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An Optimal Control Approach to Construction of Lyapunov Functions for Power System Models

Previous works in the power systems and control literature have observed the close tie between the quasi-potential function that appears in stochastic exit problems and a Lyapunov function for an underlying deterministic model associated with the stochastic system [3], [6], [7]. Given that the quasi-potential is obtained as the solution to a nonlinear optimal control problem, this raises the question of what conditions on the system model are required to lead to a computable solution. In this paper, the closed form solution for the optimal cost of control is rigorously derived for a class of nonlinear power system models. A simple model representing swing dynamics in the power system is developed to illustrate the optimal control analysis in detail.