Individual Functions Method for Power System Transient Stability Assessment

This paper introduces an alternative description of autonomous dynamical systems as a sum of individual vector fields. This structure of a dynamical system gives us the opportunity to construct individual Lyapunov-like functions to certify stability of an equilibrium point. A theorem on individual functions is developed in a quadratic form to maintain computational efficiency. As a corollary to the developed theory, we conclude that regions of attraction can be estimated by sub-level sets of individual quadratic functions, and through geometric programs they can easily be maximized efficiently. Theoretical findings in this paper are examined on transient stability problem in power systems for both single machine to infinite bus and multi-machine systems with promising results for critical clearing time estimation compared to the values obtained from time domain simulations.