Risk Management of Non-Renewable Energy Systems (eBook)

Ajit K. Verma is a Professor in Engineering, Haugesund/Stord University College, Haugesund, Norway(since March 2012) and has been a Professor (since Feb 2001) with the Department of Electrical Engineering(currently) at IIT Bombay with a research focus in Reliability and Safety Engineering. He was the Director of the International Institute of Information Technology Pune, on lien from IIT Bombay, from Aug 2009-Sep 2010. He is also a Guest Professor at Lulea University of Technology, Sweden He has supervised/co-supervised 36 PhDs and 95 Masters theses in the area of Software Reliability, Reliable Computing, Power Systems Reliability (PSR), Reliability Centred maintenance (RCM) and Probabilistic Safety/Risk Assessment (PSA). He has executed various research projects to promote industry interface and has been course co-ordinator for industry CEPs like Reliability engineering, Six Sigma, Software Inspections, Competency Tracking System and Software Reliability for IT industries. He has jointly edited books on Reliability Engineering & Quality Management and is the Springer Book Series Editor of Reliable & Sustainable Electric Power and Energy Systems Management and jointly edited a book titled Reliability and Risk Evaluation of Wind Integrated Power Systems(Springer) and is also an author of books titled Fuzzy Reliability Engineering-Concepts and Applications (Narosa), Reliability and Safety Engineering (Springer) and Dependability of Networked Computer Based Systems (Springer). He has 247 publications in various journals (over 100 papers) and conferences.

Foreword 7
Preface 9
Acknowledgments 11
Contents 12
1 Introduction 17
1.1 General 17
1.2 Sources of Energy 17
1.2.1 Renewable Energy 18
1.2.2 Nonrenewable Energy 21
1.3 Fossil Fuel Power Plants 21
1.4 Nuclear Power Plants 23
1.5 Definition of Risk 26
1.6 Risk from Various Hazards 26
1.7 History of Accidents 28
1.7.1 Three Mile Island Accident 28
1.7.2 Chernobyl Accident 29
1.7.3 Fukushima Accident 29
1.8 Need for Risk Assessment 31
1.9 Organization of the Book 32
References 33
2 Basics of Reliability 35
2.1 Introduction 35
2.2 Probability Theory 37
2.2.1 Random Experiment 37
2.2.2 Sample Space 37
2.2.3 Event 38
2.2.4 Probability 38
2.2.5 Axioms of Probability 38
2.3 Random Variable 40
2.3.1 Discrete Random Variable 41
2.3.1.1 Probability Distribution 41
2.3.1.2 Probability Mass Function 42
2.3.1.3 Cumulative Distribution Function 43
2.3.1.4 Mean 45
2.3.1.5 Variance 45
2.3.1.6 Uniform Distribution 46
2.3.1.7 Binomial Distribution 47
2.3.1.8 Poisson Distribution 48
2.3.2 Continuous Random Variable 48
2.3.2.1 Probability Density Function 48
2.3.2.2 Cumulative Distribution Function 50
2.3.2.3 Mean 50
2.3.2.4 Variance 51
2.3.2.5 Uniform Distribution 53
2.3.2.6 Exponential Distribution 55
2.3.2.7 Normal Distribution 57
2.3.2.8 Lognormal Distribution 61
2.3.2.9 Weibull Distribution 67
2.4 The Reliability Function 69
2.5 Measures of Reliability 73
2.5.1 Mean Time to Failure 74
2.5.2 Median Time to Failure 74
