wind_power_in_power_systems

Wind Power in Power
Systems

Edited by

Thomas Ackermann

Royal Institute of Technology
Stockholm, Sweden



Wind Power in Power
Systems

KTH

VETENSKAP
OCH KONST

ROYAL INSTITUTE
OF TECHNOLOGY

Electric Power
Systems

http://www.ets.kth.se/ees



Wind Power in Power
Systems

Edited by

Thomas Ackermann

Royal Institute of Technology
Stockholm, Sweden

Copyright Ó 2005 John Wiley & Sons, Ltd, The Atrium, Southern Gate, Chichester,
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Library of Congress Cataloging in Publication Data

Wind power in power systems / edited by Thomas Ackermann. II. Title.
p. cm

Includes bibliographical references and index.
ISBN 0-470-85508-8 (cloth : alk. paper)
1. Wind power plants. 2. Wind power. I. Ackermann, Thomas.

TK1541.W558 2005
621.3102136—dc22

2004018711

British Library Cataloguing in Publication Data

A catalogue record for this book is available from the British Library

ISBN 0-470-85508-8

Typeset in 10/12pt Times by Integra Software Services Pvt. Ltd, Pondicherry, India
Printed and bound in Great Britain by Antony Rowe Ltd, Chippenham, Wiltshire
This book is printed on acid-free paper responsibly manufactured from sustainable forestry in which at least
two trees are planted for each one used for paper production.

To Moana, Jonas and Nora



Contents xx

Contributors xxix

Abbreviations xxxvi

Notation xlvi

Units 1

1 Introduction 5
Thomas Ackermann
7
Part A Theoretical Background and Technical Regulations
7
2 Historical Development and Current Status of Wind Power 8
Thomas Ackermann 8
2.1 Introduction 9
2.2 Historical Background 11
2.2.1 Mechanical power generation 11
2.2.2 Electrical power generation 11
2.3 Current Status of Wind Power Worldwide 13
2.3.1 Overview of grid-connected wind power generation 16
2.3.2 Europe 16
2.3.3 North America 17
2.3.4 South and Central America 18
2.3.5 Asia and Pacific 18
2.3.6 Middle East and Africa 20
2.3.7 Overview of stand-alone generation 21
2.3.8 Wind power economics 22
2.3.9 Environmental issues 23
2.4 Status of Wind Turbine Technology 23
2.4.1 Design approaches 23
2.5 Conclusions
Acknowledgements
References

viii Contents

3 Wind Power in Power Systems: An Introduction 25
Lennart So¨der and Thomas Ackermann
25
3.1 Introduction 25
3.2 Power System History 26
3.3 Current Status of Wind Power in Power Systems 28
3.4 Network Integration Issues for Wind Power 29
3.5 Basic Electrical Engineering 32
3.6 Characteristics of Wind Power Generation 32
33
3.6.1 The wind 34
3.6.2 The physics 40
3.6.3 Wind power production 40
3.7 Basic Integration Issues Related to Wind Power 41
3.7.1 Consumer requirements 41
3.7.2 Requirements from wind farm operators 46
3.7.3 The integration issues
3.8 Conclusions 47
Appendix: A Mechanical Equivalent to Power System Operation with 47
Wind Power 48
Introduction 49
Active power balance 50
Reactive power balance
References 53

4 Generators and Power Electronics for Wind Turbines 53
Anca D. Hansen 53
53
4.1 Introduction 55
4.2 State-of-the-art Technologies 55
59
4.2.1 Overview of wind turbine topologies 62
4.2.2 Overview of power control concepts 65
4.2.3 State-of-the-art generators 66
4.2.4 State-of-the-art power electronics 69
4.2.5 State-of-the-art market penetration 70
4.3 Generator Concepts 72
4.3.1 Asynchronous (induction) generator 72
4.3.2 The synchronous generator 72
4.3.3 Other types of generators 73
4.4 Power Electronic Concepts 74
4.4.1 Soft-starter 75
4.4.2 Capacitor bank 77
4.4.3 Rectifiers and inverters 77
4.4.4 Frequency converters
4.5 Power Electronic Solutions in Wind Farms 79
4.6 Conclusions
References 79
80
5 Power Quality Standards for Wind Turbines
John Olav Tande

5.1 Introduction
5.2 Power Quality Characteristics of Wind Turbines

Contents ix

5.2.1 Rated data 81
5.2.2 Maximum permitted power 81
5.2.3 Maximum measured power 81
5.2.4 Reactive power 81
5.2.5 Flicker coefficient 82
5.2.6 Maximum number of wind turbine switching operations 83
5.2.7 Flicker step factor 83
5.2.8 Voltage change factor 84
5.2.9 Harmonic currents 84
5.2.10 Summary power quality characteristics for various wind turbine types 84
5.3 Impact on Voltage Quality 85
5.3.1 General 85
5.3.2 Case study specifications 86
5.3.3 Slow voltage variations 87
5.3.4 Flicker 89
5.3.5 Voltage dips 91
5.3.6 Harmonic voltage 92
5.4 Discussion 93
5.5 Conclusions 94
References 95

6 Power Quality Measurements 97
Fritz Santjer
97
6.1 Introduction 98
6.2 Requirements for Power Quality Measurements 98
99
6.2.1 Guidelines 104
6.2.2 Specification 105
6.2.3 Future aspects 105
6.3 Power Quality Characteristics of Wind Turbines and Wind Farms 106
6.3.1 Power peaks 106
6.3.2 Reactive power 108
6.3.3 Harmonics 109
6.3.4 Flicker 111
6.3.5 Switching operations 112
6.4 Assessment Concerning the Grid Connection 113
6.5 Conclusions
References 115

7 Technical Regulations for the Interconnection of Wind Farms to 115
the Power System 115
Julija Matevosyan, Thomas Ackermann and Sigrid M. Bolik 117
119
7.1 Introduction 120
7.2 Overview of Technical Regulations 121
122
7.2.1 Regulations for networks below 110 kV 123
7.2.2 Regulations for networks above 110 kV
7.2.3 Combined regulations
7.3 Comparison of Technical Interconnection Regulations
7.3.1 Active power control
7.3.2 Frequency control

x Contents

7.3.3 Voltage control 124
7.3.4 Tap changers 128
7.3.5 Wind farm protection 128
7.3.6 Modelling information and verification 133
7.3.7 Communication and external control 133
7.3.8 Discussion of interconnection regulations 134
7.4 Technical Solutions for New Interconnection Rules 136
7.4.1 Absolute power constraint 136
7.4.2 Balance control 136
7.4.3 Power rate limitation control approach 136
7.4.4 Delta control 137
7.5 Interconnection Practice 138
7.6 Conclusions 140
References 140

8 Power System Requirements for Wind Power 143
Hannele Holttinen and Ritva Hirvonen
143
8.1 Introduction 144
8.2 Operation of the Power System 145
146
8.2.1 System reliability 147
8.2.2 Frequency control 149
8.2.3 Voltage management 149
8.3 Wind Power Production and the Power System 151
8.3.1 Production patterns of wind power 155
8.3.2 Variations of production and the smoothing effect 156
8.3.3 Predictability of wind power production 156
8.4 Effects of Wind Energy on the Power System 160
8.4.1 Short-term effects on reserves 162
8.4.2 Other short-term effects 164
8.4.3 Long-term effects on the adequacy of power capacity 164
8.4.4 Wind power in future power systems 165
8.5 Conclusions
References 169

9 The Value of Wind Power 169
Lennart So¨der 169
169
9.1 Introduction 170
9.2 The Value of a Power Plant 170
170
9.2.1 Operating cost value 170
9.2.2 Capacity credit 170
9.2.3 Control value 171
9.2.4 Loss reduction value 171
9.2.5 Grid investment value 174
9.3 The Value of Wind Power 177
9.3.1 The operating cost value of wind power 180
9.3.2 The capacity credit of wind power
9.3.3 The control value of wind power
9.3.4 The loss reduction value of wind power
9.3.5 The grid investment value of wind power

