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.
Preface xvii
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 Analysis157
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 Estimation207
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 Reliability267
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 Availability291
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 MarkovLaplace 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 Management317
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 Subjects367
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
