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The controlling unstable equilibrium point (CUEP) method developed for the traditional network-reduction power-system (transient-stability) model requires some modification for direct stability analysis of the network-preserving power system model. This is mainly due to the peculiar nonlinear jump behaviors occurring in network-preserving power system model. An extended CUEP method suitable for direct stability analysis of network-preserving models is developed. The extended CUEP method examines both external jump behaviors and stability regions of network-preserving models. It is shown that the target point of the fault-clearing point (i.e., the initial point of the post-fault system), instead of the fault-clearing point as in classical case, plays a crucial role in direct stability analysis of network-preserving power systems models. A theoretical foundation for the extended CUEP method is developed. A variation of the extended CUEP method is presented.