An application of immersion and invariance to a class of differential algebraic systems

Abstract

Electrical power systems are naturally described by nonlinear differential-algebraic equations (DAEs). The dynamics of the dynamical components in the system such as the synchronous generators are given by the set of differential equations, while various network constraints such as power balance equations at different nodes are expressed by a set of algebraic equations. In this chapter we extend the I&I methodology to a class of differential algebraic systems, without the need for solving for the nonlinear algebraic equations explicitly.