Contents xi

9.4 The Market Value of Wind Power 180
9.4.1 The market operation cost value of wind power 180
9.4.2 The market capacity credit of wind power 181
9.4.3 The market control value of wind power 182
9.4.4 The market loss reduction value of wind power 188
9.4.5 The market grid investment value of wind power 189
194
9.5 Conclusions 195
References
197
Part B Power System Integration Experience
199
10 Wind Power in the Danish Power System
Peter Borre Eriksen and Carl Hilger 199
203
10.1 Introduction 205
10.2 Operational Issues 207
209
10.2.1 The Nordic market model for electricity trading 210
10.2.2 Different markets 211
10.2.3 Interaction between technical rules and the market 213
10.2.4 Example of how Eltra handles the balance task 215
10.2.5 Balancing via Nord Pool: first step 215
10.2.6 The accuracy of the forecasts 217
10.2.7 Network controller and instantaneous reserves 217
10.2.8 Balancing prices in the real-time market 219
10.2.9 Market prices fluctuating with high wind production 219
10.2.10 Other operational problems 220
10.3 System Analysis and Modelling Issues 221
10.3.1 Future development of wind power 223
10.3.2 Wind regime
10.3.3 Wind power forecast models 224
10.3.4 Grid connection 226
10.3.5 Modelling of power systems with large-scale wind
228
power production 231
10.3.6 Wind power and system analysis 232
10.3.7 Case study CO2 reductions according to the Kyoto
233
Protocol
10.4 Conclusions and Lessons Learned 233
References 234
236
11 Wind Power in the German Power System: Current Status and Future 237
Challenges of Maintaining Quality of Supply 238
Matthias Luther, Uwe Radtke and Wilhelm R. Winter 241
241
11.1 Introduction
11.2 Current Performance of Wind Energy in Germany
11.3 Wind Power Supply in the E.ON Netz Area
11.4 Electricity System Control Requirements
11.5 Network Planning and Connection Requirements
11.6 Wind Turbines and Dynamic Performance Requirements
11.7 Object of Investigation and Constraints

xii Contents

11.8 Simulation Results 244
11.8.1 Voltage quality 244
11.8.2 Frequency stability 248
252
11.9 Additional Dynamic Requirements of Wind Turbines 254
11.10 Conclusions 255
References
257
12 Wind Power on Weak Grids in California and the US Midwest
H. M. Romanowitz 257
259
12.1 Introduction 259
12.2 The Early Weak Grid: Background 260
260
12.2.1 Tehachapi 66 kV transmission 261
12.2.2 VARs 262
12.2.3 FACTS devices 263
12.2.4 Development of wind energy on the Tehachapi 66 kV grid 264
12.2.5 Reliable generation 264
12.2.6 Capacity factor improvement: firming intermittent wind generation 264
12.3 Voltage Regulation: VAR Support on a Wind-dominated Grid 265
12.3.1 Voltage control of a self-excited induction machine 267
12.3.2 Voltage regulated VAR control 268
12.3.3 Typical wind farm PQ operating characteristics 269
12.3.4 Local voltage change from VAR support
12.3.5 Location of supplying VARs within a wind farm 270
12.3.6 Self-correcting fault condition: VAR starvation 271
12.3.7 Efficient-to-use idle wind turbine component capacity
274
for low-voltage VARs 275
12.3.8 Harmonics and harmonic resonance: location on grid
12.3.9 Islanding, self-correcting conditions and speed of response 276
278
for VAR controls 279
12.3.10 Self-correcting fault condition: VAR starvation 280
12.3.11 Higher-speed grid events: wind turbines that stay connected through 281
282
grid events
12.3.12 Use of advanced VAR support technologies on weak grids 283
12.3.13 Load flow studies on a weak grid and with induction machines
12.4 Private Tehachapi Transmission Line 283
12.5 Conclusions 283
References 285
286
13 Wind Power on the Swedish Island of Gotland 286
Christer Liljegren and Thomas Ackermann 287
287
13.1 Introduction 287
13.1.1 History 288
13.1.2 Description of the local power system
13.1.3 Power exchange with the mainland
13.1.4 Wind power in the South of Gotland

13.2 The Voltage Source Converter Based High-voltage Direct-current Solution
13.2.1 Choice of technology
13.2.2 Description
13.2.3 Controllability

Contents xiii

13.2.4 Reactive power support and control 288
13.2.5 Voltage control 288
13.2.6 Protection philosophy 289
13.2.7 Losses 290
13.2.8 Practical experience with the installation 290
13.2.9 Tjæreborg Project 291
13.3 Grid Issues 291
13.3.1 Flicker 292
13.3.2 Transient phenomena 292
13.3.3 Stability issues with voltage control equipment 293
13.3.4 Validation 294
13.3.5 Power flow 295
13.3.6 Technical responsibility 296
13.3.7 Future work 296
13.4 Conclusions 296
Further Reading 297
References 297

14 Isolated Systems with Wind Power 299
Per Lundsager and E. Ian Baring-Gould
299
14.1 Introduction 300
14.2 Use of Wind Energy in Isolated Power Systems 300
305
14.2.1 System concepts and configurations 310
14.2.2 Basic considerations and constraints for wind–diesel power stations 311
14.3 Categorisation of Systems 312
14.4 Systems and Experience 312
14.4.1 Overview of systems 315
14.4.2 Hybrid power system experience 316
14.5 Wind Power Impact on Power Quality 316
14.5.1 Distribution network voltage levels 317
14.5.2 System stability and power quality 317
14.5.3 Power and voltage fluctuations 320
14.5.4 Power system operation 321
14.6 System Modelling Requirements 322
14.6.1 Requirements and applications 322
14.6.2 Some numerical models for isolated systems 324
14.7 Application Issues 325
14.7.1 Cost of energy and economics 325
14.7.2 Consumer demands in isolated communities 327
14.7.3 Standards, guidelines and project development approaches 328
14.8 Conclusions and Recommendations
References 331

15 Wind Farms in Weak Power Networks in India 331
Poul Sørensen 334
334
15.1 Introduction 335
15.2 Network Characteristics

15.2.1 Transmission capacity
15.2.2 Steady-state voltage and outages

xiv Contents

15.2.3 Frequency 337
15.2.4 Harmonic and interharmonic distortions 337
15.2.5 Reactive power consumption 338
15.2.6 Voltage imbalance 338
15.3 Wind Turbine Characteristics 338
15.4 Wind Turbine Influence on Grids 339
15.4.1 Steady-state voltage 339
15.4.2 Reactive power consumption 339
15.4.3 Harmonic and interharmonic emission 342
15.5 Grid Influence on Wind Turbines 343
15.5.1 Power performance 343
15.5.2 Safety 345
15.5.3 Structural lifetime 346
15.5.4 Stress on electric components 346
15.5.5 Reactive power compensation 346
15.6 Conclusions 347
References 347

16 Practical Experience with Power Quality and Wind Power 349
A˚ke Larsson
349
16.1 Introduction 349
16.2 Voltage Variations 352
16.3 Flicker 352
354
16.3.1 Continuous operation 358
16.3.2 Switching operations 360
16.4 Harmonics 361
16.5 Transients 363
16.6 Frequency 363
16.7 Conclusions
References 365

17 Wind Power Forecast for the German and Danish Networks 365
Bernhard Ernst 366
367
17.1 Introduction 367
17.2 Current Development and Use of Wind Power Prediction Tools 368
17.3 Current Wind Power Prediction Tools 370
370
17.3.1 Prediktor 370
17.3.2 Wind Power Prediction Tool 371
17.3.3 Zephyr 372
17.3.4 Previento 376
17.3.5 eWind 377
17.3.6 SIPREO´ LICO 377
17.3.7 Advanced Wind Power Prediction Tool 380
17.3.8 HONEYMOON project 380
17.4 Conclusions and Outlook 381
17.4.1 Conclusions
17.4.2 Outlook
References
Useful websites

Contents xv

18 Economic Aspects of Wind Power in Power Systems 383
Thomas Ackermann and Poul Erik Morthorst
383
18.1 Introduction 384
18.2 Costs for Network Connection and Network Upgrading 384
387
18.2.1 Shallow connection charges 388
18.2.2 Deep connection charges 388
18.2.3 Shallowish connection charges 389
18.2.4 Discussion of technical network limits 390
18.2.5 Summary of network interconnection and upgrade costs 391
18.3 System Operation Costs in a Deregulated Market 392
18.3.1 Primary control issues 392
18.3.2 Treatment of system operation costs 395
18.3.3 Secondary control issues 395
18.3.4 Electricity market aspects 396
18.4 Example: Nord Pool 397
18.4.1 The Nord Pool power exchange 398
18.4.2 Elspot pricing 403
18.4.3 Wind power and the power exchange 408
18.4.4 Wind power and the balancing market 409
18.5 Conclusions
References 411

Part C Future Concepts 413

19 Wind Power and Voltage Control 413
J. G. Slootweg, S. W. H. de Haan, H. Polinder and W. L. Kling 414
414
19.1 Introduction 416
19.2 Voltage Control 417
420
19.2.1 The need for voltage control 420
19.2.2 Active and reactive power 421
19.2.3 Impact of wind power on voltage control 425
19.3 Voltage Control Capabilities of Wind Turbines 425
19.3.1 Current wind turbine types 425
19.3.2 Wind turbine voltage control capabilities 426
19.3.3 Factors affecting voltage control 428
19.4 Simulation Results 430
19.4.1 Test system 431
19.4.2 Steady-state analysis 432
19.4.3 Dynamic analysis
19.5 Voltage Control Capability and Converter Rating 433
19.6 Conclusions
References 433
434
20 Wind Power in Areas with Limited Transmission Capacity 434
Julija Matevosyan 435

