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UBC Theses and Dissertations

Transient stability analysis of multimachine power systems by catastrophe theory Mihirig, Ali Mohamed


Transient stability analysis is an important part of power system planning and operation. For large power systems, such analysis is very demanding in computation time. On-line transient stability assessment will be necessary for secure and reliable operation of power systems in the near future because systems are operated close to their maximum limits. In the last two decades, a vast amount of research work has been done in the area of fast transient stability assessment by direct methods. The major difficulties associated with direct methods are the limitations in the power system model, determination of transient stability regions and adaptation to changes in operating conditions. In this thesis catastrophe theory is used to determine the transient stability regions. Taylor series expansion is used to find the energy balance equation in terms of clearing time and system transient parameters. The energy function is then put in the form of a catastrophe manifold from which the bifurcation set is extracted. The bifurcation set represents the transient stability region in terms of the power system transient parameters bounded by the transient stability limits. The transient stability regions determined are valid for any changes in loading conditions and fault location. The transient stability problem is dealt with in the two dimensions of transient 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 modelling problem because the effects of exciter response, flux decay and systems damping can all be included in the transient stability analysis. Numerical examples of one-machine infinite-bus and multi-machine power systems show very good agreement with the time solution in the practical range of first swing stability analysis. The method presented fulfills all requirements for on-line assessment of transient stability of power systems.

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