Control of Hopf Bifurcation and Chaos as Applied to Multimachine System

Based on bifurcation theory and center manifold theory, both linear and nonlinear controllers are 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=X c /X L ) 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. Both linear and nonlinear controllers are used to control the Hopf bifurcation and chaos. The results show that linear controller can only delay the inception of a bifurcation to some desired value of the bifurcation parameter. On the other hand, when the control objective is set to stabilize the periodic solution, nonlinear controller must be used.