20.1 Introduction
20.2 Transmission Limits

20.2.1 Thermal limit
20.2.2 Voltage stability limit

xvi Contents

20.2.3 Power output of wind turbines 438
20.2.4 Transient stability 439
20.2.5 Summary 439
20.3 Transmission Capacity: Methods of Determination 440
20.3.1 Determination of cross-border transmission capacity 440
20.3.2 Determination of transmission capacity within the country 441
20.3.3 Summary 442
20.4 Measures to Increase Transmission Capacity 442
20.4.1 ‘Soft’ measures 442
20.4.2 Possible reinforcement measures: thermal limit 443
20.4.3 Possible reinforcement measures: voltage stability limit 444
20.4.4 Converting AC transmission lines to DC for higher transmission ratings 444
20.5 Impact of Wind Generation on Transmission Capacity 445
20.6 Alternatives to Grid Reinforcement for the Integration of Wind Power 446
20.6.1 Regulation using existing generation sources 447
20.6.2 Wind energy spillage 447
20.6.3 Summary 457
20.7 Conclusions 458
References 458

21 Benefits of Active Management of Distribution Systems 461
Goran Strbac, Predrag Djapic´, Thomas Bopp and Nick Jenkins
461
21.1 Background 462
21.2 Active Management 462
464
21.2.1 Voltage-rise effect 465
21.2.2 Active management control strategies 465
21.3 Quantification of the Benefits of Active Management 466
21.3.1 Introduction 476
21.3.2 Case studies 476
21.4 Conclusions
References

22 Transmission Systems for Offshore Wind Farms 479
Thomas Ackermann
479
22.1 Introduction 481
22.2 General Electrical Aspects 482
483
22.2.1 Offshore substations 484
22.2.2 Redundancy 485
22.3 Transmission System to Shore 486
22.3.1 High-voltage alternating-current transmission 488
22.3.2 Line-commutated converter based high-voltage direct-current transmission 490
22.3.3 Voltage source converter based high-voltage direct-current transmission 497
22.3.4 Comparison 497
22.4 System Solutions for Offshore Wind Farms 498
22.4.1 Use of low frequency 498
22.4.2 DC solutions based on wind turbines with AC generators 499
22.4.3 DC solutions based on wind turbines with DC generators 500
22.5 Offshore Grid Systems 500
22.6 Alternative Transmission Solutions
22.7 Conclusions

Contents xvii

Acknowledgement 501
References 501

23 Hydrogen as a Means of Transporting and Balancing Wind Power Production 505
Robert Steinberger-Wilckens
505
23.1 Introduction 506
23.2 A Brief Introduction to Hydrogen 507
23.3 Technology and Efficiency 507
508
23.3.1 Hydrogen production 509
23.3.2 Hydrogen storage 510
23.3.3 Hydrogen transport 512
23.4 Reconversion to Electricity: Fuel Cells 514
23.5 Hydrogen and Wind Energy 516
23.6 Upgrading Surplus Wind Energy 516
23.6.1 Hydrogen products 518
23.7 A Blueprint for a Hydrogen Distribution System 519
23.7.1 Initial cost estimates 519
23.8 Conclusions
References 523

Part D Dynamic Modelling of Wind Turbines for power System Studies 525

24 Introduction to the Modelling of Wind Turbines 525
Hans Knudsen and Jørgen Nyga˚rd Nielsen 526
526
24.1 Introduction 527
24.2 Basic Considerations regarding Modelling and Simulations 532
24.3 Overview of Aerodynamic Modelling 534
535
24.3.1 Basic description of the turbine rotor 536
24.3.2 Different representations of the turbine rotor 536
24.4 Basic Modelling Block Description of Wind Turbines 539
24.4.1 Aerodynamic system 539
24.4.2 Mechanical system 541
24.4.3 Generator drive concepts 541
24.4.4 Pitch servo 546
24.4.5 Main control system 546
24.4.6 Protection systems and relays 547
24.5 Per Unit Systems and Data for the Mechanical System 552
24.6 Different Types of Simulation and Requirements for Accuracy 553
24.6.1 Simulation work and required modelling accuracy
24.6.2 Different types of simulation 555
24.7 Conclusions
References 555
556
25 Reduced-order Modelling of Wind Turbines 557
J. G. Slootweg, H. Polinder and W. L. Kling 557

25.1 Introduction
25.2 Power System Dynamics Simulation
25.3 Current Wind Turbine Types
25.4 Modelling Assumptions

xviii Contents

25.5 Model of a Constant-speed Wind Turbine 559
25.5.1 Model structure 559
25.5.2 Wind speed model 559
25.5.3 Rotor model 562
25.5.4 Shaft model 564
25.5.5 Generator model 565
567
25.6 Model of a Wind Turbine with a Doubly fed Induction Generator 567
25.6.1 Model structure 568
25.6.2 Rotor model 568
25.6.3 Generator model 570
25.6.4 Converter model 572
25.6.5 Protection system model 573
25.6.6 Rotor speed controller model 574
25.6.7 Pitch angle controller model 575
25.6.8 Terminal voltage controller model 576
577
25.7 Model of a Direct drive Wind Turbine 578
25.7.1 Generator model 579
25.7.2 Voltage controller model 579
582
25.8 Model Validation 584
25.8.1 Measured and simulated model response 584
25.8.2 Comparison of measurements and simulations
587
25.9 Conclusions
References 587
588
26 High-order Models of Doubly-fed Induction Generators 588
Eva Centeno Lo´pez and Jonas Persson 589
590
26.1 Introduction 592
26.2 Advantages of Using a Doubly-fed Induction Generator 592
26.3 The Components of a Doubly-fed Induction Generator 594
26.4 Machine Equations 595
597
26.4.1 The vector method 597
26.4.2 Notation of quantities 599
26.4.3 Voltage equations of the machine 599
26.4.4 Flux equations of the machine 600
26.4.5 Mechanical equations of the machine 601
26.4.6 Mechanical equations of the wind turbine 602
26.5 Voltage Source Converter
26.6 Sequencer 603
26.7 Simulation of the Doubly-fed Induction Generator
26.8 Reducing the Order of the Doubly-fed Induction Generator 603
26.9 Conclusions 604
References 605
607
27 Full-scale Verification of Dynamic Wind Turbine Models 607
Vladislav Akhmatov 611

27.1 Introduction
27.1.1 Background
27.1.2 Process of validation

27.2 Partial Validation
27.2.1 Induction generator model
27.2.2 Shaft system model

Contents xix

27.2.3 Aerodynamic rotor model 613
27.2.4 Summary of partial validation 618
27.3 Full-scale Validation 619
27.3.1 Experiment outline 619
27.3.2 Measured behaviour 621
27.3.3 Modelling case 622
27.3.4 Model validation 623
27.3.5 Discrepancies between model and measurements 625
27.4 Conclusions 625
References 626

28 Impacts of Wind Power on Power System Dynamics 629
J. G. Slootweg and W. L. Kling
629
28.1 Introduction 630
28.2 Power System Dynamics 631
28.3 Actual Wind Turbine Types 632
28.4 Impact of Wind Power on Transient Stability 632
636
28.4.1 Dynamic behaviour of wind turbine types 638
28.4.2 Dynamic behaviour of wind farms 645
28.4.3 Simulation results 645
28.5 Impact of Wind Power on Small Signal Stability 646
28.5.1 Eigenvalue–frequency domain analysis 647
28.5.2 Analysis of the impact of wind power on small signal stability 648
28.5.3 Simulation results 650
28.5.4 Preliminary conclusions 651
28.6 Conclusions
References 653

29 Aggregated Modelling and Short-term Voltage Stability of Large Wind Farms 653
Vladislav Akhmatov 654
655
29.1 Introduction 655
29.1.1 Main outline 656
29.1.2 Area of application 657
29.1.3 Additional requirements 658
658
29.2 Large Wind Farm Model 661
29.2.1 Reactive power conditions 661
29.2.2 Faulting conditions 663
665
29.3 Fixed-speed Wind Turbines 667
29.3.1 Wind turbine parameters 668
29.3.2 Stabilisation through power ramp 670
672
29.4 Wind Turbines with Variable Rotor Resistance 673
29.5 Variable-speed Wind Turbines with Doubly-fed Induction Generators 673

29.5.1 Blocking and restart of converter 677
29.5.2 Response of a large wind farm
29.6 Variable-speed Wind Turbines with Permanent Magnet Generators
29.7 A Single Machine Equivalent
29.8 Conclusions
References

Index

Contributors

Thomas Ackermann has a Diplom Wirtschaftsingenieur (MSc in Mechanical Engineering
combined with an MBA) from the Technical University Berlin, Germany, an MSc in
Physics from Dunedin University, New Zealand, and a PhD from the Royal Institute of
Technology in Stockholm, Sweden. In addition to wind power, his main interests are
related to the concept of distributed power generation and the impact of market
regulations on the development of distributed generation in deregulated markets. He
has worked in the wind energy industry in Germany, Sweden, China, USA, New
Zealand, Australia and India. Currently, he is a researcher with the Royal Institute of
Technology (KTH) in Stockholm, Sweden, and involved in wind power education at
KTH and the University of Zagreb, Croatia, via the EU TEMPUS program. He is also a
partner in Energynautics.com, a consulting company in the area of sustainable energy
supply. Email: [email protected].

