An Algorithm for voltage collapse point Based on the theory of Transversality in Power Systems

When a power system load parameter is over a certain value, the system will experience a saddle-node bifurcation, and voltage collapse occurs. The difficulty in getting the voltage collapse point is that the system Jacobian matrix has a simple zero eigenvalue at the critical point, causing the Newton method failure in the neighborhood of the bifurcation point. Based on the circuit models of a power system and the theory of manifold transversality, the saddle-node bifurcation point is corresponding to the non-transversal intersection between the solution manifolds of injection equations and the linear network equations in the space spanned by the bus voltage and the injection current. This research studies the characteristics of the two solution manifolds and gives an algorithm based on the Newton algorithm for getting the non-transversal point, and it also can calculate the transversal point