Handbook of Electrical Power System Dynamics – Modeling, Stability, and Control

MIRCEA EREMIA, PhD, is Full Professor in the Electrical Power Systems Department at the University Politehnica of Bucharest. He has authored or coauthored more than 150 journal and conference papers as well as ten books in the field of electric power systems. Professor Eremia has extensive experience in power system analysis and engineering education. MOHAMMAD SHAHIDEHPOUR, PhD, is Bodine Chair Professor in the Electrical and Computer Engineering Department and Director of the Robert W. Galvin Center for Electricity Innovation at Illinois Institute of Technology in Chicago. He is Editor-in-Chief of IEEE Transactions on Smart Grid and an editorial board member of IEEE Power and Energy Magazine.

Foreword xxiii Acknowledgments xxv Contributors xxvii 1. INTRODUCTION 1 Mircea Eremia and Mohammad Shahidehpour PART I POWER SYSTEM MODELING AND CONTROL 7 2. SYNCHRONOUS GENERATOR AND INDUCTION MOTOR 9 Mircea Eremia and Constantin Bulac 2.1. Theory and Modeling of Synchronous Generator 9 2.1.1. Design and Operation Principles 9 2.1.2. Electromechanical Model of Synchronous Generator: Swing Equation 13 2.1.3. Electromagnetic Model of Synchronous Generator 17 2.1.3.1. Basic Equations 17 2.1.3.2. Park Transformation 24 2.1.3.3. Park Equations of Synchronous Generator 27 2.1.3.4. Representation of Synchronous Generator Equations in Per Unit 33 2.1.3.5. Equivalent Circuits for the d- and q-Axes 38 2.1.3.6. Steady-State Operation of the Synchronous Generator 41 2.1.3.7. Synchronous Generator Behavior on Terminal Short Circuit 46 2.1.4. Synchronous Generator Parameters 55 2.1.4.1. Operational Parameters 55 2.1.4.2. Standard Parameters 59 2.1.5. Magnetic Saturation 66 2.1.5.1. Open-Circuit and Short-Circuit Characteristics 67 2.1.5.2. Considering the Saturation in Stability Studies 69 2.1.6. Modeling in Dynamic State 73 2.1.6.1. Simplified Electromagnetic Models 73 2.1.6.2. Detailed Model in Dynamic State 82 2.1.7. Reactive Capability Limits 90 2.1.7.1. Loading Capability Chart 90 2.1.7.2. The V Curves 92 2.1.8. Description and Modeling of the Excitation Systems 93 2.1.8.1. Components and Performances of Excitation Control System 93 2.1.8.2. Types and Modeling of Excitation Systems 94 2.1.8.3. Control and Protective Functions 104 2.1.8.4. Example 112 2.2. Theory and Modeling of the Induction Motor 114 2.2.1. Design and Operation Issues 114 2.2.2. General Equations of the Induction Motor 116 2.2.2.1. Electrical Circuit Equations 116 2.2.2.2. The d--q Transformation 120 2.2.2.3. Basic Equations in the d--q Reference Frame 121 2.2.2.4. Electric Power and Torque 123 2.2.3. Steady-State Operation of the Induction Motor 123 2.2.4. Electromechanical Model of Induction Motor 129 2.2.5. Electromagnetic Model of Induction Motor 131 References 134 3. MODELING THE MAIN COMPONENTS OF THE CLASSICAL POWER PLANTS 137 Mohammad Shahidehpour, Mircea Eremia, and Lucian Toma 3.1. Introduction 137 3.2. Types of Turbines 138 3.2.1. Steam Turbines 138 3.2.2. Gas Turbines 139 3.2.3. Hydraulic Turbines 140 3.3. Thermal Power Plants 143 3.3.1. Generalities 143 3.3.2. Boiler and Steam Chest Models 145 3.3.3. Steam System Configurations 148 3.3.4. General Steam System Model 151 3.3.5. Governing Systems for Steam Turbines 152 3.3.5.1. Mechanical Hydraulic Control (MHC) 153 3.3.5.2. Electrohydraulic Control (EHC) 155 3.3.5.3. Digital Electrohydraulic Control (DEHC) 157 3.3.5.4. General Model for Speed Governing Systems 157 3.4. Combined-Cycle Power Plants 158 