Vladislav Akhmatov has an MSc (1999) and a PhD (2003) from the Technical University
of Denmark. From 1998 to 2003 he was with the Danish electric power company NESA.
During his work with NESA he developed dynamic wind turbine models and carried out
power system stability investigations, using mainly the simulation tool PSS/ETM. He
combined his PhD with work on several consulting projects involving Danish wind
turbine manufacturers on grid connection of wind farms in Denmark and abroad.
Specifically, he participated in a project regarding power system stability investigations
in connection with the grid connection of the Danish offshore wind farm at Rødsand/
Nysted (165 MW). He demonstrated that blade angle control can stabilise the operation
of the wind farm during grid disturbances. This solution is now applied in the Rødsand/
Nysted offshore wind farm. In 2003 he joined the Danish transmission system operator
in Western Denmark, Eltra. His primary work is dynamic modelling of wind turbines in
the simulation tool Digsilent Power-Factory, investigations of power system stability
and projects related to the Danish offshore wind farm at Horns Rev (160 MW). In 2002
he received the Angelo Award, which is a Danish award for exceptional contributions to

Wind Power in Power Systems Edited by T. Ackermann
Ó 2005 John Wiley & Sons, Ltd ISBN: 0-470-85508-8 (HB)

Contributors xxi

the electric power industry, for ‘building bridges between the wind and the electric power
industries’. He has authored and co-authored a number of international publications on
dynamic wind turbine modelling and power system stability. Email: [email protected].

E. Ian Baring-Gould graduated with a master’s degree in mechanical engineering from
the University of Massachusetts Renewable Energy Research Laboratory in the spring
of 1995, at which point he started working at the National Renewable Energy Labora-
tory (NREL) of the USA. Ian’s work at NREL has focused on two primary areas:
applications engineering for renewable energy technologies and international assistance
in renewable energy uses. His applications work concentrates on innovative uses of
renewable energies, primarily the modelling, testing and monitoring of small power
systems, end-use applications and large diesel plant retrofit concepts. International
technical assistance has focused on energy development for rural populations, including
the design, analysis and implementation of remote power systems. Ian continues to
manage and provide general technical expertise to international programs, focusing on
Latin America, Asia and Antarctica. Ian also sits on IEA and IEC technical boards, is
an editor for Wind Engineering and has authored or co-authored over 50 publications.
His graduate research centred on the Hybrid2 software hybrid, power system design,
code validation and the installation of the University’s 250 kW ESI-80 wind turbine.
Email: [email protected].

Sigrid M. Bolik graduated in 2001 with a master’s degree in electrical engineering
(Diplom) from the Technical University Ilmenau in Germany. Currently, she works
for Vestas Wind Systems A/S in Denmark and also on her PhD in cooperation with
Aalborg University and Risø. Her research focuses on modelling induction machines for
wind turbine applications and developing wind turbine models for research in specific
abnormal operating conditions. Email: [email protected].

Thomas Bopp is currently a research associate at the Electrical Energy and Power System
Research Group at UMIST, UK. His main research interests are power system protection
as well as power system economics and regulation. Email: [email protected].

S. W. H. (Sjoerd) de Haan received his MSc degree in applied physics from the Delft
University of Technology, the Netherlands, in 1975. In 1995 he joined the Delft Uni-
versity of Technology as associate professor in power electronics. His research interest is
currently mainly directed towards power quality conditioning (i.e. the development of
power electronic systems for the conditioning of the power quality in the public elec-
tricity network). Email: [email protected].

Predrag Djapic´ is currently a research associate at the Electrical Energy and Power
System Research Group at UMIST, UK. His main research interests are power system
planning and operation of distribution networks. Email: [email protected].

Peter Borre Eriksen received an MSc degree in engineering from the Technical Uni-
versity of Denmark (DTU) in 1975. From 1980 until 1990 his work focused on the

xxii Contributors

environmental consequences of power production. Between 1990 and 1998 he was
employed in the System Planning Department of the former Danish utility ELSAM.
In 1998, he joined Eltra, the independent transmission system operator of western
Denmark. In 2000, he became head of Eltra’s Development Department. Peter Borre
Eriksen is the author of numerous technical papers on system modelling. Email:
[email protected].

Bernhard Ernst is an electrical engineer and has a master’s degree (Diplom) in measure-
ment and control from the University of Kassel, Germany. In 1994, still a student, he
joined ISET. In 2003, he completed at ISET a PhD on the prediction of wind power.
Bernhard Ernst has contributed to numerous publications on the subject of the integra-
tion of wind energy into energy supply. Email: [email protected].

Anca D. Hansen received her PhD in modelling and control engineering from the
Technical University of Denmark (DTU) in 1997. In 1998 she joined the Wind Energy
Department of Risø National Laboratory. Her work and research interests focus on
dynamic modelling and the control of wind turbines as well as on the interaction of wind
farms with the grid. As working tools she uses the dynamic modelling and simulation
tools Matlab and Digsilent Power Factory. Her major contribution is the electromecha-
nical modelling of active stall wind turbines and recently of a pitch-controlled variable-
speed wind turbine with a doubly fed induction generator. She has also modelled PV
modules and batteries. Email: [email protected].

Carl Hilger received a BSc in electrical engineering from the Engineering Academy of
Denmark and a general philosophy diploma as well as a bachelor of commerce degree.
In 1966 he joined Brown Boveri, Switzerland, as an electrical engineer and later the
Research Institute for Danish Electric Utilities (DEFU). In 1978 he became sectional
engineer in the Planning Department of Elsam (the Jutland-Funen Power Pool).
Between 1989 and 1997 he was executive secretary at Elsam and after that at Eltra,
the independent transmission system operator in the western part of Denmark. In 1998,
he was appointed head of the Operation Division at Eltra. Carl Hilger is a member of
Eurelectric Working Group SYSTINT and Nordel’s Operations Committee. Email:
[email protected].

Ritva Hirvonen has MSc and PhD degrees in electrical engineering from Helsinki
University of Technology and an MBA degree. She has broad experience regarding
power systems, transmission and generators. She has worked for the power company
Imatran Voima Oy and transmission system operator Fingrid as a power system
specialist and at VTT Technical Research Centre of Finland as research manager in
the energy systems area. Her current position is head of unit of Natural Gas and
Electricity Transmission for the Energy Market Authority (EMA) and she is actively
involved in research and teaching at the Power Systems Laboratory of Helsinki Uni-
versity of Technology. Email: [email protected].

Hannele Holttinen has MSc (Tech) and LicSc (Tech) degrees from Helsinki University of
Technology. She has acquired broad experience regarding different aspects of wind

Contributors xxiii

energy research since she started working for the VTT Technical Research Centre of
Finland in 1989. In 2000–2004 she worked mainly on her PhD on ‘Effects of Large Scale
Wind Power Production on the Nordic Electricity System’, with Nordic Energy
Research funding. Email: [email protected].

Nick Jenkins is a professor of electrical energy and power systems at UMIST, UK. His
research interests are in the area of sustainable energy systems including renewable
energy and its integration in electricity distribution and transmission networks. Email:
[email protected].

W. L. (Wil) Kling received an MSc degree in electrical engineering from the Technical
University of Eindhoven in 1978. Currently, he is a part-time professor at the Electric
Power Systems Laboratory of Delft University of Technology. His expertise lies in the
area of planning and operating power systems. He is involved in scientific organisations,
such as IEEE. He is also the Dutch representative in the Cigre´ Study Committee C1
‘System Development and Economics’. Email: [email protected].

Hans Knudsen received a MScEE from the Technical University of Denmark in 1991. In
1994 he received an industrial PhD, which was a joint project between the Technical
University of Denmark and the power companies Elkraft, SK Power and NESA. He
then worked in the in the Transmission Planning Department of the Danish transmis-
sion and distribution company NESA and focused on network planning, power system
stability and computer modelling, especially on modelling and simulation of HVDC
systems and wind turbines. In 2001, he joined the Danish Energy Authority, where he
works on the security of supply and power system planning. Email: [email protected].

A˚ ke Larsson received in 2000 a PhD from Chalmers University of Technology, Sweden.
His research focused on the power quality of wind turbines. He has broad experience
in wind power, power quality, grid design, regulatory requirements, measurements and
evaluation. He also participated in developing new Swedish recommendations for
the grid connection of wind turbines. Currently, he works for Swedpower. Email:
[email protected].

Christer Liljegren has a BScEE from Thorildsplan Technical Institute, Sweden. He
worked with nuclear power at ASEA, Vattenfall, with different control equipment,
mainly concerning hydropower, and at Cementa factory working with electrical indus-
trial designing. In 1985, he joined Gotland Energiverk AB (GEAB) and in 1995 became
manager engineer of the electrical system on Gotland. He was project manager of the
Gotland HVDC-Light project. In 2001, Christer Liljegren started his own consulting
company, Cleps Electrical Power Solutions AB (CLEPS AB), specialising in technical
and legal aspects of distributed power generation, especially wind turbines and their
connection to the grid. He has been involved in developing guidelines and recommenda-
tions for connecting distributed generation in Sweden. Email: [email protected].

