A practical guide to facilitate statistically well-founded decisions in the management of assets of an electricity grid
Effective and economic electric grid asset management and incident management involve many complex decisions on inspection, maintenance, repair and replacement. This timely reference provides statistically well-founded, tried and tested analysis methodologies for improved decision making and asset management strategy for optimum grid reliability and availability.
The techniques described are also sufficiently robust to apply to small data sets enabling asset managers to deal with early failures or testing with limited sample sets. The book describes the background, concepts and statistical techniques to evaluate failure distributions, probabilities, remaining lifetime, similarity and compliancy of observed data with specifications, asymptotic behavior of parameter estimators, effectiveness of network configurations and stocks of spare parts. It also shows how the graphical representation and parameter estimation from analysis of data can be made consistent, as well as explaining modern upcoming methodologies such as the Health Index and Risk Index.
* Offers hands-on tools and techniques for data analysis, similarity index, failure forecasting, health and risk indices and the resulting maintenance strategies.
* End-of-chapter problems and solutions to facilitate self-study via a book companion website.
The book is essential reading for advanced undergraduate and graduate students in electrical engineering, quality engineers, utilities and industry strategists, transmission and distribution system planners, asset managers and risk managers.
Reliability Analysis for Asset Management of Electric Power Grids aims to provide understanding and skills for analysing data in order to assess the reliability of components and systems. The understanding and skills support not only asset management and maintenance, but also incident management. The latter deals with unexpected failures that need to be evaluated to assist in decision-making.
The structure of the book is presented in Table 1 below. After an introduction (Chapter 1) that pictures asset management and incident management in qualitative terms, seven chapters follow. The subjects of these chapters are: the basics of statistics (Chapter 2), measures to quantify (Chapter 3), a range of statistical distributions with their aims and properties (Chapter 4), graphical analysis of data (Chapter 5), distribution parameter estimation (Chapter 6), system and component reliability (Chapter 7) and, finally, system states with their reliability, availability and redundancy (Chapter 8). These provide an arsenal of techniques that form a foundation for statistical analysis in asset and incident management. These eight chapters form the core of the course in reliability analysis.
Table 1 Overview of the subjects treated in the book.
Qualitative introduction on:
- asset management; maintenance styles
- incident management
Basics of statistics, addressing:
- concept outcomes, sample space, events, distribution, probability
- statistical functions F, R, f, h, H; combinations of distributions and processes; two bath tub models depending on child mortality type
- concept of ageing dose, power law and accelerated ageing
Measures in statistics:
- expected values; conditional values and Bayes' theorem
- moments; mean, median, mode, variance, standard deviation
- covariance, correlation, similarity index and compliance
The purpose, characteristics and use of various specific distributions:
- uniform, beta, Weibull, exponential, normal, lognormal, binomial, Poisson, hypergeometric and multinomial
Graphical data analysis and representations of distributions:
- parameter-free graphs, confidence intervals
- parametric plots: Weibull, exponential, normal and lognormal, Duane and Crow/AMSAA
- bias, efficiency, consistency and small data sets
- maximum likelihood, least squares and weighted least squares
- application to Weibull, exponential and normal distributions
- asymptotic behaviour, power function and unbiasing
- beta distribution-based and regression-based confidence limits
System and component reliability:
- block diagrams
- series systems and competing processes, parallel systems and redundancy, combined systems and common-cause failure
- analysis of complex systems
System states in terms of working versus down:
- states and transitions; failure and repair, absorbing down-states
- Markov chains and Laplace transforms
- mean time to first failure and mean time between failures
- availability and steady states
Practical applications to asset management and incident management:
- period-based, corrective, condition-based, risk-based maintenance
- health index, risk index and combined health index
- testing and quality with small test sets and accelerated ageing
- failure cases and probability forecast of next failures
Miscellaneous background subjects:
- combinatorics and the gamma function
- power functions and asymptotic behaviour
- regression analysis and regression-based confidence intervals
- sampling, Monte Carlo and random number generators
- hypothesis testing
Graph template and data tables Appendices
The final two chapters (Chapters 9 and 10) aim to provide deeper insight and may be used in parallel with Chapters 1-8. Chapter 9 discusses a range of practical cases from asset management and incident management while using the techniques as explained in the previous chapters. Per case, it is indicated from which section the information is taken. Elements of the sections can be used for illustration during the course to complement the teaching from other chapters. Interested readers from the electric power industry may choose to start with Chapter 9 and select the aspects of reliability analysis that they would like to study more deeply, then follow the references.
Chapter 10 also aims at providing deeper insight, not so much by treating practical cases, but rather by studying a range of subjects in more depth. Depending on the courses given, the topics from this chapter may be added to lectures on Chapters 1-8.
The book covers some relatively new subjects and approaches, such as:
- The difference in the meaning of statistical distribution and probability, as discussed and followed throughout the text.
- Child mortality and the bath tub model, discussed with two different meanings. Statistically often associated with a declining hazard rate, in practice the meaning of child mortality is often encountered as a weak subpopulation which does not necessarily mean a declining hazard rate at all. The two models are discussed.
- The power law concept associated with the ageing dose concept and used for discussing accelerated ageing and testing.
- Asymptotic behaviour of bias and variances, described with a three-parameter power function. This approach leads to an elegant unbiasing method in parameter estimation.
- The power function also used to approximate the normal distribution.
- The similarity index, introduced to compare distributions, which is useful for evaluating whether two distributions are the same and for estimating the number of failures yet to come. Determining the significance is discussed, and various examples are elaborated.
- Consistency between graphical analysis and parameter estimation, which means that the best fit in a graph is identical to the best fit from parameter estimation.
- Comparable views on the confidence limits based on random sampling (beta distribution) versus linear regression.
- The relation between Monte Carlo simulations and sampling from the ranked cumulative distribution space. Numerical integration and mapping the ranked F-space is discussed. The effect of quality control testing on the resulting ranked F-space and confidence limits is demonstrated.
- Much attention is paid to analysing small data sets. It is acknowledged that large data sets are necessary for accurate statistics. On the other hand, data are often scarce, with incident management and timely decision-making required. While conclusions may not be very accurate, for decision-making after unexpected failures they may be good enough and - more important - can support timely decision-making.
- The statistical models related to maintenance models, like corrective, period-based, condition-based and risk-based maintenance, as well as models like the health index, risk index and combined health index.
As shown in Table 1, a range of distributions and plotting methods are discussed, including the Poisson distribution and Crow/AMSAA plots. Five distributions stand out in the discussions:
- Weibull, because it is the asymptotic distribution for the weakest link in the chain, which applies to many failure incidents.
- Exponential, because maintained components and systems tend to have a more or less constant hazard rate, which is a property of the exponential distribution.
- Normal, because it is the asymptotic distribution for the mean and standard deviation. It helps in evaluating the accuracy of regression analysis.
- Beta, for confidence limits and ranked sampling.
- Uniform, which is fundamental to random sampling.
Additional distributions are discussed due to their peculiar properties.
The book is a considerable extension of the manuscript used for courses on system reliability at the Netherlands...