3.4.1. Generalities 158 3.4.2. Configurations of Combined-Cycle Power Plants 159 3.4.3. Model Block Diagrams of Combined-Cycle Power Plant 160 3.5. Nuclear Power Plants 167 3.6. Hydraulic Power Plants 169 3.6.1. Generalities 169 3.6.2. Modeling of Hydro Prime Mover Systems and Controls 171 3.6.2.1. General Block Diagram 171 3.6.2.2. Modeling of Turbine Conduit Dynamics 171 3.6.3. Hydro Turbine Governor Control Systems 174 3.6.3.1. Set Point Controller 174 3.6.3.2. The Actuator 176 References 177 4. WIND POWER GENERATION 179 Mohammad Shahidehpour and Mircea Eremia 4.1. Introduction 179 4.2. Some Characteristics of Wind Power Generation 181 4.3. State of the Art Technologies 184 4.3.1. Overview of Generator Concepts 184 4.3.1.1. General Description 185 4.3.1.2. Squirrel Cage Induction Generator 188 4.3.1.3. Dynamic Slip-Controlled Wound Rotor Induction Generator 189 4.3.1.4. Doubly Fed Induction Generator 190 4.3.1.5. Wound Rotor Synchronous Generator 191 4.3.1.6. Permanent Magnet Synchronous Generator 192 4.3.2. Overview of Wind Turbines Concepts 195 4.3.2.1. Fixed-Speed Wind Turbines 195 4.3.2.2. Variable-Speed Wind Turbines 195 4.3.3. Overview of Power Control Concepts 197 4.4. Modeling the Wind Turbine Generators 200 4.4.1. Model of a Constant-Speed Wind Turbine 200 4.4.2. Modeling the Doubly Fed Induction Generator Wind Turbine System 205 4.4.2.1. DFIG Model 205 4.4.2.2. Drive Train of DFIG 207 4.4.2.3. Power Converter 209 4.4.2.4. Control Strategy for the DFIG 209 4.4.2.5. Aerodynamic Model and Pitch Angle Controller 215 4.4.2.6. Operating Modes 217 4.4.3. Full-Scale Converter Wind Turbine 218 4.4.3.1. General Model 218 4.4.3.2. Model of a Direct-Drive Wind Turbine with Synchronous Generator 219 4.4.3.3. Control of Full-Scale Converter Wind Turbine 221 4.5. Fault Ride-Through Capability 223 4.5.1. Generalities 223 4.5.2. Blade Pitch Angle Control for Fault Ride-Through 225 References 226 5. SHORT-CIRCUIT CURRENTS CALCULATION 229 Nouredine Hadjsaid, Ion TriSstiu, and Lucian Toma 5.1. Introduction 229 5.1.1. The Main Types of Short Circuits 230 5.1.2. Consequences of Short Circuits 231 5.2. Characteristics of Short-Circuit Currents 232 5.3. Methods of Short-Circuit Currents Calculation 236 5.3.1. Basic Assumptions 236 5.3.2. Method of Equivalent Voltage Source 237 5.3.3. Method of Symmetrical Components 239 5.3.3.1. General Principles 239 5.3.3.2. The Symmetrical Components of Unsymmetrical Phasors 241 5.3.3.3. Sequence Impedance of Network Components 247 5.3.3.4. Unsymmetrical Fault Calculations 253 5.4. Calculation of Short-Circuit Current Components 264 5.4.1. Initial Symmetrical Short-Circuit Current I 00 k 264 5.4.1.1. Three-Phase Short Circuit 264 5.4.1.2. Phase-to-Phase Short Circuit 267 5.4.1.3. Phase-to-Phase Short Circuit with Earth Connection 268 5.4.1.4. Phase-to-Earth Short Circuit 268 5.4.2. Peak Short-Circuit Current ip 269 5.4.2.1. Three-Phase Short Circuit 269 5.4.2.2. Phase-to-Phase Short Circuit 271 5.4.2.3. Phase-to-Phase Short Circuit with Earth Connection 271 5.4.2.4. Phase-to-Earth Short Circuit 271 5.4.3. DC Component of the Short-Circuit Current 271 5.4.4. Symmetrical Short-Circuit Breaking Current I b 272 5.4.4.1. Far-from-Generator Short Circuit 272 5.4.4.2. Near-to-Generator Short Circuit 272 5.4.5. Steady-State Short-Circuit Current I k 273 5.4.5.1. Three-Phase Short Circuit of One Generator or One Power Station Unit 273 5.4.5.2. Three-Phase Short Circuit in Nonmeshed Networks 276 5.4.5.3. Three-Phase Short Circuit in Meshed Networks 276 5.4.5.4. Unbalanced Short