Eva Centeno Lo´ pez received an MSc degree in electrical engineering from Universidad
Pontificia Comillas in Madrid, Spain, in 2001, and a master’s degree at the Royal

xxiv Contributors

Institute of Technology, Stockholm, Sweden, in 2000. She then worked at Endesa,
Madrid, Spain, at the Department of Electrical Market. Currently, she works at the
Swedish Energy Agency in Eskilstuna, Sweden. Email: [email protected].

Per Lundsager started working full-time with wind energy in 1975, including R&D,
assessment, planning, implementation and evaluation of energy systems and concepts,
for wind energy and other renewables. Between 1984 and 1993 he was head of the wind
diesel development programme at Risø National Laboratory. As senior consultant he
has been advisor to the national wind energy centres in the USA, Canada, Finland,
Denmark, Russia, Estonia, Poland, Brazil, India and Egypt, regarding projects, pro-
grammes and strategies. He has also been manager and/or participant in projects and
studies in the USA, Canada and Europe, including Greenland, Eastern Europe, Africa
and Asia. Email: [email protected].

Matthias Luther received a PhD in the field of electrical switchgear devices from the
Technical University of Braunschweig, Germany. In 1993, he joined PreussenElektra
AG, Germany. He was the project manager of various European network studies,
mainly concerning system stability. Between 1998 and 2000 he was in charge of network
development and customer services at the Engineering and Sales Department of
PreussenElektra Netz. Presently, Matthias Luther is head of network planning at E.ON
Netz GmbH, Bayreuth, Germany. He is member of several national and international
institutions and panels. Email: [email protected].

Julija Matevosyan (Sveca) received a BSc degree in electrical engineering from Riga
Technical University, Latvia, in 1999. From 1999 to 2000 she worked as a planning
engineer in the Latvian power company Latvenergo. She received an MSc in electrical
engineering from the Royal Institute of Technology, Stockholm, Sweden, in 2001. She is
currently working at the Royal Institute of Technology towards a PhD on the large-
scale integration of wind power in areas with limited transmission capability. Email:
[email protected].

Poul Erik Morthorst has a MEcon from the University of A˚ rhus and is a senior research
specialist in the Systems Analysis Department at Risø National Laboratory. He joined
this institute in 1978. His work has focused on general energy and environmental
planning, development of long-term scenarios for energy, technology and environmen-
tal systems, evaluation of policy instruments for regulating energy and environment and
the assessment of the economics of renewable energy technologies, especially wind
power. He has participated in a large number of projects within these fields and has
extensive experience in international collaboration. Email: [email protected].

Jørgen Nyga˚ rd Nielsen received a BScEE from the Engineering College of Sønderborg,
Denmark, in 1984. From 1984 to 1988 he worked on developing digital control systems
and designing software for graphical reproduction systems. Between 1988 and 1994
he was a lecturer at the College of Chemical Laboratory and Technician Education,
Copenhagen. In 1996, he received an MScEE from the Technical University of
Denmark and in 2000 an industrial PhD, a joint project between the Technical

Contributors xxv

University of Denmark, the Institute for Research and Development of the Danish
Electric Utilities, Lyngby, Denmark, and Electricite´ de France, Clamart, France. In
2000 he joined the Department of Transmission and Distribution Planning of the
Danish transmission and distribution company NESA. He works on general network
planning, power system stability and the development of wind turbine simulation
models. Email: [email protected]

Jonas Persson received an MSc degree in electrical engineering from Chalmers Univer-
sity of Technology, Go¨ teborg, Sweden, in 1997 and a Tech. Lic. degree in electric power
systems from the Royal Institute of Technology, Stockholm, Sweden, in 2002. He joined
ABB, Va¨ stera˚ s, Sweden, in 1995 where he worked on the development of the power
system simulation software Simpow. In 2004 he joined STRI, Ludvika, Sweden, where
he develops and teaches Simpow. Currently, he also works at the Royal Institute of
Technology in Stockholm, Sweden, towards a PhD on bandwidth-reduced linear models
of noncontinuous power system components. Email: [email protected].

Henk Polinder received in 1992 an MSc degree in electrical engineering and in 1998 a
PhD, both from the Delft University of Technology. Currently, he is an associate
professor at the Electrical Power Processing Laboratory at the same university, where
he gives courses on electrical machines and drives. His main research interest is gen-
erator systems in renewable energy, such as wind energy and wave energy. Email:
[email protected].

Uwe Radthe was born in 1948. He received the Doctor degree in Power Engineering
from the Technical University of Dresden in 1980. In 1990 he joined PreussenElektra
and worked in the network planning department. He was involved in international
system studies as project manager and specialist of high voltage direct current transmis-
sion systems. From 2000 until 2003 he worked for E.ON Netz, responsible for system
integration of renewable energy, especially wind power generation.

Harold M. Romanowitz is president and chief operating officer of Oak Creek Energy
Systems Inc. and a registered professional engineer. He holds a BScEE from Purdue
University and an MBA from the University of California at Berkeley. He has been
involved in the wind industry in California since 1985 and received the AWEA Techni-
cal Achievement Award in 1991 for his turnaround work at Oak Creek. He has been
directly involved in efforts to improve the Tehachapi area grid over this time, including
the achievement of a better understanding of the impacts of induction machines and
improved VAR support. In 1992–93 he designed and operated a 2.88 MW 17 280 KWH
battery storage system directly integrated with wind turbines to preserve a firm capacity
power purchase agreement. He was a manufacturer of engineered industrial drive
systems for many years, produced the first commercial regenerative thyristor drives in
the USA and WattMiser power recovery drives. He has extensive experience with
dynamic systems, including marine main propulsion (10 MW), large material handling
robots, container and bulk-handling cranes, large pumps and coordinated process lines.
Email: [email protected].

xxvi Contributors

Fritz Santjer received an MSc (Diplom) in electrical engineering from the University of
Siegen, Germany, in 1989. In 1990 he joined the German Wind Energy Institute (DEWI)
where he works on grid connection and the power quality of wind turbines and wind
farms and on standalone systems. In 2000 he became head of the Electrical Systems
Group in DEWI. He has performed commercial power quality and grid protection
measurements in many different countries in Europe, South America and Asia. He is
an assessor for the MEASNET power quality procedure and is involved in national and
international working groups regarding guidelines on power quality and the grid con-
nection of wind turbines. He lectures at national and international courses. He was
involved in various European research projects concerning grid connection and power
quality of wind turbines, standalone systems and simulations of wind turbines and
networks. Email: [email protected].

J. G. (Han) Slootweg received an MSc degree in electrical engineering from Delft
University of Technology, the Netherlands, in 1998. The topic of his MSc thesis was
modelling magnetic saturation in permanent-magnet linear machines. In December
2003 he obtained a PhD from the Delft University of Technology. His thesis was on
‘Wind Power; Modelling and Impact on Power System Dynamics’. He also holds an
MSc degree in business administration from the Open University of the Netherlands.
His MSc thesis focuses on how to ensure and monitor the long-term reliability of
electricity networks from a regulator’s perspective. Currently, he works with Essent
Netwerk B.V. in the Netherlands. Email: [email protected].

Lennart So¨ der received MSc and PhD degrees in electrical engineering from the Royal
Institute of Technology, Stockholm, Sweden, in 1982 and 1988, respectively. He is
currently a professor in electric power systems at the Royal Institute of Technology.
He works with projects concerning deregulated electricity markets, distribution systems,
protection systems, system reliability and integration of wind power. Email: lennart.
[email protected].

Robert Steinberger-Wilckens received a physics degree in 1985 on the simulation of
passive solar designs. In 1993 he completed a PhD degree on the subject of coupling
geographically dispersed renewable electricity generation to electricity grids. In 1985 he
started an engineering consultancy PLANET (Planungsgruppe Energie und Technik) in
Oldenburg, Germany, of which he became a full-time senior manager in 1993. His work
has focused on complex system design and planning in energy and water supply, energy
saving, hydrogen applications, building quality certificates and in wind, solar and
biomass projects. In 1999–2000 he developed the hydrogen filling station EUHYFIS,
funded within the CRAFT scheme of the EU. In 2002 he joined the Forschungszentrum
Ju¨ lich as project manager for fuel cells. He is currently head of solid oxide fuel cell
development at the research centre. Email: [email protected].

Poul Sørensen has an MSc in electrical engineering (1987). He joined the Wind Energy
Department (VEA) of Risø National Laboratory in 1987 and now is a senior scientist
there. Initially, he worked in the areas of wind turbine structural and aerodynamic
modelling. Now, his research focuses on the interaction between wind energy and power

Contributors xxvii

systems, with special interest in modelling and simulation. He has been project manager
on a number of research projects in the field. The modelling involves electrical aspects as
well as aeroelasticity and turbulence modelling. Poul Sørensen has worked for several
years on power quality issues, with a special focus on flicker emission from wind
turbines, and has participated in the work on the IEC 61400-21 standard for the
measurement and assessment of power quality characteristics for wind turbines. Email:
[email protected].

