Frequency Variations in Power Systems

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