Probabilistic dynamic security assessment of power systems-I: Basic model

A comprehensive framework for power system security assessment which incorporates probabilistic aspects of disturbances and system dynamic responses to disturbances is presented. Standard mathematical models for power system (steady-state) power flow analysis and transient stability (dynamic) analysis are used. A linear vector differential equation is derived whose solution gives the probability distribution of the time to insecurity. The coefficients of the differential equation contain the transition rates of system structural changes and a set of transition probabilities defined in terms of the steady-state and the dynamic security regions. These regions are defined in the space of power injections. Upper and lower bounds on the time to insecurity distribution are obtained.