Circuits 277 5.4.6. Applications 277 References 289 6. ACTIVE POWER AND FREQUENCY CONTROL 291 Les Pereira 6.1. Introduction 291 6.2. Frequency Deviations in Practice 293 6.2.1. Small Disturbances and Deviations 293 6.2.2. Large Disturbances and Deviations 293 6.3. Typical Standards and Policies for "Active Power and Frequency Control" or "Load Frequency Control" 294 6.3.1. UCTE Load Frequency Control 294 6.3.1.1. Primary Control is by Governors 295 6.3.1.2. Secondary Control by Automatic Generation Controls (AGCs) 295 6.3.1.3. Tertiary Control 296 6.3.1.4. Self-Regulation of the Load 296 6.3.2. NERC (U.S.) Standards 296 6.3.3. Other Countries' Standards 297 6.4. System Modeling, Inertia, Droop, Regulation, and Dynamic Frequency Response 297 6.4.1. Block Diagram of the System Dynamics and Load Damping 297 6.4.2. Effect of Governor Droop on Regulation 298 6.4.3. Increasing Load by Adjusting Prime Mover Power 298 6.4.4. Parallel Operation of Several Generators 298 6.4.5. Isolated Area Modeling and Response 301 6.5. Governor Modeling 302 6.5.1. Response of a Simple Governor Model with Droop 303 6.5.2. Hydraulic Governor Modeling 304 6.5.2.1. Hydraulic Turbines 304 6.5.2.2. Hydraulic Governors 305 6.5.2.3. Hydraulic Turbine Model 306 6.5.2.4. PID Governor 306 6.5.3. Performance of Hydrogovernors with Parameters Variation 307 6.5.3.1. Isolated System Governor Simulations 307 6.5.3.2. Interconnected System Governor Simulations 309 6.5.4. Thermal Governor Modeling 311 6.5.4.1. General Steam System Model 311 6.5.4.2. Gas Turbine Model 312 6.5.5. Development of a New Thermal Governor Model in the WECC 315 6.5.5.1. The New Thermal Governor Model 315 6.5.5.2. Analysis of Test Data: Thermal Versus Hydro Units 318 6.6. AGC Principles and Modeling 328 6.6.1. AGC in a Single-Area (Isolated) System 329 6.6.2. AGC in a Two-Area System, Tie-Line Control, Frequency Bias 329 6.6.3. AGC in Multiarea Systems 332 6.7. Other Topics of Interest Related to Load Frequency Control 336 6.7.1. Spinning Reserves 336 6.7.2. Underfrequency Load Shedding and Operation in Islanding Conditions 336 References 338 7. VOLTAGE AND REACTIVE POWER CONTROL 340 Sandro Corsi and Mircea Eremia 7.1. Relationship Between Active and Reactive Powers and Voltage 342 7.1.1. Short Lines 342 7.1.2. Taking into Account the Shunt Admittance 346 7.1.3. Sensitivity Coefficients 346 7.2. Equipments for Voltage and Reactive Power Control 347 7.2.1. Reactive Power Compensation Devices 347 7.2.1.1. Shunt Capacitors 347 7.2.1.2. Shunt Reactors 348 7.2.2. Voltage and Reactive Power Continuous Control Devices 349 7.2.2.1. Synchronous Generators 349 7.2.2.2. Synchronous Compensators 350 7.2.2.3. Static VAr Controllers and FACTS 351 7.2.3. On-Load Tap Changing Transformers 352 7.2.3.1. Generalities 352 7.2.3.2. Switching Technologies 355 7.2.3.3. Determination of the Current Operating Tap 362 7.2.3.4. Static Characteristic of the Transformer 363 7.2.3.5. Various Applications of the OLTC Transformers for Voltage and Reactive Power Control 366 7.2.4. Regulating Transformers 371 7.2.4.1. In-Phase Regulating Transformer (IPRT) 371 7.2.4.2. Phase Shifting Transformers 372 7.3. Grid Voltage and Reactive Power Control Methods 374 7.3.1. General Considerations 374 7.3.2. Voltage--Reactive Power Manual Control 377 7.3.2.1. Manual Voltage Control by Reactive Power Flow 378 7.3.2.2. Manual Voltage Control by Network Topology Modification 378 7.3.3. Voltage--Reactive Power Automatic Control 378 7.3.3.1. Automatic Voltage Control of the Generator Stator Terminals 379 7.3.3.2. Automatic