Dynamics and Control of Electric Transmission and Microgrids

K. R. PADIYAR is Professor Emeritus, Indian Institute of Science, Bangalore, India. ANIL M. KULKARNI is Professor of Electrical Engineering, Indian Institute of Technology Bombay, Mumbai, India.

• Preface xiiiAcknowledgements xv1 Introduction 11.1 Present Status of Grid Operation 11.1.1 General 11.1.2 HVDC Transmission 41.1.3 Reliability of Electricity Supply 41.2 Overview of System Dynamics and Control 41.2.1 Power System Stability 41.2.2 Mathematical Preliminaries 6Stability of Equilibrium Point 6Steady-State Behavior 81.2.3 Power System Security 81.3 Monitoring and Enhancing System Security 101.4 Emergency Control and System Protection 111.5 Recent Developments 121.5.1 Power System Protection 121.5.2 Development of Smart Grids 131.5.3 Microgrids 141.5.4 Role of System Dynamics and Control 141.6 Outline of Chapters 14References 172 Grid Characteristics and Operation 192.1 Description of Electric Grids 192.2 Detailed Modeling of Three-Phase AC Lines 212.3 Circuit Models of Symmetric Networks 222.4 Network Equations in DQo and 𝛼𝛽o Components 232.4.1 Transformation to Park (dqo) Components 242.4.2 Steady-State Equations 252.4.3 D-Q Transformation using 𝛼-𝛽 Variables 262.5 Frequency and Power Control 282.5.1 Tie-Line Bias Frequency Control 312.6 Dynamic Characteristics of AC Grids 332.6.1 Grid Response to Frequency Modulation 332.6.2 Grid Response to Injection of Reactive Current 352.7 Control of Power Flow in AC Grids 382.7.1 Power Transfer Capability of a Line 382.7.2 Power Flow in a Line connected to an AC Transmission Grid 412.8 Analysis of Electromagnetic Transients 422.8.1 Modeling of Lumped Parameter Components 422.8.2 Modeling of a Single-Phase Line 432.8.3 Approximation of Series Resistance of Line 442.8.4 Modeling of Lossless Multiphase Line 452.8.5 Modeling of Multiphase Networks with Lumped Parameters 462.9 Transmission Expansion Planning 472.10 Reliability in Distribution Systems 482.11 Reliable Power Flows in a Transmission Network 482.12 Reliability Analysis of Transmission Networks 502.A Analysis of a Distributed Parameter Single-Phase Line in Steady State 512.A.1 Expressions for a Lossless Line 532.A.2 Performance of a Symmetrical Line 542.B Computation of Electrical Torque 55References 573 Modeling and Simulation of Synchronous Generator Dynamics 593.1 Introduction 593.2 Detailed Model of a Synchronous Machine 593.2.1 Flux Linkage Equations 603.2.2 Voltage equations 613.3 Park’s Transformation 623.4 Per-Unit Quantities 693.5 Equivalent Circuits of a Synchronous Machine 723.6 Synchronous Machine Models for Stability Analysis 763.6.1 Application of Model (2.1) 803.6.2 Application of Model (1.1) 803.6.3 Modeling of Saturation 823.7 An Exact Circuit Model of a Synchronous Machine for Electromagnetic Transient Analysis 823.7.1 Derivation of the Circuit Model 833.7.2 Transformation of the Circuit Model 873.7.3 Modeling of a Synchronous Generator in the Simulation of Electromagnetic Transients 913.7.4 Treatment of Dynamic Saliency 923.8 Excitation and Prime Mover Controllers 933.8.1 Excitation Systems 933.8.2 Modeling of Prime-Mover Control Systems 983.9 Transient Instability due to Loss of Synchronism 1013.10 Extended Equal Area Criterion 1033.11 Dynamics of a Synchronous Generator 104Network Equations 104Calculation of Initial Conditions 106System Simulation 1083.A Derivation of Electrical Torque 110References 1124 Modeling and Simulation of Wind Power Generators 1154.1 Introduction 1154.2 Power Extraction byWind Turbines 1164.2.1 Wind Speed Characteristics 1174.2.2 Control of Power Extraction 1184.3 Generator and Power Electronic Configurations 1204.3.1 Wind Farm Configurations 1224.4 Modeling of the Rotating System 1224.5 Induction Generator Model 1244.5.1 Rotor Speed Instability 1274.5.2 Modeling Issues 1304.5.3 Frequency Conversion Using Voltage Source Converters 1324.6 Control of Type IIIWTG System 1334.6.1 Rotor-Side Converter Control 1334.6.2 Grid-Side Converter Control 1364.6.3 Overall Control Scheme for a Type III WTG system 1374.6.4 Simplified Modeling of the Controllers for Slow Transient Studies 1414.7 Control of Type IVWTG System 142References 1435 Modeling and Analysis of FACTS and HVDC Controllers 1455.1 Introduction 1455.2 FACTS Controllers 1465.2.1 Description 1465.2.2 A General Equivalent Circuit for FACTS Controllers 1475.2.3 Benefits of the Application