Transient stability analysis of multimachine power systems by catastrophe theory

Abstract

Catastrophe theory is used to determine the transient stability regions of multimachine power systems. The stability region so obtained for a power system is valid for any fault location or system loading. The energy balance equation is first expanded in a Taylor series in terms of the clearing time and the system transient parameters. The energy function is then put in the form of a catastrophe manifold from which the boundaries of the transient stability region are extracted by bifurcation analysis. The transient stability problem is dealt with in terms of the two dimensions critical clearing time and transient stability limits. The transient stability limits are calculated from the bifurcation set and the critical clearing times are calculated from the catastrophe manifold equation. The proposed method permits more detailed modelling of the power system to include such effects as excitation response and flux decay.