Voltage Control by Generator Line Drop Compensation 385 7.3.3.3. Automatic High-Side Voltage Control at a Power Plant 391 7.4. Grid Hierarchical Voltage Regulation 399 7.4.1. Structure of the Hierarchy 399 7.4.1.1. Generalities 399 7.4.1.2. Basic SVR and TVR Concepts 401 7.4.1.3. Primary Voltage Regulation 402 7.4.1.4. Secondary Voltage Regulation: Architecture and Modeling 405 7.4.1.5. Tertiary Voltage Regulation 417 7.4.2. SVR Control Areas 418 7.4.2.1. Procedure to Select the Pilot Nodes and to Define the Control Areas 418 7.4.2.2. Procedure to Select the Control Generators 420 7.4.3. Power Flow Computation in the Presence of the Secondary Voltage Regulation 422 7.5. Implementation Study of the Secondary Voltage Regulation in Romania 423 7.5.1. Characteristics of the Study System 423 7.5.2. SVR Areas Selection 423 7.6. Examples of Hierarchical Voltage Control in the World 429 7.6.1. The French Power System Hierarchical Voltage Control 429 7.6.1.1. General Overview 429 7.6.1.2. Original Secondary Voltage Regulation 430 7.6.1.3. Coordinated Secondary Voltage Regulation 432 7.6.1.4. Performances and Results of Simulations 434 7.6.1.5. Conclusion on the French Hierarchical Voltage Control System 435 7.6.2. The Italian Hierarchical Voltage Control System 435 7.6.2.1. General Overview 435 7.6.2.2. Improvements in the Power System Operation 438 7.6.2.3. Conclusions on the Italian Hierarchical Voltage Control System 442 7.6.3. The Brazilian Hierarchical Voltage Control System 442 7.6.3.1. General Overview 442 7.6.3.2. Results of the Study Simulations 443 7.6.3.3. Conclusions on the Brazilian Voltage Control System 447 References 447 PART II POWER SYSTEM STABILITY AND PROTECTION 451 8. BACKGROUND OF POWER SYSTEM STABILITY 453 S.S. (Mani) Venkata, Mircea Eremia, and Lucian Toma 8.1. Introduction 453 8.2. Classification of Power Systems Stability 453 8.2.1. Rotor Angle Stability 454 8.2.1.1. Small-Disturbance (or Small-Signal) Rotor Angle Stability 460 8.2.1.2. Large-Disturbance Rotor Angle Stability or Transient Stability 461 8.2.2. Voltage Stability 462 8.2.3. Frequency Stability 467 8.3. Parallelism Between Voltage Stability and Angular Stability 469 8.4. Importance of Security for Power System Stability 469 8.4.1. Power System States 470 8.4.2. Power Flow Security Limits 472 8.4.3. Services to Meet Power System Security Constraints 473 8.4.4. Dynamic Security Assessment 474 References 475 9. SMALL-DISTURBANCE ANGLE STABILITY AND ELECTROMECHANICAL OSCILLATION DAMPING 477 Roberto Marconato and Alberto Berizzi 9.1. Introduction 477 9.2. The Dynamic Matrix 478 9.2.1. Linearized Equations 478 9.2.2. Building the Dynamic Matrix 481 9.3. A General Simplified Approach 482 9.3.1. Inertia and Synchronizing Power Coefficients 483 9.3.2. Electromechanical Oscillations 486 9.3.2.1. Oscillation Modes 486 9.3.2.2. Oscillation Amplitudes and Participation Factors 489 9.3.3. Numerical Examples 493 9.3.3.1. Application 1: Two-Area Test System 494 9.3.3.2. Application 2: Three-Area Test System 497 9.4. Major Factors Affecting the Damping of Electromechanical Oscillations 501 9.4.1. Introduction 501 9.4.2. Single Machine-Infinite Bus System: A Simplified Approach 503 9.4.3. Single Machine-Infinite Bus System: A More Accurate Approach 507 9.4.3.1. Introduction 507 9.4.3.2. Contribution to Damping Due to Generator Structure 512 9.4.3.3. Contribution of the Primary Voltage Control 514 9.4.3.4. Effect of Primary Frequency Control 537 9.4.3.5. Outline of Other Contributions 544 9.4.4. Summary of the Major Factors