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In an electric power network, initial loss of a transmission line may create transient overloads in other lines, inducing cascading failures, and possibly system wide outage. Full time domain simulations to credibly predict the wide range of possible switching actions that can lead to cascading failure events under transient conditions is extremely costly. As an alternative, this work proposes a bi-stable branch model that approximates transient line overload outages in a smooth dynamic model, amenable to analytic stability analysis. In this context, partially degraded network configurations appear as multiple equilibria in an augmented transient stability model, and vulnerability to transit to any degraded configuration may be quantified via a closed form energy function. This work develops the model, demonstrates the construction of the associated energy function, and confirms the energy to be non-increasing along system trajectories that include line overload driven failure. This work is intended as a first step to demonstrate the potential for energy function methods to contribute to cascading failure analysis. In particular, it is envisioned that short duration simulation be augmented with a computationally inexpensive energy function threshold test, to obtain (when possible) a sufficient condition for a post-disturbance state to be “captured” in the energy well about a (partially degraded network) stable equilibrium, thereby ensuring no further line outages can occur along the remaining transient trajectory.