Goran Strbac is a professor of electrical power engineering at UMIST, UK. His research
interests are in the area of power system analysis, planning and economics and in
particular in the technical and commercial integration of distributed generation in the
operation and development of power systems. Email: [email protected].

John Olav Giæver Tande received his MSc in electrical engineering from the Norwegian
Institute of Science and Technology in 1988. After graduating he worked at the Norwe-
gian Electric Power Research Institute (EFI) and then, from 1990 to 1997, he worked at
Risø National Laboratory in Denmark. After this he returned to SINTEF Energy
Research (formerly EFI), where he is currently employed. Throughout his career, his
research has been focused on the electrical engineering aspects of wind power. He has
participated in several international studies, including convening an IEC working group
on preparing an international standard on the measurement and assessment of the
power quality characteristics of grid-connected wind turbines, and is the operating agent
representative of IEA Annex XXI: Dynamic Models of Wind Farms for Power System
Studies (2002–2005). Email: [email protected].

Wilhelm R. Winter received an MSc and a PhD in power engineering from the Technical
University of Berlin in 1995 and 1998, respectively. In 1995 he joined Siemens and
worked in the department for protection development and in the system planning
department. He was involved in large-system studies including stability calculations,
HVDC and FACTS optimisations, modal analysis, transient phenomena, real-time
simulation and renewable energy systems. He was responsible for the development of
the NETOMAC Eigenvalue Analysis program. In 2000 he started working at E.ON
Netz, and is responsible for system dynamics and the integration of large-scale wind
power. Email: [email protected].



Abbreviations

A Asea Brown Boveri
ABB Alternating current
AC Aeroelastic Code
AEC Alkaline fuel cell
AFC Active management
AM Artificial neural network
ANN Available transfer capacity
ATC Alternative Transient Program
ATP American Wind Energy Association
AWEA Advanced Wind Power Prediction Tool
AWPT Atlantic Wind Test Site (Canada)
AWTS
Blade element momentum (method)
B Bipolar junction transistor
BEM
BJT Computer-aided design
Canadian Wind Energy Association
C Concerted Action on Offshore Wind Energy in Europe
CAD Cost–benefit analysis
CANWea California energy Commission
CA-OWEA CANMET Energy Diversification Research Laboratory
CBA Comite´ Europe´ en de Normalisation Electrotechnique
CEC Capacity factor
CEDRL Compressed gaseous hydrogen
CENELEC Combined heat and power (also known as co-generation)
CF Conseil International des Grands Re´ seaux E´ lectriques
CGH2 Cost of energy
CHP
CIGRE´
COE

Wind Power in Power Systems Edited by T. Ackermann
Ó 2005 John Wiley & Sons, Ltd ISBN: 0-470-85508-8 (HB)

xxx Abbreviations

CP Connection point
CRES Centre for Renewable Energy Sources
CSC Current source converter

D Danish International Development Agency
DANIDA Direct current
DC Research Institute for Danish Electric Utilities (also translated as
DEFU Danish Utilities Research Association)
German Wind Energy Institute
DEWI Doubly fed induction generator
DFIG Distributed generation
DG Danish Crowns
DKK Danish Meteorological Institute
DMI Distribution network company
DNC Distributed resources
DR Distributed renewable energy
DRE Distributed renewable energy systems
DRES Distribution system
DS Demand-side bidding
DSB Demand-side management
DSM Technical University of Denmark
DTU Deutscher Wetterdienst (German Weather Service)
DWD

E Electricite´ de France
EDF Renewable Energy Sources Act (Germany)
EEG Electric Power Research Institute (Norway)
EFI Extra high voltage
EHV Electromagnetic transients program
EMTP Ensemble Prediction System
EPS Engineering recommendation
ER Electricity Supply Board (Republic of Ireland)
ESB Electricity Supply Board National Grid (Republic of Ireland)
ESBNG Engineering technical report
ETR European Union
EU European Union 15 Member States
EU-15 European Hydrogen Filling Station
EUHYFIS European Wind Energy Conference
EWEC

F Filter
F Flexible AC transmission systems
FACTS Fuel cell
FC Fo¨ rdergesellschaft Windenergie (Germany)
FGW

Abbreviations xxxi

G General curtailment
GC Gotlands Energi AB
GEAB Gujarat Electricity Board
GEB Gujarat Energy Development Agency
GEDA Geographical information system
GIS Grid supply point
GSP Gate turn-off thyristor
GTO
High-frequency filter
H Higher heating value
HFF High Resolution Limited Area Model
HHV Hydro power plant
HIRLAM High-speed (shaft)
HPP High-voltage
HS High-voltage alternating-current
HV High-voltage direct-current
HVAC High-voltage generator
HVDC
HVG Installed capacity
International Electrotechnical Commission
I Institute of Electrical and Electronic Engineers
IC Induction generator
IEC Insulated gate bipolar transistor
IEEE Integrated gate commutated thyristor
IG Induction motor
IGBT Department of Informatics and Mathematical Modelling (Technical
IGCT University of Denmark)
IM Insitut de Recherche D’Hydro-Que´ bec
IMM Ireland
Internal rate of return
IREQ Institu¨ t fu¨ r Solare Energieversorgnungstechnik
IRL Independent system operator (also commonly used for the International
IRR Organisation for Standardisation, Geneva)
ISET Instantaneous value simulation
ISO
Royal Institute of Technology, Stockholm, Sweden
IVS
Line-commutated converter
K Load flow
KTH Lower heating value
Liquid hydrogen
L
LCC
LF
LHV
LH2

xxxii Abbreviations

LM Local Model (Lokal-Modell)
LOEE Loss of energy expectation
LOLE Loss of load expectation
LOLP Loss of load probability
LS Low-speed (shaft)
LV Low-voltage
LYSAN Linear System analysis (program module)

M Market Simulation Tool (Eltra)
MARS Mesoscale Atmospheric Simulation System
MASS Molten carbonate fuel cell
MCFC Man overboard (boot)
MOB Model output statistics
MOS Metal oxide semiconductor field effect transistor
MOSFET Million Swedish crowns (krona)
MSEK Medium-voltage
MV
North American Electricity Reliability Council
N New Electricity Trading Arrangement (UK)
NERC The Non-Fossil Fuel Obligation (UK)
NETA The Netherlands
NFFO Nordic Operational Information System
NL Net present value
NOIS New and Renewable Energy Agency (Egypt)
NPV National Renewable Energy Laboratory (USA)
NREA Net transmission capacity
NREL Normal temperature and pressure
NTC Numerical weather prediction
NTP
NWP On-load tap-changing (transformer)
Operation, maintenance and repair
O Optimal power flow
OLTC OptiSlipTM induction generator (OptiSlipTM is a registered trademark of
OM&R Vestas Wind Systems A/S)
OPF Offshore substation
OSIG
Phosphoric acid fuel cell
OSS Pulse amplitude modulated
Publicly available specification
P Point of common coupling
PAFC Probability density function
PAM Power exchange
PAS
PCC
PDF
PE

Abbreviations xxxiii

PEFC Polymer electrolyte fuel cell
PF Power factor
PG&E Pacific Gas and Electric (Company)
PI Proportional–integral (controller)
PMG Permanent magnet generator
PMSG Permanent magnet synchronous generator
PPA Power purchase agreement
PPP Power purchase price
PQ Power quality
PSDS Power system dynamics simulation
PSLF Load Flow Program (GE)
PSS/ETM Power System Simulator for Engineers [PSS/ETM is a registered
trademark of Shaw Power Technologies Inc. (PTI)]
PTC Production Tax Credit (USA)
PTI Shaw Power Technologies Inc.
p.u. Per unit
PURPA Public Utility Regulatory Policies Act (USA)
PV Photovoltaic
PWM Pulse-width modulated; pulse-width modulation
PX Power exchange

R Rutherford Appleton Laboratory (UK)
RAL Renewable energy credit
REC Red Ele´ ctrica de Espan˜ a
REE Renewable Energy Research Lab at UMass Amherst (USA)
RERL-UMASS Renewable energy source(s)
RES Root mean square
RMS Root mean square error
RMSE Reverse osmosis
RO Rounds per minute; rotations per minute
RPM Renewable portfolio standard
RPS Rheinisch-Westfa¨ lische Technische Hochschule Aachen, Germany
RWTH (Institute of Technology of the Land North Rhine-Westphalia)

S SAFT Batteries SA
SAFT Short-circuit
SC Supervisory control and data acquisition
SCADA Southern California Edison (Company)
SCE Squirrel cage induction generator
SCIG Short-circuit ratio
SCR Synchronous generator
SG Surge impedance loading
SIL Simulation of Power Systems
SIMPOW Solid oxide fuel cell
SOFC

xxxiv Abbreviations

SRG Switch reluctance generator
STATCOM Static VAR compensator
STATCON Static VAR converter
STD Standard deviation
STP Standard temperature and pressure
SVC Static VAR compensator
SvK Svenka Kraftna¨ t (Swedish transmission system operator)
SW Switch

