Zhujun Jing

Uniform asymptotic stability of hybrid dynamical systems with delay

We formulate a model for hybrid dynamical systems with delay, which covers a large class of delay systems. Under several mild assumptions, we establish sufficient conditions for uniform asymptotic stability of hybrid dynamical systems with delay via a Lyapunov-Razumikhin technique. To demonstrate the developed theory, we conduct stability analyses for delay sampled-data feedback control systems including a nonlinear continuous-time plant and a linear discrete-time controller.

Bifurcations, chaos, and system collapse in a three node power system

A model of the three node power system proposed by Rajesh and Padiyar [Electr. Power Energy Syst. 21 (1999) 375] is studied. As the bifurcation parameter Pm (input power to the generator) is changed, the system including the effects of the non-linearity exhibits complex dynamics emerging from static and dynamic bifurcations which link with the system collapse. The analyses for the model exhibit dynamical bifurcations, including three Hopf bifurcations, cyclic fold bifurcations, torus bifurcations and period-doubling bifurcations, and complex dynamical behaviors, including periodic orbits, period-doubling orbits, quasi-periodic orbits, phase-locked phenomena and two chaotic regions between two Hopf bifurcations, i.e. in the ‘Hopf window’ and intermittency chaos. Moreover, one of the two chaotic regions results from period-doubling bifurcations, and another results from quasi-periodic orbits emerging from a torus bifurcation. Simulations are given to illustrate the various types of dynamic behaviors associated with the power system collapse for the model. In particular, we first shown that the oscillatory transient may play a role in the collapse, and there are different critical points for different dominated state variables. Besides, the hard-limits and increases of the damping factor widen the feasible operating region of the power system, and prevent the torus bifurcation to occur so that some complex dynamical phenomena can be inhibited. q 2003 Elsevier Science Ltd. All rights reserved.

CHAOS BEHAVIOR IN THE DISCRETE BVP OSCILLATOR

The discrete BVP oscillator obtained through the Euler method is investigated, and also first proved that there exist chaotic phenomena in the sense of Marottos definition of chaos and two-period cycles. And numerical simulations not only show the consistence with the theoretical analysis but also exhibit the complex dynamical behaviors, including the ten-periodic orbit, a cascade of period-doubling bifurcation, quasiperiodic orbits and the chaotic orbits in Marottos chaos and intermittens chaos. The computations of Lyapunov exponents confirm the existence of dynamical behaviors.

Research of the stability region in a power system

A power system is employed to illustrate how we can apply singular perturbation theory to decompose a full system into two subsystems, slow and fast subsystems. Then, we study the qualitative properties of their solutions and finally obtain the stability region and an analytical expression of the approximate stability boundary of the operation point of the full system by numerical simulation and by computing the local quadratic approximation of the one-dimensional stable manifold at the saddle point. Furthermore, we consider the effects of changing the parameters on the size of the stability region.

COMPLEX DYNAMICAL BEHAVIORS IN DISCRETE-TIME RECURRENT NEURAL NETWORKS WITH ASYMMETRIC CONNECTION MATRIX

This paper investigates the discrete-time recurrent neural networks and aims to extend the previous works with symmetric connection matrix to the asymmetric connection matrix. We provide the sufficient conditions of existence for asymptotical stability of fixed point, flip and fold bifurcations, Marottos chaos. Besides, we state the conditions of existence for the bounded trapping region including many fixed points, and attracting set contained in bounded region and chaotic set. To demonstrate the theoretical results of the paper, several numerical examples are provided.The theorems in this paper are available more than in the previous works.

On the optimal solutions for power flow equations

A power system is always required to operate at least cost or least transmission losses when stability and reliability conditions are satisfied. The operation problems of power systems can be generally formulated as optimal power flow problems, which are nonlinear static optimization problems with a large number of equalities and inequalities. This paper aims to derive the detail conditions for the existence of an optimal power flow solution, which guarantee that a power system not only has a feasible solution but also can be operated optimally from the economic viewpoint.

Computation of limit cycle via higher order harmonic balance approximation and its application to a 3-bus power system

This work reviews and elaborates a frequency domain approximate method of estimating amplitude, frequency, and stability of the limit cycle near Hopf bifurcations. A new iterative method and new criterion for ascertaining stability are presented. The method and criterion are applied to a 3-bus dynamic power system model to give the amplitude, frequency and stability at its Hopf bifurcations. New analytic formulas for bifurcation curves are derived by using analytic method, some new saddle-node bifurcation at low voltage levels are found on the formulas. The influence of rotor inertia on the Hopf bifurcation is also studied.

Attractive Regions in Power Systems by Singular Perturbation Analysis

This paper aims to investigate attractive regions of operating points for power systems by applying singular perturbation analysis. A time-scale decomposition is performed to illustrate how the critical model can be identified with reduced-order systems and how bifurcation phenomena can be explained with such low order systems. The slow dynamics and fast dynamics including bifurcation conditions and domain of attractor of the stable equilibrium are also analyzed. We show that the attractive region of a stable equilibrium point is composed of the domain enclosed by the stable manifold of a saddle point for the simplified subsystem, and that the size of a stability region is also considerably affected by the voltage magnitude behind the transient reactance. Several numerical examples are used to demonstrate our theoretical results.