H∞Excitation Control Design for Stochastic Power Systems with Input Delay Based on Nonlinear Hamiltonian System Theory

This paper presentsH∞excitation control design problem for power systems with input time delay and disturbances by using nonlinear Hamiltonian system theory. The impact of time delays introduced by remote signal transmission and processing in wide-area measurement system (WAMS) is well considered. Meanwhile, the systems under investigation are disturbed by random fluctuation. First, under prefeedback technique, the power systems are described as a nonlinear Hamiltonian system. Then theH∞excitation controller of generators connected to distant power systems with time delay and stochasticity is designed. Based on Lyapunov functional method, some sufficient conditions are proposed to guarantee the rationality and validity of the proposed control law. The closed-loop systems under the control law are asymptotically stable in mean square independent of the time delay. And we through a simulation of a two-machine power system prove the effectiveness of the results proposed in this paper.

Nonexistence of Homoclinic Orbits for a Class of Hamiltonian Systems

We give several sufficient conditions under which the first-order nonlinear Hamiltonian systemx'(t)=α(t)x(t)+f(t,y(t)), y'(t)=-g(t,x(t))-α(t)y(t)has no solution(x(t),y(t))satisfying condition0<∫-∞+∞[|x(t)|ν+(1+β(t))|y(t)|μ]dt<+∞‍,whereμ,ν>1and(1/μ)+(1/ν)=1,0≤xf(t,x)≤β(t)|x|μ,xg(t,x)≤γ0(t)|x|ν,β(t),γ0(t)≥0, andα(t)are locally Lebesgue integrable real-valued functions defined onℝ.

Chaos and Quasi-Periodic Motions on the Homoclinic Surface of Nonlinear Hamiltonian Systems With Two Degrees of Freedom

The numerical prediction of chaos and quasi-periodic motion on the homoclinic surface of a two-degree-of-freedom (2-DOF) nonlinear Hamiltonian system is presented through the energy spectrum method. For weak interactions, the analytical conditions for chaotic motion in such a Hamiltonian system are presented through the incremental energy approach. The Poincaré mapping surfaces of chaotic motions for this specific nonlinear Hamiltonian system are illustrated. The chaotic and quasi-periodic motions on the phase planes, displacement subspace (or potential domains), and the velocity subspace (or kinetic energy domains) are illustrated for a better understanding of motion behaviors on the homoclinic surface. Through this investigation, it is observed that the chaotic and quasi-periodic motions almost fill on the homoclinic surface of the 2-DOF nonlinear Hamiltonian system. The resonant-periodic motions for such a system are theoretically countable but numerically inaccessible. Such conclusions are similar to the ones in the KAM theorem even though the KAM theorem is based on the small perturbation.