2.5.3 Mode 75
2.5.4 Variance 76
2.6 Hazard Rate Function 80
2.7 Life Characteristic Curve 82
References 87
3 Risk Analysis of Nuclear Power Plants 88
3.1 Introduction 88
3.2 Nuclear Power Plants 89
3.3 Safety Objectives of NPPs 90
3.3.1 Radiation Protection Objective 90
3.3.2 Technical Safety Objectives 91
3.3.2.1 Dose Acceptance Criteria 91
3.3.2.2 Qualitative Safety Goals 91
3.3.2.3 Quantitative Safety Goals 92
3.4 Safety Analyses 92
3.4.1 Deterministic Safety Analyses 92
3.4.2 Probabilistic Safety Assessment 93
3.4.2.1 Objectives of PSA 94
3.5 Level 1 PSA 95
3.5.1 Scope 95
3.5.2 Procedure 96
3.5.2.1 Information Collection on Design and Operation of Plant 96
3.5.2.2 Defining the Scope of Analysis 97
3.5.2.3 Identification of Initiating Events 97
3.5.2.4 Determination of Safety Functions 97
3.5.2.5 Identification of Safety Systems 98
3.5.2.6 Grouping of the IEs 99
3.5.2.7 Accident Sequence Modeling 99
3.5.3 Event Tree Analysis 100
3.5.4 Fault Tree Analysis 104
3.5.4.1 Evaluation of Fault Trees 104
3.5.4.2 Advantages of Fault Tree 104
3.5.5 Common Cause Failures 109
3.5.5.1 Common Cause Groups 110
3.5.6 Common Cause Failure Models 111
3.5.6.1 Beta Factor Model 111
3.5.6.2 Alpha Factor Model 115
3.5.6.3 Multiple Greek Letter (MGL) Model 118
3.5.7 Component Failure Probability Models 119
3.5.7.1 Operating Systems 120
3.5.7.2 Repairable Components 120
3.5.7.3 Nonrepairable Components 121
3.5.7.4 Standby Systems 122
3.5.7.5 Periodically Tested Standby Components 122
3.5.7.6 Untested Standby Components 123
3.5.7.7 Continuously Monitored Standby Components 124
3.5.8 Estimation of Parameters of Failure Models 124
3.5.8.1 Standby Failure Rate/Operating Failure Rate 125
3.5.8.2 Mean Time to Repair 125
3.5.8.3 Test Frequency and Test Duration 126
3.5.8.4 Maintenance Parameters 126
3.5.8.5 Initiating Event Frequency 126
3.5.9 Parameter Estimation Using Bayesian Analysis 127
3.5.9.1 Bayesian Estimation 128
3.5.9.2 Choosing a Prior 129
3.5.9.3 Estimation with a Conjugate Prior 129
3.5.9.4 Estimation with a Continuous Nonconjugate Prior 131
3.5.9.5 Lognormal Prior 131
3.5.10 Human Reliability Analysis 135
3.5.11 Uncertainty Analysis 135
3.5.11.1 Propagation of Uncertainty 136
3.5.12 Importance Analysis 137
3.6 Level 2 PSA 139
3.6.1 Objectives of Level 2 PSA 140
3.6.2 Steps in Level 2 PSA 140
3.6.3 Plant Damage States 141
3.6.3.1 PDS Class 1 142
3.6.3.2 PDS Class 2 143
3.6.4 Accident Progression 143
3.6.5 Containment Analysis 143
3.6.5.1 Containment Performance 144
3.6.6 Containment Event Tree Development 144
3.6.7 Reliability Analysis of Containment ESFs 146
3.6.8 Containment Failure Modes 146
3.6.9 Release Categorization and Source Term Analysis 148
3.6.10 Frequencies of Release Categories 148
3.7 Level 3 PSA 148
3.7.1 The Input and Output 148
3.7.2 Source Term 149
3.7.3 Meteorological Data and Its Sampling 150
3.7.4 Atmospheric Dispersion and Deposition 151
3.7.4.1 Gaussian Plume Model 152
3.7.4.2 Gradient Theory or K-Model 155
3.7.4.3 Atmospheric Stability and Sigma Functions 156
3.7.4.4 Wind Speed Correction with Height 157
