Reliability Evaluation of Power Systems Reliability Evaluation of Power Systems Reliability Evaluation of Power Systems

Reliability Evaluation of Power Systems

Roy Billinton PhO, OSc, FEIC, FRSC, FIEEE, PE

c. J. MacKenzie Professor of Electrical Engineering University of Saskatchewan

and Ronald N Allan PhO, FSRS, SMIEEE, MIEE, CEng

Senior Lecturer in Electrical Power Systems University of Manchester Institute of Science and Technology

SPRINGER SCIENCE+BUSINESS MEDIA, LLC

Reliability Evaluation of Power Systems

Roy Billinton PhO, OSc, FEIC, FRSC, FIEEE, PE

c. J. MacKenzie Professor of Electrical Engineering University of Saskatchewan

and Ronald N Allan PhO, FSRS, SMIEEE, MIEE, CEng

Senior Lecturer in Electrical Power Systems University of Manchester Institute of Science and Technology

SPRINGER SCIENCE+BUSINESS MEDIA, LLC

Reliability Evaluation of Power Systems

Roy Billinton PhO, OSc, FEIC, FRSC, FIEEE, PE

c. J. MacKenzie Professor of Electrical Engineering University of Saskatchewan

and Ronald N Allan PhO, FSRS, SMIEEE, MIEE, CEng

Senior Lecturer in Electrical Power Systems University of Manchester Institute of Science and Technology

SPRINGER SCIENCE+BUSINESS MEDIA, LLC

Library of Congress Cataloging in Publication Data

Billinton, Roy. Reliability evaluation of power systems. Includes bibliographies and index. 1. Electric power systems-Reliability. I.

TK 1005 .BS73 1984 621.319 Allan, Ronald N. (Ronald Norman) II. Title.

83-11049 ISBN 978-1-4615-7733-1 ISBN 978-1-4615-7731-7 (eBook) DOI 10.1007/978-1-4615-7731-7

© Roy Billinton and Ronald N Allan 1984 Originally published by Plenum Press in 1984 Softcover reprint ofthe hardcover 1st edition 1984

First published in Great Britain by Pitman Books Limited

All rights reserved. No part of this publication may he reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording and/or otherwise without the prior written permission of the publishers.

Library of Congress Cataloging in Publication Data

Billinton, Roy. Reliability evaluation of power systems. Includes bibliographies and index. 1. Electric power systems-Reliability. I.

TK 1005 .BS73 1984 621.319 Allan, Ronald N. (Ronald Norman) II. Title.

83-11049 ISBN 978-1-4615-7733-1 ISBN 978-1-4615-7731-7 (eBook) DOI 10.1007/978-1-4615-7731-7

© Roy Billinton and Ronald N Allan 1984 Originally published by Plenum Press in 1984 Softcover reprint ofthe hardcover 1st edition 1984

First published in Great Britain by Pitman Books Limited

All rights reserved. No part of this publication may he reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording and/or otherwise without the prior written permission of the publishers.

Library of Congress Cataloging in Publication Data

Billinton, Roy. Reliability evaluation of power systems. Includes bibliographies and index. 1. Electric power systems-Reliability. I.

TK 1005 .BS73 1984 621.319 Allan, Ronald N. (Ronald Norman) II. Title.

83-11049 ISBN 978-1-4615-7733-1 ISBN 978-1-4615-7731-7 (eBook) DOI 10.1007/978-1-4615-7731-7

© Roy Billinton and Ronald N Allan 1984 Originally published by Plenum Press in 1984 Softcover reprint ofthe hardcover 1st edition 1984

First published in Great Britain by Pitman Books Limited

All rights reserved. No part of this publication may he reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording and/or otherwise without the prior written permission of the publishers.

