Weijun Ji

Hard-limit induced chaos in a fundamental power system model

Abstract The paper investigates complex nonlinear phenomena in a fundamental power system model represented in a single-machine infinite-bus formulation. The generator electro-magnetics, electromechanics and its excitation control are modelled together by fourth-order differential equations. It is shown that when excitation control gains are set high (as in common industry. practice) and when the excitation hard-limits are taken into account, this representative power system model undergoes global bifurcations including period-doubling cascades which lead to sustained chaotic behaviour. Specifically sustained complex oscillations result from the interaction of hard-limits and the system transients over a large range of realistic parameter values. The emergence of strange attractors is demonstrated in the paper by detailed numerical simulations and preliminary analysis.

Coexistence of four different attractors in a fundamental power system model

This paper reports the occurrence of a rare phenomenon in dynamical systems when four different attractors namely a stable equilibrium, a stable limit cycle and two strange attractors coexist in a fundamental power system model. The paper shows that power system operation could get trapped into sustained chaotic oscillations after a large disturbance even when there exists a viable stable equilibrium point in the model.

Dynamics of a minimal power system: invariant tori and quasi-periodic motions

The paper provides an extensive analysis of local and global bifurcation phenomena in the voltage-angle dynamic interactions of a minimal power system model. Using nonlinear analysis and normal form theory, it is proved that this system will experience quasi-periodic motions near certain degenerate local bifurcations which are explicitly characterized. The results in the paper provide strong analytical evidence for the possible occurrence of complicated behavior in the power system from the interactions of voltage and angle instability mechanisms. Computational methods for the detection of invariant 2-tori in higher dimensional systems using tools from center manifold theory and normal form theory are introduced briefly and these techniques are illustrated on a fourth order power system model.

Numerical approximation of (n-1)-dimensional stable manifolds in large systems such as the power system

Abstract This paper discusses a direct method for numerical computation of the local quadratic approximations of ( n − 1)-dimensional stable manifolds for the unstable equilibria on the stability boundary in large systems. The algorithm proposed here does not require time-consuming normal form or symbolic computations. The numerical procedure is illustrated on transient stability problems in simple power system models.

Center manifold computations in bifurcation analysis of large systems such as the power system

Methods for computing the center manifold in large systems are developed in this paper. Using results from nonlinear control theory, it is shown that the problem or formally computing a center manifold is equivalent to solving a sequence of Sylvester equations. These results prove that bifurcation analysis based on center manifold computations is practically feasible even in very large-scale systems such as the power system where the large dimensionality makes traditional symbolic computations almost impossible to implement. Algorithms are illustrated by center manifold based analysis of certain local and global bifurcations in an electrical power system model.

Dynamics of a minimal power system model - invariant tori and quasi-periodic motions

The paper provides an extensive analysis of local and global bifurcation phenomena in studying the voltage-angle dynamic interactions of a minimal power system model. Using nonlinear analysis and normal form theory, it is proved that this system will experience quasi-periodic motions near certain degenerate local bifurcations which are explicitly characterized. The results in the paper provide strong analytical evidence for the possible occurrence of complicated behavior in the general power system from the interactions of voltage and angle instability mechanisms.

Chaotic motions from intermittency mechanisms in a simple power system model

This paper analyzes chaotic motions which result from exotic intermittency mechanisms in a simple power system model. The evolution of chaotic motions is illustrated by suitable time domain simulations. The global dynamic structure of the power system model is described and the intermittency induced chaotic motions are examined in detail. It is shown that extremely rich steady state phenomena exist in this power system model which originate from complicated intermittency mechanisms involving several chaotic limit sets and periodic orbits.

Hard-limit induced chaos in a single-machine-infinite-bus power system

The paper reports the prevalence of chaos in a simple power system model represented in a single-machine-infinite-bus formulation. The generator dynamics is modelled by a standard fourth order differential equation which includes minimal representations of the angle dynamics (swing equations) and the voltage dynamics (flux decay equation) together with a voltage control device (excitation control). Detailed numerical simulations are used to show that stable limit cycles induced by the excitation hard-limits exist in the system over a wide range of parameter values. Moreover, these hard-limit induced stable limit cycles undergo interesting global bifurcations including period-doubling cascades which lead to sustained chaotic behavior. The dynamics of the fourth order model studied in the paper appears to be extremely rich as evidenced by the presence of strange attractors and chaos over diverse sets of parameter values.

Numerical Approximation of (N - 1)-Dimensional Stable Manifolds in Large Systems Such as the Power System

Abstract This paper discusses a direct method for the numerical computation of local quadratic approximations of (n-1) dimensional stable manifolds for the unstable equilibria on the stability boundary in large systems. The algorithm proposed here docs not require time-consuming normal form or symbolic computations. The numerical procedure is illustrated on transient stability problems in simple power system models.