Voltage Stability Probabilistic Assessment in Composite Systems: Modeling Unsolvability and Controllability Loss

Several papers have recognized the effect of uncertainties in voltage stability analysis through probabilistic methods. In these papers, the unstable states are generally identified by the unsolvability of the power flow equations or by violations in the voltage stability margin limit. However, voltage stability problems may also be associated with a loss in voltage controllability, when a voltage control action has an effect which is contrary to what is usually expected. The main aim of this paper is to include unstable states caused by unsolvability and voltage controllability loss in the voltage stability probabilistic assessment. This goal is achieved through the combination of three techniques: the Monte Carlo Simulation Method, the nonlinear optimal power flow and the D' matrix method. These three techniques permit the inclusion of a new issue in the computation of voltage instability risk: the unstable states stemming from controllability loss.