Contents

Preface xv

1 Introduction 1

2 Generating capacity-basic probability methods 6

2.1 Introduction 6

2.2 The generation system model 9

2.2.1 Generating unit unavailability 9

2.2.2 Capacity outage probability tables 13

2.2.3 Comparison of deterministic and

probabilistic criteria 16

2.2.4 Recursive algorithm for capacity model building 18

2.2.5 Recursive algorithm for unit removal 20

2.2.6 Alternative model-building techniques 21

2.3 Loss of load indices 26

2.3.1 Concepts and evaluation techniques 26

2.3.2 Numerical examples 29

2.4 Equivalent forced outage rate 34

2.5 Capacity expansion analysis 36

2.5.1 Evaluation techniques 36

2.5.2 Perturbation effects 39

2.6 Scheduled outages 41

2.7 Evaluation methods on period bases 44

2.8 Load forecast uncertainty 45

2.9 Forced outage rate uncertainty 50

2.9.1 Exact method 51

2.9.2 Approximate method 52

v

Contents

Preface xv

1 Introduction 1

2 Generating capacity-basic probability methods 6

2.1 Introduction 6

2.2 The generation system model 9

2.2.1 Generating unit unavailability 9

2.2.2 Capacity outage probability tables 13

2.2.3 Comparison of deterministic and

probabilistic criteria 16

2.2.4 Recursive algorithm for capacity model building 18

2.2.5 Recursive algorithm for unit removal 20

2.2.6 Alternative model-building techniques 21

2.3 Loss of load indices 26

2.3.1 Concepts and evaluation techniques 26

2.3.2 Numerical examples 29

2.4 Equivalent forced outage rate 34

2.5 Capacity expansion analysis 36

2.5.1 Evaluation techniques 36

2.5.2 Perturbation effects 39

2.6 Scheduled outages 41

2.7 Evaluation methods on period bases 44

2.8 Load forecast uncertainty 45

2.9 Forced outage rate uncertainty 50

2.9.1 Exact method 51

2.9.2 Approximate method 52

v

Contents

Preface xv

1 Introduction 1

2 Generating capacity-basic probability methods 6

2.1 Introduction 6

2.2 The generation system model 9

2.2.1 Generating unit unavailability 9

2.2.2 Capacity outage probability tables 13

2.2.3 Comparison of deterministic and

probabilistic criteria 16

2.2.4 Recursive algorithm for capacity model building 18

2.2.5 Recursive algorithm for unit removal 20

2.2.6 Alternative model-building techniques 21

2.3 Loss of load indices 26

2.3.1 Concepts and evaluation techniques 26

2.3.2 Numerical examples 29

2.4 Equivalent forced outage rate 34

2.5 Capacity expansion analysis 36

2.5.1 Evaluation techniques 36

2.5.2 Perturbation effects 39

2.6 Scheduled outages 41

2.7 Evaluation methods on period bases 44

2.8 Load forecast uncertainty 45

2.9 Forced outage rate uncertainty 50

2.9.1 Exact method 51

2.9.2 Approximate method 52

v

vi Contents

2:9.3 Application 52

2.9.4 LOLE computation 54

2.9.5 Additional considerations 56

2.10 Loss of energy indices 56

2.10.1 Evaluation of energy indices 56

2.10.2 Expected energy not supplied 57

2.10.3 Energy-limited systems 61

2.11 Practical system studies 64

2.12 Conclusions 64

2.13 Problems 65

2.14 References 68

3 Generating capacity-frequency and duration method 71

3 .1 Introduction 71

3.2 The generation model 72

3.2.1 Fundamental development 72

3.2.2 Recursive algorithm for capacity model building 76

3.3 System risk indices 83

3.3.1 Individual state load model 83

3.3.2 Cumulative state load model 91

3.4 Practical system studies 94

3.4.1 Base case study 94

3.4.2 System expansion studies 97

3.4.3 Load forecast uncertainty 102

3.5 Conclusions 102

3.6 Problems 102

3.7 References 103

4 Interconnected systems 105

4.1 Introduction 105

4.2 Probability array method in two interconnected

systems 106

4.2.1 Concepts 106

4.2.2 Evaluation techniques 107

vi Contents

2:9.3 Application 52

2.9.4 LOLE computation 54

2.9.5 Additional considerations 56

2.10 Loss of energy indices 56

2.10.1 Evaluation of energy indices 56

2.10.2 Expected energy not supplied 57

2.10.3 Energy-limited systems 61

2.11 Practical system studies 64

2.12 Conclusions 64

2.13 Problems 65

2.14 References 68

3 Generating capacity-frequency and duration method 71

3.1 I ntroduction 71

3.2 The generation model 72

3.2.1 Fundamental development 72

3.2.2 Recursive algorithm for capacity model building 76

3.3 System risk indices 83

3.3.1 Individual state load model 83

3.3.2 Cumulative state load model 91

3.4 Practical system studies 94

3.4.1 Base case study 94

3.4.2 System expansion studies 97

3.4.3 Load forecast uncertainty 102

3.5 Conclusions 102

3.6 Problems 102

3.7 References 103

4 Interconnected systems 105

4.1 Introduction 105

4.2 Prob ability array method in two interconnected

systems 106

4.2.1 Concepts 106

4.2.2 Evaluation techniques 107

vi Contents

2:9.3 Application 52

2.9.4 LOLE computation 54

2.9.5 Additional considerations 56

2.10 Loss of energy indices 56

2.10.1 Evaluation of energy indices 56

2.10.2 Expected energy not supplied 57

2.10.3 Energy-limited systems 61

2.11 Practical system studies 64

2.12 Conclusions 64

2.13 Problems 65

2.14 References 68

3 Generating capacity-frequency and duration method 71

