Large deviation theory applied to power system stability

Large, interconnected electrical power systems with weak radial lines serving locations that may be far away from the generation sites are designed to operate at steady state and at constant voltage magnitude. A very large voltage change may occur as a result of unexpected load variations, and may lead to a loss of stability of the power system. This phenomenon of voltage collapse can be detrimental to the system and recovery from it may be difficult. A model of the phenomenon of voltage collapse is given that includes a treatment of the global dynamics and uses large deviation theory to describe the collapse of bus voltage magnitudes. The power system Lyapunov functions play an important role in the estimation of a security measure. This approach provides an application area for the theory of large deviations for dissipative dynamics developed by the author (1986, 1987). It also introduces to the study of power system dynamics new qualitative methods from the mathematical theory of dynamical systems. The problem of calculating large deviation asymptotics is posed as an optimal control problem solvable using Lyapunov functions