Power System Modeling for Inverse Problems

Large disturbances in power systems often initiate complex interactions between continuous dynamics and discrete events. The paper develops a hybrid automaton that describes such behavior. Hybrid systems can be modeled in a systematic way by a set of differential-algebraic equations, modified to incorporate impulse (state reset) action and constraint switching. This differential-algebraic impulsive-switched (DAIS) model is a realization of the hybrid automaton. The paper presents a practical object-oriented approach to implementing the DAIS model. Each component of a system is modeled autonomously. Connections between components are established by simple algebraic equations. The systematic nature of the DAIS model enables efficient computation of trajectory sensitivities, which in turn facilitate algorithms for solving inverse problems. The paper outlines a number of inverse problems, including parameter uncertainty, parameter estimation, grazing bifurcations, boundary value problems, and dynamic embedded optimization.