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In this work, a composite economic model predictive control (CEMPC) is proposed for the optimal operation of a stand-alone integrated energy system (IES). Time-scale multiplicity exists in IESs dynamics is taken into account and addressed using multi-time-scale decomposition. The entire IES is decomposed into three reduced-order subsystems with slow, medium, and fast dynamics. Subsequently, the CEMPC, which includes slow economic model predictive control (EMPC), medium EMPC and fast EMPC, is developed. The EMPCs communicate with each other to ensure consistency in decision-making. In the slow EMPC, the global control objectives are optimized, and the manipulated inputs explicitly affecting the slow dynamics are applied. The medium EMPC optimizes the control objectives correlated with the medium dynamics and applies the corresponding optimal medium inputs to the IES, while the fast EMPC optimizes the fast dynamics relevant objectives and makes a decision on the manipulated inputs directly associated with the fast dynamics. Meanwhile, thermal comfort is integrated into the CEMPC in the form of zone tracking of the building temperature for achieving more control degrees of freedom to prioritize satisfying the electric demand and reducing operating costs of the IES. Moreover, a long-term EMPC based on a simplified slow subsystem model is developed and incorporated into the CEMPC to ensure that the operating state accommodates long-term forecasts for external conditions. Finally, the effectiveness and superiority of the proposed method are demonstrated via simulations and a comparison with a hierarchical real-time optimization mechanism.