In this work, a composite economic model predictive control (CEMPC) is proposed for the optimal operation of a stand-alone integrated energy system (IES), aiming at meeting customers' electric and cooling requirements under diverse environmental conditions while reducing fuel consumption. Time-scale multiplicity exists in IESs dynamics is taken into account and addressed using multi-time-scale decomposition based on singular perturbation theory. Through 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 to match the time-scale multiplicity featured in IESs dynamics. The EMPCs communicate with each other to ensure consistency in decision-making. In the slow EMPC, the global control