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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.
Additional chapters introduce readers to:
the relevant control systems and eigen-analysis background;
the small-signal modelling of generators, FACTS Devices, and the power system;
approaches for tuning of automatic voltage regulators (AVRs);
the modelling of various types of stabilizers for application to generators (PSSs) and FACTS Devices (PODs).
The book will appeal to:
Recent graduates in electrical engineering who need to understand the tools and techniques currently available in the analysis of small-signal dynamic performance and design.
Practicing electrical engineers who need to understand the significance of more recent developments and techniques in the field of small-signal dynamic performance.
Postgraduate students in electrical engineering who need to understand current developments in the field and who need to orient their research to achieve practical, useful outcomes.
Undergraduate electrical engineering students in courses oriented towards electric power engineering in which there is an introductory subject in power system dynamics (for access to basic material).
Academics or faculty staff who may be teaching or supervising under graduate or post students.
Managerial staff with responsibilities in power system planning, and system stability and control.

**Author(s):** M.J. Gibbard, P. Pourbeik, D.J. Wovless

**Publisher:** The university of Adelaide Press

**Year:** 2015

**Language:** English

**Pages:** 689

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

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