Direct Assesment Of Multi-Machine Power System Stability Using Catastrophe Theory - Maithem Hassen, Kareem (UTeM, 2014)
In this dissertation catastrophe the01y is used to detennine the transient stability regions. Taylor se1ies expansion is used to find the energy balance equation in tenns of clea1ing time and system transient parameters. The energy function is tlten put in the fonn of a catastrophe manifold from which the bifurcation set is extracted. The bifurcation set represents the transient stabi lity region in tenns of the power system transient parameters bounded by the transient stability limits. The transient stability regions detennined are valid for any changes in loading conditions and fault location. The transient stability problem is dealt witl1 in the two dimensions of trans ient stability limits and critical clearing times. Transient stability limits are given by the bifurcation set and the critical clearing times are calculated from the catastrophe manifold equation. The method achieves a breakthrough in the modeling problem because the effects of exciter response, flux decay and systems damping can all be included in the transient stability analysis. Nwnerical examples of one-machine infinite-bus and multi-machine power systems show a very good agreement with the time solution in the practical range of first swing stability analysis. The method presented in this dissertation fulfills all the requirements for on-line assessment of transient stability of power systems.