This paper studies the operation and scheduling of electric loads in micro-grid, a highly automated and distributed cyber-physical energy system (CPES). We establish rigorous mathematical expressions for electric loads and battery banks in the micro-grid by considering their characteristics and constraints. Based on these mathematical models, we propose a novel real-time scheduling analysis method for priority-based energy management in micro-grid, named Significant Moments Analysis (SMA). SMA pinpoints all the crucial moments when electrical operations are requested among the micro-grid and establishes a dynamic model to describe the scheduling behavior of electric loads. Using SMA, we can check the scheduling feasibility and predict whether the micro-grid can generate enough power to support the execution of electric loads. In the case where the power is insufficient to supply load demands, SMA can provide accurate information about the amount of insufficient power and the time when the insufficiency happens. Simulated results are presented to show the effectiveness of the proposed analysis method.