3.1 I ntroduction 71

3.2 The generation model 72

3.2.1 Fundamental development 72

3.2.2 Recursive algorithm for capacity model building 76

3.3 System risk indices 83

3.3.1 Individual state load model 83

3.3.2 Cumulative state load model 91

3.4 Practical system studies 94

3.4.1 Base case study 94

3.4.2 System expansion studies 97

3.4.3 Load forecast uncertainty 102

3.5 Conclusions 102

3.6 Problems 102

3.7 References 103

4 Interconnected systems 105

4.1 Introduction 105

4.2 Prob ability array method in two interconnected

systems 106

4.2.1 Concepts 106

4.2.2 Evaluation techniques 107

5

Contents vii

4.3 Equivalent assisting unit approach to two interconnected

systems 110

4.4 Factors affecting the emergency assistance available

through the interconnections 112

4.4.1 Introduction 112

4.4.2 Effect of tie capacity 112

4.4.3 Effect of tie line reliability 113

4.4.4 Effect of number of tie lines 115

4.4.5 Effect of tie capacity uncertainty 117

4.4.6 Effect of interconnection agreements 118

4.4.7 Effect of load forecast uncertainty 121

4.5 Variable reserve versus maximum peak load reserve 121

4.6 Reliability evaluation in three interconnected systems 123

4.6.1 Direct assistance from two systems 123

4.6.2 Indirect assistance from two systems 126

4.7 Multi-connected systems 128

4.8 Frequency and duration approach 130

4.8.1 Concepts 130

4.8.2 Applications 132

4.8.3 Period analysis 134

4.9 Conclusions 136

4.10 Problems 136

4.11 References 137

Operating reserve 139 5.1 General concepts 139

5.2 PJM method 140

5.2.1 Concepts 140

5.2.2 Outage replacement rate 140

5.2.3 Generation model 141

5.2.4 Unit commitment risk 142

5.3 Extensions to PJM method 143

5.3.1 Load forecast uncertainty 143

5.3.2 Derated (partial output) states 144

5

Contents vii

4.3 Equivalent assisting unit approach to two interconnected

systems 110

4.4 Factors affecting the emergency assistance available

through the interconnections 112

4.4.1 Introduction 112

4.4.2 Effect of tie capacity 112

4.4.3 Effect of tie line reliability 113

4.4.4 Effect of number of tie lines 115

4.4.5 Effect of tie capacity uncertainty 117

4.4.6 Effect of interconnection agreements 118

4.4.7 Effect of load forecast uncertainty 121

4.5 Variable reserve versus maximum peak load reserve 121

4.6 Reliability evaluation in three interconnected systems 123

4.6.1 Direct assistance from two systems 123

4.6.2 Indirect assistance from two systems 126

4.7 Multi-connected systems 128

4.8 Frequency and duration approach 130

4.8.1 Concepts 130

4.8.2 Applications 132

4.8.3 Period analysis 134

4.9 Conclusions 136

4.10 Problems 136

4.11 References 137

Operating reserve 139 5.1 General concepts 139

5.2 PJM method 140

5.2.1 Concepts 140

5.2.2 Outage replacement rate 140

5.2.3 Generation model 141

5.2.4 Unit commitment risk 142

5.3 Extensions to PJM method 143

5.3.1 Load forecast uncertainty 143

5.3.2 Derated (partial output) states 144

5

Contents vii

4.3 Equivalent assisting unit approach to two interconnected

systems 110

4.4 Factors affecting the emergency assistance available

through the interconnections 112

4.4.1 Introduction 112

4.4.2 Effect of tie capacity 112

4.4.3 Effect of tie line reliability 113

4.4.4 Effect of number of tie lines 115

4.4.5 Effect of tie capacity uncertainty 117

4.4.6 Effect of interconnection agreements 118

4.4.7 Effect of load forecast uncertainty 121

4.5 Variable reserve versus maximum peak load reserve 121

4.6 Reliability evaluation in three interconnected systems 123

4.6.1 Direct assistance from two systems 123

4.6.2 Indirect assistance from two systems 126

4.7 Multi-connected systems 128

4.8 Frequency and duration approach 130

4.8.1 Concepts 130

4.8.2 Applications 132

4.8.3 Period analysis 134

4.9 Conclusions 136

4.10 Problems 136

4.11 References 137

Operating reserve 139 5.1 General concepts 139

5.2 PJM method 140

5.2.1 Concepts 140

5.2.2 Outage replacement rate 140

5.2.3 Generation model 141

5.2.4 Unit commitment risk 142

5.3 Extensions to PJM method 143

5.3.1 Load forecast uncertainty 143

5.3.2 Derated (partial output) states 144

viii Contents

5.4 Modified PJM method 145

5.4.1 Concepts 145

5.4.2 Area risk curves 145

5.4.3 Modelling rapid start units 148

5.4.4 Modelling hot reserve units 150

5.4.5 Unit commitment risk 151

5.4.6 Numerical examples 152

5.5 Postponable outages 156

5.5.1 Concepts 156

5.5.2 Modelling postponable outages 158

5.5.3 Unit commitment risk 159

5.6 Security function approach 160

5.6.1 Concepts 160

5.6.2 Security function model 160

5.7 Response risk 161

5.7.1 Concepts 161

5.7.2 Evaluation techniques 162

5.7.3 Effect of disturbing spinning reserve 163

5.7.4 Effect of hydro-electric units 164

5.7.5 Effect of rapid start units 166

5.8 Interconnected systems 168

5.9 Conclusions 168

5.10 Problems 169

5.11 References 170

6 Composite generation and transmission systems 172

6.1 Introduction 172

6.2 Radial configurations 173

