Association of the stability region with time scale analysis to study voltage stability

The problem of voltage stability (VS) due to large perturbations is conceptually very similar to the problem of transient stability (TS). After a large perturbation, the system will be stable if the state of the system, at the time the perturbation is cleared, is inside the stability region (SR) of the post disturbance system. However, the problem of VS has some peculiarities. Models for dynamic analysis of VS have multi-time scale properties and problems of TS and VS may coexist. VS problems are usually associated with slow dynamics and a QSS (Quasi-Steady State) model is usually employed to study this phenomenon. However, VS problems in the slow variables might be triggered by perturbations in the fast variables and TS problems might coexist with VS ones. In an effort to understand these phenomenon and extend direct methods to the analysis of VS due to large perturbation, we use time-scale decomposition to study problems of VS that are triggered by large perturbations such as short-circuits. In particular we explore a decomposition of the SR and stability boundary of singularly perturbed systems into the SRs and stability boundaries of the slow and fast systems to gain insight into the dynamics of the system and to understand its unstable modes.