Frequency Variations in Power Systems Modeling, State Estimation, and Control

Frequency Variations in Power Systems: Modeling, State Estimation and Control presents the Frequency Divider Formula (FDF); a unique approach that defines, calculates and estimates the frequency in electrical energy systems. This authoritative book is written by two noted researchers on the topic. They define the meaning of frequency of an electrical quantity (such as voltage and current) in non-stationary conditions (for example the frequency is not equal to the nominal one) and pose the foundation of the frequency divider formula. The book describes the consequences of using a variable frequency in power system modelling and simulations, in state estimation and frequency control applications.

In addition, the authors include a discussion on the applications of the frequency divider in systems where part of the generation is not based on synchronous machines, but rather on converter-interfaced energy resources, such as wind and solar power plants. This important book:

• Offers a review that clearly defines and shows how the Frequency Divider Formula can be applied
• Discusses the link between frequency and energy in power systems
• Presents a unified vision that accurately reveals the common thread that links modelling, control and estimation
• Includes information on the many implications that “local frequency variations” have on power system dynamics and control
• Contains several numerical examples

Written for researchers, academic staff members, students, specialised consultants and professional software developers, Frequency Variations in Power Systems questions the conventional transient stability model of power system and proposes a new formulation.

FEDERICO MILANO is Professor of Power System Protections and Control and Head of Electrical Engineering with the University College Dublin, Ireland.

ÁLVARO ORTEGA MANJAVACAS is Senior Power Systems Researcher with the Universidad Loyola Andalucía, Seville, Spain.

List of Figures xiii

List of Tables xix

Preface xxi

Acknowledgments xxvii

Acronyms and Abbreviations xxix

Notation xxxiii

Part I Background 1

1 Frequency in Power Systems 3

1.1 Conventional Definitions 3

1.2 Alternating Current 6

1.3 Reference Frequency 8

1.4 Transforms 13

2 Power System Model 39

2.1 Time Scales 39

2.2 Quasi-Steady-State Model 41

2.3 Differential Algebraic Equations 45

2.4 Conventional Devices 48

3 Dynamic State Estimation 77

3.1 Basic Concepts 77

3.2 Introducing Dynamics 84

3.3 Estimation of Bus Frequencies 89

4 Frequency Control 105

4.1 Introduction 105

4.2 Power Balancing 106

4.3 Power Oscillation Damping 115

4.4 Nonsynchronous Devices 125

Part II Theory 137

5 Frequency Divider Formula 139

5.1 Rationale 139

5.2 Derivation 141

5.3 Equivalent Networks 155

5.4 Inclusion of Measurements 159

5.5 Frequency Participation Factors 163

6 Frequency Makers and Frequency Takers 175

6.1 Introduction 175

6.2 Derivation 176

6.3 Taxonomy 178

6.4 Examples 187

Part III Applications 205

7 Frequency Control 207

7.1 Impact of Frequency Signals 207

7.2 Synthesis of Frequency Signals 216

8 Dynamic State Estimation 227

8.1 Machine Rotor Speeds 227

8.2 Center of Inertia 247

8.3 Applications of the RoCoP 256

9 Power System Model 261

9.1 Introduction 261

9.2 Frequency Dependent Model 262

9.3 Example 265

10 Frequency in Power Systems 269

10.1 Definitions 269

10.2 Final Remarks 269

Appendix A Data 273

A.1 Three-Bus System 273

A.2 WSCC System 273

A.3 IEEE 14-Bus System 278

A.4 New England System 281

Appendix B Irish Transmission System 291

Bibliography 293

Index 313

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