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Small-signal stability, control and dynamic performance of power systems
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Small-signal stability, control and dynamic performance of power systems

By M.J. Gibbard
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Book Description

A thorough and exhaustive presentation of theoretical analysis and practical techniques for the small-signal analysis and control of large modern electric power systems as well as an assessment of their stability and damping performance.Such systems may contain many hundreds of synchronous generators and high voltage power electronics equipment known as FACTS Devices.The book describes new techniques not only for the tuning and analysis of stabilizers for systems with many generators and FACTS Devices but also for their coordination.Of practical interest, these techniques are illustrated with relevant examples based on a multi-machine power system containing FACTS Devices for operating conditions ranging from light to peak load.By introducing new analytical concepts, using examples, and by employing production-grade software, practical insights are provided into the significance and application of various analytical techniques.

Table of Contents
  • Guide
  • Front cover
  • Back cover
  • Title page
  • Copyright page
  • Contents
  • Preface
  • List of Symbols, Acronyms and Abbreviations
  • Chapter 1
    • 1.1 Why analyse the small-signal dynamic performance of power systems?
    • 1.2 The purpose and features of the book
    • 1.3 Synchronizing and damping torques
    • 1.4 Definitions of power system stability
    • 1.5 Types of modes.
    • 1.6 Synchronous generator and transmission system controls
    • 1.7 Power system and controls performance criteria and measures.
    • 1.8 Validation of power system models
    • 1.9 Robust controllers
    • 1.10 How small is ‘small’ in small-signal analysis?
    • 1.11 Units of Modal Frequency
    • 1.12 Advanced control methods
    • 1.13 References
  • Chapter 2
    • 2.1 Introduction
    • 2.2 Mathematical model of a dynamic plant or system
    • 2.3 The Laplace Transform
    • 2.4 The poles and zeros of a transfer function.
    • 2.5 The Partial Fraction Expansion and Residues
    • 2.6 Modes of Response
    • 2.7 The block diagram representation of transfer functions
    • 2.8 Characteristics of first- and second-order systems
    • 2.9 The stability of linear systems
    • 2.10 Steady-state alignment and following errors
    • 2.11 Frequency response methods
    • 2.12 The frequency response diagram and the Bode Plot
    • 2.13 The Q-filter, a passband filter
    • 2.14 References
  • Chapter 3
    • 3.1 Introduction
    • 3.2 The concept of state and the state equations [1]
    • 3.3 The linearized model of the non-linear dynamic system
    • 3.4 Solution of the State Equations
    • 3.5 Eigen-analysis
    • 3.6 Decoupling the state equations
    • 3.7 Determination of residues from the state equations
    • 3.8 Determination of zeros of a SISO sub-system
    • 3.9 Mode shapes
    • 3.10 Participation Factors
    • 3.11 Eigenvalue sensitivities
    • 3.12 References
  • Chapter 4
    • 4.1 Introduction
    • 4.2 Small-signal models of synchronous generators
    • 4.3 Small-signal models of FACTS Devices
    • 4.4 Linearized power system model
    • 4.5 Load models
    • 4.6 References
    • Appendix 4–I Linearization of the classical parameter model of the generator.
    • Appendix 4–II Forms of the equations of motion of the rotors of a generating unit
  • Chapter 5
    • 5.1 Introduction
    • 5.2 Heffron and Phillips’ Model of single machine - infinite bus system
    • 5.3 Synchronizing and damping torques acting on the rotor of a synchronous generator
    • 5.4 The role of the Power System Stabilizer - some simple concepts
    • 5.5 The inherent synchronizing and damping torques in a SMIB system
    • 5.6 Effect of the excitation system gain on stability
    • 5.7 Effect of an idealized PSS on stability
    • 5.8 Tuning concepts for a speed-PSS for a SMIB system
    • 5.9 Implementation of the PSS in a SMIB System
    • 5.10 Tuning of a PSS for a higher-order generator model in a SMIB system
    • 5.11 Performance of the PSS for a higher-order generator model
    • 5.12 Alternative form of PSS compensation transfer function
    • 5.13 Tuning an electric power-PSS based on the P-Vr approach
    • 5.14 Summary: P-Vr approach to the tuning of a fixed-parameter PSS
    • 5.15 References
