Reliability analysis for asset management of electric power grids

498 Pages·2019·11.333 MB·English

by  Ross, Robert D

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ReliabilityAnalysisforAssetManagementof
ElectricPowerGrids
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Reliability Analysis for Asset Management of
Electric Power Grids
RobertRoss
IWO,Ede,theNetherlands
TUDelft,Delft,theNetherlands
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Thiseditionfirstpublished2019
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LibraryofCongressCataloging-in-PublicationData
Names:Ross,Robert,author.
Title:Reliabilityanalysisforassetmanagementofelectricpowergrids/
ProfDrRobertRoss,IWO,Ede,theNetherlands;TUDelft,Delft,the
Netherlands.
Description:Hoboken,NJ:Wiley,[2019]|Includesbibliographical
referencesandindex.|
Identifiers:LCCN2018031845(print)|LCCN2018033843(ebook)|ISBN
9781119125181(AdobePDF)|ISBN9781119125198(ePub)|ISBN9781119125174
(hardcover)
Subjects:LCSH:Electricpowerdistribution–Reliability.
Classification:LCCTK3001(ebook)|LCCTK3001.R652018(print)|DDC
621.319–dc23
LCrecordavailableathttps://lccn.loc.gov/2018031845
CoverDesign:Wiley
CoverImage:©iStock.com/yangphoto;EquationscourtesyofRobertRoss
Setin10/12ptWarnockProbySPiGlobal,Chennai,India
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Inremembranceofmyparentsanddedicatedtomydearwife,childrenandsister.
R.R.
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vii
Contents
Preface xvii
Acknowledgements xxi
ListofSymbolsandAbbreviations xxiii
AbouttheCompanionwebsite xxix
1 Introduction 1
1.1 ElectricPowerGrids 1
1.2 AssetManagementofElectricPowerGrids 2
1.3 MaintenanceStyles 4
(cid:2) 1.3.1 CorrectiveMaintenance 5 (cid:2)
1.3.1.1 CMInspections 6
1.3.1.2 CMServicing 6
1.3.1.3 CMReplacement 6
1.3.1.4 EvaluationofCM 6
1.3.2 Period-BasedMaintenance 7
1.3.2.1 PBMInspections 8
1.3.2.2 PBMServicing 8
1.3.2.3 PBMReplacement 9
1.3.2.4 EvaluationofPBM 9
1.3.3 Condition-BasedMaintenance 9
1.3.3.1 CBMInspections 11
1.3.3.2 CBMServicing 11
1.3.3.3 CBMReplacement 11
1.3.3.4 IntroductiontotheHealthIndex 11
1.3.3.5 EvaluationofCBM 13
1.3.4 Risk-BasedMaintenance 13
1.3.4.1 CorporateBusinessValuesandtheRiskMatrix 14
1.3.4.2 RBMInspections 17
1.3.4.3 RBMServicing 17
1.3.4.4 RBMReplacement 17
1.3.4.5 EvaluationofRBM 18
1.3.5 ComparisonofMaintenanceStyles 18
1.4 IncidentManagement 20
1.5 Summary 21
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viii Contents
2 BasicsofStatisticsandProbability 25
2.1 Outcomes,SampleSpaceandEvents 26
2.2 ProbabilityofEvents 29
2.3 ProbabilityversusStatisticalDistributions 30
2.4 FundamentalStatisticalFunctions 33
2.4.1 FailureDistributionF 33
2.4.2 ReliabilityR 34
2.4.3 ProbabilityorDistributionDensityf 35
2.4.4 ProbabilityorDistributionMassf 35
2.4.5 HazardRatehandtheBathTubModel 36
2.4.6 CumulativeHazardFunctionH 38
2.5 MixedDistributions 38
2.5.1 CompetingProcesses 39
2.5.2 InhomogeneousPopulations 41
2.5.2.1 Bayes’Theorem 42
