Parameter dependent invariant manifolds to construct approximate slow and fast models of a multi machine power system

The importance of parasitic parameters in the study of a dynamical system is brought out in this work. The neglect of these parameters in the context of invariant manifolds for a multi machine power system for transient stability is studied. Singular perturbation approach is used for the calculation of critical clearing time of a large disturbance fault using equilibrium and invariant manifolds. It is clear from the norm of the two manifolds that the relevance of inclusion of parameters is more in case of the scenario of faults at generator buses. A comparative study of critical clearing time of generator bus faults obtained from equilibrium manifold and invariant manifold is shown in the study. This means that it is advisable to employ invariant manifold instead of equilibrium manifold in the transient stability study of multi machine power system. Also, the critical clearing time obtained from the invariant manifold is closely matching with catastrophe theory method of transient stability.