(PDF) Reliability Evaluation of Power Systems, 2nd Edition.: Roy Billinton - RN Allan
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1 Introduction 11.1 Background 1
1.2 Changing scenario 2
1.3 Probabilistic reliability criteria 3
1.4 Statistical and probabilistic measures 4
1.5 Absolute and relative measures 5
1.6 Methods of assessment 6
1.7 Concepts of adequacy and security 8
1.8 System analysis 10
1.9 Reliability cost and reliability worth 12
1.10 Concepts of data 14
1.11 Concluding comments 15
1.12 References 162 Generating capacity—basic probability methods 182.1 Introduction 18
2.2 The generation system model 21
2.2.1 Generating unit unavailability 21
2.2.2 Capacity outage probability tables 24
2.2.3 Comparison of deterministic and probabilistic criteria 27
2.2.4 A recursive algorithm for capacity model building 30
2.2.5 Recursive algorithm for unit removal 31
2.2.6 Alternative model-building techniques 33
2.3 Loss of load indices 37
2.3.1 Concepts and evaluation techniques 37ix
x Contents2.3.2 Numerical examples 40
2.4 Equivalent forced outage rate 46
2.5 Capacity expansion analysis 48
2.5.1 Evaluation techniques 48
2.5.2 Perturbation effects 50
2.6 Scheduled outages 522.7 Evaluation methods on period bases 55
2.8 Load forecast uncertainty 56
2.9 Forced outage rate uncertainty 61
2.9.1 Exact method 62
2.9.2 Approximate method 63
2.9.3 Application 63
2.9.4 LOLE computation 64
2.9.5 Additional considerations 67
2.10 Loss ofenergy indices 68
2.10.1 Evaluation of energy indices 68
2.10.2 Expected energy not supplied 70
2.10.3 Energy-limited systems 73
2.11 Practical system studies 75
2.12 Conclusions 76
2.13 Problems 77
2.14 References 793 Generating capacity—frequency and duration method 833.1 Introduction 83
3.2 The generation model 84
3.2.1 Fundamental development 84
3.2.2 Recursive algorithm for capacity model building 89
3.3 System risk indices 95
3.3.1 Individual state load model 95
3.3.2 Cumulative state load model 1033.4 Practical svstem studies 105
Contents xi3.4.1 Base case study 105
3.4.2 System expansion studies 108
3.4.3 Load forecast uncertainty 114
3.5 Conclusions 114
3.6 Problems 114
3.7 References 1154 Interconnected systems 1174.1 Introduction 117
4.2 Probability array method in two interconnected systems
4.2.1 Concepts 118
| 4.2,2 Evaluation techniques | 119 |
| 4.3 Equivalent assisting unit approach to two interconnected | |
| systems | 120 |
interconnections 124
4.4.1 Introduction 124
4.4.2 Effect of tie capacity 124
4.4.3 Effect of tie line reliability 125
4.4.4 Effect of number of tie lines 126
4.4.5 Effect of tie-capacity uncertainty 129
4.4.6 Effect of interconnection agreements 130
4.4.7 Effect of load forecast uncertainty 132
4.5 Variable reserxe versus maximurn peak load reserve 132
4.6 Reliability evaluation in three interconnected systems 134
4.6.1 Direct assistance from two systems 134
4.6.2 Indirect assistance from two systems 135
4.7 Multi-connected systems 139
4.8 Frequency and duration approach 1 41
4.8.1 Concepts 141
4.8.2 Applications 142
4.8.3 Period analysis 145
idl Contents4.9 Conclusions 147
4.10 Problems 147
4.11 References 1485 Operating reserve 1505.1 General concepts 150
5.2 PJM method 151
5.2.1 Concepts 151
5.2.2 Outage replacement rate (ORR) 151
5.2.3 Generation model 152
5.2.4 Unit commitment risk 153
5.3 Extensions to PJM method 154
5.3.1 Load forecast uncertainty 154
5.3.2 Derated (partial output) states 155
5.4 Modified PJM method 156
5.4.1 Concepts 156
5.4.2 Area risk curves 156
5.4.3 Modelling rapid start units 158
5.4.4 Modelling hot reserve units 161
5.4.5 Unit commitment risk 162
5.4.6 Numerical examples 163
5.5 Postponable outages 168
5.5.1 Concepts 168
5.5.2 Modelling postponable outages 168
5.5.3 Unit commitment risk 170
5.6 Security function approach 170