2.5.2.2 FailureDistributionofanInhomogeneousPopulation 45
2.5.3 EarlyFailuresInterpretedasChildMortality 47
2.6 MultivariateDistributionsandPowerLaw 49
2.6.1 AgeingDoseandPowerLaw 49
2.6.2 AcceleratedAgeing 52
2.6.3 Multi-StressAgeing 54
2.6.4 CumulativeDistribution,AgeingDoseandCBM 56
(cid:2) 2.7 Summary 59 (cid:2)
3 MeasuresinStatistics 63
3.1 ExpectedValuesandMoments 63
3.1.1 OperationsandMeans 65
3.1.2 BayesianMean 66
3.1.3 TheMomentsofaDistribution 67
3.1.4 EXTRA:MomentGeneratingFunction 67
3.1.5 EXTRA:CharacteristicFunction 68
3.1.6 CentralMomentsofaDistribution 69
3.1.7 TheFirstFourCentralandNormalizedMoments 70
3.1.8 Mean,StandardDeviation,andVarianceofaSample 71
3.2 MedianandOtherQuantiles 73
3.3 Mode 75
3.4 MeritsofMean,MedianandModalValue 75
3.5 MeasuresforComparingDistributions 77
3.5.1 Covariance 77
3.5.2 Correlation 80
3.5.3 Cross-CorrelationandAutocorrelation 81
3.6 SimilarityofDistributions 82
3.6.1 SimilarityofCountinginDiscreteSets 82
3.6.2 SimilarityofTwoDiscreteDistributions 85
3.6.3 SimilarityofTwoContinuousDistributions 87
3.6.4 SignificanceofSimilarity 90
3.6.5 SingularityIssuesandAlternativeSimilarityIndices 95
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Contents ix
3.7 Compliance 96
3.8 Summary 97
4 SpecificDistributions 101
4.1 FractionsandRanking 101
4.1.1 UniformDistribution 102
4.1.1.1 ContinuousUniformDistributionCharacteristics 103
4.1.1.2 DiscreteUniformDistributionCharacteristics 104
4.1.1.3 EXTRA:MomentGeneratingFunctionandCharacteristicFunction 106
4.1.2 BetaDistributionorRankDistribution 106
4.1.2.1 BetaDistributionCharacteristics 107
4.1.2.2 EXTRA:MomentGeneratingFunctionandCharacteristicFunction 111
4.2 ExtremeValueStatistics 112
4.2.1 WeibullDistribution 113
4.2.1.1 Weibull-2Distribution 113
4.2.1.2 Weibull-2DistributionMomentsandMean 115
4.2.1.3 Weibull-2DistributionCharacteristics 117
4.2.1.4 EXTRA:MomentGeneratingFunction 117
4.2.2 Weibull-3Distribution 117
4.2.3 Weibull-1Distribution 118
4.2.4 ExponentialDistribution 119
4.2.4.1 ExponentialDistributionandAverageHazardRate 119
(cid:2) 4.2.4.2 ExponentialDistributionCharacteristics 123 (cid:2)
4.3 MeanandVarianceStatistics 124
4.3.1 NormalDistribution 124
4.3.1.1 CharacteristicsoftheNormalDistribution 125
4.3.1.2 EXTRA:Moments,MomentGeneratingFunctionandCharacteristic
Function 127
4.3.1.3 EXTRA:CentralLimitTheorem 128
4.3.2 LognormalDistribution 131
4.3.2.1 CharacteristicsoftheLognormalDistribution 133
4.3.2.2 EXTRA:MomentGeneratingFunctionandCharacteristicFunction 134
4.3.2.3 LognormalversusWeibull 134
4.4 FrequencyandHitStatistics 134
4.4.1 BinomialDistribution 135
4.4.1.1 MeanandVariance 138
4.4.1.2 CharacteristicsoftheBinomialDistribution 138
4.4.1.3 EXTRA:MomentGeneratingFunction 139
4.4.2 PoissonDistribution 140
4.4.2.1 CharacteristicsofthePoissonDistribution 140
4.4.2.2 DerivationofthePoissonDistribution 141
4.4.2.3 HomogeneousPoissonProcess 141
4.4.2.4 Non-HomogeneousPoissonProcess 142
4.4.2.5 PoissonversusBinomialDistribution 143
