A probabilistic approach to dynamic power system security

The problem of dynamic power system security is investigated. A probabilistic approach is chosen, and an appropriate power system model is developed for analyzing the dynamic behavior of the different operational modes of the system. The model includes the transients induced by primary and secondary disturbance events. They are modeled by switches in the model whose states depend on the instantaneous values of certain system variables. The model characterizes the interaction between the dynamic state of the system and the network topology as defined by the status of the various protective relays in the system. A dynamic security region is defined as a subset of the state-structure space of the power system such that at any moment in time an operating point within the region satisfies all the constraints required for secure power system operation. The probabilistic evolution of the state and structure is computed as the solution of a system of linear partial differential equations with matching conditions at the switching boundaries. A dynamic security measure is defined as the integral of the joint probability density of the state and structure of the system over the dynamic security region for all possible structural variations. This computation yields the probability that the power system remains secure for the range of primary events considered. Computer simulations for an example power system illustrate the utility of the approach