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

This paper develops simple but accurate continuous-time, large-signal dynamic models for a thyristor-controlled series capacitor (TCSC). The models are based on the representation of voltages and currents as time-varying Fourier series, and focus on the dynamics of the short-term Fourier coefficients. Truncating the series to keep only the fundamental components provides a natural dynamic generalization of the familiar quasi-static phasor representation. Systematic simplifications or refinements of their fundamental phasor dynamics model yield a variety of other models. The authors establish that even the simplest of these models predicts the dynamic behavior of the TCSC very accurately. Their phasor models provide a powerful basis for simulation, more than an order of magnitude faster than detailed time-domain circuit simulation. The phasor models present an attractive alternative to sampled-data models, having the advantages of simpler representation, modularity and direct compatibility with the phasor models that are routinely used to represent the dynamics of generators and other power system components.

Phasor dynamics of thyristor-controlled series capacitor systems

The electric power system is one of the largest and most complex infrastructures and it is critical to the operation of society and other infrastructures. The power system is undergoing deep changes which result in new monitoring and control challenges in its own operation, and in unprecedented coupling with other infrastructures, in particular communications and the other energy grids. This Chapter provides an overview of this transformation, starting from the primary causes through the technical challenges, and some perspective solutions.

https://www.springer.com/cda/content/document/cda_downloaddocument/9783662441596-c2.pdf?SGWID=0-0-45-1477627-p176840025

Electric Power Systems

This paper presents an analytical, linear, state-space model of a thyristor-controlled series capacitor (TCSC). First, a simplified fundamental frequency model of TCSC is proposed and the model results are verified. Using frequency response of the nonlinear TCSC segment, a simplified nonlinear state-space model is derived, where the frequency of the dominant TCSC complex poles shows linear dependence on the firing angle. The nonlinear element is linearised and linked with the ac network model and the TCSC controller model that also includes a phase-locked-loop (PLL) model. The model is implemented in MATLAB and verified against PSCAD/EMTDC in the time and frequency domains for a range of operating conditions. The model is sufficiently accurate for most control design applications and practical stability issues in the subsynchronous range.

Analytical modeling of TCSC dynamics

In their previous work, the authors have studied the phasor dynamics of thyristor-controlled series capacitors (TCSCs), and derived associated models for studying power swing oscillations in power systems. This paper presents the use of a dynamic phasor model of the TCSC in studies of subsynchronous resonance (SSR). Their earlier dynamic phasor models of the TCSC are further simplified here, and tested at typical subsynchronous frequencies. The phasor model of the TCSC is directly compatible with the conventional models used for the other system components relevant to SSR. The proposed approach to SSR analysis is an attractive alternative to approaches based on sampled-data models, and to torque-per-unit-velocity methods. The dynamic phasor approach has been tested on the IEEE first benchmark SSR model, showing outstanding agreement with more computationally demanding alternative methods for eigenvalue analysis.

SSR analysis with dynamic phasor model of thyristor-controlled series capacitor

This paper computes the small signal dynamic response of a thyristor controlled series capacitor system for use in flexible AC transmission system control design. The computation includes the effects of synchronization and the nonlinearity due to thyristor switching. Eigenvalues of the small signal dynamic response are computed and used to study the dynamic response of the Kayenta system using different methods of synchronization and a closed loop control. >

/pdf/dynamic-response-of-a-thyristor-controlled-switched-3nds4wh3sy.pdf

Dynamic response of a thyristor controlled switched capacitor

This paper develops a harmonic coupling matrix for a single phase, line commutated power converter. This matrix illustrates the coupling between the power convertor voltage and current harmonics. The authors show how this coupling matrix can be incorporated into a power system and how the system harmonics can be accurately calculated. In addition, this paper provides an example of a power system interacting with a single phase power convertor. This example system exhibits highly nonlinear and unexpected behavior which can neither be explained nor predicted by a classical solution method. In particular, there may be two steady state solutions and/or no solutions over regions for which the classical method predicts both existence and uniqueness of solutions. >

A study of nonlinear harmonic interaction between a single phase line-commutated converter and a power system

The authors describe two bifurcation instabilities of a thyristor controlled reactor (TCR) circuit in which switching times suddenly change and system stability is lost. The instabilities are unexpected because they are quite different from what might be expected from conventional theory in that they occur without the usual indications such as eigenvalues of a Jacobian matrix crossing the unit circle. The instabilities are explained and their mechanisms are illustrated by the simulation of a static volt-ampere-reactive (VAr) example with realistic parameters. In particular, it is shown how distortion of voltage and current waveforms can cause a thyristor switch-off time to disappear or a new thyristor switch-off time to suddenly appear. The consequence of the sudden change in switch-off times is that stable periodic operation of the circuit is lost and a transient will occur until the circuit settles down to a new steady state. >

Instabilities due to bifurcation of switching times in a thyristor controlled reactor

The authors study a thyristor controlled reactor circuit used for static volt ampere reactive (VAR) control of electric power systems. The circuit exhibits switching times which jump or bifurcate. The nonlinear dynamics of the circuit are studied using a Poincare/spl acute/ map and it is demonstrated that the Poincare/spl acute/ map has discontinuities and is not invertible. These novel properties illustrate some of the basic features of dynamical systems theory for switching circuits. >

Nonlinear dynamics and switching time bifurcations of a thyristor controlled reactor

The authors study a general RLC circuit with ideal diodes and periodic sources by computing the Jacobian of the Poincare/spl acute/ map. These circuits are nonlinear but have special structure allowing the Jacobian to be reduced to a simple and useful expression. The Jacobian computation is illustrated with a diode bridge rectifier circuit. >

S.G. Jalali

Papers

Dynamic response of a thyristor controlled switched capacitor

A study of nonlinear harmonic interaction between a single phase line-commutated converter and a power system

Instabilities due to bifurcation of switching times in a thyristor controlled reactor

Nonlinear dynamics and switching time bifurcations of a thyristor controlled reactor

Surprising simplification of the Jacobian of diode switching circuits