Stability analysis of power systems considering AVR and PSS output limiters

Small-signal stability analysis in a power system uses a linearized approximation of its nonlinear model to analyze its behavior when subjected to small perturbations. In this approach, there is an implicit assumption that the perturbations are small enough so the imprecisions of the linear approximation with respect to the nonlinear model remain within an acceptable range. This restricts the validity of the linearized model to a neighborhood of the equilibrium conditions under which the model was obtained. Usually, the size and shape of this neighborhood is determined by the regions in the state-space where no protective limiters are active. However, there may be situations when a relatively small perturbation drives the system to such regions, yet there is still no threat to the stable operation of the system. This paper proposes a method to find an attraction area of the system, using a linearized model with the addition of AVR and PSS output limiters, in such a way that this area includes parts of the regions of the state space where the limiters are active, therefore widening the neighborhood of the equilibrium point where stability is guaranteed. The obtained results show that this attraction area is much larger than the neighborhood defined by the region where the linearized approximation is valid, and also indicate that the linearized model, with the addition of AVR and PSS output limiters, can provide good approximations of the nonlinear system trajectories even in some parts of the regions where the limiters are active.