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. This theory is based on a generalization of the concepts introduced by Venkatasubramanian et al. (1992), for the differential algebraic equation (DAE) stability problem. Our stability problem formulation includes a large class of constrained systems. It is particularly well suited for representing systems with inequality constraints. Also, with this modeling framework, we can develop an approximate model for a DAE system that may be defined arbitrarily close to the original system. The main theoretical result of this paper is a characterization of the boundary of the restricted asymptotic stability region. Specifically, we show that the quasistability boundary includes trajectories that are tangent to the boundary of the feasible operating region. Our primary application of these results is analyzing the electric power system stability following the occurrence of a network fault.