Controlling Hopf Bifurcation and Chaos of Subsynchronous Resonance in Multimachine Power System

M.M. Alomari and B.S. Rodanski (Australia)


Nonlinear Controller, Center Manifold, Hopf Bifurcation.


One good way to convert the unstable periodic solution to a stable one is to use nonlinear controller. Nonlinear state feedback controller (Static Feedback Control) with a form of requires measurements in only two state variables. Therefore, it can be used together with a small AVR gain to stabilize the system. On the other hand, based on bifurcation theory and center manifold theory, nonlinear controller is used to control a Hopf bifurcation and chaos. The second system of the IEEE second benchmark model of Subsynchronous Resonance (SSR) is considered. The system can be mathematically modeled as a set of first order nonlinear ordinary differential equations with the compensation factor (μ=XC/XL) as a control parameter. So, bifurcation theory can be applied to nonlinear dynamical systems, which can be written as dx/dt=F(x;µ). The dynamics of the damper winding, automatic voltage regulator (AVR), and power system stabilizer (PSS) on SSR in power system are included. )( 3 1 3 1 ωω −−= rKu

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