Affecting the Damping of Electromechanical Oscillations 545 9.5. Damping Improvement 546 9.5.1. Introduction 546 9.5.2. Modal Synthesis Based on the Theory of Small Shift Poles 550 9.5.3. PSSs on Excitation Control 553 9.5.3.1. Base Case and Theory 553 9.5.3.2. Synthesis of PSSs on Excitation Control: General Case 556 9.5.4. Limitation on PSS Gains 561 9.6. Typical Cases of Interarea Or Low-Frequency Electromechanical Oscillations 564 References 568 10. TRANSIENT STABILITY 570 Nikolai Voropai and Constantin Bulac 10.1. General Aspects 570 10.2. Direct Methods for Transient Stability Assessment 572 10.2.1. Equal Area Criterion 572 10.2.1.1. Fundamentals of Equal Area Criterion 572 10.2.1.2. Calculation of the Fault Clearing Time 575 10.2.1.3. Two Finite Power Synchronous Generators 579 10.2.2. Extended Equal Area Criterion--EEAC 580 10.2.3. The SIME (SIngle - Machine Equivalent) Method 582 10.2.3.1. Method Formulation 583 10.2.3.2. Criteria and Degree of Instability 585 10.2.3.3. Criteria and Corresponding Stability Reserve 585 10.2.3.4. Identification of the OMIB Equivalent 586 10.2.4. Direct Methods Based on Lyapunov's Theory 587 10.2.4.1. Lyapunov's Method 587 10.2.4.2. Designing the Lyapunov Function 590 10.2.4.3. Determination of Equilibrium 594 10.2.4.4. Extension of the Direct Lyapunov's Method 596 10.2.4.5. New Approaches 601 10.3. Integration Methods for Transient Stability Assessment 603 10.3.1. General Considerations 603 10.3.2. Runge--Kutta Methods 608 10.3.3. Implicit Trapezoidal Rule 609 10.3.4. Mixed Adams-BDF Method 611 10.4. Dynamic Equivalents 614 10.4.1. Generalities 614 10.4.2. Simplification of Mathematical Description of a System 617 10.4.2.1. The Disturbance Impact Index 617 10.4.2.2. The Study of the Disturbance Impact Index 617 10.4.3. Estimating the System Element Significance 621 10.4.3.1. Index of the System Structural Connectivity 621 10.4.3.2. Significance of a System Element 622 10.4.4. Coherency Estimation 623 10.4.4.1. Equation of the Mutual Motion of a Pair of Machines 623 10.4.4.2. Coherency Indices 625 10.4.4.3. Clustering of Coherency Indices 628 10.4.5. Equivalencing Criteria 631 10.4.6. Center of Inertia. Parameters of the Equivalent 634 10.5. Transient Stability Assessment of Large Electric Power Systems 638 10.5.1. Characteristics of Large Electric Power System 638 10.5.2. Initial Conditions 639 10.5.3. Standard Conditions for Transient Stability Studies 639 10.5.3.1. Studied Conditions and Disturbances 639 10.5.3.2. Stability Margins 641 10.5.3.3. System Stability Requirements 642 10.5.4. Reducing the Studied Conditions by Structural Analysis 643 10.5.5. Using the Simplified Models and Direct Methods 644 10.6. Application 645 References 651 11. VOLTAGE STABILITY 657 Mircea Eremia and Constantin Bulac 11.1. Introduction 657 11.2. System Characteristics and Load Modeling 658 11.2.1. System Characteristics 658 11.2.2. Load Modeling 660 11.2.2.1. Load Characteristics 660 11.2.2.2. Static Models 662 11.2.2.3. Dynamic Models 664 11.3. Static Aspects of Voltage Stability 667 11.3.1. Existence of Steady-State Solutions 667 11.3.2. Operating Points and Zones 670 11.4. Voltage Instability Mechanisms: Interaction Between Electrical Network, Loads, and Control Devices 674 11.4.1. Interaction between Electrical Network and Load 674 11.4.2. Influence of the On-Load Tap Changer 676 11.4.2.1. Modeling the On-Load Tap Changing Dynamics 676 11.4.2.2. The Effect of Automatic Tap Changing on the Possible Operating Points 678 11.4.2.3. Influence of On-Load Tap Changing on the