S.G. Jalali

Dynamic response of a thyristor controlled switched 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. >

A stability model for the advanced series compensator (ASC)

This paper develops an accurate and general stability model for the ASC (thyristor controlled reactor). The model is valid for both the capacitive and inductive regions of the ASC operation. It is accurate in that the instantaneous voltage and current waveforms and also the fundamental component of the capacitor voltage (needed for stability) are determined every half-cycle by solving the differential equations of the ASC circuit. The model is capable of incorporating any control algorithms. The validity of the model is demonstrated by comparing the model with the Electromagnetic Transient Program (EMTP) digital simulations using step time of 10 /spl mu/s.

Switching time bifurcations in a thyristor controlled reactor

Thyristor controlled reactors are high power switching circuits used for static VAR control and the emerging technology of flexible AC transmission. The static VAR control circuit considered in the paper is a nonlinear periodically operated RLC circuit with a sinusoidal source and ideal thyristors with equidistant firing pulses. This paper describes new instabilities in the circuit in which thyristor turn off times jump or bifurcate as a system parameter varies slowly. The new instabilities are called switching time bifurcations and are fold bifurcations of zeros of thyristor current. The bifurcation instabilities are explained and verified by simulation and an experiment. Switching time bifurcations are special to switching systems and, surprisingly, are not conventional bifurcations. In particular, switching time bifurcations cannot be predicted by observing the eigenvalues of the system Jacobian. We justify these claims by deriving a simple formula for the Jacobian of the Poincare map of the circuit and presenting theoretical and numerical evidence that conventional bifurcations do not occur.

Nonlinear dynamics and switching time bifurcations of a thyristor controlled reactor circuit

We study a thyristor controlled reactor circuit used for static VAR control of utility electric power systems. The circuit exhibits switching times which jump or bifurcate as fold or transcritical bifurcations. We study the nonlinear dynamics of the circuit using a Poincare map and demonstrate that the Poincare map has discontinuities and is not invertible. The circuit has multiple attractors, moreover, the basin boundary separating the basins of attraction intersects with the Poincare map discontinuities. These novel properties illustrate some of the basic features of dynamical systems theory for thyristor switching circuits.

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

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.<<ETX>>

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

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. >

Nonlinear dynamics and switching time bifurcations of 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.<<ETX>>

Surprising simplification of the Jacobian of diode switching circuits

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.<<ETX>>