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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