Hopf Bifurcations in the Ieee Second Benchmark Model for Ssr Studies

In this paper, the first system of the IEEE second benchmark model (SBM) for subsynchronous resonance (SSR) studies is analyzed using the bifurcation theory. A nonlinear model for the SBM which consists of a synchronous generator connected to an infinite busbar through two parallel transmission lines, one of which is equipped with a series capacitor, has been developed in MATLAB. Generator damper windings are also included in the model. The existence of Hopf bifurcations in the model is verified. The stability of limit cycles (i.e. subcritical or supercritical Hopf bifurcation) is investigated by computing the first Lyapunov coefficient. The impact of the field voltage, the mechanical torque input to the generator and the infinite-bus voltage on the first Lyapunov coefficient is also explored. In the model with Automatic Voltage Regulator (AVR) and generic Power System Stabilizer (PSS), the first Lyapunov coefficient becomes negative but remains near zero indicating the existence of a generalized Hopf bifurcation. Time domain simulations verify the analytical findings.