Voltage Stability 679 11.4.3. Effect of the Generated Reactive Power Limitation 683 11.4.4. The Minimum Voltage Criteria 686 11.5. Voltage Stability Assessment Methods 688 11.5.1. Overview of Voltage Collapse Criteria 688 11.5.2. Sensitivities Analysis Method: Local Indices 695 11.5.3. Loading Margin as Global Index 698 11.5.4. Some Aspects of the Bifurcations Theory 702 11.5.4.1. Generalities 702 11.5.4.2. Hopf Bifurcation 704 11.5.4.3. Saddle-node Bifurcation 705 11.5.4.4. Singularity Induced Bifurcation 706 11.5.4.5. Global Bifurcations 707 11.5.5. The Smallest Singular Value Technique. VSI Global Index 708 11.5.6. Modal Analysis of the Reduced Jacobian Matrix 711 11.5.6.1. The V-Q Variation Modes of the Power System 712 11.5.6.2. Definition of Participation Factors in Voltage Stability Analysis 714 11.6. Voltage Instability Countermeasures 716 11.6.1. Some Confusions 716 11.6.2. Load Shedding: An Emergency Measure 717 11.6.3. Shunt Capacitor Switching 719 11.6.4. Extending the Voltage Stability Limit by FACTS Devices 719 11.6.5. Countermeasures Against the Destabilizing Effect of the Load Tap Changer 724 11.7. Application 724 References 733 12. POWER SYSTEM PROTECTION 737 Klaus-Peter Brand and Ivan De Mesmaeker 12.1. Introduction 737 12.1.1. Motivation 737 12.1.2. The Task of Protection 738 12.1.3. Basic Protection Properties and Resulting Requirements 739 12.1.4. From System Supervision to Circuit Breaker Trip 739 12.1.5. Main Operative Requirements 740 12.1.5.1. Selectivity 740 12.1.5.2. Reliability 740 12.1.5.3. Speed and Performance 741 12.1.5.4. Adaptation 741 12.1.5.5. Adaptive Protection 741 12.1.5.6. Backup Protection 741 12.1.5.7. General Remarks About Features Like Performance, Reliability, and Availability 742 12.1.6. Advantages of State-of-the-Art Protection 742 12.2. Summary of IEC 61850 744 12.3. The Protection Chain in Details 746 12.3.1. Copper Wires vs. Serial Links 746 12.3.2. Supervision 746 12.3.3. Values Measured for Protection 748 12.3.3.1. Nonelectrical Values 748 12.3.3.2. Electrical Values 748 12.3.4. Data Acquisition from Sensors 748 12.3.4.1. Sensors 748 12.3.4.2. A/D Conversion and Merging Unit 750 12.3.4.3. Time Synchronization 750 12.3.5. Protection Data Processing 751 12.3.5.1. General 751 12.3.5.2. Trip Decision and Related Information 751 12.3.5.3. Other Data Handling Features 751 12.3.6. Data Sending to the Actuators 751 12.3.7. Process Interface 752 12.3.8. Circuit Breaker 752 12.3.9. Power Supply 753 12.4. Transmission and Distribution Power System Structures 753 12.5. Properties of the Three-Phase Systems Relevant for Protection 755 12.5.1. Symmetries 755 12.5.2. Unbalance 756 12.5.3. Symmetrical Components 758 12.6. Protection Functions Sorted According to the Objects Protected 759 12.6.1. Protection Based on Limits of Locally Measured Values 759 12.6.1.1. Overcurrent and Time Overcurrent Protection 760 12.6.1.2. Overload Protection 760 12.6.1.3. Frequency Protection 761 12.6.1.4. Voltage Protection 761 12.6.1.5. Limit Supervision and Protection 761 12.6.1.6. Protection with Improvement of Selection by Time Delays 762 12.6.1.7. Protection with Improvement of Selection by Communication 763 12.6.2. Protection with Fault Direction Detection 764 12.6.2.1. Directional Protection 764 12.6.2.2. Improvement of Directional Protection by Communication 765 12.6.3. Impedance Protection 766 12.6.3.1. Distance Protection 766 12.6.3.2. Special Impedance-Based Functions 768 12.6.4. Current Differential Functions 768 12.6.4.1. Differential Protection 768 12.6.4.2. Application