Integral manifold as a tool for reduced-order modeling in nonlinear systems: A synchronous machine case study

Nonlinear systems in which invariant or, more generally, integral manifolds exist, appear in many important applications: networks with weakly coupled areas, electromechanical systems, electric machines, adaptive control, etc. In a class of such systems two-time scale properties assure the existence of "slow manifolds." When a "speed-ratio parameter" ?? is zero, some states in these systems remain constant and form a "frozen" manifold M0. The slow manifold M?? is an ??-perturbation of M0. Using a synchronous machine example, this paper presents the slow manifold as a tool for decomposition and reduced order modeling of nonlinear systems.