6.3 Conditional probability approach 174

6.4 Network configurations 180

6.5 State selection 184

6.5.1 Concepts 184

6.5.2 Application 184

6.6 System and load point indices 186

viii Contents

5.4 Modified PJM method 145

5.4.1 Concepts 145

5.4.2 Area risk curves 145

5.4.3 ModeIling rapid start units 148

5.4.4 Modelling hot reserve units 150

5.4.5 Unit commitment risk 151

5.4.6 Numerical examples 152

5.5 Postponable outages 156

5.5.1 Concepts 156

5.5.2 Modelling postponable outages 158

5.5.3 Unit commitment risk 159

5.6 Security function approach 160

5.6.1 Concepts 160

5.6.2 Security function model 160

5.7 Response risk 161

5.7.1 Concepts 161

5.7.2 Evaluation techniques 162

5.7.3 Effect of disturbing spinning reserve 163

5.7.4 Effect of hydro-electric units 164

5.7.5 Effect of rapid start units 166

5.8 Interconnected systems 168

5.9 Conclusions 168

5.10 Problems 169

5.11 References 170

6 Composite generation and transmission systems 172

6.1 Introduction 172

6.2 Radial configurations 173

6.3 Conditional prob ability approach 174

6.4 Network configurations 180

6.5 State selection 184

6.5.1 Concepts 184

6.5.2 Application 184

6.6 System and load point indices 186

viii Contents

5.4 Modified PJM method 145

5.4.1 Concepts 145

5.4.2 Area risk curves 145

5.4.3 ModeIling rapid start units 148

5.4.4 Modelling hot reserve units 150

5.4.5 Unit commitment risk 151

5.4.6 Numerical examples 152

5.5 Postponable outages 156

5.5.1 Concepts 156

5.5.2 Modelling postponable outages 158

5.5.3 Unit commitment risk 159

5.6 Security function approach 160

5.6.1 Concepts 160

5.6.2 Security function model 160

5.7 Response risk 161

5.7.1 Concepts 161

5.7.2 Evaluation techniques 162

5.7.3 Effect of disturbing spinning reserve 163

5.7.4 Effect of hydro-electric units 164

5.7.5 Effect of rapid start units 166

5.8 Interconnected systems 168

5.9 Conclusions 168

5.10 Problems 169

5.11 References 170

6 Composite generation and transmission systems 172

6.1 Introduction 172

6.2 Radial configurations 173

6.3 Conditional prob ability approach 174

6.4 Network configurations 180

6.5 State selection 184

6.5.1 Concepts 184

6.5.2 Application 184

6.6 System and load point indices 186

6.6.1 Concepts 186

6.6.2 Numerical evaluation 189 6.7 Application to practical systems 193

6.8 Data requirements for composite system reliability

evaluation 200

6.S.1 Concepts 200

6.8.2 Deterministic data 200

6.8.3 Stochastic data 201

6.8.4 Independent outages 201

6.8.5 Dependent outages 202

6.8.6 Common mode outages

6.8.7 Station originated outages

6.9 Conclusions 205

6.10 Problems 206

6.11 References 208

202

203

Contents ix

7 Distribution systems-basic techniques and radial networks 210

7.1 Introduction 210

7.2 Evaluation techniques 211

7.3 Additional interruption indices 213

7.3.1 Concepts 213

7.3.2 Customer-orientated indices 213

7.3.3 Load- and energy-orientated indices 215

7.3.4 System performance 216

7.3.5 System prediction 219

7.4 Application to radial systems 220

7.5 Effect of lateral distributor protection 223

7.6 Effect of disconnects 225

7.7 Effect of protection failures 225

7.8 Effect of transferring loads 229

7.8.1 No restrictions on transfer 229

7.8.2 Transfer restrictions 230

7.9 Probability distributions of reliability indices 235

7.9.1 Concepts 235

6.6.1 Concepts 186

6.6.2 Numerical evaluation 189 6.7 Application to practical systems 193

6.8 Data requirements for composite system reliability

evaluation 200

6.8.1 Concepts 200

6.8.2 Deterministic data 200

6.8.3 Stochastic data 201

6.8.4 Independent outages 201

6.8.5 Dependent outages 202

6.8.6 Common mode outages

6.8.7 Station originated outages

6.9 Conclusions 205

6.10 Problems 206

6.11 References 208

202

203

Contents ix

7 Distribution systems-basic techniques and radial networks 210

7.1 Introduction 210

7.2 Evaluation techniques 211

7.3 Additional interruption indices 213

7.3.1 Concepts 213

7.3.2 Customer-orientated indices 213

7.3.3 Load- and energy-orientated indices 215

7.3.4 System performance 216

7.3.5 System prediction 219

7.4 Application to radial systems 220

7.5 Effect of lateral distributor protection 223

7.6 Effect of disconnects 225

7.7 Effect of protection failures 225

7.8 Effect of transferring loads 229

7.8.1 No restrictions on transfer 229

7.8.2 Transfer restrictions 230

7.9 Probability distributions of reliability indices 235

7.9.1 Concepts 235

6.6.1 Concepts 186

6.6.2 Numerical evaluation 189 6.7 Application to practical systems 193

6.8 Data requirements for composite system reliability

evaluation 200

6.8.1 Concepts 200

6.8.2 Deterministic data 200

6.8.3 Stochastic data 201

6.8.4 Independent outages 201

6.8.5 Dependent outages 202

6.8.6 Common mode outages

6.8.7 Station originated outages

6.9 Conclusions 205

6.10 Problems 206

6.11 References 208

202

203

Contents ix

7 Distribution systems-basic techniques and radial networks 210

7.1 Introduction 210

