Time-scale decomposition in voltage stability analysis of power systems

Singular perturbation analysis is applied to a number of power system problems related to voltage stability: 1) the generator dynamics in a multimachine power system are accurately decomposed into voltage and frequency (electromechanical) dynamics; 2) the quasi-steady state representation of generators for the simulation of slow voltage transients is explained and justified; and 3) the singularity of algebraic constraints leading to what is called “loss of causality” is found to be equivalent to the instability of faster, unmodeled dynamics of network and loads