Small-signal stability, control and dynamic performance of power systems
M.J. Gibbard
Small-signal stability, control and dynamic performance of power systems

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.

Front cover
Back cover
Title page
Copyright page
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
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