4.4.3 HypergeometricDistribution 144
4.4.3.1 MeanandVarianceoftheHypergeometricDistribution 145
4.4.3.2 CharacteristicsoftheHypergeometricDistribution 146
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4.4.4 NormalDistributionApproximationoftheBinomialDistribution 147
4.4.5 MultinomialDistribution 149
4.4.5.1 Mean,VariancesandMomentGeneratingFunction 150
4.4.6 MultivariateHypergeometricDistribution 151
4.5 Summary 152
5 GraphicalDataAnalysis 157
5.1 DataQuality 158
5.2 Parameter-FreeGraphicalAnalysis 158
5.2.1 BasicGraphofaPopulationSample 159
5.2.2 CensoredData 160
5.2.3 Kaplan–MeierPlot 165
5.2.4 ConfidenceIntervalsAroundaKnownDistribution 168
5.2.5 ConfidenceIntervalswithData 172
5.2.6 AlternativeConfidenceIntervals 174
5.3 Model-BasedorParametricGraphs 176
5.4 WeibullPlot 178
5.4.1 WeibullPlotwithExpectedPlottingPosition 179
5.4.2 WeibullPlotwithMedianPlottingPosition 182
5.4.3 WeibullPlotwithExpectedProbabilityPlottingPosition 182
5.4.4 WeibullPlotwithCensoredData 183
5.4.5 ConfidenceIntervalsinWeibullPlots 185
(cid:2) 5.5 ExponentialPlot 188 (cid:2)
5.5.1 ExponentialPlotwithExpectedPlottingPosition 188
5.5.2 ExponentialPlotwithMedianPlottingPosition 189
5.5.3 ExponentialPlotwithCensoredData 190
5.5.4 ExponentialPlotwithConfidenceIntervals 190
5.6 NormalDistribution 193
5.6.1 NormalPlotwithExpectedPlottingPosition 194
5.6.2 NormalProbabilityPlotwithConfidenceIntervals 196
5.6.3 NormalPlotandLognormalData 196
5.7 PowerLawReliabilityGrowth 197
5.7.1 DuaneandCrowAMSAAPlotsandModels 197
5.7.2 NHPPModelinDuaneandCrowAMSAAPlots 200
5.8 Summary 202
6 ParameterEstimation 207
6.1 GeneralAspectswithParameterEstimation 207
6.1.1 FundamentalPropertiesofEstimators 209
6.1.1.1 Bias 209
6.1.1.2 Efficiency 209
6.1.1.3 Consistency 210
6.1.2 WhyWorkwithSmallDataSets? 211
6.1.3 AsymptoticBehaviourofEstimators 212
6.2 MaximumLikelihoodEstimators 212
6.2.1 MLwithUncensoredData 213
6.2.2 MLforSetsIncludingCensoredData 214
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Contents xi
6.2.3 MLfortheWeibullDistribution 214
6.2.3.1 MLEstimatorsforWeibull-2UncensoredData 215
6.2.3.2 MLEstimatorsforWeibull-2CensoredData 215
6.2.3.3 ExpectedMLEstimatorsfortheWeibull-2Distribution 216
6.2.3.4 FormulasforBiasandScatter 218
6.2.3.5 EffectoftheMLEstimationBiasinCaseofWeibull-2 220
6.2.4 MLfortheExponentialDistribution 221
6.2.5 MLfortheNormalDistribution 222
6.3 LinearRegression 223
6.3.1 TheLRMethod 223
6.3.1.1 LRbyUnweightedLeastSquares 224
6.3.1.2 LRbyWeightedLeastSquares 228
6.3.1.3 LRwithCensoredData 231
6.3.1.4 LRwithFixedOrigin 232
6.3.1.5 Whichisthe(Co)variable? 233
6.3.2 LRfortheWeibullDistribution 234
6.3.2.1 LRbyUnweightedLSfortheWeibullDistribution 235
6.3.2.2 LRbyWeightedLSfortheWeibullDistribution 236
6.3.2.3 ProcessingCensoredDatawiththeAdjustedRankMethod 238
6.3.2.4 EXTRA:ProcessingCensoredDatawiththeAdjustedPlottingPosition
Method 240
6.3.2.5 ExpectedLSandWLSEstimatorsfortheWeibull-2Distribution 242
(cid:2) 6.3.2.6 FormulasforBiasandScatterforLSandWLS 243 (cid:2)
