Characterization of the region of attraction of a power system transient stability model

A closed form equation is derived that describes the stable manifold for each of the n-1 type-1 unstable equilibrium points (UEPs). These stable manifolds can be obtained without having to compute the postfault stable equilibrium points for each of the stable manifolds. The equation describing the stable manifold for each UEP can be written knowing only the postfault stable equilibrium point. The n-1 stable manifolds for the UEPs constrain the power across the cutset of branches that encircle each of the n-1 generators that are not assumed to be the swing machine. For a point to lie on the stable manifolds of a specific UEP, the sum of power flows across all branches in the cutset that surround the generator that corresponds to a specific UEP must equal the sum of the power flows across this cutset at the postfault equilibrium point. These results are intuitive since the equal-area criterion could be used to characterize the region of stability for a single-machine infinite-bus system in the exact same manner