Issues for Busbar Protection 770 12.6.4.3. Application Issues for Line Differential Protection 771 12.6.4.4. Comparative Protection as Simplified Differential Protection 771 12.6.5. Protection-Related Functions 772 12.6.5.1. Breaker Failure Protection 772 12.6.5.2. Autoreclosing 772 12.6.5.3. Synchrocheck 773 12.7. From Single Protection Functions to System Protection 773 12.7.1. Single Function and Multifunctional Relays 773 12.7.2. Adaptive Protection 774 12.7.3. Distributed Protection 774 12.7.3.1. Differential Object Protection Functions 774 12.7.3.2. Directional Object Protection Functions 775 12.7.4. Wide Area Protection 775 12.7.5. General Guide 776 12.7.5.1. General Recommendations for Protection Application 776 12.7.6. Security and Dependability 779 12.7.7. Summary 780 12.8. Conclusions 780 Annex 12.1. Identification of Protection Functions 780 A.12.1. General Remarks 780 A.12.1.1. IEEE Device Numbers 780 A.12.1.2. IEC Designation 781 A.12.1.3. Logical Nodes Names 781 A.12.2. Identification List 781 References 785 PART III GRID BLACKOUTS AND RESTORATION PROCESS 787 13. MAJOR GRID BLACKOUTS: ANALYSIS, CLASSIFICATION, AND PREVENTION 789 Yvon Besanger, Mircea Eremia, and Nikolai Voropai 13.1. Introduction 789 13.2. Description of Some Previous Blackouts 792 13.2.1. August 14, 2003 Northeast United States and Canada Blackout 793 13.2.1.1. Precondition 793 13.2.1.2. Initiating Events 794 13.2.1.3. Cascading Events 795 13.2.1.4. Final State 801 13.2.1.5. What Stopped the Cascade Spreading? 801 13.2.1.6. Causes of Blackout 802 13.2.1.7. Recommendations to Prevent Blackouts 804 13.2.2. September 28, 2003 Italy Blackout 805 13.2.2.1. Precondition 805 13.2.2.2. Initiating Events 806 13.2.2.3. Cascading Events 806 13.2.2.4. Final State 810 13.2.2.5. Restoration 811 13.2.2.6. Root Causes of the Blackout 811 13.2.2.7. Recommendations to Prevent Blackouts 811 13.2.3. September 23, 2003 Eastern Denmark and Southern Sweden Blackout 812 13.2.3.1. Precondition 812 13.2.3.2. Initiating Events 812 13.2.3.3. Cascading Events 812 13.2.3.4. Final State 812 13.2.4. January 12, 2003 Blackout in Croatia 812 13.2.4.1. Precondition 812 13.2.4.2. Initiating Events 813 13.2.4.3. Cascading Events 813 13.2.4.4. Final State 813 13.2.5. May 25, 2005 Blackout in Moscow 814 13.2.5.1. Precondition 814 13.2.5.2. Initiating Events 814 13.2.5.3. Cascading Events 816 13.2.5.4. Final State 816 13.2.6. July 12, 2004 Greece Blackout 816 13.2.6.1. Precondition 816 13.2.6.2. Initiating Events 816 13.2.6.3. Cascading Events 817 13.2.6.4. Final State 817 13.2.7. July 2, 1996 Northwest U.S. Blackout 817 13.2.7.1. Precondition 817 13.2.7.2. Initiating Events 817 13.2.7.3. Cascading Events 817 13.2.7.4. Final State 818 13.2.8. August 10, 1996 Northwest U.S. Blackout 818 13.2.8.1. Precondition 818 13.2.8.2. Initiating Events 818 13.2.8.3. Cascading Events 818 13.2.8.4. Final State 818 13.2.9. December 19, 1978 National Blackout in France 819 13.2.9.1. Precondition 819 13.2.9.2. Initiating Events 819 13.2.9.3. Cascading Events 819 13.2.9.4. Final State 820 13.2.9.5. Restoration 820 13.2.9.6. Causes of Blackout 820 13.2.10. January 12, 1987 Western France Blackout 820 13.2.10.1. Precondition 820 13.2.10.2. Initiating Events 820 13.2.10.3. Cascading Events 820 13.2.10.4. Emergency Actions 821 13.2.10.5. Causes of Blackout 821 13.2.11. March 13, 1989 Hydro-Quebec System Blackout Response to Geomagnetic Disturbance 822 13.2.11.1. Precondition 822 13.2.11.2. Initiating and Cascading Events 823 13.2.11.3. Causes of the SVC Tripping 823 