On Classification and Analysis of Voltage Stabilities in Power Systems

Voltage stability problem has long been studied by many researchers mainly by means of two approaches. One is static approach where voltage stability is considered as a load flow problem, while the other is dynamic approach in which it is dealt with as a stability problem in dynamic systems. However, these separate approaches have not clarified sufficiently the whole aspect of voltage problem up to now; in fact, there are no proper criteria to determine which approach is suited to analyze voltage stability. Thus, a basic study seems to be needed under such situation. This paper investigates voltage stability problem from the viewpoint of mechanism causing voltage instability. Various dynamic factors which affect voltages are studied as much as possible. In the first place, possible voltage instability patterns are classified based on singular perturbation theory. That is, four categories of instabilities are defined mathematically. Secondly, a method of stability assessment for each instability is presented. It is clarified that the determinant of the load flow Jacobian is an effective index to approximately assess two types of the instabilities. On the other hand, the remaining instabilities require eigenvalue analyses or direct nonlinear analyses. The validity of these results is verified through numerical simulations and eigenvalue analyses, in which dynamic characteristics of generating units, loads and tap-changing transformers are taken into account.