A method based on a Lure Lyapunov function is developed to analyse subsynchronous resonance (SSR) phenomena in power systems. An improved Lure Lyapunov function used to analyse the stability of a power system including the turbine-generator (T-G) shaft is presented first. Then, a standard Lure control model for a power system with a T-G shaft is obtained. The stability of such nonlinear systems at the equilibrium points is discussed in detail. The stable operation region of the system is discussed with the proposed method. The effectiveness of the proposed method is verified by a case study. This study has shown potential benefits and the validity of the Lyapunov direct method in the subsynchronous resonance analysis. Compared with the conventional analysis method, such as eigenvalue and frequency scanning techniques, the proposed method is based on the original nonlinear system. Error, that may be introduced by Iinearisation, is avoided completely. Moreover, the stable operation region of power systems can be obtained by the proposed method.

Many engineering optimization problems frequently encounter discrete variables as well as continuous variables and the presence of nonlinear discrete variables considerably adds to the solution complexity. Very few of the existing methods can

This paper presents an adaptive strategy for controlling chaotic systems. By employing the phase space reconstruction technique in nonlinear dynamical systems theory, the proposed strategy transfoms the nonlinear system into canonical form, and employs a nonlinear observer to estimate the uncertainties and disturbances of the nonlinear system, and then establishes a state-error-like feedback law. The developed control scheme allows chaos control in spite of modeling errors and parametric variations. The effectiveness of the proposed approach has been demonstrated through its applications to two well-known chaotic systems: Duffing oscillator and Rossler chaos.

A nonlinear variable structure stabilxzer is proposed in this paper. Design of this strabilizer involves the nonlinear transformation technique, the variable structure control technique and the linear syste theory. Performance of the proposed nonlinear variable structure controller in a single machine connected to an infinite bus power system and a multi-machine system with multi-mode oscillations is simulated. The responses of the system with the proposed stabilizwer are compared with those obtained with some other kinds ofstabilizers wthen the systemis subjected to a variety of disurbances. Simulation results show that the nonlinear variable structure stabilizer gives satisfactory dynamic performance and good robustness.