Voltage collapse mechanism based on system circuit and its solution manifolds

The problem of voltage collapse in the power system occurs when the load parameter exceeds some critical value. The critical operation point is known as the nose point in the P-V curve. In this paper, the mechanism of voltage collapse is explained based on system circuit and solution manifolds. The corresponding mathematical model is derived. The proven theorem shows that the essential reason for voltage collapse is that the solution manifold of injection branch equations being not transversal with that of linear network equations. The coincidence of the nontransversal of solution manifolds with voltage collapse and static bifurcation is proved.