13.2.11.4. Equipment Damage 825 13.2.11.5. Lessons Learned 825 13.2.12. January 17, 1995 Japan Blackout After Hanshin Earthquake 826 13.2.12.1. Precondition 826 13.2.12.2. Supply and Demand 826 13.2.12.3. Damage to Electric Power Facilities 827 13.2.12.4. Restoration of Electricity Supply 828 13.2.13. European Incident of November 4, 2006 830 13.2.13.1. Precondition 830 13.2.13.2. Initiating Events 830 13.2.13.3. Cascading Events 832 13.2.13.4. Final State 833 13.2.13.5. Resynchronization 835 13.2.14. Some Lessons Learned 835 13.3. Analysis of Blackouts 835 13.3.1. Classification of Blackouts 836 13.3.1.1. Precondition 836 13.3.1.2. Initiating Events 837 13.3.1.3. Cascading Events 837 13.3.2. Blackouts: Types of Incidents 840 13.3.3. Mechanisms of Blackouts 841 13.3.3.1. Voltage Collapse 842 13.3.3.2. Frequency Collapse 842 13.3.3.3. Cascading Overload 843 13.3.3.4. System Separation 843 13.3.3.5. Loss of Synchronism 843 13.3.3.6. Generalization 844 13.4. Economical and Social Effects 847 13.5. Recommendations for Preventing Blackouts 849 13.6. On Some Defense and Restoration Actions 850 13.6.1. Defense Actions 851 13.6.2. Restoration Actions 854 13.7. Survivability/vulnerability of Electric Power Systems 856 13.7.1. Introduction 856 13.7.2. Conception 857 13.7.3. Technology of Study 858 13.7.4. Concluding Remarks 859 13.8. Conclusions 860 Acknowledgments 860 References 860 14. RESTORATION PROCESSES AFTER BLACKOUTS 864 Alberto Borghetti, Carlo Alberto Nucci, and Mario Paolone 14.1. Introduction 864 14.2. Overview of The Restoration Process 865 14.2.1. System Restoration Stages, Duration, Tasks, and Typical Problems 866 14.2.2. New Requirements 868 14.3. Black-Start-Up Capabilities of Thermal Power Plant: Modeling and Computer Simulations 869 14.3.1. Black-Start-Up of a Steam Group Repowered by a Gas Turbine 869 14.3.1.1. Black-Start-up Capability of a Single Steam Group 870 14.3.1.2. Black-Start-Up Capability of a Steam Group Repowered by a Gas Turbine 872 14.3.1.3. Control System Modifications to Improve Black-Start-Up Capabilities 874 14.3.2. Black-Start-Up of a Combined-Cycle Power Plant 877 14.3.2.1. Analysis of the Energization Maneuvers 878 14.3.2.2. Analysis of the Islanding Maneuvers 879 14.3.2.3. Description of Some Islanding Tests and Obtained Experimental Results 886 14.4. Description of Computer Simulators 888 14.4.1. Simulator of a Steam Group Repowered with a Gas Turbine 888 14.4.1.1. Gas Turbine Model and Its Validation 889 14.4.1.2. Steam Section Modeling and Its Validation 889 14.4.2. Simulator of a Combined-Cycle Power Plant 892 14.5. Concluding Remarks 896 References 896 15. COMPUTER SIMULATION OF SCALE-BRIDGING TRANSIENTS IN POWER SYSTEMS 900 Kai Strunz and Feng Gao 15.1. Bridging of Instantaneous and Phasor Signals 901 15.2. Network Modeling 903 15.2.1. Companion Model for Network Branches 903 15.2.2. Direct Construction of Nodal Admittance Matrix 906 15.3. Modeling of Power System Components 909 15.3.1. Multiphase Lumped Elements 909 15.3.2. Transformer 911 15.3.3. Transmission Line 912 15.3.3.1. Single-Phase Line Model 912 15.3.3.2. Multiphase Line Model 916 15.3.4. Synchronous Machine in dq0 Domain 918 15.3.4.1. Electromagnetic and Mechanical Machine Equations 918 15.3.4.2. Calculation of Real Part of Stator Current 920 15.3.4.3. Calculation of Imaginary Part of Stator Current 920 15.3.4.4. Calculation of Rotor Speed and Angle 922 15.3.4.5. Integration with AC Network 922 15.3.4.6. Initialization 923 15.4. Application: Simulation of Blackout 923 References 926 Index 929