    • Appendix 5–I
  • Chapter 6
    • 6.1 Introduction
    • 6.2 Method of Residues
    • 6.3 Tuning a speed-PSS using the Method of Residues
    • 6.4 Conclusions, Method of Residues
    • 6.5 The GEP Method
    • 6.6 Tuning a speed-PSS using the GEP Method
    • 6.7 Conclusions, GEP method
    • 6.8 References
    • Appendix 6–I
  • Chapter 7
    • 7.1 Introduction
    • 7.2 The excitation control system of a synchronous generator
    • 7.3 Types of compensation and methods of analysis
    • 7.4 Steady-state and dynamic performance requirements on the generator and excitation system
    • 7.5 A single-machine infinite-bus test system
    • 7.6 Transient Gain Reduction (TGR) Compensation
    • 7.7 PID compensation
    • 7.8 Type 2B PID Compensation: Theory and Application to AVR tuning
    • 7.9 Proportional plus Integral Compensation
    • 7.10 Rate feedback compensation
    • 7.11 Tuning of AVRs with Type 2B PID compensation in a three- generator system
    • 7.12 Summary, Chapter 7
    • 7.13 References
    • Appendix 7–I
  • Chapter 8
    • 8.1 Introduction
    • 8.2 Dynamic characteristics of washout filters
    • 8.3 Performance of a PSS with electric power as the stabilizing signal.
    • 8.4 Performance of a PSS with bus-frequency as the stabilizing signal.
    • 8.5 Performance of the “Integral-of-accelerating-power” PSS
    • 8.6 Conceptual explanation of the action of the pre-filter in the IAP PSS
    • 8.7 The Multi-Band Power System Stabilizer
    • 8.8 Concluding remarks
    • 8.9 References
    • Appendix 8–I
  • Chapter 9
    • 9.1 Introduction
    • 9.2 Mode Shape Analysis
    • 9.3 Participation Factors
    • 9.4 Determination of the PSS parameters based on the P-Vr approach with speed perturbations as the stabilizing signal
    • 9.5 Synchronising and damping torque coefficients induced by PSS i on generator i
    • 9.6 References
  • Chapter 10
    • 10.1 Introduction
    • 10.2 A fourteen-generator model of a longitudinal power system
    • 10.3 Eigen-analysis, mode shapes and participation factors of the 14- generator system, no PSSs in service
    • 10.4 The P-Vr characteristics of the generators and the associated synthesized characteristics
    • 10.5 The synthesized P-Vr and PSS transfer functions
    • 10.6 Synchronising and damping torque coefficients induced by PSS i on generator i
    • 10.7 Dynamic performance of the system with PSSs in service
    • 10.8 Intra-station modes of rotor oscillation [6], [7]
    • 10.9 Correlation between small-signal dynamic performance and that following a major disturbance
    • 10.10 Summary: Tuning of PSSs based on the P-Vr approach
    • 10.11 References
    • Appendix 10–I
  • Chapter 11
    • 11.1 Introduction
    • 11.2 A ‘simplistic’ tuning procedure for a SVC
    • 11.3 Theoretical basis for the tuning of FACTS Device Stabilizers
    • 11.4 Tuning SVC stabilizers using bus frequency as a stabilizing signal
    • 11.5 Use of line real-power flow as a stabilizing signal for a SVC
    • 11.6 Use of bus frequency as a stabilizing signal for the SVC, PSVC_5
    • 11.7 Tuning a FDS for a TCSC using a power flow stabilizing signal
    • 11.8 Concluding comments
    • 11.9 References
  • Chapter 12
    • 12.1 Introduction
    • 12.2 The Concept of Modal Induced Torque Coefficients (MITCs)
    • 12.3 Transfer function matrix representation of a linearized multi- machine power system and its controllers
    • 12.4 Modal torque coefficients induced by a centralized speed PSS
    • 12.5 Modal torque coefficients induced by a centralized FDS
    • 12.6 General expressions for the torque coefficients induced by conventional, decentralized PSSs & FDSs
    • 12.7 References
    • Appendix 12–I
  • Chapter 13
    • 13.1 Introduction
    • 13.2 Relationship between rotor mode shifts and stabilizer gain increments
    • 13.3 Case Study: Contributions to MITCs/Mode Shifts by PSSs and generators
    • 13.4 Stabilizer damping contribution diagrams
    • 13.5 Comparison of the estimated and actual mode shifts for increments in stabilizer gain settings
    • 13.6 Summary
    • 13.7 References
  • Chapter 14
    • 14.1 Introduction
    • 14.2 The 14-generator power system
    • 14.3 A Heuristic Coordination Approach
    • 14.4 Simultaneous Coordination of PSSs and FDSs using Linear Programming
    • 14.5 Case study: Simultaneous coordination in a multi-machine power system of PSSs and FDSs using linear programming
    • 14.6 Concluding remarks
    • 14.7 References
  • Index
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