of FACTS Controllers 1485.2.4 Application of FACTS Controllers in Distribution Systems 1505.3 Reactive Power Control 150Control Characteristics 1535.4 Thyristor-Controlled Series Capacitor 1535.4.1 Basic Concepts of Controlled Series Compensation 1555.4.2 Operation of a TCSC 1575.4.3 Analysis of a TCSC 1585.4.4 Computation of the TCSC Reactance (XTCSC) 1595.4.5 Control of the TCSC 1615.5 Static Synchronous Compensator 1665.5.1 General 1665.5.2 Two-Level (Graetz Bridge) Voltage Source Converter 1685.5.3 Pulse0020Width Modulation 1695.5.4 Analysis of a Voltage Source Converter 1715.5.5 Control of VSC 1755.6 HVDC Power Transmission 1775.6.1 Application of DC Transmission 1785.6.2 Description of HVDC Transmission Systems 1785.6.3 Analysis of a Line Commutated Converter 1805.6.4 Introduction of VSC-HVDC Transmission 1865.A Case Study of a VSC-HVDC Link 190References 1936 Damping of Power Swings 1956.1 Introduction 1956.2 Origin of Power Swings 1966.3 SMIB Model with Field Flux Dynamics and AVR 1996.3.1 Small-Signal Model and Eigenvalue Analysis 2016.4 Damping and Synchronizing Torque Analysis 2056.5 Analysis of Multi-Machine Systems 2106.5.1 Electro-Mechanical Modes in a Multi-Machine System 2106.5.2 Analysis with Detailed Models 2166.6 Principles of Damping Controller Design 2256.6.1 Actuator Location and Choice of Feedback Signals 2296.6.2 Components of a PSDC 2306.6.3 PSDCs based on Generator Excitation Systems: Power System Stabilizers 2316.6.4 Adverse Torsional Interactions with the Speed/Slip Signal 2376.6.5 Damping of Swings using Grid-Connected Power Electronic Systems 2376.7 Concluding Remarks 2416.A Eigenvalues of the Stiffness matrix K of Section 6.5.1 2426.B Three-Machine Data 244References 2447 Analysis and Control of Loss of Synchronism 2477.1 Introduction 2477.2 Effect of LoS 2477.3 Understanding the LoS Phenomenon 2497.4 Criteria for Assessment of Stability 2517.5 Power System Modeling and Simulation for Analysis of LoS 2527.5.1 Effect of System Model 2547.5.2 Effect of Changing Operating Conditions 2557.6 Loss of Synchronism in Multi-Machine Systems 2567.6.1 Effect of Disturbance Location on Mode of Separation: 2587.6.2 Effect of the Load Model 2587.6.3 Effect of Series Compensation in a Critical Line 2607.6.4 Effect of a Change in the Pre-fault Generation Schedule 2617.6.5 Voltage Phase Angular Differences across Critical Lines/Apparent Impedance seen by Relays 2617.7 Measures to Avoid LoS 2637.7.1 System Planning and Design 2637.7.2 Preventive Control During Actual Operation 2647.7.3 Emergency Control 2647.8 Assessment and Control of LoS Using Energy Functions 2657.8.1 Energy Function Method Applied to an SMIB System 2667.8.2 Energy Function Method Applied to Multi-Machine Systems/Detailed Models 2707.8.3 Evaluation of Critical Energy in a Multi-Machine System 2747.9 Generation Rescheduling Using Energy Margin Sensitivities 2747.9.1 Case Study: Generation Rescheduling 2767.A Simulation Methods for Transient Stability Studies 2767.A.1 Simultaneous Implicit Method 2777.A.2 Partitioned Explicit Method 2777.B Ten-Machine System Data 279References 2818 Analysis of Voltage Stability and Control 2838.1 Introduction 2838.2 Definitions of Voltage Stability 2848.3 Comparison of Angle and Voltage Stability 2868.3.1 Analysis of the SMLB System 2878.4 Mathematical Preliminaries 2908.5 Factors Affecting Instability and Collapse 2928.5.1 Induction Motor Loads 2928.5.2 HVDC Converter 2938.5.3 Overexcitation Limiters 2948.5.4 OLTC Transformers 2958.5.5 A Nonlinear Dynamic Load Model 2968.6 Dynamics of Load Restoration 2968.7 Analysis of Voltage Stability and Collapse 2988.7.1 Simulation 2988.7.2 Small Signal (Linear) Analysis 2988.8 Integrated Analysis of Voltage and Angle Stability 3018.9 Analysis of Small Signal Voltage Instability Decoupled from Angle Instability 3038.9.1 Decoupling of Angle and Voltage Variables 3048.9.2 Incremental RCFN 3058.9.3 Nonlinear Reactive Loads 3068.9.4 Generator Model 306Discussion 3078.10 Control of Voltage Instability 308References 3089 Wide-AreaMeasurements and Applications 3119.1 Introduction 3119.2 Technology and Standards 3119.2.1 Synchrophasor Definition 3139.2.2 Reporting Rates 3149.2.3 Latency and Data Loss 3159.3 Modeling ofWAMS in Angular Stability Programs 3159.4 Online Monitoring of Power Swing Damping 3169.4.1 Modal Estimation based on Ringdown Analysis 3179.4.2 Modal Estimation based on Probing