On Efficient Methods for Detecting Hopf bifurcation with Applications to Power System Instability Prediction

Efficient measurement of the performance index (the distance of a loading parameter from the voltage collapse or instability point) is one of the key problems in power system operations and planning such an index indicates the severity of a power system with regard to voltage collapse or instability. While much work has been done on the former problem, the latter problem poses a more severe challenge both to the engineering and mathematical communities. This paper first presents a review of the main methods for detecting Hopf bifurcation in the general field of bifurcation theory and then attempts to generalize the previously studied fold detection and index methods to the Hopf case. The proposed Hopf test functions should be of wide interest while the proposed test function based index method gives an indication of the distance of the current operating point from the Hopf instability. Promising numerical results have been obtained using some standard dynamical test systems.