Some issues with Quasi-Steady State model in long-term stability

The Quasi Steady-State (QSS) model of long-term dynamics relies on the idea of time-scale decomposition. Assuming that the fast variables are infinitely fast and are stable in the long-term, the QSS model replaces the differential equations of transient dynamics by their equilibrium equations to reduce complexity and increase computation efficiency. Although the idea of QSS model is intuitive, its theoretical foundation has not yet been developed. In this paper, several counter examples in which the QSS model fails to provide a correct approximation of the complete dynamic model in power system are presented and the reasons of the failure are explained from the viewpoint of nonlinear analysis.