On the calculation of the feasibility boundary for differential-algebraic systems

Our research is motivated by models for electric power systems. In this case typical dynamic state variables are the states of generator models (generator voltages, angles etc.) including exciter states. The instantaneous variables are usually connected with the network structure and typically include bus voltages and other load flow variables. The parameter space is composed into system parameters which are related to system topography, equipment constants, etc., and operating parameters such as voltage set-points, loads, mechanical torque, exciter gains. The dynamics of the generators, control devices and generally the load dynamics together define the dynamic equations while the algebraic constraint typically consists of the power balance equations of the network. We present an algorithm to calculate limits of parametric stability for a stable equilibrium