6.3.2.7 ComparisonofBiasandScatterinLS,WLSandML 246
6.3.3 LRfortheExponentialDistribution 249
6.3.3.1 LRbyUnweightedLSfortheExponentialDistribution 251
6.3.3.2 LRbyWeightedLSfortheExponentialDistribution 252
6.3.3.3 ProcessingCensoredDatawiththeAdjustedRankMethod 253
6.3.3.4 EXTRA:ProcessingCensoredDatawiththeAdjustedPlottingPosition
Method 255
6.3.3.5 ExpectedLSandWLSEstimatorfortheExponentialDistribution 256
6.3.4 LRfortheNormalDistribution 257
6.3.4.1 LRbyUnweightedLSfortheNormalDistribution 258
6.3.4.2 ProcessingCensoredDatawiththeAdjustedRankMethod 260
6.3.4.3 EXTRA:ProcessingCensoredDatawiththeAdjustedPlottingPosition
Method 261
6.3.4.4 ExpectedLSEstimatorsfortheNormalDistribution 262
6.3.5 LRAppliedtoPowerLawReliabilityGrowth 263
6.4 Summary 263
7 SystemandComponentReliability 267
7.1 TheBasicsofSystemReliability 267
7.2 BlockDiagrams 268
7.3 SeriesSystems 269
7.4 ParallelSystemsandRedundancy 272
7.5 CombinedSeriesandParallelSystems,CommonCause 273
7.6 EXTRA:ReliabilityandExpectedLifeofk-out-of-nSystems 276
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xii Contents
7.7 AnalysisofComplexSystems 277
7.7.1 ConditionalMethod 278
7.7.2 Up-tableMethod 280
7.7.3 EXTRA:MinimalPathsandMinimumBlockades 283
7.8 Summary 285
8 SystemStates,ReliabilityandAvailability 291
8.1 StatesofComponentsandSystems 291
8.2 StatesandTransitionRatesofOne-ComponentSystems 292
8.2.1 One-ComponentSystemwithMereFailureBehaviour 293
8.2.2 One-ComponentSystemwithFailureandRepairBehaviour 294
8.3 SystemStateProbabilitiesviaMarkovChains 297
8.3.1 ComponentandSystemStates 298
8.3.2 SystemStatesandTransitionRatesforFailureandRepair 300
8.3.3 DifferentialEquationsBasedontheStateDiagram 301
8.3.4 DifferentialEquationsBasedontheTransitionMatrix 302
8.4 Markov–LaplaceMethodforReliabilityandAvailability 303
8.5 LifetimewithAbsorbingStatesandSpareParts 306
8.6 MeanLifetimesMTTFFandMTBF 310
8.7 AvailabilityandSteady-StateSituations 312
8.8 Summary 314
(cid:2) 9 ApplicationtoAssetandIncidentManagement 317 (cid:2)
9.1 MaintenanceStyles 317
9.1.1 Period-BasedMaintenanceOptimizationforLowestCosts 317
9.1.1.1 CaseDescription 317
9.1.1.2 ReferencestoIntroductoryMaterial 318
9.1.1.3 PBMCostOptimizationAnalysis 318
9.1.1.4 Remarks 320
9.1.2 CorrectiveversusPeriod-BasedReplacementandRedundancy 321
9.1.2.1 CaseDescription 322
9.1.2.2 ReferencestoIntroductoryMaterial 322
9.1.2.3 AnalysisofCorrectiveversusPeriod-BasedReplacementand
Redundancy 323
9.1.2.4 Remarks 326
9.1.3 Condition-BasedMaintenance 326
9.1.3.1 ReferencestoIntroductoryMaterial 327
9.1.3.2 AnalysisofConditionversusPeriod-BasedReplacement 327
9.1.3.3 Remarks 329
9.1.4 Risk-BasedMaintenance 330
9.1.4.1 ReferencestoIntroductoryMaterial 330
9.1.4.2 AnalysisofRiskversusCondition-BasedMaintenance 331
9.1.4.3 Remarks 333
9.2 HealthIndex 334
9.2.1 GeneralConsiderationsofHealthIndex 334
9.2.1.1 ReferencestoIntroductoryMaterialonHealthIndexConcept
Considerations 335
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