A geometrical study on voltage collapse mechanisms of power systems

In this paper, the mechanism of voltage collapse is studied based on a nonlinear model and transversality theory, and a unified explanation of the phenomena of voltage collapse is given. The research shows that the fundamental reason for voltage collapse is due to the non-transversal intersection between solution manifolds of the injection branch equations in the voltage-current space. It is also proved that this non-transversal intersection exactly corresponds to the static state bifurcation point. These conclusions are valid no matter differential algebraic equations or power flow equations being employed.