3.7.4.5 Plume Rise 158
3.7.4.6 Sector-Averaged chi /Q Values 160
3.7.4.7 Depletion Mechanisms 163
3.7.5 Exposure Pathways and Dose Assessment 165
3.7.5.1 Cloud Shine 165
3.7.5.2 Ground Shine 167
3.7.5.3 External Dose from Radioactive Material Deposited on Skin and Clothing 168
3.7.5.4 Inhalation Dose 168
3.7.5.5 Ingestion Dose 169
3.7.6 Countermeasures 169
3.7.6.1 Short-Term Counter Measures 170
3.7.6.2 Long-Term Countermeasures 170
3.7.7 Health Effects 171
3.7.7.1 Deterministic Effects 171
3.7.7.2 Stochastic Effects 171
3.7.8 Population and Economic Data 172
3.7.9 Complementary Cumulative Frequency Distributions 172
3.8 Applications of PSA 172
3.9 Case Study: Level 1, 2, and 3 PSA Analysis of a Typical NPP 174
3.9.1 Level 1 PSA 174
3.9.1.1 Identification of Initiating Events 174
3.9.1.2 Determination of Safety Functions and Safety Systems 175
3.9.1.3 Grouping of the IEs 175
3.9.1.4 Accident Sequence Modeling 176
3.9.1.5 Development of Event Trees 176
3.9.1.6 Identification of Dominant Accident Sequences 177
3.9.1.7 Quantification of Accident Sequences 177
3.9.1.8 Emergency Core Cooling System (ECCS) 177
3.9.1.9 System Description 178
3.9.1.10 Quantification of Dominating Accident Sequence Frequency 180
3.9.2 Level 2 PSA 180
3.9.2.1 Plant Damage State 181
3.9.2.2 Accident progression 181
3.9.2.3 Containment Analysis 183
3.9.2.4 Source Term Analysis 185
3.9.3 Level 3 PSA 186
References 189
4 Seismic PSA of Nuclear Power Plants 192
4.1 Introduction 192
4.2 Probabilistic Seismic Hazard Analysis 195
4.2.1 The Poisson Process 195
4.2.2 Identification of Fault Sources 199
4.2.3 Recurrence Relationship 200
4.2.4 Source-to-Site Distance 209
4.2.5 Attenuation Relationships 215
4.2.6 Conditional Probability of Exceedence 216
4.2.7 Determining the Hazard at the Site 220
4.2.8 Logic Tree Methods 253
4.3 Seismic Fragility Evaluation 256
4.4 Accident Sequence Analysis 258
4.4.1 Seismic Event Trees 258
4.4.2 Seismic Fault Trees 259
4.4.3 Accident Sequence Evaluation 267
References 268
5 Reliability Analysis of Passive Systems 270
5.1 Introduction 270
5.2 Active and Passive Systems 270
5.3 Need for Passive Systems 271
5.4 Categorization of Passive Systems 272
5.5 Various Passive Systems Used in Advanced Reactors 272
5.5.1 High Pressure Injection by Using Accumulators 272
5.5.2 Low Pressure Gravity Driven Water Tank 273
5.5.3 Passive Isolation Condenser System 274
5.5.4 Passive Containment Cooling System 274
5.5.5 Passive Poison Injection System 276
5.6 Issues Related to Passive Systems 276
5.7 Need for Estimating Reliability of Passive Systems 277
5.8 Passive System Reliability 280
5.8.1 REPAS Methodology 280
5.8.1.1 Limitations of REPAS Approach 283
5.8.1.2 System Operating Mechanism 284
5.8.1.3 Setting up of Failure Criterion 284
5.8.1.4 Critical Parameters that Affect the System Operation 285
5.8.1.5 Identification of Critical Parameters Ranges and Probability Distributions 285
5.8.1.6 Detailed Code Modeling 286
5.8.1.7 Defining Run Sets and Best Estimate Code Run 287
5.8.1.8 Reliability Estimation 288
5.8.2 RMPS Methodology 289
