Power System Dynamics

Jan Machowski is Full Professor at the Warsaw University of Technology, Faculty of Electrical Engineering, Poland. Zbigniew Lubosny is Full Professor at Gdansk University of Technology, Faculty of Electrical and Control Engineering, Poland. Janusz W. Bialek, formerly Professor at Durham University and Edinburgh University, UK. James R. Bumby, formerly Reader at Durham University, UK.

• About the Authors xixList of Symbols & Abbreviations xxiPart I Introduction to Power Systems 11 Introduction 31.1 Stability and Control of a Dynamic System 31.2 Classification of Power System Dynamics 51.3 Two Pairs of Important Quantities 71.4 Stability of a Power System 81.5 Security of a Power System 92 Power System Components 132.1 Introduction 132.2 Structure of the Electric Power System 142.3 Generating Units 172.4 Substations 332.5 Transmission and Distribution Network 342.6 Protection 492.7 Wide Area Measurement Systems 533 The Power System in the Steady State 573.1 Transmission Lines 573.2 Transformers 643.3 Synchronous Generators 683.4 Power System Loads 1013.5 Network Equations 1103.6 Power Flows in Transmission Networks 114Part II Introduction to Power System Dynamics 1234 Electromagnetic Phenomena 1254.1 Fundamentals 1254.2 Three-phase Short Circuit on a Synchronous Generator 1304.3 Phase-to-phase Short Circuit 1534.4 Switching Operations 1644.5 Subsynchronous Resonance 1915 Electromechanical Dynamics – Small Disturbances 1955.1 Swing Equation 1955.2 Damping Power 1955.3 Equilibrium Points 1995.4 Steady-state Stability of Unregulated System 2005.5 Steady-state Stability of the Regulated System 2196 Electromechanical Dynamics – Large Disturbances 2296.1 Transient Stability 2296.2 Swings in Multi-machine Systems 2436.3 Direct Method for Stability Assessment 2466.4 Synchronization 2626.5 Asynchronous Operation and Resynchronization 2646.6 Out-of-step Protection System 2697 Wind Power 2837.1 Wind Turbines 2837.2 Generator Systems 2877.3 Induction Machine Equivalent Circuit 2917.4 Induction Generator Coupled to the Grid 2947.5 Induction Generators with Slightly Increased Speed Range via External Rotor Resistance 2977.6 Induction Generators with Significantly Increased Speed Range 2997.7 Fully Rated Converter Systems (Wide Speed Control) 3077.8 Peak Power Tracking of Variable Speed Wind Turbines 3097.9 Connections of Wind Farms 3097.10 Fault Behavior of Induction Generators 3107.11 Influence of Wind Generators on Power System Stability 3128 Voltage Stability 3158.1 Network Feasibility 3158.2 Stability Criteria 3208.3 Critical Load Demand and Voltage Collapse 3258.4 Static Analyses 3328.5 Dynamic Analysis 3428.6 Prevention of Voltage Collapse 3488.7 Self-excitation of a Generator Operating on a Capacitive Load 3499 Frequency Stability and Control 3559.1 Automatic Generation Control 3559.2 Stage I – Rotor Swings in the Generators 3689.3 Stage II – Frequency Drop 3719.4 Stage III – Primary Control 3739.5 Stage IV – Secondary Control 3789.6 Simplified Simulation Models 3879.7 Series FACTS Devices in Tie-lines 3929.8 Static Analysis by Snapshots of Power Flow 40410 Stability Enhancement 40710.1 Excitation Control System 40810.2 Turbine Control System 41510.3 Braking Resistors 41910.4 Generator Tripping 42110.5 Shunt FACTS Devices 42310.6 Series Compensators 44210.7 Unified Power Flow Controller 44910.8 HVDC Links in Transmission Network 455Part III Advanced Topics in Power System Dynamics 46711 Advanced Power System Modeling 46911.1 Synchronous Generator 46911.2 Excitation Systems 49611.3 Turbines and Turbine Governors 50511.4 Wind Turbine Generator Systems and Wind Farms 52211.5 Photovoltaic Power Plants 54411.6 HVDC Links 54811.7 Facts Devices 55711.8 Dynamic Load Models 55912 Steady-state Stability of Multi-machine Systems 56112.1 Mathematical Background 56112.2 Steady-state Stability of Unregulated System 58012.3 Steady-state Stability of the Regulated System 58913 Power System Dynamic Simulation 60113.1 Numerical Integration Methods 60213.2 The Partitioned Solution 60613.3 The Simultaneous Solution Methods 61813.4 Comparison Between the Methods 61913.5 Modeling of Unbalanced Faults 62013.6 Evaluation of Power System Dynamic Response 62214 Stability Studies in Power System Planning 62514.1 Purposes and Kinds of Analyses 62514.2 Planning Criteria 62914.3 Automation of Analyses and Reporting 64115 Optimization of Control System Parameters 64315.1 Grid Code Requirements 64315.2 Optimization Methods 64415.3 Linear Regulators 64715.4 Optimal Regulators LQG, LQR, and LQI 68115.5 Robust Regulators H2, h∞ 68515.6 Nonlinear Regulators 69315.7 Adaptive Regulators 69415.8 Real Regulators and Field Tests 70016 Wide-Area Monitoring and Control 70916.1 Wide Area Measurement Systems 70916.2 Examples of WAMS Applications 71817 Impact of Renewable Energy Sources on Power System Dynamics 73517.1 Renewable Energy Sources 73517.2 Inertia in the Electric Power System 74217.3 Virtual Inertia 75818 Power System Model Reduction – Equivalents 77518.1 Types of Equivalents 77518.2 Network Transformation 77618.3 Aggregation of Generating Units 78418.4 Equivalent Model of External Subsystem 78518.5 Coherency Recognition 78618.6 Properties of Coherency Based Equivalents 790Appendix 809A.1 Per-unit System 809A.1.1 Stator Base Quantities 809A.1.2 Power Invariance 811A.1.3 Rotor Base Quantities 811A.1.4 Power System Base Quantities 814A.1.5 Transformers 815A.2 Partial Inversion 816A.3 Linear Ordinary Differential Equations 817A.3.1 Fundamental System of Solutions 817A.3.2 Real and Distinct Roots 819A.3.3 Repeated Real Roots 820A.3.4 Complex and Distinct Roots 821A.3.5 Repeated Complex Roots 825A.3.6 First-order Complex Differential Eq. 825A.4 Prony Analysis 826A.5 Limiters and Symbols in Block Diagrams 832A.5.1 Addition, Multiplication, and Division 832A.5.2 Simple Integrator 833A.5.3 Simple Time Constant 833A.5.4 Lead–lag Block 834References 835Index 847