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Large scale power systems can be decomposed into areas each consisting of tightly coupled machines connected to other areas through weak connections. This kind of decomposition preserves the network structure and offers possibilities in developing reduced-order models and simplified direct stability analysis. Time scale separation is inherent in this decomposition. This paper investigates the use of slow and fast energy functions for the stability analysis of two-time-scale systems. We show rigorously the existence of a slow manifold and use this manifold for calculating slow energy in the system to any desired degree of accuracy. When the mode of instability is between areas (i.e., slow) it is shown that the slow energy accurately predicts the critical clearing time.