This paper presents a practical design perspective on multivariable feedback control problems. It reviews the basic issue-feedback design in the face of uncertainties-and generalizes known single-input, single-output (SISO) statements and constraints of the design problem to multiinput, multioutput (MIMO) cases. Two major MIMO design approaches are then evaluated in the context of these results.

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Multivariable feedback design: Concepts for a classical/modern synthesis

1 Introduction 2 Electromagnetic Transients 3 Synchronous Machine Modeling 4 Synchronous Machine Control Models 5 Single-Machine Dynamic Models 6 Multimachine Dynamic Models 7 Multimachine Simulation 8 Small-Signal Stability 9 Energy Function Methods Appendix A: Integral Manifolds for Model Bibliography Index

Power System Dynamics and Stability

1. Introduction. 1.1 Background. 1.2 Electrical Transmission Networks. 1.3 Conventional Control Mechanisms. 1.4 Flexible ac Transmission Systems (FACTS). 1.5 Emerging Transmission Networks. 2. Reactor--Power Control in Electrical Power Transmission Systems. 2.1 Reacrive Power. 2.2 Uncompensated Transmission Lines. 2.3 Passive Compensation. 2.4 Summary. 3. Principles of Conventional Reactive--Power Compensators. 3.1 Introduction. 3.2 Synchronous Condensers. 3.3 The Saturated Reactor (SR). 3.4 The Thyristor--Controlled Reactor (TCR). 3.5 The Thyristor--Controlled Transformer (TCT). 3.6 The Fixed Capacitor--Thyristor--Controlled Reactor (FC--TCR). 3.7 The Mechanically Switched Capacitor--Thristor--Controlled Reactor (MSC--TCR). 3.8 The Thyristor--Switched capacitor and Reactor. 3.9 The Thyristor--Switched capacitor--Thyristor--Controlled Reactor (TSC--TCR). 3.10 A Comparison of Different SVCs. 3.11 Summary. 4. SVC Control Components and Models. 4.1 Introduction 4.2 Measurement Systems. 4.3 The Voltage Regulator. 4.4 Gate--Pulse Generation. 4.5 The Synchronizing System. 4.6 Additional Control and Protection Functions. 4.7 Modeling of SVC for Power--System Studies. 4.8 Summary. 5. Conceepts of SVC Voltage Control. 5.1 Introduction 5.2 Voltage Control. 5.3 Effect of Network Resonances on the Controller Response. 5.4 The 2nd Harmonic Interaction Between the SVC and ac Network. 5.5 Application of the SVC to Series--Compensated ac Systems. 5.6 3rd Harmonic Distortion. 5.7 Voltage--Controlled Design Studies. 5.8 Summary. 6. Applications. 6.1 Introduction. 6.2 Increase in Steady--State Power--Transfer Capacity. 6.3 Enhancement of Transient Stability. 6.4 Augmentation of Power--System Damping. 6.5 SVC Mitigation of Subsychronous Resonance (SSR). 6.6 Prevention of Voltage Instability. 6.7 Improvement of HVDC Link Performance. 6.8 Summary. 7. The Thyristor--Controlled SeriesCapacitor (TCSC). 7.1 Series Compensation. 7.2 The TCSC Controller. 7.3 Operation of the TCSC. 7.4 The TSSC. 7.5 Analysis of the TCSC. 7.6 Capability Characteristics. 7.7 Harmonic Performance. 7.8 Losses. 7.9 Response of the TCSC. 7.10 Modeling of the TCSC. 7.11 Summary. 8. TCSC Applications. 8.1 Introduction. 8.2 Open--Loop Control. 8.3 Closed--Loop Control. 8.4 Improvement of the System--Stability Limit. 8.5 Enhancement of System Damping. 8.6 Subsynchronous Resonanace (SSR) Mitigation. 8.7 Voltage--Collapse Prevention. 8.8 TCSC Installations. 8.9 Summary. 9. Coordination of FACTS Controllers. 9.1 Introduction 9.2 Controller Interactions. 9.3 SVC--SVC Interaction. 9.4 SVC--HVDC Interaction. 9.5 SVC--TCSC Interaction. 9.6 TCSC--TCSC Interaction. 9.7 Performance Criteria for Damping--Controller Design. 9.8 Coordination of Multiple Controllers Using Linear--Control Techniques. 9.9 Coordination of Multiple Controllers using Nonlinear--Control Techniques. 9.10 Summary. 10. Emerging FACTS Controllers. 10.1 Introduction. 10.2 The STATCOM. 10.3 THE SSSC. 10.4 The UPFC. 10.5 Comparative Evaluation of Different FACTS Controllers. 10.6 Future Direction of FACTS Technology. 10.7 Summary. Appendix A. Design of an SVC Voltage Regulator. A.1 Study System. A.2 Method of System Gain. A.3 Elgen Value Analysis. A.4 Simulator Studies. A.5 A Comparison of Physical Simulator results With Analytical and Digital Simulator Results Using Linearized Models. Appendix B. Transient--Stability Enhancement in a Midpoint SVC--Compensated SMIB System. Appendix C. Approximate Multimodal decomposition Method for the Design of FACTS Controllers. C.1 Introduction. C.2 Modal Analysis of the ith Swing Mode, C.3 Implications of Different Transfer Functions. C.4 Design of the Damping Controller. Appendix D. FACTS Terms and Definitions. Index.

