes analysis, which segregates the analysis of failure modes and then combines the results to provide an overall reliability model for the component in question, can be used to analyze data of this type.

The data sets with more than one competing failure mode are analysed for each failure mode with a separate analysis. In the analysis for each failure mode, the failure times for the mode being analyzed are considered to be failures and the failure times for all other modes are considered to be suspensions. These are suspension times because the units would have

Statistical lifetime management for energy network components