Signals 3199.4.3 Modal Estimation based on Ambient Data Analysis 3239.5 WAMS Applications in Power Swing Damping Controllers 3279.6 WAMS Applications in Emergency Control 3309.7 Generator Parameter Estimation 3359.8 Electro-MechanicalWave Propagation and Other Observations in Large Grids 335References 33810 Analysis of Subsynchronous Resonance 34110.1 Introduction 34110.2 Analysis of Electrical Network Dynamics 34210.2.1 Equations in DQo Variables 34410.2.2 Interfacing a DQ Network Model with a Generator Model 34610.3 Torsional Dynamics of a Generator-Turbine System 35310.3.1 Damping of Torsional Oscillations 35910.3.2 Sensitivity of the Torsional Modes to the External Electrical System 36010.4 Generator-Turbine and Network Interactions: Subsynchronous Resonance 36210.4.1 Torsional Modes in Multi-Generator Systems 36810.4.2 Adverse Interactions with Turbine-Generator Controllers 37110.4.3 Detection of SSR/Torsional Monitoring 37310.4.4 Countermeasures for Subsynchronous Resonance and Subsynchronous Torsional Interactions 37410.4.5 Case Study: TCSC-Based SSDC 37710.5 Time-InvariantModels of Grid-Connected Power Electronic Systems 37810.5.1 Discrete-Time DynamicModels using the PoincaréMapping Technique 38010.5.2 Dynamic Phasor-Based Modeling 38010.5.3 Numerical Derivation of PES Models: A Frequency Scanning Approach 38310.A Transfer Function Representation of the Network 385References 38611 Solar Power Generation and Energy Storage 39111.1 Introduction 39111.2 Solar Thermal Power Generation 39211.3 Solar PV Power Generation 39211.3.1 Solar Module I-V Characteristics 39311.3.2 Solar PV Connections and Power Extraction Strategies 39311.3.3 Power Electronic Converters for Solar PV Applications 39511.3.4 Maximum Power Point Tracking Algorithms 39711.3.5 Control of Grid-Connected Solar PV Plants 39811.3.6 Low-Voltage Ride Through and Voltage Support Capability 40011.4 Energy Storage 40311.4.1 Attributes of Energy Storage Devices 40411.4.2 Energy Storage Technologies 40411.4.3 Mapping to Applications 40611.4.4 Battery Modeling 410References 41212 Microgrids: Operation and Control 41512.1 Introduction 41512.2 Microgrid Concept 41612.2.1 Definition of a Microgrid 41612.2.2 Control System 41712.3 Microgrid Architecture 41912.4 Distribution Automation and Control 42012.5 Operation and Control of Microgrids 42112.5.1 DER Units 42112.5.2 Microgrid Loads 42312.5.3 DER Controls 42312.5.4 Control Strategies under Grid-Connected Operation 42512.5.5 Control Strategy for an Islanded Microgrid 42712.6 Energy Management System 42812.6.1 Microgrid Supervisory Control 42912.6.2 Decentralized Microgrid Control based on a Multi-Agent System 43012.6.3 IndustrialMicrogrid Controllers 43112.7 Adaptive Network Protection in Microgrids 43212.7.1 Protection Issues 43312.7.2 Adaptive Protection 43412.8 Dynamic Modeling of Distributed Energy Resources 43512.8.1 Photovoltaic Array with MPP Tracker 43512.8.2 Fuel Cells 43712.8.3 Natural Gas Generator Set 43812.8.4 Fixed-SpeedWind Turbine Driving SCIG 43912.9 Some Operating Problems in Microgirds 44212.10 Integration of DG and DS in a Microgrid 44412.11 DC Microgrids 44412.12 Future Trends and Conclusions 44512.A A Three-Phase Model of an Induction Machine 448References 452A Equal Area Criterion 455An Interesting Network Analogy 456References 458B Grid Synchronization and Current Regulation 459Choice of Reference Frames 459References 462C Fryze–Buchbolz–Depenbrock Method for Load Compensation 463C.1 Introduction 463C.2 Description of FBDTheory 463C.3 Power Theory in Multiconductor Circuits 466Virtual Star Point 466Collective Quantities 467C.4 Examples 469C.5 Load Characterization over a Period 470C.6 Compensation of Non-Active Currents 471Discussion 472References 472D Symmetrical Components and Per-Unit Representation 473D.1 Symmetrical Component Representation of Three-Phase Systems 473D.2 Per-Unit Representation 476References 478Index 479

This textbook is one of the first on Power System Dynamics, Control and Stability to integrate in a straightforward and illustrative way the recently introduced modern power system components, such as Renewable Energy Sources (RES), converter interfaced generating sources, FACTS, energy storage devices, and wide area measurement systems (WAMS), in the same, common and well defined framework with the more conventional component, such as Synchronous Generators. - C. Vournas, NTUA, Athens, Greece