Thyristor-Based Facts Controllers for Electrical Transmission Systems

The general concepts associated with applying power system stabilizers utilizing shaft speed, ac bus frequency, and electrical power inputs are developed in this first part of a three-part paper. This lays the foundation for discussion of the tuning concepts and practical aspects of stabilizer application in Parts II and III. The characteristics of the "plant" through which the power system stabilizer must operate are discussed and the implications upon stabilizer tuning and performance are noted. A general approach for analyzing stabilizers utilizing an arbitrary input signal is described and applied to the frequency and electrical power input signals.

Applying Power System Stabilizers Part I: General Concepts

This paper provides a detailed account of analytical work carried out to determine the parameters of power system stabilizers (PSS) for the Darlington nuclear generating station presently under construction in eastern Ontario. The results presented are, however, of general interest and provide a comprehensive analysis of the effects of the different stabilizer parameters on the overall dynamic performance of the power system. They show how stabilizer settings may be selected so as to enhance the steady-state and transient stability of local plant modes as well as inter-area modes in large interconnected systems. In addition, it is shown that the selected parameters result in satisfactory performance during system islanding conditions, when large frequency excursions are experienced. Darlington GS, when completed by 1992, will comprise four 1100 MVA, 0.85 p.f., 1800 RPM turbine generators with "CANDU-PHW" reactors, moderated and cooled by heavy water. The station will be incorporated into the 500 kV network through three double-circuit lines. The units will be equipped with transformer-fed thyristor excitation systems and Delta-P-Omega type PSS [1, 2].

Application of power system stabilizers for enhancement of overall system stability

The phenomena of stability of synchronous machines under small perturbations is explored by examining the case of a single machine connected to an infinite bus through external reactance.

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Concepts of Synchronous Machine Stability as Affected by Excitation Control

In a previous paper [ibid., vol. 72, pt. III, June 1953, pp. 562-71], the authors presented the results of a study of the performance of two interconnected steam-electric power-generating areas as affected by frequency and tie-line power controllers. The present paper extends this study to include hydroelectric power generating areas as well. As before, the object is to determine theoretically the best values of controller gains, that is, to find those controller settings that will result in best over-all system performance. The principal criterion of good performance is, also as before, the minimizing of any oscillations in tie-line power or system frequency resulting from load disturbances to either area. Thus, stability, rather than rapidity of response, is preferred, since the system actually is continually being disturbed by small and more or less random changes of load, rather than by the step load change used as a test disturbance in the study.

Tie-Line Power and Frequency Control of Electric Power Systems - Part II [includes discussion]

IN THE past several years series capacitors for the compensation of line drop in power circuits have found increasing use,1–9 because improved and automatic voltage regulation can, in many cases, be obtained more economically by this method than by any other means.

Analysis of Series Capacitor Application Problems

The application of series capacitors to compensate long-distance high-voltage transmission lines introduces potential modes of dynamic instability caused by interactions with synchronous machines and turbine-generator shaft torsional resonance. This paper describes the modes of ihstability and analytical methods used to predict the combinations of parameters which may lead to instability. Insight into the phenomena of modal interaction, a factor causing one of the unstable modes, is provided.

Charles Concordia

Papers

Concepts of Synchronous Machine Stability as Affected by Excitation Control

Tie-Line Power and Frequency Control of Electric Power Systems - Part II [includes discussion]

Analysis of Series Capacitor Application Problems

Self Excited Torsional Frequency Oscillations with Series Capacitors

Tie-Line Power and Frequency Control of Electric Power Systems - Part II