On the Foundations of Stability Analysis of Power Systems in Time Scales

Exploring singular perturbation and stability region theory, the foundations for decomposing the stability analysis of power systems in time scales is developed and a general algorithm, for stability analysis of power systems, which has transient stability analysis and quasi-steady state analysis as particular cases, is proposed. This algorithm bridges the gap between short and mid-term stability analysis and clearly establishes the conditions to guarantee stability of the original electrical power system model in terms of stability of the fast and slow subsystems. Simple examples illustrate the application of the proposed algorithm and its ability in delineating the evolution of the power system dynamics and identifying unstable modes.