5.6.1 Concepts 170
5.6.2 Security function model 171
5.7 Response risk 172
5.7.1 Concepts 172
5.7.2 Evaluation techniques 173
5.7.3 Effect ofdistributing spinning reserve 174
5.7.4 Effect of hydro-electric units 175
5.7.5 Effect of rapid start units 176
5.8 Interconnected systems 178
5.9 Conclusions 178
5.10 Problems 179
5.11 References 1806 Composite generation and transmission systems 1826.1 Introduction 182
6.2 Radial configurations 183
6.3 Conditional probability approach 184
6.4 Network configurations 190
6.5 State selection 194
6.5.1 Concepts 194
6.5.2 Application 194
6.6 System and load point indices 196
6.6.1 Concepts 196
6.6.2 Numerical evaluation 199
6.7 Application to practical systems 204
6.8 Data requirements for composite system reliability
evaluation 210
6.8.1 Concepts 210
6.8.2 Deterministic data 210
6.8.3 Stochastic data 211
6.8.4 Independent outages 211
6.8.5 Dependent outages 212
6.8.6 Common mode outages 212
6.8.7 Station originated outages 213
6.9 Conclusions 215
6.10 Problems 216
6.11 References 2187 Distribution systems-—basic techniques and radial networks 2207.1 Introduction 220
xiv Cofttonts7.2 Evaluation techniques 221
7.3 Additional interruption indices 223
7.3.1 Concepts 223
7.3.2 Customer-orientated indices 223
7.3.3 Load-and energy-orientated indices 225
7.3.4 System performance 226
7.3.5 System prediction 228
7.4 Application to radial systems 229
7.5 Effect of lateral distributor protection 232
7.6 Effect of disconnects 234
7.7 Effect of protection failures 234
7.8 Effect of transferring loads 238
7.8.1 No restrictions on transfer 238
7.8.2 Transfer restrictions 240
7.9 Probability distributions of reliability indices 244
7.9.1 Concepts 244
7.9.2 Failure rate 244
7.9.3 Restoration times 245
7.10 Conclusions 246
7.11 Problems 246
7.12 References 2478 Distribution systems—parallel and meshed networks 2498.1 Introduction 249
8.2 Basic evaluation techniques 250
8.2.1 State space diagrams 250
8.2.2 Approximate methods 251
8.2.3 Network reduction method 252
8.2.4 Failure modes and effects analysis 253
8.3 Inclusion of busbar failures 255
8.4 Inclusion of scheduled maintenance 257
8.4.1 General concepts 257
Contents xv8.4.2 Evaluation techniques 258
8.4.3 Coordinated and uncoordinated maintenance 259
8.4.4 Numerical example 260
8.5 Temporary and transient failures 262
8.5.1 Concepts 262
8.5.2 Evaluation techniques 262
8.5.3 Numerical example 265
8.6 Inclusion of weather effects 266
8.6.1 Concepts 266
8.6.2 Weather state modelling 267
8.6.3 Failure rates in a two-state weather model 268
8.6.4 Evaluation methods 270
8.6.5 Overlapping forced outages 270
8.6.7 Forced outage overlapping maintenance 277
8.6.8 Numerical examples 281
8.6.9 Application to complex systems 283
8.7 Common mode failures 285
8.7.1 Evaluation techniques 285
8.7.2 Application and numerical examples 287
8.8 Common mode failures and weather effects 289
8.8.1 Evaluation techniques 289
8.8.2 Sensitivity analysis 291
8.9 Inclusion of breaker failures 292
8.9.1 Simplest breaker model 292
8.9.2 Failure modes of a breaker 293
8.9.3 Modelling assumptions 294
8.9.4 Simplified breaker models 295
8.9.5 Numerical example 296
8.10 Conclusions 297
8.11 Problems ' 298
8.12 References 301
xvi Contents9 Distribution systems — extended techniques 3029.1 Introduction 302
9.2 Total loss of continuity (TLOC) 303
9.3 Partial loss of continuity (PLOC) 305
9.3.1 Selecting outage combinations 305
9.3.2 PLOC criteria 305
9.3.3 Alleviation of network violations 306
9.3.4 Evaluation of PLOC indices 306
9.3.5 Extended load-duration curve 309
9.3.6 Numerical example 310
9.4 Effect of transferable loads 311
9.4.1 General concepts 311
9.4.2 Transferable load modelling 314
9.4.3 Evaluation techniques 316
9.4.4 Numerical example 317