7.2 Evaluation techniques 211

7.3 Additional interruption indices 213

7.3.1 Concepts 213

7.3.2 Customer-orientated indices 213

7.3.3 Load- and energy-orientated indices 215

7.3.4 System performance 216

7.3.5 System prediction 219

7.4 Application to radial systems 220

7.5 Effect of lateral distributor protection 223

7.6 Effect of disconnects 225

7.7 Effect of protection failures 225

7.8 Effect of transferring loads 229

7.8.1 No restrictions on transfer 229

7.8.2 Transfer restrictions 230

7.9 Probability distributions of reliability indices 235

7.9.1 Concepts 235

x Contents

7.9.2 Failure rate 235

7.9.3 Restoration times 236

7.10 Conclusions 237

7.11 Problems 237

7.12 References 238

8 Distribution systems-parallel and meshed networks 240

8.1 Introduction 240

8.2 Basic evaluation techniques

8.2.1 State space diagrams

8.2.2 Approximate methods

241

241

242

8.2.3 Network reduction method 243

8.2.4 Failure modes and effects analysis 244

8.3 Inclusion of busbar failures 246

8.4 Inclusion of scheduled maintenance 248

8.4.1 General concepts 248

8.4.2 Evaluation techniques 249

8.4.3 Coordinated and uncoordinated maintenance 250

8.4.4 Numerical example 251

8.5 Temporary and transient failures 253

8.5.1 Concepts 253

8.5.2 Evaluation techniques 254

8.5.3 Numerical example 256

8.6 Inclusion of weather effects 258

8.6.1 Concepts 258

8.6.2 Weather state modelling 258

8.6.3 Failure rates in a two-state weather model 260

8.6.4 Evaluation methods 262

8.6.5 Overlapping forced outages 262

8.6.6 Numerical examples 265

8.6.7 Forced outage overlapping maintenance 269

8.6.8 Numerical examples 273

8.6.9 Application to complex systems 275

8.7 Common mode failures 277

8.7.1 Evaluation techniques 277

x Contents

7.9.2 Failure rate 235

7.9.3 Restoration tim es 236

7.10 Conclusions 237

7.11 Problems 237

7.12 References 238

8 Distribution systems-parallel and meshed networks 240

8.1 Introduction 240

8.2 Basic evaluation techniques

8.2.1 State space diagrams

8.2.2 Approximate methods

241

241

242

8.2.3 Network reduction method 243

8.2.4 Failure modes and effects analysis 244

8.3 Inclusion of busbar failures 246

8.4 Inclusion of scheduled maintenance 248

8.4.1 General concepts 248

8.4.2 Evaluation techniques 249

8.4.3 Coordinated and uncoordinated maintenance 250

8.4.4 Numerical example 251

8.5 Temporary and transient failures 253

8.5.1 Concepts 253

8.5.2 Evaluation techniques 254

8.5.3 Numerical example 256

8.6 Inclusion of weather effects 258

8.6.1 Concepts 258

8.6.2 Weather state modelling 258

8.6.3 Failure rates in a two-state weather model 260

8.6.4 Evaluation methods 262

8.6.5 Overlapping forced outages 262

8.6.6 Numerical examples 265

8.6.7 Forced outage overlapping maintenance 269

8.6.8 Numerical examples 273

8.6.9 Application to complex systems 275

8.7 Common mode failures 277

8.7.1 Evaluation techniques 277

x Contents

7.9.2 Failure rate 235

7.9.3 Restoration tim es 236

7.10 Conclusions 237

7.11 Problems 237

7.12 References 238

8 Distribution systems-parallel and meshed networks 240

8.1 Introduction 240

8.2 Basic evaluation techniques

8.2.1 State space diagrams

8.2.2 Approximate methods

241

241

242

8.2.3 Network reduction method 243

8.2.4 Failure modes and effects analysis 244

8.3 Inclusion of busbar failures 246

8.4 Inclusion of scheduled maintenance 248

8.4.1 General concepts 248

8.4.2 Evaluation techniques 249

8.4.3 Coordinated and uncoordinated maintenance 250

8.4.4 Numerical example 251

8.5 Temporary and transient failures 253

8.5.1 Concepts 253

8.5.2 Evaluation techniques 254

8.5.3 Numerical example 256

8.6 Inclusion of weather effects 258

8.6.1 Concepts 258

8.6.2 Weather state modelling 258

8.6.3 Failure rates in a two-state weather model 260

8.6.4 Evaluation methods 262

8.6.5 Overlapping forced outages 262

8.6.6 Numerical examples 265

8.6.7 Forced outage overlapping maintenance 269

8.6.8 Numerical examples 273

8.6.9 Application to complex systems 275

8.7 Common mode failures 277

8.7.1 Evaluation techniques 277

8.7.2 Application and numerical examples 279

8.8 Common mode failures and weather effects 281

8.8.1 Evaluation techniques 281

8.8.2 Sensitivity analysis 284

8.9 Inclusion of breaker failures 285

8.9.1 Simplest breaker model 285

8.9.2 Failure modes of a breaker 286

8.9.3 Modelling assumptions 286

8.9.4 Simplified breaker models 287

8.9.5 Numerical example 288

8.10 Conclusions 289

8.11 Problems 290

8.12 References 293

9 Distributiou systems-extended techniques 295

9.1 Introduction 295

9.2 Total loss of continuity (TLOC) 296

9.3 Partial loss of continuity (PLOC) 298

9.3.1 Selecting outage combinations 298

9.3.2 PLOC criteria 299

9.3.3 Alleviation of network violations 299

9.3.4 Evaluation of PLOC indices 300

9.3.5 Extended load-duration curve 302

9.3.6 Numerical example 303

9.4 Effect of transferable loads 304

9.4.1 General concepts 304

9.4.2 Transferable load modelling 306

9.4.3 Evaluation techniques 308

