On voltage stability from the viewpoint of singular perturbation theory

This paper investigates voltage stability problems based on singular perturbation theory. The application of singular perturbation theory has made it clear that a power system can be approximated by two simplified systems S and F, which respectively correspond to slow and fast subsystems; four types of voltage instability are defined as follows:

? ? type I voltage drop, in which the system still has restoring force to its operating point;

? ? type II voltage collapse, in which the system loses the capability of keeping its operating point. This is divided into the following:

1. II-1 instability due to dynamic factor with slow responses such as tap-changing transformers, movement of centre of inertia, load changing patterns;

2. II-2 instability due to fast response dynamic factors such as load characteristics, generators, AVR, etc. This kind of instability consists of the following two types:

2.1. II-2S static bifurcation,

2.2. II-2D dynamic bifurcation.

Several features of each type of instability are studied as well as their methods of analysis. Voltage instability tends to begin with type I and then lead to one of the remaining types. The load flow Jacobian can be an effective index to approximately assess types I and II-2S instabilities, while types II-1 and II-2D require direct nonlinear analyses and eigenvalue analyses, respectively. Another point to be noted is concerned with the stability at multiple load flow solutions: it is emphasized that the lower of the multiple load flow solutions can be a stable operating point in some cases, even though most of such operating conditions belong to the type I instability; this situation can occur unless the system encounters the type II instability. The validity of the classification proposed here has been verified through numerical simulations and theoretical analyses which take into account the dynamic characteristics of generating units, loads and tap-changing transformers.