T Transmission duration curve
TDC Transverse flux generator
TFG Total harmonic distortion
THD Transmission limit
TL Tamil Nadu Electricity Board
TNEB Transmission system operator
TSO Transient stability program
TSP Fixed-speed wind turbine, with asynchronous induction generator
Type A directly connected to the grid, with or without reactive power
compensation (see also Section 4.2.3)
Type B Limited variable-speed wind turbine with variable generator rotor
resistance (see also Section 4.2.3)
Type C Variable-speed wind turbine with doubly-fed asynchronous induction
generators and partial-load frequency converter on the rotor circuit
Type D (see also Section 4.2.3)
Full variable-speed wind turbine, with asynchronous or synchronous
U induction generator connected to the grid through a full-load frequency
UCTE converter (see also Section 4.2.3)

UK Union pour la Coordination du Transport d’Electricite´ (Union for the
UK MESO Coordination of Transmission of Electricity, formerly UCPTE)
United Kingdom
V UK Meteorological Office Meso-scale Model
VDEW
VRR Verband der Elektrizita¨ tswirtschaft (German Electricity Association)
VSC Variable rotor resistance
Voltage source converter
W
WASP Wind Atlas Analysis and Application Program
WD Wind–diesel
WETEC Wind Economics and TEchnology (USA)
WF Wind farm
WPDC Wind power production duration curve

Abbreviations xxxv

WPMS Wind Power Management System
WPP Wind power production
WPPT Wind Power Prediction Tool
WRIG Wound rotor induction generator
WRSG Wound rotor synchronous generator
WT Wind turbine
WTG Wind turbine generator

X Polyethylen insulation
XLPE

Notation

Note: this book includes contributions from different authors who work in different
fields (i.e. electrical and mechanical engineering and others). Within each of these fields,
certain variables may be used for different concepts (e.g. the variable R can denote
resistance and also radius, or it can represent the specific gas constant for air). It has
been the editor’s intention to reduce multiple definitions for one symbol. However,
sometimes there will be different denotions because some variables are commonly used
within different engineering disciplines. This also means that similar concepts may not
be denoted with the same variable throughout the entire book.

English Symbols

A
a Subscribed level of power
A^g Amplitude of wind speed gust
A^r Amplitude of wind speed ramp
AR Area of wind turbine rotor; area through which wind flows

C Numerical coefficient
c Power coefficient (of a wind turbine rotor)
cP Power factor
cos ’ Flicker coefficient for continuous operation as a function of network
cð kÞ impedance angle
Flicker emission factor during normal operation
ccð kÞ Flicker coefficient for continuous operation as a function of network
cðÉk, VaÞ impedance angle and annual average wind speed
Capacitor; capacitance; DC-link capacitor
C Cost function
C(x) Installed capacity
CIC Power coefficient
CP

Wind Power in Power Systems Edited by T. Ackermann
Ó 2005 John Wiley & Sons, Ltd ISBN: 0-470-85508-8 (HB)

Notation xxxvii

D Steady-state voltage change as a percentage of nominal voltage
d Shaft damping constant; load level
D Harmonic interference for each individual harmonic n
Dn
Real part of transformer impedance
E Imaginary part of transformer impedance
eR Long-term flicker emission limit
eX Short-term flicker emission limit
EPlti Voltage source of doubly fed induction generator (DFIG) rotor converter
EPsti or permanent magnet generator (PMG) converter
E1 Magnitude of voltage source of DFIG rotor converter or PMG generator
converter
jE1j Active componant of voltage source of DFIG rotor converter or PMG
generator converter
E1 Reactive componant of voltage source of DFIG rotor converter or PMG
generator converter
E1 Voltage source of grid-side converter
Active componant of voltage source of grid-side converter
E2 Reactive componant of voltage source of grid-side converter
E2 Expected cost
E2 Average primary electrical load
Ec Wind energy output
Eload Expected value of quantity X
Ewind
E(X) Frequency
Eigenfrequency of a free–fixed shaft system
F Eigenfrequency of a free–free shaft system
f Pitch angle controller sample frequency
ffree–fixed Rotor speed controller sample frequency
ffree–free Gaussian probability function
fps Probability mass function for variable X
fss Gaussian distribution function
f(x) Capacity factor
fX(x) Power frequency
F(x)
Fcap Scale-parameter of Weibull distribution; gravity constant
FN Generation

G Wind turbine hub height; harmonic order
g Height above sea level
G Inertia constant

H
h
hsea
H

xxxviii Notation

Hg Inertia constant of the induction generator
Hgen Generator rotor inertia constant
Hm Inertia constant of generator (mechanical)
Hwr Inertia constant of wind turbine

I Current
i Harmonic current of order n
in Harmonic current of order n from source k
in,k Current as a function of time
i(t) Stator current in the rotor reference frame
iiirsrrssrs Rotor current in the rotor reference frame
I Stator current in the stator reference frame
I1 Current; complex current
I1 Rotor current of DFIG or generator current of PMG
I1 , Ref Active rotor current of DFIG or active generator current of PMG
Desired active rotor current of DFIG or desired active generator current
I1 of PMG
I1 , Ref Reactive rotor current of DFIG or reactive generator current of PMG
Desired reactive rotor current of DFIG or desired reactive generator
I2 current of PMG
I2 Current of grid-side converter
I2 , Ref Active current of grid-side converter
I2 Desired active current of grid-side converter
I2 , Ref Reactive current of grid-side converter
Ih Desired reactive current of grid-side converter
IL Maximum harmonic current
IM Phase current
IMax Maximum current amplitude
In Current-carrying capacity
IR Rated current
IS Generator rotor current
Iz Generator stator current
Capacitor current
J
J1 Charging DC current
J2 Discharging DC current
Jgen Generator rotor inertia
Jturb Wind turbine inertia

K Shaft stiffness; shape parameter of the Weibull distribution
k Base value of shaft stiffness, for use in a per unit system
kbase Flicker step factor
kf High-speed shaft stiffness in per unit
kHS

Notation xxxix

kLS Low-speed shaft stiffness in per unit
ktot Total shaft stiffness in per unit
kfð kÞ Flicker step factor
ki Inrush current factor
kiÉðÉkÞ Grid-dependent switching current factor
kspill Spilled wind energy in percent of wind energy production
kuð kÞ Voltage change factor
K Shaft torsion constant
Kp Pitch angle controller constant
KHS High-speed shaft stiffness
KLS Low-speed shaft stiffness
Ks Shaft stiffness
Kv Voltage controller constant

L Turbulence length scale; transmission line length
l Inductance
L Field inductance
Lfd Mutual inductance
Lm Rotor leakage inductance
Lsr Stator leakage inductance
Lss
Mean value of Gaussian distribution
M Mean inflow (hydro power)
mG Mean inflow (renewable power source)
mx
my Number of points
Gear ratio
N Number of pole pairs
n Maximum number of switchings
ngear Maximum number of one type of switchings within a 10-minute period
npp Maximum number of one type of switchings within a 120-minute period
N Number of wind turbines
N10
N120 Number of generator poles; pressure
Nwt Power as a function of time
Active power; wind power production; probability
P Electric power of grid-side converter
p Maximum measured power (0.2-second average value)
p(t) Maximum measured power (60-second average value)
P Power base value for use in a per unit system
P2 Power spectral density; power consumption
P0.2 Power spectral density of turbulence
P60
Pbase
PD
PDt

xl Notation

PG Additional required power production; generator electric power
PG curt Curtailed active power
PG max Maximum generated power
PG,Ref Desired generator electric power
PL Power losses on the line; active power of load
Pload Instantaneous primary electrical load
Plt Long-term flicker disturbance factor
Pm Mean power production
Pmc Maximum permitted power
PMECH Mechanical power of the wind turbine
Pn Rated power of wind turbine
Po Natural load of the line
PO Power of moving air mass; standard sea level atmospheric
pressure
PR Active power at the receiving end of the line; rated power
PREF Generator electric active power reference
PS Power delivered from kinetic energy stored in the rotating mass (turbine,
shaft and rotor)
Pst Short-term flicker disturbance factor
PT Power delivered by turbine
PTL Transmission limit
PTOC(t) Power at time t on the transmission duration curve
PW Wind power production
Pwind Instantaneous wind power output
PWIND Power of the wind within the rotor swept area of the
wind turbine
PWPDC(t) Power at time t on the wind power production duration curve
Pwt Power extracted from the wind
Px Active power of system component x
Pyear Yearly mean price
PðX ¼ xÞ Probability that variable X is equal to x

