POWER SYSTEM OSCILLATIONS

Transcription

1 POWER SYSTEM OSCILLATIONS Graham Rogers Cherry Tree Scientific Software Kluwer Academic Publishers Boston//London/Dordrecht

2 Contents 1 Introduction 1 2 The Nature of Power System Oscillations 1 Introduction 7 2 Classical Generator Model LocalModes Inter Area Mode Case Case Detailed Generator Model Local Modes Inter Area Mode 19 4 Controlled Detailed Generator Model Local Modes and Inter Area Mode 24 5 Response to System Faults 27 6 Final Discussion and Comments Classical Generator Model Detailed Generator Model Detailed Generator Model with Turbine/Governor Model 30 and Automatic Voltage Control Model 7 References 30 3 Modal Analysis of Power Systems 1 Introduction 31 2 Modal Analysis of Linear Dynamic Systems Example 34

3 Contents Lag Block Lead Lag Block Transient Feedback Block The Complete State Space Model Power System Example 2.2 Eigenvectors Modes of Oscillation Example Equal Eigenvalues 2.3 Eigenvalue Sensitivity Participation Factors 3 Modal Analysis Applied to the Detailed Generator Case with and without Controls 3.1 Detailed Generator Model 3.2 Detailed Generator Model with Controls Real Eigenvalue Unstable Complex Mode Stable Oscillatory Modes 3.3 Step Response 4 Final Comments and Discussion 5 References Modal Analysis for Control 1 Introduction 2 Transfer Functions 2.1 Transfer Function Poles and Zeros Example 2.2 Controllability and Observability 2.3 Residues Sensitivity and Residues Example Root locus and Residues Sensitivity to Dynamic Feedback Example 2.4 Frequency Response Nyquisfs Stability Criterion Example Application to Feedback Systems Power System Example 3 Synchronizing and Damping Torques 4 Summary and Conclusions 5 References Power System Structure and Oscillations 1 Introduction 2 Coherent Generator Groups 2.1 Ideal Coherency in a Multiple Generator Plant 3 Coherency in an Interconnected Power System 3.1 Reference Generators 3.2 Bus Coherency vin

4 3.3 Example 16 generator 68 bus System Tie Line Influence on Inter-area Mode Stability Response to a fault Comments on System Structure References 119 Generator Controls 1 Introduction Speed Governor Controls Hydraulic Turbine Governors Thermal Turbine Governors Turbine Governor Effects on Low Frequency Inter-area 128 Modes 3 Excitation Controls Open Circuit Stability and Response De Exciter Static Exciter References 137 Power System Stabilizers 1 Introduction Power System Stabilizer Basics Example - Single Generator Infinite Bus Static Exciter Compensation Determination using Residue 145 Angle Compensation of the Phase Lag between V ref 148 and Electrical Torque Rotating DC Exciter Stabilization of a Complete System Power System Stabilizer Placement Power System Stabilizer Design Generator Generator The Remaining Generators Evaluation of Power System Stabilizer Performance Small Signal Performance Transient Stability Comments References 168 Power System Stabilizers - Problems and Solutions 1 Introduction Generator Torsional Oscillations Speed Input Stabilizers Application of Torsional Filters Power Input Stabilizers Example DeltaP/Omega Stabilizers Example 184

5 3 Power System Stabilizers at a Plant of Identical Generators Solutions Comments References 197 Robust Control 1 Introduction Performance Specifications System Model Conventions One Degree of Freedom System Sensitivity Matrices Power System Example Power System Performance in Control Terms Step 1 Normalization Step 2 Performance Specification System Performance without Controls Excitation System Turbine Control Valve Servo System Performance with Automatic Voltage Regulator Performance with Power System Stabilizer System Performance with Turbine Governor Comments Robust Control Performance Weights Robustness of Power System Controls Nominal Performance Robust Stability Robust Performance Structured Singular Value Decentralized Controls Robust Control Design Coprime Factors and Coprime Factor Uncertainty Final Comments References 251 Damping by Electronic Power System Devices 1 Introduction System Performance without Electronic Controls Contingency Performance Static VAr Compensators SVC Location, Poles and Zeros Damping Control Design Damping Control to Modify Residue at Inter-area 263 Mode Robust FL Loop Shaping Control System Reduction Control Performance Small Signal Stability Performance Transient Stability Performance Comments 274

6 XI AI A2 Index 4 Thyristor Controlled Series Capacitor 4.1 Performance with an Uncontrolled Series Capacitor 4.2 Damping Control Design Residue Based Design 4.3 Robust Loop Shaping Design 4.4 Transient Performance 4.5 Comments on TCSC Damping Control 5 High Voltage DC Link Modulation 5.1 System Performance without Damping Control 5.2 Damping Control Input 5.3 Residue Based Damping Control 5.4 Robust Damping Control 5.5 System Performance with Robust Control Transient Performance with Damping Control 5.6 Comments on HVDC Damping Control 6 General Comments 7 References Model Data Formats and Block Diagrams 1 Load Flow Data 2 Dynamic Data 2.1 Generator 2.2 Exciter System Data 2.3 Turbine/ Governor Data 3 HVDC Data 4 Case Data 4.1 Two-Area Test Case 4.2 Two-Area Test Case with Series Capacitor 4.3 Two-Area System with Parallel HVDC Link Generator System 4.5 Single Generator Infinite Bus System 4.6 Multiple Generator Infinite Bus System Equal Eigenvalues 1 Nonlinear Divisors 1.1 Example 1.2 Time Response Calculation with Nonlinear Divisors 2 Linear Divisors 2.1 Example