9.4.4 Numerical example 308

9.5 Economic considerations 311

9.5.1 General concepts 311

9.5.2 Outage costs 313

9.5.3 Evaluation methods 315

9.5.4 Numerical example 316

9.6 Conclusions 318

Contents xi

8.7.2 Application and numerical examples 279

8.8 Common mode failures and weather effects 281

8.8.1 Evaluation techniques 281

8.8.2 Sensitivity analysis 284

8.9 Inclusion of breaker failures 285

8.9.1 Simplest breaker model 285

8.9.2 Failure mo des of a breaker 286

8.9.3 Modelling assumptions 286

8.9.4 Simplified breaker models 287

8.9.5 Numerical example 288

8.10 Conclusions 289

8.11 Problems 290

8.12 References 293

9 Distributiou systems-extended techniques 295

9.1 Introduction 295

9.2 Total loss of continuity (TLOC) 296

9.3 Partial loss of continuity (PLOC) 298

9.3.1 Selecting outage combinations 298

9.3.2 PLOC criteria 299

9.3.3 Alleviation of network violations 299

9.3.4 Evaluation of PLOC indices 300

9.3.5 Extended load-duration curve 302

9.3.6 Numerical example 303

9.4 Effect of transferable loads 304

9.4.1 General concepts 304

9.4.2 Transferable load modelling 306

9.4.3 Evaluation techniques 308

9.4.4 Numerical example 308

9.5 Economic considerations 311

9.5.1 General concepts 311

9.5.2 Outage costs 313

9.5.3 Evaluation methods 315

9.5.4 Numerical example 316

9.6 Conclusions 318

Contents xi

8.7.2 Application and numerical examples 279

8.8 Common mode failures and weather effects 281

8.8.1 Evaluation techniques 281

8.8.2 Sensitivity analysis 284

8.9 Inclusion of breaker failures 285

8.9.1 Simplest breaker model 285

8.9.2 Failure mo des of a breaker 286

8.9.3 Modelling assumptions 286

8.9.4 Simplified breaker models 287

8.9.5 Numerical example 288

8.10 Conclusions 289

8.11 Problems 290

8.12 References 293

9 Distributiou systems-extended techniques 295

9.1 Introduction 295

9.2 Total loss of continuity (TLOC) 296

9.3 Partial loss of continuity (PLOC) 298

9.3.1 Selecting outage combinations 298

9.3.2 PLOC criteria 299

9.3.3 Alleviation of network violations 299

9.3.4 Evaluation of PLOC indices 300

9.3.5 Extended load-duration curve 302

9.3.6 Numerical example 303

9.4 Effect of transferable loads 304

9.4.1 General concepts 304

9.4.2 Transferable load modelling 306

9.4.3 Evaluation techniques 308

9.4.4 Numerical example 308

9.5 Economic considerations 311

9.5.1 General concepts 311

9.5.2 Outage costs 313

9.5.3 Evaluation methods 315

9.5.4 Numerical example 316

9.6 Conclusions 318

Contents xi

xii Contents

9.7 Problems 318

9.8 References 319

10 Substations and switching stations 322 10.1 Introduction 322

10.2 Effect of short circuits and breaker operation 322

10.2.1 Concepts 322

10.2.2 Logistics 324

10.2.3 Numerical examples 324

10.3 Operating and failure states of system components 327

10.4 Open and short circuit failures 327

10.5

10.4.1 Open circuits and inadvertent opening of

breakers 327

10.4.2 Short circuits 328

10.4.3 Numerical example

Active and passive failures

10.5.1 General concepts

328

329

329

10.5.2 Effect of failure mode 331

10.5.3 Simulation of failure modes 333

10.5.4 Evaluation of reliability indices 334

10.6 Malfunction of normally closed breakers 336

10.6.1 General concepts 336

10.6.2 Numerical example 336

10.6.3 Deduction and evaluation 337

10.7 Numerical analysis of typical substation 338

10.8 Malfunction of alternative supplies 344

10.8.1 Malfunction of normally open breakers 344

10.8.2 Failures in alternative supplies 345

10.9 Conclusions 348

10.10 Problems 348

10.11 References 350

11 Plant and station availability 351

11.1 Generating plant availability 351

11.1.1 Concepts 351

11.1.2 Generating units 351

xii Contents

9.7 Problems 318

9.8 References 319

10 Substations and switching stations 322 10.1 Introduction 322

10.2 Effeci of short circuits and breaker operation 322

10.2.1 Concepts 322

10.2.2 Logistics 324

10.2.3 Numerical examples 324

10.3 Operating and failure states of system components 327

10.4 Open and short circuit failures 327

10.5

10.4.1 Open circuits and inadvertent opening of

breakers 327

10.4.2 Short circuits 328

10.4.3 Numerical example

Active and passive failures

10.5.1 General concepts

328

329

329

10.5.2 Effect of failure mode 331

10.5.3 Simulation of failure modes 333

10.5.4 Evaluation of reliability indices 334

10.6 Malfunction of normally closed breakers 336

10.6.1 General concepts 336

10.6.2 Numerical example 336

10.6.3 Deduction and evaluation 337

10.7 Numerical analysis of typical substation 338

10.8 Malfunction of alternative supplies 344

10.8.1 Malfunction of normally open breakers 344

10.8.2 Failures in alternative supplies 345

10.9 Conclusions 348

10.10 Problems 348

10.11 References 350

11 Plant and station availability 351

11.1 Generating plant availability 351

11.1.1 Concepts 351

11.1.2 Generating units 351

xii Contents

9.7 Problems 318

9.8 References 319

10 Substations and switching stations 322 10.1 Introduction 322