9.5 Economic considerations 319
9.5.1 General concepts 319
9.5.2 Outage costs 322
9.6 Conclusions 325
9.7 Problems 325
9.8 References 32610 Substations and switching stations 327
10.1 Introduction 327
10.2 Effect of short circuits and breaker operation 327
10.2.1 Concepts 327
10.2.2 Logistics 329
10.2.3 Numerical examples 329
10.3 Operating and failure states of system components 332
10.4 Open and short circuit failures 332
10.4.1 Open circuits and inadvertent opening of breakers 332
10.4.2 Short circuits 333
Contents xvii10.4.3 Numerical example 334
10.5 Active and passive failures 334
10.5.1 General concepts 334
10.5.2 Effect of failure mode 336
10.5.3 Simulation of failure modes 338
10.5.4 Evaluation of reliability indices 339
10.6 Malfunction of normally closed breakers 341
10.6.1 General concepts 341
10.6.2 Numerical example 341
10.6.3 Deduction and evaluation 342
10.7 Numerical analysis of typical substation 343
10.8 Malfunction of alternative supplies 348
10.8.1 Malfunction of normally open breakers 348
10.8.2 Failures in alternative supplies 349
10.9 Conclusions 352
10.10 Problems 352
10.11 References 35411 Plant and station availability 355
11.1 Generating plant availability 355
11.1.1 Concepts 355
11.1.2 Generating units 355
11.1.3 Including effect of station transformers 358
11.2 Derated states and auxiliary systems 361
11.2.1 Concepts 361
11.2.2 Modelling derated states 362
11.3 Allocation and effect of spares 365
11.3.1 Concepts 365
11.3.2 Review of modelling techniques 365
11.3.3 Numerical examples 367
11.4 Protection systems 374
11.4.1 Concepts 374
xvHi Contents11.4.2 Evaluation techniques and system modelling 374
11.4.3 Evaluation of failure to operate 31511.4.4 Evaluation of inadvertent operation 381
11.5 HVDC systems 382
11.5.1 Concepts 382
11.5.2 Typical HVDC schemes 384
11.5.3 Rectifier/inverter bridges 384
11.5.4 Bridge equivalents 386
11.5.5 Converter stations 389
11.5.6 Transmission links and filters 391
11.5.7 Composite HVDC link 392
11.5.8 Numerical examples 395
11.6 Conclusions 396
11.7 Problems 396
11.8 References 39812 Applications of Monte Carlo simulation 40012.1 Introduction 400
12.2 Types of simulation 401
12.3 Concepts of simulation 401
12.4 Random numbers 403
12.5 Simulation output 403
12.6 Application to generation capacity reliability evaluation 405
12.6.1 Introduction 405
12.6.2 Modelling concepts 405
12.6.3 LOLE assessment with nonchronological load 409
12.6.4 LOLE assessment with chronological load 412
12.6.5 Reliability assessment with nonchronological load 416
12.6.6 Reliability assessment with chronological load 417
12.7 Application to composite generation and transmission
systems 422
12.7.1 Introduction 422
Contents xix12.7.2 Modelling concepts 42312.7.3 Numerical applications 423
12.7.4 Extensions to basic approach 425
12.8 Application to distribution systems 426
12.8.1 Introduction 426
12.8.2 Modelling concepts 427
12.8.3 Numerical examples for radial networks 430
12.8.4 Numerical examples for meshed (parallel)
networks 433
12.8.5 Extensions to the basic approach 439
12.9 Conclusions 439
12.10 Problems 440
12.11 References 44013 Evaluation of reliability worth 44313.1 Introduction 443
13.2 Implicit'explicit evaluation ofreliability worth 443
13.3 Customer interruption cost evaluation 444
13.4 Basic evaluation approaches 445
13.5 Cost of interruption surveys 447
13.5.1 Considerations 447
13.5.2 Cost valuation methods 447
13.6 Customer damage functions 450
13.6.1 Concepts 450
13.6.2 Reliability worth assessment at HLI 451
13.6.3 Reliability worth assessment at HLII 459
13.6.4 Reliability worth assessment in the distribution
functional zone 462
13.6.5 Station reliability worth assessment 469
13.7 Conclusions 472
13.8 References 473
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