Inverse Problems in Power Systems

Large disturbances in power systems often initiate complex interactions between continuous dynamics and discrete events. Such behaviour can be modeled in a systematic way by a set of differential-algebraic equations, modified to incorporate impulse (state reset) action and constraint switching. The paper presents a practical object-oriented approach to implementing the DAIS model. 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, boundary value problems, bordercollision bifurcations, locating critically stable trajectories, and optimal control.