On adapting test function methods for fast detection of fold bifurcations in power systems

Test function methods are well known techniques to monitor a continuation method to determine if a fold (saddle-point) bifurcation point has been reached. Two such test functions due to [Abbott, 1978] and [Seydel, 1979] are considered here in a unified framework and their connection to the tangent vector index method from power system community is shown. The challenge in power systems applications is to adapt a test function method to produce a performance index that approximates the fold parameter lambda* without the need of following the solution path to the fold point (x*, lambda*). We demonstrate that the tangent vector index method, due to its connection with the mathematically justifiable test function methods, can lead to a useful performance index.