A stability theory for constrained dynamic systems with applications to electric power systems

This paper develops a stability theory for constrained dynamic systems, which are defined as dynamic systems whose state trajectories are restricted to a particular set within the state space, called the feasible operating region. A restricted stability region is defined as the intersection of the domain of attraction of the stable equilibrium point without constraints and the feasible operating region. Our results show that the boundary of the stability region for a constrained dynamic system includes trajectories that are tangent to the boundary. We then develop a computational procedure to analyze stability in an electric power system following a network fault.