10.2 Effeci of short circuits and breaker operation 322

10.2.1 Concepts 322

10.2.2 Logistics 324

10.2.3 Numerical examples 324

10.3 Operating and failure states of system components 327

10.4 Open and short circuit failures 327

10.5

10.4.1 Open circuits and inadvertent opening of

breakers 327

10.4.2 Short circuits 328

10.4.3 Numerical example

Active and passive failures

10.5.1 General concepts

328

329

329

10.5.2 Effect of failure mode 331

10.5.3 Simulation of failure modes 333

10.5.4 Evaluation of reliability indices 334

10.6 Malfunction of normally closed breakers 336

10.6.1 General concepts 336

10.6.2 Numerical example 336

10.6.3 Deduction and evaluation 337

10.7 Numerical analysis of typical substation 338

10.8 Malfunction of alternative supplies 344

10.8.1 Malfunction of normally open breakers 344

10.8.2 Failures in alternative supplies 345

10.9 Conclusions 348

10.10 Problems 348

10.11 References 350

11 Plant and station availability 351

11.1 Generating plant availability 351

11.1.1 Concepts 351

11.1.2 Generating units 351

Contents xiii

11.1.3 Including effect of station transformers 354

11 .2 Derated states and auxiliary systems 357

I 1.2. 1 Concepts 357

11 .2.2 Modelling derated states 358

11. 3 Allocation and effect of spares 36 1

11.3. 1 Concepts 361

11 .3.2 Review of modelling techniques 362

11. 3.3 Numerical examples 364

11.4 Protection systems 370

11.4.1 Concepts 370

11.4.2 Evaluation techniques and system modelling 37 1

11 .4.3 Eval uat ion of failure to operate 372

It .4.4 Eval uation of inadvertent operation 378

11.5 HVDC systems 379

I t.5.1 Concepts 379

11 .5.2

11.5.3

11.5.4

11.5.5

Typical HVDC schemes

Rectifier/ inverter bridges

Bridge equivalents 383

Converter stations 385

380 380

11 .5.6 Transmission links and filt ers 388

11.5.7 Composite HVDC link 389

11 .5.8 Numerical examples 390

11 .6 Conclusions 393

I I .7 Problems 393

11.8 References 395

12 Conclusions 397

Appendix 1 Definitions 398

Appendix 2 Analysis of the IEEE ReliabUity Test System 401

Appendix 3 Third~order equations for overlapping events 409

Solutions to problems 418

Index 428

Contents xiii

11.1.3 Including effect of station transformers 354

11 .2 Derated states and auxiliary systems 357

I 1.2. 1 Concepts 357

11 .2.2 Modelling derated states 358

11. 3 Allocation and effett of spares 36 1

11.3. 1 Concepls 361

11 .3.2 Review of modelJing lechniques 362

11. 3.3 Numerical examples 364

11.4 Protection systems 370

11.4.1 Concepts 370

11.4.2 Evaluation techniques and system modelling 37 1

11 .4.3 Eval uat ion of failure 10 operate 372

I t .4.4 Eval uation of inadvertent operation 378

11.5 HVDC systems 379

11.5.1 Concepts 379

11 .5.2

11.5.3

11.5.4

11.5.5

Typical HYOC schemes

Rectifier/ inverter bridges

Bridge equivalents 383

Converter stations 385

380 380

11 .5.6 Transmission links and filt ers 388

11.5.7 Composite HYDC link 389

11 .5.8 Numerical examples 390

11 .6 Conclusions 393

1 I .7 Problems 393

11.8 References 395

12 Conclusions 397

Appendix 1 Definitions 398

Appendix 2 Analysis of the IEEE ReliabUity Test System 401

Appendix 3 Third~order equations for overlapping events 409

Solutions to problems 418

Index 428

Contents xiii

11.1.3 Including effect of station transformers 354

11 .2 Derated states and auxiliary systems 357

I 1.2. 1 Concepts 357

11 .2.2 Modelling derated states 358

11. 3 Allocation and effett of spares 36 1

11.3. 1 Concepls 361

11 .3.2 Review of modelJing lechniques 362

11. 3.3 Numerical examples 364

11.4 Protection systems 370

11.4.1 Concepts 370

11.4.2 Evaluation techniques and system modelling 37 1

11 .4.3 Eval uat ion of failure 10 operate 372

I t .4.4 Eval uation of inadvertent operation 378

11.5 HVDC systems 379

11.5.1 Concepts 379

11 .5.2

11.5.3

11.5.4

11.5.5

Typical HYOC schemes

Rectifier/ inverter bridges

Bridge equivalents 383

Converter stations 385

380 380

11 .5.6 Transmission links and filt ers 388

11.5.7 Composite HYDC link 389

11 .5.8 Numerical examples 390

11 .6 Conclusions 393

1 I .7 Problems 393

11.8 References 395

12 Conclusions 397

Appendix 1 Definitions 398

Appendix 2 Analysis of the IEEE ReliabUity Test System 401

Appendix 3 Third~order equations for overlapping events 409

Solutions to problems 418

Index 428

Preface

This book is a sequel to Reliability Evaluation of Engineering Systems: Concepts and Techniques, written by the same authors and published by Pitman Books in January 1983. As a sequel, this book is intended to be considered and read as the second of two volumes rather than as a text that stands on its own. For this reason, readers who are not familiar with basic reliability modelling and evaluation should either first read the companion volume or, at least, read the two volumes side by side. Those who are already familiar with the basic concepts and only require an extension of their knowledge into the power system problem area should be able to understand the present text with little or no reference to the earlier work. In order to assist readers, the present book refers frequently to the first volume at relevant points, citing it simply as Engineering Systems.

