An application of Immersion and Invariance to a differential algebraic system: A power system

A stability result, based on the Immersion and Invariance (I&I) control strategy, for a class of systems with constraints is derived. The result is used to synthesize a stabilizing nonlinear control law for a single machine infinite bus (SMIB) system. The SMIB system is described by the structure preserving model (SPM) where the rotor dynamics is given by the nonlinear second order swing equation model, and the power balance equation at the generator terminal bus is given by an algebraic constraint. The actuator used is a controllable series capacitor (CSC). The CSC is modeled using a first order system. The control objective here is to stabilize the generator dynamics at a given equilibrium.