Q Reactive power
Q Reactive power of grid-side converter
Q2 Desired reactive power of grid-side converter
Q2,Ref Capacitor reactive power; reactive power of compensation
QC device
Reactive power of compensation device
QComp Generator reactive power
QG Desired generator reactive power
QG,Ref Reactive power absorbed by the network
Qimport Reactive power of load
QL Rated reactive power of a wind turbine
Qn Generator electric reactive power reference
QREF Reactive power of system component x
Qx

Notation xli

R Length along blade (local radius), measured from the hub ðr ¼ 0Þ
r Rotor winding resistance
rr Stator winding resistance
rs Cross-correlation
rxy Resistance; blade length; wind turbine radius; specific gas constant for
R air; radius of a cylinder
Resistance of smoothing inductor
R2 Field resistance
Rfd Gas constant
Rgas Short-circuit ratio at the point of connection
Rk Rotor resistance
Rr Stator resistance
Rs
Slip; complex frequency
S Apparent power; complex power
s Base power, in per unit system
S Rated apparent power of a wind turbine
Sbase Nominal apparent power of wind farm
Sn Generator rated apparent power
Spark Short circuit power
SrG Nominal three-phase power of the induction generator
Sk Transformer power capacity
SN Space vector
ST Instantaneous (momentaneous) value of a quantity for phase a
S, SðtÞ Instantaneous (momentaneous) value of a quantity for phase b
Sa(t) Instantaneous (momentaneous) value of a quantity for phase c
Sb(t) Direct axis of a space vector SðtÞ
Sc(t) Quadrature axis of a space vector SðtÞ
Sd, Sd(t) Space vector SðtÞ referred to the rotor reference frame
Sq, Sq(t) Instantaneous (momentaneous) value of a quantity for phase a in rotor
Sr, SrðtÞ reference frame
Sr,a Instantaneous (momentaneous) value of a quantity for phase b in rotor
reference frame
Sr,b Instantaneous (momentaneous) value of a quantity for phase c in rotor
reference frame
Sr,c Real part of Sr
Imaginary part of Sr
Srd Space vector SðtÞ referred to the stator reference frame
Srq Real part of Ss
Ss, SsðtÞ Imaginary part of Ss
Ss,d
Ss,q Time
Temperature
T
t
t C

xlii Notation

tTL Number of hours over which the transmission limit is exceeded
T Time; torque; temperature
T1 Cost for subscription per kW per year
T2 Price of excess power per kW per year
Tbase Base value of torque, in per unit system
Tdamping Damping torque of the shaft
Te Torque of generator (electrical)
Teg End time of wind speed gust
Tel Electrical air gap torque of the induction generator
Ter End time of wind speed ramp
Th Time period
Tm Mechanical torque produced by the wind turbine
TMECH Mechanical torque of the wind turbine
Tp Duration of voltage variation caused by a switching operation
Tsg Start time of wind speed ramp
Tshaft Incoming torque from the shaft connecting the induction generator with
the wind turbine
Ttorsion Elasticity torque of the shaft
Twr Torque of wind turbine

U Voltage; integration variable
u Voltage as a function of time
u(t) Nominal voltage
uN Stator voltage in the rotor reference frame
urs Rotor voltage in the rotor reference frame
urr Stator voltage in the stator reference frame
uss Voltage
U Fixed voltage at the end of the power system
U1 Terminal voltage
U2 Terminal voltage magnitude
U2 Desired terminal voltage magnitude
U2 ;Ref DC-link voltage
UDC Desired DC-link voltage
UDC,Ref Harmonic voltage
Uh Voltage of bus i
Ui Minium voltage at bus i
Umi in Phase-to-phase voltage
ULL Maximum voltage amplitude
UM Maximum voltage
Umax Minium voltage
Umin Root mean square value of the phase-to-phase voltage
UN of a machine
Nominal phase-to-phase voltage
Un Generator rotor voltage; voltage at the receiving end
UR Generator stator voltage reference
UREF

Notation xliii

US Generator stator voltage; voltage at the sending end
Ut Terminal voltage

V Wind speed
v Annual average wind speed
va Cut-in wind speed
vci Rated wind speed
vR Rotor tip speed
vt Wind speed at hub height of the power system
vw Wind speed at time t
vw(t) Average value of wind speed
vwa Gust component of wind speed
vwg Ramp component of wind speed
vwr(t) Turbulence component of wind speed
vwt Wind speed
V Relative wind speed
Vrel Speed of the blade tip
Vtip Wind speed
VWIND Value of water inflow
V(x)
Yearly energy production
W Spilled energy
W Energy generated by wind farm
Wspill
WW Power transmission; water inflow
Leakage reactance of the rotor
X Leakage reactance of the stator
x Mutual reactance between the stator and rotor windings
xrl Rotor self-reactance
xls Stator self-reactance
xm Reactance; power flow; cable length
xr Reactance of smoothing inductor
xs Direct axis reactance
X Quadrupol axis reactance
X2
XD Generated wind power
XQ Lumped admittance of long transmission line

Y Altitude above sea level
Y Roughness length
Ye Impedance; desired power transmission

Z
z
z0
Z

xliv Notation

Zc Transmission line surge impedance
Ze Lumped impedance of long transmission line
Zl Load impedance
ZL Line impedance
ZLD Load impedance

Greek symbols

Exponent; reference angle
Pitch angle; reference angle
const Fixed blade angle
ref Blade reference angle

Torsional displacement between shaft ends
ÁP Differences between consecutive production values
d =dt Pitch speed
Pitch angle
base Base value of pitch angle, for use in per unit system
base, el Electrical base angle
g Generator rotor angle
’ Angle between terminal voltage and current
’LD Load angle
cos ’LD Load power factor
Tip-speed ratio
opt Tip-speed ratio corresponding to the optimal rotor speed
Average
Air density
AIR Air density
xy Correlation between x and y
ðzÞ Air density as a function of altitude
Standard deviation of Gaussian distribution; total leakage factor
load Standard deviation of load time series
m Position of wind turbine
total Standard deviation of net load time series
wind Standard deviation of wind power production time series
V Characteristic time constant of induced velocity lag
’ Angle of incidence; phase angle
’1 Phase angle of voltage source of DFIG rotor converter or PMG converter
cos ’min Expected minimum power factor at full load
Flux linkage
base Base flux
Network impedance phase angle
k Amount of flux of the permanent magnets mounted on the rotor that is
coupled to the stator winding
pm Direct axis of the stator flux in rotor reference frame
Quadrature axis of the stator flux in rotor reference frame
s
rd
s
rq

Notation xlv

r Direct axis of the rotor flux in rotor reference frame
rd Quadrature axis of the rotor flux in rotor reference frame
r Stator flux in the stator reference frame
rq Stator flux in the rotor reference frame
s Rotor flux in the rotor reference frame
ss Angular frequency; angular speed
rr Base value of rotational speed, in per unit system
r Electrical base angular speed
Speed of machine
! Generator rotor speed
!base Disired generator rotor speed
!base, el Generator rotor rotational speed
!g Angular speed of the wind turbine; angular frequency of generator
!G (mechanical)
!G, Ref Angular speed (e.g. 2 fN)
!gen Turbine rotational speed
!m Optimal turbine rotational speed
Angular frequency of wind turbine
!N
!turb
!turb, opt
!wr

Units

SI Units Name Symbol

Basic unit meter m
kilogram kg
Length second s
Mass ampere A
Time kelvin K
Electric current
Temperature

SI-derived units Name Unit Symbol

Unit square meter m2
cubic meter m3
Area meter per second
Volume meter per second squared m/s
Speed or velocity kilogram per cubic meter m/s2
Acceleration cubic meter per kilogram kg/m3
Density ampere per square meter m3/kg
Specific volume ampere per meter A/m2
Current density
Magnetic field strength A/m

Derived units with special names and symbols

Unit Name Unit Symbol In SI Units

Frequency hertz Hz sÀ1
Force Newton N m kg sÀ2
Pressure pascal Pa mÀ1 kg sÀ2
Energy, work, quantity of heat joule J m2 kg sÀ2
Power watt W m2 kg sÀ3

Wind Power in Power Systems Edited by T. Ackermann
Ó 2005 John Wiley & Sons, Ltd ISBN: 0-470-85508-8 (HB)

Units xlvii

Electromotive force volt V m2 kg s
Apparent power volt ampere VA m2 kg sÀ3
Reactive power var var m2 kg sÀ3
Capacitance farad F mÀ2 kgÀ1 s4 A2
Electric resistance ohm m2 kg sÀ3 AÀ2
Electric conductance siemens S mÀ2 kgÀ1 s3 A2
Magnetic flux weber Wb m2 kg sÀ2 AÀ1
Magnetic flux density tesla T kg sÀ2 AÀ1
Inductance henry H m2 kg sÀ2 AÀ2

SI prefixes

Prefix Symbol Value Prefix Symbol Value

Atto a 10À18 Kilo k 103
Femto f 10À15 Mega M 106
Pico p 10À12 Giga G 109
Nano n 10À9 Tera T 1012
Micro m 10À6 Peta P 1015
Milli m 10À3 Exa E 1018