# Reliability Analysis for Asset Management of Electric Power Grids

Wiley - IEEE

1. Auflage März 2019

520 Seiten, Hardcover*Wiley & Sons Ltd*

**978-1-119-12517-4**

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.

Key features:

* 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.

Acknowledgements xxi

List of Symbols and Abbreviations xxiii

About the Companion website xxix

1 Introduction 1

1.1 Electric Power Grids 1

1.2 Asset Management of Electric Power Grids 2

1.3 Maintenance Styles 4

1.4 Incident Management 20

1.5 Summary 21

2 Basics of Statistics and Probability 25

2.1 Outcomes, Sample Space and Events 26

2.2 Probability of Events 29

2.3 Probability versus Statistical Distributions 30

2.4 Fundamental Statistical Functions 33

2.5 Mixed Distributions 38

2.6 Multivariate Distributions and Power Law 49

2.7 Summary 59

3 Measures in Statistics 63

3.1 Expected Values and Moments 63

3.2 Median and Other Quantiles 73

3.3 Mode 75

3.4 Merits of Mean, Median and Modal Value 75

3.5 Measures for Comparing Distributions 77

3.6 Similarity of Distributions 82

3.7 Compliance 96

3.8 Summary 97

4 Specific Distributions 101

4.1 Fractions and Ranking 101

4.2 Extreme Value Statistics 112

4.3 Mean and Variance Statistics 124

4.4 Frequency and Hit Statistics 134

4.5 Summary 152

5 Graphical Data Analysis 157

5.1 Data Quality 158

5.3 Model-Based or Parametric Graphs 176

5.4 Weibull Plot 178

5.5 Exponential Plot 188

5.6 Normal Distribution 193

5.7 Power Law Reliability Growth 197

5.8 Summary 202

6 Parameter Estimation 207

6.1 General Aspects with Parameter Estimation 207

6.2 Maximum Likelihood Estimators 212

6.3 Linear Regression 223

6.4 Summary 263

7 System and Component Reliability 267

7.1 The Basics of System Reliability 267

7.2 Block Diagrams 268

7.3 Series Systems 269

7.4 Parallel Systems and Redundancy 272

7.5 Combined Series and Parallel Systems, Common Cause 273

7.6 EXTRA: Reliability and Expected Life of k-out-of-n Systems 276

7.7 Analysis of Complex Systems 277

7.8 Summary 285

8 System States, Reliability and Availability 291

8.1 States of Components and Systems 291

8.2 States and Transition Rates of One-Component Systems 292

8.3 System State Probabilities via Markov Chains 297

8.4 Markov-Laplace Method for Reliability and Availability 303

8.5 Lifetime with Absorbing States and Spare Parts 306

8.6 Mean Lifetimes MTTFF and MTBF 310

8.7 Availability and Steady-State Situations 312

8.8 Summary 314

9 Application to Asset and Incident Management 317

9.1 Maintenance Styles 317

9.1.1 Period-Based Maintenance Optimization for Lowest Costs 317

9.2 Health Index 334

9.3 Testing and Quality Assurance 338

9.4 Incident Management (Determining End of Trouble) 342

10 Miscellaneous Subjects 367

10.1 Basics of Combinatorics 367

10.2 Power Functions and Asymptotic Behaviour 369

10.3 Regression Analysis 380

10.4 Sampling from a Population and Simulations 386

10.5 Hypothesis Testing 407

10.6 Approximations for the Normal Distribution 408

10.6.1 Power Series 409

10.6.2 Power Series Times Density f (y) 409

10.6.3 Inequalities for Boxing R(y) and h(y) for Large y 410

10.6.4 Polynomial Expression for F(y) 410

10.6.5 Power Function for the Reliability Function R(y) 410

10.6.6 Wrap-up of Approximations 412

Appendix A Weibull Plot 413

Appendix B Laplace Transforms 415

Appendix C Taylor Series 417

Appendix D SI Prefixes 419

Appendix E Greek Characters 421

Appendix F Standard Weibull and Exponential Distribution 423

Appendix G Standardized Normal Distribution 429

Appendix H Standardized Lognormal Distribution 435

Appendix I Gamma Function 441

Appendix J Plotting Positions 447

References 469

Index 473

The book features ten chapters, with the main focus on the fundamentals of statistics. The way the book is written makes it possible to be used as supplement to lectures at universities about asset management because of the following points. Each chapter features an introductory paragraph and a section at the end with a summary of the topics covered by that chapter. Furthermore, each chapter provides exemplary questions and exercises which facilitate understanding of the chapter. Additionally, the author supports his argumentation with easily understandable practical examples from the field of electrical engineering. - Nicholas Hill, TU Braunschweig, Germany

Anybody working in asset and incident management of electric power grids will greatly welcome this book if they want to understand and apply the mathematics used for assessing the reliability and availability of components and systems. The author makes a decisive step forward in presenting the knowledge and skills needed for analyzing failure data and constructing reliable systems. Throughout the book, readers can taste the thorough experience of Ross both as a practitioner and as a researcher in the field of reliability analysis. This makes the book a must-have for engineers, asset managers and risk managers who are interested in decision analysis for managing assets of electric power grids. - Rene Janssen, Associate Professor of Mathematics and Operations Research at the Netherlands Defence Academy

His interests concern reliability statistics, electro-technical materials, sustainable technology and superconductivity. For energy inventions he was granted the 2004 SenterNovem Annual award and nominated 2006 Best Energy Researcher by the World Technology Network.

This book is based on studies at KEMA and IWO, lectures at KIM (Royal Institute for the Navy), and experience with utilities.