Reliability Evaluation of Power Systems has evolved from our deep interest in education and our long-standing involvement in quantitative reliability evaluation and application of probability techniques to power system problems. It could not have been written, however, without the active involvement of many students in our respective research programs. There have been too many to mention individually but most are recorded within the references at the ends of chapters.

The preparation of this volume has also been greatly assisted by our involvement with the IEEE Subcommittee on the Application of Proba­bility Methods, lEE Committees, the Canadian Electrical Association and other organizations, as well as the many colleagues and other individuals with whom we have been involved.

Finally, we would like to record our gratitude to all the typists who helped in the preparation of the manuscript and, above all, to our respective wives, Joyce and Diane, for all their help and encouragement.

Roy Billinton Ron Allan

xv

Preface

This book is a sequel to Reliability Evaluation of Engineering Systems: Concepts and Techniques, written by the same authors and published by Pitman Books in January 1983. As a sequel, this book is intended to be considered and read as the second of two volumes rather than as a text that stands on its own. For this reason, readers who are not familiar with basic reliability modelling and evaluation should either first read the companion volume or, at least, read the two volumes side by side. Those who are already familiar with the basic concepts and only require an extension of their knowledge into the power system problem area should be able to understand the present text with little or no reference to the earlier work. In order to assist readers, the present book refers frequently to the first volume at relevant points, citing it simply as Engineering Systems.

Reliability Evaluation of Power Systems has evolved from oUf deep interest in education and oUf long-standing involvement in quantitative reliability evaluation and application of prob ability techniques to power system problems. It could not have been written, however, without the active involvement of many students in oUf respective research programs. There have been too many to mention individually but most are recorded within the references at the ends of chapters.

The preparation of this volume has also been greatly assisted by oUf involvement with the IEEE Subcommittee on the Application of Proba­bility Methods, lEE Committees, the Canadian Electrical Association and other organizations, as weIl as the many colleagues and other individuals with whom we have been involved.

FinaIly, we would like to record OUf gratitude to all the typists who helped in the preparation of the manuscript and, above all , to OUf respective wives, Joyce and Diane, for all their help and encoUfagement.

Roy Billinton Ron Allan

xv

Preface

This book is a sequel to Reliability Evaluation of Engineering Systems: Concepts and Techniques, written by the same authors and published by Pitman Books in January 1983. As a sequel, this book is intended to be considered and read as the second of two volumes rather than as a text that stands on its own. For this reason, readers who are not familiar with basic reliability modelling and evaluation should either first read the companion volume or, at least, read the two volumes side by side. Those who are already familiar with the basic concepts and only require an extension of their knowledge into the power system problem area should be able to understand the present text with little or no reference to the earlier work. In order to assist readers, the present book refers frequently to the first volume at relevant points, citing it simply as Engineering Systems.

Reliability Evaluation of Power Systems has evolved from oUf deep interest in education and oUf long-standing involvement in quantitative reliability evaluation and application of prob ability techniques to power system problems. It could not have been written, however, without the active involvement of many students in oUf respective research programs. There have been too many to mention individually but most are recorded within the references at the ends of chapters.

The preparation of this volume has also been greatly assisted by oUf involvement with the IEEE Subcommittee on the Application of Proba­bility Methods, lEE Committees, the Canadian Electrical Association and other organizations, as weIl as the many colleagues and other individuals with whom we have been involved.

FinaIly, we would like to record OUf gratitude to all the typists who helped in the preparation of the manuscript and, above all , to OUf respective wives, Joyce and Diane, for all their help and encoUfagement.

Roy Billinton Ron Allan

xv