5.8.2.1 Limitations of RMPS Methodology 293
5.8.2.2 System Considered 294
5.8.2.3 Definition of Accident Scenario 294
5.8.2.4 System Characterization 294
5.8.2.5 System Modeling 294
5.8.2.6 Identification of Relevant Parameters and Sensitivity Analysis 294
5.8.2.7 Quantification of Uncertainties 295
5.8.2.8 Propagation of Uncertainty 295
5.8.2.9 Reliability Estimation 296
5.8.3 APSRA Methodology 297
5.8.3.1 Limitations of APSRA Methodology 298
5.8.3.2 System Description 298
5.8.3.3 Failure Criteria 298
5.8.3.4 Key Parameters 299
5.8.3.5 Thermal Hydraulic Analysis 299
5.8.3.6 Failure Probability Estimation 299
5.8.4 Fuzzy Monte Carlo Simulation Approach 303
5.8.4.1 Static Reliability Analysis 305
5.8.4.2 Failure Probability Estimation 309
5.9 Mechanistic Modeling Approach 310
5.9.1 The Approach 313
5.9.2 Control Valves 314
5.9.2.1 Operating Principle 315
5.9.2.2 Failure Modes 316
5.9.2.3 Reliability Estimation 316
5.9.3 A Case Study on Feed Water System 318
References 319
6 Time-Variant Reliability Analysis 321
6.1 Introduction 321
6.2 Different Types of Load Actions 322
6.3 Failure Probability Formulations 323
6.4 Stress--Strength Interference Model 328
6.5 Poisson Process 332
6.6 Stochastic Fatigue Loading 333
6.6.1 Representing Random Sequence Loading as Random Cyclic Loading 334
6.6.2 A Case Study on Nuclear Piping 337
6.7 Out Crossing Approach 343
6.8 Strength Degradation 348
6.8.1 Stress Corrosion Cracking 349
6.8.2 Intergranular Stress Corrosion Cracking 349
6.8.3 Primary Water Stress Corrosion Cracking 349
6.8.4 Erosion Corrosion or Flow Accelerated Corrosion 349
6.8.5 Crevice Corrosion and Pitting 350
6.8.6 Erosion--Cavitation 350
6.8.7 Thermal Fatigue 350
6.8.8 Vibration Fatigue 351
6.8.9 Water Hammer 351
6.9 Stress Corrosion Cracking 351
6.9.1 Time to Initiation 353
6.9.2 Crack Size at Initiation 354
6.9.3 Crack Propagation Due to SCC 354
6.9.4 Failure Criteria 355
6.9.5 Simulation 357
6.10 Case Study on PDHR System 357
6.10.1 System Description 357
6.10.2 Stochastic Fatigue Loading 359
6.10.3 Stress Corrosion Cracking 364
6.11 Time-Dependent CDF Analysis 371
References 375
7 Risk Management of Nuclear and Thermal Power Plants 377
7.1 Introduction 377
7.2 Risk Monitor 379
7.2.1 Necessity of Risk Monitor 380
7.2.2 Various Modules of Risk Monitor 381
7.2.3 Applications of Risk Monitor 385
7.2.3.1 Allowed Outage Time (AOT) 385
7.2.3.2 Surveillance Test Interval (STI) 387
7.3 Probabilistic Precursor Analysis 388
7.3.1 Approaches for Precursor Analysis 388
7.3.2 PSA-Based Precursor Analysis 388
7.4 A Case Study on NPP Events 390
7.4.1 PPA for Plant 1 390
7.4.2 PPA for Plant 2 392
7.5 Risk-Based Inspection of Thermal Power Plants 394
7.5.1 Calculation of Risk 395
7.5.1.1 PoF Calculations 395
7.5.1.2 CoF Calculations 400
7.5.2 Risk Matrix 401
7.5.3 Effect of Inspection Intervals on Risk 403
7.5.4 Inspection Strategies Based on Risk 403
References 406
Appendix A: Response Surface Methodology 408
Appendix BSimulation Techniques 416
Appendix CFuzzy Set Theory 425
Appendix DStochastic Process Theory 429