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This paper describes a unified approach to the identification of time-varying One-machine Infinite-Bus (OMIB) equivalents based on the use of finite-differences. The key to this approach is the local decomposition of the classical two-machine equivalent into a multi-machine time-varying system that captures the interplay between machines in each critical cluster.By addressing the interplay between subgroups of coherent generators the proposed procedure opens new avenues for both the evaluation and the control of the inter-area mode phenomenon. Analytical criteria are developed which predict the existence and stability character of the system response as a function of energy concepts. Energy-based techniques are then used to infer the energy transfer among the groups of coherent generators. In addition to giving physical insight into the problem of post-fault inter-area oscillations, the method allows for the inclusion of inter-machine behavior in a systematic manner and results in a computationally efficient algorithm.The practical use of the proposed techniques is tested on a realistic 45-machine power system model representing parts of the Mexican interconnected system.